Research On The Spatial Interpolation For Precipitation Data Using Weighted Linear Regression Model

There is currently a great demand for spatial climate data sets in digital form, and today's most commonly used climate data sets have been created through the process of statistically interpolation data values from irregularly spaced station locations to a regular grid. The common methods, such as Inverse Distance Weighted (IDW), Kriging Statistics and Polynomial Approximation, can't effectively estimate the actual spatial distribution of the precipitation in the complex terrain area, because these methods were built on the assumption that the station data are spatial autocorrelation and smooth-continue in the space, and the influence of the local terrain was not considered. Accordingly, a local weighted linear regression model, considering the influence of the terrain factor, is introduced attempting to accurately interpolate the precipitation in the complex terrain areas.Precipitation is influenced by various geographic factors such as elevation, mountain slope, aspect, wind direction, effective terrain and distance to the water. In this paper, the linear relationship between precipitation and the terrain factors was sought after in the first instance, and then the local weighted linear regression for spatial interpolation method was implemented, in which the weight of each the precipitation observation is calculated by the terrain factors and the distance between the estimated point and the observation point. The climate data value of the estimated point was interpolated by the weighted linear regression model.The main contents of this paper are: (1) Exploring the quantitative global or local relationship between terrain factors and the precipitation using the exploratory spatial data analysis. (2) The linear regression model for spatial interpolation method is implemented in ArcGIS 9.0 software using ArcObjects programming. The parameter of the model is the quantitative generalization of the relationship between the terrain factors and the precipitation, and the key factor that influences the precision of the model is the selection and optimization for the parameter. (3) Selecting the representative areas for the study of precipitation interpolation; the result of the interpolation was analyzed by cross validation and known point validation, and compared with the common approaches.Case study of precipitation interpolation in Texas and Oregon shows that: (1) In the complex terrain areas, the local weighted linear regression model for precipitation interpolation could effectively estimate the actual spatial distribution of the precipitation. The model is better than the common methods such as Kriging and IDW in the areas which the terrain influence is the dominant factor for the precipitation, and in the plain the model could be considered as IDW method. (2)The choice of the quantitative parameter for the interpolation model is determined by the distribution of the station and the characteristics of the terrain. The main terrain factor, influenced the precipitation, varies with the areas. The optimal parameter values was determined by the result of the cross validation. (3) Due to the seasonal and regional characteristics of the precipitation distribution, the precision of interpolation for the model is various in different period and area of precipitation. (4) There is not optimal method of precipitation interpolation for a special area. The interpolation model should be built on the analysis of the characteristics of the terrain and the distribution of the precipitation.