Realistic sampling of anisotropic correlogram parameters for conditional simulation of daily rainfields

This paper has established a link between the spatial structure of radar rainfall, which more robustly describes the spatial structure, and gauge rainfall for improved daily rainfield simulation conditioned on the limited gauged data for regions with or without radar records. A two-dimensional anisotropic exponential function that has parameters of major and minor axes lengths, and direction, is used to describe the correlogram (spatial structure) of daily rainfall in the Gaussian domain. The link is a copula-based joint distribution of the radar-derived correlogram parameters that uses the gauge-derived correlogram parameters and maximum daily temperature as covariates of the Box-Cox power exponential margins and Gumbel copula. While the gauge-derived, radar-derived and the copula-derived correlogram parameters reproduced the mean estimates similarly using leave-one-out cross-validation of ordinary kriging, the gauge-derived parameters yielded higher standard deviation (SD) of the Gaussian quantile which reflects uncertainty in over 90% of cases. However, the distribution of the SD generated by the radar-derived and the copula-derived parameters could not be distinguished. For the validation case, the percentage of cases of higher SD by the gauge-derived parameter sets decreased to 81.2% and 86.6% for the non-calibration and the calibration periods, respectively. It has been observed that 1% reduction in the Gaussian quantile SD can cause over 39% reduction in the SD of the median rainfall estimate, actual reduction being dependent on the distribution of rainfall of the day. Hence the main advantage of using the most correct radar correlogram parameters is to reduce the uncertainty associated with conditional simulations that rely on SD through kriging.