### 2.7.2.1. Surface Runoff[¶](#surface-runoff "Permalink to this headline")

The simple TOPMODEL-based ([Beven and Kirkby 1979](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#bevenkirkby1979)) runoff model (SIMTOP) described by [Niu et al. (2005)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#niuetal2005) is implemented to parameterize runoff. A key concept underlying this approach is that of fractional saturated area \\(f\_{sat}\\), which is determined by the topographic characteristics and soil moisture state of a grid cell. The saturated portion of a grid cell contributes to surface runoff, \\(q\_{over}\\), by the saturation excess mechanism (Dunne runoff)

(2.7.26)[¶](#equation-7-64 "Permalink to this equation")\\\[q\_{over} =f\_{sat} \\ q\_{liq,\\, 0}\\\]

The fractional saturated area is a function of soil moisture

(2.7.27)[¶](#equation-7-65 "Permalink to this equation")\\\[f\_{sat} =f\_{\\max } \\ \\exp \\left(-0.5f\_{over} z\_{\\nabla } \\right)\\\]

where \\(f\_{\\max }\\) is the potential or maximum value of \\(f\_{sat}\\), \\(f\_{over}\\) is a decay factor (m\-1), and \\(z\_{\\nabla}\\) is the water table depth (m) (section [2.7.5](#lateral-sub-surface-runoff)). The maximum saturated fraction, \\(f\_{\\max }\\), is defined as the value of the discrete cumulative distribution function (CDF) of the topographic index when the grid cell mean water table depth is zero. Thus, \\(f\_{\\max }\\) is the percent of pixels in a grid cell whose topographic index is larger than or equal to the grid cell mean topographic index. It should be calculated explicitly from the CDF at each grid cell at the resolution that the model is run. However, because this is a computationally intensive task for global applications, \\(f\_{\\max }\\) is calculated once at 0.125° resolution using the 1-km compound topographic indices (CTIs) based on the HYDRO1K dataset ([Verdin and Greenlee 1996](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#verdingreenlee1996)) from USGS following the algorithm in [Niu et al. (2005)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#niuetal2005) and then area-averaged to the desired model resolution (section [2.2.3.3](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Ecosystem/CLM50_Tech_Note_Ecosystem.html#surface-data)). Pixels with CTIs exceeding the 95 percentile threshold in each 0.125° grid cell are excluded from the calculation to eliminate biased estimation of statistics due to large CTI values at pixels on stream networks. For grid cells over regions without CTIs such as Australia, the global mean \\(f\_{\\max }\\) is used to fill the gaps. See [Li et al. (2013b)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#lietal2013b) for additional details. The decay factor \\(f\_{over}\\) for global simulations was determined through sensitivity analysis and comparison with observed runoff to be 0.5 m\-1.

