A cellular automata model for dynamically describing the overland flow and sediment transport

Rainfall erosion has been calculated and predicted by various soil loss equations, but the progressions of overland flow and sediment transport are less dynamically described. In this study, cellular automata (CA) models based on single flow direction algorithm (SFD), average value multi-flow direction algorithm (AMFD) and remaining average value multi-flow direction algorithm (RAMFD) were constructed. Simultaneously, erosion model was constructed by dividing soil erosion into inter-rill, rill and gully erosions according to critical water depth. The CA models were validated at three scales: a theoretical slope, an in-situ model slope and the natural basin. The results demonstrated the efficient performance of RAMFD in the runoff ascension and recession stages while SFD and AMFD presented unconcentrated runoff distribution, especially in the in-situ slope and basin simulation. Besides, RAMFD model occurred sediment deposition in the basin upstream while SFD and AMFD presented continuous erosion. Furthermore, the runoff Nash-Sutcliffe efficiency (NSE) of three models were 0.85 - 0.95 and 0.65 - 0.94, and the erosion root mean square error (RMSE) were 0.5 - 1.0 kg/min and 0.3 - 0.45 102kg/ min in the theoretical slope and natural basin, respectively. Meanwhile, the NSE and RMSE values of RAMFD exhibited the best performance, indicating that this model effectively balanced water distribution while controlling the flow direction to a greater extent. Overall, it is justified to develop an erosion prediction model based on the classification of erosion types, and the rules governing water flow allocation will inevitably result in qualitative and quantitative differences of runoff and erosion.

Automated summary

This study constructed cellular automata models based on three flow direction algorithms and divided soil erosion into inter-rill, rill, and gully erosions. The models were validated at different scales, and the results showed that the RAMFD model performed the best in the runoff ascension and recession stages. Furthermore, the RAMFD model exhibited sediment deposition in the upstream basin while the SFD and AMFD models showed continuous erosion. Overall, the RAMFD model had the best performance in balancing water distribution and controlling flow direction.