Predicting gully occurrence at watershed scale: Comparing topographic indices and multivariate statistical models

In this study, the ability of five topographic indices to predict the gully trajectories observed in two adjacent watersheds located in Sicily (Italy) was evaluated. Two of these indices, named MSPI and MTWI, as far as we know, have never been employed to this aim. They were obtained by multiplying the stream power index (SPI) and the topographic wetness index (TWI), respectively, by the convergence index (CI). The predictive ability of the topographic indices was measured by using both cut-off independent (AUC: area under the receiver operating characteristic curve) and dependent statistics (Cohen's kappa index κ, sensitivity, specificity). These statistics were calculated also for 100 MARS (multivariate adaptive regression splines) and 100 LR (logistic regression) model runs, which used as predictors the topographic variables (i.e. contributing area, slope steepness, plan curvature and convergence index) combined into the five indices. Performance statistics of both topographic indices and statistical models were calculated using 100 random samples of 2 m grid cells, which were extracted only from flow concentration lines. This was done in order to focus the validation process on where gully erosion is more likely to occur. MSPI achieved the best predictive skill (AUC > 0.93; κ > 0.71) among the topographic indices and exhibited similar and better accuracy than local (i.e. trained and validated in the same watershed) and transferred (i.e. trained in one watershed and tested in the other one) LR models, respectively. On the other hand, MSPI performed similarly to transferred MARS runs (AUC > 0.92; κ > 0.71) but slightly worse than local MARS runs (AUC > 0.95; κ > 0.77). Based on the results of this experiment, it can be inferred that (i) including CI helps in detecting hollow areas where gullies are more likely to occur and (ii) MPSI can be a valid alternative to a data driven approach for mapping gully erosion susceptibility in areas where a gully inventory is not available, which is necessary to calibrate statistical models.