Forecast of thunderstorm with increasing advance time

A method for assessing the hail hazard of the atmospheric situation according to the output data of the global atmospheric model (GFS NCEP) with increasing lead time is proposed. The method is implemented on the basis of multivariate discriminant analysis. The evaluation of the success of the method is carried out and the preservation of its predictive potential is shown for a lead time of up to five days.


Introduction
Dangerous weather events associated with atmospheric convection make a significant contribution to the damage caused to the economies of countries by natural disasters, and have a pronounced upward trend, compounded by their lack of predictability. The main reasons for the lack of prevention of convective hazards are the lack of initial information, as well as the lack of traditional approaches for predicting local rapidly developing processes.
In recent years, the output of global mathematical models of the atmosphere has become available, including the fields of meteorological elements (stratifications of the fields of temperature, humidity, wind direction and speed) with different lead times. The output of the current model of the NOAA global Forecasting System (GFS NCEP), an analogue of the aerological probe, used in this work, has a sufficiently high reliability and allows obtaining information with a lead time of up to 10 days. There are a number of publications [1][2][3][4] using this data.
In this paper, we study the dependence of the validity of the hail forecast on the increasing up to five days in advance.

Materials and methods of research
The NOAA Global Forecasting System (GFS NCEP) became widely used and well-known in the early 90s [5][6][7]. With the growth of computing resources and changes in computer architecture, its resolution also increased. In June 2019, the global forecasting system under the NGS (Next Generation Global Prediction System) project was significantly updated. The transition to a new non-spectral block for solving dynamic equations was made, and a number of improvements were introduced in the description of physical processes at the grid scale. The dynamic core splits the atmosphere into small cubic cells located on the grid and calculates the changes in the parameters within each cell. This allows you to increase the scale of the calculated grid when modeling mesoscale storm systems to improve their forecast. The time discreteness of the model is three hours for a lead time of 0-180 hours and 12 hours for a lead time of 180-384 hours. The part of the output of the global model required for use in methods for predicting convective phenomena (analogous to an aerological sound) includes the prognostic fields of the following meteorological elements:  isobaric surfaces (hPa) and their corresponding heights (m);  air temperature (°C);  dew point temperature (°C);  wind direction (deg);  wind speed (m/s). These weather elements are calculated at various levels from 1000 to 20 hPa. The algorithm used in this paper for calculating the parameters of the atmosphere and clouds that cause the occurrence, development and intensity of hail processes is a generalization of the schemes for calculating the parameters used in existing methods for predicting convection and related weather hazards, and is, in fact, an electronic aerological diagram [8].
To predict hail, this algorithm uses the output of the global atmospheric model as input data with a lead time of 12 hours to five days: air temperature and dew points, wind direction and speed at standard levels (Earth, 800, 700, 650, 600, 500 , 400, 300 and 200 hPa). About 45 atmospheric parameters are preliminarily calculated, which are known from the existing methods of forecasting convection and associated dangerous weather phenomena. Such a number of features imposes too stringent (often unrealizable) requirements for the amount of empirical data. Therefore, it became necessary to select the most informative of them signs. This problem was solved in two ways: using the biserial correlation coefficient and factor analysis taking into account the biserial correlation coefficient [8][9][10][11][12]. Then, using the selected parameters, discriminant functions are compiled to predict hazardous events (hail).
The discriminant function obtained on the basis of the parameters selected using the biserial correlation coefficient has the form: According to the discriminant function (1), when The discriminant function obtained on the basis of the parameters selected using factor analysis and the biserial correlation coefficient has the form: where 700 V  ordered vertical air movements at 700 hPa; m t   maximum temperature difference between the cloud and the surrounding air; 1 t   vertical temperature gradient in the layer above the condensation level by 2 km; According to the discriminant function (2), «hail» is also predicted at 0 2   L , and at Note that the parameters included in the discriminant functions mainly reflect the margin of instability, moisture content and temperature regime in the hail growth zone. A distinctive feature of the discriminant function (2) is that it allows one to quantitatively take into account large-scale atmospheric movements (ordering of vertical currents), against the background of which convective phenomena develop. This is the reason for the choice of this function for further calculations.
To assess the success of the proposed hail forecasting method, a contingency table is drawn up with the following elements:

Results and discussion
Based on the high values of the correlation coefficients between the data of actual upper-air sounding and the corresponding predicted values according to the global model with increasing lead time [4], in this work, for the forecast of hail, the values of meteorological parameters were used according to the data of the global atmospheric model. The hail forecast was compiled using discriminant functions for May-August 2020 according to the geographical coordinates of the «Mineralnye Vody» station. To assess the success of the forecast, a contingency table was compiled (table 1), the data of which made it possible to calculate the criteria for the quality of the hail forecast (table 2). The division of phenomena into «hail» or «without hail» was carried out according to the observations of the paramilitary services on the active impact on meteorological and other geophysical processes located within the radius of representativeness of the actual upper-air sounding data at the «Mineralnye Vody» station (table 1).
The results of hail forecasts by discriminant functions for 24, 72 and 132 hours showed that the method under consideration meets all the criteria for the quality of forecasts. Table 2 clearly shows that the indicators of the success of the forecast with a lead time of 24 hours turned out to be high. As for the indicators for a 72-hour lead time, they turned out to be slightly lower than the indicators for hail forecasting with the same functions with a shorter lead time (24 hours). In the case of a 132-hour lead time, the forecast quality criteria turned out to be at the level or slightly higher than for the previous lead time. This is due to the fact that the calculations for this period were carried out according to the data of the global model for 2019, and as noted above, the global atmospheric model itself was improved in the same year. Note that the justification of the proposed method is equal to 70% for a lead time of 72 hours, in contrast to the similar forecast method for 24 hours (77%) and for 132 hours (72%). Thus, the criteria for the quality of forecasts, in particular, hail, with increasing lead time, meets all criteria for the quality of forecasts.

Conclusion
The criterion for the quality of forecasts of hail with increasing lead time meets all the criteria for the quality of forecasts.
Thus, the predicted values of atmospheric stratification can be used to make predictions of hazardous phenomena and weather elements (replacing the actual upper-air sounding), which cannot yet be predicted by the global models themselves. In this case, the lead time of forecasts can be brought to the periods corresponding to the medium-term periods of the weather forecast.