Measure what the coarsening removes: a precondition for interpreting spatial-resolution comparisons in ecological models

Joshua Wang 

1. Ecological models increasingly use "scale-free" downscaled climate surfaces, assuming finer resolution predicts local response better. Even a comparison that varies resolution alone can fail to test it: over a small extent, coarsening barely changes the predictors. I give a diagnostic that detects this before any model is fitted, and calibrate it.

2. The comparison was built at two British Columbia extents: a low-relief municipality ~30 km across (153 corridor polygons x 4 summers) and a ~100 km valley transect spanning 4-1,920 m (300 forest stands x 4 summers). Model A used scale-free ClimateBC values at each polygon's location and elevation; Model B averaged those same variables within coarse cells. Both were random forests predicting a satellite water-stress index under spatially-blocked, polygon-grouped cross-validation.

3. At the municipal extent the comparison was unanswerable rather than null: coarsening to 4 km removed only 12.3% of the predictors' spatial variance, leaving them correlated at median r = 0.998. Over the transect it removed 48.4%, and the hypothesis was not supported at 25 km, at a power near one in four and at a cell size the label turns on. The coarse model was better on the point estimate (paired ΔRMSE = +0.00093, 95% CI [-0.00061, +0.00257]), but the interval spans zero at both cell sizes. Under blocking the direction favours the coarse model throughout; under random folds it reverses. R² was -0.138 for the fine model and +0.003 for the coarse. Terrain and stand structure together scored highest (CV R² = +0.029, positive in 80% of folds against climate's 40%), and adding climate made it worse.

4. Synthesis. A resolution hypothesis can be untestable while looking like a null result. Before interpreting any such comparison, measure the fraction of predictor spatial variance the coarsening destroys, and treat a low fraction as disqualifying rather than a finding. The rule holds in one direction only, since below f = 0.4 a null carries no information while above it detectability turns on the number of validation blocks as much as on f.