An Improved Computational Geometry Method for Obtaining Accurate Remotely Sensed Products via Convex Hulls With Dynamic Weights: A Case Study With Leaf Area Index

Most retrieval functions used in remote sensing assume that the land surface is homogeneous. When those functions are used at a coarse spatial resolution for heterogeneous surfaces, scale effects might appear. This paper tries to develop an improved computational geometry method (ICGM) upscaling model that takes into consideration the actual distribution of surface measurements by using dynamic weights for the upper and lower envelopes of a convex hull. By aggregating to a series of simulated data at coarse spatial resolution, the weight coefficients can be determined via a least square method. To evaluate the proposed upscaling model, the leaf area index (LAI) is used as an example. The results for three sites with different degrees of heterogeneity show that the ICGM upscaling model can effectively correct for the scale effects of the LAI, and in most cases, achieve an accuracy that is comparable to that of traditional upscaling models. The relative error of the estimated LAI for the selected sites decreases from 3.35%, 11.01%, and 19.62% to an average of 0.28%, 1.48%, and 5.16%, respectively, at kilometer scale. A determination of whether retrieval functions are continuous or derivable is no longer required. Furthermore, there is no need to rely upon synchronous high spatial resolution data. Because the weight coefficients vary little at different scales, those coefficients are thought to be insensitive to different scales and can be taken as constants for a given study site. This study indicates that the proposed method is promising and feasible even for a heterogeneous landscape.