Depth distribution of interrill overland flow and the formation of rills

摘要

A Gumbel distribution for maxima is proposed as a model for the depths of interrill overland flow. The model is tested against three sets of field measurements of interrill overland flow depths obtained on shrubland and grassland hillslopes at Walnut Gulch Experimental Watershed, southern Arizona. The model is found to be a satisfactory fit to 81 of the 90 measured distributions. The shape δ and location λ parameters of all fitted distributions are strongly correlated with discharge. However, whereas a common relationship exists between discharge and δ for all depth distributions, the relationships with λ vary systematically downslope. Using the Gumbel distribution as a model for the distribution of overland flow depths, a probabilistic model for the initiation of rills is developed, drawing upon the previous work of Nearing. As an illustration of this approach, we apply this model to the shrubland and grassland hillslopes at Walnut Gulch. It is concluded that the presence of rills on the shrubland, but not on the grassland, is due to the greater runoff coefficient for the shrubland and/or the greater propensity of the shrubland for soil disturbance compared with the grassland. Finally, a generalized conceptual model for rill initiation is proposed. This model takes account of the depth distribution of overland flow, the probability of flow shear stress in excess of local soil shear strength, the spatial variability in soil shear strength and the diffusive effect of soil detachment by raindrops.