Estimation of mean rainfall over a catchment area using the relationship of maximum and mean rainfalls

As climate change has a profound impact on the hydrological cycle, the frequency and intensity of extreme rainfall events have increased significantly, and the distribution of rainfall in time and space has shown significant uneven characteristics. Therefore, rainfall in the catchment area is of vital importance to hydrological research and disaster prevention. Catchment-average rainfall is widely used in hydrological processes, especially in the issue of rainfall-runoff. This study aims to use the maximum rainfall over a catchment area to estimate the average rainfall in the catchment area.

This study first gridded the catchment and then used the ordinary Kriging method and the rainfall of the rain gauges in the catchment to estimate the rainfall in each grid. The rainfall of the grids are used to estimate the average and maximum rainfall over the catchment area. In addition, this study used the concept of probability and the maximum entropy principle to deduce that there is a strong correlation between maximum and average rainfalls and used data from the Xindian River in the north Taiwan to evaluate the feasibility of the model. The results show that the relationship between the maximum rainfall and the average rainfall in the catchment is a linear relationship passing through the origin. That is, the ratio of the average rainfall to the maximum rainfall in the catchment area is a constant that is not affected by time and space. Therefore, the relationship between the maximum rainfall and the average rainfall in the catchment area developed by this study can be used to quickly estimate the real time average rainfall of a catchment.