Methods

Overview

The Universal Soil Loss Equation was developed by the USDA Agricultural Research Service in 1965 as an empirical method to compute soil loss in agricultural fields. The Revised Universal Soil Loss Equation (RUSLE) is based on the same empirical theory as USLE but has been improved in many areas such as methods for calculating rainfall and slope parameters(Brooks, 2003). The RUSLE model is detachment capacity limited (Mitasova, ); it only takes into account erosional factors and does not consider the effects of sediment deposition. Annual erosion is calculate by combining spatially explicit raster maps according to this formula:

E = R K LS C P

Where:

E = Annual Erosion

R = Rainfall Erosivity Factor

K = Soil Erodibility Factor

LS = Slope Factor

C= Vegetative Cover

P = Management Factor

Erosion Model Diagram

Preprocessing Data

All data referred to in subsequent sections have been preprocessed in order to normalize the spatial referencing. Because the model relies on area calculations, it was essential to use an equal-area projection. Seven regions (roughly corresponding to the continents) were defined and each uses a custom Lambert Azimuthal Equal Area projection to minimize distortion. Thus global model is run in seven steps and requires each input dataset to be reprojected into each custom projection and clipped to the region's extents. In order to minimize resampling errors, each region uses a different cell size; the approximate size of a 30 arc second cell at the center lattitude of the projection.

Slope Factor

The SRTM30 Dataset (****) was used to calculate the slope factor (LS). Since the DEM was clipped to the sea mask and slope calculations require a 3x3 window, it was necessary to add a 5 pixel buffer with a value of zero around the existing DEM to prevent edge effects. Flow accumulation was calculated using the D-infinity algorithm. Slope percentages were calculated using a 3x3 moving window derivative approach (****). LS was calculated from slope and flow accumulation according to the modified method for complex terrain (Mitasova et. al. 1996, 1999)

Vegetative Management Factor

The MODIS land cover dataset (http://duckwater.bu.edu/lc/mod12q1.html), classified according to the IGBP scheme, was used to calculate the vegetative management factor (CP). Each class was assigned a CP factor; certain values were known ( ) and others were interpolated by their relative influence on erosion. The IGBP raster was then reclassified according to these values to derive a CP map.

IGBP Vegetation Class	Vegetative Management Factor (VM)
Water	0.000
Permanent Wetlands	0.000
Snow and Ice	0.000
Evergreen Needleleaf Forest	0.005
Evergreen Broadleaf Forest	0.007
Mixed Forests	0.009
Deciduous Needleleaf Forest	0.010
Deciduous Broadleaf Forest	0.012
Closed Shrublands	0.050
Woody Savannas	0.050
Open Shrublands	0.075
Grasslands	0.075
Savannas	0.080
Urban and Built-Up	0.100
Cropland/Natural Vegetation Mosaic	0.140
Barren or Sparsely Vegetated	0.200
Cropland	0.320

Soil Erodibility

K was calculated based on the USDA global soil suborder dataset, available through the NRCS (CITE). Each soil order was assigned a factor based on their described soil properties (CITE http://soils.usda.gov/technical/classification/taxonomy/ ) using the soil nomograph (USDA, 1980). The soil suborders were collapsed into orders and reclassified by their K factor.

Soil Order	K
Ocean	0.00
Shifting Sand	0.99
Rock	0.01
Ice	0.00
Gelisols	0.30
Histosols	0.20
Spodosols	0.20
Andisols	0.30
Oxisols	0.13
Verisols	0.15
Aridisols	0.32
Ultisols	0.18
Mollisols	0.38
Alfisols	0.13
Inceptisols	0.36
Entisols	0.16

Rainfall Erosivity

Using interpolated monthly rainfall data (***) spanning 40 years, the average rainfall erosivity index (R) was calculated. The modified fourniers index (MFI) has shown to be a good predictor of R. The annual MFI for each of the 40 years was calculated by

   sum( montly precipitation / total annual precipiatation) over each month

Raster algebra was used on the annual MFI grids to derive an average annual MFI. Finally the grid was interpolated to the optimal regional resolution using regularized spline tension (Mitasova, 1993).

Validation

Using the Database of World Rivers and their Sediment Yields (cite), we calculated the total sediment load (Yield x Area) for each river system. These rivers were observed over varying time spans and the observed values represent long term average sediment loading. In cases where multiple observation stations existed on a single river, the station furthest downstream was used to represent the sediment load at the coast. We joined the observed sediment data with the gtn basins (cite) yielding a vector polygon dataset of 123 rivers with known sediment values.

Using starspan, a raster-on-vector zonal statistics tool (Rueda, 2005), we calculated the total basin-wide erosion potential by taking sum of the RUSLE values within each polygon.

R used to correlate, calculate deviation (modvobs)

Attempts to improve sediment model by incorporating auxillary data

Using the esri global dams dataset, we performed a spatial intersection with our validation basins and the total dam volume per basin was calculated. Neither the total dam volume nor the volume-to-area ratio were significantly correlated with our models deviations. The Global Lakes and Waterbodies database (GLWD) was also used to calculate the total volume of lakes and resevoirs per basin. This dataset also showed no significant correlation with our model deviation. Despite the fact that dams and resevoirs have a known effect on sediment trapping, neither global dataset had a significant effect on the model.

An additional problem is that sediment transport in rivers is a highly variable phenomenon with possible deviations of 2 orders of magnitude between years. Therefore, an annual average sediment load approach is not likely to predict the sediment loading for a given year.

Citations

Rueda, C.A., Greenberg, J.A., and Ustin, S.L.  StarSpan: A  Tool for Fast Selective Pixel Extraction from Remotely Sensed Data. (2005). Center for Spatial Technologies and Remote Sensing (CSTARS), University of California at Davis, Davis, CA.

Mitasova, H., Mitas, L., 1999. Modeling soil detachment with RUSLE 3d using GIS. http://skagit.meas.ncsu.edu/~helena/gmslab/erosion/usle.html. Helena Mitasova, Lubos Mitas, University of Illinois at Urbana-Champaign.

Mitasova, H., J. Hofierka, M. Zlocha, L.R. Iverson, 1996, Modeling topographic potential for erosion and deposition using GIS. Int. Journal of Geographical Information Science, 10(5), 629-641. (reply to a comment to this paper appears in 1997 in Int. Journal of Geographical Information Science, Vol. 11, No. 6)

Mitasova, H. and Mitas, L. (1993) Interpolation by Regularized Spline with Tension: I. Theory and Implementation, Mathematical Geology, 25, 641-655.