Uncertainty analysis of bias from satellite rainfall estimates using copula method

The aim of this study is to develop a copula-based ensemble simulation method for analyzing the uncertainty and adjusting the bias of two high resolution satellite precipitation products (PERS1ANN and TMPA-3B42). First, a set of sixty daily rainfall events that each of them occurs concurrently over twenty 0.25 degrees x 0.25 degrees pixels (corresponding to both PERSIANN and TMPA spatial resolution) is determined to perform the simulations and validations. Next, for a number of fifty-four out of sixty (90%) selected events, the differences between rain gauge measurements as reference surface rainfall data and satellite rainfall estimates (SREs) are considered and termed as observed biases. Then, a multivariate Gaussian copula constructed from the multivariate normal distribution is fitted to the observed biases. Afterward, the copula is employed to generate multiple bias fields randomly based on the observed biases. In fact, copula is invariant to monotonic transformations of random variables and thus the generated bias fields have the same spatial dependence structure as that of the observed biases. Finally, the simulated biases are imposed over the original satellite rainfall estimates in order to obtain an ensemble of bias-adjusted rainfall realizations of satellite estimates. The study area selected for the implementation of the proposed methodology is a region in the southwestern part of Iran. The reliability and performance of the developed model in regard to bias correction of SREs are examined for a number of six out of those sixty (10%) daily rainfall events. Note that these six selected events have not participated in the steps of bias generation. In addition, three statistical indices including bias, root mean square error (RMSE), and correlation coefficient (CC) are used to evaluate the model. The results indicate that RMSE is improved by 35.42% and 36.66%, CC by 17.24% and 14.89%, and bias by 88.41% and 64.10% for bias-adjusted PERSIANN and TMPA-3B42 estimates, respectively. (C) 2013 Elsevier B.V. All rights reserved.