Surface Water Routing:Overland Flow Routing

5.2.1 Overland Flow Routing Formulation

Overland flow in GSSHA employs the same methods described for 1-D channel routing, except the calculations are made in two dimensions. Flow is routed in two orthogonal directions in each grid cell during each time step. The watershed boundary represents a no flow boundary for the overland flow routing and when a grid cell lies on the watershed boundary, flow is not routed across the boundary. There is an option in GSSHA to impose head boundaries along the watershed boundary and compute flows across the overland boundary. In GSSHA, Δx = Δy. Inter-cell fluxes in the x and y directions, p and q, respectively, are computed in cell ij from the depth, d_ij, at the n^th time level using the Manning equation for the head discharge relationship in the x and y directions, respectively, as

(6)

(7)

Depths in each cell are calculated at the n+1 time level based on the flows for each cell (Julien and Saghafian, 1991):

(8)

In addition to this original formulation in the CASC2D model, two additional methods of solving the equations have been added, an alternating direction explicit scheme (ADE) and an ADE scheme with an additional predictor-corrector step (ADEPC) (Downer 2002a; Downer et al., 2000). Both the ADE and ADEPC methods employ the up-gradient difference technique, Equation 3, for flows in the upstream direction (Downer, 2002a). Fluxes other than inter-cell fluxes, direct evaporation (DET), infiltration, exfiltration, are accounted for before overland routing is computed.

In the ADE method, inter-cell flows are first calculated in the x direction according to Equation 6. Depths in each row are updated based on the flows in the x direction:

(9)

Inter-cell flows in the y direction are computed using the updated depths:

(10)

Depths in each column are updated based on the flows in the y direction:

(11)

With the ADEPC method additional steps are added to improve accuracy and stability. As before, during each sweep, by rows or by columns, an estimate of heads is made based on the calculated flows, Equations 9 and 11. Next, using the updated depths, updated estimates of flow are computed at the n+1 time level

(12)

The original flows and the updated flows are then averaged to come up with an estimate of flows for the time step:

(13)

These flows are then used to update the original depths, Equations 9 and 11. This procedure is essentially the MacCormack method (MacCormack, 1969) except up-gradient differences are used in both the predictor and corrector steps. A similar method was successfully implemented by Wang and Hjelmfelt (1998).

In benchmark tests using the three methods: original explicit (EXPLICIT), ADE, and ADEPC, in an contrived watershed consisting of two converging planes (open book), the Goodwin Creek Experimental Watershed (GCEW) (Senarath et al., 2000), and Poplar Creek (Downer et al., 2002a), the ADE and ADEPC methods ran with significantly larger time steps (Downer et al., 2000). Depending on the test case, time steps could be increased from 20% to 240% with commensurate decreases in simulation times.

The routing scheme is selected using the OVERTYPE card. The default value is EXPLICIT. The most efficient scheme to use depends on the particular watershed. The ADEPC scheme can generally handle rougher terrain and typically requires less smoothing of the DEM, but the additional computational steps result in greater computation time, unless use of the ADEPC scheme permits substantially greater time steps than with one of the other two methods. For smoothed DEMs or in watersheds with smoother terrain, the ADE and EXPLICIT methods usually can be employed, with a resulting savings in execution time.

To improve stability, the timestep in both the EXPLICIT and ADE schemes is variable. The time step is not variable in the ADEPC. The addition of a variable timestep has allowed for increases in the overall model timestep when using either the EXPLICIT and ADE methods. These new methods have not been benchmarked against the ADEPC method.

5.2.2 Overland Flow Hydraulic Roughness

The GSSHA model requires that Manning roughness coefficients be assigned to every cell in the watershed mask. There are three ways to specify the hydraulic roughness of the overland flow planes in GSSHA. The first method is to apply a constant value over the entire watershed through the MANNING_N project file card. The second method is to use the MAPPING_TABLE to assign roughness coefficients using tabled values referenced to an index map. The third method is to produce a GRASS ASCII map of roughness coefficient, and provide the name of this map to GSSHA using the ROUGHNESS project file card. Table 8 provides typical values of the Manning roughness coefficient for overland flow over various surfaces:

Land Use or Cover	Recommended n-value	Range
Concrete or asphalt	0.011^a	0.01-0.013^a 0.05-0.15^d
Developed/industrial	0.0137^b	-
Bare sand	0.01^a	0.010-0.016^a
Graveled surface	0.02^a	0.012-0.03^a
Bare clay-loam (eroded)	0.02^a	0.012-0.033^a
Gullied land	-	0.320-0.357^c
Bare field – no residue	0.05^a	0.006-0.16^a
Range (natural)	0.13^a	0.01-0.32^a
Range (clipped)	0.10^a	0.02-0.24^a
Grass and pasture	-	0.05 – 0.15^a
Pasture	- -	0.235-271^c 0.30-0.40^d
Clover	-	0.08 – 0.25^a
Small grain	-	0.1 – 0.4^a
Row crops	-	0.07 – 0.2^a
Cotton/soy	-	0.246-0.261^c
Grass (bluegrass sod)	0.45^a	0.39-0.63^a 0.30-0.50^d
Short grass prairie	0.15^a	0.10-0.20^a,^d
Dense grass	0.24^a	0.17-0.30^a
Bermuda grass	0.41^a	0.30-0.48^a
Lawns		0.40-0.50^d
Forest	0.192^b	0.184-198^c
Sparsely vegetated	0.150^b	0.05-0.13^d
Dense Growth		0.40-0.50^d

Table 8 - Values of overland flow roughness coefficient Notes: ^aEngman (1986), ^bDowner (2002b), ^cSenarath et al (2000), ^dHEC (1985)

These values should be considered guidelines. Manning roughness coefficients are typically assigned from literature values and then adjusted through calibration. Additional sources of literature values are Liong et al. (1989), Engman (1986), and Ree et al. (1977). If calibrated values differ significantly from published values, there may be appropriate justification. Typical Manning roughness coefficient values for open channel flow are considerably smaller than overland flow values because of deeper flow depths in the channel.

5.2.3 Runoff Retention

Natural land surfaces contain micro-topography, small depressions, that retain water prior to runoff. The water held in the grid cell, or retention storage, never becomes direct runoff and can only be removed from the land surface as infiltration or direct evaporation. In certain regions, the retention storage can be significant. Retention storage is input as a depth (mm) in each grid cell and may be optionally input to GSSHA as:

a uniform value using the RETENTION card,
as a table of values related to index maps by using the MAPPING_TABLE project card, and the RETEN_DEPTH card without specifying a file name or
as an ASCII GRASS map through the use of the RETEN_DEPTH project file card with a specified file name.

5.2.4 Specifying Initial Depths on the Watershed

Initial depths on the overland flow plane at the beginning of the simulation may be specified by use of the INITIAL_DEPTH project file card. This card is used to specify an ASCII GRASS map containing initial overland depth values, m. This feature is rarely used.

5.2.5 Simulations without Channel Routing

It might be desirable to perform simulations without channel routing in very small watersheds lacking a defined channel network, or in the beginning stages of developing a GSSHA model of a watershed. It is always prudent to build a GSSHA model one process at a time. Getting just the overland flow portion of the model to run is always the first step in building a model. For these reasons, GSSHA may be used without channel routing. Because the channel network normally provides the outlet point, the overland cell containing the outlet must be specified during simulations without channel routing. Normally this grid cell will have the lowest elevation in the watershed. The row and column containing the outlet grid cell are specified using the OUTROW and OUTCOL cards, while the slope of the outlet grid cell is specified using the OUTSLOPE card. If channel routing is enabled through the inclusion of CHAN_EXPLIC in the project file, the OUTROW, OUTCOL, and OUTSLOPE cards are not required, and ignored if present.