The influence of sampling density on geographically weighted regression: a case study using forest canopy height and optical data
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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.Keywords:
Inverse distance weighting
Ordinary least squares
Geographically Weighted Regression
Tree canopy
Spatial heterogeneity
Abstract The concept of spatial interpolation is important in the soil sciences. However, the use of a single global interpolation model is often limited by certain conditions (e.g., terrain complexity), which leads to distorted interpolation results. Here we present a method of adaptive weighting combined environmental variables for soil properties interpolation (AW-SP) to improve accuracy. Using various environmental variables, AW-SP was used to interpolate soil potassium content in Qinghai Lake Basin. To evaluate AW-SP performance, we compared it with that of inverse distance weighting (IDW), ordinary kriging, and OK combined with different environmental variables. The experimental results showed that the methods combined with environmental variables did not always improve prediction accuracy even if there was a strong correlation between the soil properties and environmental variables. However, compared with IDW, OK, and OK combined with different environmental variables, AW-SP is more stable and has lower mean absolute and root mean square errors. Furthermore, the AW-SP maps provided improved details of soil potassium content and provided clearer boundaries to its spatial distribution. In conclusion, AW-SP can not only reduce prediction errors, it also accounts for the distribution and contributions of environmental variables, making the spatial interpolation of soil potassium content more reasonable.
Inverse distance weighting
Interpolation
Content (measure theory)
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Abstract Spatial interpolation algorithm is based on known data to predict the study area, its accuracy is of great significance to research. In different application scenarios, the interpolation method with higher accuracy should be selected. Based on ArcGIS, this paper conducts experimental analysis on inverse distance weighting method and Kriging method, so as to provide a reference for the selection of interpolation method in different application scenarios.
Inverse distance weighting
Interpolation
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Citations (11)