Model vs. design sensitivity to the ground-truth problem of rainfall observation

In this study three multi-dimensional rainfall models, the Waymire-Gupta-Rodriguez-Iturbe multi-dimensional rainfall model (WGR model) [Water Resour. Res. 20 (10) (1984) 1453], the noise forced diffusive rainfall model (NFD model) [J. Atmos. Ocean Technol. 6 (1989) 985] and the Yoo-Valdes-North model (YVN model) [Water Resour. Res. 32 (7) (1996) 2175], are compared with their applications to the ground-truth problem to capture the sensor bias using multiple raingauges. All the model parameters used are those estimated tuned to the GATE by Valdes et al. [J. Geophys. Res. (Atmos.) 95 (D3) (1990) 2101], North and Nakamoto [J. Atmos. Ocean Technol. 6 (1989) 985] and Yoo et al. [Water Resour. Res. 32 (7) (1996) 2175], respectively, and the root mean square errors (RMSEs) for each model are estimated to compare. The difference among models can be seen easily from the comparison of their spectra, which, in turn, affects the RMSEs for the ground-truth problem. Two conclusions could be deduced from the results of the study: (1) The rainfall model is the more crucial factor for the ground-truth problem than the ground-truth design. That is, the design factors, such as the number of raingauges, the size of the field of view (FOV), and the distance between the first and the last raingauges, were found to be much less sensitive to the RMSEs than the model itself. For example, the RMSEs estimated for a model could be more than twice of another model's, which could result in more than four times of satellite observations required to capture the sensor bias. However, twice the number of raingauges, twice the size of the FOV, or twice the length between the first and the last raingauges resulted in less than 20% difference of the RMSEs. (2) The model sensitivity is much higher than the parameter sensitivity to the RMSEs. For example, just about 25% difference of the RMSEs could be expected even when applying the NFD model parameters 100% bigger or smaller. Considering that the model parameters would be estimated to be within their reasonable ranges, the parameter sensitivity to the RMSEs must become much smaller than the model itself.