Land Degradation Model (LDM)

The IMAGE 2.2 Land Degradation Model (LDM) comprises a qualitative description of the land degradation process of water erosion, as described in detail by Hootsmans et al. (2001). The water erosion model is based on the work of Batjes (1996a), who used a simplified version of the Universal Soil Loss Equation (USLE) (Wischmeier and Smith, 1978).

The major input and output variables of the land degradation model are listed below:

Model input	Precipitation
	Number of wet days (assumed constant in time)
	Soil erodibility index (based on soil texture, bulk density and depth), which is assumed to be constant in time
	Relief index (assumed to be constant in time)
	Land cover types
Model assumptions	Land-use pressure index for land cover types
Model output	Water erosion susceptibility and sensitivity

The approach is based on the concepts of susceptibility and sensitivity to water erosion. Susceptibility to water erosion is based on the current terrain erodibility and rainfall erosivity. Sensitivity to water erosion describes the chance that water erosion will occur in the short term, accounting for the actual land use and land cover. Hence, the susceptibility to water erosion represents, in actual fact, the sensitivity of bare soil surfaces.

The susceptibility and sensitivity indices are calculated according to:

with:
R = rainfall erosivity index (-)
T = terrain erodibility index (-)
Ep = water-erosion susceptibility index (-)
SE = soil erodibility index (-)
Ia = relief index (-)
V = land-use pressure index (-)
Ea = water-erosion sensitivity index (-)

The different components of the model implemented in IMAGE 2.2 are discussed in more detail below.

• Rainfall erosivity index (R). The erosivity of rainfall is largely determined by the intensity of rainfall events. Soil loss only occurs during rainfall with high intensity. A proxy for R is inferred from the month with the greatest rainfall intensity (mm per day), calculated as monthly precipitation divided by number of wet days in each month. Maximum mean monthly rainfall intensities of 0-2 mm per day are assigned an index value R of 0, while those exceeding 20 mm per day are assigned a value of 1.0. Between these two extremes a linear relation is assumed. For the historical period, the New and Hulme (1999) climate data is used. For future years, R is derived from the changes in precipitation based on different scenarios generated by the climate model. The number of wet days is assumed to be constant in time, as the IMAGE model does not generate projections for this aspect.
• Terrain erodibility index (T). The terrain erodibility expresses the combined susceptibility of soil and relief. T is defined as the average of the soil erodibility and relief indices, so that the weight assigned to the combined soil indices It, Ib and Id equals that of the relief index (Ia). The terrain erodibility index is assumed not to change in the future.
• Susceptibility to water erosion (Ep). The product of rainfall erosivity (R) and terrain erodibility (T) is the index for the potential susceptibility to water erosion (Ep) of the land based on conditions of climate and terrain.
• Soil erodibility index (SE). The soil erodibility (SE) is derived from indices for soil texture, bulk density and soil depth by taking the average of the two highest values. Although this is a rather arbitrarily chosen approach, it results in an expression of the relative differences between soils. Soil characteristics were deduced from the 0.5 by 0.5 degree resolution WISE database (Batjes, 1996a; Batjes and Bridges, 1994; Batjes et al., 1997).
• Relief index (Ia). The relief index is a landform characterization (slope) derived from a digital elevation model. Landforms were calculated from the difference between minimum and maximum altitude from the 10-minute grid FNOC elevation dataset (FNOC, 1985). Ia = 1 for a difference of 300 m or more and for Ia = 0 for differences of 0 m; between these values in altitude a linear relationship is used.
• Land-use pressure index (V). Given conditions of climate, soil and relief, the protection provided by land use and land cover determines the actual sensitivity to water erosion. The geographic distribution of different land-cover types generated by the land-cover model forms the basis for the land-cover index. Land-cover indices were modified from Wood and Dent (1983a,b) as described in Hootsmans et al. (2001). Natural vegetation such as forests provide a high degree of protection against water erosion, while agriculture generally leads to the higher vulnerability of the soil surface. For grid cells with agriculture, a composite value for V is used, which is based on the distribution of agricultural crops within the specific world region. The contribution of soil and crop management, and soil conservation practices, is not included in the land-cover index.
• Water-erosion sensitivity index (Ea). The sensitivity to water erosion is derived by combining the land's susceptibility to water erosion (Ep) with the land-use pressure index (V). By multiplying the indices V and Ep with opposite scales, a compensation of effects is achieved. For example, for low values of V (high degree of protection provided by the land's cover) and high land susceptibility (high value of Ep for hilly landscapes), the water-erosion sensitivity will still be low. Contrary, when the protection provided by the land cover is low (for example, under agriculture), the sensitivity will be low if the land's susceptibility is low (for example, on non-sloping land).

Maximum correspondence with the GLASOD degradation status maps of Oldeman et al. (1991) was achieved by using a classification of water erosion-sensitivity for which about 85% of the grid cells have a calculated erosion risk that corresponds to the GLASOD water erosion status (see table below). This classification can be used as a guide when analyzing the water-erosion sensitivity indicator.

Classification of water-erosion sensitivity index
Water erosion-sensitivity index	Erosion risk
< 0.15	no/low
0.15-0.30	moderate
0.30-0.45	high
> 0.45	very high