Figure 1. Location Map of the Study Area
Estimation of dependable flow at different levels is considered one of the important parameters for planning, designing, and managing water-related projects, including hydropower generation, irrigation systems, water use, and river and reservoir sedimentation. For this purpose, the Flow Duration Curve (FDC) is developed by analyzing the available stream flow data at the site when adequate length of observed data are not available. The FDC is a valuable tool for determining the flow patterns of a river and estimating dependable flow. The FDC provides the percentage of time duration during which a stream flow (monthly, seasonal, or annual) is exceeded over a recorded period for a particular river or stream, which can be constructed by adopting the empirical method. By analyzing the FDC, the flow patterns of the Baspa river at the Kuppa barrage were determined, and the dependable flow was estimated. This paper presents a study on the assessment of monthly, seasonal, and annual dependable flow through the FDC by adopting an empirical method for the river Baspa at Kuppa barrage. The study suggests the dependable flow at different percentage levels like 75%, 90%, and 100% obtained from FDCs could be used for planning irrigation, hydropower, and drinking water projects in the study area.
The amount of stream flow exceeded for a given percentage of time is commonly used to quantify the surface water supply potential available in the river basin, which is commonly known as the water yield of the river basin. The annual yield from a catchment is the end product of various processes such as precipitation, infiltration, and evapotranspiration operating on the catchment. The annual yield is of utmost importance for planning, design, and management of water resource projects, which can be determined from its Flow Duration Curve (FDC), which gives a relationship between stream flow and the percentage of time the flow is exceeded.
The FDC (Post, 2004,/a>; Samaniego et al., 2010; Baykan, 2013) can be constructed by analyzing the available stream flow data at the site whenever adequate lengths of recorded data are not available. However, for ungauged catchments, regional FDC can be used (Holmes et al., 2002). The dependable flow at different percentage levels, viz., 75%, 90%, and 100%, obtained from FDCs can generally be used for planning irrigation, hydropower, and drinking water projects.
Dependable flow in a river is the flow that can be reliably counted on to be available over a specified period of time, such as a year. The dependable flow in the river Baspa at the Kuppa barrage can be determined using hydrological and statistical methods, such as flow duration analysis and statistical distribution analysis. In flow duration analysis, the flow data is collected and sorted in decreasing order, and a FDC is plotted that shows the percentage of time that the flow is equal to or greater than a certain flow rate. The dependable flow can then be determined by selecting a desired reliability, such as 50%, 75%, 90%, or 100%, and finding the corresponding flow rate on the curve. In statistical distribution analysis, the flow data is analyzed using statistical methods to determine the distribution of flow. The dependable flow can then be determined based on the statistical properties of the distribution, such as the mean flow or the flow exceeding a specific percentage of time. It's important to note that the dependable flow in the river baspa may be impacted by factors such as climate change, land use changes, and human activities such as water withdrawals or dam construction. Therefore, it's important to regularly update the flow data and reevaluate the dependable flow to account for these changes.
FDCs can be constructed using stream flow data using one or two methods: the empirical method or the classinterval method. A number of studies have been carried out by different researchers on the construction of FDC for various water resource applications. Smakthin (2000) applied the implicit ratio curve method to construct 1day and 1-month FDCs for the Koonap and Mooi rivers in the Eastern Cape of South Africa using synthetic stream flow data. Smakhtin and Masse (2000) suggested a method for continuous daily stream flow generation using the 1-day FDC and duration curves of a rainfall-related index, which reflects the daily fluctuations of wetness of the catchment and is similar to the antecedent precipitation index proposed by Smakhtin (2000).
Smakhtin (2001) used the FDC to estimate the magnitude and frequency of low flows in river streams and ungauged catchments, which is useful for water supply planning, waste-load allocation, reservoir storage design, the maintenance of quantity and quality of water for irrigation, recreation, and wildlife conservation. Yu et al. (2002) obtained FDCs for Cho-Shuei Creek in Taiwan, and they tested the validity of the FDCs. According to the analyzes of the uncertainty of the obtained FDCs, they determined that the polynomial method has less uncertainty than the area index method.
Tallaksen and Van Lanen (2004) gave an extensive list of possible approaches and techniques for low-flow estimation in ungauged catchments, which include regional regression, spatial interpolation, the construction of regional curves, and time series simulation.
Lane et al. (2005) developed a method to remove the climate signal from stream flow records to identify the impact of vegetation on flow from afforested catchments and quantify this impact on the FDC. Castellarin et al. (2007) applied the empirical and regional index flow methods for the construction of annual FDCs for unregulated river basins in Italy. Mohamoud (2008) developed a step-wise regression method using dependable flow, land use, and climate descriptor data and applied it to construct a FDC and predict stream flow for ungauged catchments in the Mid-Atlantic Region, USA.
Ganora et al. (2009)developed a distance-based regional model for the estimation of dimensionless FDC at sites where no or limited data are available. Baltas (2012) developed a regional model for the determination of the FDC at ungauged catchments in western and northwestern Greece, which is a hydrologically homogenous region. He also expressed that the FDC indicates the water availability at a site and is important for the estimation of the hydropower potential.
Hrachowitz et al. (2013) made an attempt to improve the ability of existing hydrological models to predict ungauged basins with reduced uncertainty and developed new and innovative models representing the space–time variability of hydrological processes for improving the confidence in predictions in ungauged catchments.
Younis and Hasan (2014) developed two regional regression models for the prediction of FDC for seasonal rivers in Iraq. They found that the estimated FDC using the MAF-PE (Mean Annual Flow-Potential Evapotranspiration) model provided better results than the estimated FDC using the CA-MAP (Catchment Area-Mean Annual Precipitation) model.
Khopade and Oak (2014) estimated runoff yield for the Nira Deoghar catchment using empirical equations. A study by Tabesh and Bhave (2015). revealed that the Soil Conservation Service (SCS) is the best-suited method among the five methods (SCS, Khosala, rational, regression, and Thomas Firing) applied in the estimation of yield from a catchment in Afghanistan with inadequate data.
Zhang et al. (2015) stated that the FDC approach was better at predicting medium to low flows in traditional calibration against the Nash–Sutcliffe efficiency or root mean square error, but when calibrated against a low flow objective function, both the FDC and rainfall–runoff models performed equally well in simulating the low flows. Müller and Thompson (2016) compared the stochastic process-based and statistical methods for FDC prediction in both stationary and non-stationary contexts for the Nepal region. He also expressed that processbased prediction approaches are favored over statistical models.
Atieh et al. (2017) carried out a study on novel models for prediction of FDCs at ungauged basins using artificial neural networks and gene expression programming in North America.
Eris et al. (2019) attempted to find the best-fit probability distribution function to low flows using the most recent data from intermittent and non-intermittent rivers in four hydrological basins across Turkey.
Ridolfi et al. (2020) proposed a new methodology to estimate FDCs at partially gauged basins (i.e., target sites) using precipitation data gauged at another basin, which is the donor site. Burgan and Aksoy (2020) created a simple FDC model for monthly stream flow data from Turkey's Ceyhan River basin. The paper describes the procedures used to estimate the dependable flow using FDC, along with an illustrative example and the results obtained from the study.
The objectives of the study include constructing the FDCs for the monthly, seasonal, and annual series of stream flow (i.e., discharge) data by adopting the empirical method and estimating dependable flow at different percentage levels like 50%, 75%, 90%, and 100%.
The empirical method is a commonly used method for constructing FDC in hydrology. The basic steps involved in constructing a flow duration curve using the empirical method are as follows:
The first step is to collect flow data, such as daily discharge measurements, at the site of interest in this case, the river Baspa at the Kuppa barrage. It is recommended to collect data over a period of at least one year to capture the full range of flow conditions. The next step is to sort the flow data in decreasing order, from the highest flow rate to the lowest. For each flow rate, calculate the exceedance probability, which is defined as the percentage of time that the flow rate was exceeded. Plot the flow rate against the exceedance probability on a graph. The result is the FDC, which represents the relationship between the flow rate and the percentage of time that it is exceeded. The dependable flow can be determined by selecting a desired reliability, such as 50%, 75%, 90%, or 100%, and finding the corresponding flow rate on the curve. This flow rate can be considered the dependable flow, as it is exceeded for the specified percentage of time.
The construction of a FDC using the stream flow observations can be performed through the empirical method (Kottegoda & Rosso, 1997), which is given below:
Observed stream flow (q(i), i=1,2,….N) are ranked in descending order, to produce a set of ordered stream flow (q(i), i = 1,2,…..N), where q(i) is the observed stream flow of ith sample, q(1) and q(N) are the largest and the smallest values in the data series respectively and N is the number of samples.
Each ordered observation q(i) is then plotted against its probability of exceedance (P(i)), which is generally dimensionless. If the weibull plotting position is used, P(i) is defined as P(i)=i/(N+1), where "i" is the descending rank assigned to the observed data. For example, rank 1 is assigned to the first largest value, rank 2 to the second largest, rank 3 to the third largest value, and so on. The ordered stream flow values are then used to calculate the exceedance probability, which is defined as the percentage of time that the flow rate was exceeded. The exceedance probability is calculated by dividing the number of days with a flow rate less than or equal to the considered flow rate by the total number of days in the data series. Finally, the flow rate and the exceedance probability are plotted on a graph, and the resulting curve is the FDC. The curve represents the relationship between the flow rate and the percentage of time that it is exceeded, and the dependable flow can be determined by selecting a desired reliability and finding the corresponding flow rate on the curve.
The constructed FDC using empirical method is used to estimate the dependable flow at different percentage levels (50%, 75%, 90%, and 100%). For example, to determine the dependable flow for a reliability level of 50%, the flow rate that corresponds to a probability of exceedance of 50% on the FDC is chosen. This flow rate would be considered the dependable flow for a reliability level of 75%, as it is exceeded only 25% of the time. Similarly, the dependable flow for a reliability level of 90% is determined by finding the flow rate that corresponds to a probability of exceedance of 10% on the FDC, and for a reliability level of 100% by finding the flow rate that corresponds to a probability of exceedance on the FDC. It's important to note that the dependable flow is a function of both the flow rate and the reliability level, and that the reliability level should be chosen based on the specific requirements of the project or application. The dependable flow can be used for various purposes, such as water resource planning, water management, and hydropower generation, among others.
In this paper, a study on the assessment of dependable flow at different dependable levels (viz., 50%, 75%, 90%, and 100%) for the river Baspa at the Kuppa barrage using the FDC empirical method was carried out. The barrage is located on river Baspa at village Kuppa near Sangla and the power house is located near village Karcham which is about 800m upstream of the confluence of rivers Satluj and Baspa. A location map of the study area is shown in Figure 1.
Figure 1. Location Map of the Study Area
For the present study, the monthly, seasonal, and annual flow data series were derived from the daily stream flow data observed at Kuppa barrage of the Baspa river for the period 1991–2017 and used for further data analysis. Table 1 presents the descriptive statistics like average, Standard Deviation (SD), Coefficient of Variation (CV), Coefficient of Skewness (CS), Coefficient of Kurtosis (CK), minimum flow, and maximum flow of the monthly, seasonal, and annual flow data series. From Table 1, it is noted that the monthly average stream flow for the period from January to December varies between 250 m3 /s and 5090 m3/s, with a maximum flow of 5090 m3 /s in the month of July. Also, from Table 1, it is noted that the average flow during the monsoon season is about 80% of the annual average flow. The CV values vary from 21.0% to 53.4% for monthly series, 27.2% to 41.9% for seasonal series, and 35.2% for annual series.
Table 1. Descriptive Statistics of Monthly, Seasonal and Annual Stream Flow Data Series of River Baspa at Kuppa Barrage
By applying the procedures of the empirical method, as described earlier, the FDCs using monthly (January to December) and annual flow series were developed and are presented in Figure 2. Also, the FDCs of four different seasons, viz., pre-monsoon (March to May), monsoon (June to September), post-monsoon (October to November), and winter (December to February), were developed and are presented in Figure 3. These FDCs were used for the computation of dependable flow at different percentage levels. From the developed FDCs, dependable flow at different percentage levels, viz., 50%, 75%, 90%, and 100%, were estimated and presented in Table 2.
Figure 2. Monthly and Annual FDCs for River Baspa at Kuppa Barrage
Figure 3. Seasonal FDCs for River Baspa at Kuppa Barrage
Table 2. Dependable Flow for Different Percentage Levels At Kuppa Barrage
The dependable flow at a barrage is the minimum amount of water that can be guaranteed to be available for use in a given period of time. This flow is dependent on a variety of factors, including climate conditions, water usage patterns, and the capacity of the barrage itself. For the Kuppa barrage, the dependable flow levels of 50%, 75%, 90%, and 100% refer to the amount of water that can be relied upon to be available at these percentages. A dependable flow level of 50% at the kuppa barrage would indicate that it can be guaranteed that at least half of the expected flow of water will be available for use during the given period of time. A dependable flow level of 75% would indicate that it can be guaranteed that at least three-quarters of the expected flow of water will be indicate that at least 90% of the expected flow of water can be relied upon. Finally, a dependable flow level of 100% at the Kuppa barrage would mean that the entire expected flow of water could be relied upon to be available for use.
The monthly FDCs would give an idea of the flow patterns of the Baspa river at the Kuppa barrage for each of these periods, showing the different levels of flow that can be expected and the percentage of time that these flow rates are present. The annual FDC would give an overall picture of the flow patterns of the Baspa river at the Kuppa barrage for the entire year, showing the different levels of flow that can be expected and the percentage of time that these flow rates are present. These FDCs can be useful for a variety of purposes, including water resource management, hydropower generation, and irrigation planning. By understanding the flow patterns of the Baspa river at the Kuppa barrage, decision-makers can make informed decisions about how to best use the water resources in the area. According to the graph values, the initial value is the highest value and continues to decrease into the lower value, in which percentage of the time flow exceeded plotted against the discharge of water leads to the very least value.
Figure 3 shows the seasonal FDCS for the river Baspa at the Kuppa barrage. Seasonal FDCs for the Baspa river at the Kuppa barrage can provide insight into the flow patterns of the river during different seasons. Pre-monsoon is the period before the onset of the monsoon season, typically from March to May, and the monsoons are the period during the monsoon season, typically from June to September. Post-monsoon is the period after the monsoon season, typically from October to December, and winter is the period from January to February. By creating FDCs for each of these seasons, the flow of the Baspa river at the Kuppa barrage varying throughout the year, including the peak flow periods during the monsoon season and the lower flow periods during the winter is seen. These seasonal FDCs can be useful for a variety of purposes, including water resource management, hydropower generation, and irrigation planning. By understanding the flow patterns of the Baspa river at the available, while a dependable flow level of 90% would Kuppa barrage during different seasons, decision-makers can make informed decisions about how to best use the water resources in the area.
In the case of each and every season, the value of the percentage of time against the discharge shows the value keeps on decreasing as time or days pass on. The seasonal FDCs for the Baspa river at the Kuppa barrage can show the percentage of time that a particular flow rate is exceeded during different seasons. The FDCs are usually plotted with flow rate on the x-axis and the percentage of time that the flow rate is exceeded on the y-axis. For each of the four seasons (pre-monsoon, monsoon, post-monsoon, and winter), the FDC will show the flow rates of the Baspa river at the Kuppa barrage and the percentage of time that these flow rates are exceeded. The FDC will typically have a decreasing value as the flow rate increases, indicating that higher flow rates are less frequently exceeded.
By using the FDC results, as presented in Table 2 and Figures 2 and 3, some of the results drawn from the research were summarized and are presented as being very applicable. For the period from January to December, the 50%, 75%, 90%, and 100% dependable flows in the river Baspa at Kuppa barrage varied from 267 m3/s to 4970.7 m3/s, 294.0 m3/s to 6232.3 m3/s, 344.7 m3/s to 7370.0 m3/s, and 365.0 m3/s to 8425.8 m3/s, respectively. The 50%, 75%, 90%, and 100% dependable flows were found to be maximum in the month of July and minimum in February. About 78% of the 50% reliable annual flow was received in the monsoon season. Similarly, it was found that 82% of 75% annual dependable flow, 79% of 90% annual dependable flow, and 75% of 100% annual dependable flow were only received in the monsoon period. The annual dependable flow at various dependable levels, viz., 50%, 75%, 90%, and 100%, were computed as 18377.3 m3 /s, 21535.1 m3/s, 27896.1 m3 /s, and 33666.0 m3/s, respectively.
The empirical method described in the paper is intended to be a simple tool for generating FDC at an ungauged basin where monthly stream flow data are available from other sources. The established FDC may have many direct practical applications. At the same time, the FDC may be converted into the actual daily stream flow time series representing natural flow conditions in a river catchment. The method may be further constructed to adjust the established curves to incorporate the effects of catchment and water resource development at the project site. The study suggested that the dependable flow obtained from FDCs at different percentage levels, viz., 75%, 90%, and 100%, could be used for the planning of irrigation, hydropower, and drinking water projects at the Kuppa barrage of the Baspa river. The study also suggested that the techniques presented in the paper would be beneficial to the stakeholders while looking for the availability of much-needed detailed stream flow time series information.
The author is thankful to Dr. R.S. Kankara, Director, Central Water and Power Research Station, Pune for providing the research facilities to carry out the study presented in this paper.