• Barker, E. H., 1992: Design of the navy’s multivariate optimum interpolation analysis system. Wea. Forecasting,7, 220–231.

    • Crossref
    • Export Citation
  • Bellamy, J. C., 1945: The use of pressure altitude and altimeter corrections in meteorology. J. Meteor.,2, 1–79.

    • Crossref
    • Export Citation
  • Benjamin, S. G., and P. A. Miller, 1990: An alternative sea level pressure reduction and a statistical comparison of geostrophic wind estimates with observed surface winds. Mon. Wea. Rev.,118, 2099–2116.

    • Crossref
    • Export Citation
  • Bluestein, H. B., 1992: Synoptic–Dynamic Meteorology in Midlatitudes. Vol. I: Principles of Kinematics and Dynamics. Oxford University Press, 431 pp.

  • Danard, M., 1989: On computing the surface horizontal pressure gradient over elevated terrain. Mon. Wea. Rev.,117, 1344–1350.

    • Crossref
    • Export Citation
  • Garratt, J. R., 1984: Some aspects of mesoscale pressure field analysis. Aust. Meteor. Mag.,32, 115–122.

  • Mesinger, F., 1990: “Horizontal” pressure reduction to sea level. Preprints, Int. Tagung für Alpine Meteorologie, Engelberg, Switzerland, Schweizerische Meteorologische Anstalt, 31–35.

  • ——, and R. E. Treadon, 1995: “Horizontal” reduction of pressure to sea level: Comparison against the NMC’s Shuell method. Mon. Wea. Rev.,123, 59–68.

    • Crossref
    • Export Citation
  • NWS, 1963: Manual of barometry. Federal Meteorological Handbook No. 7, U.S. Government Printing Office. [Available from NOAA/National Weather Service, Washington, DC 20233.].

  • Pauley, P. M., N. L. Baker, and E. H. Barker, 1996: An observational study of the “Interstate 5” dust storm case. Bull. Amer. Meteor. Soc.,77, 693–720.

    • Crossref
    • Export Citation
  • Peyrefitte, A., 1986: The plateau anticyclone of the western United States. Ph.D. dissertation, University of Utah, 123 pp. [Available from University Microfilms International, 300 N. Zeeb Road, Ann Arbor, MI 48106.].

  • Sangster, W. E., 1987: An improved technique for computing the horizontal pressure-gradient force at the earth’s surface. Mon. Wea. Rev.,115, 1358–1369.

    • Crossref
    • Export Citation
  • Saucier, W. J., 1955: Principles of Meteorological Analysis. University of Chicago Press, 438 pp.

  • Seaman, R. S., 1997: A comparison of some methods for reduction of pressure to sea level over Australia. Aust. Meteor. Mag.,46, 15–25.

  • Stackpole, 1970: Revised method of 1000 mb height computation in the PE model. Tech. Procedures Bull. 57, NOAA/NWS, 6 pp. [Available from NOAA Library, Silver Spring, MD 20910.].

  • Weaver, J. F., and J. J. Toth, 1990: The use of satellite imagery and surface pressure-gradient analysis modified for sloping terrain to analyze the mesoscale events preceding the severe hailstorms of 2 August 1986. Wea. Forecasting,5, 279–298.

    • Crossref
    • Export Citation
  • View in gallery

    Manual analysis of reported (standard) SLP at 0000 UTC 30 November 1991. Isobars are drawn at a 2-mb interval and labeled with the value minus 1000 mb. Reported SLP values were available at stations indicated by a solid dot. Altimeter settings only were available at stations indicated by an open circle. A bold line connects the stations from San Francisco, CA, to Winnemucca, NV, that are used to compare reduction methods in Fig. 4. Terrain elevation (5′ resolution) is shaded, with white indicating elevations below 300 m, and increasingly darker shading for elevations above 300 m, 1000 m, 2000 m, and 3000 m, respectively.

  • View in gallery

    SLP computed from the 0000 UTC 30 November 1991 NORAPS analysis using the simple technique, with isobars drawn at a 2-mb interval. A bold line indicates the location of the interpolated values depicted in Fig. 5. The NORAPS terrain elevation is shaded at an interval of 200 m and labeled in units of 100 m. The region depicted in this figure was used to compute the 25 × 25 gridpoint averages for Table 1.

  • View in gallery

    Specific virtual temperature anomaly (S*) as a function of surface pressure altitude (zp) for 0000 UTC 30 November 1991. Observed values from central California and Nevada are indicated with a “+” and values computed from the NORAPS analysis along the SFO–WMC line are indicated with a “○,” with selected values further indicated with a “♦.” The bold line portrays the least squares fit to the observed values; the thin line portrays the least squares fit to the selected NORAPS values. These two lines were used to define the S′ functions for the Weaver and Toth (1990) adjusted altimeter setting, as described in the text.

  • View in gallery

    (a) SLP (mb) for 0000 UTC 30 November 1991 computed using various reduction techniques with observational data from the indicated stations along the SFO–WMC line portrayed in Fig. 1; (b) sea level temperature (K) used in the computation of SLP in (a); and (c) terrain elevation (m) both at individual stations and interpolated to the SFO–WMC line portrayed in Fig. 2 from the 5′ terrain dataset.

  • View in gallery

    (a) SLP (mb) for 0000 UTC 30 November 1991 computed using various reduction techniques with NORAPS analysis data and interpolated to the SFO–WMC line portrayed in Fig. 2; (b) sea level temperature (K) used in the computation of SLP in (a); and (c) NORAPS terrain elevation (m).

  • View in gallery

    (a) Geostrophic wind speed (m s−1) for 0000 UTC 30 November 1991 computed from SLP fields using various reductions with NORAPS analysis data and interpolated to the SFO–WMC line portrayed in Fig. 2; (b) observed wind speeds and gusts and model-analyzed winds interpolated to the SFO–WMC line; and (c) NORAPS terrain elevation (m).

  • View in gallery

    Comparison of SLP and 1300-m pressure (mb) for 0000 UTC 30 November 1991. Both SLP and 1300-m pressure were extrapolated from observational surface data at the stations along the SFO–WMC line portrayed in Fig. 1 using the surface pressure (computed from the altimeter setting), the current surface virtual temperature, and the standard atmosphere lapse rate (the Simple SLP #2 technique). The axis for the 1300-m pressure was shifted to overlay the RNO 1300-m pressure value on the RNO SLP value, in order to facilitate comparison of horizontal variations in pressure between the two levels. The solid circle depicts the 1300-m pressure interpolated from the OAK sounding.

  • View in gallery

    SLP computed from the 0000 UTC 30 November 1991 NORAPS analysis using the Mesinger (1990) technique, with isobars drawn at a 2-mb interval. Effective sea level temperatures (°C) are shaded at an interval of 2°C.

  • View in gallery

    Estimate of error in SLP reduction associated with errors in surface virtual temperature and assumed lapse rate. The simple technique was applied here using the NORAPS analysis data. A uniform value of 1 or 2 K was added to or subtracted from the mean boundary layer temperature or a value of 1 or 2 K km−1 was added to or subtracted from the standard atmosphere lapse rate in order to examine the effect of such errors.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 418 161 6
PDF Downloads 360 165 6

An Example of Uncertainty in Sea Level Pressure Reduction

View More View Less
  • 1 Naval Postgraduate School, Monterey, California
Full access

Abstract

Difficulty analyzing mesoscale features in California and Nevada for a 1991 case study prompted a review of techniques for sea level pressure (SLP) reduction and an evaluation of the performance of the various techniques for the U.S. west coast states at 0000 UTC 30 November 1991. The objective of any SLP reduction procedure is to provide a pressure field that portrays meteorological features rather than terrain features, a difficult goal to meet in this region given the steep terrain gradients on the western slopes of the Sierra Nevada range. The review and evaluation are performed both for techniques applicable at individual stations and for techniques applicable at grid points in a model analysis or forecast.

When using station data, one would like to perform a manual or objective analysis of SLP with the greatest number of stations possible by adding stations that report only altimeter setting to the stations that report both SLP and altimeter setting. The results of the comparison show that the incorporation of altimeter-setting stations into an analysis of SLP was found to be practical only at elevations less than 300 m. Above this, the standard reduction includes empirical corrections that cannot be easily duplicated, and the other reduction techniques yielded values that varied over a large enough range that the uncertainty associated with the choice of technique becomes too great to permit the analysis of weak mesoscale features. At such low elevations, the various techniques examined gave similar results; therefore, the simple reduction is recommended. In elevated plateau regions, a pressure analysis on a geopotential surface at approximately the mean terrain height is recommended to minimize reduction errors. No satisfactory solution was found for regions with steep terrain gradients.

Computing SLP from model objective analyses or forecasts that are in the model’s native vertical coordinate, typically the terrain-following sigma coordinate, poses a different set of problems. The model terrain field is usually smoothed and so contains regions where it differs significantly from the actual terrain. This is sufficient in itself to yield reduction errors that have a coherent mesoscale signature. In addition, SLP fields computed using available techniques vary widely in areas of higher terrain elevation, sometimes producing mesoscale features that suspiciously coincide with terrain features and so suggest reduction error. These mesoscale pressure artifacts are also often associated with unrealistic geostrophic wind speed maxima. The Mesinger method of defining the below-ground temperature field by horizontal interpolation across terrain features after interpolating the model sigma-level objective analyses to pressure surfaces worked best for this case. It produced values that agreed reasonably well with the manual SLP analysis and with the 1300-m pressure analysis over Nevada, without generating an artificial geostrophic wind speed maximum.

Corresponding author address: Patricia M. Pauley, Department of Meteorology, Code MR/Pa, Naval Postgraduate School, 589 Dyer Road, Room 254, Monterey, CA 93943-5114.

Email: pmpauley@nps.navy.mil

Abstract

Difficulty analyzing mesoscale features in California and Nevada for a 1991 case study prompted a review of techniques for sea level pressure (SLP) reduction and an evaluation of the performance of the various techniques for the U.S. west coast states at 0000 UTC 30 November 1991. The objective of any SLP reduction procedure is to provide a pressure field that portrays meteorological features rather than terrain features, a difficult goal to meet in this region given the steep terrain gradients on the western slopes of the Sierra Nevada range. The review and evaluation are performed both for techniques applicable at individual stations and for techniques applicable at grid points in a model analysis or forecast.

When using station data, one would like to perform a manual or objective analysis of SLP with the greatest number of stations possible by adding stations that report only altimeter setting to the stations that report both SLP and altimeter setting. The results of the comparison show that the incorporation of altimeter-setting stations into an analysis of SLP was found to be practical only at elevations less than 300 m. Above this, the standard reduction includes empirical corrections that cannot be easily duplicated, and the other reduction techniques yielded values that varied over a large enough range that the uncertainty associated with the choice of technique becomes too great to permit the analysis of weak mesoscale features. At such low elevations, the various techniques examined gave similar results; therefore, the simple reduction is recommended. In elevated plateau regions, a pressure analysis on a geopotential surface at approximately the mean terrain height is recommended to minimize reduction errors. No satisfactory solution was found for regions with steep terrain gradients.

Computing SLP from model objective analyses or forecasts that are in the model’s native vertical coordinate, typically the terrain-following sigma coordinate, poses a different set of problems. The model terrain field is usually smoothed and so contains regions where it differs significantly from the actual terrain. This is sufficient in itself to yield reduction errors that have a coherent mesoscale signature. In addition, SLP fields computed using available techniques vary widely in areas of higher terrain elevation, sometimes producing mesoscale features that suspiciously coincide with terrain features and so suggest reduction error. These mesoscale pressure artifacts are also often associated with unrealistic geostrophic wind speed maxima. The Mesinger method of defining the below-ground temperature field by horizontal interpolation across terrain features after interpolating the model sigma-level objective analyses to pressure surfaces worked best for this case. It produced values that agreed reasonably well with the manual SLP analysis and with the 1300-m pressure analysis over Nevada, without generating an artificial geostrophic wind speed maximum.

Corresponding author address: Patricia M. Pauley, Department of Meteorology, Code MR/Pa, Naval Postgraduate School, 589 Dyer Road, Room 254, Monterey, CA 93943-5114.

Email: pmpauley@nps.navy.mil

1. Introduction

Sea level pressure (SLP) is arguably the most widely used meteorological field, allowing the user to infer surface circulations, estimate the degree to which observed winds are ageostrophic, and examine the surface features that provide organization for sensible weather such as clouds and precipitation. Direct measurement of sea level pressure is possible for the large portions of the earth that are at or very near sea level. However, the reduction of pressure to sea level in regions where the surface elevation is well above sea level requires some sort of extrapolation that must be performed carefully in order to get meaningful results.

“Meaningful” in this context signifies that SLP reduction provides a pressure field that portrays meteorological features rather than terrain features.1 Various authors have phrased this general standard in terms of specific aspects of the SLP field. Most stress that SLP reduction should minimize fictitious pressure gradients arising from the reduction process and yield reasonable pressure gradients and therefore geostrophic winds that are reasonable relative to the observed surface winds (e.g., Benjamin and Miller 1990; Weaver and Toth 1990;Seaman 1997). In addition, Mesinger and Treadon (1995) state that the SLP field resulting from the reduction process should as far as possible “maintain the shape of the isobars in surfaces of constant elevation” and “reflect the changes in the horizontal of the magnitudes of horizontal pressure gradients, as these exist at the ground surface,” the latter of which restates the requirement for reasonable pressure gradients.

This note reviews available SLP reduction techniques and, using the above criteria, evaluates their performance for the U.S. west coast states at 0000 UTC 30 November 1991, a few hours after the multiple-vehicle collisions that occurred on Interstate 5 in a dust storm in California’s San Joaquin Valley. This study was motivated by difficulties encountered in preparing the manual sea level pressure analyses presented in Pauley et al. (1996). As shown in Fig. 1, fewer stations reporting SLP are available than would be desirable for making a mesoscale pressure analysis in California. Notably, there are no stations reporting SLP in the Sierra Nevada in east-central California. A small number of additional stations report altimeter setting, but adding them into the analysis is not trivial. The first part of this comparison of reduction techniques is to examine procedures that are applicable to station data and to determine whether any of the techniques are able to reasonably add stations that report only altimeter setting to those that report both altimeter setting and SLP in manual or objective analyses of SLP.

Furthermore, the SLP field computed from the Navy Operational Regional Analysis and Prediction System (NORAPS) analysis (Fig. 2) does not precisely reproduce the features depicted in the manual analysis (Fig. 1). The NORAPS objective analysis uses a multivariate optimum interpolation technique to analyze increments (differences between observations and the background field interpolated to observation locations) on mandatory pressure levels (Barker 1992). Observations include surface data (land and marine), upper-air data (rawinsonde and PIBAL), ARINC Communications Addressing and Reporting System (ACARS) and conventional aircraft winds, and satellite-derived cloud-track winds, surface wind speeds, and temperature soundings, while the background field is provided by a 6-h NORAPS forecast. The analyzed increments are then interpolated to the model’s terrain-following sigma levels and added to the sigma-level background fields to yield the analysis that provides the initial conditions for the model forecast. Therefore, pressure defined on the model’s lowest sigma level is analogous to surface pressure, and computing the SLP field from the NORAPS analysis is equivalent to computing sea level pressure from surface pressure at individual model grid points. The second part of this comparison of reduction techniques is to evaluate procedures to compute SLP from model sigma-coordinate analyses and forecasts and to determine how well the resulting SLP fields compare with those from objective or manual analyses of SLP data at stations.

2. Methods for reducing pressure to sea level

The hypsometric equation provides the mathematical basis for reducing pressure to sea level. There are several equivalent forms of this equation; Eq. [3.10(2)] from Saucier (1955) is used here for reference. With minor changes in notation, this equation is given by
pSLpsfczsfcKT
where pSL is the sea level pressure (hPa), psfc is the (station) pressure at the earth’s surface (hPa), zsfc is the surface elevation (m),2 K is a constant (29.28980 m/K), and T* is the mean virtual temperature (K) for the fictitious air column between the earth’s surface and sea level.
Differences between reduction techniques using this or other forms of the hypsometric equation amount to differences in the specification of T*. A mean virtual temperature that is too warm (cold) results in sea level pressures that are too low (high). As pointed out in the Manual of Barometry (NWS 1963, pp. 7-5), T* for the fictitious below-ground air column should be consistent with T* for actual above-ground air columns of similar depth at nearby lower-elevation locations, in order to obtain a coherent SLP pattern. Commonly, T* is approximated as the average of some surface virtual temperature T*sfc and a sea level virtual temperature T*SL that is obtained by extrapolating T*sfc downward using a constant virtual lapse rate γ*, such that
i1520-0434-13-3-833-e2
Typically, this lapse rate is set to the standard atmosphere lapse rate, γs, equal to 6.5 K km−1.

a. Standard reduction (e.g., NWS 1963, chap. 7 and appendix 7)

This is the reduction that results in the SLP values in the U.S. Surface Airways hourly reports, here referred to as “reported” SLP. The mean virtual temperature forthe fictitious below-ground layer in this case is written as
i1520-0434-13-3-833-e3
The first term in (3), Tsfc, is an average of the current surface temperature and the surface temperature from 12 h earlier. The averaging is performed in order to minimize diurnal variations, which are greater at mountain and plateau stations than in the free atmosphere at a similar altitude. The second term is called the standard lapse rate correction. Note that neglecting moisture effects, the sum of the first two terms is equivalent to (2), with the substitution of Tsfc for T*sfc and γs for γ*. The third term in (3) represents a humidity correction, where esfc is the surface vapor pressure and Ch (a function of zsfc) is the humidity correction factor. This term converts the mean ambient temperature of the fictitious column to a mean virtual temperature. In principle an observed value should be used for esfc, but in practice a climatological value that is a function of Tsfc is used.

A fourth and final term, the “correction for plateau effect and local lapse rate anomaly,” first accounts for a departure of the “actual” lapse rate from the standard atmosphere value and, second, limits the annual variation in SLP at high-altitude stations to that for sea level stations. As pointed out in the Manual of Barometry (NWS 1963, appendix 7.2), it has been recognized since Ferrel’s work more than 100 years ago that, like the diurnal variation, the annual variation in virtual temperature at mountain and plateau stations is greater than in the free atmosphere at similar altitudes, leading to sea level pressures that are too high in winter and too low in summer and necessitating a correction. These two corrections are in practice combined, written as a function of Tsfc, and applied only at stations with elevations greater than 1000 ft (305 m). Values are determined empirically on a station by station basis.

Since the standard reduction involves corrections that are empirically determined, it is difficult to replicate without exact knowledge of the empirical factors. This means that it is difficult to apply this technique to stations where the correction has not been previously determined (see NWS 1963, chap. 7 and appendix 7, for details) and it is virtually impossible to apply it to model analyses and forecasts.

b. Simple reduction

This method has been used by the author and others, primarily for its simplicity. It differs from the standard reduction by not attempting to account for departures in lapse rate from standard and not correcting for the plateau effect. The standard atmosphere lapse rate γs is used in (2) with some measure of the surface virtual temperature T*sfc. In the calculations presented in this note, either the average of the virtual temperatures at the current time and approximately 12 h earlier or the current virtual temperature is used for T*sfc with the observational data, while the surface virtual temperature corresponding to the mean virtual potential temperature of the lowest nine sigma levels—approximately the lowest 50 mb—is used with the NORAPS analysis data. Using the average of the current virtual temperature and that from 12 h earlier with the standard atmosphere lapse rate was also referred to as the World Meteorological Organization (WMO) method by Seaman (1997).

c. Altimeter setting (e.g., Bluestein 1992, 61–63)

In the United States, the altimeter setting is entered into an aircraft’s altimeter so that the indicated altitude is equal to the station elevation when the aircraft is on the ground (e.g., Bellamy 1945). The altimeter setting is the SLP that would exist if the temperature distribution were equal to that in the standard atmosphere with no moisture correction. The tropospheric standard atmosphere is defined as having a sea level pressure of 1013.25 mb, a sea level temperature of 288.15 K, and a lapse rate of 6.5 K km−1. The sea level temperature T*SL (in K) needed for the altimeter setting reduction is the standard atmosphere temperature corresponding to a pressure equal to the altimeter setting, shown by Bluestein [1992, 63, Eq. (2.1.67)] with minor changes in notation to be
i1520-0434-13-3-833-e4
The surface temperature T*sfc (in K) is set to the standard atmosphere temperature corresponding to the station elevation (in m), computed from
T*sfcT*SLzsfc
Equation (1) can be combined with (2), (4), and (5) to yield an expression for the altimeter setting. Bluestein [1992, 63, Eq. (2.1.68)] gives the resulting equation (with minor changes in notation) as
i1520-0434-13-3-833-e6
Note that the use of standard atmosphere dry-bulb temperatures means that altimeter setting is a function only of surface pressure and surface elevation. Thus, surface pressure can be easily and uniquely obtained from the altimeter setting by inverting (1) and defining the temperatures from (4) and (5), given the surface elevation. Altimeter setting is often used for mesoscale analyses in regions without significant topography, since it is reported at roughly 25% more stations than report SLP (Benjamin and Miller 1990). However, to the extent that the actual atmosphere departs from standard, some sort of correction is needed if altimeter settings are to be analyzed in regions of sloping terrain.

d. Weaver and Toth’s adjusted altimeter setting (Weaver and Toth 1990)

This complex altimeter setting correction is based on the Sangster (1987) method for computing the surface geostrophic wind and makes use of altimeter corrections (D values) as proposed by Bellamy (1945). The first step in this technique is to select a reference pressure altitude z′ on which the analysis is performed. Since the meteorological features of interest in this case occur in California’s Central Valley where elevations (and pressure altitudes) are generally less than 100 m, z′ is selected to be zero for this case. Note that a pressure altitude of zero is not the same as sea level; rather, zero pressure altitude occurs at the actual altitude where the pressure equals the standard atmosphere sea level pressure, 1013.25 mb.

The second step is to plot values of specific virtual temperature anomaly, defined as
STTpTp
as a function of zp, the pressure height in the standard atmosphere. Here T* is the observed virtual temperature at a particular station, and Tp is the standard atmosphere temperature at height zp. Bellamy (1945) showed that the standard atmosphere temperature (in K) could be computed from surface pressure (in mb) using the formula
i1520-0434-13-3-833-e8
The pressure altitude zp (in m) can then be computed from
i1520-0434-13-3-833-e9
A sample plot of S* is shown in Fig. 3 using observational data from selected stations in California and Nevada at the map time portrayed in Fig. 1. The plot is then used to determine a functional relationship between S* and (zpz′), either subjectively or objectively. For this case, a least squares linear fit yields S* = −0.00249375 − 0.00001299(zp − 0). The adjustment parameter S′ is then given by S′ = −0.00249375 − 0.00001299(zp − 0)/2.
Finally, the adjusted altimeter setting ADJALT (in in. Hg) is found from
Szpz
where ALT is the altimeter setting (in. Hg) and the quantity (ΔD/ΔALT) is computed from Sangster’s (1987) approximate expression for D values, such that
ADJALT values in this study are converted to millibars for comparison with other methods.

e. Shuell reduction (Stackpole 1970; Mesinger and Treadon 1995)

This is the reduction algorithm that has been used since 1970 at the National Centers for Environmental Prediction, (NCEP, formerly the National Meteorological Center) to derive a sea level pressure field from model forecasts and analyses that is reasonably comparable to the standard reduction performed at individual stations. In this case, T* is set to the average of the“ground” temperature, TG, originally extrapolated using γs from the temperature in the lowest model layer above the boundary layer (but set to the temperature in the lowest model layer for more recent models), and the 1000-mb temperature, T0, extrapolated from TG using γs. In the calculations presented here, the mean boundary layer virtual potential temperature is used to determine TG. These two temperatures are checked against the maximum value, T0M, which is set to 17.5°C. The mean temperature T* used in the reduction is therefore determined as one of the following three cases:

  1. If both TG and T0 are less than T0M, T* is set to their average.

  2. If only T0 is greater than T0M, T* is set to the average of TG and T0M.

  3. If both TG and T0 are greater than T0M, T* is set to the average of TG and T0 = T0M − 0.005(TGT0M)2.

An additional correction using the “tendency method” is also applied to forecast SLP fields. This correction assumes that the difference between the SLP field computed from the model’s analysis using the Shuell reduction and the SLP field analyzed from station values using the standard reduction remains constant for the duration of the forecast. The difference between the two (Shuell minus standard) is added to forecast values to yield the corrected values.

A similar technique is used in portraying operational NORAPS SLP fields (C. S. Liou 1997, personal communication). Reported SLP values are used in the analysis of the 1000-mb height field, which is then used to derive the SLP field for the analysis. The pressure difference between sea level and the surface is computed for the analysis; this pressure difference, modified by the mean temperature tendency of the lowest third of the NORAPS atmosphere, is then used in computing the SLP field for the NORAPS forecasts. Finally, a Laplacian smoother is applied to smooth the SLP analysis at points where the terrain elevation is nonzero. The degree of smoothing is related to the terrain height (E. H. Barker 1997, personal communication). Note that this technique was not used in deriving SLP fields for the research version of NORAPS used in this paper.

f. MAPS reduction (Benjamin and Miller 1990)

This reduction is used for the Mesoscale Analysis and Prediction System (MAPS) also referred to as the Regional Update Cycle (RUC). In order to provide a smoother SLP, the 700-mb virtual temperature is extrapolated to the surface using γs to yield T*sfc. Then T*SL is extrapolated from T*sfc also using γs. Benjamin and Miller (1990) also suggest using virtual temperatures from a sigma level above the boundary layer (e.g., 200 mb above the surface) in place of the 700-mb virtual temperatures, if sigma-level data are available. In the calculations presented in this note, both methods are used, the latter with virtual temperatures from the 0.785 sigma level.

g. Horizontal reduction (Mesinger 1990)

This reduction was developed to ameliorate the unnatural-looking small-scale high pressure center collocated with the highest mountains in western Colorado that was frequently seen in NCEP’s Eta Model forecasts in spite of filtering being applied (F. Mesinger 1998, personal communication). Noise in the SLP field was especially a problem for the mesoscale version of the Eta Model. This technique differs fundamentally from the previously discussed techniques, in that temperature at each model level is interpolated horizontally into the region that lies below ground rather than extrapolating vertically from the surface temperature. The horizontal interpolation is performed by solving
2T
at below-ground points using the temperatures just outside of the mountains as boundary conditions. In the case of the Eta Model, this temperature is located on the vertical face of the “step” mountains. As applied here, the NORAPS analysis sigma-level data are first interpolated to pressure levels at a 50-mb increment. Temperature at below-ground points is found by solving (12) using sequential overrelaxation with a relaxation constant of 1.815; temperatures at the above-ground points closest to the terrain provide the boundary conditions for the relaxation. Fewer than 100 iterations were needed for the temperatures to converge to within 0.001K, with fewer than 50 needed at pressure levels from 850 to 700 mb. After the below-ground temperatures are defined on each pressure level, the temperatures are used to compute the height field below ground. Finally, the sea level pressure field is extrapolated downward from the nearest pressure level above sea level.

3. Sea level pressure for 0000 UTC 30 November 1991

Figure 1 displays a manual analysis of standard SLP as reported in the hourly Surface Airways observations at the stations indicated with solid dots. The overall field is characterized by high pressure offshore of Washington (WA) and Oregon (OR) and low pressure in southern California (CA). Mesoscale features discussed in Pauley et al. (1996) include the inverted trough in central CA along the Central Valley, the slight ridging near Bakersfield (BFL), and the sharp trough extending westward from the low center in southern CA. The inverted mesoscale ridge in western Nevada (NV) is also of interest in terms of defining the eastern side of the inverted trough over central CA. Note that in CA, few stations are present at higher elevations, and no station with an elevation greater than 1000 m reports SLP. This makes the exact shape of the inverted trough uncertain. In addition, the inverted ridge was smoothed by the author rather than drawn exactly to the data since only two stations support it, Lovelock (LOL) and Fallon Naval Air Station (NFL), and since their values were judged to be excessive: 1022.1 mb at LOL and 1021.5 mb at NFL, approximately 2 mb higher than analyzed. These two stations had anomalously high pressure throughout the day as can be seen in the manual analyses in Fig. 10 in Pauley et al. (1996). Figure 1 also shows that surface winds offshore generally exceed 15 m s−1, surface winds in the Central Valley exceed 10 m s−1 at many sites, and surface winds in Nevada and Utah are generally light (5 m s−1 or less). The surface wind directions over most of the region are oriented nearly perpendicular to the isobars and the wind speeds appear to have little relationship to the SLP gradient, both of which imply substantial ageostrophy.

In comparison, the SLP field from the 60-km resolution NORAPS analysis is shown in Fig. 2. [The characteristics of this research version of the NORAPS data assimilation system are briefly summarized in the introduction and discussed in Pauley et al. (1996).] This SLP field was computed using the simple technique with the mean boundary layer virtual potential temperature as described above. Note that the model terrain field (Fig. 2) is greatly smoothed compared to the actual terrain (Fig. 1). Here, California has a broad coastal plain in place of the Coast Ranges and the Central Valley, and a more moderate slope to approximately 2000 m in the Sierra Nevada in place of the steep slope to more than 3000 m. While the large-scale aspects of theNORAPS SLP field agree with the manual analysis in Fig. 1, the mesoscale features have differences. The inverted mesoscale trough that is located over the Central Valley in the manual analysis is centered at approximately the same location in the NORAPS field, although here it corresponds to the western edge of the NORAPS Sierra Nevada. The trough also has a higher amplitude than it does in the manual analysis, as does the low center in southern California and the sharp trough extending westward from it. The greatest difference in mesoscale features, however, is in the inverted ridge, which is higher in amplitude than in the manual analysis and is aligned with the highest model terrain rather than being located in western NV.

One of the questions raised by this comparison is whether the inverted ridge in NV is a real (i.e., meteorological) feature or an artifact of the reduction. In order to examine this further, values of SLP computed using the above techniques are compared along a line from San Francisco, CA (SFO), to Winnemucca, NV (WMC), roughly perpendicular to the axes of the inverted trough in the Central Valley and the inverted ridge in NV. The Lake Tahoe airport (TVL), located at the south end of Lake Tahoe, was added for comparison with Truckee (TRK), located at the north end of the lake. A large-scale pressure difference of 1.5 mb between TVL and TRK was estimated from Fig. 1 and added to the TVL SLP values to facilitate comparison. Figure 4a portrays SLP values computed from the observational data at the stations connected by the line in Fig. 1 (as well as TVL), while Fig. 5a portrays values computed from the NORAPS analysis data and interpolated to the line depicted in Fig. 2. In addition, Figs. 4b and 5b portray the sea level temperatures used in each technique except the standard SLP reduction, whose sea level temperature cannot be readily reconstructed. Sea level temperatures are depicted, rather than surface temperatures or mean temperatures for the below-ground layer, in order to examine whether a particular method creates unrealistic below-ground temperature gradients without depicting gradients associated with changes in altitude. Terrain elevation is shown in Figs. 4c and 5c to portray its relationship to SLP reduction.

Figure 6 portrays the geostrophic wind speeds associated with the various SLP reductions using NORAPS analysis data, as well as the observed and model-analyzed wind speeds from the lowest sigma level (σ = 0.999). The NORAPS terrain field is repeated here to facilitate comparison of the wind field with terrain features. As described above, the observed winds are moderately strong and gusty near the coast and in the Central Valley, while light winds are present in Nevada. No observations are present to describe conditions on the western slopes of the Sierra Nevada. In contrast, the NORAPS analysis winds range from 6 m s−1 near the western end of the SFO–WMC line to 12.7 m s−1 at the eastern end. The differences between the observed and the analysis winds arise because surface winds from land stations are not used in the NORAPS analysis. Rather, the surface winds in the analysis result from a combination of background values from a 6-h forecast and analysis increments that are nearly geostrophic because of the linkage imposed between the momentum and mass fields in this multivariate analysis scheme. The observed and analysis winds are presented as a basis for judging the degree to which the geostrophic winds are reasonable.

These graphs show that the various methods yield nearly the same SLP value (and so nearly the same geostrophic wind speed) when the elevation is less than 300 m despite a large variation in sea level temperature, but considerable differences in SLP and geostrophic wind are present for elevations greater than 1000 m. Thus, the analysis of the western half of the inverted trough is not sensitive to reduction technique, while the analysis of the inverted ridge is quite sensitive. An examination of the various methods follows, with the performance of a particular reduction method judged by its ability to yield (a) a reasonable pressure gradient and geostrophic wind speed (Benjamin and Miller 1990; Weaver and Toth 1990; Mesinger and Treadon 1995; Seaman 1997), and (b) reasonable pattern agreement with analyses on constant elevation surfaces (Mesinger and Treadon 1995).

In order to examine this second criterion, a test calculation was made for the stations along the SFO–WMC line, in which pressures were computed (using the simple reduction with the current virtual temperature) at a height of 1300 m rather than at sea level. This should yield minimal reduction error at Reno (RNO), LOL, and WMC, where the station elevations are 1344, 1190, and 1312 m, respectively. Figure 7 presents the 1300-m pressure at these stations compared to SLP values computed using the same technique. The 1300-m pressures indicate only slight ridging at LOL and confirm that the reported SLP at LOL was erroneously high. It is interesting to note that the large difference in pressure between Sacramento, CA (SAC), and TRK is not seen in the 1300-m pressures. Although the 1300-m pressures in the western portion of the SFO–WMC line are extrapolated upward from near-sea-level surface values and so are more subject to reduction error than those in the eastern portion of the line, the 1300-m pressure interpolated from the 0000 UTC Oakland (OAK) (solid circle) sounding confirms that the pressure gradient along the SFO–WMC line at this level is weak.

The first reduction technique to be examined is the simple reduction, which is computed from observational data in two ways. The values labeled “Simple SLP #1” are computed using the 12-h average surface virtual temperature. Figure 4a shows that this technique yields values that are 2–3 mb higher than the reported (standard) SLP at RNO, LOL, and WMC, as a result of neglecting the “correction for plateau effect and local lapse rate anomaly.” The ridge at LOL has a magnitude similar to that in the standard reduction, but greater than that in the 1300-m pressures, indicating that both the standard and simple reductions exaggerate this feature. However, a comparison of values at TVL and TRK, both of which report altimeter setting but not SLP, shows that TVL’s SLP is consistent with RNO’s and Mather Airport’s (MHR’s), while TRK’s SLP is 1.4 mb higher than RNO’s.

The second calculation (Simple SLP #2) used the current surface virtual temperature without any temporal averaging. The pressure values from this technique are lower in NV (Fig. 4a) since the 0000 UTC temperatures are warmer than the 12-h mean (Fig. 4b). This is especially true at LOL, leading to a weaker and more realistic inverted ridge. An examination of the 1200 UTC temperature at LOL that was included in the 12-h average shows that it is considerably colder than the surrounding stations, likely a result of cold air drainage into the dry lake bed at this location. On the other hand, using the current virtual temperature has little effect at TRK, since surface temperature remained cold throughout the day, varying only between −5.0° and −3.9°C. TVL has a higher pressure by this method, since its early morning temperature was warmer than its 0000 UTC temperature.

When used with the NORAPS analysis data, the simple reduction is based on the mean boundary layer potential temperature, resulting in the field depicted in Fig. 2. The extrapolated sea level temperatures are quite warm along the western third of the SFO–WMC line, but decrease by nearly 10 K to nearly uniform temperatures over the elevated plateau in the eastern half of the line (Fig. 5b). Although the warm temperatures are warmer, the cool temperatures are similar to those from Simple SLP #2 using observational data but without the minima at TVL/TRK and LOL. As a consequence, the inverted ridge is west of its location in the observational data (Figs. 4a and 5a), placed just east of the highest terrain elevation (Fig. 5c). Note that the Shuell technique yields values that are only slightly higher than the simple reduction (Fig. 5a), with an average difference of −0.2 mb in the 25 × 25 gridpoint domain depicted in Fig. 2 (Table 1). The temperatures along the SFO–WMC line were cool enough to not be capped by the 17.5°C maximum.

Both the simple technique and the Shuell technique yield a strong pressure gradient along the western slope of the NORAPS Sierra Nevada that leads to a geostrophic wind maximum of over 30 m s−1, compared to the 20 m s−1 geostrophic winds at the lower elevation stations farther west and in the inverted ridge (Fig. 6a). Compare these values with the weaker, nearly constant model-analyzed surface winds depicted in Fig. 6b and with the weak pressure gradient implied by the nearly constant 1300-m pressures along the SFO–WMC line in Fig. 7. Geostrophic winds from these two techniques also increase to 35 m s−1 in Nevada, east of the inverted ridge. This suggests that these two techniques exaggerate the inverted ridge and the pressure gradients on either flank.

The altimeter setting technique provides the lowest SLP values in the inverted ridge, approximately 2–3 mb lower than the standard reduction using observational data (Fig. 4a) and as much as 5 mb lower than the simple reduction using NORAPS data (Fig. 5a). In fact, in the entire 25 × 25 gridpoint domain the altimeter setting values average 1.8 mb lower than the simple reduction (Table 1). As a result, values are almost constant along the SFO–WMC line in Fig. 4a except at TVL, with only slight troughing at SAC and slight ridging at LOL. The discrepancy between values at TRK and TVL suggests that one of them might have an error in the reported altimeter setting, although the values at both stations at this time are consistent with earlier and later values. In Fig. 5a, altimeter setting values decrease overall, with slight troughing at the highest terrain and slight ridging in western NV. The NORAPS values are also lower than the observed altimeter settings by about 2 mb along the western half of this line, a consequence of the NORAPS terrain being higher than the station elevations by around 300 m given the unrealistically warm temperatures used in the extrapolation. Figures 4b and 5b show that, out of all of the methods examined, this technique’s nearly constant sea level temperature is the warmest by roughly 5 K along the eastern half of the line. This unrealistically warm temperature, in fact, leads to the slight troughing over the highest terrain that is portrayed in Fig. 5a and likely is responsible for the low value at TVL in Fig. 4a; the NORAPS altimeter setting field (not shown) depicts the trough extending southeastward along the highest elevations of the NORAPS Sierra Nevada. The altimeter setting gradient on the western flank of the trough coincides with the NORAPS terrain gradient and leads to a geostrophic wind speed maximum that is almost as large as that for the simple technique (Fig. 6a), even though the latter portrays a ridge in this location.

The Weaver and Toth (1990) method for adjusting altimeter setting yields pressures that are close to those from the standard reduction even though the reference level of zero does not precisely equate to sea level (Fig. 4a). The values at RNO and WMC nearly match, but higher values are present at TVL and TRK and only minimal ridging is seen at LOL. It is interesting, but merely fortuitous, that these values most closely match the manual analysis of the ridge. However, it is more noteworthy that the amplitude of the ridge also closely matches that of the 1300-m ridge. The effective sea level temperatures produced by this method approach the Simple SLP #2 temperatures, except at LOL (Fig. 4b). The assumed linear relationship between S′ and zp yields a warmer temperature at LOL compared to RNO and WMC since it has a lower elevation (Fig. 4c), in contrast to the colder temperature observed there.

The Weaver and Toth adjustment was also applied to the NORAPS altimeter settings using the same function for S′ derived for the observational data. As in the observational case, this adjustment yields pressures that are higher than the altimeter setting (Fig. 5a). The troughing over the highest terrain is also damped, as is the geostrophic wind speed maximum to its west. However, the function for S′ based on the observational data is not really appropriate for these data, as shown in Fig. 3. These values of S* (plotted as circles in Fig. 3) were computed from data on the lowest sigma level and interpolated to the SFO–WMC line. Fitting a line to the seven points that describe the greatest variation in pressure altitude yields a very different intercept and slope from that based on observational data. However, computing the adjusted altimeter setting based on this new relationship between S′ and zp gives values that differ little from the altimeter setting, with an average difference of 0.0 mb and an rms difference of only 0.3 mb over the 25 × 25 gridpoint domain, compared to an average difference of −0.9 mb and an rms difference of 1.2 mb between the altimeter setting and the adjusted values using the original function for S′.

While the function assumed for S′ yields adjusted altimeter settings that compare well to the standard reduction along the SFO–WMC line, such would not be the case for the field of adjusted altimeter setting over a domain as large as depicted in Figs. 1 and 2. Over the entire domain, the adjusted altimeter settings differ from the simple SLP values by as much as +10.8 and −3.4 mb for the first form of S′ and as much as +12.5 and −2.2 mb for the second, similar to the maximum positive and negative differences of +13.8 and −2.3 mb for the unadjusted altimeter setting (Table 1). The specific virtual temperature anomaly S* varies spatially as well as with pressure altitude, with values computed from the NORAPS analysis (not shown) as high as +0.35 associated with the low center in southern CA and values as low as −0.45 offshore of Oregon, locations with similarly low elevations. In comparison, values plotted in Fig. 3 vary between only +0.01 and −0.03. The Weaver and Toth (1990) technique was developed for mesoscale analysis and so is best applied over a small domain where the variation in S* with altitude is greater than its spatial variation.

In contrast to the altimeter setting that produces the lowest pressures in the inverted ridge, the Benjamin and Miller (1990) technique based on 700-mb temperatures (labeled Benjamin and Miller #1) leads to the highest pressures of the techniques examined. The values using observational data (Fig. 4a) are 3–5 mb higher than the standard reduction along the eastern half of the line, while the values using NORAPS analysis output (Fig. 5a) are 2–4 mb higher than the simple reduction and average 1.5 mb higher over the 25 × 25 gridpoint domain (Table 1). The higher pressures in the ridge computed from NORAPS analysis data are also associated with the greatest pressure gradient of all the techniques examined and so the greatest geostrophic wind speed maximum on the western flank of the inverted ridge, with a peak value in excess of 40 m s−1 (Fig. 6a). The sea level temperatures are the coldest of all the methods along the eastern half of the line at roughly 10 K colder than the altimeter setting temperature (Figs. 4b and 5b). Since this method extrapolates a sea level temperature using the standard atmosphere lapse rate as do most of the methods, the cold sea level temperatures imply that the surface temperatures extrapolated from 700 mb are colder than observed, which would occur if the actual lapse rate were greater than standard. Indeed, a deep surface-based adiabatic layer was widespread on this day [see soundings for Oakland, Vandenberg, Edwards AFB, and Mercury, in Figs. 12 and 20 in Pauley et al. (1996)]. This method also portrays a strong gradient in sea level temperature in the western half of the domain, reflecting a strong 700-mb front in this region. The presence of an upper front would lead to an erroneous front in the extrapolated surface temperatures and so an erroneous pressure gradient in regions with high terrain elevations, providing a case where this method is not expected to perform well. Here, the upper front has minimal influence since the stations at this end of the line are at low elevations, but even so it does shift the inverted trough over CA toward the coast.

The Benjamin and Miller #2 reduction is based on the sigma-0.785 temperature. The extrapolated sea level temperatures are warmer along the eastern half of the line, yielding lower pressures compared to Benjamin and Miller #1 (Figs. 4 and 5) and weaker geostrophic wind speeds (Fig. 6a). This sigma surface is also beneath the upper front along the western half of the line, yielding temperatures that vary by only a few degrees along the entire line. However, the sigma-0.785 surface passes through the upper front offshore and farther south. This has little influence on the resulting pressure field in this case, but again would yield an artificial pressure gradient if the upper front were located over higher terrain elevations. The average difference between these SLP values and those from the simple reduction is −1.8 mb over the 25 × 25 gridpoint domain (Table 1).

The final method examined here was the “horizontal” reduction proposed by Mesinger (1990). Horizontally interpolating temperature yields sea level temperatures that are relatively warm with little gradient along the SFO–WMC line (Fig. 5b). The resulting pressures are therefore relatively low, with values closest to the Weaver and Toth adjusted altimeter settings (Fig. 5a). A weak trough is present somewhat east of its position in the manual analysis, and a weak ridge is present close to the position in the manual analysis. Geostrophic wind speeds are stronger than the model analysis winds by roughly a factor of 2, but show a similar variation, with no maximum along the western slope of the Sierra Nevada (Fig. 6). Over the 25 × 25 gridpoint domain, this technique yields SLPs that differ from the simple reduction by an average of only 0.1 mb (Table 1).

The horizontal interpolation procedure used here connects isotherms across the below-ground region with nearly linear segments and without any constraint on the vertical variation of temperature. While this procedure works well when the below-ground region is relatively small, it is more questionable when the below-ground region is large, as it is in the western United States at 850 mb and below. The possibility therefore exists that unrealistic lapse rates may result from this interpolation. An examination of the interpolated temperature profile in the vicinity of RNO and LOL (not shown) demonstrates that the lapse rate is dry adiabatic or slightly superadiabatic from 700 mb down to 950 mb, then nearly isothermal from 950 to 1000 mb. The surface pressure is close to 800 mb in this region; thus the adiabatic lapse rate in the top 100 mb of this layer results from the analysis and is consistent with nearby soundings. However, the horizontal interpolation yields a superadiabatic lapse rate in the 800–950-mb layer, with the potential temperature at 950 mb greater than that at 800 mb by 2 K. A lapse rate that is exactly adiabatic would be more realistic, yielding a colder layer mean temperature and a somewhat stronger inverted ridge. However, it is also unlikely that a shallow surface-based stable layer would exist below a deep adiabatic layer in late afternoon, implying that this layer is too cold and so at least partially offsets the previous error. The Mesinger (1990) technique, even so, does avoid the cold maxima in extrapolated sea level temperature that were found beneath the highest terrain in western NV using the simple reduction or the Benjamin and Miller reduction.

4. Summary and conclusions

A review of sea level pressure reduction techniques and an evaluation of their performance was undertaken to address two problems noted by the author in a previous study, namely estimating sea level pressure (SLP) from station data so a manual or objective analysis might incorporate stations only reporting altimeter setting as well as those reporting both SLP and altimeter setting, and computing an SLP field from model analyses or forecasts that can be compared to a manual or objective analysis of SLP, both in the context of mesoscale analysis. A troublesome case was examined that suggests only partial solutions to these problems.

A manual analysis of the reported SLP for 0000 UTC 30 November 1991 depicted several mesoscale features embedded in a northwest–southeast pressure gradient, including an inverted trough aligned with California’s Central Valley, an inverted ridge in western Nevada, ridging near Bakersfield, CA, on the windward side of the Tehachapi Mountains and troughing in the Los Angeles Basin on the lee side of the Tehachapis. The comparison of reduction techniques showed that almost any technique provides acceptable results when performing the reduction at stations with elevations less than roughly 300 m, the elevation above which the standard reduction includes the correction for the plateau effect and the local lapse rate anomaly. The stations along California’s coast and in the Central Valley (including Bakersfield) as well as the western quarter of the SFO–WMC line in the NORAPS fields had nearly the same values regardless of technique. Therefore at elevations below 300 m, stations reporting altimeter setting only can be incorporated into an analysis of reported SLP by computing surface pressure from the altimeter setting and then SLP from the surface pressure and virtual temperature. Although in this case, the raw altimeter settings (converted to mb) were quite close to values from the other techniques since the temperatures at lower elevations in CA were close to standard, the simple reduction using the current temperature is recommended for more general use. This is consistent with the results of Garratt (1984), who shows that computing SLP using the mean monthly temperature (as is done operationally in Australia) rather than observed temperatures can introduce an error of 2 mb at an elevation of only 250 m for anomalously warm summertime prefrontal conditions. The altimeter setting can have similar errors when the observed temperatures depart significantly from standard.

On the other hand, the mesoscale inverted ridge in western Nevada posed a significant difficulty for the analysis and was quite sensitive to reduction method. A test calculation was made for the stations along the SFO–WMC line, in which pressures were computed (using the simple reduction with the current virtual temperature) at a height of 1300 m rather than at sea level, approximately the mean surface elevation in Nevada. The 1300-m pressure at these stations indicates only slight ridging at LOL and confirms that the reported SLP at LOL was erroneously high (Fig. 7). Since extrapolating to sea level through a large depth can exaggerate errors due to erroneous or unrepresentative surface temperatures, performing a local mesoscale analysis on a geopotential surface (or a pressure surface) that is near the mean terrain elevation is recommended to minimize reduction errors in elevated plateau regions such as western Nevada. This technique was used as part of the Weaver and Toth (1990) adjusted altimeter setting; however, it can be easily adapted to simpler reduction methods, as was done here and as suggested by Danard (1989), using data from any station reporting altimeter setting.

An examination of temperatures suggests that the reported SLP value at LOL was too high as a result of using the anomalously cold 1200 UTC temperature in the standard reduction. The SLP reduction methods that did not use the 1200 UTC temperature produced a more reasonable pressure at this station and a more reasonable amplitude for the inverted ridge at this location. The Weaver and Toth (1990) altimeter setting adjustment best matched the standard reduction while reducing the sensitivity to local effects. In addition, this reduction was able to match the pressure gradient at 1300 m over Nevada. However, the functional relationship between S′ and zp is valid only over a region small enough that the dependence of S* on terrain elevation is greater than its spatial variation, the latter resulting from horizontal gradients of virtual temperature. This would be true in this case for a region roughly 5° latitude × 5° longitude centered on the Sierra Nevada. In addition, the functional relationship for S′ would have to be derived anew for each map time and each mesoscale region to be analyzed, making this technique more applicable for research applications than for operational use. The Benjamin and Miller (1990) technique using either 700-mb temperatures or sigma-0.785 temperatures also reduces sensitivity to local effects. Seaman (1997) found that this technique usually worked better than the current method in use in Australia, which is based on monthly mean temperatures rather than observed station temperatures, and better than the Simple SLP #1. However, the Benjamin and Miller (1990) technique can perform poorly in the presence of an upper front or a lapse rate that differs significantly from standard. In this case, the observed lapse rate below 700 mb was nearly adiabatic, with the result that this method gave temperatures that were too cold and pressures that were too high.

Even though some of the methods were successful in reducing the amplitude of the ridge in western NV, none were able to reasonably incorporate TRK into the analysis. A comparison of TVL with MHR and RNO shows that values for this station fit the overall gradient somewhat better than did values for TRK. These two stations have the highest elevations along the SFO–WMC line and so errors in the extrapolated below-ground temperatures would have the greatest effect, whether related to unrepresentative or erroneous surface temperatures or a poor choice of lapse rate for the below-ground layer. Reducing the pressure to 1300 m rather than sea level yielded a smaller difference between TVL or TRK and RNO (Fig. 7), but still required extrapolating 612 or 498 m, respectively, downward and so still is subject to significant error. That the TVL values differ less than the TRK values suggests that the altimeter setting for the latter may be in error.

It is also interesting to note that extrapolating the 1300-m pressure from the surface virtual temperature at the low elevation stations along the SFO–WMC line yields values that are nearly the same as those at RNO, LOL, and WMC and that are consistent with the 1300-m pressure computed from the OAK sounding at this time (Fig. 7). Even so, the potential exists for introducing significant errors by extrapolating upward from the surface through a large depth such as this. The magnitude of the error in an upward extrapolation can be estimated if sounding data are available, but rawinsonde soundings are relatively infrequent and of much coarser horizontal resolution than surface data. No good solution was found for the problem of depicting mesoscale features in the pressure field in regions with a large terrain gradient.

The depiction of the inverted mesoscale trough and ridge using data from the NORAPS analysis was also found to depend greatly on the reduction method, with differences between the model topography and station elevations leading to increased sensitivity in some locations. For example, SAC has a station elevation of 6 m and little sensitivity to reduction method using observational data, but the same location in the NORAPS terrain field had an elevation of more than 300 m and had more than 1-mb variation in SLP between methods. Thus, differences between model-analyzed and “observed” SLP can result from the difference between the model’s smoothed terrain and the actual station elevations, even if a technique were available to exactly mimic the standard reduction. It is important to be aware of the model’s depiction of terrain when interpreting mesoscale features in a model SLP field, especially when using higher-resolution mesoscale models that use terrain fields with mountains that are higher, steeper, and smaller scale than their predecessors and so have the potential for large reduction errors on a small scale.

Aside from any differences between the model’s smoothed terrain and the actual terrain, computing SLP from model gridpoint data can lead to terrain-induced features in the SLP field that arise from reduction error. The altimeter setting reduction assumed temperatures that were too warm in the below-ground layer and so depicted a trough along the highest terrain and a geostrophic wind speed maximum collocated with the terrain gradient on the western slope of the Sierra Nevada range. Although the observed surface winds were strong and gusty west of the Sierra, the model-analyzed winds had no maximum in this region suggesting that this wind speed maximum is erroneous. On the other hand, the Benjamin and Miller (1990) methodology applied to the NORAPS analysis data gave temperatures that were too low and pressures that were too high, also leading to a geostrophic wind speed maximum. The Shuell and simple techniques were similar to each other with somewhat lower pressures; however, reduction errors are still suspected since the inverted ridge is oriented along the highest terrain, the extrapolated sea level temperature depicts a minimum below the highest terrain, and a geostrophic wind speed maximum is again present on the western slope of the Sierra Nevada.

The Mesinger (1990) and Weaver and Toth (1990) reductions depicted only a slight mesoscale trough–ridge pattern, with an inverted ridge similar to that in the 1300-m pressures and with no geostrophic wind speed maximum on the western slope of the Sierra Nevada. These methods performed better than the others because they do not depend on model surface temperatures and because they permit a variable below-ground temperature profile that is constant horizontally for a particular analysis in the Weaver and Toth method and fully variable for the Mesinger method. However, the Weaver and Toth (1990) reduction is fairly difficult to apply, since its results are sensitive to the derivation of S′ to define the below-ground temperature structure. This derivation is quite subjective, with substantially different results obtained with alternate choices for the points used to define the linear function, and it is valid only over a limited region. The Mesinger horizontal interpolation technique can lead to a somewhat unrealistic below-ground temperature structure, such as the slightly superadiabatic below-ground lapse rate near Reno in this case. Even so, the Mesinger (1990) technique performed best for this case in terms of avoiding features in the pressure or temperature fields that coincide with the highest terrain in the Sierra Nevada and in terms of providing a reasonable geostrophic wind speed distribution even in regions of strong terrain gradient. This can be seen by comparing the Mesinger (1990) SLP field in Fig. 8 with the simple SLP field in Fig. 2. Of all the methods examined, the Mesinger (1990) method provides the best continuity between the model-analyzed or forecast above-ground temperatures and the below-ground derived temperatures.

As stated earlier, the differences between these techniques amount to differences in the assumed temperature profile for the fictitious below-ground layer, which is typically specified in terms of a surface temperature and a constant lapse rate. Therefore, an estimate of the error in SLP reduction associated with the assumed surface temperature and lapse rate was also made. As shown by Garratt (1984), the error in SLP associated with errors in the assumed temperature for the below-ground column is a function of the terrain elevation, the surface pressure, and the temperature itself. Consequently, it is difficult to make a general statement about the magnitude of such errors. Instead, this estimate is based on the simple reduction using the NORAPS analysis data and was made by adding or subtracting a uniform 1–2 K from the surface temperature or 1–2 K km−1 from the lapse rate. These values were chosen as conservative estimates of the error present in these quantities. Results along the SFO–WMC line are presented in Fig. 9, which shows that a 1-K error in surface temperature is roughly equivalent to a 1 K km−1 error in lapse rate. Little error in SLP is present at low-elevation stations, with the error increasing to about ±0.5 mb in the inverted ridge. Note that the point with an elevation of 300 m has SLP errors just over 0.1 mb. Averaging the error over the 25 × 25 gridpoint domain yields ±0.5 mb for a surface temperature error of ±1 K and ±0.4 mb for a lapse rate error of ±1 K km−1. Doubling the surface temperature error and the lapse rate error doubles the sea level pressure error to ±0.9 and ±0.8, respectively. Since a representative surface temperature is not known to greater accuracy than 1 K and since an appropriate value for the below-ground lapse rate could easily be 1 or 2 K km−1 higher or lower than the standard value typically assumed, the analysis of the inverted ridge in NV could easily have an error of 1 mb or more, confirming that this feature may not be “real.” However, it should also be noted that the magnitude of the estimated error would still permit a reasonable analysis of higher-amplitude features such as the synoptic-scale plateau anticyclone. Peyrefitte (1986) showed that plateau anticyclones having two or more closed isobars at a 4-mb interval are characterized by a general absence of cloudiness as one would expect for an anticyclone.

Acknowledgments

The author would like to thank Dr. E. H. Barker, NRL—Monterey, for providing theNORAPS analysis fields; Dr. Steven Chiswell, then of North Carolina State University, for providing the coded SAs; and Dr. Chi-Sann Liou, for explaining the technique used operationally to compute SLP for NORAPS. The author’s appreciation also goes to the anonymous reviewers, whose comments led to many improvements in the paper. The author would also like to thank Dr. Ashton Peyrefitte for providing a copy of his dissertation and Drs. E. H. Barker, Fedor Mesinger, and Stan Benjamin, and Mr. Forrest Williams for their comments on the manuscript. The support of the Office of Naval Research Program Elements 0601153N and 0602435N is gratefully acknowledged.

REFERENCES

  • Barker, E. H., 1992: Design of the navy’s multivariate optimum interpolation analysis system. Wea. Forecasting,7, 220–231.

    • Crossref
    • Export Citation
  • Bellamy, J. C., 1945: The use of pressure altitude and altimeter corrections in meteorology. J. Meteor.,2, 1–79.

    • Crossref
    • Export Citation
  • Benjamin, S. G., and P. A. Miller, 1990: An alternative sea level pressure reduction and a statistical comparison of geostrophic wind estimates with observed surface winds. Mon. Wea. Rev.,118, 2099–2116.

    • Crossref
    • Export Citation
  • Bluestein, H. B., 1992: Synoptic–Dynamic Meteorology in Midlatitudes. Vol. I: Principles of Kinematics and Dynamics. Oxford University Press, 431 pp.

  • Danard, M., 1989: On computing the surface horizontal pressure gradient over elevated terrain. Mon. Wea. Rev.,117, 1344–1350.

    • Crossref
    • Export Citation
  • Garratt, J. R., 1984: Some aspects of mesoscale pressure field analysis. Aust. Meteor. Mag.,32, 115–122.

  • Mesinger, F., 1990: “Horizontal” pressure reduction to sea level. Preprints, Int. Tagung für Alpine Meteorologie, Engelberg, Switzerland, Schweizerische Meteorologische Anstalt, 31–35.

  • ——, and R. E. Treadon, 1995: “Horizontal” reduction of pressure to sea level: Comparison against the NMC’s Shuell method. Mon. Wea. Rev.,123, 59–68.

    • Crossref
    • Export Citation
  • NWS, 1963: Manual of barometry. Federal Meteorological Handbook No. 7, U.S. Government Printing Office. [Available from NOAA/National Weather Service, Washington, DC 20233.].

  • Pauley, P. M., N. L. Baker, and E. H. Barker, 1996: An observational study of the “Interstate 5” dust storm case. Bull. Amer. Meteor. Soc.,77, 693–720.

    • Crossref
    • Export Citation
  • Peyrefitte, A., 1986: The plateau anticyclone of the western United States. Ph.D. dissertation, University of Utah, 123 pp. [Available from University Microfilms International, 300 N. Zeeb Road, Ann Arbor, MI 48106.].

  • Sangster, W. E., 1987: An improved technique for computing the horizontal pressure-gradient force at the earth’s surface. Mon. Wea. Rev.,115, 1358–1369.

    • Crossref
    • Export Citation
  • Saucier, W. J., 1955: Principles of Meteorological Analysis. University of Chicago Press, 438 pp.

  • Seaman, R. S., 1997: A comparison of some methods for reduction of pressure to sea level over Australia. Aust. Meteor. Mag.,46, 15–25.

  • Stackpole, 1970: Revised method of 1000 mb height computation in the PE model. Tech. Procedures Bull. 57, NOAA/NWS, 6 pp. [Available from NOAA Library, Silver Spring, MD 20910.].

  • Weaver, J. F., and J. J. Toth, 1990: The use of satellite imagery and surface pressure-gradient analysis modified for sloping terrain to analyze the mesoscale events preceding the severe hailstorms of 2 August 1986. Wea. Forecasting,5, 279–298.

    • Crossref
    • Export Citation

Fig. 1.
Fig. 1.

Manual analysis of reported (standard) SLP at 0000 UTC 30 November 1991. Isobars are drawn at a 2-mb interval and labeled with the value minus 1000 mb. Reported SLP values were available at stations indicated by a solid dot. Altimeter settings only were available at stations indicated by an open circle. A bold line connects the stations from San Francisco, CA, to Winnemucca, NV, that are used to compare reduction methods in Fig. 4. Terrain elevation (5′ resolution) is shaded, with white indicating elevations below 300 m, and increasingly darker shading for elevations above 300 m, 1000 m, 2000 m, and 3000 m, respectively.

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Fig. 2.
Fig. 2.

SLP computed from the 0000 UTC 30 November 1991 NORAPS analysis using the simple technique, with isobars drawn at a 2-mb interval. A bold line indicates the location of the interpolated values depicted in Fig. 5. The NORAPS terrain elevation is shaded at an interval of 200 m and labeled in units of 100 m. The region depicted in this figure was used to compute the 25 × 25 gridpoint averages for Table 1.

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Fig. 3.
Fig. 3.

Specific virtual temperature anomaly (S*) as a function of surface pressure altitude (zp) for 0000 UTC 30 November 1991. Observed values from central California and Nevada are indicated with a “+” and values computed from the NORAPS analysis along the SFO–WMC line are indicated with a “○,” with selected values further indicated with a “♦.” The bold line portrays the least squares fit to the observed values; the thin line portrays the least squares fit to the selected NORAPS values. These two lines were used to define the S′ functions for the Weaver and Toth (1990) adjusted altimeter setting, as described in the text.

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Fig. 4.
Fig. 4.

(a) SLP (mb) for 0000 UTC 30 November 1991 computed using various reduction techniques with observational data from the indicated stations along the SFO–WMC line portrayed in Fig. 1; (b) sea level temperature (K) used in the computation of SLP in (a); and (c) terrain elevation (m) both at individual stations and interpolated to the SFO–WMC line portrayed in Fig. 2 from the 5′ terrain dataset.

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Fig. 5.
Fig. 5.

(a) SLP (mb) for 0000 UTC 30 November 1991 computed using various reduction techniques with NORAPS analysis data and interpolated to the SFO–WMC line portrayed in Fig. 2; (b) sea level temperature (K) used in the computation of SLP in (a); and (c) NORAPS terrain elevation (m).

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Fig. 6.
Fig. 6.

(a) Geostrophic wind speed (m s−1) for 0000 UTC 30 November 1991 computed from SLP fields using various reductions with NORAPS analysis data and interpolated to the SFO–WMC line portrayed in Fig. 2; (b) observed wind speeds and gusts and model-analyzed winds interpolated to the SFO–WMC line; and (c) NORAPS terrain elevation (m).

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Fig. 7.
Fig. 7.

Comparison of SLP and 1300-m pressure (mb) for 0000 UTC 30 November 1991. Both SLP and 1300-m pressure were extrapolated from observational surface data at the stations along the SFO–WMC line portrayed in Fig. 1 using the surface pressure (computed from the altimeter setting), the current surface virtual temperature, and the standard atmosphere lapse rate (the Simple SLP #2 technique). The axis for the 1300-m pressure was shifted to overlay the RNO 1300-m pressure value on the RNO SLP value, in order to facilitate comparison of horizontal variations in pressure between the two levels. The solid circle depicts the 1300-m pressure interpolated from the OAK sounding.

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Fig. 8.
Fig. 8.

SLP computed from the 0000 UTC 30 November 1991 NORAPS analysis using the Mesinger (1990) technique, with isobars drawn at a 2-mb interval. Effective sea level temperatures (°C) are shaded at an interval of 2°C.

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Fig. 9.
Fig. 9.

Estimate of error in SLP reduction associated with errors in surface virtual temperature and assumed lapse rate. The simple technique was applied here using the NORAPS analysis data. A uniform value of 1 or 2 K was added to or subtracted from the mean boundary layer temperature or a value of 1 or 2 K km−1 was added to or subtracted from the standard atmosphere lapse rate in order to examine the effect of such errors.

Citation: Weather and Forecasting 13, 3; 10.1175/1520-0434(1998)013<0833:AEOUIS>2.0.CO;2

Table 1.

Comparison of SLP computed by various methods using the NORAPS analysis data. Differences are computed over the 25 × 25 gridpoint domain depicted in Fig. 2 with respect to the simple reduction, with a positive difference indicating that the simple SLP is greater.

Table 1.

1

While the atmosphere can interact with terrain to produce pressure variations that are on the scale of variations in terrain elevation and that have meteorological significance, a poor pressure reduction can also lead to features on this scale that are erroneous, that have no meteorological significance, and that may be difficult to distinguish from meteorological features. It is the latter rather than the former that one would like to minimize.

2

The units for elevation and for the constant K are listed as m and m/K, respectively, following common practice. But, to be precise, the meters here and elsewhere in this paper are geopotential meters given the use of a constant for the acceleration of gravity.

Save