Module Runoff

Overview

Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the Module Basin where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

Main Processes

Manning Equation

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

Failed to parse (Cannot write to or create math temp directory): Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)

where:

Q	is the overland flow (m3/s)
A	is the area of the cross-section (m2)
n	is the Manning coefficient (s/m1/3)
Rh	is the hydraulic radius (m)
S	is the slope of the water surface (m/m)

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

Figure 1: Cell scheme

where:

h	is the water column (m)
w	is the cell width (m)

Hydraulics radius

The hydraulic radius is evaluated by the formula:

Failed to parse (Cannot write to or create math temp directory): \[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only R_h=h. Therefore the Manning's equation can be simplified as:

Failed to parse (Cannot write to or create math temp directory): \[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)

Slope

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

Failed to parse (Cannot write to or create math temp directory): \[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)

where:

H	is the water level (m)
h(i,j)	is the water column (m)
T(i,j)	is the Topography (m)
j	is X direction
i	is Y direction

Failed to parse (Cannot write to or create math temp directory): \[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)

where:

sx	is the slope in the X direction (m)
H(i,j-1)	is the water column at the left face of the cell (m)
H(i,j)	is the water column at the right face of the cell (m)
DZX	is width of the cell in the X direction (m)

Failed to parse (Cannot write to or create math temp directory): \[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)

where:

sy	is the slope in the Y direction (m)
H(i-1,j)	is the water column at the left face of the cell (m)
H(i,j)	is the water column at the right face of the cell (m)
DZY	is width of the cell in the X direction (m)

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

Failed to parse (Cannot write to or create math temp directory): s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)

where:

s	is the slope (m)

Manning cofficient

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

Calculated Flows

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

Figure 2:Flow directions

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

• Flow to the river when the water level of the river is lower that soil one

Figure 3: Flow to the river

• Flow from the river when the water level is higher than the soil one

Figure 4: Flow from the river

Other Features

How To Generate Manning Coefficients

Manning coefficients must be provided in runoff data file.

Options:

• Use a constant value
• Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] $\Longrightarrow$ [Shape to Grid Data] and provide:

(i) the grid (model grid)

ii) the land use shape file

iii) the corespondence between land use codes and Manning

Use Manning inicialization with Module FillMatrix standards in the block:

<BeginOverLandCoefficient>
FILE_IN_TIME           : NONE
INITIALIZATION_METHOD  : ASCII_FILE
REMAIN_CONSTANT        : 1
DEFAULTVALUE           : 0.08
FILENAME               : ..\..\GeneralData\Runoff\Mannings200m_v2.dat 
<EndOverLandCoefficient>

References

<references/>