Surface metrics: scaling relationships and downscaling behavior

Context: Considerable research has examined scale effects for patch-based metrics with the ultimate goal of predicting values at finer resolutions (i.e., downscaling), but results have been inconsistent. Surface metrics have been suggested as an alternative to patch-based metrics, although far less is known about their scaling relationships and downscaling potential. If successful, downscaling would enable integration of disparate datasets and comparison of landscapes using different resolution datasets. Objectives: (1) Determine how surface metrics scale as resolution changes and how consistent those scaling relationships are across landscapes. (2) Test whether these scaling relationships can be accurately downscaled to predict metric values for finer resolutions. Methods: Various scaling functions were fit to 16 surface metrics computed for multiple resolutions for a set of landscapes. Best-fitting functions were then extrapolated to test downscaling behavior (i.e., predict metric value for a finer resolution) for an independent set of validation landscapes. Relative error was assessed between the predicted and true values to determine downscaling robustness. Results: Seven surface metrics (Sa, Sq, S10z, Sdq, Sds, Sdr, Srwi) fit consistently well (R² > 0.99) with a 3rd order polynomial or power law. Of those, the scaling functions for Sa, Sq, and S10z were able to predict metric values at a finer resolution within 5 %. Three metrics, (Ssk, Sku, Sfd) were also notable in terms of fit and downscaling. Conclusions: Many metrics exhibit consistent scaling relations across resolution, and several are able to accurately predict values at finer resolutions. However, prediction accuracy is likely related to the amount of information lost during aggregation.