Low-flow Frequency Analysis Research Articles

Non-stationary low flow frequency analysis under climate change

Analysis of low river flows provides important information for effective management of water resources in a region. Despite the critical importance of understanding low flow dynamics, there is a gap in the literature regarding the use of non-stationary models to analyze low flow data under climate change in Turkey. In this research, low flow series from 80 measuring stations in Turkey are investigated by employing both stationary and non-stationary models based on the Generalized Additive Models for Location, Scale and Shape (GAMLSS). For constructing non-stationary models, 31 explanatory variables consisting of time, precipitation, temperature and atmospheric oscillation indices were used to model the parameters of the chosen distributions. The results show that stationary models are more successful at 7 stations, while non-stationary models are more successful at 73 stations. Comparisons between non-stationary models showed that for most stations, the best performing models were non-stationary models with annual precipitation as covariates. In addition, successful results were obtained when Western Mediterranean Oscillation and North Atlantic Oscillation indices were used as explanatory variables. Additionally, this study investigated 20 and 50-year return levels by fitting the non-stationary frequency distribution models for low flows over historical and projection periods under SSP2-4.5 and SSP5-8.5 climate scenarios. GAMLSS incorporated annual total precipitation, which is the most effective explanatory variable for low flows, as a covariate, and thus changes in low flows were analyzed. The results show that decreases are expected in low flows, except for the stations in the upper Euphrates basin compared to the historical period.

Comparative Study of Low Flow Frequency Analysis Using Bivariate Copula Model at Soyanggang Dam and Chungju Dam

A univariate analysis that relies solely on precipitation data in low flow frequency analysis is a technique to express meteorological drought, so it is limited to analyzing the characteristics of hydrological drought related to available water resources. In addition, if the data for the model calibration are insufficient, the uncertainty of a single variable limits the construction of a reliable model. To improve this problem, a frequency analysis was performed by constructing a bivariate copula model as a multivariate model with a high correlation between variables targeting reservoir inflows. The methodology utilizes the theory of runs to identify low flow events, establishing a threshold based on the mandatory regional water supply plan, and determining the low flow duration and cumulative water deficit. The Gumbel copula function, effective in capturing correlations between hydrological variables, was applied to derive a joint bivariate probability distribution, facilitating the calculation of combined low flow event return periods. This study compared low flow frequencies at Soyanggang dam (’74–’22) and Chungju dam (’86–‘22), which are in the same Han River basin but have different capacities and water demands, using a bivariate copula model. The top four extreme low flow events for the two adjacent dam basins did not occur in the same year and, in the years of the extreme low flow events at one of the two dam basins, there was an insignificant magnitude at the remaining dam basin. This result is noteworthy because it shows that the possibility of extreme low flow events appearing simultaneously in both watersheds is not as high as expected. The operational efficiency can be improved by setting the coordinated operation rules of the two reservoirs using the copula dependency structure.

Low Flow Frequency Analysis at Triang River Streamflow Station

Low flow analysis is essential for determining the communities’ water supply. As water supply is a necessity for human daily survival, it is crucial to recognize that the availability of water can have a significant impact on local livelihoods and the sustainability of local populations. Triang River is a tributary of the Pahang River in Peninsular Malaysia. The existence of the Triang Water Intake and Treatment Plant along the Triang River stream serves to determine the low flow magnitudes and frequency curves for the Triang River streamflow station using the Weibull, Gringorten, and Cunnane plotting position formulas. Based on 20 years of historical data, this study analyzed the annual minimum streamflow data for 1-, 4-, 7-, and 30-day durations as well as the average recurrence intervals (ARIs) of 2-, 5-, 10-, 20-, 50-, and 100-year streamflow data. These three plotting position formulas were successfully used to estimate the low flow magnitudes for the various durations and different ARIs. The findings can serve as a guide for developing future water resource projects that take into account the Triang River’s low flow data.

A Hybrid Approach for Regional Low-Flow Frequency Analysis for the Upper Tigris and Euphrates Basin

The Tigris and Euphrates basin is a challenging watershed because its water resources are critical for five countries. Therefore, this research analyzed and estimated the low flow index and its risk of occurrence. Based on 30 unregulated stations in the upper Tigris and Euphrates basin, different low flow indexes were estimated. A multivariate and hybrid principle component regression (PCR) regional model was used to assign the relationship between basin characteristics and low flow indexes in the homogeneous regions. The model performance showed that the principle component regression outperformed the regression models. The jackknife procedure indicated that the model performance for short-duration low flows is weak, but it is relatively good for long-duration low flows. This study suggests that hydrologic drought of the Tigris and Euphrates basin should be investigated more carefully for better water resources management in the changing socio-environmental system of the Middle East.

A mixed distribution approach for low-flow frequency analysis – Part 2: Comparative assessment of a mixed probability vs. copula-based dependence framework

Abstract. In climates with a warm and a cold season, low flows are generated by different processes, which violates the homogeneity assumption of extreme value statistics. In this second part of a two-part series, we extend the mixed probability estimator of the companion paper (Laaha, 2023) to deal with dependency of seasonal events. We formulate a copula-based estimator for seasonal minima series and examine it in a hydrological context. The estimator is a valid generalization of the annual probability estimator and provides a consistent framework for estimating return periods of summer, winter, and annual events. Using archetypal examples we show that differences in the mixed estimator are always observed in the upper part of the distribution, which is less relevant for low-flow frequency analysis. The differences decrease as the return period increases so that both models coincide for the severest events. In a quantitative evaluation, we test the performance of the copula estimator on a pan-European data set. We find a large gain of both mixed distribution approaches over the annual estimator, making these approaches highly relevant for Europe as a whole. We then examine the relative performance gain of the mixed copula versus the mixed distribution approach in more detail. The analysis shows that the differences in the 100-year event are actually minimal. However, the differences in 2-year events are considerable in some of the catchments, with a relative deviation of −15 % to −25 % in the most affected regions. This points to a prediction bias of the mixed probability estimator that can be corrected using the copula approach. Using multiple regression models, we show that the performance gain can be well explained on hydrological grounds, with weak seasonality leading to a high potential for corrections and strong seasonal correlation reinforcing the need to take this potential into account. Accordingly, the greatest differences can be observed in mid-mountain regions in cold and temperate climates, where rivers have a strongly mixed low-flow regime. This finding is of particular relevance for event mapping, where regional severity can be misinterpreted when the seasonal correlation is neglected. We conclude that the two mixed probability estimators are quite similar, and both are conceptually more adequate than the annual minima approach for mixed summer and winter low-flow regimes. In regions with strong seasonal correlation the mixed copula estimator appears most appropriate and should be preferred over the mixed distribution approach.

A mixed distribution approach for low-flow frequency analysis – Part 1: Concept, performance, and effect of seasonality

Abstract. In seasonal climates with a warm and a cold season, low flows are generated by different processes so that the annual extreme series will be a mixture of summer and winter low-flow events. This leads to a violation of the homogeneity assumption for all statistics derived from the annual series and gives rise to inaccurate conclusions. In this first part of a two-paper series, a mixed distribution approach to perform frequency analysis in catchments with mixed low-flow regimes is proposed. We formulate the theoretical basis of the mixed distribution approach for the lower extremes based on annual minima series. The main strength of the model is that it allows the user to estimate return periods of summer low flows, winter low flows, and annual return periods in a theoretically sound and consistent way. Using archetypal examples, we show how the model behaves for a range of low-flow regimes, from distinct winter and summer regimes to mixed regimes where seasonal occurrence in summer and winter is equally likely. The examples show in a qualitative way the loss in accuracy one has to expect with conventional extreme value statistics performed with the annual extremes series. The model is then applied to a comprehensive Austrian data set to quantify the expected gain of using the mixed distribution approach compared to conventional frequency analysis. Results indicate that the gain of using a mixed distribution approach is indeed large. On average, the relative deviation is 21 %, 39 %, and 63 % when estimating the low flow with a 20-, 50-, and 100-year return period. For the 100-year event, 75 % of stations show a performance gain of >10 %, 41 % of stations > 50 %, and 25 % of stations > 80.6 %. This points to a broad relevance of the approach that goes beyond highly mixed seasonal regimes to include the strongly seasonal ones. We finally correlate the performance gain with seasonality indices in order to show the expected gain conditional to the strength of seasonality expressed by the ratio of average summer and winter low flow seasonality ratio (SR). For the 100-year event, the expected gain is about 70 % for SR=1.0, 20 % for SR=1.5, and 10 % for SR=2.0. The performance gain is further allocated to the spatial patterns of SR in the study area. The results suggest that the mixed estimator is relevant not only for mountain forelands but to a much wider range of catchment typologies. The mixed distribution approach provides one consistent approach for summer, winter, and annual probabilities and should be used by default in seasonal climates with a cold winter season where summer and winter low flows can occur.

Plotting Position for Low Flow Frequency Analysis at Jempol River Streamflow Station

Low flow frequency analysis is an important technique for calculating the probability of river flow availability during crucial low flow seasons, such as drought. It is also useful to predict the low flow information of a river in volume and frequency for future planning and construction of water resource projects since the low flow has a significant impact on water quality, water supply, and river sustainability conditions. Therefore, this study was performed to determine the low flow frequency analysis of the Jempol River streamflow station using Weibull and Gringorten plotting position formulas. The average recurrence interval (ARI) of 2-, 5-, 10-, 25-, 50-, and 100-year were determined based on 18 years of historical streamflow data. The study illustrates the annual minimum flow magnitude of 1-, 4-, 7-, and 30-day durations for the study area. It shows that the Gringorten formula tends to give higher estimation values up to 18% compared to the Weibull formula when the flow duration increase. Therefore, the outcome of this study could be used in the future for any project related to the low flow information of Jempol River.

Stochastic Watershed Model Ensembles for Long‐Range Planning: Verification and Validation

AbstractDeterministic watershed models (DWMs) are used in nearly all hydrologic planning, design, and management activities, yet they cannot generate streamflow ensembles needed for hydrologic risk management (HRM). The stochastic component of DWMs is often ignored in practice, leading to a systematic bias in extreme events. Since traditional stochastic streamflow models used in HRM struggle to account for anthropogenic change, there is a need to convert DWMs into stochastic watershed models (SWMs) to generate ensembles for use in HRM. A DWM can be converted to an SWM using a post‐processing (pp) approach to add error to the DWM predictions. Many pp methods advanced in the area of flood forecasting are useful in HRM and for correcting extreme event biases. Selecting a suitable error model for pp is challenging due to nonnormality, skewness, heteroscedasticity, and autocorrelation. We develop a parsimonious pp method based on an autoregressive (AR) model of the logarithm of the ratio of the observations and simulations, which leads to AR model residuals that are approximately symmetric and independent. We document the value of pp for improving flood and low flow frequency analysis and we reintroduce the concepts of verification and validation of stochastic streamflow ensembles to ensure that the SWM can reproduce both statistics it was and was not designed to reproduce, respectively. These concepts are illustrated on a Massachusetts basin using the USGS Precipitation Runoff Modeling System, with an additional analysis indicating the approach may be applicable to 1,225 other sites across the United States.

Low flow frequency analysis of Tawi River discharge at Jammu location

In present study Tawi River was selected for low flow frequency analysis (LFFA). Tawi River is left bank tributary of Chenab River. LFFA is useful to measure various parameters as mean annual runoff (MAR); mean daily flow (MDF), Q20, Q50, Q90, Q20/Q90, Q50/Q90, Q90/Q50; the average of annual series of minimum ten-day average (MAM10); and the average of annual series of minimum seven-day average (MAM7), 10Q10, 10Q2, 7Q10 and 7Q2. By separating, the 40 years discharge data in 20-20 years' time period, significant change is observed; 15% change observed in MCM, 12.97% change in Q20 and 12.32% change in Q50. Flow duration curves show significant change in discharge of the Tawi River particularly during 5-25% exceedance probability. Monthly discharges show mixed trends with increase in discharges as 42.68%, 81.47% and 42.91% during October, November and June months and decrease in discharges as 13% to 48% during January, March, April, July, August, and December.

Nonstationary flood and low flow frequency analysis in the upper reaches of Huaihe River Basin, China, using climatic variables and reservoir index as covariates

Conventional water infrastructure designs for flood and low flows are usually based on the assumption of stationarity of extreme events. However, recent evidence suggests that the influences of climate variability and human activities have made the hypothesis of stationarity questionable. In this study, we used the generalized additive models for location, scale, and shape (GAMLSS) to construct a nonstationary model in which the parameters of the selected distributions were modelled as a function of climatic variables (i.e., climate indices and precipitation) and/or the reservoir index (RI). The nonstationary models were then used to analyse annual flood and low flow frequency at four hydrological stations in the upper reaches of the Huaihe River Basin, including Dapoling (DPL), Changtaiguan (CTG), Zhuganpu (ZGP), and Xixian (XX) stations. Annual floods were represented by the maximum daily streamflow in each year, and low flows were represented by the 95th quantile of the daily streamflow (Q95) in each year. The change point and trend analysis revealed that the flood series of the ZGP station and the low flow series of the DPL and XX stations exhibited significant downward and upward trends (p < 0.1)), respectively. The low flow series of the ZGP station showed a significant change point in 1980 (p < 0.1). GAMLSS modelling results showed that, in comparison with stationary models, nonstationary models that included precipitation and the Arctic Oscillation climate index as covariates for the gamma distribution location parameter provided a superior description of the flood series at the four stations. Nonstationary models that incorporated precipitation and/or RI as covariates for the Weibull distribution parameters fit the low flow series better than stationary models at all stations. Furthermore, we found that nonstationary models outperformed stationary models in terms of flood frequency analysis, covering all flood observation points and capturing the generally decreasing trend in flood series, as well as a decrease in the scatter of estimated flood value magnitudes. For the low flow frequency analysis, the comparison results showed that the nonstationary and stationary models performed identically for the DPL, CTG, and XX stations, where no significant change point was detected. However, for the ZGP station, where a significant change point was detected, the nonstationary models performed better than the stationary models and could accurately capture the changes in the magnitude of the estimated low flow values before and after the change point. Overall, the proposed nonstationary model can serve as a tool for nonstationary frequency analysis of flood and low flow series under the influence of climate variability and reservoir regulations, thus providing a reference for regional water infrastructure design.

Low flow frequency analysis of Tawi River discharge at Jammu location

Low flow frequency analysis of Tawi River discharge at Jammu location

Comparison of Generalized Extreme Value, Log Normal and Weibull Distributions for Assessment of Low-Flow

Assessment of low-flow is an important aspect for water quality management, reservoir storage design, determining minimum release policy and safe surface water withdrawals. For which, the annual minimum d-day average flow is generally adopted procedure for characterizing the low-flow in a stream, which can be obtained by averaging the flow using moving average method for ‘d’ consecutive days viz., 7-, 10-, 14- and 30- days. This paper presents a study on comparison of three probability distributions such as Generalized Extreme Value, 2-parameter Log Normal (LN2) and Weibull adopted in estimation of low-flow for river Cauvery at Kollegal gauging site. The parameters are determined by three methods viz., method of moments, maximum likelihood method and L-Moments (LMO), and are used for estimation of low-flow. The adequacy of fitting probability distributions adopted in low-flow frequency analysis is evaluated by quantitative assessment through Goodness-of-Fit (viz., Chi-Square and Kolmogorov-Smirnov) and diagnostic (viz., correlation coefficient and root mean squared error) tests, and qualitative assessment using the fitted curves of the estimated low-flow. The results of quantitative and qualitative assessments indicate that LN2 (LMO) is better suited amongst three distributions adopted in estimation of 7-, 10-, 14- and 30- day low-flows for river Cauvery at Kollegal site.

Assessment of probability distributions and analysis of the minimum storage draft rate in the equatorial region

Abstract. Rapid urbanization in the state of Selangor, Malaysia, has led to a change in the land use, physical properties of basins, vegetation cover and impermeable surface water. These changes have affected the pattern and processes of the hydrological cycle, resulting in the ability of the basin region to store water supply to decline. Reliability on water supply from river basins depends on their low-flow characteristics. The impacts of minimum storage on hydrological drought are yet to be incorporated and assessed. Thus, this study aims to understand the concept of low-flow drought characteristics and the predictive significance of river storage draft rates in managing sustainable water catchment. In this study, the long-term streamflow data of 40 years from seven stations in Selangor were used, and the streamflow trends were analyzed. Low-flow frequency analysis was derived using the Weibull plotting position and four specific frequency distributions. Maximum likelihood was used to parameterize, while Kolmogorov–Smirnov tests were used to evaluate their fit to the dataset. The mass curve was used to quantify the minimum storage draft rate required to maintain the 50 % mean annual flow for the 10-year recurrence interval of low flow. Next, low-flow river discharges were analyzed using the 7 d mean annual minimum, while the drought event was determined using the 90th percentile (Q90) as the threshold level. The inter-event time and moving average was employed to remove the dependent and minor droughts in determining the drought characteristics. The result of the study shows that the lognormal (2P) distribution was found to be the best fit for low-flow frequency analysis to derive the low-flow return period. This analysis reveals September to December to be a critical period in river water storage to sustain the water availability during low flow in a 10-year occurrence interval. These findings indicated that hydrological droughts have generally become more critical in the availability of rivers to sustain water demand during low flows. These results can help in emphasizing the natural flow of water to provide water supply for continuous use during low flow.

Applicability of Lindley Distribution for Hydroelectric Dam Operations in the Dry Season

The long-term low-flow data are necessary for efficient planning of water resources and for estimating accurate quantiles via runoff data analysis at point. However, the short recording time period, low confidence, inconsistent distribution model, and parameter estimation method, make it difficult to estimate a proper low-flow quantile for each return period. In this study, the Lindley distribution model, which is a mix of the exponential and the gamma distribution models and has been verified as efficient by previous studies, was used to analyze the low-flow frequency using dam inflow data. We studied its applicability via comparison with statistics of observed data and other models already used for low-flow frequency analysis. For this, we carried out a performance analysis through a low-flow frequency analysis of inflow data from the hydroelectric dam and the reappearance capacity assessment of observed data at the Han river watershed. As a result, the hydrological applicability of the Lindley distribution model and its relative qualitative and quantitative excellence compared to the existing model were verified.

A neural network ensemble approach with jittered basin characteristics for regionalized low flow frequency analysis

Previous studies have shown that the predictive ability of artificial neural networks can be improved by combining multiple models. This study presents a jittering-based neural network ensemble approach to obtain improved regional low flow estimates at ungauged sites. The fundamental idea of the jittered ensemble is to add noises to the explanatory variables and thereby augments the training data sets to develop the network models based on different but associated training data. To evaluate the performance of the jittered ensemble, this study employs two different neural network architectures, a single-output neural network model and a multi-output neural network model. In addition, a jittered ensemble approach is coupled with the variable importance measuring algorithm to infer the relationship between basin characteristics and predicted low flow quantiles. Effectiveness of the proposed methods is demonstrated using selected basins in the northeastern United States. Results suggest that the jittering-based ensemble model is able to consistently outperform a single modeling approach. Also, improvement is achieved even using small sizes of ensembles although a sufficient sample size offers more reliable predictions. Finally, this study recognizes that the effects of the basin characteristics varied or remained constant based on the low flow quantiles considered.

Bivariate low flow return period analysis in the Mahanadi River basin, India using copula

ABSTRACTAssessments of low flows of major river of India are essential for effective management of drought and irrigation water demand/supply mechanism. In the present work, bivariate low flow frequency analysis of Mahanadi basin, that had significant variations in hydrological behaviour from upstream to downstream, was done for two major low flow characteristics, namely, severity and occurrence . Three Copulas have been tested for their applicability to estimate the joint return period of low flow at 2, 5, 10, 20, 50 years return periods. According to the Akaike information criterion (AIC) value, the Clayton Copula and the Frank Copula were found to be the most suitable for the stations in Basantapur and Kantamal, respectively. Further, the conditional low flow return periods were estimated and were found useful for low flow management and ecological analysis in the Mahanadi basin.

Introduction of the GAM model for regional low-flow frequency analysis at ungauged basins and comparison with commonly used approaches

Generalized Additive Models (GAMs) are introduced in this study for the regional estimation of low-flow characteristics at ungauged basins and compared to other approaches commonly used for this purpose. GAMs provide more flexibility in the shape of the relationships between the response and explanatory variables in comparison to classical models such as multiple linear regression (MLR). Homogeneous regions are defined here using the methods of hierarchical cluster analysis, canonical correlation analysis and region of influence. GAMs and MLR are then used within the delineated regions and also for the whole study area. In addition, a spatial interpolation method is also tested. The different models are applied for the regional estimation of summer and winter low-flow quantiles at stations in Quebec, Canada. Results show that for a given regional delineation method, GAMs provide improved performances compared to MLR.

Low-flow frequency analysis at ungauged sites based on regionally estimated streamflows

Estimation of low-flow quantiles or indices at ungauged sites is traditionally done through regional low-flow frequency analysis. However, traditional methods imply a prior aggregation of the regional information due to the usual focus on a given quantile. This leads to loss of information for estimating additional quantiles or performing additional applications. In the present study, the recently proposed regional streamflow based frequency analysis (RSBFA) approach is evaluated for the estimation of low-flow quantiles. The approach, originally applied to floods, is based on regionally estimating the daily streamflow series at the ungauged site to later obtain hydrological quantiles through a local frequency analysis. In the present study, the RSBFA approach is applied to low flows through a case study in the province of Quebec, Canada, considered in prior traditional regional low-flow studies. Although the RSBFA approach does not systematically lead to the best results, its relevance resides in the fact that the whole regionally estimated daily streamflow series is provided at the ungauged site. This allows an easy estimation of low-flow quantiles associated to particular durations, such as the 7-day (30-day) average low flows corresponding to a return period of 2 or 10 years (5 years). Furthermore, a large range of additional low-flow quantiles, such as q95% (streamflow expected to be exceeded 95% of the time divided by the catchment area), may be obtained from the regionally estimated streamflow series with a very good performance. Therefore, any specific or absolute, annual or seasonal low-flow quantile may be easily obtained by a local low-flow frequency analysis without repeating the regional procedure. The approach does not require complex models, and it may also allow combining regional and local information in a straight forward manner.

Frequency Analysis of Low and High Flows in Trend

Hydrological variables are under the effect of the climate change impacts, and therefore, this study concentrates on the frequency analyses of low and high flows depending on the duration, leading to a new approach. The durations are selected as month, season, 6‐month, and year coupled with the return periods 2‐, 5‐, 10‐, 20‐, 50‐, 100‐, 200‐, and 500‐years. The frequencies are equivalent to the reverse of these return periods. Increasing and decreasing trends are identified within the low and high flows, and the necessary graphs are presented. Similar to intensity‐duration‐frequency (IDF) curves, the proposed frequency‐flow‐duration curves are obtained instead of flow‐duration‐frequency (QDF) curves. The curves present important inputs for many hydrological events including flood forecasting, dam reservoir calculations, urban drainage design evaluations, transportation network planning, availability of agricultural land, groundwater recharge, etc. Furthermore, the flow values that may appear over n‐year frequency on the curves are calculated by taking into consideration the Gamma cumulative probability distribution function. For the study area with applications Görele River, Turkey, flow measurements are used and the necessary conclusions are derived. As a result, the comparison for high and low values separately present significant information so that monotonically decreasing trend are generally observed for high values (wet periods) and non‐monotonically increasing trend for low values (drought periods).

Frequency analysis of low flows in intermittent and non-intermittent rivers from hydrological basins in Turkey

Abstract This study attempts to find out the best-fit probability distribution function to low flows using the up-to-date data of intermittent and non-intermittent rivers in four hydrological basins from different regions in Turkey. Frequency analysis of D = 1-, 7-, 14-, 30-, 90- and 273-day low flows calculated from the daily flow time series of each stream gauge was performed. Weibull (W2), Gamma (G2), Generalized Extreme Value (GEV) and Log-Normal (LN2) are selected among the 2-parameter probability distribution functions together with the Weibull (W3), Gamma (G3) and Log-Normal (LN3) from the 3-parameter probability distribution function family. Selected probability distribution functions are checked for their suitability to fit each D-day low flow sequence. LN3 mostly conforms to low flows by being the best-fit among the selected probability distribution functions in three out of four hydrological basins while W3 fits low flows in one basin. With the use of the best-fit probability distribution function, the low flow-duration-frequency curves are determined, which have the ability to provide the end-users with any D-day low flow discharge of any given return period.