Regional Flow Duration Curve Estimation and its Application


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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi Joel Nobert1, Jackson Ndayizeye2, Simon Mkhandi3
1 University of Dar es Salaam, Water Resources Engineering, Box 35131, Dar es Salaam, Tanzania. 2 Water Engineer, World Vision Burundi, P.O Box 3 University of Dar es Salaam, Water Resources Engineering Department, Box 35131, Dar es Salaam, Tanzania
Abstract On Kitenge River in September 1986. Recently, the water level in the Rwegura reservoir has decreased and this has resulted in a reduction in generated power and hence power rationing. The reservoir is situated in an un-gauged catchment and therefore, there is a fundamental need to develop a method that can be used to assess the hydrology in periods of low flow. A flow duration curve for Rwegura ungauged catchment was developed through Regionalization approach. Based on spatial rainfall pattern, a hydrological homogeneous region in which the catchment belongs was derived. For each gauged site, a dimensionless monthly flow duration curve was derived and a regional dimensionless flow curve was found by averaging the dimensionless flow duration curves of all gauged sites. Multiple regression equation was then developed to find relationship between mean monthly flow (index flow) for the gauged sites and catchment characteristics such as catchment area, mean catchment slope, mean elevation of the catchment, station elevation, stream length, stream slope and mean annual precipitation. The derived regression equation was used to find the index flow at Rwegura ungauged site and thereafter the flow duration curve was found as a product of dimensionless regional flow duration curve and index flow. The validation was based on the comparison of the few available observed stream flow data (1980 – 1983) and the Nash efficiency criterion was found to be 91%. The derived flow duration curve was used to characterize the low flow in the range from 70% and 90% of time flow is equalled or exceeded. The monthly flow which is
equalled or exceeded 90% of time Q90 is 16.8 m3 / s . This flow is known as the lowest flow
estimated for Rwegura and therefore it can be used to assess the reliability of hydropower generation in Rwegura ungauged Catchment.
Key words: Regionalization, ungauged catchments, Flow Duration Curve (FDC), Hydropower
1 INTRODUCTION
Burundi is faced with a range of problems in the energy sector. DRC has been the major source of electric energy for Burundi since 1958 when Rusizi hydroelectric generation plant was constructed on Rusizi River on the border between Rwanda and DRC at the outlet of Lake Kivu. In order to have a secure source of energy within the country, Burundi constructed Rwegura hydropower plant on Kitenge River in September 1986. This new power station was designed to produce 18 MW and 64 GWh of electrical energy annually supplying electric energy to the different towns in Burundi using two transmission lines; the Rwegura-Bujumbura and Rwegura-Ngozi via Kayanza.
During the Rwegura project, Kitenge River was believed to have sufficient water for both irrigation and future power projects downstream contradictorily to the current situation. In fact, Rwegura power plant is actually even facing many problems due to the decrease of water level in the reservoir which has resulted in a reduction in generated power, creating shortfalls on the demand. This has resulted in a system of allocation of power by priority by the national company of Water and power distribution administration (REGIDESO) which gives precedence to hospitals, followed by industries, whereas residences rarely get power, and this has become an issue of concern. Nevertheless, Rwegura reservoir is situated in an un-gauged catchment and the stream flows were recorded for a short period of four years consecutively from 1980 to 1983, the period through which Rwegura hydropower plant was designed. The lack of adequate hydrological data introduces uncertainty in both the design and management of water resources. Consequently, there is a fundamental need to develop methods that can be used to assess the hydrology during times of low flow.

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi
the design and management of water resources. Consequently, there is a fundamental need to develop methods that can be used to assess the hydrology during times of low flow.
The estimation of flow characteristics of ungauged catchments is usually based on transferring or extrapolating information from gauged to ungauged sites, a process called regionalization (Nathan et al, 1990). The regionalization of flow duration curves appears therefore to be an operative tool when dealing with ungauged catchments or short stream flow records (Castellarin et al, 2004). An initial step in regionalization is the process of delineation of sub-catchments with similar hydrological response. In this case, the region may be defined by stream flow characteristics (Burn & Boorman, 1993) or by physical and climatic characteristics (Acreman & Sinchair, 1986). Once a homogeneous region is successfully identified, the regionalized flow duration curves could be implemented using statistical approach or non statistical (parametric and graphical) approaches (Castellarin et al, 2004).
In this study, all available data (climatic and streamflow data) within the chosen study area were used to identify gauged catchments with similar hydrological responses with Rwegura catchment. Regional multiple regression equation was then derived to illustrate relationship between streamflows and catchments characteristics.
1.1. Description of the Study Area
Burundi is divided into two major river basins i.e. Congo basin and Nile basin. Rwegura catchment is entirely located in Kibira National park of Burundi where climate is tropical. The monthly average temperature recorded at the weather station of Rwegura over a period of fifteen years (1990-2005) is 15.4oC. A major part of the year experiences rainfall, with intermittent periods of dryness. Rainfall is heavier from September to May with a short dry season from January to February. Rwegura catchment has an estimated area of 231.5 km2. The major inlet river is Kitenge and Mwokora at the outlet of the catchment. The geographical location of the catchment is as shown in Figure 1.
1.2. Data Availability and Analysis
Every hydrological analysis depends on the acquisition of relevant data. In this study both time series (rainfall and streamflows) and spatial data (Digital Elevation Model (DEM) of 90m- resolution) were used for the analysis. Rainfall data was used to classify preliminary homogeneous region while stream flow data were used for homogeneity test and discordance measurement to validate the region initially delineated either geographically or climatically. Rainfall and stream flows data were obtained from the Geographic Institute of Burundi (IGEBU), Ministry of Water Resources, Environment and Land Management of Burundi. The records vary in starting and ending dates and the length of the available records. The selection of the time series data was based on the quality of the data collected from the various stations at various times. The main purpose for rainfall analysis is to derive the spatial rainfall distribution so as to identify the rainfall region in which Rwegura catchment is located. In this case, the World Meteorological Organization (WMO) suggests a record length of at least 30 years.
The rainfall gauge stations included in the whole country were checked and only rainfall stations whose record length is greater or equal to thirty years were selected from the set. In Rwegura catchment, only one rainfall gauge station with record length of 44 years (1964-2008) was identified. The similarity in terms of spatial rainfall distribution is more accurate when the concurrent period of record is considered for the whole rainfall stations. For this reason, the starting and ending date of record became a criterion for selecting the rainfall gauge stations which could be used to identify the regions with similar spatial rainfall characteristics with the Rwegura catchment. The selected rainfall data for the analysis and the computed mean annual rainfall is presented in Table 1.
Currently, there are few direct stream flow measurements. The rating curves of some rivers are not yet determined and most of the gauging stations have short records. Therefore, the stage- discharge relationship was used to determine the required streamflows record where the stage data were available.

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi
Digital Elevation Model (DEM) was used to identify catchments characteristics (catchment area, mean catchment slope, mean elevation of the catchment, station elevation, stream length and stream slope). These catchments characteristics are very important in deriving multiple regression equation showing relationship between stream flows and catchment’s characteristics as independent variables.

Figure 1: Hydrological Map of Burundi Showing Location of Rwegura

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi

Station ID
10011 10027 10036 10039 10040 10044 10046 10061 10068 10075 10080 10082 10083 10085 10112 10116 10123 10125 10127 10149 10161 10164 10167 10169

Longitude
29.32 29.82 29.65 30.23 29.85 29.68 29.92 30.17 29.75 30.33 29.42 29.23 29.82 30.00 30.08 30.10 29.35 30.55 30.35 30.40 29.77 29.52 29.57 30.07

Table 1: Rainfall data used in the analysis

Latitude Altitude

Starting year

Ending Year

-3.32 -2.85 -2.98 -3.78 -3.37 -3.57 -3.42 -3.10 -3.37 -3.65 -3.28 -2.72 -4.13 -3.60 -3.53 -4.00 -3.60 -3.23 -2.85 -2.73 -3.82 -2.92 -3.18 -3.15

783.0 1760. 1806. 1250. 1624. 2097. 1645. 1600. 1814. 1308. 877.0 1509. 1450. 1770. 1616.00 1260.00 971.00 1750.00 1756.00 1650.00 1822.00 2302.00 2166.00 1170.00

1927 1938 1931 1962 1930 1931 1964 1953 1933 1967 1935 1954 1935 1934 1954 1960 1956 1931 1927 1930 1960 1964 1963 1934

2008 1994 1998 2005 2008 2008 2008 2008 2002 2008 1990 2008 2008 2004 2008 2008 2000 2008 2008 2000 2008 2008 1996 2001

Period of
Record 81 56 67 43 78 77 44 55 69 41 55 54 73 70 54 48 44 77 81 70 48 44 33 67

Mean Annual Rainfall
816.16 1306.10 1341.96
1222 1179.57 1464.47 1189.46
1156.3 1338.42
1151.6 1064.5 1840.9 1255.3 1221.47
1126 1162 966 1196 1091 1085 1334 1664 1607 1234

1.3. Delineation of Homogeneous Regions
The preliminary delineation of the homogeneous regions considered the climatic conditions and the topographical characteristics of a particular region. The catchments which belonged into the same climatic zone or topographic zone formed a preliminary homogeneous region. Climatic regions were derived from the spatial distribution of the mean annual rainfall. The spatial coverage of the mean annual rainfall was estimated using Kriging interpolation techniques. The topographical zones were derived from the topographic map for the area.
A homogeneity tests based on Coefficient of Variation (CV) and discordance measure were then applied to verify if the preliminary delineated region is homogeneous. In this case the streamflows data was used and the region is confirmed to be homogeneous if it satisfies both criteria of homogeneity
tests. In regionalization, assumptions must be made about the statistical similarity of the sites in a
region. To investigate the similarity the values of mean coefficient of variation (CV) and the site-to-site coefficient of variation of the coefficient of variation (CC) were used.
For coefficient of variation (CV) homogeneity test, for each site in a region the mean, standard deviation and coefficient of variance are calculated.

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi

¦ni
Qij Qi j 1n (1)
i

¦ ni

2

Qij  Qi

V i

j1

(2)

ni  1

CV V i

(3)

i Qi

Where Qi Mean flow rate of site i, Qij Flow rate of station j in region i, Vi Standard

deviation CVi Coefficient of variance.

The regional mean coefficient of variation and standard deviation were then estimated as presented below.

¦ CV N CVi

(4)

i1 N

¦ N

2

CVi  CV

V cv

i1

(5)

N

According to Mkhandi & Kachroo (2000), a region is homogeneous if the coefficient CC is small
while Sine and Ayalew (2004) suggested that a region is declared to be homogeneous if CC V cv CV
is less or equal to 0.3. The discordance measure is intended to identify those sites that are grossly discordant with the group as a whole. It estimates how far a given site is from the centre of the group.

L-moment is developed for this purpose and the formulas are summarized below:

¦ ª¨§ Ni ¸· º



1

N

«¨©

K

¸ ¹

»X

k 0,1,2,..., N 1

(6)

10K N i 1 « ¨¨§ N 1¸¸·» i

«¬ © K ¹»¼

¦ Mˆ

1 N ª¨¨§ i1¸¸· º «© J ¹ » X

j 0,1,2,..., N 1

(7)

1 j0

N i 1 «¬

¨§ ¨©

N

1 j

¸· ¸¹

»¼

i

i Rank of observed flow data in ascending order
The first few moments are given by the expressions shown below:
L1 M 100
L2 M100  2M101

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi

L3 M100  6M101  6M102

L4 M100 12M101  30M102  20M103

(8)

L-moment ratios are defined as:

t L2 L1

t Lr

Where r t 3

(9)

r

L2

t : Measure of scale and dispersion LCV , t3 : Measure of skewness LCs , t4 : Measure of

kurtosis LCk

If U i > @ t i , t3 i , t4 i T is the vector containing the t, t3, t4 values for site i , then the group average

for N sites within the region is given by:

¦ 1 N

U

Ui

(10)

N i1

The regional standard deviation is given by:

¦ N

T

S N 1 1 Ui U Ui U

(11)

i1

The discordance measure is defined by:

D 1 U U T S 1 U U

(12)

i 3i

i

According to Sine and Ayalew (2004), a suitable criterion to classify a station as discordant is that Di
should be greater or equal to 3 Di t 3 .

1.4. Relationship Between Index Flow and Physical Catchment Characteristics
The multiple regression equation showing a linear relationship between index flow and catchment characteristics and mean annual rainfall was determined using LINEST function of MS Excel spreadsheet. Note that the index flow can be either mean annual flow or mean monthly flow depending on the time interval considered for the Flow Duration Curve (FDC). In this study, the monthly flow duration curve was adopted, therefore the mean monthly flow for the gauged sites was considered as index flow. The multiple regression equation is as shown in equation (13).

Y m1X1  m2 X 2  m3 X3  ...  mn X n  b

(13)

Where X 1 , X 2 ,.......X n represents the physical catchment characteristics and the mean annual

rainfall m1 , m2 , ….., mn and b are coefficients and Y is the index flow.

1.5. Derivation of Flow Duration Curve (FDC) for Ungauged Site
The following steps were adopted by the author in deriving the flow duration curve: (1) Standardizing the flow duration curve for all gauged river basins by dividing the empirical flow duration curve by the index stream flow; the index stream flow in this case was the average of monthly streamflows for all the stations with records; (2) A graphical regional dimensionless flow duration curve is then obtained by averaging the standardized empirical flow duration curve of all gauged river basins in the study region. The flow duration curve for ungauged catchment located within the study area was then

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi

estimated as the product of the dimensionless regional flow duration curve and an estimated index stream flow for the catchment.
1.6. Low Flow Characteristics
According to the World Meteorological Organization, low flow percentiles from the FDC are often
used as key indices of low flow, the flow that is exceeded for 95 percent of the period of record Q95
is commonly used to characterize the low flow. In this study, since the river is not perennial, instead of
Q95 which is specific for perennial rivers, Q70 and Q90 were used as indicators of low flow
characteristics at Rwegura catchment.

2 RESULTS AND DISCUSSIONS

2.1. Delineated Homogeneous Regions

The spatial distribution of the mean annual rainfall as estimated using kriging interpolation technique indicates that Rwegura catchment is entirely located in rainfall region whose range of annual rainfall is between 1300 mm and 1900 mm. Homogeneity tests for all the streamflow gauging stations within the region is as presented in Tables 2 & 3.

Table 2: Coefficient of variation (CV) homogeneity test results

¦ ¦ Stream flow

ni

gauging Stations

Qij

Qi j 1n V i

i

ni

2

Qij  Qi

j1

ni  1

CV V i i Qi

11006 11021 11019 11020 11032 11033
Stream flow Station
11006 11021 11019 11020 11032 11033

8.84

8.58

0.97

4.51

4.06

0.90

6.05

3.30

0.55

5.92

4.34

0.73

4.37

3.03

0.69

13.27

7.83

0.59

¦ CV N CVi 0.73 i1 N

¦ N

2

CVi  CV

V cv

i1

N

0.17

CC V cv 0.23 CV

Table 3: Discordance measure homogeneity test results

U i  U Ui  U i  U T U i  U

0.021324 0.032560 0.005202 0.004799 0.010562 0.004013

0.010201 0.005098 0.004134 0.049E-06 0.00311364 0.002809

Di

1 3

U

i

 U

T

S

1 U

i

U



0.2125208

0.1062075

0.0861352

1.0208E-05

0.0648675

0.0585208

¦ S N 1 1N 14Ui U Ui U T 0.016 i1

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi
From Tables 2 & 3, it can be observed that both homogeneity tests have confirmed the homogeneous region. However, the entire region comprises of both ungauged and gauged catchments. All ungauged catchments were automatically excluded from the analysis because the statistical test is based on the available stream flow data. Furthermore, the results of homogeneity tests are valid if the considered gauged catchments form a geographic continuous region. Therefore, only the catchments forming the geographically continuous region (Figure 2) were considered in deriving the flow duration curve for the ungauged catchment.

Figure 2: Delineated hydrologically homogeneous regions

2.2. Flow Duration Curve and Low Flow Analysis

A dimensionless flow duration curve was obtained by averaging the standardized empirical flow duration curve of all gauged sites as shown in Figure 3.

Ratio of monthly streamflow and index flow

5 4.5
4 3.5
3 2.5
2 1.5
1 0.5
0 0%

Monthly FDC for 11006 Monthly FDC for 11032 Monthly FDC for 11033 Regional FDC

20%

40%

60%

80%

Percentage of time flow is exceeded

Figure 3: Dimensionless flow duration curves

100%

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi

Index flow and catchments characteristics derived from DEM are shown in Table 4. The Multiple regression equation coefficients describing the relationship between catchment characteristics, mean annual rainfall and the index flow are presented in equation (14). The multiple regression equation was used to estimate the index flow (scale factor) for ungauged Rwegura catchment with an area of 231.5 km2 and finally the flow duration curve for the catchment was estimated by multiplying the dimensionless regional flow duration curve by the estimated of index flow. The validation was based on the comparison of the few available observed stream flow data (1980-1983) and the estimated flow duration curve. The plot of observed and estimated Flow duration curves is shown in Figure 4 and the Nash-Sutcliff efficiency (NSE) coefficient was found to be 0.91.

Y 26.56 u AREA  12.17 u ELEVATION  18.23 u MAP  59499 .02

(14)

Monthly streamflows (m3/s)

140

120 Observed FDC
100 Estimated FDC 80

60

40

20

0 0%

20%

40%

60%

80%

Percentage of time flow is exceeded

100%

Figure 4: Observed and estimated flow duration curves for Rwegura catchment

Figure 5 illustrates the low flow characteristics of Rwegura gauging station. It can be observed that the flow corresponding to Q70 and Q90 are 26.7m3/s and 16.8m3/s, respectively.

Figure 5: Estimated FDC for Rwegura ungauged site and Low flow indices

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Regional Flow Duration Curve Estimation and its Application in Assessing Low Flow Characteristics for Ungauged Catchment. A Case Study of Rwegura Catchment-Burundi

Table 4: Index flow, mean annual rainfall and derived catchment parameters

Gauged site

X1
Catchment area (km2)

11006 11032 11033

291.5 432.5 488.2

X2 Stream length (km)

X3 Catchment elevation (m)

26.8

1416.0

26.6

1819.6

33.5

1783.6

X4 Mean annual rainfall (mm)
1908 1427 1382

X5 Stream slope (%)
28 17 18

Mean monthly flow (m3/s) 266.94 153.23 373.69

3 CONCLUSION
Flow duration curve and minimum flows for Rwegura ungauged site were successfully analyzed. From the estimated flow duration curve for Rwegura ungauged site, the monthly flow which is equalled or
exceeded 90% of time Q90 is 16.8 m3 / s . This flow is known as the lowest flow for Rwegura
ungauged catchment and therefore this value can be taken into consideration in assessing the reliability of Rwegura Power generation and environmental flow requirement in Rwegura ungauged Catchment.
4 ACKNOWLEDGMENTS
This work was supported through financial support from Nile Basin Applied Training Project (ATP). The authors would also like to acknowledge the support of facilities provided by the Water Resources Engineering Department, University of Dar es Salaam, Tanzania.
5 REFERENCES
1. Acreman, M.C. and Sinclair, C.D. (1986), Classification of drainage basins according to their physical characteristics; an application for flood frequency analysis in Scotland, Journal of Hydrology, 84, 365–380.
2. Burn, D. H. and Boorman, D. B. (1993), Estimation of hydrological parameters at ungauged catchments, Journal of Hydrology, Volume 143, 429–454.
3. Castellarin, A., Galeati, G., Brandimarte, L., Montanari, A. and Brath, A. (2004), Regional flow duration curves: Reliability for ungauged basins, DISTART, Universita` di Bologna, Viale Risorgimento 2, and 40136 Bologna, Italy
4. Mkhandi, S. H. and Kachroo, R. K. (2000), Flood frequency analysis of Southern Africa: Delineation of homogeneous regions, Research Report, Water Resources Engineering Programme, University of Dar es Salaam, Tanzania.
5. Nathan, R.J. and McMahon, T.A. (1990), Identification of Homogeneous Regions for the Purposes of Regionalization, Journal of Hydrology, Vol. 121, pp. 217-238, Dec.
6. Sine, A. and Ayalew, S. (2004), Identification and Delineation of Hydrological Homogeneous Regions-The case study of Blue Nile River Basin, Proceedings, Lake Abaya Research Symposium, 2004.

AUTHORS BIOGRAPHY
Joel Nobert: is a holder of PhD in Water Resources Engineering. He is currently a lecturer in the Department of Water Resources Engineering, University of Dar es Salaam, Tanzania. The author is also a member in GIS and modelling cluster of Nile Basin Capacity Building Network for River Engineering (NBCBN-RE).
Jackson Ndayizeye: is a holder of Masters in Water Resources Engineering and currently he is working as a Water Engineer with World Vision international organization in Burundi.
Simon Mkhandi: is a holder of PhD in hydrology and a senior lecturer at the University of Dar es Salaam, Water Resources Engineering Department.

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Regional Flow Duration Curve Estimation and its Application