Analysis and long-term forecasting of climatic characteristics of the mountains is laborious and extremely difficult due to complex vertical and horizontal differentiation of climatic fields and insufficient number of weather stations in the region. We have developed a method for statistical forecast of average monthly temperature in the surface air layer and monthly precipitation for the mountain areas with an annual lead time.

The method is based on the description of monthly dynamics of the mentioned factors expressed in percent of their average annual monthly values measured in situ. Such a dynamics remains the same throughout the study territory, regardless of its height and exposure. To convert the relative values of temperature and precipitation into their conventional units of measurements (°C and mm) one needs just mean annual January and July values of air temperature and precipitation for the territory under study. By the example of the Altai-Sayan mountain country, it is shown that the use of observation data for 6–7 years obtained from several reference weather stations ensure reliable prediction. The forecast is equally true for any part of the mountainous country due to spatial generalization of relative changes in these factors. The universal criterion A for assessing the quality of various predictive methods (including those, which do not use the model quality indices RSR and Nash–Sutcliffe) is proposed.

The criterion is the error of predictive method S_diff normalized by standard deviation S_obs of observations from their average and equals to S_diff/ S_obs. It is associated with NSE and RSR indices through dependencies RSR = A and NSE = 1–RSR² = 1–2A². The proposed criterion was used in assessing the quality of temperature and precipitation forecasts; it was close to the theoretically best one for statistical prognoses.