# Surface processes

If not all rainfall infiltrates puddles form at the surface. Before runoff is starting a small amount of water will be stored in the surface micro relief. This part of the model serves to purposes: to calculate the amount of water stored by the micro relief that is not moving , and to calculate the width of the overland flow when runoff starts.

The surface storage is based on the micro relief that is characterized by the random roughness (Onstad, 1984). Radom roughness is the standard deviation of surface elevation, measured on a small scale. This is usually done along a transect using a pinboard (a board with pins every cm) or by scanning a surface of 1 to several m2. Some reserchers eliminate the highest and lowets 10% of the measurements before calculating the standard deviation

Surface storage is calculated using the Maximum Depression Storage (MDS). This is the threshold value above which surface micro depressions overflow. The MDS is determined by Kamphorst et al. (2000) from 221 digital elevation models of various types of micro relief, in a wide variety of agricultural circumstances and soil types. Following the work of Onstad 1984) Kamphorst et al. (2000) found (n = 221, R2 = 0.88):``` MDS = 0.243·RR + 0.010·RR2 - 0.012·RR·S```

in which RR is the standard deviation of surface heights (cm) and S is the terrain slope (%). Kamphorst et al. (2000) tested 6 different roughness indices but found that the standard deviation of the heights gave the best relation with MDS (cm). However, in openLISEM  it is assumed the MDS is not a hard threshold, water already starts to flow between pixels. Based on a GIS analysis the water released from a pixel is:
`hflow = (h-sds)·(1-exp(-h·(h-sds)/(mds-sds)))  and h>sds`

where h is the total water height (cm) and SDS is the starting depression storage which is arbitrarily set at 10% of the MDS.

The width of the flow w is calculated as the fraction of area ponded in a pixel, multiplied by the pixel width dx:
`w = fpa·dx = dx·(1-exp(-1.875*(h/RR))`

The ponded area also influences the splash erosion, as splash directly on ponded surfaces has less effect than on dry soil (see splash detachment).

`w = dx·fpa + roadwidth`
`hro = (hflow·fpa·dx + hroad·roadwidth)/dx`
Note that the road width is always smaller than the cell size dx, and in case of the presence of a channel, the channel width takes precedence (so that `road width + channel width < dx`)