3.Generating Discharge Map
3-1 Water Balance Model
The authors used Water Balance Model
developed by An&Tateishi(1995). Figure 3-1 shows
computing scheme of grid-based Water Balance
Model. Water surplus and deficit corresponds to the
positive or negative value of the difference between
precipitation and potential evapotranspiration.
Water surplus and deficit are estimated for each
grid cell. Figure 3-2 shows flowchart of the
computation.
Figure 3-1 water balance model
reference) An and Tateishi (1995)
Figure 3-2 Computation of water surplus and water deficit
reference) An and Tateishi (1995)
3-2 Producing DDM (Drainage Direction Matrices)
For ground elevation data and
drainage network data, GTOPO30
and DCW (Digital Chart of World) are
used respectively. The authors
applied the algorithm by Ochi S.
(1999) to produced DDM.
At the grid cells whose slope
gradient is more than 1 degree, water
run down to one of the neighboring
grid cell, which has the lowest
elevation value. Especially at the flat
grid cells whose slope gradient is less
than 1 degree, DCW rather than
GTOPO30 is used in determining to
avoid endless loop of the runoff
direction. Direction value such as
figure 3-3 is given in each grid cells.
Figure 3.3 Definition of directions
Step 1:
In deciding the direction of runoff
on a river, a target is set to be a grid cell on a river and a
goal is set to be a grid cell on sea. Figure 3-4 shows
relationship of the target and goal.
1) The grid cell downstream of the target cell is
searched by the DDM.
2) The target is shifted to the connected one.
The above procedure is repeated until the target
reaches the goal cell. If the target cell cant reach the goal
cell, DDM on the stuck grid cell is modified so that the
target cell can reach the sea.
Figure 3.4 Step 1 of producing DDM
Step 2:
In deciding the direction of runoff on slope, a target is
set to be a grid cell on slant and a goal is set to be a grid
cell on sea and river. Figure 3-5 shows relationship of
the target and goal.
1) The grid cell downstream of the target cell is
searched among grid cells adjoining to the target
by the DDM.
2) The target is shifted to the connected one.
Figure 3.5 Step 2 of producing DDM
The above procedure is repeated until the target cell
reaches the sea and river.
As a result, all grid cells on land territory run down
either to sea along DDM.
3-3 Generating Discharge Map
As figure 3-3 shows, DDM has numerical value of 1
byte(unsigned char) in each grid cell. On a river, 2,4,6,
and 8 is given by the DDM. On the other grid cells, value
from 1 to 9 is given by the DDM. Value 0 is given to
sea territory, and value 5 is given to grid cells on slope
which have no direction of runoff. Discharge Map can be
generated using value of water balance and value of the
DDM. Figure 3-6 shows an example of producing the Discharge Map.
1) Each grid cell of the water balance matrix is set to 1.
2) The current grid cell is set up as a source cell. Connected neighbor grid cell is
found by means of the DDM.
3) The content of the source cell is added to the content of the connected
neighbor grid cell.
4) If value of DDM is 0 or 5, this calculation is finished.
When this procedure is repeated on all grid cells, discharge map is generated. For
example, figure 3-7 shows discharge map in Asia.
| Water Balance Matrix |
Direction Matrix |
Discharge Matrix |
 |
Figure 3-6 Example of producing discharge map
Figure 3-7 Discharge Map in Asia
3-4 Verification of Discharge Map
The authors verified the discharge map, by comparing the simulation output with
the observation data on several points by GRDC. This intimate verification is going
on. This result of comparison will prove that the simulation is almost accurate. But
we will be able to derive better result from improving the water balance model.
