Generalised spatial error for validation

Validation of spatial prediction models is still dominated by global metrics such as root mean square error (RMSE), which summarize average model performance but can underrepresent the spatial concentration and heterogeneity of prediction errors. To complement existing residual-diagnostic approaches, we propose the Generalised Spatial Error (GSE), a validation metric that combines local RMSE with local error variance and assigns greater weight to neighborhoods with unstable performance. We evaluated GSE using nine predictive models for vascular plant species richness in the Murray–Darling Basin (MDB), Australia. Across models, GSE was consistently 20.29–24.40% higher than RMSE, reflecting the total increase from variance-weighted aggregation of local error magnitude and instability. Maps of local error variance further showed that predictive instability was concentrated mainly in the species-rich eastern part of the basin. Sensitivity analyses based on geographical area, elevation and species-richness stratification yielded consistent differences between GSE and RMSE, supporting the robustness of GSE across contrasting environmental settings. These results suggest that GSE provides a useful complementary metric for diagnosing spatial reliability beyond average prediction accuracy and for identifying locations where model predictions are less dependable for environmental assessment and decision-making.