A generalization of inverse distance weighting method via kernel regression and its application to surface modeling

Abstract

The inverse-distance weighting (IDW) method is considered as one of the most popular deterministic methods and is widely applied to a variety of areas because of its low computational cost and easy implementation. In this paper, we show that the classical IDW is essentially a zeroth-order local kernel regression method with an inverse distance weight function. Thus, it suffers from various shortcomings, such as the boundary bias. Considering the advantages of the local polynomial modeling technique in statistics, the classical IDW was generalized into a higher-order regression by the Taylor expansion and then computed by means of a weighted leastsquares method. Surface modeling of rainfall fields in China indicated that the generalized IDWs with the first-and secondorders are more accurate than the classical IDW in terms of root mean square error (RMSE). The example of digital elevation model construction with a group of sample points showed that the two generalized IDWs have better RMSE and mean error than the classical IDW. Furthermore, the second-order IDW has a better performance than the ordinary kriging in terms of RMSE. A theoretical analysis demonstrated that the gradient-plus-inverse distance squared method presented by Nalder and Wein (Agric For Meteorol 92(4): 211-225, 1998) is a first-order form of the generalized IDW expanded on spatial coordinates and elevation. In a word, the generalized IDW can incorporate multiple covariates, which can better explain the interpolation procedure and might improve its accuracy.

Least Squares Compactly Supported Radial Basis Function for Digital Terrain Model Interpolation from Airborne Lidar Point Clouds

“…IDW is a type of deterministic method for multivariate interpolation with a known scattered set of points [40]. To predict a value for any unmeasured location, IDW uses the measured values surrounding the prediction location.…”

Differences in Accessibility of Public Health Facilities in Hierarchical Municipalities and the Spatial Pattern Characteristics of Their Services in Doumen District, China

“…The migrant population was mainly concentrated in the southwest of Doumen District, with scattered density in the south, and low density in the southeast and north. The spatial equity of multilevel public health service facilities was evaluated by combining the permanent and migrant population density, the spatial accessibility of public health service facilities, and the spatial service scope of Doumen District [39]. The spatial equilibrium of the different public health service facilities in Doumen was measured by the Gini coefficient (Table 3).…”

Acquisition of rainfall in ungauged basins: a study of rainfall distribution heterogeneity based on a new method

“…The Thiessen Polygon method assumes that rainfall varies abruptly across the boundary of the polygon and that rainfall is uniformly distributed within the sub-region, which is unphysical. The IDW method assumes that the interpolated points are more influenced by the closer stations than the far ones, and thus uses the reciprocal of the squared distance as the weighting factor (Chen et al, 2015). The disadvantage of this method is that the interpolation error is large when the data is significantly different from the neighboring points.…”