Assessing and Modifying the Formula for Estimating the Conditional Transition Probabilities and Daily Precipitation Variance under the Influence of Climate Change

Abstract In the predicting process of climate change, accurate assessments require the use of downscaling methods to estimate the parameters of precipitation characteristics. Among the current methods of statistical downscaling, two-point and four-point methods on conditional transition probabilities and the approximation method on daily precipitation variance have led to widespread adoption in various studies around the world because of their straightforwardness, convenience, and practicability. However, two-point and four-point methods underestimated the probability of wet days following wet days in arid and semiarid region, and the approximation method has something in overestimation on daily precipitation variance. Building upon previous works, this study introduced the weighting method on conditional transition probability and the regression method on daily precipitation variance to develop a modified approach. All methods were validated using 100-yr daily precipitation data from Tucson (U.S.) and 60-yr precipitation data from five stations in China. Results showed that all three methods demonstrated strong performance in estimating conditional transition probabilities. The weighting method reduced the biases in the semiarid region. The approximation method exhibited errors in estimating the daily precipitation variance indicated by the negative model efficiency (ME) of self-test in both semiarid and humid regions, while the regression method showed a strong relationship between daily and monthly precipitation variance with high ME of self-test. High ME of validation tests demonstrated that the regression method is highly applicable in both climatic regions. All the results implicated that the weighting method and the regression method introduced in this paper enhance the accuracy of estimation and can be utilized not only in the humid region but also in the semiarid region.