Prasanna Dahal
Local Roads Bridge Programme
Abstract
A review of methods used, and their results, for
different hydrological methods was presented. The review considered up to eight
methods (WECS/DHM, Dickens’, modified Dickens’, BD Richards’s, Snyder’s,
Rational method, Fuller’s formula and regional method) of flood forecast common
in Nepal. The focus of the study was flood discharge of 100 years return period
(Q100) , which is used as design discharge for bridge-design. Using
each of these methods, the discharge values were obtained for various catchment
areas. The catchment features (basin slope, longest flowpath, average basin
width etc.) required as inputs for different hydrological methods were obtained
from Digital Elevation Model (DEM) and stream network of the watershed using
ArcHydro tool in ArcGIS 10.1. These values were used to predict (Q100)
using each of the mentioned methods. Sensitivity analysis was carried out for
three methods viz. Dickens’, Fuller’s formula and Rational method. Value of Q100
derived from each of these methods depend predominantly on its catchment area.
Therefore, variation in Q100 that results from assigning incorrect
value in these methods for different values of catchment areas were
demonstrated. Also, using the value of the calculated Q100,
variation in Top width of a river, which determines bridge span in design of a
bridge, was calculated. For the catchment area and same method, the greatest
Top width calculated was found to vary more than 200% of the minimum top width.
Also, values of Q100 obtained from these methods were compared
against Gumbel projected discharge from nine of the gauged hydrological
stations of DHM. These Gumbel-projected discharge considered were calculated
assuming gauged discharge values follow Gumbel distribution, and were assumed
to be ‘accurate’ values. One of the eight considered hydrological methods were
deemed ‘preferable method’ based on the how close their prediction came with
the gauged values. Regional
method was found to provide closest value for most cases (six out of
nine).
Keywords: WECS/DHM, Dickens’
Method, Modified Dickens’ Method, Snyder’s Method, Rational Method, Fuller’s
formula, Regional Method, BD BD Richards Method, Return Period, Q100
, ArcHydro tool, ArcGIS, Hydrological
Stations, River Top Width.
Calculation of extreme flood value is crucial for
constructions of civil structures like bridges, highways, dams, culvert etc.,
also for identifying flood control measures (Alam & Matin, 2005). A good
prediction of a flood likely to occur at certain time period goes long way in
making civil engineering works effective, economic as well as life-saving.
Current practices of high flood determination include processes ranging from
empirical formulae to advance modeling. A well-researched study can give
empirical formula that can be expected to give reliable results. Similarly, a
well-established model can be used to predict the value of discharge at the
extreme event. However, use of formulae that are not researched to be valid for
Nepalese basins is not recommended as they may not produce reliable results.
Similarly, use of model with incorrect set up (such as too much assumptions,
incorrect values of land properties like curve number and improper lag time
etc.), is also likely to produce unreliable discharge value. Predicting Q100,
as is required in construction of important civil structures like bridges and
hydropower headworks, is a difficult
task. Use of untested methods adds more to the uncertainty. Dominant methods in
hydrology estimation in Nepal involves use of formulae from methods such as
Snyder (Jakeman, Littlewood, & Whitehead, 1990), BD Richards (Colombi & RICHARDS, 1978), Dickens (1865) (Jakeman et
al., 1990), WECS/DHM (Chitrakar, n.d.; Shrestha, Chaudhary, Maskey, &
Rajkarnikar, 2010), Fuller’s formula (1914), Regional, Rational (Dooge, 1957; Linsley, 1986) as
described in popular hydrology books (Subramanya, 1994) or use of popular
modeling software HEC-HMS. Both the methods have merits but there could be room
for questions of reliability to be raised. If the prediction is based on
formulae given these methods , there are questions of both the ambiguity in use
of constant , and their merit in use in Nepal. For example, use of Snyder’s
method requires value of constant such as Ca, Ct , Cp etc. which are defined by
basin features whose values are difficult to get correct. Similarly, use of
Rational method or Dickens’ method requires careful selection of their respective
constant values which are difficult to get it right all the time. Even if these
values are precisely chosen, there is still the question of their validity in
Nepalese context given their origin was for other regions.
Introduction to hydrological methods considered
Methodology
Sensitivity Analysis
For each hydrological method, sensitivity analysis were
carried out, to help figure out the probable maximum and minimum value of
design discharge for one arbitrary catchment, that of Lorkhu khola at
Ramechhap. The catchment features as well as its location is shown Figure 1.
For each of the methods used to calculate the design discharge, values of
different watershed-specific constants were assigned. The constants were
assigned values ranging from the least recommended to the maximum recommended.
For example, Dickens’ method requires assigning value to C which ranges from 7
to 28. Two cases are considered, one with 7 as the C value and the other with
28. The design discharge calculated from both cases, for different catchment
area, is plotted in first figure of Figure 3. Also, the difference in the
discharge value is computed to demonstrate the effect a poorly chosen constant
value can have.
Figure 1 Location of Lorkhu Khola bridge
Figure 2 River cross section considered for calculation if Top Width
Figure 3 was prepared for each method, showing a range of
possible design discharge (Q100) for different catchment areas . To
further demonstrate the effect, the variation of top width of waterway
corresponding to the varied discharge is plotted in Figure 4, Figure 6,and
Figure 5. Manning’s equation (equation 1) was used to find depth of flow, which
in return was used to find top width of water way for a discharge value. A
typical hill area cross section of a river was considered as shown in Figure 2.
Also, two values for the longitudinal bed slope of the water-way was
considered; minimum and maximum from the 12 calculated river slope, as shown in
Figure 4.Two extreme scenarios were considered; first maximum Q100
value by a method and minimum slope (which should result in maximum river flow
depth) and second minimum Q100
value for a method with maximum slope.
…….Equation
1
Figure 3 DHM
gauged sites used in this study (with Corresponding Station’s Index No.)
Figure 4
Longitudinal slope along the 12 different river profile (unit less)
Variation check. For another part of the study, Q100 was
predicted from a series of extreme yearly flood data using the Gumbel’s method
(Gumbel, 2012; Pickands III, 1975). The discharge values from nine different
gauged stations (as listed in the Table 1, and as shown in Figure 3) across the
country were plotted. For all these gauged stations, necessary watershed features
(watershed area, longest flow path, slope etc., as given in Table 2) were
calculated using GIS (ArcHydro tool). The data, along with predicted
precipitation for 100 years return period, was used to predict Q100
value from different hydrological methods, viz. Snyder’s, BD Richards’s,
Dickens’, WECS/DHM, Modified Dickens’, Fuller’s formula, Rational and Regional
and presented in Table 3 and Figure 7. The variation {(Gauged discharge value –
Discharge value from the method)2 } was calculated in Table 4 for
each of these methods to figure out the method that gives consistently close
value to the gauged value.
Results
Sensitivity Analysis
Results. The proper use of constants value
in methods used for design discharge calculations needs special attentions.
Their worth is truly obtained only with proper selection of the constant
values. A carefree approach can result in big variation in discharge. For a
same method, take for example Modified Dickens’ example as shown in Figure 3, predicted discharge can vary as
much as 400 cumecs for watershed area 100 km2 with highest value being 300%
more than the lowest value. Also, the variation is as much as 6000 cumecs for
watershed area 2000km2 with the highest value nearly 400% more than the lowest
value predicted. All these changes are a result of different value assigned to
constant within the limit specified. Similarly, the variation in Top-Width of a
river was found to be as much as 10.7m, 11.8m, and 10.5m for Modified-Dickens
method, Fuller’s formula and Rational method respectively. The variation can
result in huge price variation in construction of a river bridge, as well as
jeopardize mathematics involved in of bridge which requires use of discharge
value for pier and abutment design.
Figure 5 Range of Q100 (cumecs) for different
catchment area (sq. km) for different methods
Figure 6 Variation in Q100 & river-top-width
per catchment size for different methods
Variation-Check
Result. There were massive variation in
discharge value computed from different methods to the one gauged values.
Maximum variation produced by WECS was 7500cumecs, by Dickens’ method was 10000
cumecs, while Modified Dickens method produced a difference in excess of 24000
cumecs. Similarly, Snyder’s method, Fuller’s formula and rational method
produced variation in excess of 7000 cumecs, 12000cumecs,8000cumecs and 5000
cumecs respectively. Refer Figure 7 and Table 3 for detail of the variation. Out
of the nine calculated method WECS, Fuller and rational method produced only
one result closest to the real value compared to their rival methods. Whereas Regional method’s
prediction was closest to the gauged value in six out of nine methods. Clearly,
regional method seems best method for prediction because of its predicted value
was closest to the gauged value for 66.67%
of cases, as shown by the Table 4. Although the analysis lacks spine
because of limited number of cases considered (only 9 cases), still the
prediction given by regional method cannot be ignored. It is recommended that
regional method be used.
Figure 7 Q100 derived from various
methods for the nine gauged stations
Recommendations
It is recommended that during bridge design, there be a
proper consideration for value obtained from regional method as it seems to
most closely approximate the value from the gauged stations.
Discussion
The review presented here bases its findings on discharge
values from nine stations, those listed in Table 1. The small number (nine)
means there is not enough credibility in the result it presents. The same analysis must be carried out for
larger pool of data to establish a rule that might be accurate for most cases.
The paper could not perform analysis on those data as there were not enough
data available. However, if the data is available, the new result that the same
process of study gets will be far more
reliable. However, in absence of further study, this may be considered
satisfactory for the time being.
References
Alam, M. J. B., & Matin, A. (2005). Study of
plotting position formulae for Surma basin in Bangladesh. Journal of Civil
Engineering (IEB), 33(1), 9–17.
Chitrakar, P. (n.d.).
MICRO-HYDROPOWER DESIGN AIDS MANUAL.
Dooge, J. C. (1957).
The rational method for estimating flood peaks. Engineering, 184(1), 311–313.
Gumbel, E. J. (2012).
Statistics of extremes. Courier Dover Publications.
Jakeman, A. J.,
Littlewood, I. G., & Whitehead, P. G. (1990). Computation of the
instantaneous unit hydrograph and identifiable component flows with
application to two small upland catchments. Journal of Hydrology, 117(1),
275–300.
Linsley, R. K.
(1986). Flood estimates: how good are they? Water Resources Research, 22(9S),
159S–164S.
Pickands III, J.
(1975). Statistical inference using extreme order statistics. The Annals of
Statistics, 119–131.
Shrestha, M. K.,
Chaudhary, S., Maskey, R. K., & Rajkarnikar, G. (2010). Comparison of the
Anomaly of Hydrological Analysis tools used in Nepal. Journal of Hydrology
and Meteorology, 7(1), 30–39.
Subramanya, K.
(1994). Engineering hydrology. Tata McGraw-Hill Education.
Tables
Table 1
List of stations gauged by DHM whose data are
used in the study
Station
No.
|
Site
Name
|
Watershed
Area (sq. km)
|
460
|
Rajaiya
|
442.37
|
445
|
Arughat
|
1709.42
|
589
|
Pendheradovan
|
2594.2
|
670
|
Rabuwa Bazar
|
3748.57
|
684
|
Majhitar
|
4046.73
|
447
|
Betrawati
|
4643.22
|
630
|
Pachuwarghat
|
4868.9
|
450
|
Devghat
|
18235.28
|
695
|
Chatara
|
18911.1
|
Note: The station number given in
the table refers to the station number given by the DHM. The watershed area was
calculated from ArcHydro tool in ArcGIS using DEM and stream network of Nepal.
The coordinate of the stations was given by DHM on its website.
Table 2
Catchment Features (an example)
Site Name
|
Pendheradovan
|
Watershed area (km2)
|
2594.2
|
Longest flow Path (km)
|
167.42
|
Centroidal elevation (m)
|
1401
|
High Elevation (m)
|
2371
|
Low Elevation (m)
|
127.35
|
Precipitation (24 hour in
mm)
|
310.90
|
Note: The table presents an example
of the inputs received for each stations. These inputs were assumed to define
the watershed features, and their values were used to compute Q100 from the
discussed eight hydrological methods.
Table 3
Values for coefficients b, c and ft used
in Regional method
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Note: The table contains values of
b, c and ft. Values of b and c are used to figure out a discharge
value for a watershed according to which river basin it falls, which is
multiplied by ft to find the discharge for different return period. Since
the study is focused on bridge design, only the return period of 100 years was
considered.
Table 4
Discharge value (Q100) obtained for
different methods, including the gauged value
Station No.
|
Water-shed Area
|
Q100 gauged
|
WECS
|
Dickens’
|
Modified Dickens’
|
BD Richards’
|
Snyder’s
|
Fuller’s
|
Rational
|
Regional
|
460
|
442.4
|
965.2
|
1284
|
1350
|
1567
|
1783
|
2434
|
110
|
5305
|
540
|
445
|
1709.4
|
1240.2
|
3459
|
3722
|
4970
|
2082
|
2476
|
325
|
4676
|
1735
|
589
|
2594.2
|
8334.2
|
4698
|
5089
|
7069
|
5820
|
7731
|
454
|
8167
|
2488
|
670
|
3748.6
|
4121.1
|
6155
|
6707
|
9636
|
2711
|
3136
|
610
|
5581
|
3420
|
684
|
4046.7
|
3476.5
|
6511
|
7103
|
10276
|
4174
|
4749
|
648
|
8389
|
3654
|
447
|
4643.2
|
2170.9
|
7203
|
7875
|
11532
|
3853
|
4559
|
723
|
6176
|
4115
|
630
|
4868.9
|
2897.3
|
7458
|
8160
|
12000
|
4422
|
4950
|
751
|
8085
|
4287
|
450
|
18235.3
|
14954.6
|
19662
|
21969
|
36053
|
19503
|
22081
|
2161
|
20863
|
13417
|
695
|
18911.1
|
12405.6
|
20194
|
22577
|
37157
|
17602
|
19596
|
2225
|
21119
|
13846
|
Note: The discharge value given
under each heading, for different hydrological gauged stations of Nepal, is in
cumecs. Although the table is titled ‘Discharge for different methods’, it does
include value of watershed area of each stations since watershed area is the
most important feature for the watershed as far as its direct relation to
discharge is considered. Data contained in ‘Q100 gauged’ field contains
discharge value of return period 100 years from the gauged stations. But none
of these stations have been observed for 100 years, hence the peak discharge of
each year was considered and assumed to follow Gumbel distribution. Using the
analysis for Gumbel projection, a discharge value for return period 100 years
was obtained for each of these nine stations.
Table 5
Variation in Predicted discharge values(from
different methods) from the Gauged values
Station No.
|
WECS/DHM
|
Dickens’
|
Modified Dickens’
|
BD Richards’
|
Snyder’s
|
Fuller’s
|
Rational
|
Regional
|
460
|
318.64
|
385.2
|
602.19
|
817.97
|
1468.8
|
854.8
|
4339.5
|
425.4
|
445
|
2219.06
|
2481.6
|
3729.5
|
842.13
|
1235.3
|
914.9
|
3435.9
|
495.2
|
589
|
3635.98
|
3245.1
|
1264.7
|
2513.94
|
603.19
|
7880.1
|
167.6
|
5845.7
|
670
|
2034.36
|
2585.8
|
5514.8
|
1410.63
|
985.17
|
3511.6
|
1459.8
|
701.0
|
684
|
3034.7
|
3626.7
|
6799.07
|
697.94
|
1272.7
|
2828.4
|
4912.6
|
177.5
|
447
|
5031.74
|
5703.9
|
9360.74
|
1682.255
|
2387.6
|
1447.5
|
4005.3
|
1944.0
|
630
|
4560.62
|
5262.8
|
9102.22
|
1524.26
|
2052.6
|
2145.9
|
5188.0
|
1389.8
|
450
|
4707.18
|
7014.4
|
21098.46
|
4548.84
|
7125.9
|
12793.7
|
5908.5
|
1537.7
|
695
|
7788.64
|
10171.4
|
24751.23
|
5196.29
|
7190.9
|
10180.8
|
8713.2
|
1440.0
|
Note: Highlighted cells refer to
the closest Q100 value to the gauged discharge value, obtained from eight
methods. The values under each heading is the difference of discharge (cumecs)
from the respective gauged Q100 of the station.
