Characterizing the calibration domain of remote sensing models using convex hulls

The ever-increasing availability of remote sensing data allows production of forest attributes maps, which are usually made using model-based approaches. These map products are sensitive to various bias sources, including model extrapolation. To identify, over a case study forest, the proportion of extrapolated predictions, we used a convex hull method applied to the auxiliary data space of an airborne laser scanning (ALS) flight. The impact of different sampling efforts was also evaluated. This was done by iteratively thinning a set of 487 systematic plots using nested sub-grids allowing to divide the sample by two at each level. The analysis were conducted for all alternative samples and evaluated against 56 independent validation plots. Residuals of the extrapolated validation plots were computed and examined as a function of their distance to the model calibration domain. Extrapolation was also characterized for the pixels of the area of interest (AOI) to upscale at population level. Results showed that the proportion of extrapolated pixels greatly reduced with an increasing sampling effort. It reached a plateau (ca. 20% extrapolation) with a sampling intensity of ca. 250-calibration plots. This contrasts with results on model’s root mean squared error (RMSE), which reached a plateau at a much lower sampling intensity. This result emphasizes the fact that with a low sampling effort, extrapolation risk remains high, even at a relatively low RMSE. For all attributes examined (i.e., stand density, basal area, and quadratic mean diameter) estimations were generally found to be biased for validation plots that were extrapolated. The method allows an easy identification of map pixels that are out of the calibration domain, making it an interesting tool to evaluate model transferability over an area of interest (AOI). It could also serve to compare “competing” models at a variable selection phase. From a model calibration perspective, it could serve a posteriori, to evaluate areas (in the auxiliary space) that merit further sampling efforts to improve model reliability.