The influence of sampling density on geographically weighted regression: a case study using forest canopy height and optical data

Abstract

Geographically weighted regression (GWR) extends the conventional ordinary least squares (OLS) regression technique by considering spatial nonstationarity in variable relationships and allowing the use of spatially varying coefficients in linear models. Previous forest studies have demonstrated the better performance of GWR compared to OLS when calibrated and validated at sampled locations where field measurements are collected. However, the use of GWR for remote-sensing applications requires generating estimates and evaluating the model performance for the large image scene, not just for sampled locations. In this study, we introduce GWR to estimate forest canopy height using high spatial resolution Quickbird (QB) imagery and evaluate the influence of sampling density on GWR. We also examine four commonly used spatial analysis techniques – OLS, inverse distance weighting (IDW), ordinary kriging (OK) and cokriging (COK) – and compare their performance with that using GWR. Results show that (i) GWR outperformed OLS at all sampling densities; however, they produced similar results at low sampling densities, suggesting that GWR may not produce significantly better results than OLS in remote-sensing operational applications where only a small number of field data are collected. (ii) The performance of GWR was better than those of IDW, OK and COK at most sampling densities. Among the spatial interpolation techniques we examined, IDW was the best to estimate the canopy height at most densities, while COK outperformed OK only marginally and produced larger canopy height estimation errors than both IDW and GWR. (iii) GWR had the advantage of generating canopy height estimation maps with more accurate estimates than OLS, and it preserved patterns of geographic features better than IDW, OK or COK.