Integrating Entropy and Copula Theories for Hydrologic Modeling and Analysis

Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula theories provides new insights in hydrologic modeling and analysis, for which the development and application are still in infancy. Two broad branches of integration of the two concepts, entropy copula and copula entropy, are introduced in this study. On the one hand, the entropy theory can be used to derive new families of copulas based on information content matching. On the other hand, the copula entropy provides attractive alternatives in the nonlinear dependence measurement even in higher dimensions. We introduce in this study the integration of entropy and copula theories in the dependence modeling and analysis to illustrate the potential applications in hydrology and water resources

Estimating differential entropy using recursive copula splitting

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods. The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions. Numerical examples demonstrate that the method is accurate for distributions with compact and non-compact supports, which is imperative when the support is not known or of mixed type (in different dimensions). At high dimensions (larger than 20), our method is not only more accurate, but also significantly more efficient than existing approaches

A preliminary assessment of GPM-based multi-satellite precipitation estimates over a monsoon dominated region

Following the launch of the Global Precipitation Measurement (GPM) Core Observatory, two advanced high resolution multi-satellite precipitation products namely, Integrated Multi-satellitE Retrievals for GPM (IMERG) and Global Satellite Mapping of Precipitation (GSMaP) version 6 are released. A critical evaluation of these newly released precipitation data sets is very important for both the end users and data developers. This study provides a comprehensive assessment of IMERG research product and GSMaP estimates over India at a daily scale for the southwest monsoon season (June to September 2014). The GPM-based precipitation products are inter-compared with widely used TRMM Multi-satellite Precipitation Analysis (TMPA), and gauge-based observations over India. Results show that the IMERG estimates represent the mean monsoon rainfall and its variability more realistically than the gauge-adjusted TMPA and GSMaP data. However, GSMaP has relatively smaller root-mean-square error than IMERG and TMPA, especially over the low mean rainfall regimes and along the west coast of India. An entropy-based approach is employed to evaluate the distributions of the selected precipitation products. The results indicate that the distribution of precipitation in IMERG and GSMaP has been improved markedly, especially for low precipitation rates. IMERG shows a clear improvement in missed and false precipitation bias over India. However, all the three satellite-based rainfall estimates show exceptionally smaller correlation coefficient, larger RMSE, larger negative total bias and hit bias over the northeast India where precipitation is dominated by orographic effects. Similarly, the three satellite-based estimates show larger false precipitation over the southeast peninsular India which is a rain-shadow region. The categorical verification confirms that these satellite-based rainfall estimates have difficulties in detection of rain over the southeast peninsula and northeast India. These preliminary results need to be confirmed in other monsoon seasons in future studies when the fully GPM-based IMERG retrospectively processed data prior to 2014 are available