Considerations for interpolating rain gauge precipitation onto a regular grid

The aim of this study is to used heavy precipitation data from Slovenia to find the highest resolution from the Numerical Weather Prediction model where the model cell averaged interpolated fields of 24hour rain gauge precipitation which was independent of the interpolation method. 20 out of 104 observed heavy precipitation cases from the period of 1995-2002 in Slovenia were selected, in which 10 were convective and 10 stratiform. Three different interpolation methods were used: Universal Kriging, Inverse Distance Weighted and Radial Basis Functions. Each method was aggregated and direct interpolation was performed. The cross-validation results showed that the interpolation errors were as large as 50 % of the observed precipitation maximum (in our case from 50 to 110 mm). This indicates that an interpolation into high resolution or into a point is not reliable. Also, the interpolation cross-validation errors, the Root Mean Squared Error and Mean Absolute Error, were larger for stratiform precipitation than for convective precipitation. The reason for these errors seems to be that for the convective cases there was a smaller area with heavy precipitation and a large area with weak or no precipitation. The smaller area with spatially very variable precipitation contributed significantly to errors while the larger did not. Conversely, this was not the case for stratiform precipitation cases where precipitation and corresponding errors occurred all over the domain. Model grids were interpolated with three different resolutions of 4, 8 and 16 km. The condition for a method-independent interpolation entitled that every model grid cell had to have at least one to two rain gauges inside and possibly more in the very near vicinity. The highest possible model resolution should therefore be close or lower as the double of average distance to the closest neighbor in the rain gauge network, which in our case occurred at 16 km. Also, a certain procedure for interpolation was followed: first, the interpolation into high resolution and secondly, aggregation into the final resolution. A simple interpolation into a point in the middle of the model grid cell did not produce interpolation independent results even at a lower resolution. When using the right procedure at 16 km, the maximum differences between interpolation methods were usually less than 15 % of the observed precipitation maximum.