THE USE OF PRESSURE ALTITUDE AND ALTIMETER CORRECTIONS IN METEOROLOGY

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  • 1 Institute of Tropical Meteorology, Rio Piedras, Puerto Rico *
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Abstract

This discussion presents a scheme that has been found to be very convenient for the three-dimensional representation of the pressure and temperature fields in the atmosphere both for forecasting and for aircraft operations. The terms pressure altitude (zp), altimeter correction (D) and specific temperature anomaly (S) are defined and their physical interpretation discussed. The hydrostatic equation, the geostrophic and gradient wind equations, and the thermal wind equations are stated in terms of these parameters. All necessary tables and calculation diagrams including a thermodynamic chart called the pastagram are presented. Applications of the proposed scheme to pressure-height computations, wind calculations, aircraft operations and general synoptic analysis are given together with a number of examples.

Abstract

This discussion presents a scheme that has been found to be very convenient for the three-dimensional representation of the pressure and temperature fields in the atmosphere both for forecasting and for aircraft operations. The terms pressure altitude (zp), altimeter correction (D) and specific temperature anomaly (S) are defined and their physical interpretation discussed. The hydrostatic equation, the geostrophic and gradient wind equations, and the thermal wind equations are stated in terms of these parameters. All necessary tables and calculation diagrams including a thermodynamic chart called the pastagram are presented. Applications of the proposed scheme to pressure-height computations, wind calculations, aircraft operations and general synoptic analysis are given together with a number of examples.

JOURNAL OF METEOROLOGYVOLUME 2, NUMBER 1MARCH 1945THE USE OF PRESSURE ALTITUDE AND ALTIMETER CORRECTIONS IN METEOROLOGY By John C. BellamyInstitute of Tropical Meteorology, Rio Piedras, Puerto Rico * (Manuscript Received, May 6, 1945)ABSTRACTThis discussion presents a scheme that has been found to be very convenient for the three-dimensionalrepresentation of the pressure and temperature.fields in the atmosphere both for forecasting and for aircraftoperations. The terms pressure altitude (zp), altimeter correction (D) and specific temperature anomaly (S)are defined and their physical interpretation discussed. The hydrostatic equation, the geostrophic andgradient wind equations, and the thermal wind equations are stated in terms of these parameters. Allnecessary tables and calculation diagrams including a thermodynamic chart called the pastagram arepresented. Applications of the proposed scheme to pressure-height computations, wind calculations, aircraftoperations and general synoptic analysis are given together with a number of examples.TABLE OF CONTENTS1. Introduction. ............... 12. Definitions and theory. ............................. 23. Techniques of calculation., ......................... 94. The pastagram.. .................................. 436. 'Theoretical wind calculations. ......7. Applications to aircraft operations. ..8. Weather chart analysis in terms of altimeter corrections.5. Pressure-height computations. .......... 55.................... 65Conversion tablesla.lb.2a.2b.2c.2d.2e.2f.3a.3b.3c.4.5.6a.6b.Conversion of pressure parameters (range:- 3000 ft 5 zp 5 80,000 ft) .................Conversion of pressure parameters (range:- 2000 ft 5 2,s 10,000 ft) .................Conversion from p in inches of mercury to D infeet at sea level.. ...............Conversion from p in millimeters ofin feet at sea level. .........................Conversion from p in millibars to D in feet at sealevel. .....................................Conversion from fi in inches of mercury to D inmeters at sea level. .........................Conversion from p in millimeters of mercury to Din meters at sea level. .......................Conversion from p in millibars to D in meters atsea level. ..................................Conversion from p in millibars to D in feet at standard levels (z in feet). ........................Conversion from p in millibars to D in feet at standard levels (z in kilometers)Conversion from p in millibars to D in meters atstandard levels (z in kilometers) ..............Relation between S and T (in degrees centigrade)for various pressure altitudes in feet.. .........Relation between S and 1" (in degrees centigrade)for various pressure altitudes in meters. .......Virtual temperature corrections. ................Virtual temperature anomaly corrections. ...........101317181920.212222242833364242* The Institute of Tropical Meteorology is operated jointly bythe University of Puerto Rico and the University of Chicago.1. Introduction. This article presents the results ofa search for convenient parameters with which todescribe the atmospheric pressure and temperaturefields. In this search the following factors were considered :1. Ease of conversion, if required, from the parameters with which actual measurements of pressure and temperature are made (or can easily bemade) to those parameters which are convenientfor the meteorologist to use.2. Simplification of calculations involving thehydrostatic and gradient wind equations. Particularattention was given to this point since both of theseequations are almost always used at the presenttime, either qualitatively or quantitatively, for thedetermination, representation and forecasting ofthe wind. Also-it seems probable that they willalways be useful as the first approximation to thesolution of the equations of motion.3. Simplicity, clearness and convenience of graphically representing the pressure and temperaturefields on charts and diagrams. Here the primaryconsideration was the simplicity of the relationshipsbetween the graphical representations and thehydrostatic and gradient wind equations, since itis felt that the primary meteorological use of thesefields is the determination and representation of thewind field. Secondary consideration was given to theusefulness of these representations for pilots, navigators, surveyors, etc., so that a minimum of effortand time is required for the meteorologist to givethem the desired information.From these considerations it seems that the pressurealtitude, z,, and a quantity called the altimeter correction, D, are the most convenient parameters with12 JOURNAL OF METEOROLOGYwhich to represent pressure quantitatively in mostroutine meteorological work. Also, a quantity calledthe specific temperature anomaly, S, is a convenientparameter with which to represent temperature quantitatively for many meteorological considerations.These parameters are defined and a detailed description of their properties and use is given below..2. Definitions and theory.Pressure altitude z,. The pressure altitude representsthe quantitative value of the pressure at a given pointby giving the height above a given standard pressureat which that pressure occurs in a standard atmosphere. Thus, the physical concept of pressure altitudeis very similar to that commonly used with otherparameters of pressure, such as the height of a standardmercury column which can be supported by thatpressure, or the depth (pressure head) of water in astandard water column at which that pressure occurs.The dissimilarity between pressure altitude and themost commonly used pressure parameters is a resultof the compressibility of the air. Thus pressure altitudeis not linearly related to such common pressureparameters as inches of mercury, feet of water, millibars, pounds per square inch, etc., which are linearlyrelated to each other. Also, since the height of zeropressure in a compressible fluid is indeterminate,pressure altitude is essentially measured from thebottom of the column up, instead of from the top ofthe column down as is the case with mercury or watercolumns. Hence, when the value of the pressure altitude increases, the values of these other commonpressure parameters decrease and vice versa. However, as will be seen later, incorporation of the compressibility of the air into the pressure parameterresults in a simplification of routine hydrostatic andgradient wind calculations.Even at present upper-air pressures are commonlymeasured and thought of in terms of the pressurealtitude used to calibrate aircraft altimeters (the pressure altitude obtained with the N.A.C.A. or U. s.Standard Atmosphere). Because of this, and since thisstandard atmosphere is sufficiently representative ofmean world wide conditions, the U. S. Standard pressure altitude, z,, is used throughout this work.The U. S. Standard Atmosphere can be defined asfollows :1. The standard pressure at zero value of thepressure altitude (z, = 0) is that pressure whichwill support a standard mercury column 760 mmhigh. Hence, the zero of pressure altitude is merelydefined as being that point at which the pressurecan be expressed as 760 mm of mercury and canbe at any height above mean sea level.2. The standard temperature, T,, is 15°C atz, = 0 and decreases upward with a uniform lapserate pf 6.5"C/km (1.9812"C/1000 ft) until it becomes equal to - 55°C at z, = 10,769.2 m or35,332.0 ft, above which point it is constant at thisvalue.3. The air is assumed to obey the perfect-gaslaws and to contain no water vapor, the acceleration of gravity is assumed to be constant atg, = 980 cm/sec2, and it is assumed, that no verticalaccelerations of the air are present.Using this definition of the standard atmosphereand the hydrostatic relationship with the equation ofstate, a one-to-one relationship between pressurealtitude and the absolute pressure units, such asmillibars, pounds per square inch, etc., can be derived.The formulae obtained in this way can then be considered as being a mathematical definition of a newpressure parameter, pressure altitude, so that thequantitative value of the pressure at a given pointcan be specified completely by giving the value of thepressure altitude of that point. For example, sayingthat the value of the pressure altitude at a given pointis 10,000 feet denotes that the pressure at that pointhas a given value equal to the pressure which occursat 10,000 feet above the zero point in the standardatmosphere. This pressure could be measured directlywith an aircraft altimeter set at 29.02, and its valuecould be, but usually need not be, converted to avalue of 697 millibars, or 20.58 inches of mercury, etc.It is, of course, very important to keep in mind thatthe actual level at which the pressure altitude is10,000 feet can be at almost any height (but probablyfairly close to 10,000 feet) and usually is not exactly10,000 feet. Similarly, if it is desired to give the timesequence of the pressure at a given point, for instanceat an airport, it could be given as measured 29.90,29.92 and 29.94 inches of mercury, or equally completely as + 20 feet, 0 feet and - 20 feet of pressurealtitude. The calculations and a graphical table of theconversion between pressure altitude and millibars,inc'hes of mercury and millimeters of mercury aregiven later.Since the standard atmosphere is used solely as ameans of providing parameters for expressing theintensity of pressure, the pressure at any point in theactual atmosphere is used to determine the corresponding point at which that pressure occurs in the standardatmosphere. Thus the various other properties at thatpoint in the standard atmosphere can be used to statethe intensity of this pressure. For example, forpressures that occur in the stanclard troposphere(T 2 - 55°C) one can specify the intensity of pressureby giving the value of the standard temperature, T,(instead of giving the pressure altitude), which occurs.JOHN C. BELLAMY 3at that pressure, since a one-to-one relationship existsbetween the pressure, the standard temperature andthe pressure altitude. Since the standard atmosphereused here has an isothermal stratospheric region thestandard temperature cannot be used as a parameterof pressure above the tropopause. However, in thisregion the hydrostatic equation still provides that thepressure altitude is a continuous single-valued functionof the pressure, so that the use of a standard isothermalstratosphere does not essentially affect the use ofpressure altitude as a pressure parameter. Similarly,since the pressure and temperature are defined atall points in the standard atmosphere, the values ofthermodynamic quantities such as the standard density p,, the standard potential temperature e,, etc.,are considered in this way as being essentially parameters with which one could specify the pressure at anypoint in the actual atmosphere.Altimeter correction D. A very convenient quantityfor representing the spacial distribution of pressureis the altimeter correction D, defined as the differencebetween the height above mean sea level z, of anypoint in the atmosphere, and the pressure altitude z,,which occurs at that point, orD = z - z,.(1)The value of D at any point in the atmosphere thus isa function of both the height of the point and thepressure occurring at that point. Thus, if desired, Dcan be considered as being a parameter with which tospecify the intensity of pressure on any horizontalsurface. Conversely, D can also be considered as beinga parameter with which to specify the height at whichany given constant pressure occurs in the atmosphere.Considering D as a pressure parameter at a givenheight z above mean sea level, the intensity of pressurecan be thought of as being given by the depth, z - z,,measured from that height down to the height abovemean sea level at which that pressure occurs in astandard atmosphere (which is in the standard verticalposition such that everywhere the value of the pressure altitude is numerically equal to the height abovemean sea level). Thus this concept is very similar tothat of the pressure head, especially since the relativepressure head (Le., the depth of water measured fromthe surface of the water on which the atmosphericpressure is acting) is usually used.Another way of considering D as a pressure parameter is to think of D as being the vertical displacementof the standard atmosphere from its standard position(z = zp at all points) required to obtain the observedpressure at the height above mean sea level considered.In other words, this vertical displacement of thestandard atmosphere is the displacement necessary toobtain the same weight of air above the height considered in both the actual and standard atmospheres.For example, if the value of D at a point 10,000 feetabove mean sea level were to increase from 0 feet to+ 100 feet, the value of the pressure altitude at thatpoint would decrease from 10,000 feet to 9900 feetand the value of the pressure expressed in millibarswould increase from 697 mb to 699.5 mb. The increasein weight of the air above this point (2.5 mb) is thenequivalent to the weight of the standard atmospherebetween the values of z, = 9900 feet and z, = 10,000feet, and this increase in weight above the point canbe considered as being equivalent to that obtained byraising the standard atmosphere through a distanceequal to the change of D, + 100 feet, so that thepressure value z, = 9900 feet occurs at the heightz = 10,000 feet.The use of D thus provides a pressure parameterwhich takes account of the compressibility of the airwithout changing its sense of increase with respect tothe absolute pressure units. Lines of constant D on amap of conditions at any constant height z are thenmerely isobars labeled in terms of the displacementof the standard atmosphere from its standard positionrequired to obtain the same weight of air above thatlevel as in the actual atmosphere.Considering D as a height parameter specifying theposition of a given pressure z,, this height, D = z - z,,is measured from the height above mean sea level atwhich that pressure occurs in the standard atmospherein its standard position instead of from mean sealevel. Hence, lines of constant D on a map representingconditions on a surface of constant pressure are merelycontour lines of that surface with the origin of verticalmeasurement at the standard height above mean sealevel of that pressure.Altimeter setting P. The relationship between thealtimeter correction D and the altimeter setting Pcan conveniently be obtained by considering the construction of an aircraft altimeter as schematicallyrepresented in Figure 1. Plate A, which is fixed withrespect to the aircraft, is marked with a linear heightscale z and an Altimeter Setting Index I,. Plate B,which can be rotated with the knob and gear K withrespect to Plate A, has mounted on it an aneroid pressure element and an indicating hand. The linkagebetween the pressure element and the indicating handis such that the angular displacement of the handfrom a zero (z, = 0) position, marked in the diagram(but not on present altimeters) by the AltimeterCorrection Index ID, is directly proportional to thepressure altitude z,, and is such that the angularscale of z, is the same as the angular scale of thez markings on Plate A. Ring C, which can be rotatedwith respect to Plate A through the same angle, butin the opposite direction, as Plate B, is marked with aPressure Altitude Variation Index Iz, and an Altimeter Setting Scale P. The P scale is a pressure scale,4JOURNAL OF METEOROLOGYFIGURE 1.usually marked in terms of the pressure parameterinches of mercury, with angular dimensions the same(but in the opposite direction) as a correspondingpressure altitude scale with the same dimensions asthe z markings on Plate A. Plate B and Ring C are soarranged that, when they are rotated (in oppositedirections with knob K) so that the indices Iz, and10 are opposite each other, they are both opposite thezero of the z scale, and the 29.92-inch (z, = 0) markof the P scale is opposite the index I,.The procedure for setting an altimeter consists ofmoving the pressure element, Plate B, with knob K,so that the hand points to the height on the heightscale z of the position of the altimeter in the atmosphere. The position of Plate B must then be such thatthe index ID is opposite the value of D = z - z,occurring at the point in the atmosphere considered.Thus the process of setting an altimeter can easilybe thought of as being a mechanical method of addingthe altimeter correction D to the pressure altitude z,as measured by the altimeter, to obtain the heightabove mean sea level z. From Figure 1 is seen thatwhen the altimeter is set, the index Iz, points to thevalue of - D-on the z scale, and the value of Pon the P scale, to which the index I, points, corresponds to a movement of the P scale through a pressure altitude of - D. Thus the altimeter setting Pcan be defined as being the pressure, expressed ininches of mercury, which is equal to a pressure altitudeof the negative of the value of D at the point considered.The usual definition of the altimeter setting can bestated as the pressure, expressed in inches of mercury,which would occur at sea level if a U. S. Standardatmosphere (standard virtual temperature at allvalues of the pressure) were between the point considered and sea level. That these two definitions givethe same numerical result is seen by the fact that thevalue of D can be considered as the vertical displacement of the standard atmosphere from its standardposition required to have the observed pressure at theheight considered. With this displacement the pressure altitude that would then occur at mean !sea levelwould be equal to - D.The use of the altimeter setting for determinationsof the height of an aircraft in tht: upper air is anindirect procedure. If it is desired to set the altimeterso that it always reads the height of the aircraft, thevalues of the altimeter settings that apply must begiven for the various heights (not pressures) considered, since the reading of the altimeter is then a"height". But the pilot has no direct means of determining his height to determine the altimeter settingthat should be used at his particular position. Thus,fundamentally, he must perform a series of successiveapproximations, such as, guess at the applicable setting, read the indicated height, determine the applicable setting for this height from the meteorologicaldata, reset the altimeter for this setting, determine theapplicable setting for the new indicated height, etc.,etc. On the other hand, the determination of heightsin the upper air by a correction procedure (Le., addingalgebraically the value of D from meteorological datato the indicated pressure altitude with the altimeteralways set at 29.92 inches or with I, and Iz, at 0)is direct and convenient since the applicable D can begiven directly in terms of the measured z,.The use of the altimeter-setting procedure for determining when the aircraft gets to a given predeterminedelevation (such as in landing procedures) is directand convenient since then the setting that applies atthat point in the atmosphere can be preset into thealtimeter. This setting can be given to flying personneleither as the altimeter setting P, to be set under theindex I,, or as the altimeter correction D, to be setunder the index ID if available, or to be set with theindex Iz, opposite - D. The use of P has the advantage of eliminating the possible confusion causedby the positive and negative signs of D. The use of Dhas the advantage that the pilot has the choice ofusing either the setting or the Correction procedure,and the greater simplicity of the concept involvedshould lead to better understanding of the meaningof the altimeter setting.Specific temperature anomaly S. A quantity forspecifying the temperature, that is convenient formany meteorological uses, is the specific temperatureJOHN C. BELLAMY5anomaly S defined in terms of the variation of theactual temperature T from the standard temperatureTp at any given pressure, byT - T,s=------.m1,It is seen that, in general, S is a function of both temperature and pressure since T, is defined as thestandard temperature at a given pressure. However,at any given pressure T, is a constant and S can thenbe used as a parameter with which to describe thetemperature and is directly proportional to T whichin this formula is in degrees of the absolute scale.The hydrostatic equation. The hydrostatic equation,a very good approximation of the actual relationshipconnecting height, pressure and temperature, assumesthat all vertical forces, such as the vertical componentof the Coriolis force or the inertial forces due to verticalaccelerations, are small enough to be neglected withrespect to the vertical pressure gradient force and theweight of the air. In other words, it is assumed thatthe weight of a column of air is supported by thedifference in pressure force between the bottom andthe top of the column..In the actual atmosphere (with a density p and anacceleration of gravity g) the weight of a column ofair of unit horizontal cross section and height Az ispgAz. This weight must be balanced by the verticalpressure gradient force, which is also the weight of thestandard column of air from z, at the bottom of thecolumn to zp + Az, at the top of the column. ThuspgAz = ppgpAz, or, going to the limit as Az 4 0, thehydrostatic equation can be written(3)The density of a gas at a given pressure is inverselyproportional to the temperature and directly proportional to the molecular weight of the gas, so thatPP T md-=-P TPm,where md is the effective molecular weight of dry(standard) air and m is the effective molecular weightof the actual air. Hence,(4)dz T mag,82, TP m g- = --If D is used as a pressure parameter, since D = z - zpandthe hydrostatic equation can be written as1mgIf D is considered as a height parameter, since dD dz dz, az,the hydrostatic equation can also be written as1,mdgpT-- T,(6)TmagP mg1=Virtual temperature T*. The numerical calculationof the hydrostatic equations can be systematized andsimplified by the introduction of the virtual temperature T* which absorbs the small variations of themolecular weight and of gravity in the relativelylarge variations of the temperature parameter. T* canbe defined by_dz, T,mg TPIn other words, this virtual temperature is that temperature which dry air at a given pressure and actedupon by a standard gravity must have in order thatits weight per unit volume be the same as the weightper unit volume of the actual air at that pressure.*To express this definition of the virtual temperaturein terms of the mixing ratio w of the mass of watervapor to the mass of dry air in a given sample of air,consider the mixture of a unit mass of dry air and amass w of water vapor. The total pressure of a given.volume of this mixture is equal to the sum of thepartial pressures due to the dry air and the watervapor, and these pressures are directly proportionalto the respective masses and inversely proportionalto the respective effective molecular weights. Thus,for the total mass 1 + w, in any given volumel+w w 1 1+w-- -- +- or m=mdm mw md (1 +sw)*Henceg l+w* It is to be noted that the virtual temperature as used here isdifferent from the usual definition of virtual temperature,6JOURNAL OF METEOROLOGYRearranging this equation for a difference methodof calculation,T* - T = T[( 2- i)(w> + (,)+ g, - g+ (2 - 1 ) ( e) ( 531. (9)l+wThe hydrostatic equation can then be written interms of T* asororThese forms are obtained from equations (4), (5)and (6).SpeciJic v'irtual temperature anomaly S*. Analogousto the definition of the virtual temperature, the specificvirtual temperature anomaly S* can be defined bymdgpT-- T,(13)mgT* - T,s* Ez TP TPBy using equation (2) it follows that(14)mag,l+S*=(l+S)-.mgBy using a process similar to that employed in developing equation (9) one obtainss* - s = (1 + S) [(2-9(&)+ + (gy) + (2- 1)x'x(+-)(y)]. (15)The three forms of the hydrostatic equation canthen be written in terms of S* asandaz- = 1 + s*,82,dD S*-=dz 1 + s*'aDdz,-- s*.Pressure gradient force F,. The expression for thevalue of a pressure gradient force F, (the force perunit mass acting on a parcel due to the spacial pressure variations) in terms of the spacial gradients ofthe pressure parameter z, can be obtained by considering that there is a gradient d~,~/d[ present at apoint where E is in the arbitrary direction of the forceF,. The total force per unit cross-sectional area corresponding to a change of pressure altitude of Azioequals the weight of the standard ail- column betweenthe heights of z, and z, + Az,, or ppgpAzp. Since foithe limit of a unit length in the [ dii-ectionwe have that(19)82,atPFP = PPgP - The plus sign is used since Fp has the same sense as apositive increase of zp.*The horizontal component of the pressure gradientforce (Fp)n, using the definition T* = Tmdg,/mg andusing n as a horizontal coordinate in the direction ofthe total horizontal pressure gradient, can then bewritten asT*(FPL = g- (2) = g(l + sj:) (2) . (20)TP z 2Also, since we are considering conditions on a constantlevel surface so thatT* dD(FPL = - g-( -) = - g(l + S*)( E) an . (21)T, 8%The horizontal pressure gradient force (F,) canalso be expressed in terms of the slope of a constantpressure surface (az/dn)F. From Figure 2 it is seenFIGURE 2.* This formula is very similar to that obtained for other common pressure units. For example, in terms of It, the height of astandard mercury column which can be supported by a givenpressure pF, = pogo(ah/aE) where PO and go are the standardmercury density and the standard acceleration of gravity, respectively.JOHN C. BELLAMY 7thatIf we also assume that the hydrostatic equation appliesso that (F,): = g, we have thatAlso, since (&/an), is the variation of the height zof a constant pressure surface with respect to n(measured on a horizontal surface) so that (azlan),= (aD/an),,Geostrophic wind equation. Since the horizontal component of the Coriolis force per unit mass at a givenlatitude 4 and for a given horizontal component ofthe wind velocity v is F, = - 2Qvsin 4 where Q isthe angular velocity of the earth, the geostrophicwind equation can be written as2Qvsin+=g--(---) T* az, =g(l+S*)($), (24)TP e 22Qv sin 4 = - g= - g(l + S*)( E) , (25)anIn this notation the positive direction for the distancen is taken to be at right angles to the left of the direction of motion so that the geostrophic wind blowswith low values of z,, but with high values of D and z,to its right in the northern hemisphere.Gradient wind equation. Inclusion of the centrifugalforce per unit mass V2/R~, where V is the gradientwind and RT is the radius of curvature of the trajectories of the air, gives the gradient wind equationin terms of the parameters z, zp or D,V2aDan=- g(1 + S*)( -) ,In this notation, then, if the radius of curvature isin the direction of the Coriolis force (Fig. 3a), thecurvature is anticyclonic and the negative sign is used.If the radius of curvature is cyclonic (Fig. 3b), the1-I.FIG. 3a. Air trajectory with anticyclonic curvature in the northern hemisphere.YFIG. 3b. Air trajectory with cyclonic curvature in the northern hemisphere.positive sign is used. Thus a cyclonic gradient windblows around high values of z, and low values of zand D; an anticyclonic gradient wind blows aroundlow values of zp and high values of z and D.Thermal wind equation. Since the gradient windvelocity is determined by the horizontal pressuregradients, and since the horizontal pressure gradientschange with elevation in a manner determined bythe hydrostatic equation, particularly if horizontaltemperature gradients are present, the shear of thewind along a vertical line is primarily a function of8 JOUR.NAL OF METEOROLOGYthe horizontal temperature gradients. This combination of the concepts of the gradient wind and hydrostatic equations, namely the thermal wind equation,can then be obtained by vectorial differentiation (i.e.,taking account of the changing direction of the horizontal coordinate n) with respect to z of the gradientwind equation (28). This givesor since the hydirostatic equation is azp/az= 1/(1+S*),by substitution from equation (28) we getx--- d In (1 + S*) g( In (in: '*I) . (32)az zAlso, since 1 + S* = T*/Tp,Similarly, vectorial differentiation of the gradientwind equation (31) with respect to z, and substitutionof the hydrostatic equation do/&, = S* givesIn these equationsare the vectorial shears, with respect to z and z,,respectively, of the sum of the horizontal Coriolisand centrifugal fforces per unit mass.Furthermore, Vz a In (1 + S*)2QV sin 4 f RT) azRT az T* T,262V sin 4 =t -In (or(is the part of this shear in the direction of the sumof the Coriolis and centrifugal forces themselves dueto changes in the vertical of the temperature factor1 + S* or T*/T, in the constant level form of thegradient wind equation.Likewiseis the part of this shear of force in the direction n'of the gradient of the quantity 1 + S* or T*/Tp ona constant level surface, andas* (!IT*+), Or -:(.z),is the value of this shear of force, with respect to z,,which is then in the direction n' OF the horizontalcomponent of the virtual temperature gradient on aconstant pressure surface.Since the Coriolis force is frequently larger thanthe centrifugal force in general these equations statethat the vertical shear of the wind is approximatelyparallel to the virtual temperature isotherms with thehigh temperature to the right of this shear in thenorthern hemisphere.Advective local temperature changes. If it is assumcdthat the motion of the air is approximately along aconstant pressure surface and that the temperatureof any given parcel of air is changing very slowly, therate of temperature change at any given point inspace can be expressed, with the aid of equations (34)and (35), in terms of Vnf, the horizontal componentof the wind normal to the virtual isotherms, asas* as*at P-- -- vnJ( a,.) =oraT* aT*- =- VnI( ,,.) =at PSimilarly, for approximately horizontal flow, withV,, being the horizontal component of the wind normal to the isolines of 1 + S* or T*/Tp on a constantlevel surface,a In (1 + S*)= VnIat zJOHN C. BELLAMYaorsphereaRlmdap 1and z, = -(To - T,); (45)T, = TO( i) ain the standard stratosphere3. Techniques of calculation.Conversion of pressure parameters. The definition ofthe U. S. Standard Atmosphere and the conversionfrom millimeters and inches of mercury to z, and T,are given in the National Advisory Committee forAeronautics Technical Reports Number 218 by WalterS. Diehl (2) and Number 538 by W. G. Brombacher(1). A conversion table (5) from each millibar of p tofeet of z, is given in USAAF Weather Division ReportNO. 708. This mathematical definition of the relationship between the pressure parameters p (inches ofmercury, millimeters of mercury or millibars) and theparameters zp and T, can be obtained by using thehydrostatic equation and the definition of the U. S.Standard Atmosphere.The hydrostatic equation in the standard atmosphere can be written assince the vertical pressure-gradient force per unitvolume in terms of the pressure parameter p is dp/dz,and this must balance the weight of a unit volumepp g,. Then, using the concept of a perfect gas for thestandard dry atmosphere, p, = mdp/RT,, where R isthe universal gas constant, so thatd lnp mdgpdZP RT,(41)-_-Th.e mathematical definition of the U. S. StandardAtmosphere, which is then the definition of the conversion between the pressure parameters z, and T,,can be written as follows:.the temperature To = 288"A,[ the pressure Po = 1013.25 mb.At zP = 01 (42)In the standard troposphere T, = To - az,.In the standard stratosphere T, = 218"A.(43)(44)Substituting these relationships into equation (41)and integrating, we get that in the standard tropo(46)RT,, p,m&p PZ, = z,, + 2.30259 ___ log10 - .In these formulae the values of the constants usedareT,, = 218"A,a = 1.9812"C/1000 ft,z,, = 35,332.0 ft,p, = 234.511 mb,CYR-- - 0.190285.m&pThese equations have been used for calculatingTables 1 through 3 for the conversion of pressureparameters. These tables are designed to be used asfollows :Tables la and lb-These are graphical tables fortwo-way conversion between any two of the pressureparameters z, in feet, zp in meters, T, in degreescentigrade, p in millibars, p in inches of mercury, andp in millimeters of mercury. Table la covers therange - 3000 ft _< z, 5 80,000 ft, and lb (drawn to alarger scale for greater accuracy) covers the range- 2000 ft 5 z, _< 10,000 ft. These tables are meantto be used primarily for occasional conversions, suchas making up a specific numerical table, since it isfelt that numerical tables are usually more convenientfor routine work.Tables 2a through 2f-These tables give the pressure conversions from p in inches of mercury, inmillimeters of mercury or in millibars, measured ator reduced to sea level, to the value of D at sea levelexpressed in feet or meters. Thus they can be used for:1. converting mercurial pressure observations actuallymade at sea level to D; 2. conversion of past andpresent "sea-level" pressure maps in inches, millimeters or millibars to D; 3. conversion of the altimeter setting P expressed in inches, millimeters ormillibars, for any point in the atmosphere to thecorresponding value of the altimeter correction Dapplying at that point. The specific parameters usedin any given table are denoted by the followingnotation: The vertical position referred to is given inthe presuperscript, the unit of measurement used isgiven in the postsuperscript, and the parameterentered in the body of the table is denoted as beinga function of the argument of the table. For example,the notation z=oDft (s=opin) denotes the conversionfrom the value of p, expressed in inches of mercury,10JOURNAL OF METEOROLOGYu0z0W WLCt0EcE"0.0aBVI0LPE- P-0 c 0u)?!?!u) VIeLJ-IImallciICInI1PI1.nn5EEIPsNc"JOH8 C. BELLAMY1112JOURNAL OF METEOROLOGYnH:0,0I 10 .- -NOHN C. BELLAMY1314JOURNAL OF METEOROLOGYJOHN C. BELLAMY16JOURNAL OF METEOROLOGYJOHN C. BELLAMY17 TABLE 2aConversion from p in Inches of Mercury to D in Feet at Sea LevelraDft (z-ofiin)inches27.027.127.227.327.427.527.627.727.827.928.028.128.228.328.4 ,28.528.628.728.828.929.029.129.229.329.429.529.629.729.829.930.030.130.230.330.430.530.630.730.830.931.031.131.231.331.431.531.631.731.831.932.032.132.232.332.432.532.632.732.832.9.o.oo-28102710261025102410-23202220212020201920- 18201730163015301440- 1340124011501050960- 860770670580480- 390300200 11020+ 70 160 2 60 350 440+ 530 620 710 800 890+ 9801070116012501340+ 14301520161016901780+18701960204021302220+ 230023902480256026500.01- 28002700260025002400-23102210211020101910- 18101720162015201430- 1330123011401040950- 850760 660570480- 380290200 10010+ 80 1702 70 360450+ 540 630 720 810 900+ 9901080117012601350+ 14401530161017001790+ 1880197020502 1402230+231024002490257026600.02-27902690259024902390- 230022002 10020001900- 18001710161015101420- 1320122011301030940- 840750650560470- 3702801909000+ 90 180280370460+ 550640 730 820910+ 10001090118012701360+ 14501540162017101800+ 18901970206021502240+232024102490258026700.03-27802680258024802380- 22902190209019901890- 17901700160015001410-1310121011201020930- 830740640550460- 36027018080+ 10+ 100 190 280 380470+ 560 650740830 920+lolo1100119012801370+ 14601540163017201810+ 19001980207021602240+233024202500259026700.04-27702670257024702370- 22802180208019801880- 17801690159014901400- 1300121011101010920- 820730640540450- 35026017070+ 20+ 110 200 290 380480+ 570 660750 840 930+ 10201110120012901380+ 14601550164017301820+19001990208021702250+234024302510260026800.05-27602660256024602360-22702170207019701870- 17801680158014801390- 1290120011001000910- 810720630530440- 34025016070+ 30+ 120 210 300 390480+ 580670 760 850 940+ 10301120121013001380+ 14701560165017401830+19102000209021702260+235024302520261026900.06-27502650255024502360-22602160206019601860- 17701670157014701380- 128011901090990900- 810710620520430- 340240 150 60+ 40+ 130 220 310 400490+ 580 6807 70 860950+ 10401130122013001390+ 14801570166017501830+ 19202010210021802270+236024402530261027000.07-27402640254024402350-22502150205019501850- 17601660156014601370- 1270'11801080990890- 800700610510420- 33023014050+ 140 230 320 410 500+ 590 680780 870960+ 10501140122013101400+ 14901580167017601840+ 19302020211021902280+23702450254026202710+ 400.08-27302630253024302340- 22402140204019401840- 17501650155014601360- 126011701070980880- 790690600500410- 320220 130 40+ 50+ 150 240 330 420510600690780870960050140230320410+15001590-. ..680.760.850+ 19402030211022002290+237024602550263027200.09-27202620252024202330-22302130203019301830- 17401640154014501350- 1250116010609708 70- 780680590490400- 310210 120 30+ 60+ 160 250 340430520+ 610700790880970+ 10601150124013301420+15101600169017701860+ 19502040212022102300+23802470255026402130-18JOURNAL OF METEOROLOGYmm69069 16926936946956966976986997007017027037047057067077087097107117127137 1471571671771871972072 172272372472572672772872973073 173273373473573673773873974074 17427437447457467477487490.0- :!6502610:!5702530:!490- :!450;!41023702330;!300-:!2602!220;!la0;!140:!loo- 2!060;!020199019501910- 18701830179017501720- 16801640160015601530- 14901450141013701340- 13001260122011801150-1 110107010301000 960- 920 880850 810770- 740700660620590- 550510480440400 TABLE 2bConversion from p in Millimeters of Mercury to D in Feet at Sea Levelz=aDft (zwpmm)0.2- 26402600256025202480- 24402400237023302290-22502210217021302090- 2050202019801940I900- 18601820179017501710- 16701630159015601520- 14801440140013701330- 12901250121011801140- 110010601030 990950- 910 880 840 800770- 730 690650 620 580- 540 510470430 3900.4-26302590255025102480- 24402400236023202280-22402200216021202090-20502010197019301890- 18501820178017401700- 16601620159015501510- 14701430140013601320- 12801240121011701130- 109010601020980940- 910870830790760- 720680650610570- 5405004604203900.6-26202580255025102470- 24302390235023102270-22302190216021202080- 20402000196019201890- 18501810177017301690- 16601620158015401500- 1460. 1430139013501310- 12801240120011601120- 109010501010970940- 900 860820790750680640600560- 710- 5304904504203800.8-26202580254025002460-24202380234023002260-22302 19021502110, 20701990195019201880- 18401800176017201690- 2030- 16501610157015301500- 14601420138013401310- 12701230119011501120- 108010401000970930- 890 850 820 780740- 710 6 70 630590 5 60- 5204804504103 70mm7507517527537547557567577587597607617627637 647657667677687697707717727737747757767777787797807817827837 8478578678778878979079 17927937947957967977987998008018028038048058068078088090.0- 3703302902 60220- 180 150 1107040+o 40 70 110 140+ 180220250 290330+ 360400430470510+ 540580610650 680+ 720760790 830860+ 900 93097010001040+ 10701110115011801220+ 12501290132013601390+ 14301460150015301570+160016301670170017400.2- 360 320 280 250 210- 170 140 1007030+ 10 40 80 120 150+ 190 220 260 300 330+ 370 400440480510+ 550 580 620 660 690+ 730 760 800 830870+ 900 940 98010101050+ 10801120115011901220+ 12601290133013601400+ 14301470150015401570+161016401680171017500.4- 350310 280240 200- 1701309060- 20+ 10 50 90 120 160+ 200 2302 70300340+ 380410450480 520+ 560 590630 660 700+ 730 7 70 810 840 880+ 910 95098010201050+ 10901120116011901230+ 12601300133013701400+ 14401470151015401580+161016501680172017500.6- 340 3102 70230200- 160 120 90 50 10+ 20 60 90 130 170+ 200 240270 310350+ 380 420460490530+ 560 600 630670 710+ 740 780 810 850 880+ 920 95099010201060+I1001130117012001240+12701310134013801410+ 14501480152015501590+ 16201660169017201760--_0.8- 340300 260230 190- 150 120 80 40 10+ 30 60 100 140 170+ 210 2 50 280 320 350+ 390 430460 5005304- 570 610 640 680710+ 750780 820 850 890+ 930 960100010301070+11001140117012101240+12801310135013801420+ 14501490152015601590+16301660170017301770-_JOHN C. BELLAMY1810185018801920191820186018901920$19501990202020602090+19601990203020602100+ 19702010204020802110825 +2290826 2320827 2360828 2390829 24202-31802880259022902000-171014301140 860 5803-31502850256022601970-169014001120840 560- 310 30+ 240 510780+lo40131015701830- 280 10+ 260 530 800+lo70133015901850TABLE 2b (cont.)0.2 I 0.40.60.8 II mm I 0.00.40.60.8mm0.2+21202160219022302260+229023302360240024300.0$17701810184018801910+1950198020102050208081081 1812813814815816817818819+1780 I +1790+179018301860r9001930+ 19702000203020702100+I800 )I 820 1 +21201840 82 1 2150+21302160220022302270+23002340237024002440+21402170221022402270+23102340238024102440+21402180221022502280+232023502380242024501870 2 1901900 11 iii 22201940 2250 TABLE 2cConversion from p in Millibars to D in Feet at Sea Level.-OD ft (z=opmb)mb045678990091092093094095096097098099010001010102010301040105010601070108010901100- 32402940265023502060- 177014901200920640- 360 90+ 180450720+ 9901250151017802030+2290- 32 102910262023202030- 174014601170890610- 340 60+ 210480750+ 10101280154018002060+2320-31202830253022301940- 166013701090810530- 250+ 20 290 560 830+ 1090136016201 8802 140+2390- 30902790250022101920- 163013401060780500- 230+ 50 320590860$11201380165019002160+ 2420- 30602760247021801890- 160013101030750470- 200+ 70 350 620880+11501410167019302190+2440- 30302730244021501860- 157012901000720450- 170+ 100370 640 910$11701440170019602210+2470- 30002710241021201830- 15401260980700420- 140+ 130400670 940+ 12001460172019802240+2490- 29702680238020901800-15101230 950670 390- 120+ 160 430 6909 60+ 12301490175020102270+2520+2340 +23702090 I 211020JOURNAL OF METEOROLOGYinches27.027.127.227.327.427.527.627.727.827.9. 28.028.128.228.328.428.528.628.728.828.929.029.129.229.329.429.529.629.729.829.9. 30.0 30.1 '30.2 30.3 30.430.530.630.730.830.931.031.131.231.331.431.531.6. 31.731.831.932.032.132.232.332.432.532.632.732.832.90.00- 858827797766736- 706676646615586- 556526496467437- 408379350320292- 263234205176148-1199162345+ 23 51 79107134+162190218245273+300327354381408+436463489516543+570597623650676+ 702729755781807 TABLE 2dConversion from p in Inches of Mercury to D in Meters at Sea Level ( P')r-oDm 1-0 in0.01- 855824794763733- 703673643613583- 553523493464434- 405376347318289- 260231202173145-11688 59 313+ 265381109137+ 165193220248275+3023303573 8441 1+438465492519546+573599626652679+ 70573 17587848100.02- 85282 179 1760730- 700670640610580- 550520490461432- 402373344315286-257228199171142-1138558280+ 28 56 84112140+168195223251278+306332360387414+441468495522549+57560262865568 1+ 7087347607868130.03- 849818787757727- 69766763 7607576- 547517487458429- 399370341312283-254225196168139-11182 5425+35987115143+171198226253281+308335362390417+44447 1498524551+57860563 1658684+710737763789815+ 310.04- 8468157 84754724- 694664634604574- 544514485455426- 396367338309280-251222194165136- 108 7951 22+6+ 34 62 90118146+173201229256283+310338365392419+ 446473500527554+58160 7634660687+7137397667928180.05- 84281278175172 1-69166163 1601571- 54151148245242 3- 3943 64335306277- 2482 19191162133- 105764820+9+ 376593120148+176204231259286+31334 1368395422+449476503530557+583610636663689+7167427687948200.06- 839809778748718- 68865862 8598568- 538508479449420-391361332303274- 245217188159131- 1027445 17+ 12+ 406795123151+ 179207234262289+316343370398425+452479506532559+586612639666692+718745771797823'0.07- 836806775745715- 685655625595565- 535505476446417- 388358329271300 .-.2432 14185156128- 9971 42 14+ 15+ 42 7098126154+1822092372 64291+31934637340042 7+454481508535562+ 589615642668695+7217477738008260.08- 833803772742712- 682652622592562- 532502473443414- 385356326297268- 240211182153125- 96 68 39 11+ 17+ 4573101129157+184212240267294+321349376403430.+457484511538565+59161864467 169 7+ 723750. 776802828--0.09- 8308007 69739709- 679649,619589559- 529499470- 44041 1-382353323294266- 237208179151122- 936537 8+ 20+ 4876104132160+1872152422702974-324351379406433+460481514540567+ 594620647673700+726752779 .._80583 1JOHN C. BELLAMY21 TABLE 2eConversion from p in Millimeters of Mercury to D in Meters at Sea Level"OD" (c-opmm)mm69069 1692693694695696697698699700701702703704I 705 706 707 708 7097 1071171271371471571671771871972072 17227237247257267277287297307317327337347357367377387397407417427437447457467477487490.0- 807795783771759- 747735724712700- 68867666465264 1- 629617605594582-570558547535523-512500488477465- 45444243 1419407-396384373361350- 338327315304292-281270259'247236- 224213202190179- 1681571461341230.2- 805793781769757- 74573372 1709698- 686674662650638- 626615603591579- 56855654453252 1- 509498486474463-451440428416405-393382370359.348-336325313302290-279268256245233- 222211199188177- 1661551431321210.4- 802.7907787667 54- 74373 1719707695- 68367 165964863661260 1589577- 565554542530518- 507495484472460- 44943742 6414402-391379368357345- 334322311299288- 624-2772652 5424323 1-220208197186175- 1641521411301180.6- 800788776764752728717705693- 740-681669657645633- 622610598586575- 56355 1539528516- 50549348 1470458- 447435423412400- 389377366354343-332320309297286-274263252240229-217206195184172- 1611501391271160.870:69(mm- 798786774762750- 7387267 142ll- 67866665564363 1-6196085965 84572- 560549537525514- 50249 1479467456- 44443342 1409398-386375363352341-329318306295283- 272261250238227204193181170- 159-215148137,1251147507517527537547557567577587597607617627637647657667677687697707717727737 747757767777787797807817827837 8478578678778878979079 17927937947957967977987998008018028038048058068078088090.0- 112101897867- 564533 22 11+o 11 22 33 44+ 2;778899+I10121132143154+ 165176187198208+219230241252263+273284295306317+327338349360370+381392403413424+435445456467477+4884985095195300.2- 10998877665- 54 4231209+ 1:+ 2;2435478090101+112123134145156+ 167178189200211+221232243254265+276287297308319+330340351362372+38339440541542 6+437447458469479+ 49050051152 15320.4- 107968574 62- 51 4029 187+4 14 27 38 49+ 6071 82 93104+115125136147158+ 169180191202213+224234245256267+27828930031032 1+332343353364375+385396407418428+43945046047 148 1+4925025135245340.6- 105948371 60- 49 3827154+7 17 29 40 51+ 62 73 8495106+117128139150161+ 172182193204215+2262372472582 69+280291302312323+334345355366377+387398409420430+441452462473483+4945045155265360.8- 103 9280 6958- 4736 24 132+9 19 31 42 53+ 64 758697108+119130141152163+174185195206217+2282392502 60271+282293304315325+3363473583683 79+390400411422432+443454464475486+496507517528538220.6+651662672682693JOURNAL OF METEOROLOGY0.8 .+653 ,664674685695 TABLE 2e (cont.)0.6 I 0.8 11 mm810811812813814815816817818819+541 +54355 1 553561 563572 574583 585+593 +595603 605614 616624 626635 63 7- 86 2+ 80163244+325406485565- 78+6 89171252+333414493572- 61+ 221051872 69- 52 - 44+ 31 + 39113 122195 203277 2857607707 80790800810820830840-- 2740240020601720-- 13901060740410908909009109201460-k 1760206023500.00.20.40.4+ 545555566576587+ 597608618628639+ 645655666676687+697707718728739+64765 7668678689+ 69970972073074 1+ 64966067068069 1+701712722732743820568578 580 823589 1 591 11 824+703 +705714 724 1 716 726 825610 612 826620630641 1 643 /I 829 TABLE 2fConversion from p in Millibars to 'D in Meters at Sea Level. z=oDm (z-opb)--0-988897806717628_- 540453366281195-11127+ 56138220+30138146254 1620+ 698314617 1-825mb90091092093094095096097098099010001010' 102010301040105010601070108010901100.9-- 906815726637549-4613752892 04120- 36+ 47130212293+373454533612690+ 768-979888797708619-531444358272187- 103 19+ 64146228+309'38947054962 7+ 706-970879788699610- 522435349263179- 94 11+ 72154236+317397477557635+713- 942851761672584-496410323238153'- 69+ 14 97179260+341422501580659+737-961 . -951870 1 860779 770690 68 1- 933 - 924 -915842752663 654 645575 1 566 1 557601 1 593I-514 - 505427 I 418341 332255 246-470I 384306 298- 48840 131522914522 1 212136 1 128170 I 162430509588+721 $729643 I 651TABLE 3a Conversion from p in Millibars to D in Feet at Standard Levelsmb 101 11 2 13 141 5 16 17 18 19 z = 5,000 feet.P in ftDft (z io ftmb$1-2710236020301690- 1360103071038060+ 250 56087011801490+ 179020902380-2670233019901660- 13301000670 350 30+ 280 600 91012101520+ 182021202410- 2640230019601620- 12909606403200+ 320 63094012401550+185021502440- 2600226019201590- 1260930610290+ 30+ 350 66097012701580+ 188021802470-2570223018901560- 1230900580250+ 60+ 380 690100013001610+191022102500-2530220018601520-1190870540220+ 100+ 410720103013301640+ 194022402530- 2500216018201490-1160 830 510 190+ 130+ 440 750106013601670+1970227025602470213017901460-1130 800 480 160+ 160+ 470780109014001700+zoo022902590-2430209017601420- 10907 70450130+ 190+ 500 810112014301730+ 203023202620JOHN C. BELLAMY 23-16201230 850470 100+ 270 630 990 TABLE 3a (cont.)mb 10 11) 2 13 14 15 16 17 18 19 z = 10,000 feet-1580119081044060+ 3006701030630640650660670680690700710720730740-2560210016301180-25702170- 178013901000620250+ 120 490 85012101560+ 19102260-2520 -24702050 20001590 15401130 1090- 25302130- 1740' 1350960590210+ 160 52088012401600+ 19502290550560570580590- 24902090- 17001310930 550 170+ 200 560 92012801630+ 19802330- 960 - 910 510 470 70 30+ 360 + 400 7 80 830- 245020.50- 16601270 890 510 140+ 230 600 96013101670+20202360+1410182022302630-24102010+1450187022702670- 23701970-2990243018801330- 23301930- 15401160770 40030+ 340700106014201770+21202460-2930237018201280- 22901890- 15001120 740 360+ 10+ 380 740110014601810+21502500-2710215016001070-22501850- 1460.1080700 320+ 50+ 410 780114014901840+21902530-26502 10015501020-22101810- 14301040 660 290+ 80+ 450 810117015301880+22202570- 800 280+ 230 7301230- 750 230+ 280 7801280~.~~1350 13801700 1 1740- 540 20+ 480 9801480750760- 490+ 30 53010301.530+20502400+20902430z = 15,000 feet510 -2800 -2750520 I X3:: I 2280530 1820-27102240' 17701320- 870420+ 10 440870+1290170021102510- 26602 19017301270- 820 380+ 60 490 910+ 1330174021502550-26102 14016801220- 780 330+ 100 530950+1370178021902590-2420196015001040- 600 160+ 270. 7001120+ 1540195023502750- 23801910~. ~.14501000540 I 1410 I 1360- 730290+ 1405701000- 690 250+ 190 6101040- 640 200+ 230 6601080+1500191023102710- 550 120+ 320 7401160+ 1580199023902790600 I +1200 I -1-1250610 1620 1660620630z = 20,000 feet4104204304404.50460470480490500510-2880232017701230- 700 180+ 330 8301330+18102290- 2820226017101170- 650 130+ 380 8801380+ 18602340-2760221016601120- 590 80+ 430 9301430+19102390- 260020401500960- 440+ 80 58010801570+20502530- 248019301390860+ 180 68011801670+21502620- 330- 254019901440910- 390+ 130 63011301620+21002580+1720 +17702200 1 2250+1960 +20102440 I 248024-239020901780JOURNAL OF METEOROLOGY-236020601750 TABLE 3bConversion from p in Millibars to D in Feet at Standard Levelsa in kmDft (z in km robPI- 14801180 890 590300- 20+ 270 550 8301110+13901660193022002470- 14501150 860570 280+ 10 300580 8601140+14101690196022302500-.15001180870570 2 60-1470 -14401150 1120840 810 540 510230 200+1540182021102390+157018502 1402420-2410 -23802070 20401740 1700-2234020001670+ 200 520 83011301440+ 240 + 270 550 580 860 8901160 11901470 1500+174020402330+1770 +18002070 21002360, 2390-252022101900-. 160013001010710420-. 130+ 150 440 7201000+ 12801550182020902360- 248021801870- 15701270980680390- 100+ 180470 7501030+ 13001580185021202390- 245021501840- 15401240950650360- 70+ 210 4907 801050+ 13301610188021502420- 242021201810- 15101210920620 330- 50+ 240 520 8001080+13601630190021702440-2300 -22701990 I 19601690 1660-224019301630- 13301040740450160+ 130 410 690 9701250+15201800207023302600870880890900910920930940950960970980990- 233020201720- 14201120830540 250+ 403206108901170+ 14401710199022502520- 13901090 800.- 13601070770480190...510220+ 70 I + 100 350 380.-.640 660920 1 9401190 ' 122010001010102010301040+1470 I +15001740 17702010 20402280 23102550 2580-246021301810- 242021001780- 239020701750-236020401720- 140010907 80480170+ 130 43072010201310+1590188021602440- 233020101690- 13701060750440140+ 160460 75010501340+ 162019102 1902470- 229019701660- 1.3401030720410110+ 19049078010701360+ 1650194022202500-226019401620- 13101000690 38080+ 220 520 81011001390+ 1680197022502530- 223019101590- 12809706603505055084011301420+1710199022802560+ 250.- 220018801560.- 125094063032020-t .28b 57087011601450-t 1740202023002580-217018501530- 1220 910 600 290+ 10+ 310 600 90011901480+ 1770205023302610820830840850860870880890900910920930940950960970980630 660 6901220$.15101790~20802360-231019701640- 131098065033020+ 30061092012201530+ 183021302420-227019401600950620300+ 20+ 330 640 9501260' 1560+ 186021602450- 1270- 2240190015709105902 70+ 50+ 360670 98012901590+189021902480- 1240770780790800' 810820830840850860870880890900910920- 2480214018001140820490170+ 14045076010701380+ 168019802270- 1470- 244021001770- 14401110780460 140+ 170 49080011001410+171020102300-221018701540-1210 880 5 60 240-k 80+ 390700101013201620+ 192022102510-217018401500-1170850 530 210+ 1101080, 750430 370110 1 80 I 50+ 420 730104013501650+ 195022402 540JOHN C. BELLAMY 25-230019501600-1250900 TABLE 3b (cont.)mb 10 111 2 13 14 15 16 17 18 19 z=2km-227019101560-1210870-259022301880- 15301180 840 500 160+ 170 500 82011501470+178021002410-248021201770- 25502 1901840- 14901140800460130+ 200 530 86011801500+181021302440-244020901740-252021601810- 14601110770430 90+ 240 560 89012101530$184021602470-1420108073040060-241020501700- 13501010 670 3300+ 330 660 99013101620+ 194022502560-1390104070036030-237020201670- 1320970630290+ 40+ 370 690102013401660+ 197022802590+ 270 600 92012401560- 234019801630- 1280940600260+ 70+ 400 730105013701690+ 200023102620+ 300 630 950128015907207307407507 60770780790800$810820830840850860870-265022701900-261022301860-15301160800450100+ 250 60094012801610-1490113077041060+ 290 63097013101640 530z"$ 1 190+ 100 + 140-178013901010630260+ 430 I + 470 760 790-174013509705902206506606706806907007107207307401080 11101400 1 14301720 1750- 193015401160780410- 40+ 330 69010501400$203023402650+ 110 480 84011901540+206023702680+ 150 + 180 510 550870 9101230 12601580 1610+1880 I +1910 2220;.% I 2530z = 2.5 km- 2800-276023802010- 16401270 910 550 200+ 150 490 84011801510+ 184021702500-272023501970- 16001240-269023101930- 15701200840 480 130+ 220 560 90012401580+191022402560-257022001820- 1460109073038030+ 320 670101013401680+201023302660- 253021601780- 14201060700340+ 10+ 360 700104013801710+204023702690-2500 I -2460670680690700710720730740750760770780790~. . .242020502120 20801750 1 1710- 16801310950590240+ 110 460 80011401480- 13801020 660 310+ 40+ 390 730107014101740- 1350980630280+ 80880520170180530870210540880200530+ 430 770111014401780+181021402460+1940 +19702270 23002590 1 2630+2070 $21102400 1 24302720 2750a=3km- 2720630 640 I 2330- 26802290- 189015001120740370+o37073010901440+17902 1402480- 26402250- 26002210- 182014301050670290+ 70 440 80011601510+ 186022002550-2560 -25202170 I 2130- 24802090- 24402050- 16601270890520150+ 220 580 94013001650$200023402680-24102010- 16201240860480110+ 260 620 98013301680+203023802720- 23701970- 15801200 820 44070+ 290 660101013701720+207024102750- 17001310930560180-185014701080700330+ 40400 76011201470750 +1750760 1 2100770 2440+ 18202170251022402580TABLE 3b (cont.)-274023001860, 14301010- 590 170+ 230 6301030+143018102200-2700226018201390960- 550 130+ 2706701070+146018502230-15901110 650 180+ 270+ 7201160159020202440-1540 -14901070 1020 600 550 140 90+ 310 + 360+ 760 + 8001200 12401630 16802060 21002480 2530+ 5801020146018902320+ 630 + 6701070 11101500 15501930 19802360 2400- 540+ 3059011401680+2210- 480+ 9065012001740+2270~-252018301160500+ 140 770-245017601090440+ 200 830310320330340 '-3080 -3010 -2940 -28702380 2310 2240 21701700 1630 1560 14901030 960 890 830z=4km5505605705 80590600610620630640650660670-- 28302390195015201090-- 670 2 60+ 150 5509504-135017402120-27902340191014701050- 630 220+ 190590990+ 139017702160- 2650221017801350920- 500 90+ 3107101110+ 150018902270-2610217017301300880- 460 50+ 3507501150+ 154019302310-2560212016901260840- 420 10+ 390 7901190+I58019702350- 2520208016501220 800- 380+ 304308301230+162020002390- 2480204016001180750+ 704708701270+ 166020402420- 340- 24301990156011307 10- 300+ 110 510 9101310+ 1700208024608z=5kmI-28102320- 18301350880410+ 40+ 490940137018102230-27602270- 17801300830470+ 90+ 540980142018502270-27102220-26602170-26102120-2510 -2460.2020 1 1970-24101930- 1440970510 50+ 400+ 8501290172021502570480490-- 28602360-25602070-- 1880520 920530 4601250780320 230540 I 0+ 130 I + 180 I + 220550560570580590+ 450891)2190z=6km420430440450460470480490500510520-27402 1901650-- 1120600 8092018802360+ 420+ 1400- 26902 1401600- 1070540 30+ 470960+ 145019302400- 263020801540- 1010490+ 20 5201010+lSOO19802450-258020301490- 960 440+ 70 5701060+155020302500-2520 ,19701440- 910 390+ 120 6201110+ 160020702540- 247019201380- 860340+ 170 6701160+ 164021202590-241018701330- 800 290+ 220 7201210+169021702630-236018101280- 750240+ 270 7701260+ 174022102680-230017601220- 700190+ 320 8201310+179022602730-225017001170- 650 130+ 370 87013503.184023102770=7km- 264020206420830- 250+ 310 87014101950+ 2480-258019601360770- 200+ 370 92014702000-2510190013007 10- 140+ 430 98015202060- 245018401240660- 80+ 480103015802110II-- 3020239017801180-- 600 204- 54010901630t-2160- 2830221016001010- 420+ 14070012501790+2320-29502330' 17201120- 2890227016601070-276021501540950- 370+ 200 76013101840-270020801480890- 310+ 260 81013601900 3 60. 370 380 390400410420430440450+2530 I +2580 I +2630+2370 I +2420=8km- 280021001430760- 120+ 520113017402330- 273020401360700- 50+ 580120018002390- 266019701290630- 259019001220570+ 70700132019202510350360-- 370$- 260 89015002100- 310+ 33095015602160- 240+ 390101016202210- 180+ 450107016802270+ 10 6401260~~~ijio 14401980 I 20402570 2620~~370. 3803901860245026JOHX C. BELLAMY 27-21801420 670+ 50760TABLE 3b (cont.)-21101340 600+ 120830,270 -2810280 I 2030290 1270300310320330340- 520+ 200 90015802250I-26601780- 920 100+ 70014802240-2570 -24801690 1600- 840 - 760 20 + 60+ 780 8601560 16302310 23902302402 502 60270280290-273019501190- 450+ 27097016502320- 29302040-1180 340+ 47012502010- 28401950- 1090260+ 55013302090- 510+ 310110018602610- 265018701120- 380+ 340104017202380- 420+ 390117019402680-27501860- 1010 180+ 63014002160200210220230240250-257018001040- 310+ 410111017902450- 25801550580+ 3501240+2100-25001720970- 230+ 480118018502520870+ 709801850z = 10 km-..770 680+ 170 + 2601070 11501930 2020- 24201640890+ 550124019202580- 160170180190200210-2700 -2570 -2450 -2330 -2210 -2090 -1970 -1850 -1730 -16201500 1380 1270 1150 1040 930 810 700 590 480370 260 150 40 + 70 + 170 + 280 + 390 + 490 + 600+ 700 + 810 + 910 +lo10 +1120 +1220 +1320 +1420 +1530 +16301730 1820 1920 2020 2120 2220 2320 2410 2510 2600z = 11 km140150160170180-2470 I -2370 I -2260 I -2160 I -2060-3480 -3330 -3180 -3040 -2890 -2750 -2600 -2460 -2320 -2180-2040 -1900 -1760 -1620 -1490 -1350 -1220 -1080 - 950 - 820+ 210 + 330 + 460 1550 1660 2690 2800 40 '13;: 1430+ 580 + 710 + 830 + 950 +lo70 +11901780 1900 2010 2130 2240 2350 2470 2580690 560 430 300 1701460 1360 1260 ii60 1060+ 1330 440 1 +,E! 1 +:!! 1 +,58! 1 + 1680490120130140150+2190 I +2270 I +2360 1 $2440 1 +2520-3430 -3260 -3080 -2910 -2740 -2570 -2410 -2240 -2080 -19101750 1590 1430 1280 1120 960 810 650 500 350 200 50 + 90 + 240 + 390 + 530 + 680 + 820 + 960 +1100+1240 +1380 +1520 +1660 +1890 +1930 +2060 +2200 +2330 +2460-2340 -22601570 1 1490820 740100 -3960110 1970120 150130 +1530- 90+ 620-3760 -3550 -3350 -3140 -2940 -2740 -2550 -2350 -21601780 1590 1410 1220 1040 860 680 500 320+ 20 + 200 + 370 + 540 + 710 + 870 +lo40 +1200 +13701690 1850 2000 2160 2320 2470 2630 2780 2930. ~~~131019902650- 20+ 690138020602710- 23901520- 670+ 150 94017102460- 1960 960 20+ 8901760+2610- 23001430- 590+ 230102017902530 15201 21902780 2840-2210 -21301350 I 1260-1860 I -1750 1 -1650+2690 I +2770 I +286028 JOURNAL OF METEOROLOGY90 --2890 -2660 -2430 -2200100 -- 680 - 480 - 270 - 70110 +1310 +lSOO +1690 +1870-1980 -1760 -1540 -1320 -1110 - 890+ 140 + 340 + 530 + 730 + 930 +11202060 2240 2420 2600 2780 296070 --4870 -457080 2080 181090 + 390 + 620 TABLE 3cConversion from p in Millibars to D in Meters at Standard LevelsiinkmDm rmkm mb(' P 1-4280 -3990 -3710 -3430 -3150 -2880 -2610 -23401560 1310 1050 810 5 60 320 80 + 160+ 850 +lo80 +1300 +1520 +1740 +1960 +2170 239087088089090091092093094095096097098099010001010102010301040607080- 766673580-488397306217128- 40+ 471342 19305+389473556638720-4820 -4470 -4130 -3800 -3470 -3140 -2820 -2510 -2200 -18901590 1290 1000 710 430 150 + 130 + 400 + 670 + 940+1200 +1470 +1720 +1970 +2230 +2470 2720 2960 3200 3440- 757663571 .-479388297208119- 31+ 56142228313+39748156464672850 --536060 154070 +1690- 747654561-470379288199110- 22+ 65151237321$406489572654736-4940 -4530 -4130 -3740 -3360 -2980 -2610 -2250 -18901190 850 520 190 + 140 + 460 + 770 +lo80 +1390+1990 +2280 +2570 +2850 3130 3410 3680 3950 4220z = 0.5 km40 --6750 -623050 2070 166060 ,+1740 +2090- 738645552-4613 70279190101- 14+ 73'159245330+414498580663744-5720 -5230 -4750 -4280 -3820 -3370 -2930 -25001250 850 460 80 + 300 + 670 +lo30 +1390+2430 +2760 4-3090 +3420 3 740 4050 4360 4670-729 1 -719-710617525636 626543 I 534-701608515-451 1 -442360 351-5+ 82168254338 261?:: 1 17293 84+490177262347+ 12 99185271355+ 211081942793 64+439522605687769- 433 - 424342 1 333252 244+448531613695777 154'ti 1 66+42250658967 1752+4315145976797 60~~-691598506-41532423514557+ 30116202288372+456539622703785- 68258949 7- 40631522613749+ 391252112963 80+464547630712793820830840- 749650553850860870880890-45636126617380950960970980+460547634719+47856565 1737+486573659745- 683580478- 673570468 82+ 15+1102052993922 485+576667756 72+ 24+120215309402494+585676765-767658551-756 -745647 637540 529131 29+ 72172121 111 19 9 + 92+ 1% 192+572667762+582677771JOHN C. BELLAMY 29 TABLE 3c (cont.)mb 10 111 2 13 14 15 16 17 18 19 z=lkm- 73964 1543-44735225716371+ 21112203292381+469556642728- 70961 1514-41832322913643+ 4914023031940 7+495582668754- 69960 15043142 1912634+ 58149239328416+ 504590677762- 409- 690592495- 3993042 1011725+ 6715824833742 5+512599685771- 680582485- 39029520110815+ 76167256346434+5216086947 79- 670572476-380285191986+ 85176265355443+530616702788- 660563466-71962 1524-37127618289+3+ 941852 7436345 1-428238+ 30 + 39I a;; I E 103920 194930 283940 I 372+53962 5711796z = 1.5 km770780790800810820830840850860870880890900910920- 755652550- 44834824915053+ 44139234327420+512603694- 745642539-43833823914143+ 53.148243337429+521612703- 73463 1529-42832822913134+ 63158253346439+ 530621712- 72462 1519-41831821912124+ 72167262355448+53963072 1-71461 1509- 40830820911114+ 821'27271364457+549640730- 70460 1499- 3982981991014+ 911862813 74466+558649739- 693590489- 388288190 91+5+ 101196290383475+567658748- 662560458-358259160 63+ 34+ 129224318411503+ 5946857 74-378 -368279 1 269180 170z=2km720730740750760770780790800810820830840850860870- 789680572-46535925515250+ 52152251350447+ 544639734- 778669561-45534924514239+ 62162261359457+553648743- 734626519-412307204101+1+ 10220230 1399496+591686781- 723615508-402 .29719390+ 11+112212310408505+601696790~- 71260449 7-391286183 80+ 22+ 122221320418515+610705799- 70259348627617370+ 32+ 132231330428524+ 620715809- 380- 691583476-37026616260+ 42+ 14224 1' 340437534+ 629724818- 444 -433 - 423338234271 281 291466+ 563658753TABLE 3c (cont.)750760770780790+ 35 + 45 + 56 + 67 + 77141 151 162 172 182245 255 266 276 286' 348 358 369 379 389450 46 1 471 481 49 1480490500510520530540550560570580590--872 -856 -841 -826 -811 -796 -781 -766 -750 -735720 705 690 676 661 646 63 1 616 60 1 587-572 -557 -543 - 528 -513 -499 - 484 -470 -455 - 440426 411 397 383 368 354 339 325 311 296282 268 253 239 225 211 197 182 168 154140 126 112 98 84 70 56 42 20 141 + 13 + 27 + 41 + 55 + 68 . +82 + 96 +lo9 +1234-137. +lSO +164 +178 +191 +205 +218 4-232 +245 +259272 286 299 313 326 340 353 366 380 393406 420 433 446 459 472 485 499 512 - 525538 551 564 . 577 590 603 616 629 642 655668 68 1 693 706 719 732 745 757 770 783z = 2.5 km670 -830 -819 - 807690-- 761646533-422311201 93+ 14+ 12022432 7430532+632731830- 79668 1567-455344.' 23412619+ 8819329639950 1+ 602702801- 784669556- 444333223115-8+ 98203307410511.+612712810- 772658544- 433322212104+3+ 109214317420522+62272 1820- 749' 635522-41130019183+ 24+ 130234338440542+ 642741840700 -511 - 499 - 488 -477 - 466720800810820z=3km.-- 830709-- 589471354238124-- 11+ 101211320428+53564 1745-818697-577459342226112+111222233 1439+ 545651755- 806685- 565447330215101+ 12123233342449+556662766- 794673- 55343531920390+ 1;:244353460+567672776- 782661- 541424307. 19278+ 3414525536347 1+577- 682 786- 769649- 530412296181: 67+ 451562663 7448 1+588693796-757637- 51840028416956+lE277385492+ 598703807- 74562 5- 506389- 272158 44+ 67178288396503+ 609714817- 733613-49437726114633t. 78189.298407514+62072482 7-72160 1- 482 365 249, 135 22+ 89200309417524+630734838630640650660670680690700710720730740750760770z=4km550560570580590600610620630640650660670-- 863728594462332-- 2044- 4678170291+411529646.-8507 14580449 319- 192 66+ 59182303+42354 1658- 836701567436307- 179 53+ 71194315+435553670-822687554 ,423294- 166 41+ 84206327+447565681- 809674541410281- 154 28+ 96218339. +459 576 693- 795660528397268- 141 16+ 10823 1351+470588704- 782647515384255- 128 3+ 1202433 63+482600716- 768634501371243-116+9133255375+49461 1728- 755620488358230- 103+ 22 145. 267 387+ 506623739- 741607475345217- 91+ 1:;279399+51863 5751z=5km TABLE 3c (cont.)mb IO 111 2 13 14 15 16 17 18 19 z=6km-24587+ 67219369+51666 1803- 80263 5470- 309150+ 15;310+457603747-229 72+ 832343 84$530675818- 785618454- 293134+ 21174324+472617761310 - 940320 726330 517340 313- 751585421,-2611032043 54+so1646789+ 52-918 - 897 -875 -854705 684 663 642496 476 . 455 435293 273 253 233-735 -718568 1 552405 389- 83262 1414213-16+176- 701535373-213 56+ 98250399+ 545689832-811600394193+4195- 684519357- 197 41+113265413+ 560704846+ 23214402585765420430440450460470480490500510520f42 + 62233 252420 439603 62 1782 800- 836668502- 341181 25+1282 80+428574718360370380390- 76860 143 7-277119+ 36189339+487632775+ 81 +lo0 +119 +138 +157271 290 309 327 346457 476 494 512 530639 657 675 693 711-819651486-325166 10$144295+443589732- 761525295- 737501272z=7km300310320330340I- 160 - 138 - 115 - 93+ 60 + 82 +lo3 +1252 74 295 316 337483 504 524 545687 707 727 ' 747I- 843654470289-112+ 622323995631 +723e=8km- 71$146358565767360 1 -919 I -900 I -881 1 -862- 49+168379586787- 82463545 1271- 94+ 79. 2494155 79+739- 702437-180+ 69311545773- 805617433253- 67541 1-155+ 94334568795- 786598415235- 59+1132824486112502602702 80,290- 767580397218- 42+ 130299465627- 359 -333104 79+142 +167382 405614 637- 748561378200- 25+ 14731648 1643+803200 - 785 - 753210 474 444220 177 148230 +lo7 +134240 379 405250 +641 +667-721 - 690 -658 -627 - 596414 384 354 324 295119 91 62 34 5+162 +189 +217 +244 +271432 458 484 511 537+693 +718 +744 +769 +795- 5652652985 63+820+ 23- 535 - 504235 206325 352589 615+845 +a70+ 51 + 79400410420430440- 182 7- 165+ 10181349514- 147+ 27198365530- 129+ 45215382546- 77+ 96265+ 164332498432595+755450 I +659 I +675 I +691 I +707$771 1 +787I , , ,579373173 I 153 I 133350 I -114 I - 94 I - 74 I - 55 I - 35365 383' 549 I 567729 747I I I ,s=9km-713-689 . -666455 1 432227 205- 642409182+ 38253463667867270 - 858 - 833 - 809 - 785280 1 618 1 595 ~ 571 1 548290 386 363 340 318. ~.478250- 27+ 189400606807- 5 +17t210 1 23242 1 442627 647827 I 847z = 10 km- 838568- 307 55+191429660-811542- 282 30+215452682- 783516-256 5+239475705- 756489-231+ 20263499728- 729463- 205+ 45287522750- 648385- 130+11835859 181832 JOURNAL OF METEOROLOGYTABLE 3c (cont.)170180190z = 12 km.- 822458112- _"150160170180- 78542279___62 1 579 537 49 5 454 413 372 331 290 250209 170 130 91 52+ 178 + 215 + 252 + 289 + 326 + 363 399 435 47 1 507542 578 613 648 683 718 752 786 820 85413 + 25 + 64 4- 102 + 140+247556- 992 - 940 16 + 29486 437+ 421 463- 74838745- 388 - 836 - 785 - 734 - 683 -- 633 - 584+ 74 + 118 + 162 + 206 + 250 4- 293 + 336389 341 294 247 200 153 107505 546 587 628 669 710 750+279586120130140150-711- 1045 535 61+ 379z = 13 km-1021 429+ 112 611- 601248+ 86+404705- 959 - 898 - 837 - 777 -- 718 - 659373 318 262 207 153 99+ 164 + 215 + 266 + 317 4- 367 + 416659 706 753 800 847 893- 565214+119100110120130+435735-1209 -1146 600 543 45 + 8+ 465 514- 529180+151$46576590 - 881 - 810 - 741 - 672 - 603100 209 146 83 21 + 41110 + 400 + 457 4- 514 + 571 62 7- 493146+ 183- 536 - 469 - 403 -- 338 - 273+ 102 + 163 + 223 + 282 + 341682 738 793 847 90 1+49679470 -1485 -1394 -1305 -121780 634 554 476 39990 + 119 + 190 + 259 + 328imI -inhi I -io16 I - 971 I - 926 I - 882 I - 838 I - 794 I - 750 I -- 707 I - 664-1130 -1044 - 960 - 876 -- 794 - 714322 247 172 98 25 + 48+ 397 + 464 + 531 + 597 f- 662 72760 -1469 -1363 -1259 -1157 -1057 - 958 4470 485 394 305 217 13080 + 366 + 446 + 524 + 601 + 678 + 753- 860 - 764 -. 670 - 577 + 124 + 206 + 286+ 8;: 902 975 1048z = 14 km50 -1632 -1506 -1382 -1260 -1141 -1024 469 363 259 157 57 + 4270 + 515 + 606 + 695 + 783 + 870 95660- 909 - 796 -- 685 - 576+ 140 + 236 +- 330 + 4231040 1124 1206 128640 -2056 -1899 -1745 -1595 -1448 -1305 -1164 -1027 -- 89350 632 506 382 2 60 141 21 + 91 + 204 4- 31560 + 531 + 637 + 741 + 843 + 943 +lo42 1140 * 1236 1330- 1083 486+ 60 563- 761+ 4241423z = 15 kmJOHN C. BELLAMY600700800900330.9 1 :o1.1 1.11.3 1.31.4 1.4- 30002000 1000+o 1000 2000 3000 4000+ 5000 6000 7000 8000 9000+ 1000011000120001300014000+ 1500016000170001800019000+2000021000220002300024000+2500026000270002800029000+3000031000320003300034000+35000235332 TABLE 4Relation between S and T (in degrees centigrate) for Various Pressure Altitudes in Feet-0.20-37.839.441.0-42.644.245.847.348.9- 50.552.153.755.356.9- 58.460.061.663.264.8- 66.468.069.571.172.7- 74.375.977.579.180.7-82.283.885.487.088.6-90.191.793.394.996.5-98.1-98.6-0.19- 34.936.538.1-39.741.342.944.546.1-47.749.350.952.654.2-55.857.459.060.662.2-63.865.467.068.670.2-71.873.475.076.678.2- 79.881.483.084.786.3-87.989.591.192.794.3-95.9-96.4100 0.2200 1 3:; 1 0.3300 0.5 0.6 I 0.6400 500 I 0.8 0.8-0.18-32.033.635.2-36.838.540.141.743.3-45.046.648.249.851.5-53.154.756.358.059.6-61.262.864.566.167.771.072.674.275.8- 77.579.180.782.384.0- 69.3-85.687.288.890.592.1-93.7-94.20.20.30.50.60.81 .o1.11.31.5-0.17- 29.030.732.3- 34.035.637.238.940.5-42.243.845.547. f48.7- 50.452.053.755.357.0- 58.660.361.963.565.2- 66.868.5.70.171.873.4- 75.176.778.380.081.6-83.384.986.688.289.9-91.5-92.1-0.16-26.127.729.4-31.132.734.436.137.7- 39.441.142.744.446.0-47.749.451.052.754.4- 56.057.759.461.062.7- 64.466.067.769.371.0-72.774.376.077.779.3-81.082.784.386.087.6-89.3- 89.9Interpolations0.20.30.50.70.81 .o1.11.31.5-0.15-23.124.826.5-28.229.931.633.234.9-36.638.340.041.743.3-45.046.748.450.151.8-53.555.156.858.560.2-61.963.665.266.968.6- 70.372.073.775.377.0-78.780.482.183.885.4-87.1-87.7-0.14- 20.221.923.6-25.327.028.730.432.1-33.835.537.238.940.6-42.444.145.847.549.2- 50.952.654.356.057.7- 59.461.162.864.566.2-67.969.671.373.074.7- 76.478.179.881.583.2-84.9- 85.5-0.13- 17.319.020.7-22.424.225.927.629.3-31.132.834.536.237.9-39.741.443.144.846.6-48.350.051.753.555.2-56.958.660.462.163.8-65.567.269.070.772.4-74.175.977.679.381.0-82.8-83.30.20.30.50.70.81 .o1.21.31.50.20.30.50.70.81 .o1.21.31.50.20.30.50.70.91 .o1.21.41.50.20.30150.70.9~ ..1 .o1.21.41.5-0.12- 14.316.117.8- 19.621.323.024.826.5-28.330.031.833.535.2-37.038.740.542.244.0-45.747.449.250.952.7- 54.456.257.959.761.4-63.164.966.668.470.1-71.973.675.377.178.8-80.6-81.20.20.30.50.70.91 .o1.21.41.6-0.11-11.413.114.9- 16.718.420.222.023.7-25.527.329.030.832.5-34.336.137.839.641.4-43.144.946.748.450.2-51.953.755.557.259.0- 60.862.564.366.067.8-69.671.373.174.976.6- 78.4- 79.00.20.40.50.70.91.11.21.41.634JOURNAL OF METEOROLOGYTABLE 4 (cont.)-0.10- 0.09- 0.08- 0.07.- 0.06-0.05- 0.02-+ 15.113.111.2+ 9.27.3 5.3 3.4 1.5- 0.52.44.3 6.3 8.2- 10.212.114.116.017.9- 19.921.823.825.727.6- 29.631.533.535.437.4- 39.341.243.245.147.1- 49.050.952.954.856.8- 58.7- 59.4-0.01- 0.04+ 9.27.3 5.4+ 3.5 1.6- 0.3 2.24.1- 6.07.99.811.713.6- 15.517.419.321.223.1-25.026.928.830.732.6-34.636.538.440.342.2- 44.146.047.949.851.7- 53.655.557.459.361.2-63.1-63.7- 0.03+12.110.2 8.3+ 6.4 4.4 2.50.6- 1.3- 3.25.27.19.010.9- 12.814.81.6.718.620.5-22.524.426.328.230.1-32.134.035.937.839.8-41.743.645.547.449.4-51.353.255.157.159.0- 60.9-61.5- 300020001000+o 1000 2000 30004000+ 5000 60007000 8000 9000+ 10000110001200013000' 14000+ 1500016000170001800019000+2000021000220002300024000+2500026000270002800029000+3000031000320003300034000+35000235332- 8.4'10.2:12.0- YL3.8:l5.6:l7.4l9.120.9-22.724.526.328.129.8-31.633.435.237.038.8-40.542.344.145.947.7-49.551.253.054.856.6- 58.460.261.963.765.5-67.369.170.972.674.4- 76.2- 76.8- 5.57.39.1- 10.9,12.714.516.318.1- 19.921.723.525.327.1-28.930.732.534.436.2-38.039.841.643.445.2-47.048.850.652.454.2- 56.057.859.661.463.2- 65.066.868.670.472.2- 74.0- 74.6- 2.64.46.2- 8.0 9.911.713.515.3-17.119.020.822.624.4-26.328.129.931.733.6-35.437.239.040.842.7-44.546.348.150.051.8- 53.655.457.259.160.9-62.764.566.468.270.0-71.8- 72.4+ 0.4- 1.5 3.3- 5.27 .O8.810.712.5- 14.416.218.119.921.7- 23.625.427.329.131.0-32.834.636.538.340.2-42.043.845.747.549.4-51.253.1* 54.956.758.6- 60.462.364.166.067.8-69.6- 70.3+ 3.3 1.4- 0.4- 2.3 4.16.0. 7.99.7-11.613.415.317.219.0- 20.922.824.626.528.3- 30.232.133.935.837.7-39.541.443.245.147.0-48.850.752.654.456.3-58.160.061.963.765.6-67.5-68.1+ 6.2 4.42.5+ 0.6- 1.3 3.2 506.9- 8.810.712.614.516.3- 18.220.122.023.925.7-27.629.531.433.335.2-37.038.940.842.744.6-46.548.350.252.154.0- 55.957.759.661.563.4- 65.3-65.9+ 18.016.0'14.1+12.110.1 8.2. 6.24.3+ 2.3 0.3- 1.6 3.6 5.5- 7.59.511.413.415.3- 17.319.321.223.225.1-27.129.131.033.034.9-36.938.940.842.844.7-46.748.750.652.654.6-56.5-57.2Interpolations1002003004005006007008009000.20.40.50.70.91.11.21.41.60.20.40.50.70.91.11.31.41.60.20.40.50.70.91.11.31.51.60.20.40.60.70.91.11.31.51.70.20.40.60.20.40.60.20.40.60.20.40.60.20.40.60.20.40.60.81 .o1.21.41.61.8JOHN C. BELLAMY+0.0335+O.lO+0.0421.619.617.515.524.522.420.3- 18.3+ 3.2 1.2- 0.84.92.9- 7.09.011.0+ 5.9 3.8 1.82.3- 0.3- 4.46.48.5-17.219.221.223.325.3-27.429.431.433.535.5-14.716.718.820.922.9-25.027.029.131.233.2-37.639.641.743.745.7-35.337.439.441.543.5-47.8-48.5-45.6-46.30.20.40.60.81 .o1.21.50.20.40.60.81 .o1.31.50.20.40.60.91.11.31.51.71.90.20.40.60.91.11.31.51.71.9TABLE 4 (cont.)0.00+0.01t-0.02+0.05+0.06+0.07+0.08t0.09\+20.919.017.0+15.013.011.0 9.0 7.1+ 5.1 3.1 1.1- 0.8 2.8- 4.86.88.810.712.7- 14.716.718.720.722.6-24.626.628.630.632.5-34.536.538.540.542.4-44.446.448.450.452.4- 54.3- 55.0+23.921.919.9+17.915.913.911.9 9.9+ 7.9 5.9 3.9 1.9- 0.1- 2.14.1 6.1 8.110.1- 12.114.116.118.120.1-22.124.126.128.130.1-32.134.136.138.140.1-42.144.246.248.250.2-52.2-52.8+26.824.822.8+20.818.716.714.712.7+10.7 8.6 6.6 4.6 2.6+ 0.6- 1.5 3.5 5.57.5- 9.511.613.615.617.6- 19.621.723.725.727.7-29.831.833.835.837.8-39.941.943.945.947.9- 50.0- 50.6+35.633.631.5f29.427.325.223.221.1+ 19.016.914.812.810.7+ 8.66.5 4.42.40.3- 1.8 3.9 6.08.010.1- 12.214.316.418.420.5-22.624.726.828.830.9-33.035.137.239.241.3-43.4- 44.1+38.636.534.4+32.330.228.126.023.9+21.819.717.615.513.4+11.39.27.1 5.0 2.9+ 0.8- 1.3 3.45.57.6- 9.711.813.916.018.1- 20.222.324.426.528.6-30.732.834.937.039.1-41.2-41.9+41.539.43.7.3+35.233.030.928.826.7+24.622.420.318.216.1+ 14.011.89.77.6 5.5+ 3.4 1.2- 0.93.0 5.1- 7.29.411.513.615.7- 17.820.022.124.226.3- 28.430.632.734.836.9-39.0-39.7+44.542.340.2$38.035.933.831.629.5+27.325.223.120.918.8+ 16.614.512.410.2 8.1+ 5.9 3.8 1.7- 0.5 2.6- 4.86.99.011.213.3- 15.517.619.721.924.0-26.228.330.432.634.7- 36.8-37.6+47.445.243.1+40.938.836.634.432.3+30.128.025.823.721.5+ 19.317.215.012.910.7+ 8.5 6.4 4.2 2.1- 0.1- 2.24.4 6.68.710.9- 13.015.217.419.521.7-23.826.028.230.332.5-34.7-35.4+50.348.246.0+43.841.639.437.335.1+32.930.728.526.424.2+22.019.817.615.513.3+11.1 8.96.74.62.4+ 0.2- 2.04.1 6.3 8.5- 10.712.915.017.219.4-21.623.825.928.130.3-32.5-33.2- 3000 2000 1000+o 1000 2000 3000 4000+ 5000 6000 7000 8000 9000+ 1000011000120001300014000+ 1500016000170001800019000+2000021000220002300024000+2500026000270002800029000+3000031000320003300034000+3500023533227.725.1+23.6 1 t26.5+13.4 I +16.211.4 14.2 12.15.3 8.013.1 10.615.1 I 12.6Interpolations0.20.40.60.81 .o1.21.41.61.80.20.40.60.81 .o1.21.41.61.80.20.40.60.81 .o1.21.41.61.80.20.40.60.81 .o1.21.41.61.90.20.20.40.70.91.11.31.51.72.01002003004005006007008009000.20.40.60.81 .o1.21.41.61.81.11.31.536JOURNAL OF METEOROLOGY\- 1000 900 800 700 600- 500 400 300 200 100+o 100 200 300 400+ .so0 600 700 800 900+ 1000 1100 1200 1300 1400+ 1500 1600 1700 1800 1900+ 2000 2100 2200 2300 2400+ 2500 26002700 2800 2900+ 3000 3100 3200 3300 3400+ 350036003700 3800 3900+ 4000 41004200'4300 4400+ 45004600 4700 4800 4900 TABLE 5Relation between S and T (in Degrees Centigrade) for Various Pressure Altitudes in Meters-- 0.20---37.437.938.439.039.5--40.040.541.041.642.1--42.643.143.644.244.7-45.245.746.246.847.3-47.8' 48.348.849.449.9- 50.450.951.452.052.5-53.053.554.054.655.1-- 55.656.156.657.257.7--58.258.759.259.860.3-- 60.861.361.862.462.9-- 63.463.964.465.065.5-- 66.066.567.067.668.1-0.19-34.4 .35.035.536.036.6-37.137.638.138.739.2-39.740.240.841.341.8-42.342.943.443.944.4-45.045.546.046.547.1-47.648.148.749.249.7- 50.250.851.351.852.3- 52.953.453.954.555.0- 55.556.056.557.157.6-58.158.759.259.760.2- 60.861.361.862.462.9-63.463.964.565.065.5-0.18-31.532.032.633.133.6-34.234.735.235.836.3-36.837.437.938.439.0-39.540.040.641.141.6-42.242.743.243.844.3-44.845.445.946.447.0 -47.548.048.649.149.6- 50.250.751.251.852.3-52.853.453.954.455.0- 55.556.056.657.157.6-58.258.759.259.860.3- 60.861.461.962.463 .O-0.17-28.629.129.630.230.7-31.331.832.332.933.4-34934.535.035.636.1-36.637.237.738.338.8-39.339.940.441.041.5-42.042.643.143.744.2-44.745.345!846.446.9-47.448.048.549.149.6-50.150.751.251.852.3-52.853.453.954.555.0-55.556.156.657.157.7-58.258.859.359.860.4-0.16-25.626.226.727.227.8-28.328.929.430.030.5-31.131.632.232.733.3-33.834.334.935.436.0-36.537.137.638.238.7-39.339.840.440.941.4-42.042.543.143.644.2-44.745.345.846.446.9-47.548.048.549.149.6- 50.250.751.351.852.4- 52.953.554.054.555.1- 55.656.256.757.357.8-0.15-22.723.223.824.324.9-25.426.026.527.127.6-28.228.729.329.830.4-31.031.532.132.633.2-33.734.334.835.435.9-36.537.037.638.138.7-39.239.840.340.941.5-42.042.643.143.744.2-44.845.345.946.447.0-47.548.148.649.249.7- 50.350.851.451.952.5-53.153.654.254.755.3-0.14- 19.720.320.821.422.0-22.523.123.624.224.8- 25.3.25.926.427.027.628.729.229.830.4-28.1-30.931.532 .O32.633.1-33.734.334.835.435.9-36.537.137.638.238.7-39.339.940.441.041.5-42.142.643.243.844.3-44.945.446.046.647.1-47.748.248.849.449.9-50.551.051.652.252.7 ,-0.13- 16.817.317.918.519.0- 19.620.220.721.321.9-22.423.023.624,l24.7- 25.325.826.427.027.528.729.229.830.4-28.1- 30.931.532.132.6-33.2-33.734.334.935.436.0-36.637.137.738.338.8- 39.440.040.541.141.7- 42.242.843.443.944.5-45.145.646.246.747.3-47.948.449.049.650.1-0.12.- 13.814.415.015.516.1- 16.717.317.818.4. 19.0- 19.620.120.721.321.8-22.423.023.624.124.7-25.325.826.427.027.6-28.128.729.329.930.4-31.031.632.132.733.3-33.934.435.035.636.1-36.737.337.938.439.0-39.640.140.741.341.9- 42.443.043.644.244.7-45.345.946.447.047.6~.-.-0.11- 10.911.512.012.613.2- 13.814.414.915.516.1-16.717.317.818.419.0- 19.620.120.721.321.9-22.523.023.624.224.8-25.325.926.527.127.7- 28.228.829.430.030.6-31.131.732.332.933.4-34.034.635.235.836.3-36.937.538.138.739.2- 39.840.441.041.542.1-42.743.343.944.445.0+ 5000 5100.5200 5300 5400+ 5500 5600 5700 5800 5900+ 6000 6100 6200 6300 6400+ 6500 6600 6700 6800 6900+: 7000 7100 7200 7300 7400f 750076007700 7800 7900f 8000 8100 8200 8300 8400+ 8500 8600 8700 8800 8900+ 9000 9100 9200 9300 9400+ 9500 9600 9700 9800 9900+ 1000010100102001030010400+ 105001060010700210769-0.20- 68.669.169.670.270.7-71.271.772.272.8.73.3-73.874.374.875.475.9- 76.476.977.478.078.5- 79.079.580.080.681.1-81.682.182.683.283.7-84.284.785.285.886.3- 86.887.387.888.488.9- 89.489.990.491.091.5-92.092.593.093.694.1-94.695.195.696.296.7-97.297.798.2-98.6~-0.19- 66.066.667.167.668.1- 68.769.269.770.370.8-71.371.872.3 .72.973.4- 73.974.475.075.576.0- 76.677.177.678.178.7- 79.2i19.780.380.881.3-81.882.482.983.483.9-84.585.085.586.086.6-87.187.688.288.789.2- 89.790.390.891.391.8-92.492.993.493.994.5-95.095.596.0-96.4-0.18-63.564.064.565.165.6-66.166.767.267.768.3- 68.869.369.970.470.9-71.572.072.673.173.6- 74.174.775.275.776.3- 76.877.377.978.478.9- 79.580.080.581.181.6-82.182.783.283.884.3- 84.885.385.986.486.9-87.588.088.589.189.6-90.190.791.291.792.3-92.893.393.9-94.2JOHN C. BELLAMYTABLE 5 (cont.)-0.17- 60.961.562.062.563.1-63.664.264.765.265.8- 66.366.967.467.968.5-69.069.670.170.671.2-71.772.372.873.373.9- 74.475.075.576.076.6-77.177.678.278.779.3- 79.8'80.380.981.482.0-82.583.083.684.184.7-85.285.786.386.887.4-87.988.489.089.590.1- 90.691.191.7-92.1-0.16-58.458.959.560.060.6-61.161.662.262.763.3- 63.864.464.965.566.0-66.667.167.768.268.7-69.369.870.470.971.5-72.072.673.173.774.2-74.875.375.876.476.9-77.578.078.679.179.7- 80.280.881.381.882.4- 82.983.584.084.685.1-85.786.286.887.387.9-88.488.989.5- 89.9-0.15-55.856.456.957.558.0- 58.659.159.760.260.8-61.361.962.463.063.6-64.164.765.265.866.3- 66.967.468.068.569.1-69.670.270.771.371.8-72.472.973.574.174.6-75.275.776.376.877.4-77.978.579.079.680.1-80.781.281.882.382.9- 83.484.084.585.185.7-86.286.887.3-87.7-0.14- 53.353.854.454.955.5-56.156.657.257.758.3- 58.959.460060.561.1-61.762.262.863.363.9- 64.465.065.666.166.7-67.267.868.468.969.5- 70.070.671.271.772.3- 72.873.474.074.575.1- 75.676.276.777.377.9- 78.479.079.580.180.7-81.281.882.382.983.5- 84.084.685.1-85.5-0.13- 50.751.351.852.453.0- 53.554.154.755.255.8-56.456.957.558.158.6-59.259.860.360.961.5-62.062.663.163.764.3- 64.865.466.066.567.1-67.768.268.869.469.9- 70.571.171.672.272.8- 73.373.974.575.075.6-76.276.777.377.978.4- 79.079.580.180.781.2-81.882.482.9-83.3-0.12-48.248.749.349.950.4-51.051.652.252.753.3- 53.954.455.055.656.2-56.757.357.958.559.0- 59.660.260.761.361.9-62.563.063.664.264.7-65.365.966.567.067.6- 68.268.769.369.960.5-71.071.672.272.873.3- 73.974.575.075.676.2- 76.877.377.978.579.0- 79.680.280.8-81.237-0.11-45.646.246.847.347.9-48.549.149.650.250.8-51.452.052.553.153.7- 54.354.955.456.056.6-57.257.758.358.959.5-60.160.661.261.862.4- 63.063.564.164.765.3-65.866.467.067.668.2- 68.769.369.970.571.1-71.672.272.873.473.9-74.575.175.776.376.9- 77.478.078.6- 79.038JOURNAL OF METEOROLOGYTABLE 5 (cont.)- 1000 900 800 700 600- 500 400 300 200 100+ 100"200300400+ 500 600 700 800 900+ 1000 1100 1200 1300 1400+ 1500 16001700 1800 1900+ 20002100220023002400+ 250026002 700 28002900+ 300031003200 33003400+ 35003600370038003900+ 40004100420043004400+ 45004600470048004900-.0.10- 7.98.59.19.710.3- 10.911.512.012.613.2- 13.814.415.015.616.1- 16.717.317.918.519.1- 19.620.220.821.422.0- 22.623.223.7' 24.324.9-25.526.126.727.227.8-28.429.029.630.230.8-31.331.932.533.133.7- 34.334.935.436.036.6-37.237.838.438.939.5-40.14:1.340.74:1.94,2.5- 0.09- 5.05.66.26.87.4- 8.08.59.19.710.3- 10.911.512.112.713.3- 13.914.515.616.2- 16.817.418.018.619.2, 15.1- 19.820.421.021.622.2-22.723.323.924.525.1-25.726.326.927.528.1- 28.729.229.830.431.0-31.632.232.833.434.0- 34.635.235.836.337.0-37.538.138.739.340.0-0.08- 2.12.73.33.84.4- 5.05.6 6.26.87.4- 8.08.69.29.810.4-11.011.612.212.813.4- 14.014.615.215.816.4- 17.017.618.218.819.4- 20.020.621.221.822.4-23.023.624.224.825.4-26.0 '26.627.227.828.4-29.029.630.230.831.4-32.032.633.233.734.3-35.035.536.136.737.3~- 0.07+ 0.90.3- 0.30.91.5- 2.12.73.33.94.5- 5.25.8 6.47.07.6- 8.28.8 9.410.010.6-11.211.812.413.013.6- 14.214.815.416.016.6- 17.217.818.519.119.7- 20.320.921.522.122.7-23.223.924.525.125.7 '-26.326.927.528.128.7-29.329.930.531.131.8-32.433.033.634.234.8-0.06+ 3.8 3.22.62.0 1.4+ 0.8 0.2- 0.4 1.1 1.7- 2.32.93.54.14.7- 5.35.9 6.6. 7.27.8- 8.49.09.610.210.8-11.412.112.713.313.9- 14.515.115.716.417.0- 17.718.318.919.520.1- 20.621.221.822.423.0-23.724.324.925.526.1-26.727.327.928.529.2- 29.830.431.031.632.2-0.05+ 6.8 6.15.54.94.3+ 3.7 3.1 2.4 1.8 1.2+ 0.6- 0.0 0.6 1.3 1.9- 2.5 3.13.7 4.35.0- 5.66.26.87.48.0- 8.6 9.39.910.511.1-11.712.413.013.614.2- 14.815.416.116.717.3- 17.918.519.219.820.4-21.021.622.222.823.5- 24.124.725.325.926.6-27.227.828.429.029.6- 0.04+ 9.79.18.57.87.2+ 6.6 6.05.34.74.1+ 3.5 2.82.2 1.6 1 .o+ 0.4- 0.30.9 1.5 2.1- 2.83.44.04.65.2- 5.96.57.17.78.4- 9.09.610.210.911.5-12.112.713.414.014.6- 15.215.916.517.117.7- 18.419.019.620.220.8-21.522.122.723.324.0-24.625.225.826.527.1 '-0.03+12.712.011.410.810.1+ 9.5 8.9 8.27.67.0+ 6.45.7 5.14.53.8+ 3.2 2.6 1.9 1.30.7+ 0.0- 0.6 1.2 1.82.5- 3.13.74.35.05.6- 6.26.97.58.18.8- 9.410.010.611.311.9- 12.513.213.814.415.1- 15.716.317.017.618.2- 18.9 e19.520.120.721.4-22.022.623.323.924.5--0.024-15.615.014.313.713.14-12.411.811.210.59.91- 9.2 8.68.07.36.7+ 6.1 5.44.8 4.13.5-I- 2.92.2 1.6 1 .o0.3-- 0.30.91.62.22.9-- 3.54.14.85.46.0-. 6.77.37.98.69.29.90.51.11.82.43.03.74.315.015.6-. 16.216.917.518.118.8-. 19.420.020.721.322.0-0.01+ 18.517.917.316.616.0+15.314.714.013.412.8+12.111.510.810.29.5+ 8.9 8.3 7.6 7.0 6.3+ 5.7 5.04.43.73.1+ 2.5 1.8 1.2 0.5- 0.1- 0.7 1.42.02.73.3- 4.0 4.6 5.2 5.96.5- 7.27.88.5 9.19.8- 10.411.0 11.712.313.0- 13.614.314.915.516.2- 16.817.518.118.819.4JOHN C. BELLAMYTABLE 5 (cont.)\s \\ZP \+ 5000 5100 5200 5300 5400+ 5500 5600 57005800 5900+ 6000 6100 6200 6300 6400+ 6500 6600 6700 6800 6900+ 7000 7100 7200 7300 7400+ 75007600 77007800 7900+ 8000 8100 8200 8300 8400+ 8500 8600 8700 8800 8900+ 9000 9100 9200 9300 9400+ 9500 9600 9700 9800 9900+ 1000010100102001030010400+ 105001060010700210769-0.10-43.043.644.244.845.4-46.046.647.147.748.3-48.949.550.150.651.2-51.852.453.053.654.2- 54.7'55.355.956.557.1-57.758.358.859.460.0- 60.661.261.862.362.9-63.564.164.765.365.9- 66.467.067.668.268.8-69.470.070.571.171.7- 72.372.973.574.074.6-75.275.876.4- 76.8-0.09-40.541.141.742.342.9-43.444.044.645.245.8-46.447.047.648.248.8-49.450.050.551.151.7- 52.352.953.554.154.7-55.355.956.557.157.6- 58.258.859.460.060.6- 61.261.862.463 .O63.6- 64.164.765.365.966.5-67.167.768.368.969.5- 70.1 70.7. 71.2 71.8 72.4- 73.073.674.2- 74.6- 0.08-37.938.539.139.740.3-40.941.542.142.743.3- 43.944.545.145.746.3- 46.947.548.148.749.3- 49.950.551.151.752.3-52.953.554.154.755.3- 55.956.557.157.758.3- 58.959.560.160.761.3-61.962.563.163.664.2- 64.865.466.066.667.2- 67.868.469.069.670.2- 70.871.472.0-72.4- 0.07-35.436.036.637.237.8-38.439.039.640.240.8-41.442.042.6&3.243.8-44.445.145.746.346.9-47.548.148.749.349.9- 50.551.151.752.352.9- 53.554.154.755.355.9- 56.557.157.758.459.0-59.660.260.861.462.0-62.663.263.864.465.0-65.666.266.867.468.0- 68.669.269.8- 70.3- 0.06-32.833.4. 34.034.735.3-35.936.537.137.738.3-38.939.540.240.841.4-42.042.643.243.844.4-45.045.746.346.947.5-48.148.749.349.950.5-51.251.852.453.053.6- 54.254.855.456.056.7-57.357.958.559.159.7-60.360.961.562.262.8-63.464.064.665.265.8- 66.467.067.7-68.1- 0.05- 30.330.931.532.232.7-33.334.034.635.235.8-36.437.137.738.338.9-39.540.140.841.442.0-42.643.243.944.545.1-45.746.346.947.548.2-48.849.450.050.651.3-51.952.553.1.53.754.3- 55.055.656.256.857.4-58.058.759.359.960.5-61.161.862.463.063.6- 64.264.865.5-65.9- 0.04-27.728.329.029.630.2- 30.831.532.132.733.3- 34.034.635.235.836.4-37.137.738.339.039.6-40.240.841.442.142.7-43.343.944.645.245.8-46.447.147.748.348.9-49.650.250.851.452.0-52.753.353.954.555.2- 55.856.457.057.758.3- 58.959.560.260.861.4-62.062.763.3-63.7- 0.03-25.225.826.427.127.7-28.328.929.630.230.8-31.532.132.733.434.0- 34.635.235.936.537.1-37.838.439.039.740.3-40.941.642.242.843.4-44.144.745.346.046.6-47.247.948.549.149.7- 50.451.051.652.352.9- 53.554.254.855.456.1- 56.757.357.958.659.2- 59.860.561.1-61.5-0.02-22.623.223.924.525.1-25.826.427.127.728.3- 29.029.630.330.931.5-32.232.833.434.134.7-35.336.036.637.337.9-38.539.239.840.441.1-41.742.443.043.644.3-44.945.546.246.847.4-48.148.749.450.050.6-51.351.952.553.253.8- 54.555.155.756.457.0-57.658.358.9- 59.439- 0.01-20.120.721.322.022.6-23.323.924.625.225.8- 26.527.127.828.429.1- 29.730.331.031.632.3-32.933.634.234.935.5-36.136.837.438.138.7- 39.440.040.641.341.9-42.643.243.944.545.1-45.846.447.147.748.4- 49.049.750.350.951.6- 52.252.953.554.254.8- 55.456.156.7- 57.240JOURNAL OF METEOROLOGYTABLE 5 (cont.)- 1000 900 800 700 ,600- 500 400 300 200 100+ lox2 00300400+ 500 600 700 800 900+ 1000 1100 1200 1300 1400+ 1500 1600 1700 1800 1900+ 2000 2100 2200 2300 2400+ 2500 26002700 , 2800 2900+ 3000 3100 3200 3300 3400+ 35003600370038003900+ 40004100 4200 43004400+ 4500460047004800 49000.00+2 1.520.820.210.5113.9+ 18.21'7.616.916.315.6+lS.O14.313.713.012.4+11.711.110.4 9.8 9.1+ 8.57.8 7.26.5 5.9+ 5.2 4.6 3.9 3.3 ;!.6+ 2.0 1.30.70.0- 0.6- 1.2 1.9 2.5 3.2 3.8- 4.5 5.1 5.8 6.47.1- 7.7 EL4 9.09.710.3-11.011.612.312.913.5- 14.114.815.416.116.7+O.Ol$24.423.823.122.521.8+21.220.519.819.218.5+17.917.216.615.915.2+ 14.613.913.312.612.0+11.310.610.09.38.7+ 8:O 7.46.76.1 5.4+ 4.74.1 3.42.8 2.1+ 1.50.8 0.1- 0.5 1.2- 1.82.53.1 3.84.4- 5.15.8 6.47.17.7- 8.49.09.710.311.0-11.7'12.313.013.614.3f0.02+27.426.726.125.424.7+24.123.422.722.121.4+20.820.119.418.818.1+17.416.816.115.614.8+14.113.512.812.111.5+ 10.810.19.58.88.2+ 7.56.86.25.54.8+ 4.2 3.5 2.9 2.2 1.5+ 0.9 0.2- 0.5 1.1 1.8- 2.43.13.84.45.1- 5.86.47.17.78.4- 9.19.7. 10.411.111.7+0.03+30.329.729.028.327.6+27.026.325.625.024.3+23.623.022.321.621.0+20.319.619.018.317.6+16.916.315.614.914.3+13.612.912.211.610.9+ 10.29.6 8.98.27.6+ 6.9 6.2 5.6 4.9 4.23.52.92.21.50.9+ 0.2- 0.5 1.1 1.8 2.5- 3.13.84.5 5.1 5.8- 6.57.27.88.59.2+0.04+33.332.631.931.230.6+29.929.228.527.927.2f26.525.825.224.523.8+23.122.521.821.120.4+19.819.118.417.717.0+16.415.715.014.313.7i13.012.311.611.010.3+ 9.6 8.9 8.3 7.6 6.9+ 6.2 5.6 4.9 4.2 3.5+ 2.9 2.2 1.50.8 0.2- 0.5 1.2 1.9 2.5 3.2- 3.9 4.6 5.25.96.6$0.05+36.235.534.934.233.5+32.832.131.430.830.11-29.429.729.028.327.7+27.026.325.624.923.2+22.621.921.220.519.8+ 19.218.517.817.116.4+15.715.114.413.713.0+12.311.611.010.3 9.6+ 8.9 8.2 7.6 6.9 6.2+ 5.54.84.13.5 2.8+ 2.1 1.40.7 0.0- 0.6- 1.32.02.7 3.44.1+0.06+39.238.537.837.136.4+35.735.034.333.633.0+32.331.630.930.229.5+28.828.127.426.826.1+25.424.724.023.322.6+21.921.220.619.919.2+18.517.817.116.415.7+15.014.413.713.012.3+11.610.910.2 9.5 8.8+ 8.2 7.5 6.86.1 5.4+ 4.74.0 3.3 2.6 2.0+ 1.3 0.6- 0.1 0.8 1.5$0.07+42.141.440.740.039.3+38.637.937.236.535.8+35.234.533.833.132.4+31.731.030.329.628.9+28.227.526.826.125.4+24.724.023.3. 22.621.9+21.220.519.919.218.5+17.817.116.415.715.0+ 14.3 13.6 12.9' 12.211.5+ 10.810.1 9.48.7 8.0+ 7.3 6.6 5.9 5.2 4.5+ 3.9 3.2 2.5 1.8 1.14-0.08+45.144.443.743.042.2$41.540.840.139.438.7+38.037.336.635.935.2+34.533.833.132.431.7+31.030.329.628.928.2+27.526.826.125.424.7+24.023.322.621.921.2+20.519.819.118.417.7+17.016.315.614.914.2+ 13.512.812.111.410.7+10.0 9.3 8.6 7.8 7.1+ 6.45.7 5.04.33.6+0.09-t48.047.346.645.945.2+44.543.743.042.341.6+40.940.239.538.838.1+37.436.736.035.234.5+33.833.132.431.731.0+30.329.628.928.227.5,+26.726.025.324.623.9+23.222.521.821.120.4+19.718.918.217.516.8+16.115.414.714.013.3+12.611.911.210.49.7+ 9.0 8.3 7.6 6.9 6.2+0.10+51.050.249.548.848.1+47.446.745.945.244.5+43.843.142.441.740.9+40.239.538.838.137.4+36.635.935.234.533.8+33.132.431.630.930.2+29.528.828.127.426.6+25.925.224.523.823.1+22.321.620.920.219.5+18.818.117.316.615.9+15.214.513.813.112.3+11.610.910.29.58.8+ 5000 5100 5200 5300 5400+ 5.500 560057005800 5900+ 6000 6100 6200 6300 6400+ 6500 66006700 6800 6900+ 7000 7100 7200 7300 7400+ 7500 7600 7700 7800 7900+ 8000 8100 8200 8300 8400+ 8500 86008700 8800 8900+ 9000 9100 9200 9300 9400+ 9500 96009700 9800 9900+ 1000010100102001030010400+ 1050010600107002107690.00- 17.518.118.819.420.1-20.721.422.022.723.4- 24.024.625.325.926.6-27.227.928.529.229.8-30.531.131.832.433.1-33.734.435.035.736.3-37.037.638.338.939.6-40.240.941.542.242.8-43.544.144.845.446.1-46.747.448.048.749.3- 50.050.651.351.952.6- 53.253.954.5-55.0+O.Ol- 14.915.616.316.917.6- 18.218.919.520.220.8-21.522.222.823.524.1- 24.825.426.126.727.4-28.128.729.430.030.7-31.432.032.733.334.0-34.635.335.936.637.3-37.938.639.239.940.5-41.241.942.543.243.8-44.545.145.846.447.1-47.848.449.149.750.4-51.051.752.4-52.8+0.02- 12.413.013.714.415.0- 15.716.4. 17.017.718.4- 19.019.720.321.021.7-22.323.023.724.325.0-25.626.327.027.628.3- 29.029.630.330.931.6-32.332.933.634.334.9-35.636.336.937.638.2-38.939.640.240.941.6-42.242.943.544.244.9-45.546.246.947.548.2-48.949.550.2-50.6JOHN C. BELLAMYTABLE 5 (cont.)+0.03- 9.810.511.211.812.5- 13.213.914.515.215.9- 16.517.217.918.519.2- 19.920.521;221.922.6- 23.223.924.625.225.9-26.627.227.928.629.3- 29.930.631.331.932.6-33.333.934.635.335.9- 36.637.338.038.639.3-40.040.641.342.042.6-43.344.044.745.346.0- 46.747.348.0-48.5$0.04- 7.3 8.0 8.69.310.0- 10.711.312.012.7.13.4- 14.014.715.416.116.7- 17.418.118.819.420.1- 20.821.522.122.823.5- 24.224.925.526.226.9-27.628.228.929.630.3-30.931.632.333.033.6-34.335.035.736.337.0-37.738.439.039.740.4-41.141.842.443.143.8-44.545.145.8-46.3+0.05- 4.7 5.4 6.1 6.87.5- 8.18.89.510.210.9-11.512.212.913.614.3- 15.015.616.317.017.7- 18.419.119.720.421.1-21.822.523.123.824.5-25.225.926.627.227.9-28.629.330.030.731.3-32.032.733.434.134.8-35.436.136.837.538.2-38.839.540.240.941.6-42.342.943.6-44.1+0.06- 2.2 2.93.5 4.2 4.9- 5.6 6.37.07.78.4- 9.19.710.411.111.8- 12.513.213.914.615.3- 15.9,16.617.318.018.7- 19.420.120.821.522.2-22.823.524.224.925.6-26.327.027.728.429.0-29.730.431.131.832.5-33.233.934.635.235.9- 36.637.338.038.739.4- 40.140.841.4-41.9$0.07+ 0.4- 0.3 1 .o 1.7 2.4- 3.1 3.84.55.2 5.9- 6.67.3 8.08.7 9.4- 10.010.711.412.112.8- 13.514.214.915.616.3- 17.017.718.419.119.8-20.521.221.922.623.3- 24.024.625.326.026.7-27.428.128.829.530.2- 30.931.632.333.033.7- 34.435.135.836.537.2-37.938.639.3- 39.7+0.08+ 2.9 2.2 1.5 0.80.1- 0.6 1.42 .o2.73.4- 4.14.8 5.5 6.2 6.9- 7.6. 8.3 9.0 9.710.4-11.111.812.513.213.9- 14.615.316.016.717.4- 18.118.819.520.220.9-21.622.323.023.724.4-25.125.826.527.227.9-28.629.330.130.831.5-32.232.933.634.335.0-35.736.437.1-37.6+0.09+ 5.5 4.84.1 3.42.7+ 1.9 1.20.5- 0.20.9- 1.6 2.3 3.03.74.4- 5.15.86.57.38.0- 8.7 9.410.110.811.5- 12.212.913.614.315.0- 15.816.517.217.918.6- 19.320.020.721.422.1-22.823.624.325.025.7-26.427.127.828.529.2-29.930.631.332.132.8-33.534.234.9-35.441+050+ 8.07.3 6.6 5.9 5.2+ 4.53.73.0 2.3 1.6+ 0.9 0.2- 0.5 1.2 2.0- 2.73.44.14.85.5- 6.27.07.7 8.4 9.1- 9.810.511.212.012.7- 13.414.114.815.516.3- 17.017.718.419.119.8- 20.521.322.022.723.4-24.124.825.526.327.0-27.728.429.129.830.6-31.332.032.7-33.242JOURNAL OF METEOROLOGY TABLE 6aVirtua! Temperature Corrections:P - Tin degrees centigrade12345678910111213141516171819202122232425262728293031' 323334353637383940---- 2013.20.30.50.60.80.91.11.2I .41.5-00.20.30.50.70.81 .o1.1 .1.31.51.61.82.02.1' 2.32.42.62.72.93.13.23.43.53.73.94.04.24.34.54.74.85 .o5.15.35.45.65.75.96.16.26.4+200.20.30.50.70.91.11.21.41.61.81.92.12.32.42.62.82.93.13.33.53.63.84.04.14.34.54.74.85.05.25.35.55.75.96.06.26.46.56.76.9400.20.40.60.80.91.11.31.51.71.92.12.22.42.6 .2.83.03.13.33.73.94.14.24.44.64.85.05.25.35.55.75.96.16.26.46.66.87.07.27.33.5 .1234567.8910111213141516171819202122232425262728293031323334353637383940which occurs at z = 0 to the value of D, expressed infeet, at z = 0. The specific tables included areTable 2a .=ODft(l=Opin) or Dft(Pin),Table 2b z=ODft(r=Opmm) or Dft(Pmm),Table 2c z=oDft(r=opmb) or Dft(Pmb),Table 2d z=ODm (=p' 0 In ) or Dm(Pin),Table 2e z=oDm(z=opmm) or Dm(Pmm),Table 2f z=oDm(z=opmb) or Dm(Pmb).Tables 3a through 3c-These tables give the pressure conversions from p, in millibars, which occurs atvarious constant elevations above sea level to thevalues of D in feet or meters at those levels. They areconvenient for conversion of past and present radio TABLE 6bVirtual Temperature Anomaly Corrections s* - s-0.100.001.001.002.002.003.003.004.004.005.005- 0.050.001.001.002.002.003.003.004.005.005.006.006.007.007.008.008.009.009.010.011.0110.000.001.001.002.002.003.004.004.005.005.006.007.007.008.008.009.009.010.011.011.012.012.013.014.014.015.015.016.016.017.018.018.019.019.020.02 1.02 1.022.022.023.023+0.050.001.001.002.002.003.004.004.005.006.006.007.007.008.009.009.010.011.011,012.012.013.014.014.015.015.016'.017.017.018.019.019.020.020.02 1.022.022.023.023.024.025-+O.lO0.001.oo 1.002.003.003.004.005.005.006.007.007.008.008.009.010.010.011.012.012.013.014.014.015.016.016.017.017.019.019.020.021.02 1.022.023.023.024.025.025.026.oiasonde reports and climatic summaries such as theU. S. Weather Bureau Form No. 1l09. The specifictables which are included are the conversion to D infeet at z = 5000, 10,000, 15,000 and 20,000 feet andto D in feet and meters at z = 0.5, 1.0, 1.5, 2.0, 2.5,3.0, 4, 5, 6,' 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,19, and 26 km. The specific tables are indicated by anotation similar to that described above. For example,the notation 2=5000 ft D( ft 2=5000 ftpmb) denotes the tableof conversion from p, expressed in millibars, whichoccurs at z = 5000 ft to the value of D, expressed infeet, at z = 5000 ft.Relation between S and T at various ;bressure altitudes.Table 4 gives the value of T, in degrees centigrade,JOHN C.for each value of S which is an integral multiple of0.01 and for each value of zp which is an integralmultiple of 1000 feet. Table 5 is the same as Table 4except that the values of z, used in Table 5 are integralmultiples of 100 meters. Linear interpolation in eitherdirection is possible since the defining equation for Scan be written as T = (1 + S)(To - CYZ,).Tables 4 and 5 have been found to be most usefulfor converting meteorological analyses of temperaturedistribution in terms of the parameter S to the parameter T for dissemination to pilots, etc. This use isdiscussed more fully in the sections on space crosssections and mean temperature charts. Usually theconversion from T to S is most convenient on thermodynamic diagrams upon which lines of constant Shave been entered. Tables 4 and 5 are convenient forplotting these S lines on such thermodynamic diagrams as the adiabatic chart, the tephigram, the Stuvediagram, etc. A special thermodynamic diagram, the"pastagram," which is described in the next section,has been found to be especially convenient for theseconversions.Both of these tables could be used for numericalpressure-height computations, but, since graphicalpressure-height computations are usually more convenient, such numerical computations are not discussed in this article.4. The pastagram. The pastagram is a thermodynamic chart designed to facilitate meteorologicalwork with the parameters zp and D, especially forpressure-height computations. On this chart the ordinate represents the pressure altitude z, on a linearscale, and the abscissa represents the specific temperature anomaly S also on a linear scale. Its use in pressureheight computations is described in the next section.In the standard stratospheric region the standardtemperature T, is defined to be constant, so thatS = (T - Tp)/Tp is a linear function of the temperature T. Also in this region dz, = (RT,/mdg,)d In p sothat, since T, is constant, z, is a logarithmic functionof the pressure p. Hence in the standard stratosphericregion the pastagram is merely an adiabatic diagram(coordinates of lnp and T) with isobars drawn forround values of a constant times the logarithm of p.For all pressures, since$ TdInp =$3dzp=- =$ (1 + S)dz, = - mdgp Jf Sdz,,R Rthe pastagram is a "true" thermodynamic diagram,that is, the heat energy released in any thermodynamiccycle undergone by a parcel of air is proportional tothe area enclosed by a plot of that cyclic process onthe pastagram.BELLAMY 43Charts of various thermodynamic quantities havebeen drawn in such a way as to provide underlays ortransparent overlays to be used in conjunction withbasic pastagrams upon which only z,, Sand sometimesT are entered. This arrangement eliminates the confusion caused by many sets of lines on one diagramand is convenient since it has been found that a greatdeal of useful information can be obtained from plotsof soundings on the basic pastagrams without thenecessity of using overlays or underlays. The underlays are used primarily for plotting soundings on thebasic pastagrams and are most efficient if the basicpastagrams are printed on transparent (tracing) paperalthough a light table can be used for this plotting.Specific transparent overlays are desirable for suchthermodynamic calculations as determining numericalvalues of various thermodynamic quantities such aspotential temperature, equivalent potential temperature, stability studies, cloud analysis, etc. Illustrations of the basic pastagrams and some underlays oroverlays are given in Plates I through VIII. Thetheory of construction of these charts is not givensince the pastagram is essentially just a reorientationof the coordinates which occur on most other thermodynamic diagrams. A description of the plates follows.The description of the soundings shown is given in thediscussion of Plate VI. This is a basic pastagram upon whichsoundings can be plotted with the use of underlays.The 0°C isotherm is entered so that the pressurealtitude of the freezing level is immediately apparentand so that a reference line for the shape of an isothermal lapse rate in the standard troposphere isavailable. The standard tropopause (2, = 35,332.0 ft)is entered since the appearance and interpretation ofsoundings on the pastagram change abruptly at thisline. For example, isotherms above this line arestraight vertical lines. This change of interpretationat the standard tropopause is discussed more fully inconnection with Plate 111.Plate II. This is a basic pastagram like Plate I butis for work in terms of meters instead of feet.Plate III. This is a basic pastagram which is convenient for much routine work, especially pressureheight computations in terms of feet. The conversionscale from millibars to pressure altitude on the leftside has been included as an aid in plotting datawhich are reported in terms of millibars. An underlay,such as described in the discussion of Plate IV, is afurther aid for this conversion when a great deal ofroutine plotting is required.Since there is an abrupt change of the slope of theisotherms at the standard tropopause, simple straightline interpolations of the pressure-temperature relationship between points on opposite sides of thisline cannot be made. A convenient method of interPlate 1.44 JOURNAL OF METEOROLOGYpolating between such points, as A (2, = 33,000 ft,T = - 44°C) and B (2, = 37,000 ft, T = - 52°C)on Plate 111, is demonstrated by the following example.Locate point .A' at the same pressure as point AI (z, = 33,000 ft) and at the value of S (+ 0.05) corresponding to the value of T, in the standard stratosphere, that occurs at point A. Thus point A' can beobtained by following the isotherm through point Ato the standard tropopause, and then vertically downto point A' at the same pressure as point A. Thenpoint C is located at the standard tropopause on thestraight line joining points A` and B, and the brokenline A CB represents the interpolation between pointsA and B. This interpolation process would be eliminated if a mandatory level (such as 400 mb in presentprocedures) were provided at the pressure altitude of35,332 ft (10,769 m).Plate IV. This is a basic pastagram exactly similarto Plate 111 but for work in terms of meters instead offeet.Plate V. This plate is designed primarily as anunderlay for plotting soundings reported in terms ofmillibars on Plate I or 11. A similar plate withoutthe isotherms can be used for plotting such soundingson Plate 111 or 1V. Another similar plate without themillibar lines is convenient for plotting aircraft soundings (or any other soundings with pressures reportedin terms of pressur: altitude) and, as a transparentoverlay, for determining temperatures in "C or "Ffrom such plots as given on Plates I and 11.Plate VI. The values of the potential temperature 8on the dry adiabats, which slope from lower right toupper left, are given in degrees of the absolute scale.A change from the usual quantitative definition ofpotential temperature was made so that the valueof e as given here is the value of the temperature of agiven parcel of air if that parcel were to be moved1 dry adiabatically to the pressure of the zero of thepressure-altitude scale (1013.25 mb) instead of to1000 mb. It is felt that this change is desirable sincethe location of the 1000-mb pressure value is inconvenient if most routine work is done in terms ofpressure altitude. Also, the zero of the pressure-altitude scale, 760 mm or 1013.25 mb, is the standardpressure usually used in physics and chemistry. Therelationship between 0 as used here and 0' (in termsof 1000 mb) is thenIThe following table gives the difference 0 - e' :forvarious values of 8' or e in `A. TABLE 7e` or 81 240 260 280 300 320 340 360 380 400 4:!0 440 460 480 500e - e' 0.9 1.0 1.1 1.1 1.2 1.3 1.4 1.4 1.5 1.6 1.7 1.7 1.8 1.9I__The lines which slope from lower left to upper rightrepresent round values of the mixing ratio w in gramsof water vapor per kilogram of dry air, correspondingto a saturated parcel at the temperature ana pressureof any given point of the pastagram. `The third set oflines are the moist adiabats, drawn for each ten degreesof equivalent potential temperature OF as defined byRossby (4) except that, in harmony with the definitionof 0, the standard pressure for eE is taken to be thezero of the pressure-altitude scale instead of 1000 mb.Plate VI can be used as a transparent, overlay fordetailed thermodynamic calculations, such as determining the values of w, e or eE, stability or energycalculations, etc., with soundings plotted on basicpastagrams.The w and 0 lines have been placed on the samediagram to facilitate plotting the lifting condensationlevels of the points of a sounding, as illustrated bythe plots on Plates I, I1 and IV. It has been foundconvenient to use the following procedure for routineplotting:1. Plot the pressure-temperature relationshipwith Plate V used as an underlay.2. Using Plate VI as an underlay, draw lines (insome distinctive color) from each reported pointof step 1 along the dry adiabats through these pointsto the` corresponding lifting condsensation levels.These condensation levels will then be at the intersections of the dry adiabats and t'he lines for theactual mixing ratios of the points considered.Some of the information which can be obtainedfrom such plots on Plates I, 11, I11 or IV, withoutusing overlays, is:1. A qualitative idea of the relative humidity atany point can be gotten because this quantity isapproximately inversely proportionail to the lengthof the lines along the dry adiabats.2. The stability of the column is indicated sincethe dry adiabatic lapse rate is given by the linesalong the dry adiabats and the moist adiabaticlapse rate can be estimated with a little experiencebecause the moist adiabats tend to be vertical.3. The height of the base of convective clouds isobtained directly from the lifting condensation plot.This height is conveniently expressed in terms of thepressure altitude in conformity with the needs ofaircraft operations.4. The position of the freezing (OT) isotherm,again conveniently given in terms of pressure altitude, is immediately apparent.JOHN' C. BELLAMY 455. Air-mass identification is convenient on apastagram since the vertical (S) lines representtemperature departures from standard (averagemiddle-latitude) conditions and the departures thatoccur in the actual air are clearly represented bythe mean horizontal positions of the soundings.For example, the S = 0 line is a plot of the standard(average middle-latitude) pressure-temperature relationship; the sounding on Plate I, approximatelyalong the S = 0 line, is a typical middle-latitudesounding, slightly on the tropical side ; the soundingon Plate 11, far to the right in the troposphere andto the left in the stratosphere, is a typical mTsounding; the sounding on Plate IV, far to the leftin the troposphere and far to the right in thestratosphere, is a typical GP sounding.6. Since most soundings appear on the averageas approximately vertical lines (except perhaps inthe region of the tropopause), the S lines of thepastagram provide convenient reference lines withwhich changes, in space or time, between soundingsplotted on separate sheets of paper can be easilydetermined. The examples given in the time crosssection of Figure 10 illustrate the ease with whicheven the moderate changes in that sequence areseen.Plate VII. This plate is designed for use as anunderlay or overlay for conversion between the relative humidity h of a given parcel of air and the mixingratio w of that parcel.Using e, as the saturation vapor pressure at a giventemperature and w, as the saturation mixing ratioof a given parcel of air, we can writemwhesmwPw RTpd md(P - he,)w=-=RTandm,w, =md(: - 1)Thus, eliminating the factor @/e8 from these equations,the relationship between the variables w, w8 and hcan be written asThis relationship was then used, with mw/md = 0.622,for plotting the h values corresponding to the variousvalues of w along any given 0 line, since the value ofw, occurring at the intersection of that e line and thezero pressure-altitude line (h = 100 per cent) is determined by the 0 and w coordinates.As an example of the use of this diagram, supposethat it is known that the relative humidity h at somepoint such as point A (this would actually be plottedon the basic pastagram but is shown on Plate VII)is 50 per cent. Then the saturation mixing ratio(w = 10 gm/kg) at that point is given by the.w linethrough it, so that point B on this w line and the zeropressure-altitude line can be determined. Then, following along the e line through point B (287.2'A) topoint C at the 50 per cent h line, the actual mixingratio at point A (5 gm/kg) can be read from the wlines. The lifting condensation level (point E), forthe parcel at point A, can then be determined byfollowing the w line through point C until it intersectsthe 0 line through point A. Similarly, the dew point(point D), for the parcel at point A, can be determinedby following the w line through point C until it intersects the pressure-altitude line (on the basic pastagram) through point A.5. Pressure-height computations.General remarks. An attempt has been made totransform the hydrostatic equation so that routinepressure-height calculations can be made with maximum accuracy in a minimum of time. It is felt thatthis has been accomplished in the transformation ofthe hydrostatic equation intoor, in an integrated form,=Pz=pZD - =plD = lPl S*dz,.(47)In the physical interpretation of this equation, Dis considered as a height parameter which gives theheight of any given pressure surface; z, is the pressureparameter with which the intensity of pressure isspecified; and S* = (T* - Tp)/T, is the temperatureparameter with which the temperature of the air atany given pressure is specified. Thus it has beenassumed that the distribution of temperature as afunction of pressure, not height, has been measuredor estimated so that the conversion from the temperature parameter T in "C to S can be accomplished.This assumption is consistent with present proceduressince all present upper-air soundings, made with radiosondes or airplanes, give the distribution of temperature as a function of pressure, not height. Evenin cases in which the temperature is measured orestimated as a function of height and not pressure, aconvenient procedure is to use successive approximations of the temperature as a function of pressure(starting with z = z,) and the techniques describedhere.46 JOURNAL OF METEOROLOGYDetermination of heights of pressure surfaces fromsoundings. The determination of the heights of anydesired pressure surfaces, in terms of z, and D, fromsoundings which give the temperature as a functionof the pressure can conveniently be accomplished bythe foglowing steps. (This procedure is described interms of using a pastagram, but it applies equally wellto the use of any thermodynamic diagram on whichlines of z, and S are entered.)1. Plot the observed temperature-pressure relationship on Plates I, 11, I11 or IV with an underlayof Plate V if required. This step then effectivelymakes the conversion of the temperature parameterfrom T to S, and the conversion of the pressureparameter from millibars to pressure altitude ifrequired. This work could thus be simplified forfuture radiosonde observations by calibrating thepressure elements and reporting soundings in termsof pressure altitude instead of millibars.2. Plot the virtual temperature-pressure relationship. Since the mixing ratio at each significant levelis usually determined, this can be accomplishedfrom equation (9) or (15).In these equations [ g, - g I is never much greaterthan 2 cm/sec2 so that I (g, - g)/gl is usually lessthan 0.002. Hence the virtual temperature correctiondue to variations of gravity is usually less than0.6"C so that it can be neglected for any but themost accurate work. In any case, for one station thiscorrection sensibly amounts to a shift of the entiretemperature-pressure curve a constant amount(1 + S) [ (gp - g)/g 1 units of S to the right ifg > 980 cm/sec2 and to the left if g < 980 cm/sec2,since for this purpose percentage variations of1 + S and g in the vertical are negligible.Neglecting (or applying separately) the effect of(g, - g)/g and neglecting the last term in thebrackets of equation (9) or (15), which is less than0.002 times the value of (md/mw - l)w/(l + w),the virtual temperature correction can be expressed (with md/mu, = 1.6077) asWT* .- T sz 0.6077T(48)(49)l+wlorWS* - S N 0.6077(1 + S)- .1CWFor very accurate work small cardboard scales forseveral values of (1 + S), giving the correctionS* - S, to be added to S to obtain S* for anygiven value of w can be made. The virtual temperature pressure curve can then be mechanically plottedwith these scales as a function of the mixing ratiosat the significant levels. These corrections, or thecardboard scales, can conveniently be made withthe aid of Table 6b. For most work, however, theapproximation S* - S = 0.6~is sufficiently accurate. Thus the temperaturepressure curve should be shifted to the right approximately 0.006 units of S (&.-tenths of thedistance between S lines on the pastagram) foreach ten grams per kilogram actual mixing ratioto get the virtual temperature-pressure curve.3. Determine the thickness of the layers betweenall desired pressure surfaces using equation (47).The quantity FD - +lD) can be written as(".zD - "p1D) is the actual geometric thickness between these two pressure surfaces, (+% - %z),minus the thickness of the standard atmospherebetween the same two pressure surfaces, (zp2 - z,~).Since z, is used as the pressure parameter, the conversion from (ZPZD - zplD) to pz - IP~Z) can beaccomplished by mentally adding (zPz - z,~) to(ZPzD - "p1D). Thus the actual numerical conversionis seldom required and (Ep2D - '~11)) is used as aparameter with which the thickness of the layer ofair between any two pressure surfaces is described.The value of this thickness anomaly (Ep2D - z~lD)is then determined by the area A,, S dz, enclosedon the pastagram between the horizontal lines forthe two pressures considered, the vertical line forS = 0, and the line representing (the actual distribution of S* (the virtual temperature-pressuresounding) as a function of z,. On pastagrams drawnin terms of feet (Plates I and III), since lines aredrawn for each 1000 feet of z, and each 0.01 of S,the area in each square formed by the zp and S linescorresponds to a thickness anomaly (rpZDft - 'plDft)of 1000 x 0.01 = 10 feet. Similarly on the pastagrams drawn in terms of metes (Plates I1 and IV)the area in each rectangle formed by the z, andS lines corresponds to a thickness anomaly of100 x 0.01 = 1 meter. This thickness anomaly between any two pressures can then be easily determined by counting the rectangles of the z, and Slines enclosed between those pressures, the S = 0line and the virtual temperature sounding.This counting process is many times simplifiedif an average virtual temperature anomaly, 8* isdetermined and used with the equation+zD - 'p1D = S*(Z,~ - ~~1). (51)(50)+zD - '.ID =(Lp2~ - "~12) - (zP2 - ~~1).ThusZZd *E* is then that value of S* such that as much areais included, between zpl and zp2 and the S* sounding,to the right of the 8* line as to the left of the 8*line. This is of the greatest advantage when thethickness between round values of z, is desiredsince then the multiplication process can be autoJOHN C. BELLAMY 47matically accomplished by imagining the S linesto be labeled in terms of (z,~ - z,i)S. For example,if the thickness between each multiple of 5000 feetof z, is desired it can be imagined that the S= +O.Olline is labeled as SOOO(+ 0.01) = + 50 ft, theS = - 0.02 line as - 100 ft, etc. Then the determination of any thickness such as (Zp1+6000ftD - +1D). can be determined by inspection from the s* lineextending vertically from z, to z, f 5000 ft.4. Determine the value of D at one point of thesounding. For radiosonde work the only place thatboth the height and pressure are known, hence theonly place that D can be determined without usingthe hydrostatic equation, is the surface. The valueof D at the surface is obtained by converting thestation pressure, in say inches of mercury 'as measured with a mercurial barometer at the time ofrelease, to pressure altitude, with some table suchas Table 1, and algebraically subtracting this pressure altitude zp from the height above sea level z ofthe ivory point of the barometer. For any particularradiosonde station it would be advantageous toconstruct a table of the form of Tables 2a-2f forthe direct conversion from inches of mercury to Dat the height of the barometer. Table 1 could beused to construct this additional table. For airplanesoundings, especially when the height of at leastone point is determined with a radio altimeter, thevalue of D can be determined directly as the difference of the height above sea level z, as determinedwith the radio altimeter, and the pressure altitudez,, as determined with the pressure altimeter.5. Determine the heights D of all desired pressure surfaces by successively adding the thicknessanomalies as determined in 3. to the value of Dat the one known point. D is thus determined as afunction of z, so that the conversion to the heightsabove sea level z can be very simply obtained byadding z, to D. However, since this is such a simpleprocess, and since, as described later, it is convenient to use D directly in meteorological mapanalysis, this determination of D at the desiredpressure surfaces can usually be considered as representing the completion of the pressure-height computations. It has been found convenient in routine work withmaps analyzed in terms of D to make the followingphysical interpretation of this process. One can writeZPZD = ZplD + (WZD - ZP~D). (52) and =p2D are the heights, measured up fromz = zPl and z = zP2, of the constant pressure surfacesz,l and zp2, respectively. (zp2D - zplD) is the geometricthickness of the layer between these two pressureand is used as the parameter with which the meanvirtual temperature between the two pressure surfacesis specified, since this thickness can vary only if themean virtual temperature between these two fixedpressure surfaces varies. Thus for most purposes, suchas drawing charts of mean isotherms, it is convenientto label these mean isotherms in terms of the parameter (EplD - zplD), instead of in "C, since then thepressure-height calculations can be performed withmaximum ease.The sounding plotted on Plate I provides a sampleof this technique of pressure-height calculation. Thesteps for this calculation are:1. The sounding was plotted with Plates V andVI as an underlay from the reported values of T,p and w.2. The virtual temperature-pressure curve (thelight dashed curve) was plotted 0.06 units of S tothe right of the temperature-pressure curve for each10 gm/kg of w.3. The thickness anomalies in feet between thevarious pressure surfaces were determined andentered in parentheses to the right of the diagram.For example, the value of (5000 ftD - SfcD), fromthe surface to z, = 5000 ft, is + 40 ft since 4squares (to the nearest integral number of squares)are enclosed between the S = 0 line, the z, line forthe surface point, the z, = 5000 ft line and thevirtual temperature curve. Also, the value of(loooo ftD - 5000 '"0) = + 30 ft was determined bylocating a mean S line from z, = 5000 ft toz, = 10,000 ft. This line occurred about threetenths of the way from the S = 0 line to theS = 0.02 line which was imagined as being labelled+ 100 ft.4. The value of SfcD = Sfcz - Sfczp was determined from the reported surface pressure, Sfcp = 974mb or Sfc~p = 1090 ft (from Table le), and theheight above sea level of this station, Sf% = 1250 ft,as SfcD = 1250 - 1090 = + 160 ft.5. The values of D in feet at each integral multiple of z, = 5000 ft were then determined by successive additions of the thickness anomalies, asshown at the right of the diagram.The soundings plotted on Plates I1 and IV wereevaluated in exactly similar fashion, with the valuesof the thickness anomaly and D entered in meters, foreach kilometer of z,. For the sounding on Plate 11,Sf% = 5m, Sfcp = 1018 mb, Sf%, = - 39 m fromTable Id, so SfcD = 5 - (- 39) = + 44 m. For thesounding on Plate IV Sf% = 506 m, SfCp = 960 mb,Sfc~p = 453 m from Table le, so sfcD = 506 - 453= + 53 m.This technique of pressure-height evaluation thusBsurfaces minus the "standard thickness" (zpa - z,~),provides for very accurate pressure-height computa48 JOURNAL OF METEOROLOGYtions by simple addition and subtraction of smallnumbers. This is possible since the accurate calculations involving logarithms or large numbers have beendone once and for all in the definition of pressurealtitude as the pressure parameter. Thus it is in general, as convenient to make these calculations between arbitrary pressure surfaces as between predetermined standard pressure surfaces since the difficult calcula tions in the definition of pressure altitude have already been made for all pressure values. This is to be con trasted with the common procedures in terms of millibars in which the thicknesses between standard isobaric levels (say each 100 mb) have been similarly calculated and tabulated for convenience, but in which the calculations involving nonstandard pressure sur faces are in general niuch more difficult. This con sideration is becoming more important since a great deal of data at arbitrary pressure values is becoming available from aircraft equipped with radio altimeters. Also the possibility of easily obtaining the height of any desired pressure surface, not just a few predeter mined surfaces, seems to be very desirable.Determination of pressures at constant-level surfacesfrom soundings. The pressures at predetermined constant-level surfaces, determined from soundings inwhich the temperature is measured as a function ofthe pressure, must essentially be calculated by successive approximations since the temperature distribution as a function of height is not known at theoutset. This problem can conveniently be solvedalmost directly with very little error by the followingprocedure.1. Determine the heights, expressed in terms ofD, of those constant pressure surfaces for which thenumerical value of the pressure altitude is equal tothe numerical value of the height above sea levelat which the pressure is desired. For example, thefirst step in determining pressures at z = 5000 ft,10,000 ft, 15,000 ft, etc., is to determine the valueof D at the pressure surfaces where zp = 5000 ft,10,000 ft, 15,000 ft, etc. This step is accomplishedby the previously described technique.2. Convert the value of D at these constant pressure surfaces, "p="D, to the value of D at thecorresponding constant level surfaces, z=aD. Sincez='D can conveniently be thought of as a parameterwith which to describe the pressure at the levelz = a, this usually completely solves the problem,although, if desired, the value of z='D can be converted to millibars by means of Table 3c.A rapid method of making this conversion isa. Locate the approximate pressure altitudez, = a - zp=aD of the point on the pastagram.b. Determine the area enclosed by this pressurealtitude line and the lines for z, = a, S = 0 andthe S* sounding. This area then approximatelyrepresegts the value of (,='D - zp=aD).c. Add this approximate value of the area to thevalue of "P=~D. This result is then the approximatevalue of '="D, and except in very extreme cases itwill not be in error by more than 30 feet.d. For very accurate work a more exact value of(,=,D - 'pzuD) could then be obtained by usingthe result of step c to locate the pressure altitudeline corresponding to the level z = a and repeatingthe process.As an example, the calculation for the pressureat z = 15,000 ft for the sounding on Plate I isa. Locate a point at z, = 15,000 - 300 = 14,700ft on the sounding.the nearest 10 ft) since slightly more than one halfof a square is enclosed by the sounding betweenz, = 15,000 ft and z, = 14,700 ft.c. Then 2=15000 ftD = + 300 + (- 10) = + 290ft. By Table 3c this can be converted, if desired, tob. Then(r=15000 ftD - Zp-15000 ftD) = - 10 ft (toz=15000 ftp = 578 mb.The convenience of this technique in comparisonwith the method of determining these pressures froma pressure-height curve constructed from the heightsof each round 100-mb pressure surface results primarily from the possibility of easily finding the heightof those particular pressure surfaces which are on theaverage at nearly the same vertical position in theatmosphere as the desired constant level surfaces.Thus it is not necessary to draw a pressure-heightcurve to obtain a first approximation. Also the dualinterpretation of D as either a height or pressureparameter saves considerable time in routine workbecause unit conversions are not necessary.Pressure-height extrapolations. The extrapolation ofthe pressure-height relationship in regions where temperature soundings are not available is usually veryeasy in terms of D and z,. Some examples of suchextrapolations are1. The simplest assumption for extrapolation interms of D is that S* = 0, in other words thatT* = T, or that the virtual temperature of theactual air is the same at all pressures as in thestandard atmosphere. For such an assumptionaD/az, = 0 or D is a constant in t'he vertical equalto its value at the point at which it is known.This concept is commonly used in the usual definition of the altimeter setting in which the pressureat a point is reduced to sea level by use of theassumption that the standard atmosphere existsbetween the point considered and sea level. Thusin this case, as seen before, the value of D at sealevel is assumed to be the same as at the pointconsidered. This concept is also useful in repreJOHN C. BELLAMY 49Range of zp in ftActual D in ftExtrapolated D in ftError in ftsenting the pressure distribution on the surface ofthe earth and will be described more fully underthe discussion of the surface chart.The assumption that D does not vary in the vertical is quite accurate when extrapolations throughsmall vertical distances are required since, for anyprobable values of S*, (I."D - +ID) = 8* (zP2 - zPi)becomes very small for small values of (z,2 - z,I).For example, in the majority of actual conditions18" I 5 0.05 so that, for an accuracy of extrapolation of 10 feet a range of IzP2 - zP11 of about 200feet can be used, while for an accuracy of extrapolation of 100 feet a range of Izp2 - zpll of about2000 feet can be used. This type of extrapolation isvery important in the determination of drift inaircraft and is discussed more fully in the sectionon that subject.2. Extrapolations from points at which theheight, pressure and temperature are known canconveniently be made by assuming that the valueof S* throughout the column considered is equal toits value at the known point. This assumption isthen equivalent to assuming that the lapse rate isroughly moist adiabatic (6.S°C/km) in the troposphere and isothermal in the stratosphere. Thegeneral extrapolation formula for this assumptionis thenZPD - ZPOD = *p0S*(zp - zp0),(53)where +OD, zpoS* and z,o. are the values of thesequantities at the known point and zpD is the valueof the height (or pressure) parameter at the desiredpoint of extrapolation where the pressure altitudeis equal to 2,.As an extreme example of the vertical distancethrough which such an extrapolation can safely bemade, consider that the actual lapse rate in thetroposphere is isothermal, as represented by lineEFGH in Plate 111. Then, assuming that the value ofzpoD at point E is equal to - 200 feet, the actualvalues, the extrapolated values, and the errors in theextrapolation of D, to the nearest ten feet, at thevarious points are given in Table 8.TABLE 8.Point IE F G H 0 1000 2000 5000-200 -190 -170 - 60-200 -190 -180 -1500 0 10 90corresponding pressure-altitude (constant pressure)surface, or vice versa when it is impossible or inconvenient to obtain a plot of the sounding between thesetwo' surfaces. Since these two surfaces are seldomseparated by more than 2000 feet, this approximationof the lapse rate should seldom lead to an error ofmore than 20 feet. z=aD, a parameter of the pressureat z = a, can be considered to be the distance, measuredin the standard atmosphere, from a height where thepressure is ~=~z, to the height of the pressure surfacez, = a. Similarly +="D, a parameter of the height ofthe pressure surface Z, = a, can be considered asbeing the distance, measured in the actual atmosphere,from the height z = a where the pressure is z=a~p tothe height of the pressure surface z, = a. Hence thesetwo distances are measured between the same twopressure surfaces, one in the standard atmosphereand the other in the actual atmosphere. Thus, sincewe are assuming that S* (hence T*/T,) is constantbetween these surfaces, we can writeT*D- = z=aD(l + S*).(54)zp=aD = z=aTPPlate VI11 has been drawn to solve this equationdirectly. It consists of a transparent overlay of quasihorizontal lines for "="D, superimposed on Plate I tobe used with the S* values of Plate I (or Plate 111).This overlay is so constructed that the values of zp=aDare represented by the horizontal lines on Plate I (or111). Numerically corresponding z=aD and *p=aD linesintersect each other at S* = 0. Hence the labels ofthe z=aD lines also apply to the zp=QD lines throughthese intersection points. It follows that this platecan be used to convert zp=aD to z=OD and vice versafor any level (any value of a) since the value of S*for any level can easily be determined on Plate 111with the values of zp and T*. As an example of theuse of this plate, the value of z=150w ftD for the sounding plotted on Plate I is given by locating point A atthe value of zp=15000 'tD = + 300 ft and at the valueof 2p=15000 ftS* = 0.015, determined from the soundingon Plate I. Thus rr;15000 'tD = + 290 ft read from theslanting lines of Plate VIII. Similarly for some otherlevels in this sounding, the values are given in Table 9.TABLE 9Point I a Ip=iZD S' 1=0D~~~35,000 +520 ft 0.031 +so0 ft +630 ft40,000 +650 ft 0.020Plates IX and X are conversions of Plate VI11 inwhich the values of zEOD have been converted to millibars and the values of S* have been converted to T*at either the constant level or constant pressure surface. The description of the construction and use of50 JOURNAL OF METEOROLOGYthese plates is given on Plate IX. They have beendesigned primarily for the conversion from pressuresin millibars at the various constant level surfaces tothe heights of the corresponding pressure surfaces, sothat these constant pressure charts can easily bedrawn from present and past U. S. radiosonde reports.It has been found that a very efficient method ofcalculating the pressures in millibars at these constantlevel surfaces for the original encoding of this type ofdata consists of calculating the heights (in D) of thenumerically corresponding pressure-altitude surfacesand using these plates (or the previously describedmethod) for the final conversion. Some examples ofthe use of these plates are1. Given: z=lOOOO ftp = 707 mb,s=lOOOO ftT = + 10°C.,then zp=loooo ftD = + 400 ft.2. Given: ~=20000 ftp = 445 mb, the11 ZP=~OOOO ftD = - 970 ft.z=20000 ftT = - 50°C.I3. Given: zp-10 kmD = + 1000 ft, Zp-10 kmT = - 53°C;then kmp = 277 mb.Utilization of aircraft reports of pressure-height data.One of the best sources of pressure-height data overoceanic areas are data from aircraft equipped withradio and pressure altimeters. The reporting of D atthe corresponding values of the pressure altitude is anefficient method of distributing these data. This system has several advantages, namely:..1. D is easily obtainable by subtracting the pressure-altimeter reading (corrected for instrumentalerrors) from the radio-altimeter reading.2. D is useful in itself for navigators in driftdeterminations.3. The vertical position of the observation canbe given with sufficient accuracy to the nearest100 feet since the variations of D in 100 feet arealmost always less than 10 feet.4. When vertical position is given in terms ofpressure altitude (in contrast to geometric altitude)no change in the form of aircraft reports is necessitated when the flight is over land or when no radioaltimeter is available.5. When vertical position is given in terms ofpressure altitude (in contrast to millibars) geometricheights are apparent by adding D, and conversionfrom the observational pressure parameter is eliminated.6. Reports in terms of D (in contrast to almostany other common parameter) are immediatelyapplicable to analysis of the pressure distribution onvertical cross sections.7. The vertical extrapolation of these reports (asseen in this section) to standard surfaces for "horizontal" analysis is convenient.A convenient general assumption foc the lapse ratebetween the observation point and the standard"horizontal" surface is that S* is equal to its value,as determined by z, and T at the observation point,throughout this column. Thus the general equation forthis assumption (53) applies to this problem and canconveniently be solved on the pastagram. As an example, assume that it was determined that at somepoint zPo = 21,000 ft, zpoT = - 17°C and zpOD =+ 1080 ft (point J, Plate 111). Then the value of Dat z, = 20,000 ft (for analysis of the contours ofthe z, = 20,000-ft surface) would be estimated asrp=20000 ftD + 1080 - 40 = + 1040 ft, where the- 40 feet corresponds to the area JJ`K`K sincezp - zPo is negative. Further, the value of D atz = 20,000 ft (for analysis of the isobars in terms ofD at z = 20,000 ft) would be estimated as 2=20000 ftD= 1040 - 40 = + 1000 ft (by area KK'L'L sincethis extrapolati6n is to be taken to a pressure altitudeof z, = 20,000 - 1040 = 19,000 ft). Finally, thevalue of p at z = 20,000 ft (for analysis of the isobarsin terms of millibars at 20,000 ft) would bePlate XI has been constructed as an aid in makinglarge numbers of these extrapolations to the value ofD at the nearest round 5000-foot pressure-altitudesurface. The hyperbolae of equal areas on the pastagram can conveniently be placed on a transparentoverlay (or printed in a different color) and used withPlate 111 as shown. Some examples, of the use ofPlate XI are1. given:^, = 9,000 ft, T = + 8"C, D = + 320ft; then zp=loooo ftD = + 320 + 40 = + 360 ft.2. Given:zp = 11,00Oft, T = + 9"C, D = + 410ft; then zp=loooo ftD = + 410 - 60 = + 350 ft.3. Given:z, = 2,00Oft, T = - 2"C, D = - 200ft; then =p=OD = - 200 + 90 = - 11'0 ft.4. Given:z, = 23,00Oft, T = - 38"C,D = - 1140ft; then rp=25000 ftD = - 1140 - 60 = - 1200 ft.z=20000 ft mb I 20000 ftD ft) = 485 mb frorn Table 3a.P (=If constant level analysis is desired, the conversionfrom zp=aD to z=aD can then be made directly on thepastagram by means of Plate VIII. Similarly the conversion to z=ap can be made from this last step withTable 3a or directly from the first step with PlateIX or X.Extrapolations from surface data. In the general caseany type of temperature distribution can be assumedand the extrapolations can be carried out by means ofthe methods given for evaluation of soundings. Forother specific assumptions special diagrams can bemade to facilitate the extrapolations.A very convenient scale for extrapolating surfaceobservations to the 10,000-ft and 20,000-ft levels, the"Isobaric Contour Extrapolation Scale" shown onPlate XII, has been designed by Capt. William J.JOHN C. BELLAMY 51Plumley, Capt. Reid A. Bryson and Lt. John W.Bookston, U. S. Army Air Forces. It has been designedfor use in connection with observations in oceanicareas where the reporting stations are close to sealevel. The scale relates sea-level pressure (in millibars),mean virtual temperature (in degrees centigrade orFahrenheit), surface temperature (in degrees centigrade or Fahrenheit), low cloud type, height of lowcloud base, and the value of D (in feet) at z, = 10,000 ftor 20,000 ft.Sea-level pressure lines are horizontal and labelledalong the left-hand border. The large numbers increasing upward are used for calculations of D atz, = 10,000 ft. The small numbers decreasing upwardare used for calculations of D at z, = 20,000 ft.Temperature lines are vertical and the temperatureincreases from left to right in degrees Fahrenheit orcentigrade. The diagonal lines which extend upwardfrom right to left are lines of constant D (in feet) atzp = 10,000 ft. The diagonal lines which .extend upward from left to right are lines of constant D (in feet)at z, = 20,000 ft.A sliding strip (the portion between the double lineson Plate XII) contains the scales of temperature andtfiree index indicators IO, IIOOOO, and IZOOOO. When IO onthe sliding scale is set opposite Io on the fixed scale(as printed in Plate XII), the value of D at bothz, = 10,000 ft and zp = 20,000 ft is determined forany selected mean virtual temperature (read on thetemperature scale) and sea-level pressure.When I;oooo on the sliding scale is set opposite LooOoon the fixed scale, the temperature scale is used toindicate surface temperature rather than mean virtualtemperature. The use of the Izooo~ indicator is analogous to the use of the I1oooo indicator. The additionalsymbols below the sliding scale are the cloud indicators. The numbers below each cloud symbol denotethe height of the cloud base in the international code.If I1oooo on the sliding scale is set opposite any cloudindicator in the I~oooo fixed group, a correction isintroduced for the difference between the lapse ratefor a particular cloud type and the U. S. Standardlapse rate of minus 6.5" C/km. Sea-level pressure andsurface temperature then determine the value of Dat z, = 10,000 ft.The following assumptions have been made as tolapse rates for particular low cloud types. A dryadiabatic lapse rate was assumed to exist up to thebase of the cloud, a moist adiabatic lapse rate throughthe cloud, a two-degree centigrade inversion at thetop of the cloud (four-degree centigrade inversion forstratus or stratocumulus) and the U. S. Standard lapserate above the inversion. To correct for the moisturein the atmosphere two. degrees centigrade were addedto the mean temperature of the column from sea levelto z, = 10,000 ft, and one degree centigrade wasadded to the mean temperature of the column fromsea level to z, = 20,000 ft. Fair weather cumulusclouds were assumed to have tops at 4000 feet if theheight of their base is 3, 4, or 5 in terms of the international code. If the height of the base is 6 the topswere assumed to be at 6100 feet and if it is 8 the topswere placed at 9300 feet. Swelling cumulus were assumed to have tops at 8000 feet if the cloud bases arecoded 3, 4 or 5, at 9000 feet if the bases are coded as 6,and at 11,000 feet if the bases are coded as 8. Cumulonimbus were assumed to have tops higher than 20,000feet. Stratus or stratocumulus were assumed to have athickness of 1500 feet for height of bases coded as 1through 6.Example 1.Given :Sea-level pressure, 1010 mb.Surface temperature, 80°F.Cloud type, swelling cumulus, height of bases 5.Find D at z, = 10,000 ft and at z, = 20,000 ft.Procedure:1. Set I~oooo of sliding scale opposite symbol forswelling cumulus with base marked 5 in theI10000 fixed group.2. At the intersection of the T equal 80°F lineand the sea-level pressure line for 1010 mb,read the value of D = + 400 ft at z, = 10,000ft.3. Set Izoooo of sliding scale opposite the appropriate cloud symbol in the Izoooo fixed group.4. At the intersection of the T equal 80°F lineand the sea-level pressure line for 1010 mb (onthe outer pressure scale), read the value ofD = + 1050 ft at z, = 20,000 ft.Example 2.Given :Sea-level pressure, 1010 mb.Mean virtual temperature between sea level andMean virtual temperature between sea level andFind D at zp = 10,000 ft and at z, = 20,000 ft.1. Set Io of the sliding scale opposite Io of thefixed scale (as in Plate XII). At the intersection of + 7°C and 1010 mb (on the innerpressure scale), read D = - 10 ft at z, = 10,000 ft.2. At the intersection of - 6°C and 1010 mb (onthe outer pressure scale), read D = - 150 ftat z, = 20,000 ft.z, = 10,000 ft is 7°C.z, = 20,000 ft is - 6°C.Procedure :.52 JOURNAL OF METEOROLOGY6. Theoretical wind calculations.Geostrophic wind calculations. Using 52 = 0.2625 hr-1and g = 980 cm/sec2 and expressing v in knots, z andD in feet and n in degrees of latitude, equations (26)and (27) for conditions on a constant pressure surfacecan be writtenv sin 40.357 =- (g)p=-($). P (55)The similar equation for conditions on a constantlevel surface isv sin 40.357 2(56)-- -- (1 +S*)( E).This latter equation thus contains the additionalfactor, (1 + S*), which, if set equal to one, can causean error of at most about 10 per cent (S* = 0.1)but in most cases would cause an error of less thanabout 5 per cent. Hence (in harmony with commonpractice in which density variations at one level areneglected) if (1 + S*) is set equal to one the numericalcalculation of the geostrophic wind (in terms of D)on either constant level or constant pressure surfacesis the same and independent of vertical position.This is in contrast with the ordinary methods ofgeostrophic wind calculation (in terms of pressure)which necessitate the use of different constants fordifferent levels. Thus D as a pressure parameter atconstant, levels provides for added convenience inthese calculations.Plate XI11 gives the solution of these equations(neglecting S* in the constant level case) in terms ofthe horizontal distance corresponding to a change of D(or z) of 100 feet. Some examples of its use are:1. The spacing of 100-foot contour lines for a25-knot (29 mi/hr or 13 m/s) wind at a latitude of35" is 2.5 degrees of latitude (150 nautical miles, 172statute miles or 278 kilometers).2. The geostrophic wind component normal to aline along which the value of D changes at a rateof 100 feet per 60 nautical miles (1 degree of latitude) at a latitude of 25" is 85 knots (98 mi/hr, 44m/s or 34 degrees of latitude per 24 hours).Other techniques of solving the geostrophic windequation are given under the sections on drift determinations and space cross sections.Gradient wind calculations. It has been found convenient to calculate the gradient wind speed V interms of the geostrophic wind speed v. Substituting2Qv sin 4 for the various expressions of the pressuregradient force in the gradient wind equations (28)(31), one obtainsV2v- v= =t 252RT sin 4.(57)With V and v expressed in knots, RT expressed indegrees of latitude and 52 set equal to 0.2625 hr-1this becomesTP= =t 3.15RT sin 4).(58)v-vPlate XIV has been drawn according to this equationwith the left portion for the minus sign (anticycloniccurvature) and the right portion for the plus sign(cyclonic curvature). The speed scales can be used asindicating miles per hour instead of knots if theauxiliary RT scale at the bottom is used. Some examples of solving the gradient wind. equation withPlate XIV are1. Given : At latitude 40" a radius of curvature of20 degrees of latitude and a geostrophic wind velocity (from Plate XIII) of 50 knots. Point A islocated at RT = 20 degrees of latitude and 4 = 40".If the curvature is cyclonic, the gradient windvelocity at point B is 45 knots. If the curvature isanticyclonic, the gradient wind velocity at point Cis 60 knots.2. Given: An observed wind of 50 knots at 30"latitude and an estimated cyclonic radius of curvzture of 5 degrees of latitude. Point D is located atRT = 5 degrees of latitude and 4 == 30". The geostrophic wind (point E for V = 50 knots) is 83 knots.The spacing of 100-foot D lines from Plate XI11 is0.85 degrees of latitude or 60 miles.Thermal wind calculations. The usual simplificationsof the thermal wind equation (34), that is, neglectingthe effect of V2/R~ and neglecting the temperaturefactors in the constant level scheme, result in thesimplified equation,a252~ sin 4 as*az,(59)Expressing v in knots, zp in feet and .n' in degrees oflatitude and integrating through a linite differenceof pressure altitude zp2 - zpl, this can then be writtenAv sin C$aS*(zPz - zPl)0.357 an'This formula is very similar to that for the geostrophicwind equation and Plate XI11 can conveniently beused to solve it. For this purpose1. The velocity scale is used as the scale of themagnitude of the shear of the wind, in knots, whichoccurs through a vertical distance corresponding toan arbitrary change of pressure altitude.JOHN C. BELLAMY 532. The spacing scale is used as the scale for thespacing of isolines of the quantity +ZD - +ID drawnfor intervals of 100 ft. It is apparent from equation(60) that the pattern of these lines is the same asthe pattern of the mean isotherms for the samelayer. It follows, therefore, that the quantity=pzD - zplD can be used directly as a temperatureparameter making it unnecessary, for most purposes, to convert its values into values of the meantemperature in degrees.An example of this use of Plate XI11 is as follows:If at latitude 30' the magnitude of the shear of thewind between the pressure altitude z, = 5000 ft andz, = 10,000 ft is 20 knots, the spacing of isolines ofzp-10000 ftD - ep=5000 ft D drawn for 100-ft intervals is.3.6 degrees of latitude or 250 miles. Since this scaleapplies to an arbitrary range of pressure altitude, thecalculation in this example could also be used to give,for a shear of 20 knots from z = 5000 ft to z = 10,000ft, the approximate spacing of 100-ft lines of thequantity z=loooo ftD - 2=5000 FtD which can be used asan approximate parameter of the mean isothermsbetween these constant-level surfaces.7. Applications to aircraft operations.Drift determinations with radio and pressure altimeters. In general the value of D can easily be determined in an airplane at any given instant by subtracting the value of the pressure altitude, as determinedwith a pressure altimeter, from the value of the heightabove sea level as measured with a radio altimeter.If such determinations are made at two differenttimes the component of the geostrophic wind normalto the track over which the airplane has travelledbetween these two observations can be calculated.The drift angle of the airplane can then be determinedwith the aid of this value of the cross wind and thetrue air speed of the airplane.'/ !AFIGURE 4.Figure 4 illustrates the geometry involved in thisPoint A is the position of the airplane at the timeof the first observation of the altimeter correction,Di.Point B is the position of the airplane at the timeof the second observation, Dz.Point C is the position the airplane would haveat the later time if there were no wind.problem.d is the wind distance travelled between readingsand is proportional to the wind speed and in thedirection of the wind.Since a geostrophic wind is assumed, so that thewind blows parallel to lines of constant D (isobarsor contour lines), the value of D at point C is alsoequal to D2.TAS is the air distance travelled between observations which is proportional to the true air speedand is in the direction of the heading of the airplane.GS is the ground distance or track actuallytravelled between readings which is proportionalto the ground speed.6 is the drift angle.d, is the component of the wind distance normald, is the component of the wind distance paralleld,' is the component of the wind distance normald,' is the component of the wind distance parallelto the track.to the track.to the heading.to the heading.The geostrophic wind relationship gives the component of the wind normal to any distance, x, alongwhich a given pressure gradient occurs. Thus, if x istaken as the ground distance GS, d, is determined.The drift angle 6 is then given by the formula sin 6= (E,/TAS. On the other hand, if x is taken as theair distance TAS, d,' is determined. The drift angleis then given by the formula sin 6 = d,'/GS. Thusan accurate determination of the drift angle requiresan estimate of the ground speed in both procedures.The choice of which of these two procedures shouldbe used (they both give the same result) seems to beprimarily one of personal preference. The first procedure will be used in the rest of this article.When no other navigational aid is available forobtaining the ground speed the value of the driftangle must be approximated by using TAS instead ofGS. The error due to this approximation is, however,usually quite small since the head or tail componentof ordinary winds has little effect on the drift anglefor high-speed aircraft. Even a rough estimate ofthe head or tail wind component from, say, a windforecast sensibly eliminates this error in the driftangle. It is possible to use a double-drift procedurewith this technique to determine the total geostrophicwind vector, but usually the time involved in flyingoff course makes this impractical.The geostrophic wind equation for this purpose canbe expressed as21.4 Dz - D1v, = - , (61) sin 4 xwhere v, is expressed in knots, x (the ground distance)is expressed in nautical miles, DZ and D1 are expressed54 JOURNAL OF METEOROLOGYin feet, 9 is the mean latitude of points A and B, andthe differential expression (aD/an), has been replacedby the finite diflerence expression (D2 - Dl)/x. A calculation diagram which has been found to be convenient for these isomputations is given in Plate XV.Instructions and an example of its use are given in thediagram.It has been found that in most cases in temperateand arctic latitudes it is necessary to obtain the valuesof D1 and D2 to a relative accuracy of about 10 feetin order to obtain satisfactory accuracy in the driftangles. This can be accomplished with careful use ofpresent equipment since it is the relative accuracy thatis important, that is, any constant error in either orboth of the altimeters is eliminated in the subtractionprocess. Thus it is possible to make most of thesecalculations directly from the readings of the twoaltimeters. However, since absolute observations ofD are very important as meteorological data for otheruses, and since in some cases it is necessary to makehydrostatic calculations in the drift determinations,it is usually desirable to apply the available instrumental corrections to the readings of the altimeters toobtain as great an accuracy as possible for z and z,before they are subtracted to give D. Since such (evenrelative) accuracy is very difficult to obtain whenflying over land this method of drift determination islimited to use over oceans or large lakes. Close to theequator the pressure gradients are very small. forusual wind speeds so that excessive flight times between observations are required to obtain measurablevalues of D2 - D1. Thus the usefulness of this methodis limited in tropical regions. Some cases have beenobserved, however, in which at least the direction ofdrift has been given as near to the equator as 5 degreesof latitude.Since the geostrophic wind equation used refers toconditions on a constant pressure surface the successive determinations of D should be adjusted, using thehydrostatic equation, to the same pressure surface.In usual "level" flight the airplane is kept approximately at a constant value of the pressure altitude(pressure-altimeter reading set at 29.92) but slightvariations (of the order of 300 feet) from the flightlevel" are constantly occurring due to turbulence,etc. For such "level" flight the necessary hydrostaticcalculations are automatically accomplished by usingD in the computations since D seldom varies in avertical distance of this amount by more than 10 feet.In climbs or descents the necessary hydrostatic calculations can conveniently be made by using the following procedure with a pastagram such as Plate 111.I11. Locate the points on the pastagram corresponding to the pressure altitudes, z,l and zp2, andtemperatures, T1 and Tz, of the air at the two timesof observation.2. Determine the value of zp2D~ - zp*D1, thechange of D at the horizontal position of the firstobservation, from the pressure altitude of the firstobservation to the pressure altitude of the secondobservation. This quantity is the area enclosed bythe lines z, = zpl, zp = z,~, S = 0 and the linejoining the two points of step 1, and is equal to thenumber of enclosed squares of the z, and S linesmultiplied by 10 feet. The algebraic sign of thisquantity isa. Positive if the points of step 1 are to the rightb. Positive if the points of step 1 are to the leftc. Negative if the points of step 1 are to the rightd. Negative if the points of step 1 are to the leftof the S = 0 line and zp1 < z,2.of the S = 0 line and z,l > zp2.of the S = 0 line and Z,I > zp2.of the S = 0 line and zp1 < zp2.3. Determine the value of zp2D1 by algebraicallyadding the value of .p2D1 - zplD1 to the observedvalue of "p1D1.4. Use D2 - +2D1 for D2 - D1 in the drift anglecalculations.Two examples of the hydrostatic cal!culation, shownon Plate 111, are given in Table 10.TABLE 10~~z zp T D WZDI -WID1 @DI Dz -*PZDIPoint feet feet OC feet feet feet feetFirst observation P 9870 9220 -15 -650Secondobservation Q 11460 10850 -16 -610First observation S 15910 15300 0 4-610Secondobservation R 14720 14120 0 4-600-70 -720 4-110-70 4-540 4- 60~Pressure-pattern flying.* The determination of Dwith radio and pressure altimeters while in flight provides a method for the continual adjustment of flightplans to take fullest advantage of winds in long flightsover water. The original flight plans can best be madefrom the meteorologist's forecast of the wind distribution. If these forecasts are given to the navigator inthe form of a map analyzed in terms of D at the flightpressure altitude, the values of D observed in flightcan conveniently be used to make relatively smallcorrections. Slight changes in flight plan can then bemade en route to take fullest advantage of the actualwind conditions. It is felt that the development anduse of these procedures will prove to be very valuablesince minimum flight times and minimum fuel con* This is the term applied by H. E. Hall (3) and associates ofTranscontinental and Western Air, Inc. in tkeir extensive workof choosing ,flight paths which use the winds to fullest advantage.sumption can thus be obtained. Furthermore, theincreased amount of observational data and the moredirect and detailed verification of forecasts shouldresult in better general forecasting procedures.Height determinations. As seen in the discussion ofaltimeter settings, the altimeter correction D is a veryconvenient parameter with which the meteorologistcan give pressure-height data to flying personnel foruse over land or when radio altimeters are not available. These data can conveniently be given in theform of constant pressure maps, vertical space crosssections or vertical time cross sections, all analyzed interms of D with the vertical position indicated in termsof pressure altitude.The following procedure can be used for determining elevations of aircraft above sea level over land incoastal regions when a radio altimeter is available.This method is often needed since it is usually quitedifficult to determine accurately the height of theparticular land surface beneath the airplane at anygiven instant. If an observation of the value of Dwith both radio and pressure altimeters is made overthe water, and direct wind observations at the flightlevel are made, the change in D along the flight level(constant pressure surface) from this observationalpoint to any desired point over the land can be calculated by using the geostrophic wind equation,21.4 aDsin +( z >,*v, = - (62)In this equation aD is the value of this "horizontal"change in D, in feet, an is the distance in nauticalmiles between the two points, 4 is the average latitudeof the two points and v, is the component of the windin knots normal to the line joining the two points.Thus a value of D at the desired point over land isdetermined. This value is independent of forecasterrors and of any constant instrumental errors of thepressure altimeter. The value of z is then obtained byadding D to z,.This procedure also offers the possibility of determining the elevation of land surfaces in unsurveyedregions. For this purpose several approximately simultaneous wind observations and readings of radio andpressure altimeters over a known elevation and theunknown point could be made. These observationswould be made at some convenient constant pressuresurface which is everywhere above the terrain andabove the level of frictional influences, so that thegeostrophic (or gradient) wind equation could be usedto determine the applicable value of D over the desiredpoint. Such determinations could probably be madequite accurately, even far inland under favorableweather conditions, with two or more airplanes inwhich the altimeters are carefully calibrated withJOHN C. BELLAMY 55respect to each other.Weather chart analysis in terms of altimeter corrections.It has been found that the altimeter correction D isa very convenient parameter with which to representthe spacial distribution of pressure and temperatureon maps and cross sections. In fact the concept of thealtimeter correction originated in a search for somesuch parameter with which one could convenientlyrepresent the continuous pressure distribution in thevertical as well as in the horizontal.The representation of the spacial distribution ofpressure can conveniently be accomplished with eitherthe constant pressure scheme or the constant levelscheme. As shown in this section the similarity of thetwo schemes and the convenience of either for routinework become more marked if z, and D are used asparameters of pressure and height respectively in theconstant pressure scheme and if D and z are used asthe parameters of pressure and height respectively inthe constant level scheme.Figure 5 is an example of the similarity of these twoschemes in a "horizontal" representation. The solidlines are contours, in terms of D, of the constant pressure surface, z, = 20,000 ft measured from z = 20,000ft. The dotted lines are isobars at z = 20,000 ftmeasured by the displacement D, of the standardatmosphere required to obtain the observed pressureat any given point on the map. In order to show thecorrespondence of this representation with the common one in millibars at z = 20,000 ft, a constantlevel chart analyzed in terms of millibars was preparedfor the same data (Fig. 6). The solid lines are isobarsin terms of millibars while the dotted lines are isobarsin terms of D and are identical with the dotted linesin Figure 5.The constant pressure scheme is used in this articleto illustrate analysis in terms of D since it is felt thatit is usually more convenient than the constant levelscheme. As seen in the section on pressure-heightextrapolations, the conversion from the constant pressure scheme to the constant level scheme, especiallyif z, is used as the pressure parameter in the constantpressure scheme and D is used as the pressure parameter in the constant level scheme, can easily beaccomplished. Some of the reasons why the constantpressure scheme was chosen are1. Since most upper-air observations made withradiosonde or aircraft record pressure, not height,these observations are directly applicable to representation in the constant pressure scheme withoutrequiring pressure-height computations or estimations.2. Calculations of height and of geostrophic, gradient and thermal winds are in general more convenient in the constant pressure scheme. In fact56 JOURNAL OF METEOROLOGYFIGURE 5.FIGURE 6.JOHN C. BELLAMY 57it seems that the most convenient method of makingthese calculations in the constant level scheme is touse the formulae for the constant pressure schemeas the first approximate solution by substituting zfor z, in the formulae.3. Thermodynamic representations and calculations are more convenient in the constant pressurescheme since then the independent variable in thespacial representations is itself a thermodynamicquantity. Thus immediate correlation between thespacial representations and the thermodynamic diagram is obtained; in many cases the spacial representations can then be used directly as thermodynamicdiagrams. This point is illustrated by the time crosssection described below.4. The constant pressure scheme (in terms of z,)is more directly useable by flying personnel sincein the upper air direct determination of the pressurealtitude, and hence the corresponding positions onthe charts, is always donvenient while the directdetermination of height is usually more inconvenient or even impossible.Constant pressure charts. Figures 5, 7 and 8 aresynoptic examples of contour analysis (solid lines interms of 0) of constant pressure surfaces for therespective values zp = 20,000 ft, z, = 10,000 ft andz, = 5000 ft. These charts then have, in general, thesame interpretation as any other contour map of aconstant pressure surface; for instance, the gradientwind blows parallel to the contour lines and the speedof the geostrophic wind is inversely proportional tothe spacing of the contour lines. The latter relationship is independent of the particular surface considered,so that the analysis in terms of D has the addedconvenience that numerical comparison of the intensity of the circulations at various levels is obtainedfrom the numerical values of D. Also these chartsdirectly provide flight personnel with the altimetercorrection (which can also easily be used as an altimeter setting) that applies to an interval of elevationnear the respective pressure altitudes drawn for.The above choice of constant pressure surfaces provides several conveniences such as the following :1. The winds, as reported at round values of z,can conveniently be placed directly on the map forthe corresponding value of z,, since on the averagez, occurs at z. This point is of primary importancesince accurate contour analysis requires the use ofwind reports with the gradient wind relationship.Also most upper-air wind forecasts are desired atround values of z, or z.2. It is convenient to determine by means ofpressure-height computations, the heights of anyround value of the pressure altitude for use withthe winds already reported at the correspondingvalues of z. In general, the pressure-height computations to such arbitrary levels are relatively muchmore difficult by ordinary methods.3. Contour analysis in terms of D for round valuesof z, is efficient since z can be obtained by simpleaddition without conversion of units.4. The conversion from constant level charts toconstant pressure charts, and vice versa, for anydesired level, is in general convenient only if theconstant pressure charts are drawn for those surfaces for which the pressure altitude is numericallyequal to the height above sea level of the constantlevel considered. This is very important for preserving the usefulness of past constant level chartswhen a change to the constant pressure scheme ofanalysis is made.Mean temperature charts. Figures 7 and 8 are examples of mean virtual temperature charts drawn interms of the thickness of the layer between the respective constant pressure surfaces. The dotted lines onFigure 7 represent the thickness between z, = 10,000ft and z, = 20,000 ft and are labelled in terms of thethickness parameter zp=20000 ftD - rp=lOOOO ftD. Thisquantity is also a parameter for the mean virtualtemperature. Similarly the dotted lines on Figure 8These charts can be interpreted either as thicknesscharts with the lines labelled in terms of +zz - z*lzor as mean virtual temperature charts with the lineslabelled in terms of "C. Thermal wind computationsin terms of Ip2D - zplD can conveniently be made withPlate XIII.in the vertical provides a representation of theaverage lapse rate. For example, assuming that= + 200 ft the lapse rate is the same as theU. S. Standard (approximately moist adiabatic). If100oo ftD - IOoo ftD = + 100 ft the lapse rate is relatively stable; and if loooo ftD - 6000 'tD = + 300 ft the'lapse rate is relatively unstable.For most purposes mean temperature charts seemto be more convenient than actual temperature chartsfor given pressures. This is primarily a result of thegreater ease with which wind reports and the thermalwind equation can be used as aids in making accurateanalyses. The winds that are ordinarily plotted on theconstant pressure charts can then also be used todetermine the shears applying to the mean temperature charts. This work is facilitated if the winds areplotted on the constant pressure charts as vectors.The shears applying to the mean temperature chartsare then immediately available by superposition of therespective constant pressure charts. The mean temperature analysis can be obtained by graphically subare drawn for Zp~10000 ftD - zp-5000 ftD.A comparison of numerical values of +zD 16000 ftD - 10000 ftD = + 200 ft, then if 10000 ftD - 5000 ftD58 JOURNAL OF METEOROLOGY*.a*. .. . . .. . . . . . . , . ..AUGUST 25, 1944 ,0400 tlp-lOOOOft Dfl(zp=20000f1Dft~zp=10000flDfl). . . . . . . .FIGURE 7.JOHN C. BELLAMY 59FIGURE 9.FIGURE 10.60 . JOURNAL OF METEOROLOGYtracting the contour analysis of the lower surfacefrom that of the upper surface after these contouranalyses have been made (using the wind reports andthe gradient wind equation). This intersection methodwas used to determine the mean temperature analysesin Figures 7 and 8.Time cross sections. Time cross sections (with timeas abscissa and pressure altitude as ordinate) arevery useful in analysis and forecasting. In general itis desirable to enter all the observed meteorologicalconditions that occur over a given station on thischart, so that they can all be conveniently comparedwith each other and correlated with representationson various other charts.Figure 10 is an example of such a time cross section.The surface reports, in this case for each 3-hourlyinterval, are recorded on station circles near the top.The upper-air wind observations are plotted at thevalue of z, equal to the reported value of z with thetop of the chart as north. Each full barb correspondsto 10 miles per hour. For accurate analysis-it shouldbe remembered that these winds occur at a distance Dbelow the level at which they are plotted on the crosssection. The radiosonde observations are plotted assoundings on essentially basic pastagrams similar toPlate I but on a smaller scale. For this purpose eachhour of the time scale is also used to represent aninterval of S of 0.01; the S = 0 lines are taken to beat the 0000- and 1200-time lines; the 0°C isothermsfor these values of S and z, are entered. The soundingsare plotted with underlays similar to Plates V and VIand can be examined for thermodynamic details withthe aid of an overlay similar to Plate VI although this. need not be done for most routine interpretations ofthe soundings. It has been found that these soundings(with virtual temperature plots not shown here) canbe conveniently used for accurate pressure-heightcomputations. The values of zpD and zp+5000 ftD - IPDhave been calculated for the soundings shown. Theirvalues have been plotted to the left of each soundingcurve with =pD entered at the respective values of z,and with zp+5000 ftD - zpD entered in parentheses halfway between these positions.The analysis.entered on the time cross section inFigure 11 consists of isolines of 'PD. The data weretaken from Figure 10. Such an analysis can be directlycorrelated with the D analysis on various other charts.The D analysis of a time cross section can be interpreted as follows:1. The D values show directly the height of anypressure surface at any time, since the height abovesea level can be determined by adding the value ofD to the corresponding value of z,.2. The vertical variations in intensity and theslope of the various pressure systems as they passover the station are shown directly.3. The vertical spacing of the D lines is inverselyproportional to the temperature anomaly of the air(see equation (18)) so that a useful representationof the temperature distribution is also obtained.For example, if the value of D increases with height,the temperature is warmer than the 1J. S. Standard ;and if the D lines come closer together in time, theair is warming over that station in time. Also, whenever the D lines are vertical the temperature is thesame as the U. S. Standard temperature.4. The horizontal spacing of the D lines is inversely proportional to the height tendency aD/atat any point considered so that this height tendencyis zero when the D lines are horizontal. This heighttendency can be considered as an approximatemeasure of the pressure tendency at a fixed level.The analysis on the time cross section in Figure 12is an analysis of S*, in units of 5OOOS*, for the samedata. This S* analysis can be interpreted as follows:1. The vertical spacing of the S* lines is inverselyproportional to the ,lapse rate dS*/i)z,, so that thelapse rate relative to the U. S. Standard lapse rate,which is approximately moist adiabatic, is apparent.Thus if S* increases with height the atmosphere isrelatively stable, if the S* lines are vertical theatmosphere has the same stability as the U. S.Standard, and if S* decreases with height the atmosphere is relatively unstable.2. The local rate of change of temperature(dS*/at), = (l/Tp) (dT*/at), is inversely proportional to the horizontal spacing of the S* lines andthe temperature remains constant with time if theS* lines are horizontal.At times, especially in the tropics, it has also beenfound useful to analyze time cross sections in termsof 24-hour pressure (or height 0) arid temperature(S* or rp+5000 ftD - "PO) changes in order to representmore clearly small pressure and temperature changesand to eliminate diurnal effects.Space cross sections. Figure 13 is an example of aspace cross section which is analyzed in terms of D.This cross section is synoptic with the maps discussedpreviously.The analysis in terms of D can be given the following interpretations:1. The height of any pressure surface in the crosssection is given directly by the value of D at thatpoint. This can then also be thought of, if desired,as giving the pressure at any height.2. The vertical extent and orientation of pressuresystems are clearly and conveniently shown.JOHNCBELLAMY61FIGURE 11.FIGURE 12.62 JOURNAL OF METEOROLOGY3. The vertical spacing of the D lines is inverselyproportional to the temperature parameter S* sothat, as discussed in connection with the time crosssection, the D lines also provide a representation ofthe temperature field.4. The horizontal spacing of the D lines is inversely proportional to the horizontal componentof the geostrophic wind normal to the plane of thecross section. Thus the wind is either calm or parallelto the plane of the cross section if the D lines arehorizontal. Space cross sections have proved to beuseful as an aid in making wind forecasts, especiallywhen forecasts of the wind at several different levelsalong one flight path are desired. The geostrophicwind scale given in Plate XI11 applies directly toany point of the cross section.The analysis of the space cross section in Figure 14is in terms of S* in units of 5OOOS* and can be giventhe following interpretations :1. Since the hydrostatic equation can be writtenasthe pressure-height calculations between any twopressure surfaces separated by a pressure -altitudeof 5000 feet can be made by simple addition orsubtraction. The pressure-height computations canalso very easily be made between arbitrary pressuresurfaces by first multiplying the mean value 5OOOS*by an appropriate factor.2. The value of the temperature in degrees centigrade can be obtained, if desired, directly fromTable 4 or Table 5 or from a pastagram. This stepis usually not desired, however, since the value of S*is a quantitative measure of the temperature of theair with respect to the standard temperature atthat pressure.3. The vertical spacing of the S* lines provides auseful representation of lapse rates and stabilityas discussed for the time cross section.4. The horizontal spacing of the S* lines is inversely proportional to the component of the windshear in the vertical which is normal to the planeof the cross section. Thus the diagram in Plate XI11can be used directly to compute the shear in 5000-ftlayers from the S* analysis (in units of 5OOOS*)given on the cross section.As an example of the conveniencfe of using theparameters z,, D and S* in the analysis of space cross 'sections, the following procedure has been found to beprofitable for making wind forecasts along one routeat several different levels. For this purpose the horizontal scale x of the space cross section is chosen totake into account the variations in the geostrophic andthermal wind due to latitude differences by definingdx = sin q5 dl where dl is the actual length measuredon the earth along the cross section. `Then, choosingthe correct scale for x, the geostrophic wind equationcan be written as v,, = (dD/ax), and the thermalwind equation can be written asIn these equations v,, is. conveniently expressed inFIGURE 13.JOHN C. BELLAMY 63FIGURE 14.knots, D is expressed in feet, and the values of x arelabeled on the space cross section. Thus, these equationsapply equally well at any point on the cross section, anda given horizontal spacing of D or S lines means agiven cross component of the wind or shear, independent of the position on the particular cross sectionthat is considered. For forecasting and other purposesit is convenient to divide the cross section into verticalstrips or zones. If the zones are chosen to be suitablevalues of x in width, all geostrophic and thermal windcalculations are very simply made by additions, subtractions and division or multiplication of smallintegers. For,example, if the difference of D across azone 10 units of x wide were 100 feet, the mean crosscomponent of the wind in this zone would be tenknots. The steps for making the forecast in this procedure are1. Analyze the space cross section in terms of S*.For this all radiosonde and aircraft reports areutilized to determine S* values at the points ofobservation and the interpolations are made usingthe thermal wind equation with all available wind' reports. The S* analysis is labeled in terms of theunit (5OOOS*) to facilitate hydrostatic calculationsof the form given by equation (63).2. Forecast the mean temperature distribution onthis cross section in terms of S*, using advection asindicated by the various constant pressure andmean temperature charts, as an aid in determiningthe expected change of the S* distribution.3. Check the consistency of this forecast with theforecast values of D on two or more of the constantpressure charts and by constructing pastagrams(usually on the space cross section itself) at severalpoints along the cross section.4. Determine, by simple addition, the value of Dat all desired levels and at the end points of eachdesired zone.5. Determine the cross wind, in knots, in thezones by simple subtraction of D values.6. Determine the direction of the wind at alllevels for which prognostic constant pressure chartsare drawn, and estimate the directions at all otherdesired levels.7. From the direction and cross component, determine the total wind speed.These calculations are simple enough so that theycan be accomplished in a short enough time to makethis procedure practical. However, it is very doubtfulif that would be the case if, say, millibars were usedas the parameter with which to specify pressure, sincethe conversion of units and multiplicative factorsnecessarily involved in the calculations are quite timeconsuming.Surface chart. If D is used as the parameter withwhich to express the pressure field in the upper air,D should also be used for analysis of the surface chartso that continuity and direct correlation of surfaceand upper-air conditions are possible. The use of Das the pressure parameter on the surface chart alsohas several advantages over using the "sea level"pressure expressed in millibars.From the principle that the primary. purpose ofmaking a pressure analysis is to represent the hori64 . JOURNAL OF METEOROLOGYzontal wind field, it follows that the pressure analysisshould provide as accurate and easy solutions of thegradient wind equation as possible. In general thesea-level pressure map is unsatisfactory for this purpose since the extrapolations to sea level are made byassuming that the mean temperature of the fictitiouscolumn down to sea level depends on the temperatureobservations at the surface. Hence the "sea level" mapis a function of the temperature of the air as well asthe pressure so that, especially for high plateau regions, the sea-level pressure pattern is distorted byhorizontal temperature gradients as compared withthe actual pressure pattern occurring at the surface.In contrast to this, for any set of observations madeat approximately the same elevation, an analysis interms of the observed values of D at the surfaceaccurately represents the actual pressure field at thatmean elevation, since D remains constant for hydrostatic extrapolations through short vertical distances.If desired, the surface chart in terms of D can alsobe considered as a sea-level chart in which the extrapolation assumption is that the temperature of theair is always the same as the standard temperature.Similarly, if desired, the surface D analysis can alsobe interpreted as a contour chart of the z, = 0 constant pressure surface. It seems, however, that themost direct interpretation, not involving the idea ofextrapolations, is to consider the surface D chart asdirectly representing the conditions occurring at thesurface of the earth, and then the geostrophic windrelationship can be directly applied to any approximately horizontal region of the chart. This interpretation of D has direct meaning for flying personnel,surveyors, etc., since the value of D is then thealtimeter correction, which can also be used as analtimeter setting applicable to the surface.The use of D as the pressure parameter on the surface chart also simplifies the required conversionsfrom (or to) the parameters in which pressure isactually measured. For this purpose a table could bemade for the particular elevation z of any given station, giving the direct conversion from inches or millimeters of mercury to feet or meters of D, as desired.This conversion is simpler than the customary reduction to sea-level pressure in millibars since the temperature observations need not be considered. Evenfor mercurial barometer observations actually madeat sea level the use of Table 2a or 2b is in general asconvenient as a conversion table from inches ormillimeters of mercury to millibars. Of greater importance is the possibility of always being able todetermine easily the actual pressure observationsthat were made at any given station from the reportsof the value of D at that station. A convenient methodof doing this is to subtract the reported value of Dfrom the height of the station, z, and to convert the.resulting value of z, to inches or millimeters of mercurywith Table 1. In general this conversjon is impossiblewith surface pressure reports in terms of the sea-levelpressure in millibars since the particular reductiontables, and even the temperatures used to enter thesetables, are not generally available. This factor is ofprimary importance since the introduction of thefictitious column of air in all sea-level pressure reportsmakes it very difficult, and usually (even impossible,to obtain accurate continuity and comparison ofsurface conditions with upper-air conditions.Figure 9 is an example of a surface chart analyzedin terms of these two pressure parameters. The solidlines are drawn for values of D at the surface and thedotted lines are drawn for values of the sea-levelpressure in millibars. This map, and many more, havebeen constructed by Lt. J. L. Clayton, U. S. ArmyAir Forces. This work has been quite difficult due tothe unknown extrapolations made in the reporteddata available. Special graphs were constructed toestimate the values of D at the surface from the surface temperature and the sea-level pressure reports inthose regions for which altimeter settings were notavailable. Unfortunately those regions included themountainous ones in which the only significant variations between the two methods of representation areto be expected. However, from this work it seemsthat, in general, the analysis in terms of D does moreclosely represent the gradient wind flow than does thesea-level pressure chart.AcknowledgmentThe author wishes to thank the members of theUniversity of Chicago, especially Mr. V. P. Starr, andthe University of Puerto Rico and many officers in theU.S.A.A.F. for their aid and encouragement in thiswork.REFERENCES(1) Brombacher, W. G.1935 Altitude-Pressure Tables Based on the United States Standard Atmosphere. tJ. S. National Ad visory Committee for Aeronautics, Report No. 538.1926 Standard Atmosphere-Tables and Data. U. S. National Advisory Committee for Aeronautics, Re port No. 218.Use of Pressure Pattern Flying Over the NorthAtlantic. Bull. Am. Met. SOC., Feb.Thermodynamics Applied to Air Mass Analysis.M.I.T. and Woods Hole Oceancgraphic InstitutionPapers in Physical Oceanography and Meteorology,Vol. 1, No. 3.(5) 1944 Determination of Absolute Height and Wind for Aircraft Operations. USAAF Weather Division Re port No. 708 (revised).(2) Diehl, W. S.(3) Hall, H. E. 1945(4) Rossby, C.-G.1932JOHN C. BELLAMY65PASTAGRAM FOR ZpR, S,PLATE I.66JOURNAL OF METEOROLOGYPASTAGRAM FOR zPm, S,STA.MM ~~~~8~223.4 TIME.UQL,I'.- . - I. I. -L' ' . 4478. . ... - .. - . . . ... . - I- 1.- 1- I--I . I--LfW-..I ! ! !,! : ! ! ! !L.! I I I I I I I I I IIll\I I #/I L,+I5 6(+5 3)+I 0 3(+5 9)+4 4PLATE 11.67PLATE 111.68JOURNAL OF METEOROLOGYPASTAGRAM FOR zOm,s, T'~.T~.~?PLATE IV.69PLATE V.70\J0UR'jNA;L OF METEOROLOGYPASTAGRAM FOR dmQ,eoA,+oA,PLATE VI.JOHN C. BELLAMYPASTAGRAM FOR wpncO ,dA, h%71PLATE VII.72JOURNAL OF METEOROLOGYPLATE VIII.JOHN C. BELLAMY73t.nW0c51)mi2w0LT51)t.ni20Ng- 0N30g-08e00- m8-- I8T00- ?80(uI06JIg- 74 JOURNAL OF METEOROLOGYdWa3JOHN C. BELLAMY75CDPYRIGHT 845 by WEbTHERMbSTERS, IN& 5608 INGLESIOE. WICAGO 3% ILL. FolM Ha JC8 45WOSPLATE XI.76 JOURNAL OF METEOROLOGYd bl .dd k5 4 6&dr31l!I &dr drP31an no n84 + Ti 35?ISOBARIC CONTOUR EXTRAPOLATION SCALEUPJOHN C. BELLAMYGEOSTROPHIC AND THERMAL WIND SCALENOIEi The aoshed latitude lines are to be used with ten times the labled value of either the spacing or the speed al-om77PLATE XIII.JOURNAL OF METEOROLOGY78W3taa2300sz0> 0a0 LL I2.'C0W >Iz04aWswv)+0zYz>uW>K0LLIc:c-JWcsaciaWaI)I>K30LL0v)3aaaaW3I4 >cc.3 0a0sz0>Iza0 LLL0aIr0W>czswaaaWJOHN C. BELLAMY79e

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