The least squares method in estimating the accuracy of surface air temperature projections based on ensembles of regional climate models

The study is devoted to the search for the optimal methodical approach for bias correction of surface air temperature from real climatic indicators for the territory of Ukraine, obtained in the projections of ensembles of regional climate models (RCM) based on the use of regression analysis, namely the least squares method (LSM) with various options of its application. The procedure included: searching for weight coefficients of linear regression equations to minimize the deviation of the forecast from the observations for each model and each grid node of the 10 RCM for two climatic periods 1961—1990 and 1991—2010; obtaining, on the basis of equations with established coefficients, the averaged errors of ensembles of models for various variants of LSM application; and determining the limits of the application of such methodical approaches to the formation of an optimal ensemble. Among all options for using forecasting functions, it was found that the most accurate was the option of applying LSM to differences (shifts) in values between periods when one uses monthly values of the climate indicator. In general, the use of monthly values showed the best approximation of the model data to the observation data used from the E-OBS database. It was found that in a certain period the approximation of the LSM is significantly better than the average, but the advantage is lost if the obtained weighting factors are used in another period. For further use, the proposed approach can be modernized in the direction of more detailed clustering in time and space, which will allow adjusting the model data even closer to the observed ones. However, our results make us doubt the feasibility of applying such an approach to the forecast of climate fields, since they are not stationary and can significantly transform over time. In this case, arithmetic averaging and averaging of shifts or the delta method remain the optimal choice for forming a prognostic ensemble of RCM.