No abstract

No abstract

Accurate and reliable gridded data sets are important for analyzing extreme weather and climate events. Specifically, these data sets should produce extreme value statistics that are close to reality. Here we use various statistical methods to evaluate the quality of four gridded data products in representing daily precipitation extremes. The data products are the COSMO-REA6 regional reanalysis, the ERA5 global reanalysis, and the E-OBS and HYRAS gridded observation-based data sets. The statistical methods we use offer a thorough insight into the quality of the different data sets by providing temporal and spatial extreme value statistics of daily precipitation. Our results show that all data sets except HYRAS underestimate the magnitude of daily precipitation extremes when compared with weather station data. Moreover, the reanalysis data sets give generally worse extreme value statistics of daily precipitation than the gridded observation-based data sets. In particular, the reanalysis data sets often fail in reproducing the accurate timing of observed daily precipitation extremes. Plain Language Summary Gridded data products provide long-term estimates of climate variables such as temperature and precipitation at regularly spaced grids on the Earth. They are an important source for the research of extreme weather. For example, for investigating the change in frequency and intensity of heavy precipitation over time. To achieve reliable results, we need such data products to be able to accurately represent extreme weather events. To verify if this is the case, we evaluate the quality of several gridded data products in representing heavy daily precipitation events and find that there is room for improvement.

Abstract:We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form:is the Caputo fractional derivative of order α ∈ (0, 1) with respect to the time variable t, B is a second order elliptic operator with respect to the space variable x ∈ R d andẆ H a time homogeneous fractional Gaussian noise of Hurst parameter. We obtain conditions satisfied by α and H, so that the square integrable solution u exists uniquely.