A Spatial Interpolation Model for Daily Minimum Temperature over Mountainous Regions

Spatial interpolation of daily temperature forecasts and observations issued by public weather services is frequently required to make them applicable to agricultural activities and modeling tasks. In contrast to the long term averages like monthly normals, terrain effects are not considered in most spatial interpolations for short term temperatures. This may cause erroneous results in mountainous regions where the observation network hardly covers full features of the complicated terrain. We developed a spatial interpolation model for daily minimum temperature which combines inverse distance squared weighting and elevation difference correction. This model uses a time dependent function for 'mountain slope lapse rate', which can be derived from regression analyses of the station observations with respect to the geographical and topographical features of the surroundings including the station elevation. We applied this model to interpolation of daily minimum temperature over the mountainous Korean Peninsula using 63 standard weather station data. For the first step, a primitive temperature surface was interpolated by inverse distance squared weighting of the 63 point data. Next, a virtual elevation surface was reconstructed by spatially interpolating the 63 station elevation data and subtracted from the elevation surface of a digital elevation model with 1 km grid spacing to obtain the elevation difference at each grid cell. Final estimates of daily minimum temperature at all the grid cells were obtained by applying the calculated daily lapse rate to the elevation difference and adjusting the inverse distance weighted estimates. Independent, measured data sets from 267 automated weather station locations were used to calculate the estimation errors on 12 dates, randomly selected one for each month in 1999. Analysis of 3 terms of estimation errors (mean error, mean absolute error, and root mean squared error) indicates a substantial improvement over the inverse distance squared weighting.