Conditional simulation of spatial rainfall fields using random mixing: a study that implements full control over the stochastic process

Abstract. The accuracy of spatial precipitation estimates with relatively high spatiotemporal resolution is of vital importance in various fields of research and practice. Yet the intricate variability and intermittent nature of precipitation make it very difficult to obtain accurate spatial precipitation estimates. Radars and rain gauges are two complementary sources of precipitation information: the former are inaccurate in general but are valid indicators of the spatial pattern of the rainfall field; the latter are relatively accurate but lack spatial coverage. Several radar–gauge merging techniques that can provide spatial precipitation estimates have been proposed in the scientific literature. Conditional simulation has great potential to be used in spatial precipitation estimation. Unlike commonly used interpolation methods, conditional simulation yields a range of possible estimates due to its Monte Carlo framework. However, one obstacle that hampers the application of conditional simulation in spatial precipitation estimation is the need to obtain the marginal distribution function of the rainfall field with sufficient accuracy. In this work, we propose a method to obtain the marginal distribution function from radar and rain gauge data. A conditional simulation method, random mixing (RM), is used to simulate rainfall fields. The radar and rain gauge data used in the application of the proposed method are derived from a stack of synthetic rainfall fields. Due to the full control over the stochastic process, the accuracy of the estimates is verified comprehensively. The results from the proposed approach are compared with those from three well-known radar–gauge merging techniques: ordinary Kriging, Kriging with external drift, and conditional merging, and the sensitivity of the approach to two factors – the number of rain gauges and the random error in the radar estimates – is analysed in the same experimental context.