Low flow analysis provides crucial information for the planning and design water resource development, risk assessment and environmental flow management. Understanding the low flow regimes and evaluating the magnitudes for incorporating in water resources management is vital for the countries like Ethiopia where demand for water is increasing. However, there were hardly enough studies in understanding the trends of low flow and frequency analysis. Therefore, this study focuses on evaluation of the trends in low flows and regional low flow analysis in the Blue Nile Basin, Ethiopia. In order to carry out the study, 15 river sub-basins in the Blue Nile Basin were selected based on the long term data availability and presence of quality of data. The 3-day sustained low flow (3d-slf), the 7-day sustained low flow (7d-slf) and the 14-day sustained low flow (14d-slf) models were used to extract the data from the daily time series stream data obtained from MoWIE. Trends in low flow were analyzed separately by using Mann-Kendall (MK) trend test. Low flow frequency analysis was used to estimate the long term low flow quantiles. In addition, regional analysis for estimating the quantiles for ungaged catchments was also developed based on the regional growth curve and catchment characteristic of drainage basins. The results indicated that 3d-slf, 7d-slf and 14d-slf models of low flow series indicated no significant difference for each station at 95% CI. Out of the 15 selected stations, 12 of stations have indicated decreasing; two stations indicated increasing and remaining one station with no trend. Mainly decreasing trend was associated with the land cover and climate change which results in increasing runoff and evapotranspiration respectively. Weibull distribution—GEV and LGN was found best fit based on the L-Moment Ratio Diagram (L-MRD). Hence quantile estimations have indicated diminishing magnitudes of low flow quintiles for 2 - 500 years return periods. Regional low frequency analysis has provided a very good relationship between discharge and catchment characteristics with an R2 of 0.72. Where area (A) and rainfall (R) followed by slope were found sensitive to compute in developing the regional region equations between mean low flows and the physiographic data. This study indicated that there needs to be a new water management scenario and adaptation mechanism of climate change and land use land cover dynamics for utilizing water resource in the Blue Nile Basin.
Low flow is the smallest sustained average daily flow rate or volume with time [
Decreasing in low flow would impact the environmental flow in a given ecosystem and affect multi-purpose operations which depend on that water system such as river and lakes. It could happen due to different ways, for instance groundwater pumping close to the head of a perennial river during the dry season [
Low flow frequency curves describe the relationship between the magnitude of river low flows and the recurrence interval or return period. It can also be derived from data from monitoring stations and regionalized for use at any location along the basin’s river network, by relating the spatial differences to geographical regions and to variations in upstream sub-basin characteristics. Low flow frequency analysis and predictions generally have to deal with the inadequacy or deficiency of observations for the site of interest [
In the Blue Nile Basin an increase in population over the past few years has put great pressure on the natural resources, where it has led to increase in demand for more water and agricultural land and resulting deforestation [
The Upper Blue Nile River “Abbay” basin (
basic rocks (dominantly basalts) and the lowland part near the Sudanese border was composed of basement complex rocks and metamorphic rocks [
The general methodology of this study follows four main approaches 1) extracting the low flow data and data quality analysis, 2) analyzing and evaluating the trends of low flow data from the selected 15 flow stations in the Blue Nile Basin, 3) low frequency analysis for selected station in the basin and 4) regionalization of the low flow for estimating the quantiles for the ungaged catchments.
Data needed for this study were collected from different organization in order to use for low flow trends, frequency and regional frequency analysis. Limited record length was typically a major challenge interpret the results of trend analysis, as there are often few homogeneous records on which the statistical analysis could be carried out. The stream flow data used for the low flow analysis was obtained from the Ministry of Water Irrigation and Electricity (MoWIE). Among the functional stream flow stations in the basin 15 river gaging stations (
ID | River/Sub basin | Gaging location | Geographical position in UTM | Area | |
---|---|---|---|---|---|
North | East | km2 | |||
1 | Amen | Dangila | 1,246,201 | 267,104 | 89.15 |
2 | Andassa | Bahir Dar | 1,271,589 | 334,578 | 596.38 |
3 | Angar-greater | Nekemte | 1,060,930 | 220,413 | 1099.03 |
4 | Angar-lower | Nekemte | 1,032,779 | 249,835 | 619.66 |
5 | Chemoga | Debremarkos | 1,138,754 | 361,295 | 364.25 |
6 | Gelgel abbay | Marawi | 1,257,136 | 285,380 | 1656.00 |
7 | Gelgel beles | Mandura | 1,235,578 | 212,387 | 676.56 |
8 | Gulda | Dembecha | 1,166,512 | 335,870 | 249.28 |
9 | Hoha | Asossa | 1,122,346 | 678,950 | 161.12 |
10 | Indris | Guder | 1,019,788 | 358,631 | 118.13 |
11 | Mendel | Tis Abbay | 1,268,152 | 364,364 | 91.35 |
12 | Muger | Chancho | 1,056,459 | 443,536 | 549.49 |
13 | Neshi | Shambo | 10,781,717 | 308,031 | 322.43 |
14 | Sibilu | Chancho | 1,028,748 | 467,164 | 380.12 |
15 | Urgessa | Gembe | 897,894 | 232,531 | 19.11 |
Evaluating the presence and absence of trends in low flow for the selected stations was carried out by using the Mann and Kendall (MK) trend test [
S = ∑ i = 1 n − 1 ∑ j = i + 1 n sgn ( x j − x i ) (1)
where xj and xi are the daily values in days’ j and i, j > i, respectively and
sgn ( x j − x i ) = { 1 if x j − x i > 1 0 if x j − x i = 0 − 1 if x j − x i < 0
If n < 10, the value of |S| is compared directly to the theoretical distribution of S derived by Mann and Kendall.
Z S = { S − 1 V ( S ) if S > 0 0 if S = 0 S + 1 V ( S ) if S < 0 (2)
The MK trend test ZS statistics (Equation (2)) determines the presence of decreasing or increasing trend if is negative and positive respectively. The test statistic ZS is also used a measure of significance of trend. If |Zs| is greater than Zα/2, where α represents the chosen significance level (e.g.: 5% with Z0.025 = 1.96) implying that the trend is significant [
V ( S ) = n ( n − 1 ) ( 2 n + 5 ) − ∑ t = 1 m t i ( t i − 1 ) ( 2 t i − 5 ) N (3)
The purpose of low frequency analysis in this study was to estimate the long term quantiles of for different return periods and regionalize estimations in order to compute the low flows for ungaged estimates. Detail procedure of the frequency analysis used in this study was presented as follows.
1) Selection of low flow models
The K days sustained low flow method of data extracting was used to prepare the data for low flow trends and frequency analysis for the selected stations. Where the lowest K day’s stream flow data per year has been averaged to obtain k days sustained (mean) low flow (Kd-slf) as presented in equation 4. Three different models have been used for selecting the low flow data series for this study including the three days-sustained low flow (3d-slf) model, the seven days-sustained low flow (7d-slf) model and the fourteen days sustained low flow (14d-slf) model.
Kd-slf = ∑ i = n − 2 n x i K (4)
where K is the number of sustained days, n is the number of data in time series (365 and 366 in leap years) and Xi the daily time series of stream flow (m3/s)
2) Data quality analysis
Checking the data quality of the K day sustained low flow data series was vital as it enhances the analysis. Some of the common methods to assess the data quality carried out before the low flow analysis includes outliers and independency. Where the outlier test evaluates the presence of extreme (high and low) values in the low flow data series was carried out by using [
3) L-moments
[
4) Selection probability distribution
a) L-Moment Ratio Diagram (L-MRD)
One of the main applications of L-moments is identification of the probability distribution of the observed phenomena using the L-MRD. This was based on relationships between the L-moment ratios [
5) Selection of parameter estimation method
After selecting the best fit probability distribution for each station the parameters of probability distribution could be estimated in a number of estimation techniques. Some of methods of parameter estimation [
a s = α s = M 1 , o , s = 1 N = ∑ i = 1 N ( 1 − F ) s X i (5)
b r = β r = M 1 , r , 0 = 1 N = ∑ i = 1 N F i r X i (6)
where
α 0 = β 0 β 0 = α 0
α 1 = β 0 − β 1 β 1 = α 0 − α 1
α 2 = β 0 − 2 β 1 + β 2 β 2 = α 0 − 2 α 1 + α 2
α 3 = β 0 − 3 β 1 + 3 β 2 − β 3 β 3 = α 0 − 3 α 1 + 3 α 2 − α 3
F in Equations (5)-(6) can be estimated from the plotting position formulas among the many for this specific study it was estimated by [
F = i − a N + 1 − 2 a (7)
Hosking (1986 and 1990) indicated the L-moments, which are linear functions of PWMs and defined in terms of the PWMs α and β by Equations (8)-(11)
l 1 = α 0 = β 0 (8)
l 2 = α 0 − 2 α 1 = 2 β 1 − β 0 (9)
l 3 = α 0 − 6 α 1 + 6 α 2 = 6 β 2 − 6 β 1 + β 0 (10)
l 4 = α 0 − 12 α 1 + 30 α 2 − 20 α 2 = 20 β 3 − 30 β 2 + 12 β 1 − β 0 (11)
where the ratio of L-moments (τr) used in this study were analogous to conventional moment ratios as defined by [
τ = l 2 l 1 (12)
τ r = l r l 1 for r ≥ 3 (13)
where ll is a measure of location, τ is a measure of scale and dispersion (LCv), τ3 is a measure of skewness (LCs), and τ4 is a measure of kurtosis (LCk) defined by Equations (14)-(16)
L-Coefficient of variation (LCv) = τ = l 2 l 1 (14)
L-Coefficient of skewness (LCs) = τ 3 = l 3 l 2 (15)
L-Coefficient of kurtosis (LCk) = τ 4 = l 4 l 2 (16)
6) Quantile estimation of low flows
The estimated parameters for specific probability distributions were used to calculate quantiles of low flows for different return periods. This was carried out by using the distribution function, in which the parameters of the distribution were replaced by their estimates and the relationship between return periods (T) and probability of exceedance (F). In low flow frequency analysis the assumption for the relationship between the low flows quantiles with return period was based on the exceedance probability as indicated in Equation (17).
F = 1 T (17)
where F is the probability distribution function and T is the return period
In order to carry out the regional low flow analysis initially the homogeneous group of stations has to be identified and categorized by using the L-MRD and coefficient of variation of coefficient of variation (C-C) test. The station year method was used for estimating the standardized long term quantiles for developing the regional frequency curve. The station year methods pull the standardized low flow values as one station for each homogenous group. The best probability distribution for each homogenous group (pulled standardized data) was fit by using similar to procedures as discussed in above sections. Using this probability distribution, the long term standardized quantiles was estimated for various return periods such as 2, 10, 25, 50, 100, 200 and 500 years. The regional growth curve was established as the relationship between the standardized quantiles and return periods for each return period. Hence the estimated standardized quantile was used to compute the normal low flow quantiles for both gaged and ungaged stations was using the relationship under Equation (18).
Q T = Q ¯ * X T (18)
where QT is the low flow for T-years of return period, Q ¯ is the n-day sustained average annual low flow, XT standardized quantile of for T years return period.
To compute the low flow quantiles for ungaged catchment using equation 18, the relationship between the n-day sustained average annual low flow of gaged stations and physical catchment characteristics has to be set up. Developing the relationship between the sustained average annual low flow and the catchment characteristics was also used for predicting the low flow quantiles at any point where the regional frequency curve was derived. In order to carry out the prediction, there are a number of measurable physical characteristics of catchments that could have significant relationship with the n-day sustained average low flow. Several physical catchment characteristics have been used for developing models to simulate the n-day sustained annual low flows for the ungaged catchments. The non-linear regression (Equation (19)) was used to develop a relationship between the average annual low flow for ungaged catchments in Blue Nile River basin. For this study the mainly used(easily measurable) physical catchment characteristics such as area (A), rainfall (R), slope (S), stream length (L) and shape factor (F) was considered as independent variables.
Q ¯ = C A a S s R r L t F t (19)
where Q ¯ is the average n day sustained low flow each station, A is the drainage of the selected station in square kilometers, S is average Slope expressed in percentage, R is the mean annual rainfall in millimeters, L is the length of stream, F is shape factor of the catchments. The parameters a, r, s, t and c of physical catchment characteristics were also estimated using multiple non-linear regression technique.
The three low flow data extraction models (3d-slf, 7d-slf and 14d-slf) in the selected 15 stations have been summarized and presented in
River/Gaging station | Period | Duration | 3d-slf (m³/s) | 7d-slf (m³/s) | 14d-slf (m³/s) | Average | Standard deviation |
---|---|---|---|---|---|---|---|
Amen | 1988-2005 | 18 | 0.002 | 0.003 | 0.005 | 0.003 | 0.002 |
Andassa | 1990-2004 | 15 | 0.988 | 0.996 | 1.023 | 1.002 | 0.018 |
Anger-greater | 1994-2004 | 11 | 3.532 | 3.856 | 3.467 | 3.618 | 0.208 |
Anger-lower | 1981-2002 | 22 | 1.478 | 1.589 | 1.794 | 1.620 | 0.160 |
Chemoga | 1973-2009 | 37 | 0.044 | 0.047 | 0.053 | 0.048 | 0.005 |
Gilgel Abay | 1980-2008 | 29 | 1.483 | 1.483 | 1.483 | 1.483 | 0.000 |
Gilgel Beles | 1982-2005 | 24 | 0.361 | 0.378 | 0.436 | 0.392 | 0.039 |
Gulda | 1962-2003 | 42 | 0.117 | 0.124 | 0.136 | 0.126 | 0.010 |
Hoha | 1966-2002 | 37 | 0.831 | 0.853 | 0.882 | 0.855 | 0.026 |
Indrias | 1986-2004 | 19 | 0.076 | 0.081 | 0.087 | 0.081 | 0.006 |
Mendel | 1987-2003 | 17 | 0.036 | 0.038 | 0.041 | 0.038 | 0.003 |
Mugher | 1975-2002 | 28 | 0.086 | 0.09 | 0.096 | 0.091 | 0.005 |
Neshi | 1963-2002 | 40 | 0.209 | 0.216 | 0.227 | 0.217 | 0.009 |
Siblu | 1981-2002 | 22 | 0.075 | 0.077 | 0.08 | 0.077 | 0.003 |
Urgessa | 1979-2002 | 24 | 0.139 | 0.145 | 0.151 | 0.145 | 0.006 |
Average | 0.630 | 0.665 | 0.664 | 0.653 | 0.020 | ||
Standard deviation | 0.956 | 1.033 | 0.962 | 0.984 | 0.043 |
Source of Variation | SS | dof | MS | F | P-value | F-crit |
---|---|---|---|---|---|---|
Between Groups | 0.077813 | 2 | 0.039 | 0.015 | 0.98 | 3.22 |
Within Groups | 105.402 | 42 | 2.51 | |||
Total | 105.4798 | 44 |
The outliers found from the low flow data tie series were very few in numbers and was decided and was removed before further analysis. From all of the stations there were not higher outlier greater than the upper bound and the fewer existing ones in four stations were below the lower bound. Where one lowest outliers were found from the stations of Anger-lower, Hoha, Mendel and Neshi stations. The minimum of sustained low flow value’s in Anger-lower data series was 0.03 m3/s (in 1983) which was far below the lower outlier (XL) bound (0.08358 m3/s). In Hoha station sustained low flow (0.001 m3/s) recorded in 1978 was lower than the outlier (XL) bounds (0.00273 m3/s). Similarly in Mendel station the minimum sustained low flow was 0.0017 m3/s recorded in 2003, which was lower than the lower outlier (XL) bound (0.0023 m3/sec). In Neshi station XL the lowest low flow value was 0.049 m3/sec observed in the year of 1981 lower than the lower outlier (XL) bound (0.056 m3/s). Hence these values were removed from the data series of each station.
An independence test where the assumption in the use of statistical distribution for extreme flow analysis of the sample data should be random without any serial correlation. It helps describes the strength of the relationship between a value in a series and that preceding it by one-time interval. Based on the W-W test all the selected stations sustained low flow data series was found independent. Hence the data series was accepted for the trend and frequency analysis of the low flows. All of the selected stations low flow data series were not stationary and homogenous except one station namely Gilgel Belles which likely could be the presence of trends.
The trend test on low flow for the selected stations were carried out by using the Mann-Kendall (MK) test as discussed in the methodology section. As presented in
There could be several reasons for decreasing of low flows in the Blue Nile Basin. Some of this includes change in physical characteristics of catchment such as the land cover change in rivers basins. For instance, the change of the forest to agricultural land could largely increase runoff in the rainy season and reduce the low flows in dry seasons. This has been indicated in some of the Blue Nile Basin in different studies such as [
River/Gaging station | Kendall’s tau | S | Var(S) | p-value (two-tailed) | Sen’s Slope |
---|---|---|---|---|---|
Amen | −0.494 | −38 | 266.67 | 0.023 | −2E−4 |
Andassa | −0.559 | −50 | 330.00 | 0.007 | −0.033 |
Anger-greater | −0.556 | −25 | 0.00 | 0.029 | −1.584 |
Anger-lower | 0.595 | 91 | 0.00 | 0.000 | 0.288 |
Chemoga | −0.513 | −40 | 0.00 | 0.015 | −0.007 |
Gilgel Abay | −0.604 | −180 | 1829.33 | 0.0001 | −0.062 |
Gilgel Belles | 0.336 | 85 | 0.00 | 0.026 | 0.023 |
Gulda | −0.566 | −397 | 6325.00 | 0.0001 | −0.005 |
Hoha | 0.322 | 203 | 5389.00 | 0.006 | 0.006 |
Indrias | −0.446 | −68 | 696.00 | 0.011 | −0.007 |
Mendel | −0.433 | −52 | 0.00 | 0.020 | −0.003 |
Mugher | −0.275 | −95 | 2289.67 | 0.049 | −0.003 |
Neshi | −0.744 | −58 | 0.00 | 0.000 | −0.024 |
Siblu | −0.418 | −84 | 1064.67 | 0.011 | −0.002 |
Urgessa | 0.325 | 68 | 1094.67 | 0.043 | 0.003 |
Station | Period (G.C) | Duration | Change (%) | Trend |
---|---|---|---|---|
Amen | 1988-2005 | 18 | 57.1 | decreasing |
Andassa | 1990-2004 | 15 | 33.3 | decreasing |
Anger_greater | 1994-2004 | 11 | 24.1 | decreasing |
Anger_lower | 1981-2002 | 22 | 43.3 | Increasing |
Chemoga | 1973-2009 | 37 | 98 | decreasing |
Gilgel Abay | 1980-2008 | 29 | 68 | decreasing |
Gilgel Belles | 1982-2005 | 24 | - | No trend |
Gulda | 1962-2003 | 42 | 85 | decreasing |
Hoha | 1966-2002 | 37 | 10.1 | Increasing |
Indris | 1986-2004 | 19 | 80 | decreasing |
Mendel | 1987-2003 | 17 | 60 | decreasing |
Mugher | 1975-2002 | 28 | 60 | decreasing |
Neshi | 1963-2002 | 40 | 72.5 | decreasing |
Siblu | 1981-2002 | 22 | 47 | decreasing |
Urgessa | 1979-2002 | 24 | 78 | decreasing |
more than 50% and the study also indicated decrease in low flows in the Gumara watershed (sub basin of Blue Nile Basin). [
Basin). [
In addition, climate change could also be responsible due to an increasing temperature in the region which increases open water and soil water evaporation. This reduces the low flow to go down due to decrease of soil water in the ground water due to increasing evaporation. In Blue Nile Basin there were several sub basin specific studies which indicated an increase in trends of temperature causing an increasing evapotranspiration such studies include National Meteorological Agency [
Similar to the trend analysis the data extraction was used based on the 3d-slf, 7d-slf and the 14d-slf data series. It was also known identified that based on the ANOVA result (
For this specific study the moment ratio diagrams were used for two purposes 1) to identify the best fit probability distribution for each station and 2) to select homogeneous regions based on the best fit probability distributions and statistical tests for regionalization purpose. Based on the results from the L-MRD (
Stations | Probability distribution |
---|---|
Amen | Weibull |
Andassa | Log Normal (LGN) |
Anger (Gr) | Weibull |
Anger (Lt) | Weibull |
Chemoga | Generalized Extreme Value (GEV) |
Gilgel Abay | Weibull |
Gilgel Beles | Weibull |
Gulda | Log Normal (LGN) |
Hoha | Generalized Extreme Value (GEV) |
Indrias | Weibull |
Mendel | Weibull |
Mugher | Generalized Extreme Value (GEV) |
Neshi | Weibull |
Siblu | Weibull |
Urgessa | Weibull |
As discussed in the methodology section the parameter for the selected probability distributions, parameter has been estimated by using the PWM as summarized in
Rivers/gaging stations | Probability distribution | Parameter estimation method | Homogenous groups |
---|---|---|---|
Amen | Weibul | PWM | Group-1 |
Anger_greater | |||
Anger_lower | |||
Gilgel Beles | |||
Gilgel Abay | |||
Indrias | |||
Mendel | |||
Neshi | |||
Siblu | |||
Urgessa | |||
Andassa | Log Normal (LGN) | PWM | Group-2 |
Gulda | |||
Hora | Generalized Extreme Value (GEV) | PWM | Group-3 |
Mugher | |||
Chemoga |
Using the selected probability distributions and parameter estimations the low flow parameters have been estimated for return period starting from 2 - 500
years as indicated in
The first step in regionalization was identifying the homogeneous regions or clustering based on different techniques. In this study the moment ratio diagram specifically the L-MRD was used for identifying the homogeneous groups. In addition the Coefficient of Variation of Coefficient of Variation (C-C) test was also carried out to further verify the homogenous regions. Based on the results from the L-MRD and CC based test the homogeneous regions were categorized as indicated in
Using the catchment characteristics as in order to drive the low flows the best fit nonlinear regression was established. The relation between the predicted and observed low flows indicated a good predicting capability with an R2 of 0.73 (
Q ¯ = 0.201 A 1.0412 S − 0.013 R − 1.089 F 0.074 (20)
Stations | Best fit Probability distribution | Regional low flow Growth curve equations. |
---|---|---|
Amen | Weibull | Q T = 0.059 + 1.039 [ log ( 1 / T ) ] 1 / 3.85 |
Anger_Great | ||
Anger_Lower | ||
Gilgel Beles | ||
Gilgel Abay | ||
Indrias | ||
Mendel | ||
Neshi | ||
Siblu | ||
Urgessa | ||
Andassa | Log Normal (LGN) | Q T = 0.073 + 0.653 [ 1 − ( − log 1 / T ) ] 1 / 4.574 |
Gulda | ||
Hoha | Generalized Extreme Value (GEV) | Q T = e 0.33 + U 0.468 |
Mugher | ||
Chemoga |
The results in this study have indicated mainly a decrease in low flows values for the selected stations in the Blue Nile Basin. This was attributed to the catchment dynamics especially land cover change and climate change over the river basins. In addition to that, the current vegetation cover in basin is largely converted to the eucalyptus tree which consumes high water from the soil due to large evapotranspiration. Hence watershed management targeting the main changes in watersheds mentioned above with afforestation and climate adaptation should be in place to mitigate and keep the health of rivers. The L-Moment ratio diagram provides a practical method to identify the underlying distribution for a given station. The use of the L-Moment ratio diagram was very convenient that one can compare the fit of several distributions using which are superior to conventional moment ratios because L-moments are less biased than ordinary moments. Low flow frequency analysis has indicated that the long term low flow quantiles for short and long term return periods indicted by large decreasing low flow quantiles even in some of the stations were found the “no flow”. Using the growth curve and the relation between low flows with catchment characteristics could help for estimating the low flows quantiles for water resource planning and management.
Assefa, K. and Moges, M.A. (2018) Low Flow Trends and Frequency Analysis in the Blue Nile Basin, Ethiopia. Journal of Water Resource and Protection, 10, 182-203. https://doi.org/10.4236/jwarp.2018.102011