A new uncertainty estimation approach with multiple datasets and implementation for various precipitation products

Abstract

Ensemble estimates based on multiple datasets are frequently applied once many datasets are available for the same climatic variable. An uncertainty estimate based on the difference between the ensemble datasets is always provided along with the ensemble mean estimate to show to what extent the ensemble members are consistent with each other. However, one fundamental flaw of classic uncertainty estimates is that only the uncertainty in one dimension (either the temporal variability or the spatial heterogeneity) can be considered, whereas the variation along the other dimension is dismissed due to limitations in algorithms for classic uncertainty estimates, resulting in an incomplete assessment of the uncertainties. This study introduces a three-dimensional variance partitioning approach and proposes a new uncertainty estimation (Ue) that includes the data uncertainties in both spatiotemporal scales. The new approach avoids pre-averaging in either of the spatiotemporal dimensions and, as a result, the Ue estimate is around 20 % higher than the classic uncertainty metrics. The deviation of Ue from the classic metrics is apparent for regions with strong spatial heterogeneity and where the variations significantly differ in temporal and spatial scales. This shows that classic metrics underestimate the uncertainty through averaging, which means a loss of information in the variations across spatiotemporal scales. Decomposing the formula for Ue shows that Ue has integrated four different variations across the ensemble dataset members, while only two of the components are represented in the classic uncertainty estimates. This analysis of the decomposition explains the correlation as well as the differences between the newly proposed Ue and the two classic uncertainty metrics. The new approach is implemented and analysed with multiple precipitation products of different types (e.g. gauge-based products, merged products and GCMs) which contain different sources of uncertainties with different magnitudes. Ue of the gauge-based precipitation products is the smallest, while Ue of the other products is generally larger because other uncertainty sources are included and the constraints of the observations are not as strong as in gauge-based products. This new three-dimensional approach is flexible in its structure and particularly suitable for a comprehensive assessment of multiple datasets over large regions within any given period.