Assessing the local uncertainty of precipitation by using moving window geostatistical models

- A framework was proposed to assess the local uncertainty of precipitation.
- The marginal distribution in each window was fitted using Legendre polynomials.
- The prediction uncertainty accuracy of the proposed framework was the best of all.

Precipitation is a very important input variable for numerous models in many scientific fields such as hydrology, agriculture, ecology, and environmental sciences. However, precipitation often exhibits considerable spatial variability and cannot be adequately modeled by commonly used geostatistical techniques, particularly in terms of the prediction uncertainty accuracy, which is of great significance to determine the effects on various models' prediction uncertainty. In this paper, a moving-window copula-based geostatistical method was proposed to assess the local spatial uncertainty of precipitation. By incorporating non-stationary, non-Gaussian, and distance-weighted spatial statistics, many geostatistical techniques can be regarded as a special case of the proposed method. Especially, in this paper, the marginal distribution in each window was fitted using Legendre polynomials. Although the proposed method has the potential to improve both prediction accuracy and the prediction uncertainty accuracy, the case study showed that the prediction accuracy of the proposed method was not better than commonly used geostatistical techniques (i.e., ordinary kriging, moving window kriging, and the global copula-based method). However, the prediction uncertainty accuracy was the best of all. The moving-window copula-based geostatistical method allows the estimation of the full conditional distribution of the precipitation at any ungauged site. With the full conditional distributions, various analyses and decisions can be conducted and made. Moreover, in the sense of statistics, more accurate results could be expected.