Forecasting Local Weather by Means Ol Model Output Statistics

Home , Model output statistics

William H. Klein and Harry R. Glahn forecasting local weather T echniques Development Laboratory National Weather Service, NOAA by means ol model Silver Spring, Md. 20910 output statistics

Abstract vice by developing automated forecasts of each of the Experience over the past decade has shown that objective weather elements listed above. forecasts of local weather elements can best be obtained 2. Two methods of statistical-numerical prediction by using statistical methods to complement the raw output of numerical prediction models. One of the most Figure 1 illustrates two methods of combining statistical successful techniques for accomplishing this is called and numerical techniques. The first, called the perfect Model Output Statistics (MOS). The MOS method in- prog method, utilizes observed historical data to specify volves matching observations of local weather with out- local weather elements from concurrent (or nearly con- put from numerical models. Forecast equations are then current) weighted combinations of meteorological param- derived by statistical techniques such as screening eters. To use the derived equations for making a fore- regression, regression estimation of event probabilities, cast, we apply them to the output of numerical prog- and the logit model. In this way the bias and inaccuracy nostic models which simulate the observed circulation, of the numerical model, as well as the local climatology, as shown by the dashed arrow. Although errors in the can be built into the forecast system. MOS has been numerical prediction will inevitably produce correspond- applied by the Techniques Development Laboratory to produce automated forecasts of numerous weather elements including precipitation, temperature, wind, clouds, ceiling, visibility, and thunderstorms. In this paper, the derivation and operational application of MOS forecasts for each of these elements are discussed. Many of the products are transmitted nationwide over facsimile and/or teletypewriter; others are provided for internal use within the National Weather Service. Ultimately, a completely automated, computer-worded, local weather forecast will be produced routinely as part of a program for Automation of Field Operations and Services (AFOS). 1. Introduction More than any other single factor, the remarkable success of numerical weather prediction during the past decade has helped transform weather forecasting from an art into a science. However, only limited success has been achieved by purely numerical models in forecasting such weather elements as the occurrence, type and amount of precipitation, maximum and minimum temperatures, thunderstorms and tornadoes, surface winds, cloudiness, ceiling, and visibility. In fact, most models do not even predict these variables directly. Yet, these are precisely the elements of greatest concern to the vast bulk of our population. Our experience in the last 10 years has shown that improved forecasts result when the raw output from numerical models is processed by mod- ern statistical methods. In this paper we describe how we are accomplishing this in the Techniques Develop- FIG. 1. Two methods of combining numerical and statistical ment Laboratory (TDL) of the National Weather Ser- weather forecasting in schematic form.

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Unauthenticated | Downloaded 10/10/21 07:49 PM UTC Vol. 55, No. 10, October 1974 ing errors in the statistical forecast, the latter will im- TABLE 1. Verification of objective maximum/minimum tem- prove each time the former is improved. An advantage perature forecasts, averaged at 49 cities, made once a day (0000 GMT) for the period 1 April-30 June 1972, of this method is that stable forecasting relations can from NMC prognostic data by MOS and be derived for individual locations and seasons from a Perfect Prog Systems. long period of record. A disadvantage is that it takes no account of errors and uncertainties in the numerical Perfect model. The perfect prog method has been applied many Statistic MOS prog times since its initial use by Klein et al (1959), but in a) Today's Max the past few years it has been gradually replaced by Mean absolute error (°F) 3.3 3.9 the second method. However, it is still extremely useful Correlation between forecast and observed .82 .78 for forecasting relatively rare events where local factors Mean algebraic error (°F) 0.3 0.8 are very important. For example, it is being applied on Standard deviation of forecasts (°F) 6.9 6.5 an operational basis in the National Weather Service to b) Tonight's Min produce automated forecasts of the water level on Lake Mean absolute error (°F) 3.4 3.9 Erie (Richardson and Pore, 1969) and extratropical storm Correlation between forecast and observed 1 .76 .71 surges along the Atlantic coast (Pore et al, 1974). Mean algebraic error (°F) -0.3 -0.6 The second statistical technique has been named Standard deviation of forecasts (°F) 5.2 5.1 Model Output Statistics (MOS) by Glahn and Lowry (1972a). Instead of a long period of observed data, the c) Tomorrow's Max predictor sample in MOS usually consists of a rela- Mean absolute error (°F) 4.2 4.6 Correlation between forecast and observed .74 .70 tively short period of prognostic data produced by Mean algebraic error (°F) 0.3 0.2 numerical models. Thus, the MOS method involves Standard deviation of forecasts (°F) 6.3 6.6 archiving the output from numerical models and matching it with observations of local weather. Forecast equa- d) Tomorrow Night's Min tions are then derived by using a variety of statistical Mean absolute error (°F) 3.9 4.4 techniques to be illustrated later. In this way the bias Correlation between forecast and observed .64 .65 Mean algebraic error (°F) -0.1 -1.2 and inaccuracy of the numerical model, as well as the Standard deviation of forecasts (°F) 4.8 5.3 local climatology, can be automatically built into the forecast system. Another characteristic of MOS is that it can include many predictors not readily available to the perfect prog method, such as vertical velocity, forecast projection. Results quite similar to Table 1 were boundary layer potential temperature, 3-dimensional recently obtained under operational conditions at 126 air trajectories, etc. Because of these advantages, the cities during the four-month period from September MOS technique has, for most uses, proven to be more through December 1973 (Hammons and Klein, 1974). successful than the perfect prog method in recent years. Table 2 gives another comparison of MOS and per- Until last year our most notable application of the fect prog forecasts. This is for the probability of precipi- perfect prog method was the preparation of automated tation during standard 12-hr periods at 86 stations across forecasts of maximum and minimum surface temperatures the United States. The forecasts were made in an opera- (Klein and Lewis, 1970). However, in August of 1973, tional environment over a five-month test period (Janu- the operational system for making these forecasts was ary-May 1972) by means of the MOS technique de- shifted to MOS because of its greater accuracy and con- scribed by Lowry and Glahn (1974) and the perfect prog venience (Klein and Hammons, 1973). Table 1 presents method described by Klein (1971). The forecasts were several verification statistics for forecasts of maximum verified in terms of the P-score (Brier, 1950) and com- and minimum temperatures during four periods at 49 pared to climatology. Both objective forecasts exhibited cities for a three-month test period in the spring of skill relative to climatology; as might be expected, their 1972. The first line in each section shows that during skill decreased with forecast projection. However, the all four periods the MOS forecasts had lower mean abso- MOS forecasts were clearly superior to the perfect prog lute errors than the perfect prog forecast. The second line shows that the MOS forecasts had higher correlation coefficients with the observed temperatures during TABLE 2. Improvement in P-score over climatology (%) for all periods but the last. The third line shows that the probability of precipitation forecasts for five-month bias of the MOS forecasts was negligible on the average. period, 1 Jan-31 May 1972, for 86 stations. The fourth line shows that the variability of the MOS forecasts was somewhat larger than the variability of the Forecast period MOS Perfect prog Local perfect prog forecasts in the first two periods but con- First 30.4 19.7 39.3 siderably less in the last two periods. This is an asset of Second 24.1 14.4 23.8 the MOS system since the variance of its forecasts is a Third 15.0 9.1 15.3 function of their skill, which naturally decreases with Fourth 6.4 0.3 NA

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Unauthenticated | Downloaded 10/10/21 07:49 PM UTC Bulletin American Meteorological Society forecasts during all periods. In fact, except for the first the three-dimensional trajectory model of Reap (1972). period, the MOS forecasts were about as good as those Hence, it is popularly known as PEATMOS (PE And produced subjectively by local forecasters of the Na- Trajectory Model Output Statistics). Since the trajectory tional Weather Service (last column). Similar results model produces only 24-hr forecasts, some of our MOS were found by Glahn et al. (1971) for an earlier test products have been developed from the PE model only period (October-December 1970). (PEMOS). The remainder of this article will deal with the application of PEATMOS and PEMOS to almost all 3. TDL's MOS system the elements contained in a routine weather forecast. The MOS technique was first developed by Glahn and Systematic archiving of output from the PE and Lowry (1972a) who initially used output from the Sub- trajectory models began in October 1969 and has con- synoptic Advection Model (SAM) (Glahn and Lowry, tinued to date. In an attempt to account for the pre- 1972b). Later they obtained improved results by adding dominance of the different weather regimes in winter output from the six-level baroclinic Primitive Equation and summer, the year has been divided into two parts: (PE) model of Shuman and Hovermale (1968). This ap- the cool season, consisting of the six months October plication of MOS (called SAPEMOS for SAM and PE through March, and the warm season, composed of six Model Output Statistics) led to successful forecasts of months April through September. The relatively short probability of precipitation (Glahn and Lowry, 1969), period of record has precluded further stratification by conditional probability of frozen precipitation (Glahn time of year. To account for seasonal trend within these and Lowry, 1972a), surface wind speed and direction seasons, the sine and cosine of the day of the year have (Glahn, 1970a; Barrientos, 1970), maximum temperature been included as potential predictors. (Annett et al., 1972), ceiling (Bocchieri and Glahn, 1972), Observed surface weather reports have been ac- and visibility (Bocchieri et al., 1974). However, these quired from the National Climatic Center in Asheville, forecasts, like SAM,1 were limited to the first 24 hr in N.C., for each of the 254 first-order stations plotted in the eastern half of the United States. Fig. 2. Numerical model output at each of these stations Because of the limitations of the SAPEMOS fore- has been obtained by biquadratic interpolation from casts, they have been replaced by another type of MOS NMC and trajectory model grids. The observations have product which covers the entire conterminous United then been matched with the numerical predictors on a States for projections out to 60 hr. This MOS is based local basis. Thus, the surface weather has been pre- upon output from the PE model mentioned above and dicted from collocated variables, in contrast to the correlation field method in which the predictors may be i The operational use of SAM by the National Weather Service ended in October 1973. At that time it was replaced located hundreds of miles from the forecast point (Klein by another model called SUM (Subsynoptic Update Model) etal., 1959). which covers the conterminous United States (Grayson and Although our numerical predictors are always located Bermowitz, 1973). at the same point as the predictand weather element,

FIG. 2. Locations of 254 stations in the 50 states for which routine weather observations are being collected for matching with numerical model output. 1219

Unauthenticated | Downloaded 10/10/21 07:49 PM UTC Vol. 55, No. 10, October 1974 they are not necessarily valid at the same time. Because otherwise local scheme. Considerable experimentation the numerical models can be systematically too slow or has indicated that smoothing of numerical output should too fast, predictors within ±24 hr of the predictand time be increased with increasing forecast projection, decreas- have also been found useful in certain cases. ing elevation, and decreasing scale of the predictor. Another procedure which has increased the utility of 4. Single station equations the numerical predictors is space smoothing. Averaging over 5, 9, or 25 grid points frequently removes spurious a. Temperature perturbations from "noisy" numerical output, particu- Many of the points discussed in the preceding section are larly from elements of smaller scale such as vertical illustrated in Table 3, which lists the potential pre- velocity and relative humidity. Smoothing also intro- dictors used to derive forecast equations for maximum duces information from surrounding grid points to an and minimum surface temperature (Klein and Ham-

TABLE 3. Potential predictors of maximum and minimum surface temperature for screening regression. Numbers indicate valid time of predictors in hours after 0000 GMT. Stars indicate the predictor was smoothed by 5 points (*) or 9 points (**). Tomorrow Predictor Today max Tonight min Tomorrow max night min a) Trajectory Model Surface temperature 24, 24* 24, 24* 24, 24* 24*, 24** Surface dew point 24* 24* 24* 24** 850-mb temperature 24, 24* 24, 24* 24, 24* 24*, 24** 700-mb temperature 24, 24* 24, 24* 24, 24* 24*, 24** 700-mb 12-hr net vert displ 24* 24* 24** 24** 700-mb 24-hr net vert displ 24* 24* 24** 24** 850-mb 12-hr net vert di$$>l 24* 24* 24** 24** 850-mb 24-hr net vert displ 24* 24* 24** 24** 700-mb relative humidity 24* 24* 24** 24** 850-mb relative humidity 24* 24* 24** 24** 700-mb-surface mean rel hum 24* 24* 24** 24** Surface 12-hr horiz conv 24* 24* 24** 24** b) PE Model 1000-mb height 24 36 48 48* 850-mb height 24 36 48 48* 500-mb height 12, 24 24, 36 36, 48 48, 48* 1000-500-mb thickness 12, 24 24, 36 36, 48 48, 48* 1000-850-mb thickness 12, 24 24 36, 48 48, 48* 1000-mb temperature 12, 24, 24* 24*, 36, 36* 36*, 48, 48* 48, 48*, 48** 850-mb temperature 12, 24, 24* 24*, 36, 36* 36*, 48, 48* 48, 48*, 48** 700-mb temperature 24 24 24* 24* Boundary layer potential temp 12, 24, 24* 24*, 36, 36* 36*, 48, 48* 48, 48*, 48** Boundary layer U wind 12, 24* 24*, 36* 36*, 48* 48*, 48** Boundary layer V wind 12, 24* 24*, 36* 36*, 48* 48*, 48** 850-mb U wind 24* 24* 24** 24** 850-mb V wind 24* 24* 24** 24** 700-mb U wind 24 24 24* 24* 700-mb V wind 24 24 24* 24* 400-1000-mb mea® rel hum 12*, 24* 24*, 36* 36**, 48** 48*, 48** Precipitable water 18* 30* 42** 42** Precipitation amount 24 36* 48* 48** 850-mb vertical velocity 24* 24* 24** 24** 650-mb vertical velocity 24* 24* 24** 24** c) Other Variables Sine day of year 00 00 00 00 Cosine day of year 00 00 00 00 Latest surface temperature G6 — — — Latest surface dew point m — — — Latest cloud cover 06 — — — Latest surface U wind 06 — — — Latest surface V wind 06 — — — Latest surface wind speed 06 — — — Previous min 00 — — — Previous max 00

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TABLE 4. Sample equations for estimating the U and V wind components and the wind speed 12 hr in advance (from 00 GMT) at Kansas City. Data sample consisted of 607 days from the cool seasons of 1969-73. Cumulative reduction Cumulative standard error Valid of variance of estimate (kt) Coefficients Predictor time Units (GMT) U V 5 U V 5 U V 5 Regression Constant — — — — — — — -1.368 — .835 .197 kt 1. Boundary layer U wind 1200 .593 .017 .003 3.56 7.32 4.03 .092 .080 .041 m sec-1 2. Boundary layer V wind 1200 .624 .639 .006 3.42 4.44 4.03 -.082 -.046 -.054 m sec-1 3. Boundary layer wind speed 1200 .630 .639 .388 3.40 4.44 3.16 .008 .145 .075 m sec-1 4. Observed wind speed 0600 .634 .648 .521 3.38 4.38 2.80 .057 -.114 .447 m sec-1 5. Observed U wind 0600 .695 .648 .521 3.08 4.38 2.80 .408 -.058 -.006 m sec"1 6. Observed V wind 0600 .697 .688 .521 3.07 4.13 2.80 -.043 .414 .009 m sec-1 7. Boundary layer V wind 1800 .698 .743 .522 3.07 3.75 2.79 .025 .406 .031 m sec-1 8. Boundary layer U wind 1800 .730 .745 .522 2.90 3.73 2.79 .351 .117 -.056 m sec"1 9. Boundary layer wind speed 1800 .730 .745 .545 2.90 3.73 2.72 -.001 .012 .231 m sec"1 10. Mean relative humidity 1200 .731 .747 .555 2.90 3.72 2.69 .012 -.016 .021 % mons, 1973). The predictors were carefully selected from for each of 228 stations, four projections, two run times, the output of PE and trajectory models to include all and two seasons, for a total of 3648 multiple regression available factors which might contribute to surface tem- equations. All equations were required to have exactly perature such as height, thickness, temperature, wind, 10 terms since recent research by Annett et al. (1972), moisture, and vertical velocity at various levels and pro- and Bocchieri and Glahn (1972) has indicated this is jections. For the first period forecast, eight surface near the optimum number of predictors for continuous synoptic reports were included as predictors to give the variables and for samples of this size. latest observed conditions at the station. These are re- ported at 0600 and 1800 GMT, 6 hours after the initial b. Surface wind time of the numerical models (0000 or 1200 GMT), but Ten-term individual station equations were also derived still early enough to be used operationally. by Carter (1973) to forecast surface wind at 233 stations Since temperature is a continuous, rather normally by applying screening regression to continuous pre- distributed variable, forecast equations were derived by dictors. As with temperature, surface synoptic reports a standard screening regression program such as that available 6 hr after numerical model input time were used by Miller (1958). Separate equations were derived screened for the initial projection. However, only the

FIG. 3. An automated 18-hr forecast of most probable category of cloud amount valid at 1800 GMT, 23 September 1973. Lines labeled 1+ divide the clear and scattered areas, 24- the scattered and broken areas, and 3+ the broken and overcast areas. Category 4 (overcast) areas are shaded. 1221

Unauthenticated | Downloaded 10/10/21 07:49 PM UTC Vol. 55, No. 10, October 1974 PE model was used as numerical input; the trajectory not occur often enough in a small data sample to allow model was not used in this application of MOS. Separate derivation of reliable single station equations. There- equations were derived for U and V wind components fore, we have combined data from a number of stations and for wind speed S for seven projections at 6-hr within each of several homogeneous regions; a single intervals from 12 to 48 hr. equation was then derived for each region. In applica- Some constraints were imposed on the selection of tion, the equation is used at each station within the predictors. For any given station and projection, the region with input data appropriate to that particular three equations for U, V, and S all contain the same 10 station. This has been called the generalized operator predictors, but with different regression coefficients and technique by Harris et al. (1963) and Russo et al. (1966). constants, as illustrated in Table 4. Further, the first three predictors were forced to be the boundary layer a. Probability of precipitation forecasts of U, V, and S for the valid time of the wind For example, Fig. 4 illustrates 14 regions used by Lowry predictand. The remaining seven predictors were se- and Glahn (1974) to forecast the probability of precipi- lected one at a time by using at each step the mete- tation from PEATMOS data during the warm season of orological variable for which the variance of any of the 1973. The boundaries were determined by analyzing the three predictands was reduced by the largest fractional frequency of precipitation with different values of PE amount. predictions of mean relative humidity. Within each c. Cloud amount region a standard set of the 100 most valuable binary predictors from PE and trajectory models was offered Another weather element for which single station equa- for screening by the REEP program. Different predictor tions have been derived by the MOS technique is cloud sets were required for each of four projections; the set amount (Glalin, 1974a). Here, PE and trajectory model for the second period is illustrated in Table 5. predictors, but not observed surface data, were used to develop forecast equations for the probability of each of four categories of sky cover; namely, clear, scattered, b. Ceiling and Visibility broken, and overcast. Thus, the predictand was binary; A similar set of 14 regions was used by Globokar (1974) the predictors were expressed in both continuous and to derive equations for the probability of each of five binary form. This application of regression has been categories of ceiling and five categories of visibility from called REEP (degression Estimation of £vent Probabili- PEATMOS data. He employed, as predictors, surface ties) by Miller (1964). After the probability of each observations, as well as PE and trajectory model output, cloud category was determined, the best single category and expressed the independent variables in both binary was obtained by a method described by Glahn (1974b). A sample categorical forecast yielded by this procedure is and continuous form. A sample equation resulting illustrated in Fig. 3. from his use of the REEP program is illustrated in Table 6. Note that the 24-hr forecast of ceiling depends 5. Generalized operator equations upon physically meaningful variables such as mean It is frequently important to predict relatively rare events (1000-400 mb) relative humidity, observed ceiling, sur- such as heavy rain, low ceiling, or tornadoes. These do face relative humidity, boundary layer divergence and

TABLE 5. One hundred binary predictors screened for PEATMOS PoP during second period (24-36 hr). Smoothing Time Field Model (points) (hours) Binary limits Units 700-mb net vertical displacement TJ 1 24 -10, 0, 10, 20, 30, 40 mb Mean relative humidity TJ 5 24 40, 45, 50, 55, 60, 65, 70 % 850-mb vertical velocity PE 5 24 -.5, -.2, .2, .5 jub sec 1 650-mb vertical velocity PE 5 24 -.5, -.2, .2, .5 jub sec-1 Total totals index PE, TJ 5 24 30, 35, 40, 42, 44, 46 C K index PE, TJ 5 24 5, 10, 15, 20 C Precipitable water PE 1 30 60, 90, 120 in. X 102 Precipitable water PE 5 30 30, 60, 90 in. X 102 850-mb height PE 5 36 1,481; 1,517; 1,535; 1,553 m Boundary layer U wind PE 5 36 -2, 0, 2, 4 m sec-1 Boundary layer V wind PE 5 36 — 2, 2, 5, 7 m sec-1 Boundary layer vertical velocity PE 5 36 -.5, -.2, 0, .2 lib sec"1 Mean relative humidity PE 5 36 55, 60, 65j 70, 75, 80, 85 % Mean relative humidity PE 9 36 50, 55, 60, 65, 70, 75, 80 % Boundary layer humidity PE 5 36 55, 60, 65, 70, 75, 80, 85 % Boundary layer humidity PE 9 36 50, 55, 60, 65, 70, 75, 80 % Second layer humidity PE 5 36 55, 60, 65. 70, 75, 80, 85 % Second layer humidity PE 9 36 50, 55, 60, 65, 70, 75, 80 % 12-hr precip. amount PE 1 36 0, 3, 8, 15, 25 in. X 102

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FIG. 4. Fourteen regions used in the development of summer equations for forecasting the probability of precipitation. Each region has one set of equations applicable to each station (located by dots) in that region. vorticity, precipitable water, and 850-mb relative activity was summarized within grid boxes, roughly 190 humidity. km on a side, grouped into three regions, as illustrated in Fig. 5. Regression runs were carried out for two defini- c. Thunderstorms tions of the radar predictand. In one run, the event Larger regions were utilized by Alaka et al. (1973) and predicted was the occurrence of a convective echo within Reap (1974) to derive equations for forecasting the a box. In the other run, the only cases used were those probability of thunderstorms and severe local storms with a convective echo within a box, and the event from PE and trajectory model predictors. Their pre- predicted was the occurrence of an intense line echo. dictand data were tabulated from summary maps pre- The line-echo definition was based on a study by Bonner pared by the radar development unit at the National and Kemper (1971) relating echo characteristics on radar Severe Storms Forecast Center in Kansas City. Radar summary maps to severe weather reports. Therefore, the

TABLE 6. Equations for estimating the five CAT CIG valid at 2400 GMT in Region 8 (Ohio, Indiana, Illinois, Iowa, Michigan, and Missouri). Input includes predictors from 0000 GMT model runs and 0600 GMT observations. (C) indicates predictor is continuous. Projection Coefficients Predictor Limit (tau) Smoothing CATl CAT2 CAT3 CAT4 CAT5 1. PE MRH (C) 24 5 pt. -.0001 .0002 .0014 .0021 -.0036 2. OBS CIG <2000 ft 06 None .007 .014 .042 .071 -.133 3. TJ SFC RH <70% 24 None -.001 -.012 -.021 -.079 .112 4. PE BL DIV < -.8 sec"1 24 5 pt. .006 .024 .022 .011 -.063 5. PE MRH <86% 30 5 pt. -.008 -.075 -.106 .017 .172 6. OBS CIG <150 ft 06 9 pt. .063 .073 -.011 -.013 -.112 7. COS DOY (C) 00 None .017 .043 .017 .056 -.133 8. PE BL VORT <.9 sec-1 24 5 pt. -.006 -.013 -.036 -.032 .088 9. PE P WATER <9 kg/m2 30 9 pt. -.011 -.033 -.021 .012 .053 10. TJ 850 RH (C) 24 9 pt. .0002 .0006 .0003 .002 -.003 11. TJ SFC RH <85% 24 None -.015 -.083 -.073 .025 .145 12. PE P WATER <16 kg/m2 18 9 pt. .003 .001 .023 .062 -.089 Constants .019 .144 .146 -.149 .840

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Unauthenticated | Downloaded 10/10/21 07:49 PM UTC Vol. 55, No. 10, October 1974 was used by Bermowitz (1974) to predict quantitative precipitation from PEATMOS data. He forecast the probability of each of five categories of precipitation amount by means of the REEP technique. Although large amounts of precipitation occur infrequently and prediction is difficult, preliminary results have been encouraging.

6. The logit model The logit model has been used by Glahn and Bocchieri (1974) to estimate the conditional probability of frozen precipitation [PoFP(P)], i.e., given the occurrence of precipitation, what is the probability it will be frozen? The logit, introduced into the meteorological literature by Brelsford and Jones (1967) and Jones (1968), fits an S-shaped curve to a categorical predictand as a function of continuous predictors. In our application, the single FIG. 5. Grid used in tabulating radar data for thunderstorm station and generalized operator approaches were com- forecasting. Boxes are approximately 190 km on a side and bined. Output from the PE model only was used are grouped into three regions: Central, Eastern, and Gulf (PEMOS), and the development proceeded in two steps. Coast. First, for each of 186 stations, a "50%" value was found for each of three variables predicted by the PE first set of regression equations forecasts the probability model—850-mb temperature, 1000-500-mb thickness, and of general thunderstorms and the second set forecasts the boundary layer potential temperature. For instance, the (conditional) probability of severe thunderstorms, given value of the 850-mb temperature which indicates a 50-50 the occurrence of an ordinary thunderstorm. A sample chance of frozen precipitation at a particular station 24-hr forecast is illustrated in Fig. 6. (provided precipitation occurs) was found. These 50% values were determined by using the logit model to fit d. Quantitative precipitation data from three winter seasons (single station approach). A completely generalized approach, in which the entire Secondly, the deviations from the 50% values were conterminous United States is treated as one region, determined for each station for each variable; the rela-

FIG. 6. An automated 24-hr forecast of thunderstorm probability (solid lines) and conditional probability of severe thunderstorms (dashed lines) valid at 0000 GMT 15 June 1973. The isopleth interval is 20% for thunderstorms and 5% for severe thunderstorms. 1224

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FIG. 7. An automated 12-24 hr PoP forecast and 12-hr PoFP(P) forecast made from the PE run of 0000 GMT 15 December 1973. The PoP forecasts are shown as solid lines at 10% intervals from 5 to 95. The PoFP(P) forecasts are shown as dashed lines for values of 10, 50, and 90%. The areas defined by PoP isopleths 45 to 65% and above 85% are shaded. Areas where snow or rain may be expected (PoP > 45%) are indicated by stars or dots separated by the 50% value of PoFP(P). tive frequency (for those cases when precipitation oc- ables. In order to get stable results in this last step, data curred) of frozen precipitation was then computed, again for all stations were combined (generalized operator). with the logit model, as a function of these new vari- In addition to the meteorological variables, station ele-

FIG. 8. A guidance package of automated forecasts for Washington, D.C., in digital form. Included are predictions of maximum and minimum temperature, probability of precipitation, conditional probability of frozen precipitation, wind direction and speed, probability of thunderstorms, conditional probability of severe thunderstorms, cloud amount, quantitative precipitation, ceiling, and visibility.

Unauthenticated | Downloaded 10/10/21 07:49 PM UTC Vol. 55, No. 10, October 1974 vation and the first harmonic of the day of year were guidance package of MOS forecasts expected to result used as predictors. from this experiment is illustrated in Fig. 8. Forecasts of PoFP(P) are disseminated routinely by Our MOS project is illustrated in schematic form in facsimile and teletypewriter; an example of the facsimile Fig. 9. We are archiving all operational numerical product, which includes both PoP and PoFP(P) fore- models for later processing by the MOS computer pro- casts, is shown in Fig. 7. This is a completely automated grams. Thus far, MOS has been applied to SAM, PE, weather forecast which combines probability forecasts and trajectory models. Later it will be tested on the out- (in isopleth form) with categorical forecasts of rain or put of the limited area fine mesh (LFM) model of How- snow (shaded). croft (1971), the SUM model of Grayson and Bermowitz (1973), and the boundary layer model (BLM) described 7. Concluding remarks by Gross et al. (1972). The first 10 weather elements on The MOS forecast techniques described in the preceding the right side of Fig. 9 have already been discussed. three sections are in various stages of implementation at Forecast equations for the last two (fog and surface dew the National Meteorological Center (NMC). The pre- point) will be derived at a future date. Ultimately, this dictions of probability of precipitation, conditional prob- type of combined numerical-statistical output will pro- ability of frozen precipitation, and maximum and mini- vide accurate guidance to the field for all surface weather mum surface temperatures are fully operational and elements on the synoptic and subsynoptic scales. How- transmitted twice daily over nationwide facsimile and ever, application of similar techniques on the important teletypewriter. MOS forecasts of surface wind direction mesoscale must await the development of accurate opera- and speed, ceiling, and visibility are transmitted over tional numerical models on a very fine mesh. Unfor- teletypewriter on a request/reply basis and are scheduled tunately, this development may be some years away. to go on twice-daily facsimile in late 1974. During the warm season, MOS predictions of the probability of Acknowledgments. We wish to thank the entire staff thunderstorms and the conditional probability of severe of the Techniques Development Laboratory for their local storms are made available to forecasters in both dedicated efforts of the past five years which have made digital and map form once a day. Predictions of cate- this article possible. Special thanks go to Frank Lewis, gory of sky cover and precipitation amount are provided Chief, Computer Systems Branch, for handling the opera- as guidance to forecasters at NMC on an experimental tional implementation of most of the MOS products. basis. Later in the year we plan to combine all these MOS products to produce a completely computer-worded References forecast (Glahn, 1970b) of local weather conditions as Alaka, M. A., W. D. Bonner, J. P. Charba, R. L. Crisci, R. C. part of an experiment in automation of field operations Elvander, and R. M. Reap, 1973: Objective techniques for and services (AFOS) (Lowry et al., 1974). A sample digital Forecasting thunderstorms and severe weather. Report No. FAA-RD-73-117. Techniques Development Laboratory, Silver Spring, Md., 97 pp. Annett, J. R., H. R. Glahn, and D. A. Lowry, 1972: The use of model output statistics (MOS) to estimate daily maximum temperatures. NOAA Technical Memorandum NWS TDL-45, 14 pp. Barrientos, C. S., 1970: An objective method for forecasting winds over Lake Erie and Ontario. ESS A Technical Memorandum WBTM TDL-34, 20 pp. Bermowitz, R. J., 1974: Forecasting quantitative precipitation with use of model output statistics. Preprint Fifth Confer- ence on Weather Forecasting and Analysis, Boston, Mass., Amer. Meteor. Soc., 75-78. Bocchieri, J. R, and H. R. Glahn, 1972: The use of model output statistics for predicting ceiling height. Mon. Wea. Rev., 100, 869-879. , R. L. Crisci, H. R. Glahn, F. Lewis, and F. T. Globokar, 1974: Recent developments in the National Weather Ser- vice program for the automated prediction of ceiling and visibility. /. Appl. Meteor., 13, 277-288. Bonner, W. D., and J. E. Kemper, 1971: Broad-scale relations between radar and severe weather reports. Preprint, Seventh Severe Local Storms Conference, Boston, Mass., FIG. 9. The MOS program in schematic form. Output from Amer. Meteor. Soc., 140-147. the operational numerical models on the left can be processed Brelsford, W. M., and R. H. Jones, 1967: Estimating prob- by complex combination of computer programs in the middle abilities. Mon. Wea. Rev., 95, 570-576. to produce automated forecasts of any weather element on Brier, G. W., 1950: Verification of forecasts expressed in the right. terms of probability. Mon. Wea. Rev., 78, 1-3. 1226

Unauthenticated | Downloaded 10/10/21 07:49 PM UTC Bulletin American Meteorological Society Carter, G. M., 1973: Use of model output statistics in auto- Jones, R. H., 1968: A nonlinear model for estimating prob- mated prediction of surface winds. TDL Office Note 73-4, abilities of K events. Mon. Wea. Rev., 96, 383-384. 9 pp. Klein, W. H., 1971: Computer prediction of precipitation Glahn, H. R., 1970a: A method for predicting surface winds. probability in the United States. J. Appl. Meteor., 10, ESSA Technical Memorandum WBTM TDL-29, 18 pp. 903-915. ——, 1970b: Computer-produced worded forecasts. Bull. , and G. A. Hammons, 1973: Use of model output sta- Amer. Meteor. Soc., 51, 1126-1131. tistics for automated prediction of max/min temperatures. , 1974a: An objective cloud forecasting system. Preprint, TDL Office Note 73-3, 9 pp. Fifth Conf. Weather Forecasting and Analysis, Boston, , B. M. Lewis, and I. Enger, 1959: Objective prediction Mass., Amer. Meteor. Soc., 79-80. of five-day mean temperature during winter. J. Meteor., , 1974b: Problems in the use of probability forecasts. 16, 672-682. Preprint, Fifth Conf. Weather Forecasting and Analysis, , and F. Lewis, 1970: Computer forecasts of maximum Boston, Mass., Amer. Meteor. Soc., 32-35. and minimum temperature. J. Appl. Meteor., 9, 350-359. , and D. A. Lowry, 1969: An Operational Method for Lowry, D. A., and H. R. Glahn, 1974: An operational model Objectively Forecasting Probability of Precipitation. ESSA for forecasting probability of precipitation. To be pub- Technical Memorandum WBTM TDL-27, 24 pp. lished in J. Appl. Meteor. Abstract in Bull. Amer. Meteor. , , G. W. Hollenbaugh, and J. R. Annett, 1971: Statis- Soc., 1972, 53, p. 80. tics of Numerical Prediction Models. Preprint, International , W. H. Klein, H. R. Glahn, and R. L. Crisci, 1974: Fore- Symposium on Probability and Statistics in the Atmo- cast applications associated with AFOS. Preprint, Fifth spheric Sciences, Honolulu, Hawaii, 15-20. Conf. Weather Forecasting and Analysis, Boston, Mass., , and , 1972a: The use of model output statistics Amer. Meteor. Soc., 7-12. (MOS) in objective weather forecasting. J. Appl. Meteor Miller, R. G., 1958: A statistical procedure for screening pre- 11, 1203-1211. dictors in multiple regression. Final Report; Contract No. , and , 1972b: An operational subsynoptic advection AF 19(604)-1590, The Travelers Weather Research Center, model (SAM). J. Appl. Meteor., 11, 578-585. Inc., Hartford, Conn., 238 pp. , and J. R. Bocchieri, 1974: Predicting the conditional , 1964: Regression estimation of event probabilities. Tech- probability of frozen precipitation. NOAA Technical Memorandum NWS TDL-51, 33 pp. nical Report No. 1, Contract No. 1 Cwb-10704, The Trav- Globokar, F. T., 1974: Computerized ceiling and visibility lers Research Center, Inc., Hartford, Conn., 153 pp. forecasts. Preprint, Fifth Conf. Weather Forecasting and Pore, N. A., W. S. Richardson, and H. P. Perrotti, 1974: Analysis, Boston, Mass., Amer. Meteor. Soc., 228-233. Forecasting extratropical storm surges for the Northeast Grayson, T. H., and R. J. Bermowitz, 1973: A subsynoptic coast of the United States. NOAA Technical Memorandum update model and forecast system with application to NWS TDL-50. aviation weather. Final Report, FAA Contract No. Reap, R. M., 1972: An operational three-dimensional tra- FA67WAI-131, Techniques Development Laboratory, Sil- jectory model. /. Appl. Meteor., 11, 1193-1202. ver Spring, Md., 48 pp. , 1974: Thunderstorm and severe weather probabilities Gross, E., R. Jones, and R. McPherson, 1972: A description based on model output statistics. Preprint, Fifth Conf. of the NMC planetary boundary layer model. NMC Weather Forecasting and Analysis, Boston, Mass., Amer. Office Note 75, 40 pp. Meteor. Soc., 266-269. Hammons, G. A., and W. H. Klein, 1974: Operational tem- Richardson, W. S., and N. A. Pore, 1969: A Lake Erie storm perature forecasts by means of model output statistics. surge forecasting technique. ESSA Technical Memorandum Paper presented at 54th Annual Meeting of American Geo- WBTM TDL-24, 23 pp. physical Union, Washington, D.C., April 1974. Russo, J. A., I. Enger, and G. T. Merriman, 1966: A statistical Harris, R. G., J. G. Bryan, and J. E. MacMonegle, 1963: approach to the 12-48 hr. prediction of precipitation Terminal weather prediction studies. Technical Note 3, probability. Final Report, Contract No. Cwb-11100, The Contract No. AD 19(626)-16, The Travelers Research Cen- Travelers Research Center, Inc., Hartford, Conn., 107 pp. ter, Inc., Hartford, Conn., 103 pp. Shuman, F. G., and J. B. Hovermale, 1968: An operational Howcroft, J. G., 1971: Local forecast model: Present status six-layer primitive equation model. J. Appl. Meteor., 7, and preliminary verification. NMC Office Note 50, 6 pp. 525-547.

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