Estimation of spatial distribution of t-year precipitation with 5 km resolution

Abstract:

We estimated the spatial distribution of t-year precipitation such as 100-year precipitation, 50-year precipitation, and so on in Japan. If the return period of t-year precipitation, t, is greater than the data size (number of data of time series of annual maxima), then we use a traditional parametric method by which some probability distributions are used and goodness-of-fit results are mutually compared. The criterion of goodness-of-fit that we used is the Takara–Takasao criterion (1988). The criterion is designated as the standard least squares criterion (SLSC) in Japan. We designate this case as a ‘case for a few samples’. However, if the number of data of time series of annual maxima is greater than the return period t, then the case is that for numerous samples. For the case, we used Takara’s method (2006), which uses a nonparametric probability distribution.

For both cases for a few samples and for numerous samples, the bootstrap method is applied to ascertain the variation of the estimated t-year precipitation obtained using the parametric or nonparametric probability distribution we chose. We emphasize that Monte-Carlo-like simulations are not necessary for the case with numerous samples: a theoretical solution exists for the bootstrap method. We show the theoretical solutions. Furthermore, the data we used are solutions obtained using CGCM (KAKUSHIN-5 km data). Therefore, data with very high spatial resolution of 5 km can be used. Even if sparsely distributed precipitation data are used, high-resolution data can be obtained using CGCM data.