Vol. 128, No. 3 * Pages 287–398 * July - September 2024

It is well known that the recent global warming intensifies the magnitude of rainfalls due to the increase in water content in the atmosphere. Therefore, the probability of exceeding the previously observed extreme precipitation values also increases with the experienced climate change, and forecasting extreme weather events is becoming more important. This paper presents a new polynomial regression approach and software (PolReg), where future extreme precipitations exceeding all previous observations are estimated for each month of year by using prediction bounds with a level of certainty at 95%. The presented method determines the degrees and coefficients of best-fitting polynomials for each precipitation station and forecasts the expected extreme value for each month of year by using the determined polynomials. The performance of the method is tested by removing and estimating a total of 792 highest observed monthly total precipitation values of 66 precipitation stations in Turkey (the highest observation for each month of year for each station). The results show that the proposed method and the provided software have a high performance and accuracy in estimating future precipitation extremes and might be applied in many disciplines dealing with forecasting probable extreme values.