A Novel Method for Interpolating Daily Station Rainfall Data using a Stochastic Lattice Model

Rain gauge data are routinely recorded and used around the world. However, their sparsity and inhomogeneity make them inadequate for climate model calibration and many other climate change studies. Various algorithms and interpolation techniques have been developed over the years to obtain adequately distributed datasets. Objective interpolation methods such as inverse distance weighting (IDW) are the most widely used and have been employed to produce some of the most popular gridded daily rainfall datasets (e.g., India Meteorological Department gridded daily rainfall). Unfortunately, the skill of these techniques becomes very limited to nonexistent in areas located far away from existing recording stations. This is problematic as many areas of the world lack adequate rain gauge coverage throughout the recording history. Here, we introduce a new probabilistic interpolation method in an attempt to address this issue. The new algorithm employs a multitype particle interacting stochastic lattice model that assigns a binned rainfall value, from a given number of bins to each lattice site or grid cell, with a certain probability according to the rainfall amounts observed in neighboring sites and a background climatological rain rate distribution, drawn from the available data. Grid cells containing recording stations are not affected and are being used as "boundary" input conditions by the stochastic model. The new stochastic model is successfully tested and compared against two widely used gridded daily rainfall datasets over the Indian landmass for data from the summer monsoon seasons (June-September) for 1951-70.