Copula-based interpolation methods for air temperature data using collocated covariates

This paper introduces two copula-based interpolation methods to produce air temperature maps in a data-scarce area: a spatial copula interpolator including covariates, and a mixed copula interpolator. The methods allow a construction of the conditional distribution of air temperature given the collocated covariates. Our study compared the new methods with the spatial copula interpolator, the ordinary kriging predictor and the cokriging predictor. Daily mean air temperature was used from weather stations and ERA_Interim reanalysis weather data at 174 locations in the Qazvin Plain, Iran. Spatial copula interpolator including covariates resulted in more precise predictions as shown by leave-two-out cross-validation. Visual inspection of air temperature maps demonstrated that the new methods well represented spatial variability of air temperature at a 1 km spatial resolution. The results showed an improved performance of the new methods to describe both spatial variability and co-variability between variables. The methods are potentially useful for other sparsely and irregularly distributed weather data.