Projeto LOICZ rivers

1. RIVER DISCHARGE
L.T. David* and E.L. Peñaflor
*ldavid@msi01.cs.upd.edu.ph
loicz@usa.net

2. 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.

3. INPUT PARAMETERS
•MONTHLY PRECIPITATION
•MONTHLY ATMOSPHERIC TEMPERATURE
•WATERSHED AREA

4. 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 watershed
r (mm) is the monthly precipitation for the watershed
Di is the number of days for the month
T (oC) is the monthly atmospheric temperature

5. • 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

6. 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

7. 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.

8. Comparison: calculated vs. measured
AGNO RIVER
CALCULATED: 6.73E+9 m3/yr
MEASURED: 6.66E+9 m3/yr
% DIFFERENCE: 1%
Annual Discharge
0.E+00
2.E+09
4.E+09
6.E+09
8.E+09
Agno
Patalan-...
Alam
inos
Balingasay
D
agupan
Aringay
Bauang
m
3
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.

9. SOUTH
CHINA
SEA
SOUTH CHINA
I N D O N E S I A
M A L A Y S I A
PHILIPPINES
THAILAND
CAMBODIA
VIETNAM
The model was additionally applied to rivers
discharging into the South China Sea.

10. MONTHLY DISCHARGE
Cambodia
0.0E+00
1.0E+04
2.0E+04
m
3
yr
-1
China
0.0E+00
5.0E+05
1.0E+06
1.5E+06
m
3
yr
-1
Indonesia
0.E+00
5.E+04
1.E+05
2.E+05
m
3
yr
-1
Malaysia
0.E+00
5.E+05
1.E+06
m
3
yr-1
Philippines
0.E+00
5.E+04
1.E+05
2.E+05
m
3
yr-1
Thailand
0.E+00
1.E+05
2.E+05
3.E+05
4.E+05
5.E+05
m
3
yr-1
Vietnam
0.E+00
1.E+06
2.E+06
3.E+06
m
3
yr-1
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.

11. 3.9E+11
1.3E+11
8.8E+11
4.1E+11
1.2E+11
9.2E+11
0.E+00
2.E+11
4.E+11
6.E+11
8.E+11
1.E+12
C
h
i
n
a
T
h
a
i
l
a
n
d
*
V
i
e
t
n
a
m
m3
yr-1
Calculated
Measured
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%.

12. Additional Application
In 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.

13. EQUATIONS
VT = 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 watershed
Ax (km2) is the total watershed area
eo (mm) is the calculated monthly evapotranspiration for the watershed
r (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

14. 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
J
a
n
M
a
r
M
a
y
J
u
l
y
S
e
p
t
N
o
v
m
3
yr
-1
Mamantel-Candelaria
0.E+00
1.E+09
2.E+09
3.E+09
4.E+09
5.E+09
J
a
n
M
a
r
M
a
y
J
u
l
y
S
e
p
t
N
o
v
m
3
yr
-1
Chumpan
0.E+00
5.E+08
1.E+09
2.E+09
2.E+09
J
a
n
M
a
r
M
a
y
J
u
l
y
S
e
p
t
N
o
v
m
3
yr
-1

15. Comparison: model vs. ratio
Laguna 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

16. 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.

17. 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

18. 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).

19. 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)