Precipitation interpolation using digital terrain model and multivariate regression in hilly and low mountainous areas of Hungary

The relationship between precipitation and elevation is a well-known topic in the field of geography and meteorology. Radar-based precipitation data are often used in hydrologic models, however, they have several inaccuracies, and elevation can be one of the additional parameters that may help to improve them. Thus, our aim in this article is to find a quantitative relationship between precipitation and elevation in order to correct precipitation data input into hydrologic models. It is generally accepted that precipitation increases with elevation, however, the real situation is much more complicated, and besides elevation, the precipitation is dependent on several other topographic factors (e.g., slope, aspect) and many other climatic parameters, and it is not easy to establish statistically reliable correlations between precipitation and elevation. In this paper, we examine precipitation-elevation correlations by using multiple regression analysis based on monthly climatic data. Further on, we present a method, in which these regression equations are combined with kriging or inverse distance weighting (IDW) interpolation to calculate precipitation fields, which take into account topographic elevations based on digital terrain models. Thereafter, the results of the different interpolation methods are statistically compared. Our study areas are in the hilly or low mountainous regions of Hungary (Bakony, Mecsek, Börzsöny, Cserhát, Mátra and Bükk montains) with a total of 52 meteorological stations. Our analysis proved that there is a linear relationship between the monthly sum of precipitation and elevation. For the North Hungarian Mountains, the correlation coefficients were statistically significant for the whole study period with values between 0.3 and 0.5. Multivariate regression analysis pointed out that there are remarkable differences among seasons and even months. The best correlation coefficients are typical of late spring-early summer and October, while the weakest linear relationships are valid for the winter period and August. The vertical gradient of precipitation is between one and four millimetres per 100 metres for each month. The statistical comparison of the precipitation interpolation had the following results: for most months, co-kriging was the best method, and the combined method using topography-derived regression parameters lead to only slightly better results than the standard kriging or IDW.