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

Abstract

Most retrieval functions used in remote sensing assume that the land surface is homogeneous. When those functions are used at 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.

Polygon-Based Algorithms for N-Satellite Constellations Coverage Computing

“…Performing analysis involving the Earth's surface is a wellknown issue in Geography and Satellite Applications [33], [34]. Involving astrodynamics such as Constellation-to-ground coverage analysis and non-spherical models of the Earth further increases the complexity of the problem [35], [36]. Since dealing with any non-euclidean plane is challenging, the issue is usually approached by making compromises, simplifications, and assumptions.…”

“…We identify three main items in the case of the study of the Earth's surface: i) assuming a spherical Earth model, ii) restricting analysis on small regions, and iii) restricting analysis far from the poles. Some provide the bases for comprehensible and easy-to-implement methods, which are precise enough for specific applications [36], [37], but fall short when pushed outside their limits.…”

AM–GM Algorithm for Evaluating, Analyzing, and Correcting the Spatial Scaling Bias of the Leaf Area Index

“…On the heterogeneous surfaces, the skewness and kurtosis of the random variable may be large, and the AM-GM algorithm may exhibit a better performance for the computation of µ and LAI scaling bias. In the improved CGM, the relative errors decreased from 3.35%, 11.01%, and 19.62% to an average of 0.28%, 1.48%, and 5.16%, respectively, at kilometer scales [26]. Jiang et al indicated that the LAI scaling bias decreased to around 0.27 by the TSEM, Wavelet-Fractal (WF), and Fractal theory (TT) [30].…”

“…However, empirical methods require external factors that limit their applicability. On the other hand, a series of universal methods have been provided [8,[21][22][23][24][25][26]. For instance, the computational geometry method (CGM) sets the upper and lower envelopes of the retrieval model to achieve accurate parameter estimation at coarse resolutions [21].…”

“…However, the true distribution of parameters is not considered. Chen et al addressed the limitations of the CGM algorithm by introducing variable weights instead of fixed weights [26]. Nevertheless, the inherent flaw of the CGM method-its inability to express the scaling bias using a formula-has yet to be resolved.…”