19
Why Model?
For many a study area, often there is an incomplete river discharge data, if any exists at all. This modified Schreiber model allows for the estimation of river discharges using commonly available local parameters. The model has been shown to be robust for tropical and sub-tropical
areas.
INPUT PARAMETERS
•MONTHLY PRECIPITATION
•MONTHLY ATMOSPHERIC TEMPERATURE
•WATERSHED AREA
EQUATIONS
Vq = Ax (exp (-eo/r+0.001))(r/2.74*10-6 Di)
eo = 1.0 * 109 exp (-4.62*103/(273.15+T))
Where Vq (m3 yr-1) is the total calculated monthly runoff
Ax (km2) is the total watershed area
eo (mm) is the calculated monthly evapotranspiration for the watershedr (mm) is the monthly precipitation for the watershed
Di is the number of days for the month
T (oC) is the monthly atmospheric temperature
• Calculation of watershed area and comparison to measured discharge using the rivers discharging into Lingayen Gulf, Philippines
• Application of model to rivers surrounding the South China Sea and using the results to determine inter-country variability
EXAMPLES
LINGAYEN GULF
Lingayen Gulf, located in the northwestern part of the Philippines, has 7 major rivers and 5 of which have gauge measurements. The largest is the Agno River, located at the southwestern side of the Gulf.
LANDSAT TM OF LINGAYEN GULF
Determining the watershed area. The area of the
corresponding watershed for each river can be determined using a topographic map.
As shown in the given example, the highest points around the watersheds of the 7 rivers of Lingayen Gulf are taken as indicators of the natural boundaries.
Comparison: calculated vs. measured
AGNO RIVER
CALCULATED: 6.73E+9 m3/yr
MEASURED: 6.66E+9 m3/yr
% DIFFERENCE: 1%
Annual Discharge
0.E+002.E+094.E+09
6.E+098.E+09
m3 yr-1
Calculated
Measured
The calculated annual discharges of the 7 rivers around Lingayen Gulf as shown here in blue were compared to the measurements available from 5 of the rivers as shown here in maroon. The biggest observed difference is for Agno River. The calculated discharge is about 1% higher than the measured.
SOUTH
CHINA
SEA
SOUTH CHINA
I N D O N E S I A
M A L A Y S I A
PHILIPPINESTHAILAND
CAMBODIA
VIETNAM
The model was additionally applied to rivers discharging into the South China Sea.
MONTHLY DISCHARGECambodia
0.0E+00
1.0E+04
2.0E+04
m3yr-1
China
0.0E+00
5.0E+05
1.0E+06
1.5E+06
m3yr-1
Indonesia
0.E+00
5.E+04
1.E+05
2.E+05
m3yr-1
Malaysia
0.E+00
5.E+05
1.E+06
Philippines
0.E+00
5.E+04
1.E+05
2.E+05
Thailand
0.E+00
1.E+05
2.E+05
3.E+05
4.E+05
5.E+05
Vietnam
0.E+00
1.E+06
2.E+06
3.E+06
The model was applied to individual river and the results were summarized to give a per country total discharge. As can be seen the discharge signature of Malaysia and Indonesia are similar to each other but very different from the rest of the countries surrounding the South China Sea.
There are times when characterizations of large geographic expanses are desired. Often though there is not enough data for adequate comparisons. The model can be used to obtain reliable data for comparisons.
3.9
E+11
1.3
E+11
8.8
E+11
4.1
E+11
1.2
E+11
9.2
E+11
0.E+00
2.E+11
4.E+11
6.E+11
8.E+11
1.E+12
m3yr-1
CalculatedMeasured
5.45%
4.17%
4.98%
* excluding Khong river
Comparison: calculated vs. measured
Results of the model (blue) were also compared to available measured data (green). Average difference is 5%.
Additional ApplicationIn areas where there are existing river discharge
data, often the gauges are located several lengths upstream in order to eliminate the tidal effects in the measurements. The shortcoming of this however, is that the inputs from the watershed below the gauging station are no longer considered. The modified Schreiber model allows for the estimation of additional surface flow below the gauging station. This use of the model has been shown to be robust for tropical
and sub-tropical areas.
EQUATIONSVT = VM + Vq
Vq = Ax (exp (-eo/r+0.001))(r/2.74*10-6 Di)
eo = 1.0 * 109 exp (-4.62*103/(273.15+T))
Vq (m3 yr-1) is total calculated monthly runoff from the remaining watershedAx (km2) is the total watershed area
eo (mm) is the calculated monthly evapotranspiration for the watershedr (mm) is the monthly precipitation for the watershed
Di is the number of days for the month
T (oC) is the monthly atmospheric temperature
VM (m3 yr-1) is the total measured monthly runoff as measured upstream
Where VT (m3 yr-1) is the total monthly runoff
Laguna de Terminos, Mexico has 3 major rivers, Mamantel-Candelaria, Chumpan and Palizada with a combined average discharge of 10 x 109 m3 yr-1. These measurements were however, taken several kilometers upstream (shown here in triangles). The approach is then to apply the model to the watershed below the gauge stations to obtain the total discharge.
Palizada
0.E+00
5.E+09
1.E+10
2.E+10
m3 yr-1
Mamantel-Candelaria
0.E+001.E+092.E+09
3.E+094.E+095.E+09
m3 yr-1
Chumpan
0.E+00
5.E+08
1.E+09
2.E+09
2.E+09
m3 yr-1
Comparison: model vs. ratioLaguna de Terminos, Mexico
0.E+00
1.E+10
2.E+10
3.E+10
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
m3 yr-1
Applying the model to the watershed below the gauge increased the total discharge of the 3 rivers to 12 x 109 m3yr-1. Most of the additional discharge is seen during the wet season of June to October as shown here in green. For comparison, compensating for the ungauged watershed area using ratio and proportion is shown in light blue. The dark blue line shows the original measured total discharge. Expert knowledge of your systems would dictate which approach is closer to the real system behavior. In the case of Laguna de Terminos, the author decided to use the model results.
ANNUAL DISCHARGE (m3yr-1)
MODEL : 12 x 109
RATIO : 11 x 109
MEASURED : 10 x 109
SENSITIVITY ANALYSES
• sensitive to location & scope of meteorological station - remember that the water that discharges from the rivers comes from the watersheds upstream and therefore if possible choose meteorological data from corresponding stations.
• monthly data only - DO NOT take annual data and divide that by 12 months. The numbers you will get won’t be reliable. • sensitive to watershed area measurement - if available use watershed measurements by local experts. Specifically, when comparing measured and calculated, make sure to use the same watershed area as base.
LIMITATIONS
• unrealistically low results for very dry and warm months
• overestimate for months with torrential rains
• overestimate for areas where there is significant groundwater storage
Example of a system with extreme seasonal precipitation
Sabarmati is located in a region of India which stays dry throughout the year except for the months of July and August which are characterized by torrential rains.
Sabarmati River
0.E+00
1.E+09
2.E+09
3.E+09
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov
m3 yr-1
Applying the model to the system (green), therefore, does not simulate the exact discharge characteristics (purple). Another possible reason for the discrepancy is the fact that the meteorological data is taken not from the upper watershed but downstream where there gauge is also located (shown in blue triangle).
Comparison: model vs. ratio
Applying the model to the total watershed increased the total discharge from 29 x 107 m3yr-1 to 21 x 108 m3yr-1. Most of the additional discharge is seen during the wet season of June and July as shown here in light blue. For comparison, compensating for the ungauged watershed area using ratio and proportion is shown in green (16 x 108 m3yr-1). The dark blue line shows the original measured discharge. Expert knowledge of the system would dictate which approach is closer to the real system behavior.
Calculations: model vs. ratio
0.E+00
5.E+09
1.E+10
2.E+10
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
m3 yr-1
Measured
Model
Ratio
WATERSHED AREA (km2) going to highlighted rivers gauged: 12,950 (dark blue)total: 71,380 (dark+light)
