Geostatistical Interpolation Using Copulas and its Use in Operational Forecasts

Extreme meteorological and hydrological events have the potential to affect the daily life in multiple ways if proper and timely steps are not taken to deal with such events. For appropriate steps to be taken for mitigating the effects of extreme events it is very necessary that reliable forecast are available for important meteorological variables. Operational forecasts (whether deterministic or ensemble) made by any state institution are strongly based on data obtained from observational network stations of the state. Given that observational networks are not usually very dense it is always very important to have comprehensive spatial estimates of important meteorological variables at unobserved locations. A rather new geosatistical approach Copula is used in this study for spatial interpolation of important meteorological variables such as precipitation, temperature and wind gusts. Observational network of gauging stations under operational use of Deutscher Wetterdeinst (DWD, German weather services) are used to calculate empirical Copulas for precipitation, temperature and wind gusts. Using the concept of spatial theoretical Copulas, relationships are developed between each variable for different separating distances and finally interpolation is made for unobserved points. The advantage of using Copulas over other interpolation methods is that instead of one averaged value of variable, complete distribution of variable is interpolated to unobserved location. This gives better opportunity to make uncertainty analysis by studying the confidence intervals of the interpolated values. Extreme events can thus be specifically considered when forecasts or forecast verifications are made.