Models to improve winter minimum surface temperature forecasts, Delhi, India

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1 Meteorol. Appl. 11, () DOI:.17/S Models to improve winter minimum surface temperature forecasts, Delhi, India A. P. Dimri Research and Development Center Snow and Avalanche Study Establishment, Him Parisar, Sector 37A, Chandigarh, India 13 Accurate forecasts of minimum surface temperature during winter help in the prediction of cold-wave conditions over northwest India. Statistical models for forecasting the minimum surface temperature at Delhi during winter (December, January and February) are developed by using the classical method and the perfect prognostic method (PPM), and the results are compared. Surface and upper air data are used for the classical method, whereas for PPM additional reanalysis data from the National Center of Environmental Prediction (NCEP) US are incorporated in the model development. Minimum surface temperature forecast models are developed by using data for the winter period The models are validated using an independent dataset (winter 199 9). It is seen that by applying PPM, rather than the classical method, the model s forecast accuracy is improved by about % (correct to within ± C). 1. Introduction The northwest region of India is severely affected by cold conditions during the winter season. This hampers many outdoor activities, public utility services and also leads to acute human discomfort and sometimes death. Intense low minimum surface temperatures can produce inversions at ground level, which means that suspended particulates in the atmosphere are slow to disperse, resulting in poor visibility. Over hilly regions, namely Jammu and Kashmir, Himachal Pradesh and Uttaranchal, very low minimum surface temperatures may lead to ground frosts, with concomitant negative economic effects on agriculture and forestry. A sound knowledge of minimum surface temperatures is therefore essential in forecasting cold conditions in northwest India. In India, various researchers have employed the conventional classical method for developing deterministic approach for forecasting various meteorological variables. Forecasting based on the perfect prognostic method (PPM), one of the dynamical statistical methods, using numerical model outputs is still in an incipient stage. Kendall & Stuart (19), Panofsky & Brier (19) and WMO (19) provide detailed descriptions of various forecasting techniques based on statistical methodology. Singh & Jaipal (193) developed a subjective method of forecasting minimum surface temperature at Delhi by subjective deduction of the direction of the advecting wind as a potential predictor, but the technique was not totally objective. Mohan et al. (199) developed a method for forecasting maximum temperature over Ozar, Maharastra. Raj (199) evolved a scheme for predicting minimum surface temperatures at Pune by analogue and regression methods. Charantoris & Liakatas (199) have studied minimum surface temperature forecasts employing Markov chains. Kumar & Maini (199) have demonstrated a method based upon statistical interpretation and observed values of one or two seasons in order to obtain a bias-free forecast. Rao et al. (199) have fine-tuned the output of a numerical model (TL1) by employing statistical and synoptic methods. Mohanty et al. (1997) have developed a statistical method using the classical method for prediction of minimum surface temperature during winter and maximum surface temperature during summer at Delhi. Further, Raj (199), employing an optimal set of predictors, used a regression technique for forecasting maximum temperatures at Madras. Dimri et al. () have made use of multivariate statistical regression techniques in forecasting minimum and maximum surface temperatures at Manali. Maini et al. () employed PPM for forecasting precipitation and temperature during the monsoon season. Most of these studies use historical real time observations. Moreover, they are either semi-objective or subjective in nature. In the present study, short-range, location specific, deterministic forecasting of the minimum surface temperature is carried out by employing the conventional classical method, using historical real time observations available at the time of issuing the forecast. A comparison is then made with PPM, which, as well as using these historical real time observations, uses information about the future state of the atmosphere taken from numerical model outputs (NCEP reanalysis data) at the time of the forecast. In 19

2 A. P. Dimri this study the time frame of the forecast is restricted to hours because of limits to forecast skill and because of its usefulness in meeting operational requirements. Section of the paper discusses methodologies used for prediction purposes. Section 3 deals with the data used in this study. In section the climatology of the minimum surface temperature at Delhi is explained, and section 5 describes the development of models using the classical method and PPM. Results and discussion are presented in section. Finally, section 7 provides broad conclusions.. Methodology There are essentially three separate techniques for applying statistical methods in meteorology. A particular technique may make use any or all the types of meteorological variables. By convention these techniques are named in a hierarchical manner: the classical method, which uses only classical predictors from observational data that are offset in time from the predictand (the variable to be forecasted, e.g. minimum surface temperature); the Perfect Prognostic Method (PPM), which uses perfect prognostic predictors, observed or analysed, but which may also use classical predictors; and Model Output Statistics (MOS) or the imperfect prognostic method, which uses one or more predictors derived from numerical model output. These methods are briefly discussed below..1. Classical method Until the use of numerical models, regression models were developed for forecasting the weather. Such statistical techniques necessarily incorporated a time lag; for example, if one wanted to develop a scheme for forecasting next-day minimum surface temperatures, the input would consist only of observational data available at the time that the forecast is to be made. This situation can be expressed as Ŷ t = f( x ) (1) where Ŷ t is the estimate (forecast) of the predictand (dependent variable) Y at the time t, and X is a vector of observational data (independent variables) at the time (the observations are not necessarily made at time but must be made available at that time). This technique has become known as the classical approach (Klein 199). In application, the input is the same as in development, meaning that actual values of the independent variables are used in obtaining the forecasts. Such classical methods are very useful and are important for very short-range forecasting, e.g. from a few hours to one day. This method could also be used for long-range forecasting such as rainfall during the 13 monsoon season. The classical method is easy to develop and use, and does not depend on the numerical weather prediction (NWP) products... Perfect Prognostic Method (PPM) As numerical models are implemented and improved, it is natural to seek to exploit their output to the greatest possible extent. However, these models do not predict many of the weather variables with which users are concerned, such as minimum and maximum surface temperature or visibility. This situation has resulted in the development of the Perfect Prognostic Method (Klein 199). A concurrent relationship between the predictand variable and the predictors is developed, which can be expressed as Ŷ t = f (X t ) () where Ŷ t is the estimate of the predictor variable Y at time t, and X t is a vector of observations of variables that can be predicted by numerical models valid for time t. The time relationship need not be exactly concurrent but it is much more ahead and close to forecast time t. In the development of the regression equation with a dependent data set of Y, X are obtained only from the past observations at future time t. However, in the case of the practical application for forecasting of Ŷ t, X t are obtained from numerical model output. This approach assumes that the model output is to be as good as the actual observations, i.e. perfect (hence the name perfect prognostic ). Developments of perfect prognostic equations are similar to the development of classical regression equations, where observed predictors are used to quantify the observed predictand..3. Model Output Statistics (MOS) In PPM the developed model is independent of the numerical model outputs. The developed statistical model can be used with the output of X t from any NWP model provided it is assumed that the NWP output is exactly the same as the actual observations. Thus, although the perfect prognostic technique makes use of numerical model output; it is not necessarily true that the statistical relationship between Y and X obtained from past observations are sufficient for time t when X t is estimated by numerical models (equation ). In order to overcome this problem, the Model Output Statistics (MOS) technique was developed (Glahn & Lowry 197). In this approach, a large sample of model output is collected and a statistical relationship is developed, which can be expressed as Ŷ t = f ( ˆX t ) (3) where Ŷ t is the estimate of the predictand Y at time t, and ˆX t is a vector of the forecast s predictors obtained

3 Improving winter MST forecasts, Delhi mainly from numerical models. The numerical model predictions ˆX t need not be limited to time t but could be valid either before or after time t; however, the projection times of the different variables will usually be grouped around t. In application, equation (3) is used to develop the necessary forecast model... Comparison of the classical, PPM and MOS methods The classical method is most useful for very shortrange forecasting. It is simple to use, observations are usually abundant for model development, and there is no dependence on NWP models to complicate the application. This method is of limited use for providing a medium-range forecast beyond day 1. To improve both the time range and quality of the forecast, NWP output needs to be used as predictors. The PPM has additional advantages. First, the model development is based on actual observations. This enables availability of data for development and hence stability of the statistical model. The developed models are independent of NWP models and hence will not change if NWP models are subsequently modified. The drawback is that the technique assumes that the NWP model is perfect. Poor predictability of NWP models will result in wrong conclusions. However, the range of the forecasts is better compared to those produced using the classical method since incorporating NWP predictions brings the inherent strength of NWP models in forecasting events several hours to a few days in advance. The MOS method is the best for medium-range forecasting ( days ahead) provided a sufficient sample of NWP model output is available for development of the statistical model and provided the NWP model itself does not undergo major changes. Use of the MOS method usually requires more planning than the other techniques because the desired model output may not be saved without special arrangements. The major disadvantage is that the relationship developed for one NWP model may not hold for another model. Therefore, if the operational NWP model were changed substantially, a new statistical relationship would need to be developed. Such redevelopment can be done only after the new NWP model has been used for a long enough period to provide an adequate data sample for statistical models to be developed. 3. Data In order to obtain a reliable and relatively long dataset, a meteorological station situated about 15 km to the northwest of central Delhi (henceforth referred to as Delhi) was selected as the location to be used for this study. During winter, most of northwest India is subject to very low temperatures, so the whole winter season December, January and February (DJF) is considered for the study. Data for these months from 195 to 199 are used to develop the forecast models for predicting minimum surface temperature. The models performances were evaluated using independent data from two years (DJF, 199 9). In general, the minimum surface temperature at Delhi occurs at about 3UTC. In the formulation of the model equations, surface and upper air observations corresponding to UTC and 1UTC are utilised. In addition, for PPM, NCEP reanalysis data at.5.5 latitude/longitude is used. While verifying the model with independent data, predictors selected by the models at or after the forecast issuing time are interpolated from NCEP reanalysis data. The lead time of the forecast has been chosen as hours on the basis of availability of data, usefulness and operational requirements. The -hour forecast of the minimum surface temperature is issued at 3UTC valid for the next day. Before selecting potential predictors, care was taken to carry out quality control of observational data and to fill data gaps. In order to detect and correct errors, the mean ( x) and standard deviation (σ )ofall the parameters were calculated. All observations of individual parameters that lie outside ( x ± 3σ ) were isolated and examined. After examining previous and subsequent meteorological observations and synoptic weather conditions, outliers were replaced by suitable values. Once the errors were identified and corrected, the next step was to identify the missing data and to fill the data gaps using suitable interpolations. The individual data gaps were filled using linear interpolation. Observations at nearby observatories were also noted, while filling the individual data gaps. By doing so, quality control checks and checks on the space, time and synoptic conditions ensured that consistency was achieved. The data selected for the study consisted of surface and upper air at Delhi; the surrounding stations utilised were Patiala, Jodhpur, Ambala, Halwara, Pathankot, Sirsa, Suratgarh and Agra. The geographic locations of these stations are shown in Figure 1. The list of potential predictors and their notation used in this study are given in Table 1.. Climatology To understand the minimum surface temperature variation, a climatological study is carried out by studying the nature of the distribution of minimum surface temperature and establishing its relationship with the potential predictors. Since minimum surface temperature depends considerably on the local features as well as on moving synoptic systems (advective processes), it is wise to establish the statistical distribution of temperature. In studying climatological characteristics, developmental and independent data are utilised. 131

4 A. P. Dimri + Selected place of study PTK-Pathankot DLH-Delhi SIR-Sirsa JDP-Jodhpur AMB-Ambala HLW-Halwara PTL-Patiala SRT-Suratgarh Figure 1. Location of stations considered for study and data. The frequency distribution of the minimum surface temperature during winter is shown in Figure (development data) and Figure 3 (independent data), which indicates that the distribution of minimum surface temperature is close to the normal distribution with a slight skewness to the right. Sample statistics are given in Table. A study of the average minimum surface temperatures during winter indicates that the lowest minimum surface temperature generally occurs around 3UTC. But on rare occasions lowest minimum surface temperatures have been recorded at other times. Such instances were mainly due to a strong inversion or to the clearing of an overcast sky. In most of the analyses, minimum surface temperatures are associated with eastward moving synoptic weather systems from the mid-atlantic, called western disturbances (WD). The arrival of a WD over northwest India can be identified by the fluctuating behaviour of certain meteorological parameters. With the passage of a WD, a general increase in dry bulb and dew point temperatures Table 1. List of potential predictors and their notations in this study. Predictors and their notations Stations Total Surface Dry bulb (TT) and dew point (TD) temperature, maximum Delhi, Ambala, Sirsa, Halwara, 7 (T max ) and minimum (T min ) temperature and their hour Pathankot, Jodhpur, Suratgarh changes ( TT, TD, T max, T min ), dew point depression (DPD), relative humidity (rh), total cloud amount (TTLN), wind speed(ff) and wind direction (dd) Upper air Dry bulb (TT) and dew point (TD) temperatures, mixing Delhi, Patiala, Jodhpur 11 ratio (w), zonal (U) and meridional (V) components of wind at standard pressure levels (5, 7, 5 and 3 hpa) and thermal advection, winds shear, lapse rate, between different levels from surface to 3 hpa Persistence Minimum surface temperature (T min 1 ) Delhi 1 Total number of predictors 19 13

5 Improving winter MST forecasts, Delhi %Frequency Temperature ( o C) Range Figure. Frequency distribution of development data (DJF 195 9) of minimum surface temperature. is observed, and winds turn from westerly through easterly to southerly, which tends to result in a rise in minimum surface temperature. After the passage of the system the sky clears, the dry bulb and dew point temperatures decrease, winds become cold and dry, and consequently the minimum surface temperature falls. The persistence of the minimum surface temperature was also studied to examine its effect on model predictions (see Table 3). It shows absolute changes of 1 C, C,..., 5 C in observed minimum surface temperature over hours using both development and independent data for the classical method and PPM. It is apparent that the model could inherit a variable nature %Frequency Temperature ( o C) Range Figure 3. Frequency distribution of independent data (DJF 199 9) of minimum surface temperature. 133

6 A. P. Dimri Table. Statistics for minimum surface temperature using development data and independent data. Development data Independent data (DJF 195 9) (DJF 199 9) Mean. 7. Standard deviation.9.9 Highest Lowest.. Range while making the prediction. In addition, this model is capable in predicting high degree of deviation with much skill and robustness. 5. Development of the model A multiple regression technique stepwise regression (Draper & Smith 191) is used for selecting statistically significant predictors. In order to develop a multiple regression equation for forecasting minimum surface temperature, 19 potential predictors are utilised as listed in Table 1. These consisted of surface and upper air observations and derived parameters. At the first step all 19 predictors are subjected to screening in the forecast of minimum surface temperature. Many of these parameters are intercorrelated and each is measured with a certain degree of observational error. Therefore, it is necessary to identify a few potential predictors which can explain most of the variance of the predictand. This is accomplished by a forward method of selection by multiple regression, in which significant predictors are picked in a stepwise fashion. As a result, a small number of predictors can be selected which contain practically all the linear predictive information of the entire set with respect to a specific predictand and satisfy a statistical significance test. In this study the Fishers F-test is utilised to select significant predictors at the 95% confidence level. The stepwise procedure continues by adding one predictor at a time to the model. All the predictors included in the model are rechecked, and at this stage any predictor that is not statistically significant in the presence of other predictors is removed. The procedure terminates when the new predictor fails to reduce the variance by at least.5% or does not satisfy statistical significance at the prescribed 95% confidence level (F = 3.9). In this procedure, six predictors out of 19 are retained and used in the final multiple regression equations for prediction of minimum surface temperature Minimum surface temperature forecasts using the classical method The minimum surface temperature forecast equation using the conventional classical method for hours is shown in Table, along with the variance explained by the selected predictors and their cumulative variance. Table shows that the -hour forecast equation consists of six predictors. Here only those predictors are considered for the model development, which are real time observations and are available at the time of issuing the forecast. All the selected predictors indicate a relationship between moisture at the selected place of study, i.e. Delhi, and the temperature at stations to the northwest of Delhi. The increase in moisture will lead to a higher minimum surface temperature, which normally occurs at the approach of a WD. Stations to the northwest of Delhi indicate that after the passage of WD, colder temperatures become important as an advection mechanism. 5.. Minimum surface temperature forecast using the Perfect Prognostic Method The minimum surface temperature forecast equation using PPM for hours is shown in Table 5. The variance explained by each of the selected predictors and the cumulative variance explained by all of them are also expressed in the table. Six potential predictors have been incorporated into the forecast equation. In this approach, historical data available at the time of issuing the forecast and model outputs at or after the time of issuing the forecast are put through a selection screening process. This will lead to a more accurate prediction, as information regarding the future state of the atmosphere is available. This gives a prior indication of advection Table 3. Absolute -hour change in observed minimum surface temperature. Development data (DJF 195 9) Independent data (DJF 199 9) Error range PPM Classical method PPM Classical method (39.9%) 19 (53.%) 7 (3.5%) 7 (3.%) 1.1. (.7%) (.9%) (.%) (.%) (1.7%) 7 (1.%) 9 (1.%) 9 (1.5%) 3.1. (.%) 17 (.%) 1 (9.1%) 1 (9.1%) (.%) (.1%) (5.7%) (5.7) (.1%) 11 (.%) (3.7%) 1 (.3%) Total 31 (%) 31 (%) (%) (%) 13

7 Improving winter MST forecasts, Delhi Table. Minimum surface temperature forecast model by the classical method: equation, predictors and reduction of variances. -hour forecast issued at 3UTC. Equation: Y =.37 + (.3339 A1) + (.19 A) + (.31 A3) + (.13 A) + (.3 A5) + (.9 A) Sl No. Predictor Time (UTC) Level Place Correlation VE CVE A1 TT 3 Surface Halwara A TD Surface Delhi A3 TD 5hPa Delhi A TD 15 Surface Delhi A5 TTLN 3 Surface Delhi A T min 1 Surface Delhi MCC =. VE: Variance explained, CVE: Cumulative variance explained, MCC: Multiple correlation coefficient processes. It also has a major advantage in that stable forecasting can be established for individual locations over long periods of time.. Results and discussion The models developed for forecasting minimum surface temperature are tested using development data for December, January, February and independent data sets for the same months Forecast equations developed by both the methods are discussed below. The -hour minimum surface temperature forecast along with the actual values of development data (DJF 195 9) are given in Figure and Table. Similarly, the -hour minimum surface temperature forecast along with the actual values of independent data (DJF 199 9) are presented in Figure 5 and Table. It can be seen that model responds very well to the variation in the actual minimum surface temperature. The error analysis of the forecasts for both development and independent data using the classical method and PPM is given in Table. From Figures and 5, and Table, it is apparent that PPM gives a much better forecast than the classical method. In PPM, 75 9% of the forecasts are correct within ± C, whereas in the classical method 7 3% of the forecasts are correct within ± C of the actual value. This result indicates that information of synoptic weather systems in advance makes a definite improvement in forecast skill. Therefore, perfect prognosis of the predictors from a reanalysis dataset and/or numerical models leads to a stable and always better forecast. The reasons for large deviations have been analysed for the development and independent data. It is seen that thundershowers with overcast sky conditions occurred between UTC and 3UTC (the period when the daily minimum surface temperature normally occurs) on those days. The precipitation is not included as a forecast element in the equation, which may cause large deviations. The forecast model does not include any synoptic processes such as rain, thunderstorms, and changes in surface wind, in the forecast equation for minimum surface temperature. Similarly, investigation of the independent data shows that the dry bulb temperature happened to be higher than for the subsequent days. This alone resulted in the estimate of minimum surface temperature being higher. In most cases, it was found that the rapid movement of synoptic systems associated with rain and thunderstorms, which passed across the station in less time than the selected range of the forecast ( hours), resulted in a sudden change in certain predictors of the forecast equation, which resulted in large deviations. Further analysis Table 5. Minimum surface temperature forecast model using the Perfect Prognostic Method: equation, predictors and reduction of variances. -hour forecast issued at 3UTC. Equation: Y = (.53 A1) + (.1717 A) + (.5 A3) + (.75 A) + (.5 A5) + (.1 A) Sl No. Predictor Time (UTC) Level Place Correlation VE CVE A1 TT Surface Patiala A T min 1 3 Surface Delhi A3 w 5hPa Delhi A TD Surface Delhi A5 ff Surface Delhi A TD 1 Surface Delhi MCC =.9 VE: Variance explained, CVE: Cumulative variance explained, MCC: Multiple correlation coefficient 135

8 (a) (b) 1 1 A. P. Dimri Temperature C (c) 1 (d) Temperature C Data Points Data Points Actual Clas PPM Actual Clas PPM Figure. Observed and hour forecast of minimum surface temperature by classical and perfect prognostic method for developmental data set of (a) DJF 195 ; (b) DJF 19 7; (c) DJF 197 ; (d) DJF 19 9.

9 Improving winter MST forecasts, Delhi (a) Temperature C (b) Temperature C Data Points Actual Clas PPM Figure 5. Observed and -hour forecast of minimum surface temperature using the classical and Perfect Prognostic methods for independent dataset of (a) DJF ; (b) DJF of forecast and actual values for independent datasets indicate that day-to-day minimum surface temperature variations are quite homogeneous in nature, as indicated by root mean square error (rmse) value assuming persistence alone. In Table, the skill scores of the forecast are estimated as: [ ] Skill score = 1 RMSE m RMSE % () p where, RMSE m and RMSE p stand for rmse of the model prediction and of the persistence of the minimum surface temperature respectively. A positive skill score indicates a better performance of the model over persistence, whereas a negative skill score indicates that the model lacks the skill even to match persistence. Though there are few occasions when the forecast errors of minimum surface temperature exceed C, the skill scores given in Table clearly indicate that the developed equations have positive skill and perform better than the persistence with dependent as well as independent data sets. Also, better accuracy and fewer errors are found in the PPM compared with the classical method. Model results show that PPM shows more robustness than the classical method. 137

10 A. P. Dimri Table. Error analysis and skill scores for minimum surface temperature (-hour forecast) for Perfect Prognostic Method and the classical method. Development data (DJF 195 9) Independent data (DJF 199 9) Error range PPM Classical method PPM Classical method (5.%) 19 (5.%) 95 (5.%) (35.%) (5.%) 3 (.5%) 5 (5.) 57 (31.7%).1 3. (5.5%) 35 (9.%) 3 (1.%) 7 (15.%) (.5%) 13 (3.%) 13 (7.%) (11.1%).1 5. (5.5%) 7 (1.9%) 3 (1.7%) 9 (5.%) 5.1 (%) 5 (1.3%) 1 (.%) 3 (1.7) Total 31 (%) 31 (%) (%) (%) ABS RMS P-ABS P-RMS.1... SKILL (%) CC ABS: Absolute Error, RMS: Root mean square error, P-ABS: Absolute error assuming persistence, P-RMS: RMS error assuming persistence, SKILL: Skill score, CC: Correlation coefficient 7. Conclusions Short range, location specific, deterministic prediction of surface weather elements is one of the challenging problems in weather forecasting. Further, the impacts of orographical and topographical features make the prediction more difficult. In order to provide such specific forecasts, it is necessary to develop mesoscale models, which require a large number of observations to be taken at frequent intervals and at numerous locations (mesoscale network) surrounding the specific location. This naturally places a heavy demand on computer resources. In addition, the task is made more difficult by the need to better understand mesoscale physical processes and to include them in the model. On the other hand, for short-range forecasts, statistical methods can meet the requirement at a specific location. The demonstrable accuracy and skill in the shortrange, location specific, deterministic prediction by PPM over the classical method is a strong indicator for its use in numerical model outputs. Minimum surface temperature is well predicted by PPM (75 9% within ± C of the actual values) but to a lesser extent by the classical method (7 3%). PPM has a skill score of 5% in the developmental sample whereas the score for the classical method is.%. Similarly, for the independent data, the respective skill scores are.% and 31.1%. Also, employing PPM shows a significant improvement in error values. It is possible to further improve the forecast by incorporating numerical model outputs in the developmental model itself, i.e. by using model output statistics (MOS). Acknowledgements The author acknowledges the India Meteorological Department (IMD) and the National Center of Environmental Prediction (NCEP), US for providing valuable datasets used in this study. The author is extremely grateful to Group Captain Ajit Tyagi, Indian Air Force, for his help in accomplishing this work. References Charantoris, T. & Liakatas, A. (199) Study of minimum surface temperatures employing Markov chains. Mausam 1:9 7. Dimri, A. P., Mohanty, U. C., Madan, O. P. & Ravi, N. () Statistical model based forecast of minimum and maximum temperature at Manali. Current Science (): Draper, N. R. & Smith, H. (19) Applied Regression Analysis. New York: Wiley and Sons, 7pp. Glahn, H. R. & Lowry, D. A. (197) The use of model output statistics (MOS) in objective weather forecasting. J. Appl. Meteorol. 11: Kendall, M. G. & Stuart, A. (19). The Advanced Theory of Statistics. vol., London: Griffin, pp Klein, W. H. (199) The computer s role in weather forecasting. Weatherwise : Klein, W. H. & Hammons, G. A. (1975) Maximum/minimum surface temperature forecast based on model output statistics. Mon. Wea. Rev. 3: 79. Klein, W. H., Lewis, B. M. & Enger, I. (1959) Objective prediction of five-day mean temperatures during winter. J. Appl. Meteorol. 1: 7. Kumar, A. & Maini, P. (199) Statistical interpretation of general circulation model: a prospect for automation of medium range local weather forecast in India. Mausam 7:

11 Improving winter MST forecasts, Delhi Maini. P., Kumar, A., Singh, S. V. & Rathore, L. S. () Statistical interpretation of NWP products in India. Meteorol. Appl. 9:1 31. Mohan, V., Jargle, N. K. & Kulkarni, P. D. (199) Numerical prediction of daily maximum temperature over Ozar. Mausam : 7. Mohanty, U. C., Ravi, N., Madan, O. P. & Paliwal, R. K. (1997) Forecasting minimum surface temperature during winter and maximum temperature during summer at Delhi. Meteorol. Appl. :37. Panofsky, H. A. & Brier, G. W. (19) Some application of statistics to meteorology. University Park, Pennsylvania, pp : 191. Raj, Y. E. A. (199) Prediction of winter minimum surface temperature of Pune by analogue and regression methods. Mausam : 175. Raj, Y. E. A. (199) On forecasting daily maximum temperature at Madras. Mausam 9: 95. Singh, D. & Jaipal. (193) On forecasting night minimum over New Delhi. Mausam 3: Rao, P. S., Sasseendran, S. A., Rathore, L. S. & Bahadur, J. (199) Medium-range weather forecasts in India during Monsoon 199. Meteorol. Appl. 3: WMO (World Meteorological Organization) (19) Technical Report no