Chapter 6. TRIGRS Model for Guwahati City
6.2. Surface Hydrology
The program, TRIGRS, uses a simple method for routing of surface runoff from cells that have excess surface water to adjacent downslope cells where it can either infiltrate or flow farther down slope. Runoff at a particular cell is assumed to occur when the precipitation and runoff supplied from upslope cells exceed the infiltration capacity or the rate of actual infiltration estimated at that cell for a particular time step.
The saturated hydraulic conductivity is generally considered the limiting case for the infiltration capacity for saturated and tension-saturated soils (Hillel, 1982; Iverson, 2000).
Tension-saturated state represents the in-situ condition wherein the pore-water pressure is less than the atmospheric pressure (i.e., considered negative) while the soil being in a saturated state. This condition generally prevails in the capillary zone of the soil, just above the water table. The hydraulic conductivity is considered constant and equal to the saturated permeability. The purpose of routing the surface runoff is to prevent the loss of excess precipitation that cannot infiltrate at the cell of application. Simple runoff routing model allows diverting excess water from impervious areas onto more permeable downslope areas.
6.2.1. Runoff
The infiltration at each cell is computed as the sum of the precipitation plus any runoff from upslope cells with the limitation that infiltration cannot exceed the saturated hydraulic conductivity. The excess, if any, is considered runoff and is diverted to adjacent downslope cells.
;
;
ru ru sat
in
sat ru sat
RI R RI R k
Q
k RI R k
(6.1)
where, Qin is the rate of infiltration, RI is the applied rainfall intensity,
Rru is the run-off from upslope cells, (≥ 0), ksat is the saturated hydraulic conductivity,
;
0 ;
ru sat ru sat
rd
ru sat
RI R k RI R k
R
RI R k
(6.2)
where, Rrd is the run-off from the cell, diverted to adjacent downslope cells.
The run-off between adjacent cells is assumed to occur instantaneously and is not modelled as overland flow. The runoff from one-time step is not carried over to the next.
Thus, excess water that runs off a cell during any given time step will either infiltrate at another cell or reach the edge of the model within that time step. The routing method enforces mass balance for each time step at individual cell level. The total precipitation at all the cells therefore is equal to the water that infiltrates at all the cells and the water that flows to edges of the problem domain without infiltrating within that particular time step.
In addition to runoff from cells where precipitation exceeds the infiltration capacity, water is assumed to run off from any cells where the water table is initially at the ground surface and the initial (steady) rate of infiltration is negative. TRIGRS is capable of modelling exfiltration from such cells using the mass balance calculations. Water from such cells runoffs to the adjacent downslope cell(s).
TRIGRS avoids iteration for satisfying mass balance for the entire problem domain.
Therefore, to ascertain that the runoff routing is efficient TRIGRS computes the infiltration
and runoff at cells in order from the topographically highest cell(s) to the lowest. Hence, the topographic data have to be properly indexed. The digital elevation model (DEM) should be adjusted in GIS software to be hydrologically consistent. This adjustment is a selective smoothing process accomplished by raising the elevation of single-cell closed depressions to match surrounding cells, and slightly raising or lowering the elevation of cells in flat areas to produce flow directions that are consistent with surrounding topography.
6.2.2. Topographic Indexing and Flow Routing
TopoIndex (Topographic Index) is a companion utility program with the TRIGRS code that prepares a group of data files for the runoff-routing calculations. The TRIGRS program uses these data to control the order of runoff routing calculations as described above.
TRIGRS will compute infiltration based on the rainfall input without routing any excess surface water if this step is skipped.
The program TopoIndex uses a two-step process to index the cells from highest to lowest elevation. The first step, sorting the cell elevations, consists of defining an index using the 'Heapsort' algorithm (Press et al., 1986). The second step corrects the index by comparing the indices of neighboring cells to their relative positions along downslope paths. The output files of TopoIndex also contain a list of grid cells and their downslope neighbors, along with a list of weighting factors that determine what proportion of the runoff is transferred to each neighboring downslope cell.
Thus, the output of the TopoIndex defines a continuous runoff flow path from upslope cell to downslope cell and the ratios by which the runoff of one cell will be divided into the adjacent downslope cells. TopoIndex provides the user several options for determining how excess water will be distributed among the downslope cells. Figure 6.1 shows the distribution weights of the various methods alongside the DEM. Figure 6.1 (a) shows the DEM of 9 cells, with the elevation value of each cell. The runoff is considered to occur from the shaded cell marked 'C' to adjacent downslope cells. Figure 6.1 shows the weighting factors for the (b) D-
∞ method, (c) uniform distribution to all adjacent downslope cells, (d) D-8 method, (e) slope proportional distribution and (f) weighting factor proportional to square of slope. Comparing the weights with the elevation values, the distribution pattern of the runoff can be observed.
The D-∞ method assumes that water flows down the steepest slope, and computes the direction of steepest slope and attempts to direct flow in that direction by partitioning the flow between the two cells nearest to the steepest slope direction. The weighting factors are
proportional to the angles between the grid directions and the dip direction of the facet as described by Tarboton (1997). D-∞ method is physically more realistic than any of the other methods implemented in TopoIndex, and is used in the steady-state regional slope stability program SINMAP (Pack et al., 1998).
Figure 6.1 (a) DEM elevation values; (b), (c), (d), (e) and (f) Weighting factors for runoff distribution from the arbitrary cell marked C.