Using Copulas to Evaluate Rationality of Rainfall Spatial Distribution in a Design Storm

Abstract

In the absence of long-series streamflow records in plain areas, design storm, which serves as the most important input in a hydrologic model, plays an important role in flood control and water resources management. For a large drainage basin, design storm may be estimated for sub-basins separately; thus the spatial distribution of design storm needs to be carefully treated. However, few studies have been carried out to evaluate the rationality of the spatial distribution in a design storm, which means the storm over space should be in accordance with actual needs or its distributing patterns. Taking the Tai Lake Basin (TLB), 3-d Copula-based models combining extreme rainfall of different sub-basins were built using long-term rainfall data, and conditional probabilities of sub-basins encountering certain amounts of rainfall were investigated to evaluate the rationality of the design storm. Results show that the spatial distribution of the design storm based on a typical year is hardly rational, in which rainfall of the northeastern part of the basin is suggested to be weakened while in the southwest to be strengthened; after the rainfall is redistributed based on long-term information, it shows a better rationality of spatial distribution. Such information provides valuable significance in guiding flood control of TLB, and the considered evaluating method can be used for similar basins in plain areas.

Application of Copula Functions for Rainfall Interception Modelling

“…Moreover, copula functions have been used several times for rainfall analysis and modelling. Some examples of this include: for rainfall frequency analysis in order to estimate reliable design rainfall (e.g., [32][33][34][35][36][37]), for disaggregation of rainfall data (e.g., [38,39]), to construct intensity-duration-frequency (IDF) curves for different purposes (e.g., [40][41][42]), for rainfall generation and modelling (e.g., [43][44][45]), for drought analyses and characterisation of drought properties (e.g., [46][47][48][49][50][51][52][53][54][55][56][57]), and for other rainfall related analyses (e.g., [58][59][60][61][62][63][64]). However, one should bear in mind that research dealing with copula functions is also very intense in the Statistics Probability category (e.g., more than 250 papers were published in 2017 in this category according to the Web of Science database).…”