USA CERL                                                                                                                          GMSLab

  Using Soil Erosion Modeling for Improved Conservation Planning: 
A GIS-based Tutorial

 

Methods:

Spatial modeling of erosion and deposition with USPED 

USPED (Unit Stream Power - based Erosion Deposition) is a simple model that predicts the spatial distribution of erosion and deposition rates for a steady state overland flow with uniform rainfall excess conditions.  It assumes that the erosion process is transport capacity limited. The model is based on the theory originally outlined by Moore and Burch (1986) with numerous improvements. For the transport capacity limited case, we assume that the sediment flow rate qs(r) is at the sediment transport capacity T(r), r=(x,y) which is approximated by (Julien and Simons 1985)
|qs(r)|  =  T(r) =  Kt (r) |q(r)|m sin b(r)n


where b(r) [deg] is slope,  q(r)is water flow rate, Kt(r) is transportability coefficient, which is dependent on soil and cover; m, n are constants that vary according to type of flow and soil properties. For overland flow the constants are usually set to m=1.6, n=1.3 (Foster 1993). Steady state water flow can be expressed as a function of upslope contributing area  per unit contour width A(r)[m]

|q(r)| =  A(r) i

where i[m] is uniform rainfall intensity (note: approximation by upslope area neglects the change in flow velocity due to cover). No experimental work was performed to develop parameters needed for USPED, therefore we use the USLE or RUSLE parameters to incorporate the approximate impact of soil and cover and obtain at least a relative estimate of net erosion and deposition. We assume that we can estimate sediment flow at sediment transport capacity as

T = R K C P Am (sin b)n

where R~im, KCP~Kt and LS=Am sin b n , and m=1.6, n=1.3 for prevailing rill erosion. For prevailing sheet erosion,  m=n=1. Then the net erosion/deposition is estimated as a change in sediment flow rate expressed by a divergence in sediment flow:

ED  =  div (T . s)  =  d(T*cos a)/dx  +  d(T*sin a)/dy

where a [deg] is aspect of the elevation surface (or direction of flow minus gradient direction). Caution should be used when interpreting the results because the USLE parameters were developed for simple plane fields and detachment limited erosion. Therefore to obtain accurate quantitative predictions for complex terrain conditions they need to be re-calibrated ( Foster 1990, Mitasova et al 1997 reply).

The following equation shows the relationship between the erosion and deposition and shape of terrain given by its curvatures. For the uniform soil and cover properties represented by Kt=const., the  net erosion/deposition rate is estimated as a divergence of the sediment flow (see Appendix in Mitas and Mitasova 1998):

ED(r) = div qs(r) = Kt { [grad h(r)] . s(r) sin b(r) - h(r) [kp(r) + kt(r)] }

where s(r) is the unit vector in the steepest slope direction, h(r) [m] is the water depth estimated from the upslope area A(r), kp(r) is the profile curvature (terrain curvature in the direction of the steepest slope), kt(r) is the tangential curvature (curvature in the direction tangential to a contour line projected to the normal plane). Topographic parameters s(r), kp(r), kt(r) are computed from the first and second order derivatives of a terrain surface approximated by  RST (Mitasova and Mitas, 1993; Mitasova and Hofierka, 1993; Krcho 1991). According to the 2D formulation, the spatial distribution of erosion and deposition is controlled by the change in the overland flow depth (first term) and by the local geometry of terrain (second term), including both profile and tangential curvatures. The bivariate formulation thus demonstrates that the local acceleration of flow in both the gradient and tangential directions, which are related to the profile and tangential curvatures, play equally important roles in the spatial distribution of erosion/deposition. The interplay between the magnitude of water flow change and both terrain curvatures reflected in the bivariate formulation determines whether erosion or deposition will occur.

 

Up
colors.html
ArcView Commands for Computing USPED
ArcMap Commands for Computing USPED
GRASS Commands for Computing USPED using GIS

HOME                                                        H. Mitasova, et al.,  Geographic Modeling Systems Lab, UIUC