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Evaluating the accuracy of precipitation products is essential for many applications. The traditional method for evaluation is to calculate error metrics of products with gauge measurements that are considered as ground truth. The multiplicative triple collocation (MTC) method has been demonstrated powerful in error quantification of precipitation products when ground truth is not known. This study applied MTC to evaluate five precipitation products in Germany: two raw satellite-based products (CMORPH and PERSIANN), one reanalysis product (ERA-Interim), one soil moisture–based product (SM2RAIN-ASCAT), and one gauge-based product (REGNIE). Evaluation was performed at the 0.5° daily spatial–temporal scales. MTC involves a log transformation of data, necessitating dealing with zero values in daily precipitation. Effects of 12 different strategies for dealing with zero values on MTC results were investigated. Seven different triplet combinations were tested to evaluate the stability of MTC. Results showed that different strategies for replacing zero values had considerable effects on MTC-derived error metrics, particularly for root-mean-square error (RMSE). MTC with different triplet combinations generated different error metrics for individual products. The MTC-derived correlation coefficient (CC) was more reliable than RMSE. It is more appropriate to use MTC to compare the relative accuracy of different precipitation products. Based on CC with unknown truth, MTC with different triplet combinations produced the same ranking of products as the traditional method. A comparison of results from MTC and the classic TC with additive error model showed the potential limitation of MTC in arid areas or dry time periods with a large ratio of zero daily precipitation. [ABSTRACT FROM AUTHOR]

Spatial and temporal patterns of trends in annual and seasonal precipitation over Germany during 1951–2013 were analysed using the ensemble empirical mode decomposition (EEMD) method. Three widely used and recognized high‐resolution observation‐based gridded precipitation products, the Climatic Research Unit (CRU) time‐series data, Global Precipitation Climatology Centre (GPCC) Full Data Reanalysis data and the EU‐FP6 project ENSEMBLES derived data set (EOBS), were used and compared. Comparison among different products showed that the CRU used a considerably lower number of gauge stations (maximum 36) in the construction of gridded product over Germany and should be used with great caution for other applications, and overall CRU presented less precipitation and smaller inter‐annual variability; GPCC and EOBS agreed well in the spatial and temporal distribution of seasonal and annual precipitation, as well as the identified trends. The spatiotemporal analysis of trends showed that trends in precipitation during 1951–2013 were, in most cases, highly nonlinear and varying over time. In particular, the spring, summer and autumn precipitation showed large variations in trends. Therefore, the assumption of linear trends on which previous studies were based is invalid. Annual precipitation showed increasing trends in over 66% of Germany (particularly northern and eastern Germany), and the magnitude of increasing trends were generally enhanced over time, e.g. GPCC showed that the average magnitude of increasing trends rose from 6.3% for the 1951–1980 period to 12% for the 1951–2013 period. There were considerable spatial and temporal variabilities in trends in seasonal precipitation totals over Germany. This study is among one of the first studies applying the EEMD method to a comprehensive analysis of time‐varying trends in precipitation over Germany, which is expected to improve our understanding of the complex and nonlinear regional climate system. Spatial and temporal patterns of the EEMD‐derived trend of the four seasonal precipitation totals (DJF, MAM, JJA, SON; the trend is presented as the percentage of the climatology mean during the whole period 1951–2013 for easy interpretation and comparison) from EOBS for five different periods, with ending years of 1980, 1990, 2000, 2010 and 2013. [ABSTRACT FROM AUTHOR]