MAY 1994 JANJIC 927The Step-Mountain Eta Coordinate Model: Further Developments of the Convection, Viscous Sublayer, and Turbulence Closure Schemes ZAVI~A I. JANJI~*University Corporation for Atmospheric Research, National Meteorological Center, Washington, D.C.(Manuscript received 12 March 1993, in final form 9 August 1993) ABSTRACT The step-mountain eta model has shown a surprising skill in forecasting severe storms. Much of the creditfor this should be given to the Betts and Miller (hereafter referred to as BM) convection scheme and the MellorYamada (hereafter referred to as MY) planetary boundary layer (PBL) formulation. However, the eta modelwas occasionally producing heavy spurious precipitation over warm water, as well as widely spread light precipitation over oceans. In addition, the convective forcing, particularly the shallow one, could lead to negativeentropy changes. As the possible causes of the problems, the convection scheme, the processes at the air-water interface, andthe MY level 2 and level 2.5 PBL schemes were reexamined. A major revision of the BM scheme was made, anew marine viscous sublayer scheme was designed, and the MY schemes were retuned. The deep convective regimes are postulated to be characterized by a parameter called "cloud efficiency." Therelaxation time is extended for low cloud efficiencies, and vice versa. It is also postulated that there is a rangeof reference equilibrium states. The specific reference state is chosen depending on the cloud efficiency. Thetreatment of the shallow cloud tops was modified, and the shallow reference humidity profiles are specifiedrequiring that the entropy change be nonnegative. Over the oceans there are two layers: (a) a viscous sublayer with the vertical transports determined by themolecular diffusion, and (b) a layer above it with the vertical transports determined by the turbulence. Theviscous sublayer operates in different regimes depending on the roughness Reynolds number. The MY level 2.5 turbulent kinetic energy (TKE) is initialized from above in the PBL, so that excessiveTKE is dissipated at most places during the PBL spinup. The method for calculating the MY level 2.5 masterlength scale was rectified. To demonstrate the effects of the new schemes for the deep convection and the viscous sublayer, tests weremade using two summer cases: one with heavy spurious precipitation, and another with a successful 36-hforecast of a tropical storm. The new schemes had dramatic positive impacts on the case with the spuriousprecipitation. The results were also favorable in the tropical storm case. The developments presented here were incorporated into the eta model in 1990. The details of further researchwill be reported elsewhere. The eta model became operational at the National Meteorological Center, Washington,D.C., in June 1993.1. Introduction Mesinger (1984) proposed the so-called eta coordinate using a steplike mountain representation (seealso Mesinger and Janji6 1984, 1985, 1987). In contrastto the sigma coordinate (Phillips 1957), the eta coordinate surfaces are quasi-horizontal everywhere. At thesame time the simplicity of the sigma system lowerboundary condition is preserved. With the eta coordinate, three major problems canbe anticipated: (a) the internal boundaries at the ver * Current affiliation: Department of Meteorology, College ofPhysics, University of Belgrade, Belgrade, Yugoslavia. Corresponding author address: Profi Zavi~a I. Janji6, Departmentof Meteorology, College of Physics, University of Belgrade, P.O. Box550, YU-11001 Belgrade, Yugoslavia.tical sides of the mountain walls, (b) the code optimization, and (c) the physical package. The first twowere discussed by Mesinger et al. (1988). They imple-.mented the eta coordinate in the "minimum physics,"sigma coordinate HIBU (Hydrometeorological Institute and Belgrade University) limited-area model. Thismodel will be referred to as the "eta model." The etamodel is defined on the semistaggered Arakawa E grid(e.g., Mesinger and Arakawa 1976) and uses the technique for preventing grid separation (Mesinger 1973;Janji6 1974, 1979; Vasiljevi6 1982) in combinationwith split-explicit time differencing (Mesinger 1974;Janji6 1979). The horizontal advection used in themodel has a built-in strict nonlinear energy cascade control (Janji6 1984a,b; Janji6 and Mesinger1984). The problem of the physical package was addressedby Janji6 (1990) (see also Janji6 1988a; Janji6 et al.1988a; Janji6 et al. 1988b). The package was based onc 1994 American Meteorological Society928 MONTHLY WEATHER REVIEW VOLUME122the Mellor-Yamada level 2.5 scheme (Mellor and Yamada 1974, 1982), the Mellor-Yamada level 2 schemefor the "surface" layer (Mellor and Yamada 1974,1982) with a dynamical turbulence layer several metersdeep at the bottom, surface processes designed following Miyakoda and Sirutis ( 1977, 1983 ) and Miyakodaet al. (1986), fourth-order lateral diffusion with thediffusion coefficient depending on the deformation (cf.Smagorinsky 1963; Miyakoda and Sirutis 1977, 1983;Miyakoda et al. 1986) and the turbulent kinetic energy(TKE) (cf. Lilly 1962; Xu 1988), conventional largescale precipitation with evaporation, slightly modifieddeep and shallow convection schemes proposed byBetts (1986) and Betts and Miller ( 1986, hereafter referred to as the BM scheme or the BM formulation)~and the National Meteorological Center (NMC) version of the Goddard Laboratory for Atmospheres(GLA) radiation scheme (Davies 1982; Harshvardhanand Corsetti 1984). For additional details on the etamodel the reader is referred to the documentation prepared by Black ( 1988 ), Gerrity and Black ( 1987 ), andLazi6 and Telenta (1990). The most comprehensive testing, tuning, and furtherdevelopment of the model have been carried out atNMC, Washington, D.C. With varying resolutions andintegration domain sizes, the eta model has also beenimplemented in the tropics (Lazi6 1990, 1993a,b; Lazi6and Telenta 1990; Rogers et al. 1991 ), over Europe(e.g., Janji6 and Lazi6 1988), as well as in many othergeographical areas all over the word. An interestingfeature of the model is that little retuning is neededwhen the horizontal resolution is changed. As a matterof curiosity, the model was successfully run even with4-km grid spacing in a realistic simulation of a precipitation event over Sicily (S. Ni~kovi6 1993, personalcommunication). The "standard" resolution used in most runs was80 km in the horizontal and 16 layers in the vertical.The model atmosphere extended up to 100 hPa. Thedepths of the layers slowly increased from the groundup to the middle of the atmosphere and then decreasedas the top of the model atmosphere was approached.The "standard" integration domain covered the NorthAmerican continent and the adjacent waters. For thisregion, the NMC products were used in order to specifythe initial and the boundary conditions, as well as forthe verification. As a robust, quick-response tool, themodel with the standard resolution and the standardintegration domain was also used for the experimentsdiscussed in this paper. Note that increased resolution and approximatelyequidistant eta coordinate surfaces are needed in thelower troposphere in order to resolve the mountainswell and to treat the interaction between the atmosphere and the underlying surface approximatelyequally well over both low-lying and elevated terrain.Applying this principle with the standard vertical resolution, the height of the lowest model level above theunderlying surface--that is, the depth of the model"surface layer"--was about 150 m, and accordingly,the depth of the lowest model layer was about 300 m. Black and Mesinger (1989), Mesinger and Black(1989), and Mesinger et al. (1990) reported on furtherimprovements of the model. Among these, the schemefor the vertical advection of moisture was replaced bya scheme based on the piecewise linear method (PLM)approach (Carpenter et al. 1990), and the viscous interfacial sublayer between the surface and the atmosphere was added. In addition, the convection schemewas revised and retuned in cooperation with Betts. Finally, due to technical reasons the GLA radiationpackage was replaced by the Geophysical Fluid Dynamics Laboratory (GFDL) scheme. The results of the tests carded out at NMC werepresented by Black and Janji~ (1988), Black and Mesinger ( 1989, 1991 ), Black et al. ( 1989, 1990), Mesingerand Black ( 1989, 1991 ), Mesinger et al. (1990), Rogerset al. ( 1991 ), and Ward (1990). In most of these studies, special attention was paid to precipitation as animportant prognostic variable, which is perhaps mostdifficult to predict accurately. In the periods considered,the eta model generally had a considerable advantageover the operational NMC regional precipitation forecasts produced by a sophisticated model with comparable resolution over North America and adjacent waters and requiring about the same computational effort.Concerning the synoptic features, an overall impressionwas that the main advantage of the eta model over theoperational NMC regional forecasting system wereimproved predictions of major storm systems (e.g.,WGNE 1989, 1990). In the tropics the model was tested in 48-h simulations of the tropical cyclones from the AustralianMonsoon Experiment (AMEX) period (Lazi~ and Telenta 1990; Lazifi 1990, 1993a,b). From the synopticpoint of view, the results were considered as remarkablygood, both in absolute terms and compared to the results obtained with other models (Lazi~ and Telenta1990; Lazi~ 1990, 1993a, b).-In the NMC quasi-operational and experimental runs the model also showeda surprising skill in forecasting the development, deepening, and subsequent movement of tropical stormsin the warm part of the year (e.g., Black et al. 1989;Mesinger et al. 1990; Ward 1990; Rogers et al. 1991 ). Undoubtedly, much of the credit for the successfulforecasts of the precipitation and the storm systemsshould be given to the BM convection scheme and theplanetary boundary layer (PBL) formulation. However, the tests revealed that on some occasions themodel tended to produce heavy spurious precipitation,particularly over warm water. Although the precipitation over the oceans could not be verified due to thelack of observations, indirect evidence, such as developments of spurious lows, suggested that the precipitation was too heavy.MAY 1994 JANJIC 929 This problem has been known for some time, andthe aforementioned modification of the vertical advection of moisture, the reformulation and retuning ofthe convection scheme, and the introduction of theviscous sublayer were actually aimed at coping with it.Although significant improvement was achieved, theoccasional heavy spurious precipitation would not goaway, impairing severely the forecasts when it showedup in full strength. Another problem that the eta modelshared with many other models was widely spread excessive light precipitation over water. Both problems could be dealt with by an ad hoctechnique for reducing the surface fluxes. It was felt,however, that an indiscriminate reduction of the fluxescould impair the ability of the model to handle thesevere storms. To examine the problems involved andto test the techniques developed, two extreme summercases were chosen. In the case starting at 0000 UTC20 July 1989, an unsuccessful 48-h forecast with heavyspurious precipitation was obtained. In contrast to that,in the case of 0000 UTC 31 July 1989, the version ofthe model run quasi-operationally at NMC produceda successful 36-h forecast of the Tropical Storm Chantal(Black et al. 1989).2. Excessive precipitation and other problemsa. Heavy spurious precipitation In the case of 20 July, a single grid point was selectedfor a closer inspection in the middle of a heavy spuriousconvective precipitation area in the Gulf of Mexico.At this point a strong instability existed in the surfacelayer even in the initial data. The difference betweenthe virtual potential temperatures at the top of the surface layer and the sea surface was -2.52-C. As can beinferred from the example shown in Fig. 1, later on inthe forecast the perpetuation of the instability seemsto have been assisted, if not caused, by the deep convection. In the figure, the model temperature profile isshown (diamonds connected by solid line) after 505time steps, or about 34 h of forecast time, together withthe BM reference profile in the previous call of theconvection subroutine (squares connected by the solidline). As can be seen from the figure, the convectionscheme produces a strong cooling at the cloud bottom(model level 15 ) and quite modest warming at upperlevels. The PBL schemes respond by producing largeexchange coefficients trying to remove the instability.In the surface layer, the Mellor-Yamada level 2 exchange coefficients for heat (and moisture) and momentum [cf. Janji6 1990, Eqs. (4.6) and (4.7)] wereKmf- = 22 m2 s-~ and KMsfc = 17 m2 s-~, respectively.At the top of the lowest model layer (the interface ofthe model layers 15 and 16), TKE and the MellorYamada level 2.5 heat (and moisture) and momentumexchange coefficients [cf. Janji6, 1990, Eqs. (3.4)]reached q2~516/2 = 0.2 m2 s-z, Ktt,s,6 = 89 m2 s-l,and Ka4,s,6 = 36 m2 s-I, respectively. As a result, theheat and moisture were transferred upward, warming(and moistening) the cloud bottom and at the sametime cooling (and drying) the subcloud layer, therebyincreasing the instability of the surface layer. In thenext call of the convection, the cloud bottom is cooledand dried again.b. The deep convection scheme over water: Diagnostics and sensitivity tests The performance of the deep convection schemeover water is especially interesting because a virtuallyunlimited supply of latent and sensible heat is available.In the present study, the "entropy change"V 308.0 ~07,2t 306.4 305.6P 304.80 t 304.0 303.2r 302.40m 301.6P 300.8 300.0Point IB!:5, 6ulf, ntsd=505 12 13 14 15 16 sfc I~lodel level (from top to bottom) ~> I'lodel Prof, nRef. Prof. (t-D FIG. 1. The temperature profile at a point with heavy convective precipitation (diamonds)after 505 time steps, or about 34 h of forecast time, and the convective temperature referenceprofile in the previous call of the convection subroutine (squares).930 MONTHLY WEATHER REVIEW VOLUME122was introduced as a diagnostic quantity. Here, thesummation is performed from the cloud top to thecloud bottom, Ap are the depths of the model layersin terms of pressure, and cv and Lwv are the specificheat at constant pressure and the latent heat of thewater vapor transition, respectively. The symbols ATand Aq denote the changes of temperature and specifichumidity within a convection time step At; that is, At AT= (Tref- T~)-, Tcipitation). Typically, the more precipitation is produced by the large-scale precipitation the better. (iv) There was a positive impact of switching offthe convection when the large-scale precipitation starts. (v) Finally, asomewhat less well-defined sensitivitywas found to the specification of the reference cloudbottom and freezing-level humidity. However, none of the listed devices, separately orcombined, proved to be capable of eliminating or sufficiently reducing the spurious precipitation and at thesame time preserving to an acceptable extent the skillof the model in forecasting strong convectively drivencirculations. At Aq = ( q,~r - .q'~) -- . (2.2)In (2.2) the subscript refindicates the equilibrium reference profiles (Betts 1986 ), the superscripts n denotethe values of temperature and specific humidity at themodel levels at the beginning of the time step, and 7'is a constant relaxation time (Betts 1986). The temperature T appearing in the denominator of (2.1) isdefined as the mean Over the time step; that is, AT T = T" +--. (2.3) 2 At the chosen steady convective point over the sea,the entropy change (2.1) was decreasing with timeeventually approaching zero, while the precipitationAPB produced in a time step was increasing. The ratioof AS/zXPB was about 50 times larger at the beginningthan at the end of a 48~h forecast. This may be viewedas a process that in the limit approaches an adiabaticregime resembling that of the large-scale precipitation,except for the fact that the precipitation occurs at muchlower threshold values of relative humidity. In addition,on rare occasions, nonzero precipitation was observedaccompanied by a negative entropy change. In suchcases the deep convection was aborted, similarly as inthe case of the negative precipitation (Betts 1986). The sensitivity tests revealed that suppressing thedeep convection had a generally positive impact on thespurious precipitation. For example: (i) Increasing the relaxation time 7', the amount ofthe spurious precipitation could be considerably reduced in the case of 20 July. However, in some. othercases, overextending the relaxation time led to the replacement of the heavy spurious convective precipitation by the heavy spurious large-scale precipitation. (ii) The scheme showed sensitivity to restrictionswith respect to the stability of the reference profiles,primarily at higher levels. (iii) Sensitivity was also detected in the distributionof the precipitation between the convection and thelarge-scale precipitation (controlled by the thresholdrelative humidity for the onset of the large-scale prec. The shallow convection scheme problems A rather disturbing feature of the BM shallow convection scheme was first discovered in the NMC medium-range forecasting system. It was noticed that theshallow convection may transport both moisture andheat downward (M. Iredell 1989, personal communication). The early response to the problem was justto abort the convection if the reference profile is lessstable than the model profile. The entropy change test introduced later in the etamodel revealed that on many occasions the shallowconvection was associated with decreasing entropy.This was particularly the case at the points where thedeep convection algorithm was replaced by the shallowone because of negative precipitation (Betts 1986). Inthe BM scheme jargon, such points are called swappoints. The number of points passing the test increasedwhen the modification above the cloud top introducedto represent the inversion (Betts 1986) was excludedfrom the entropy change calculation.d. Identification of possible problem areas Concerning the excessive precipitation, two mostlikely scenarios emerge as candidates for closer inspection. 1 ) The spurious convection fuels itself by creatingtoo strong thermal instability below the cloud bottomand thus forcing the PBL schemes to transport toomuch heat and moisture from the underlying oceansurface. 2) There is a physical mechanism limiting the vertical turbulent fluxes, but the PBL schemes fail to reproduce this mechanism properly, so that excessiveheat and moisture are supplied to the convectivecolumn. Evidence was accumulating suggesting that insteadof retuning and/or minor modifications, a more substantial revision of the convection scheme might bedesirable. The ad hoe techniques tested in section 2bfailed to eliminate or sufficiently reduce the spuriousprecipitation and at the same time preserve the abilityMAY 1994 JANJI~ 931of the model to forecast strong convectively driven circulations. The negative entropy changes, associatedparticularly with the shallow convection, could hardlybe considered acceptable in a process that was assumedto be thermodynamically driven. The arbitrariness ofthe shallow cloud top specification at the swap points(Betts 1986) was another unattractive feature of thescheme. On the other hand, the PBL could not be accusedof all the difficulties. If a layer of air is kept at a constanttemperature and humidity at the bottom and constantly cooled and dried at the top, the PBL schemesrespond by producing large turbulent fluxes trying toremove the superadiabatic (in terms of the virtual potential temperature) lapse rates. One should recall thatin many situations the ability of the PBL to generatelarge turbulent fluxes leads to spectacular forecasts ofstrong convectively driven circulations. Nevertheless,the question whether and under what conditions theturbulent fluxes can be overestimated by the PBL certainly requires careful examination. This applies alsoto the viscous sublayer at the air-water interface. Thus, the following three major areas requiringcloser examination were identified: 1 ) the deep and shallow convection schemes, 2) the processes at the interface between the sea andthe air (the viscous sublayer), and 3) the Mellor-Yamada level 2.5 and level 2 turbulence schemes used above the surface layer and inthe surface layer, respectively.3. Revised convection schemea. Deep convection Within the BM concept, the deep convection isviewed as a thermodynamically driven process thattransports the heat and moisture upward in order toremove or reduce the conditional instability. The precipitation is produced in the process. These verticaltransports of heat and moisture will be called "convective mixing" or just "mixing." The entropy changeAS defined by (2.1) will be used as the measure of theintensity of the mixing. Note that with total enthalpyof a column unchanged, a negative change of enthalpyat lower levels and a positive one at higher levels resultin a positive entropy change since the temperature isgenerally decreasing with height. With the revised scheme the concept of the convection as a process of basically thermodynamic nature isretained. As already discussed in the preceding section,the convective columns over the sea, which eventuallydevelop heavy precipitation, evolve through a range ofconvective regimes. One of the basic postulates of therevised scheme is that the basic features of these regimescan be characterized by a parameter that will be called"cloud efficiency." This parameter is defined by E =constl (3.1) cv 2~ ATAp'Here, consh is a nondimensional constant and P isthe mean temperature of the cloud ~ _- Z (r~ + Ar/2)/Xp, (3.2) Pbot -- Ptopwhere the subscripts hot and top denote the values atthe cloud bottom and at the cloud top. The expressionappearing in the denominator of (3.1), cv ~ ArAp = APB (3.3) const2 'is proportional to the single time-step precipitationas defined in the BM formulation. As can be seen from(3.1)- (3.3), the cloud efficiency is proportional to themean cloud temperature and the entropy change andinversely proportional to the BM single time-step precipitation. It does not depend on the ratio of At and r,except through the mean temperatures in (2.3) and(3.2). This dependence can be disregarded since thetemperature changes AT/2 are two to three orders of'magnitude smaller than the temperatures T". Alternatively, Tin (2.3) and (3.2) could be replaced by T",but as can be easily verified, the impact of this modification would be negligible. Note that E is a nondimensional parameter. The efficiency it measures is theability of the convective column to transport the enthalpy upward and at the same time produce as littleprecipitation as possible. With the experience reported in the preceding section, it seems natural to relate the convective regimedefined by th9 cloud efficiency with the convectiveforcing. Thus, an assumption is made that the convective forcing is proportional to an increasing functionof the cloud efficiency F(E); that is, starting from (2.2), atF( E) AT = ( Tre~ - T~) ~, T AtF(E)aq = (qref - q~)~, (3.4)or At AT= (rref -- Tn) r/F(E------"~' At Aq = (qref - qn)_ (3.5) r/F(E) 'As can be seen from (3.5), the modification (3.4) canbe interpreted as a new definition of the relaxation time rx F(E) ' (3.6)where r is a constant as before. Note that the relaxationtime (3.6) is increasing with decreasing cloud efficiency,932 MONTHLY WEATHER REVIEW VOLUME 122and vice versa. Depending on the relaxation time, theconvective regimes will be considered "fast" or "slow." With the new definition of the relaxation time, thesingle time-step precipitation takes the formorAp = APBF(E), (3.7) AP = const2[ ~ cp(Trer - Tn)Ap] At (3.8) TIRecalling point (i) of section 2b, the decision to defineF as an increasing function of E seems to be a step itthe right direction. In this way, the heavy precipitationis slowed down in the case of the low cloud efficiency,which appeared beneficial in some cases. Concerningthe form of the function F, with the present knowledgeone has'little choice butto use th'e first-order approximation, that is, to assume it to be linear. Note thatthe formulas (3.4)- (3.8) are identical to the standardBM formulas for F = 1. As the major deviation from the original concept ofthe BM scheme, it is further postulated that there is nosingle convective equilibrium state but rather a rangeof equilibrium states toward which the column shouldbe forced in the course of its convective history. In thisregard two fundamental questions arise. 1 ) What are the characteristics of various convectiveequilibrium states, and how should they be representedin the parameterization scheme? 2) What are the large-scale parameters, if any, controlling the transition from one regime to another? The temperature profiles proposed by Betts (1986)seem to be a rather steady feature of the deep moistconvection. In contrast to that, as can be inferred fromthe Betts (1986) data, the observed humidity profilesare more variable. Thus, it is assumed that the humidityprofiles are the main identifying features of the differentconvective equilibrium states. As in the BM formulation, constructing the firstguess reference profiles, the moisture is expressed interms of dsp = P~t - P,where p is pressure at a model level and Psat is the saturation pressure in the dry-adiabatic ascent startingfrom that level. Concerning the choice of the parametercontrolling the transition between the equilibriummoisture profiles, it is again assumed to be the cloudefficiency; that is, dsp~ef(p) = G(p, E).Here, the superscript 1 followed by the subscript refdenotes the first-guess reference profile. To incorporatethis assumption into the parameterization scheme, twoextreme dspr~ef profiles are defined, corresponding, respectively, to (a) a drier, faster (in the sense of therelaxation time), predominantly mixing stage with highcloud efficiency and to (b) a mature, moister and slower(in the sense of the relaxation time), predominantlyrainmaking stage with low cloud efficiency. In eachtime step, the equilibrium dsp~-f's are assumed to bedefined in between these two profiles by the functionG(p, E). Concerning the form of function G, fromwhat has been said, dsp~ef'S should be decreasing withincreasing cloud efficiency,, and as in the case of thefunction F, one has little choice but to assume G tobe linear. As in the BM formulation, the final referenceprofiles are constructed by requiring that the enthalpyof the equilibrium reference state be the same as thatof the model. In practice, the constant consh appearing in the definition of the cloud efficiency (3.1) is estimated experimentally. The value that has been used for sometime in the eta model is consh = 5. Also, an upper anda lower limit are imposed on E; that is, El < E < E2.With the chosen value ofconsh, E2 is set to 1, and thelower limit El = 0.20 is determined empirically. Inaddition, in order to prevent the two-grid-interval oscillation in time, the cloud efficiency used in the actualcalculations is defined as aE~* + bE~-l En = a + b = 1, (3.9) 2 'where En* is given by (3.1). The values chosen are a= b = 0.50. The function F(E) is defined bywhere E is obtained from (3.9). The experimentallydetermined extreme values F~ = 0.70 and F2 -- 1 correspond to the extreme values of the cloud efficiencyEl and E2. For example, with these values, for theminimum cloud efficiency E~ the equivalent relaxationtime (3.6)increases to rl = 4285 s compared to 3000s corresponding to the maximum cloud efficiency E2.Similarly,dspr~er(p) = dsp~ef~(p) + (E [dsper2(p) - dsp~fl(p) ]As before, the subscripts 1 and 2 represent the twoextreme profiles, E is the cloud efficiency, and the superscript 1 followed by the subscript ref denotes thefirst-guess reference variables. However, since thedsp~r's have to be defined before the final referenceprofiles are constructed, the cloud efficiency from theprevious time step, that is, En-~, is used in the aboveformula: The vigorous mixing stage is assumed to be.characterized by relatively dry profiles, while a moisterprofile is used for the "decaying," rain-making stageapproaching the pseudoadiabatic large-scale precipiMAY 1994 JANJIC 933ration process. In the case of the extreme fast (in thesense of the relaxation time) equilibrium profile, atthe three characteristic levels of the BM scheme, thecloud bottom, the freezing level, and the cloud top,dsp~ef2's are -38.75, -58.75, and -18.75 hPa, respectively. For the extreme slow (in the sense of therelaxation time) equilibrium humidity profile, the I ~dspree, s are proportional to those for the fast profile,where the factor of proportionality is of the order ofFs = 0.60. If negative precipitation is encountered, the deepconvection is aborted and the shallow convection isattempted (the swap is performed). The same is donein the case of the negative entropy change, even if theprecipitation is positive. In the tests a considerable sensitivity was found withrespect to the choice of the humidity profiles and thelower limit for the cloud efficiency. Generally, moisterslow profiles are more effective in reducing the convective precipitation and turn it earlier into the largescale precipitation. The reduction of the convectiveprecipitation can be explained by increased storage ofwater in the column and the reduced gradient of thespecific humidity between the cloud bottom and thelevel below. In addition to the increased equilibriumstate humidity in the column, a smooth transition tothe large-scale precipitation is presumably further facilitated by the extended relaxation time that allowsthe column to reach the threshold value for the onsetof the large-scale precipitation earlier. Early attempts to apply a unified convection schemefor both sea and land resulted in a slight degradationof the precipitation scores over land. Since the situationwas not clear, at that time no modification of the BMscheme was made over land.b. Shallow convection As in the case of the deep convection, a number ofmodifications have been introduced into the shallowconvection scheme. Instead of prescribing arbitrarycloud tops at the swap points, the shallow cloud topsare identified by the jump in the relative humidity (assuggested by Betts). This procedure is extended alsoto the regular shallow convection points in order touse everywhere the same parameterization scheme forthe same physical process. Note that the stability changecould also be used for defining the cloud tops. Shifting the cloud top one level up and applying thespecial technique for defining the tint-guess referencevalues of temperature and moisture in order to represent the inversion (Betts 1986) was abandoned. Theclouds with enhanced and modified cloud tops failedthe entropy change test much too often. Except for the level above the cloud, the first-guesstemperature profile is again obtained following the BMformulation. Since the precipitation is not allowed, asbefore, the final reference profiles are obtained enforcing separately the enthalpy conservation for T and q(Betts 1986). Thus, the final reference profile for temperature can be constructed independently from thehumidity profile. The major deviation from the BM scheme is againthe procedure used for constructing the reference humidity profiles. Closer inspection of the Betts (1986)data reveals that the humidity profiles depend on thestability of the temperature profiles. Less stable temperature profiles are associated with higher relative humidities at upper levels, and vice versa. Thus, eventhough the interpretation of the constant dsp profilesin terms of relative humidity is not straightforward,the prescription of constant dsp's in the original formulation seems to be too crude. In addition, if theassumption that the shallow convection is a thermodynamically driven process is still to be valid, a reference profile defined in this way should be consideredpreliminary until the point passes the entropy' changetest. The basic idea was that the requirement for the positive entropy change should be incorporated into thespecification of the humidity profile rather than constructing a "trial" profile hnd then testing it for theentropy change.' Thus, if ASr= ~ [cv(Tr~: T~)] Ap, (3.10) ASq= ~ - -[Lwv(qr~--qn)]Ap, (3.11) ~ 1 Tree + T" 2 ' (3.12) r~it is required that ASr + /XSq =/5, (3.13)where b is a nonnegative number still to be determined. The equilibrium moisture profile is defined as a linear function of a suitably chosen function of pressureQ(p); that is, qref = qreftop q- c[Q(p) - Q(ptop)], (3.14)where Oqref C -- -- = const, (3.15) OQ(p)and the subscript reftop denotes the value on the reference profile at the cloud top. The two unknown constants in (3.14), qreftop and c, can be determined from(3.13) and the requirement ~ qreeAp = ~ q~Ap, (3.16)following from the enthalpy conservation constraint(Betts 1986). Namely, taking into account the definitions (3.11 ) and (3.12), the entropy change formula(3.13 ) can he rewritten in the form934 MONTHLY WEATHER REVIEW VOLUME 122 [['2Lwv(qrEYref q- qn)] ~n ap -- - aSr + &Combining this formula with (3.16) and (3.14), aftersome algebra, one obtainsallqrcttov + al2c = Aa21qreftov -t- a22c = B,whereall ~--- Z(3.17) T=f + T~' ap a~2 = ~ [Q(p) - Q(ptoP)] Trcf + T~ a2~ = ~ gkp; a22= Z [Q(P)-Q(ptov)] Ap - ,xSr + b q~,Xp - -A= 2Lwv + Z T~r + Y~' B=Zq~'XP' (3.18)From (3.17) and (3.18), the unknown constants q~enovand C are easily calculated. After testing several otherpossibilities, the function Q(p) = T=r(p) was chosen. The yet' unanswered question is that of the specification of the entropy change ~ in (3.13 ). According toBetts ( ! 986) and Betts and Miller (1986), the shallowconvection is a Process operating between buoyant lowlayers and an inversion aloft. The inversion preventsthe occurrence of the penetrative convection. Themoisture is transported upward and the heat is transported downward. Note that this requires that in (3.13 ).the contributions of the heat transport (3.10) and themoisture transport (3.11 ) be of the opposite signs, thatis, negative and positive, respectively- Thus, the shallowconvection maintains a delicate balance with a low (ifany at all') entropy yield 6. One Of the major concerns with the BM shallowconvection scheme was to tune it in such a way as toprevent collapsing of the inversions into the saturatedsurface layers. The revised shallow convection appearsto be less on the defensive side in this respect. In the48-h integra.tions of the eta model the cloud tops wereslowly rising and the inversions were strengthening withtime. The effect on the vertical moisture transport couldbe detected indirectly through the changes of the pre:cipitation intensity and pattern. All these featuresshowed sensitivity to the specification of 6, which thusappears to be a Convenient tuning parameter. As onewould expect, by reducing 6, the rising and strengthening of the inversions, as well as the precipitation areaand intensity, were reduced- In practice, the positive contribution of ~XSq definedby (3.11 ) is required to be ( 1 + t~) times the absolutevalue of the negative contribution of ,xSr defined by(3Ji0), where' t~'= 0.05. Thus, b is actually relatedto I/x&-I. Numerical experimentation revealed that even withthe revised scheme there are still conditionally unstableregimes other than the BM deep convection that donot fit into the described image of the shallow convection. In such cases the shallow convection is aborted.For example, zkSr can be positive. Also, with Q(p)= T~ef(p), the scheme obviously does not work in anatmosphere approaching the isothermal one. The negative slope of the reference humidity profile c, the supersaturation (according to the criterion for the onsetof the large-scale precipitation), and the too unstablereference virtual potential temperature profiles (assuggested by Betts) are not allowed. In addition, anabsolute upper limit for the shallow cloud tops had tobe introduced somewhat above the 500-hPa level. Itwas found that computational instability may developover elevated terrain if this limit is exceeded.4. Surface fluxes and PBLa. Viscous sub/ayer.' Genera/approach As reported by Mesinger et al. (1990), a viscoussublayer was incorporated into the eta model followingDeardorff (1974) and Zilitinkevitch (1970). This formulation was subsequently replaced by a more daborate and effective one as described herein. The viscous sublayer is allowed to operate only overwater. The reason for this is that over land a soil slabof finite depth is used in order to describe the evolutionof the variables at the lower boundary, so that it is notthe surface variables that are used to estimate the surface fluxes but rather the mean values representativeof the slab. Following Liu et al. ( 1979, hereafter referred to asLKB), in the immediate vicinity of a smooth surface[LKB, Eq. (8)1, [ ( Uo- Ux=O~ 1-exp O--Ox=D2[1-exp(- zu'llrFol'~-~2X]j\zt./ (4.2,Here, the subscript $ denotes the surface values; thesubscript 0 (for the time being) indicates.the values ata height z above the surface where the molecular diffusivities are still dominant; Dl, D2, and D3 are parameters to be discussed in more detail later; u. is the friction velocity; v, x, and X are the molecular diffusivitiesfor momentum, heat, and water vapor, respectively;and Fv, Fo, and Fq are the turbulent fluxes of momentum, heat, and water vapor above the viscous sublayer. For a small argument ~' of the exponential functionsin (4.1)-(4.3),MAY 1994 JANJI~ 935 Z. UII, = :2'oU, Zqlt, ~- -- ~', (4.4) D~v D2X D3X 1 - exp(-D ~ ~', (4.5)so that, using (4.4) and (4.5), (4.1)-(4.3) can be approximated by Uo-Us=(~)Fv, (4.6) 0o-0~= (4.,, Ix%. qo-qs=\xIHere, the heights zu, zo, and Zq are defined by (4.4);that is, ~'vDt zv - , (4.9) ~XD2 zo - , (4.10) ~XD3 zq = ~ (4.~)At this point the following simplifying modeling assumptions are made. * There are two distinct layers: (i) a thin viscous sublayer immediately above the surface, where the ve~ical transpoNs are determined entirely by the molecular diffusion, and (ii) a turbulent layer above it, where the ve~ical transpo~s are defined entirely by the turbulent fluxes. ~ The depths of the viscous sublayers for the re spective physical variables are defined by (4.9) (4.11 ) for a chosen fixed value of ~.Note that with the definitions of the depths of the viscous sublayers (4.9)-(4.11 ) the values of the relevantphysical quantities at the interfaces of the viscous andthe turbulent layem are those denoted by the subscript0 in (4.6)-(4.8). Using the Mellor-Yamada level 2 discrete momentum and heat exchange coefficients, K~st~ and Knst~,respectively [cfi Janji6 1990, Eqs. (4.6)-(4.7)], theturbulent fluxes in the surface layer above the viscoussublayer are represented by Fe ~ (U~m - U0), (4.12) Fo = ~ (01m - 00), (4.13) F~ = ~ &z~ (qlm -- q0)- (4.14)Here, the subscript lm denotes the variables at the lowest model level, Aze is either the equivalent height ofthe lowest model level that takes into account the presence of the "dynamical turbulence layer" at the bottomof the surface layer (Janjifi 1990), or simply Z~m - Zoas in a later modification (Mesinger and Lobocki1991 ). In the shallow dynamical turbulence layer theratio of the height z and the Monin-Obukhov lengthscale (Monin and Obukhov 1954) is small so thatthe logarithmic profiles are used [cf. Janji~ 1990,Eq. (4.8)]. Substituting (4.12)-(4.14) into (4.6)-(4.8), oneobtains ~U (wO -- US) = \-~2e ] (Wlm- w0)' (4.15) ~o (0o - Os) = \ AZe (0,m -- 00), (4.16) ~q (qo -- as) = \ Aze ] (qlm -- q0)- (4.17)Note thin (4.15)-(4.17) reflect the requirement forthe continuity of the finim-difference fluxes across theinterfaces between the two layers. Solving (4.15)(4.17 ) for the vmables Mth the subscript 0, one obtains Us + [(KMsfcZU)/(P~Je)] $1m Uo = , (4.~8) 1 + (K~r~z~)/(V~Ze) O s + [ ( KHsfc ZO) / ( X ~Ze ) ] Olm 0o = , (4.19) 1 + (Kmr~zo)/(x~zO qs + [(KHsfcZq)/(X~Ze)]qlm qo = (4.20) 1 + (Km~cZO/(X~z~)Thus, the required lower boundaw conditions for theturbulent layer ~e expressed as weighted means of thev~ues at the surface and at the lowest model level.Note that (4.18)-(4.20), together with (4.9)-(4.11 ),represent a closed system provided the parameters D~,D2, D3, and f are known. The eta model surface layer ~th the viscous sublayerover the oceans is schemmically shown in Fig. 2. Inthe figure, Z~m is the heist of the lowest model leveland zi stands for the depths of the viscous sublayersfor momentum ze, heat zo, and moisture %. The viscous sublayer over the oceans is assumed tooperate in three differem re~mes: (i) smooth and transitional, (ii) rout, and (iii) rough with spray, depending on the roughness Reynolds number Rr - ZoU. '(4.21 )Here,0.11v 0.018 u~Zo= --+ -- (4.22)U, g936 MONTHLY WEATHER REVIEW VOLUME 122- vv vv~vvvvv~vv~ FIG. 2. The eta model surface layer with the viscous sublayer overthe oceans. The symbol zi stands for the depths of the viscous sublayersspray the breaking waves and the spray are assumedto provide a much more efficient way of exchange ofheat and moisture between the ocean and the air thancan be accomplished by the molecular viscosity. Notethat instead of in terms of Rr the boundaries betweenthe regimes can be also defined in terms of u,, sinceRr is a monotonic function of u,.b. Determination of the parameters For the parameters Di, D2, and D3 appearing in(4.1)-(4.3), LKB suggest [Eq. (11)] D~ = MRr~/4 (4.24) (4.25)D2 = MRr~/4 Pr~/2D3 = MRrv4 Sc~/2,(4.26)for momentum, heat, and moisture, and Zlm is the height of the lowest -,model layer. 'where Pr = v/x is the Prandtl number, Sc = v/X is theand = - Uo)J . (4j23) \ AZe ](U~m- Note that the definitions of z0 and u, have beenchanged compared to those'of Janji6 (1990). Theroughness length Zo as a function of u, is shown in Fig.3. When the Reynolds number exceeds a prescribedvalue Rrr the flow ceases to be smooth and the roughregime is entered. In the rough regime the momentumis transported also by pressure forces on the roughnesselements so that (4.1) loses validity (LKB). Consequently, the viscous sublayer for momentum is turnedoff. However, for heat and moisture, the viscous sublayer is still operating until the rough regime with sprayis reached at a critical value Rrs when the viscous sublayer collapses completely. In the. rough regime withSchmidt number, and M is a constant, but differentfor different regimes. With these definitions and thedefinition (4.21 ), (4.9)-(4.11 ) take the form zv = (4.27) u,L \ v / j ] zr = Pr]/2 (4.28) U,L \ v / Zq = u, L ~ v /For the smooth re,me L~ used the vMue of M, whichwas dose to 30. When the flow ceases to be smooththey surest the value of about 10, which fits best theMangamlla et ~. (1973) data. These two v~ues arealso applied in the eta model for the co~espondingre~mes. At the present level of approximation, thePrandtl number and the Schmidt number were as0.010000.00 ~ 0(0,0000.00001 0.01 0.06 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.51 0.56 0.61 0.66 0.71 0.76 U* , z0 FIG. 3. The roughness length Zo (m) as a function of u, (m s-~).MAY 1994 J A N J 1C 937sumed to be the same--that is, Pr = Sc = 0.71and the molecular viscosity for momentum was v= 0.000015. The molecular diffusion coetticients forheat and moisture, x and 3,, are determined by v, Pr,and Sc. Concerning the values of the Reynolds number atwhich the transitions between the different regimes occur, they are determined empirically. Subjectivelyjudged, the best results in the two cases considered wereobtained with Rrr = 3.4 and Rrs = 42, or in terms ofu,, with the values u,r = 0.30 m s-~ and u,s = 0.70m s-~, respectively. These values qualitatively agree inthe order of magnitude with the laboratory measurements (2-3 for Rrr and 50-80 for Rrs). A better agreement is probably hard to expect. With ~' -- 0,50, and the chosen values of the otherparameters, the depths (4.27)-(4.29) in meters areshown in Fig. 4 as functions of u, for various turbulentregimes. Note the changes of the regimes at U,r = 0.30m s-~ and u,s = 0.70 m s-~. In the practical implementation, u, for the currenttime step is calculated from (4.23) using K~usfc and U0from the previous time step. Thus obtained, u, is thenused in (4.22) to update z0. With the depths Zu, zr,and Zq being calculated from (4.27)-(4.29), the lowerboundary conditions for the Mellor-Yamada level 2surface layer U0, 00, and q0 can now be obtained from(4.18 )-(4.20) using KMsrc and Kmrc from the previoustime step. However, in order to prevent the two-gridinterval oscillation in time, the average values of Uo,00, and qo from the present and the previous time stepsare actually used.c. Mellor-Yamada level 2.5 As a deviation from the usual practice, in the etamodel TKE is initialized from above within the PBLin order to preserve the ability of the level 2.5 schemeto respond quickly to possible large thermal instabilitiesin the initial conditions and to speed up the PBLspinup. In this way the level 2.5 scheme is dissipatingexcessive TKE rather than producing it at most placesduring the PBL spinup period. An aspect of the level 2.5 scheme that was also reexamined in some detail is the definition of the masterlength scale l. As already pointed out, several methodshave been proposed for estimating this quantity (e.g.,Zilitinkevitch 1970; Mellor and Yamada 1974, 1982;Galperin et al. 1988). In the eta model the diagnosticformula [Mellor and Yamada 1974; Miyakoda andSirutis 1977; Janji6 1990, Eqs. (3.8)] of the form lo~zr I zlqdpl- -- lo = a a = const ~z + 10' j'ps ' qdp lOT (4.30)was used for some time. In (4.30), Ps and Pr are pressures at the bottom and at the top of the model atmosphere, respectively, t~ is the von Kfirmfin constant,and a is an empirical constant. Note that in the Blackadar formula [the first one in (4.30)] l tends to ~z forsmall z and to an asymptotic value lo when z becomeslarge. An upper limit was imposed on 10, and followingGalperin et al. (1988), in stably stratified flows l wasnot allowed to exceed 5 / 00\-~/2 o. 3q[~gTzz) +n, (4.31)where H was a positive constant. The Galperin et al.( 1988 ) formula alone [i.e., the formula (4.31 ) with H= 0 ] was producing too small values of l in unstable 0.1000n[o~fa 0.01 O(ceHe 0.001 (ights 1 o.ooo~ l',,,,,,,JJ'"'"lll',,,,,, ,,,,,,Jll'"'"'lJJl,,,,,,, ,,,,,,,,'lJJl'"'"'"lll',,,,,,,,,, ,,,,,,,',lt 0.0! 0.06 0.1! 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.51 0.56 0.61 0.66 0.71 1.1~ ~. zT,q ,', zUFIG. 4. The depths Zu, zr, and z~ (m) as functions of u, (m s-~) in various turbulent regimes. Note the jumps at u, = 0.30 and 0.70 rn s-~.938 MONTHLY WEATHER REVIEW VOLUME 122regimes. In addition to this technique, the methodstested in the eta model included those of Zilitinkevitch(1970), as well as Blackadar style formulas combinedwith prescribed constant 10, or l proportional to thevertical resolution at upper levels. A systematic overallimpact of the changes could not be identified as longas the values of/in the PBL were of the order of thoseobtained by Mellor and Yamada (1974) and Janji6(1990). The exception was very large l's within thePBL, which tended to make the precipitation problemworse. Thus, sufficient justification for abandoning ormodifying the method (4.30) could not be found, particulafiy in view of the rectification of the procedurefor the computation of lo'described in the next subsection.d. Mellor-Yamada level 2 and the surface fluxes Reexamining the performance of the surface layer,(as suspected by Betts) it was found that in near-neutralconditions with weak wind over water, the equivalentbulk aerodynamic coefficients estimated from the level2 fluxes could be several times larger than those measured under similar conditions. The only major difference was that the water temperature was 4-C in themeasurements and over 25-C in the experiments. As can be seen from Mellor and Yamada (1982) orJanji~ [1990, Eqs. (4.6) and (4.7)], for example, theturbulent exchange coefficients for momentum KMsfcand heat Knsfc are proportional to the square of thelength scale l. The length scale l was assumed to varylinearly with z reaching the value of the level 2.5 masterlength scale (4.30) and (4.31 ) at the top of the lowestmodel layer (Janji~ 1990). The most straightforward response to the problemwould be to impose an ad hoc low upper limit on l.However, as discussed previously, this was consideredto be a dangerous practice that could inhibit the abilityof the model to produce large surface fluxes needed tofeed tropical storms, for example. Fortunately, any action of this kind turned out to be unnecessary. Theproblem was found to be due to an inconsistency inthe implementation of the method (4.30) and (4.31 ).When calculating the integrals in the formula for 10,all values ofq were used, including those at the pointswhere q2 was set to its minimum allowed value. Thislower limit acts as zero for q2 and should not have beentaken into account. For example, if there is no TKEin the entire column, that is, ifq2 is set to its minimumvalue, the formula for l0 in (4.30) would neverthelessyield the maximum value. When this inconsistencywas removed, the level 2.5 l's were reduced, and therestriction (4.31 ) was lifted as it became unnecessary. With the near-neutral stratification of the marinesurface layer and the weak wind, a deep PBL does notdevelop, so that after eliminating the inconsistency,the level 2.5 l's obtained from formula (4.30) remainedwell below their prescribed maximum allowed values.Being calculated from the level 2.5 master length scale,the level 2 l's in the surface layer were considerablyreduced as well, so that the computed marine surfacefluxes dropped to, or below, the measured values.However, in order to be on the safe side, the parametera appearing in (4.30) was reduced to 0.075 over thesea. The problems with the surface layer and the PBLover land were different, so that a was increased to0.20 in order to avoid the reduction of the level 2.5master length scale and consequently the level 2/'s inthe surface layer. More specifically, during the coldpart of the year some cyclones with stable or nearneutral surface layers tended to overdevelop due toinsufficient surface friction. In such a situation, the reduction of the level 2/'s could only aggravate the problem. To avoid large underestimation of the level 2fluxes in the near-neutral conditions, particularly inthe marine surface layer, a lower limit was prescribedfor the level 2/'s. The described modifications had little effect on theforecasts. This is not surprising considering that therehas been little difficulty with the near-neutral marinesurface layers with weak wind. The problems have always been associated with strong thermal instabilities.5. Review of major experimental results The sensitivity to the reformulated shallow convection and the rectification and retuning of the PBLschemes were discussed in more detail in the corresponding subsections. One may recall that the revisedshallow convection had a detectable impact on theforecasts, while it was much less so with the PBLchanges. To demonstrate the effects of the reformulated BMscheme for the deep convection and the newly designedviscous sublayer scheme, two summer cases were used.Recall that in the case starting at 0000 UTC 20 July1989, an unsuccessful 48-h forecast with heavy spuriousprecipitation over warm water was obtained. As demonstrated by Black et al. (1989), in contrast to that inthe case of 0000 UTC 31 July 1989, the version of themodel run quasi-operationally at NMC produced asuccessful 36-h forecast of the development of theTropical Storm Chantal. In the control runs, the BMdeep convection scheme without the modifications wasapplied and the viscous sublayer was turned off. In Fig. 5, the verifying mean sea level pressure analysis valid at 0000 UTC 22 July 1989 is shown (leftpanel), together with the verifying analysis of the accumulated 24-h precipitation valid at 1200 UTC 21July 1989 (right panel). Note that the precipitationverifications are available only at 1200 UTC, and atthe time of the study were produced only over the eastern part of the United States. The verification datashown are defined on a grid with the resolution of about190 km. Nevertheless, the verification map can be usedat least for a qualitative assessment of the 36-h precipitation forecasts.MAY 1994 JANJIQ 939SEA LEVEL PRESSURE1000-500 THICKNESSVALID OOZ 22 JUL B9 O0-H ETA FCST LFr, GRiO'-1 ':~ .2q-HA RCCUM PRECIP [MM) V~RTF~CATTOXVALID 12Z 21JUL 89 LFMFIG. 5. Verifying mean sea level pressure analysis valid at 0000 UTC 22 July 1989 (left panel), and verifying accumulated 24-h precipitation analysis valid at 1200 UTC 21 July 1989 (right panel). The forecasts of the mean sea level pressure valid at0000 UTC 22 July 1989 obtained in the 48-h test runsare presented in Fig. 6. The control forecast with theBM deep convection scheme and without the viscoussublayer (upper left panel), the forecast with the reviseddeep convection but without the viscous sublayer (upper right panel), the forecast with the BM deep convection scheme but with the new viscous sublayerscheme (lower left panel), and the forecast with therevised deep convection and the new viscous sublayerscheme (lower right panel) are displayed. As can beseen from the figure, in the control run (upper leftpanel) a spurious cyclone with two closed isobars andthe central mean sea level pressure of 997 hPa developed over the northeastern part of the Gulf of Mexicoand adjacent southern states. The center of the cyclonewas at the coastline of the western part of Florida. Theobserved pressure at this location was about 1017 hPa.When applied separately, the revised deep convectionscheme (upper right panel) and the newly designedviscous sublayer scheme (lower left panel) each correctly shifted the center of the low westward, but therevised BM scheme more so than the viscous sublayer.The revised convection scheme (upper right panel) wasalso more successful in increasing the pressure in thecenter of the coastal low to 1007 hPa, as compared to1006 hPa in the case of the new viscous sublayer (lowerleft panel). The pressures at the location of the centerof the coastal cyclone in the control run were increasedby the two schemes by about 12 and 11 hPa, respectively. Both schemes developed secondary lows farthernorth over land: over Alabama in the case of the revisedBM scheme, and farther west over Mississippi in thecase of the viscous sublayer. With the two new schemesapplied in combination (lower right panel), the coastalcyclone and the northern low over land filled furtherand merged into an elongated weak trough extendingin the north-south direction. The pressure at the location of the center of the coastal cyclone in the controlrun increased by about 17 hPa to about 1014 hPa.Thus, with the two new schemes applied in combination, a good 48-h mean sea level pressure forecastwas obtained, which in the critical areas agreed withinabout 2 hPa with the verifying analysis shown in theleft panel of Fig. 5. The 36-h test forecasts of the accumulated 24-h precipitation valid at 1200 UTC 21 July 1989 are presented in Fig. 7. The control forecast (left panel) andthe forecast with the revised deep convection and thenew viscous sublayer scheme (right panel) are shown.In the control run, vast areas of sustained heavy precipitation developed over the sea by the second day ofthe forecast. The precipitation maximum off the coastof western Florida exceeded 210 mm. This heavy precipitation area extended to the southeast reaching thesecondary maximum of over 90 mm northwest off thewestern tip of Cuba. The third, smaller and more isolated maximum of over 50 mm was located off thecoast of the Carolinas. Light (and at places not so light)precipitation covered most of the west Atlantic andwas also spread over vast areas of the east Pacific. Thedescribed precipitation forecast over sea could not beverified due to the lack of the observed data. However,as can be seen from the verification map in the rightpanel of Fig. 5, at least in the southern and easterncoastal areas, as well as over western Cuba, the precipitation was generally largely overpredicted. At the sametime, the observed offshore precipitation maximumsouth of the Texas-Louisiana border did not appearin the forecast2 Farther inland, the precipitation washeavier than in the verification map over parts of Alabama and Georgia, and too light in the Carolinas.The precipitation was also too light in the tongue protruding from the northeast into Arkansas. In addition,940 MONTHLY WEATHER REVIEW VOLUME I22SER LEVEL PRESSURE (MS)IO00-500 MB THICKNESS (ORM) fiS-H ETR ?CST BH NOLK8SER LEVEL PRESSURE (MB)IO00-SO0 MB THICKNESS (ORM)VRLID OOZ 22 JUL 89 ~' - - '., ,,',.-,* '.~4.-. ~ '-.,,, ',,, ~ "~ , ~.,-.: 'qS-H ETR FCST MODOM NOLKB FlG. 6. Forecasts of m~an sea level pressure valid at 0000 UTC 22 July 1989 obtained in 48-h test runs starting from 0000 UTC 20 July1989. The control forecast with the BM deep convection scheme and without the viscous sublayer (upper left panel), the forecast with therevised deep convection but without the viscous sublayer (upper right panel), the forecast with the BM deep convection scheme but withthe new viscous sublayer scheme (lower le,ft p~nel ), and the forecast with the revised deep convection and the new viscous sublayer scheme(lower right panel) are displayed.the light precipitation over land did not cover a sufficiently large area. , As can be seen from the right panel of Fig. 7, withthe revised deep convection and ,the new viscous sublayer scheme, the areas of heavy precipitation over thesea disappeared. The heavy precipitation area appearing in the control run in the Gulf of Mexico was greatlyreduced. The precipitation maximum moved northacross 'the coastline of western Florida and decreasedto just over 40 mm. The'secondary heavy precipitationarea extending to the southeast in the Caribbean Seavanished. Only a'disconnected area of light precipitation was left over the western part of Cuba and adjacentwaters. The smaller, and more isolated maximum offthe coast of the Carolinas moved slightly northeast,toward Cape Hhtteras, and its intensity was reducedto just over 20 mm. Considerable areas of light precipitation over the oceans were mopped up, particularlyin the east Pacific. As can be seen from the verificationmap in the right panel of Fig. 5, the precipitation forecast in the southern and eastern coastal areas, as wellas over Cuba, was generally greatly improved. Theamount of the predicted accumulated precipitation inthese/treas agrees qualitatively with the observed values, although the observed offshore maximum southof the Texas-Louisiana border is still missing. The predicted value and the location of the maximum off thecoast of Carolinas were als0 improved. Farther inland,the precipitationwas still heavier than in the verification map over parts of Florida, Alabama, and Georgia,and too light in the Carolinas. A' qualitative improvement was achieved by producing more precipitationinside the tongue protruding from the northeast intoArkansas. However, the location of the newly develM^Y 1994 JANJ I(2 9412H-H RCCUM PRCCIP MM) 3G-H -TR FCST BM NOLCB 2q-H RCCUM PR~CIP (MMT 3G-H ~TR FCST MODBM LKB FIG. 7. Forecasts of the accumulated 24-h precipitation valid at 1200 UTC 21 July 1989 obtained in 36-h test runs starting from 0000UTC 20 July 1989. The control forecast with the BM deep convection scheme and without the viscous sublayer (left panel) and the forecastwith the revised deep convection and the new viscous sublayer scheme (right panel) are displayed.oped maximum exceeding 20 mm did not coincidewith that of the maximum in the verification map.Finally, as another step in the right direction, the areaof the light precipitation over land was visibly largerthan in the control run. In the case considered, the occurrence of the welldeveloped spurious low over warm water was accompanied by the unrealistically heavy precipitation. Thishas been no exception. As a rule, the development ofspurious lows over warm water coincides with heavyprecipitation. With the heavy spurious precipitation of the 0000UTC 20 July 1989 case under control, the questionarises as to whether the modifications introduced impair the ability of the model to forecast the heavy precipitation events such as tropical storms. To find out,the model was run starting from the 0000 UTC 31 July1989 data. At 1200 UTC 1 August 1989, the center of the Tropical Storm Chantal was off the coast of Texas, southof the Texas-Louisiana border (cf. Black et al. 1989;Climate Analysis Center 1989). Over the next 12 h,the storm advanced northwest across the coast of Texas,filling quickly. By 0000 UTC 2 August 1989, the centerof the storm was far inland, and the tropical cycloneturned into a weak low in the mean sea level pressurewith the closed 1008-hPa isobar (cfi Climate AnalysisCenter 1989). The 36- and 48-h forecasts of the mean sea levelpressure obtained in the test runs starting from 0000UTC 31 July 1989 are presented in Fig. 8. The 36-hcontrol forecast with the BM deep convection schemeand without the viscous 'sublayer (upper left panel),the 36-h forecast with the revised deep convection andthe new viscous sublayer scheme (upper right panel),the 48-h control forecast with the BM deep convectionscheme and without the viscous sublayer (lower leftpanel), and the 48-h forecast with the revised deepconvection and the new viscous sublayer scheme (lowerright panel) are displayed. In the 36-h control forecast(upper left panel) verifying at 1200 UTC 1 August1989 the cyclone was well developed. There were fiveclosed isobars, and the pressure at the cyclone centerwas about right (cf. Black et al. 1989). However, thesize of the vortex was overestimated. The center of thecyclone was over the sea, somewhat on the Louisianaside south of the Texas-Louisiana border. Over thenext 12 h of the control forecast, the cyclone was moving over water predominantly westward. It was fillingbut not quickly enough. In the 48-h forecast (lowerleft panel) verifying at 0000 UTC 2 August 1989, thecyclone finally reached the coast of Texas. However,the center of the cyclone stayed over water. In the 36-h forecast with the revised deep convectionand the new viscous sublayer scheme (upper rightpanel) verifying at 1200 UTC 1 August 1989, the cyclone was also well developed but somewhat less thanbefore. There were four closed isobars and the pressureat the cyclone center was slightly overpredicted (cf.Black et al. 1989). Note that one can hardly expectthe correct forecast of the central pressure with thehorizontal resolution of 80 km. The size of the vortexwas somewhat reduced compared to the control run.The center of the cyclone was still over the sea southof the Texas-Louisiana border. However, careful inspection reveals a slight improvement of the predictedtrack. Over the next 12 h of the forecast, the improvement of the track becomes evident. The storm advanced north-northwest across the coast of Texas, filling, but not quickly enough. In the 48-h forecast (lowerright panel) verifying at 0000 UTC 2 August 1989 thecenter of the storm was far inland. However, the cy942 MONTHLY WEATHER REVIEW VOLUME 122SER LEVEL RRESSURE (NB)IO00-SO0 M8 THICKNESS (ORM) 36-H [TR FCST BM NOLKBVRLIO t2Z I RUG 89SEFI LEVEL RRESSURE INS)1000-500 /'/S THICKNESS IORM)VRLIO I2Z RUG 8S' it3S-H ETR FCST MOOSM LK8 .SER LEVEL PRESSURE -MB) 'SER LEVEL PRESSURE (MS)]O00-SO0 N8 '[HICKNESS (DRM) qS-H EIR FCST SM HOLES 1000-500 PiB THICKNESS (ORIfi)qS-H CTR FCST'MOOSM L~B FIG. 8. Forecasts of mean sea level pressure obtained in 36- and 48-h test runs starting from 0000 UTC 31 July 1989. The 36-h controlforecast with the BM deep convection scheme and without the viscous sublayer (upper left panel), the 36-h forecast with the revised deepconvection and the new viscous sublayer scheme (upper right panel), the 48-h control forecast with the BM deep convection scheme andwithout the viscous sublayer (lower left panel), and the 48-h forecast with the revised deep convection and the new viscous sublayer scheme(lower right panel) are displayed.clone stayed east-southeast of the observed location,and the pressure at its center remained too low (cf.Climate Analysis Center 1989)..6. Conclusions and review of further efforts The eta model has demonstrated a remarkable skillin forecasting the development and movement of severe storms (Black and Mesinger 1989, 1991; Black etal. 1989, 1990; Lazi6 1990, 1993a,b; Lazi6 and Telenta1990; Mesinger and. Black 1989, 1991; Mesinger et al.1990; Rogers et al. 1991; Ward 1990; WGNE 1989,1990). However, it was also occasionally producingheavy spurious precipitation over warm water, as wellas widely spread light ~)recipitation ~over oceans. In addition, the.convecti'vE~ forcing, particularly the shallowone, could produqe negative entropy changes. ,' Looking for the possible causes of the problems, three.major areas of research were identified: (i) the deepand the shallow convection schemes, (ii) the processesat the interface between the sea and the air, and (iii)the Mellor-Yamada level 2 and level 2.5 schemes. Asthe outcome, (i) a major revision of the BM schemeover the oceans was made, (ii) a new flexible viscoussublayer scheme was designed, and (iii) the MellorYamada level 2 and level 2.5 schemes were retuned. The deep convective regimes are postulated to becharacterized by a parameter called "cloud efficiency."The relaxation time is extended for low cloud etliciencies, and vice versa. It is also postulated that there is arange of reference equilibrium states instead of a singleone. The specific reference state is chosen dependingon the cloud efficiency. The treatment of the shallowcloud tops was modified, and the shallow reference huMAY 1994 JANJI(2 943midity profiles are specified requiring that the entropychange be nonnegative. Two layers are introduced over the oceans: (a) aviscous sublayer with the vertical transports determinedentirely by the molecular diffusion, and (b) a layerabove it with the vertical transports determined onlyby the turbulence. The viscous sublayer operates indifferent regimes depending on the roughness Reynoldsnumber. The MY level 2.5 TKE is initialized "from above"in the PBL, so that excessive TKE is dissipated at mostplaces during the PBL spinup. The method used forcalculating the MY level 2.5 master length scale wasrectified. In this way, possible overestimation of thelevel 2 surface fluxes over water is also avoided in thecase of near-neutral conditions with weak wind. To demonstrate the effects of the new schemes forthe deep convection and the viscous sublayer, tests weremade using two summer cases: one with heavy spuriousprecipitation, and another when the version of themodel run quasi-operationally at NMC Washingtonproduced a successful 36-h forecast of a tropical cyclone(Black et al. 1989). In the case with the excessive precipitation, each of the two schemes had large and aboutequal positive impacts on the mean sea level pressureforecasts. In contrast to the control run, the newschemes used in combination resulted in a successful48-h forecast of the mean sea level pressure. The 36-hpredicted accumulated 24-h precipitation was broughtmuch closer to reality. The results were also favorablein the tropical storm case in the sense that the abilityof the model to predict its development was preserved.In addition, compared to the control run, the cyclonetrack was noticeably improved, particularly at the laterstages of the forecast. Early attempts to apply the unified convection scheme over both sea and land resulted in a slight deg radation of the precipitation scores over land. However, experiments performed at NMC demonstrated that the precipitation scores can be noticeably improved, ex tending the new concept over land but using dryer hu midity profiles (F. Mesinger 1991, personal commu nication). Despite the successes of the newly designed convec tion and viscous sublayer schemes, the episodes of ex cessive precipitation and overdevelopments of the as sociated systems over warm water have not been com pletely eliminated. These episodes often have been associated with pathological features in the initial con ditions such as strong instability in terms of the virtual potential temperature in the surface layer accompanied by strong wind at the lowest eta model level. Such fea tures can hardly be found in nature and are suspected to be a result of inconsistencies between the eta model and the assimilation system. Naturally, atmospheric models are continuously evolving and, therefore, it is not advisable to discuss too specific details of a model, particularly the tuningconstants. This principle was not strictly followed herein order to make the experimental results reproducible.The specifics presented in the paper were incorporatedinto the eta model in 1990 and do not necessarily coincide with those of the latest version of the model,which has become operational at NMC in June 1993.It is hoped that more details on further developmentswill be reported elsewhere. For example, subsequentto the research reported here, some details of the deepconvection algorithm have been modified at NMC(J. P. Gerrity 1992, personal communication). Also,the problem of the surface fluxes was readdressed byMesinger and Lobocki ( 1991 ). Another modificationrelevant for the surface fluxes calculations was addinga thin lowest eta layer (F. Mesinger, personal communication). Although the increased resolution is always welcome, such a layer represents a deviation fromthe basic eta coordinate philosophy that requires highvertical resolution and approximately equidistant etasurfaces in the lower troposphere in order to resolvethe mountains well and to treat the interactions between the atmosphere and the underlying surface approximately equally both over low-lying and elevatedterrain. For this reason, relatively deep surface layershave been used in most experiments with the eta model,so that the surface layer has remained a potentiallyweak point and thus an area naturally attracting scientific interest. Acknowledgments. This research was supported bythe University Corporation for Atmospheric Research(UCAR). The work reported here was done during theauthor's visit to NMC, Washington, D.C., in 1989 and1990. The experimental results presented, and most ofthose referred to, were produced using the NMC databases and computer facilities. The author is indebtedto Dr. Thomas L. Black of NMC for many useful discussions, as well as for handling the interfaces with theNMC data archives, graphics and data reformatting,reinterpolations, and conversions. On several occasions, his suggestions on the model parameters to belooked at facilitated early identification and eliminationof several problems. While working on the convectionscheme, the author had the privilege of several longand productive discussions with Dr. Alan Betts, whois given credit for his contributions in the text of thepaper. The author is also indebted to Mr. B. Telentaof the Federal Hydrometeorological Institute, whobrought to the author's attention the entropy changesobserved in Mr. Telenta's 3D convective cloud model.The meticulous work of Dr. Joe Gerrity of NMC onthe diagnostics and performance of the convectionschemes prompted and influenced the direction of theresearch reported. The support of Dr. Eugenia Kalnaythat the author enjoyed was certainly most helpful. Theauthor is indebted to Ms. Du~anka ~;upanski for rerunning the test cases discussed in the paper and forproducing the plots. Many contacts with Prof. Fedor944 MONTHLY WEATHER REVIEW VOLUME 122Mesinger helped to finalize the text of the paper. Theauthor also wishes to thank numerous other people hecontacted during the visit and had productive discussions with and to whom injustice is done by not mentioning them by name. In the early planning and decision-making period and in the preparation of the paper the author had the support of the Association forScience of Serbia. In addition, the author is gratefulfor the most efficient and effective handling of a numberof practical problems by Ms. Meg Austin, Dr. Bill Curtis, and all other nice UCAR people. Finally, the authorwishes to thank to his family for support, and his nurse,Ms. Jadranka Zdravkovi&REFERENCESBetts, A. K., 1986: A new convective adjustment scheme. Part I: Observational and theoretical basis. Quart. J. Roy. Meteor. Soc., 112, 677-691. , and M. J. Miller, 1986: A new convective adjustment scheme. Part It: Single column tests using GATE wave, BOMEX and arctic air-mass data sets. Quart. J. Roy. Meteor. Soc., 112, 693 709.Black, T. 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