Annual Flow Duration Curves Research Articles

Advancing low-flow quantile estimation: The role of areal scale factor (ASF) and annual flow–duration curves

Abstract Estimating the streamflow corresponding to a particular probability is of great importance in many hydrological studies, such as determining hydroelectric water potential, assessing water quality, and investigating sedimentation and drought. This paper aims to effectively estimate low-flow quantiles since hydrologic droughts motivate the study. The study illustrates a methodology, where droughts are characterized by the lower part of the flow–duration curve (FDC), and offers a perspective estimating low-flow quantiles related to the basin characteristics. Low-flow quantiles are derived both from traditional FDCs curves and median annual FDCs (AFDCs). As an innovation, the concept of areal scale factor, which represents a scaling ratio between the basin area and flow quantiles, was introduced. Unlike many other parametric approaches, this study models the streamflow quantiles depending on the basin characteristics instead of the parameters in the analytical equation of FDCs. The methodology was evaluated for the Western and Southwestern Anatolia regions in Turkey. The outcomes were compared for two types of FDCs in two regions. The approach gave similar results for both study regions. AFDCs provided a distinct advantage over traditional FDCs, especially for low-flow quantiles, due to the superiority of AFDCs in estimating streamflow quantiles of intermittent streams.

A graphical non-parametric hydrologic alteration test using flow duration curves

ABSTRACT Utilizing annual flow duration curves (FDCs), the modified Mood’s median test (MMMT) was applied to quantiles of the median annual FDCs at 122 disturbed sites in the conterminous US. A simple graphical tool based on the MMMT was combined with a false discovery rate multiple comparison procedure to illustrate the field significance of hydrologic alteration over a wide range of streamflow conditions. Hydrologic disturbance was mostly caused by dams, although other forms of alteration were explored. In addition, 249 minimally regulated Hydro-Climatic Data Network (HCDN) sites were investigated to assess regional climatic drivers of hydrologic alteration. Results indicate that dams can have varying effects on the hydrologic regime, but generally impact low flows more often than high flows in the US. At HCDN sites, we observe significant changes to hydrologic regimes in many regions, especially to low and median flows in the upper midwestern and eastern US.

Numerical design and optimization of a hydraulic micro-turbine adapted to a wastewater treatment plant

Wastewater Treatment Plants (WWTPs) are considered as an Ultra Low Head (ULH) hydraulic resource. This has provoked an inadequate extraction of its potential energy by Micro Hydroelectric Plants (MHP) due to the improper relationship between the size and performance of the turbine. Thus, this work proposes the optimized design of a turbine composed of an intake-runner-diffuser, which looks for the maximum energy extraction from this kind of hydraulic resource. The annual Flow Duration Curve (FDC) of a WWTP effluent was examined to determine the flow rate with which the maximal available energy could be extracted through an adequate runner design. A 3D computational model of the intake-runner-diffuser was optimized by coupling a Computational Fluid Dynamics (CFD) software with a Multi Island Genetic Algorithm, while the pressure and flow field of the selected cases were qualitative and quantitatively analyzed. It was found that with the lowest Reaction Degree (RD), a propeller turbine reached its highest efficiency and pressure ratio coefficient, extracting 76% of the annual available energy of the hydraulic resource. In this way, the maximal exploitation of a ULH resource through the turbine design of the MHP system instead of adapting turbines from Large Hydropower Plants (LHP) could help to establish an actual and attractive project cost-benefit ratio.

River runoff components change variably and respond differently to climate change in the Eurasian Arctic and Qinghai-Tibet Plateau permafrost regions

Cryohydrological processes in the Eurasian Arctic and Qinghai-Tibet Plateau (QTP) permafrost regions have been changing rapidly, yet the details of the river runoff changes are still obscure. Here we use multidecadal natural daily discharge data to compute annual flow duration curves (FDCs) and percentile flows for 20 Eurasian Arctic and QTP river basins with permafrost underlain. We provide detailed trends of various percentile flows that almost all runoff components change variably, either with the distinct magnitude or opposite direction or both. We demonstrate that the lower flows increase monotonically faster than higher flows. Most low flows increase while the high flows show spatial heterogeneity with both increased and decreased trends observed. The portion of deep and total groundwater flow in total discharge increases, with the deep groundwater flow increases faster. Interestingly, the river runoff components respond differently to climatic change factors. The low flows, mainly sustained by groundwater, are more sensitive to warming than high flows, while the high flows are more sensitive to precipitation than low flows. Our results may suggest an increased subsurface hydrological connectivity under the warming climate and thawing permafrost. We show that FDCs have the potential to reveal the long-term runoff components change. Future climatic change may alter the shapes and distributions of FDCs since the asynchronous changes of runoff components, which have important implications for cold region river management and mitigation under climatic change.

Regional Modeling of Long-Term and Annual Flow Duration Curves: Reliability for Information Transfer with Evolutionary Polynomial Regression

AbstractThe estimation of long-term flow duration curves (FDC) and annual flow duration curves (AFDC) are frequently required for water resources planning and management at ungauged catchments. The...

Operating Small Hydropower Plants in Greece under Intermittent Flow Uncertainty: The Case of Tsiknias River (Lesvos)

In arid and semi-arid parts of the world, river exploitation is intensive, involving water storage for irrigation or hydropower generation. In Greece, 100 small hydropower plants (SHPs) take advantage of less than 10% of the hydropower potential of low flow streams (<2 m3/s), a very small amount in relation to the 70% of the European Union. The energy policy of complete decarbonization of the country by 2023 on a national scale opens the road for new investments in SHP projects, especially in intermittent-flow streams of the Greek islands. Simulated flows by the Modello Idrologico SemiDistribuito in continuo (MISDc model) are used to construct the annual flow duration curve (FDC) to study and assess the hydropower potential of an intermittent stream (Tsiknias river, Lesvos, Greece). For Tsiknias River, but also for six other intermittent-flow rivers of Crete island, the capacity factor (CF), which represents the mean annual power of the hydropower plant, should remain >75% to exploit the river’s potential. The FDC and CF are essential in designing SHP projects in intermittent-flow streams with long no-flow periods. The development of public participatory approaches and a closer cooperation among policy makers and stakeholders should work to promote hydropower exploitation and accelerate licensing procedures.

Future shifts in extreme flow regimes in Alpine regions

Abstract. Extreme low and high flows can have negative economic, social, and ecological effects and are expected to become more severe in many regions due to climate change. Besides low and high flows, the whole flow regime, i.e., annual hydrograph comprised of monthly mean flows, is subject to changes. Knowledge on future changes in flow regimes is important since regimes contain information on both extremes and conditions prior to the dry and wet seasons. Changes in individual low- and high-flow characteristics as well as flow regimes under mean conditions have been thoroughly studied. In contrast, little is known about changes in extreme flow regimes. We here propose two methods for the estimation of extreme flow regimes and apply them to simulated discharge time series for future climate conditions in Switzerland. The first method relies on frequency analysis performed on annual flow duration curves. The second approach performs frequency analysis of the discharge sums of a large set of stochastically generated annual hydrographs. Both approaches were found to produce similar 100-year regime estimates when applied to a data set of 19 hydrological regions in Switzerland. Our results show that changes in both extreme low- and high-flow regimes for rainfall-dominated regions are distinct from those in melt-dominated regions. In rainfall-dominated regions, the minimum discharge of low-flow regimes decreases by up to 50 %, whilst the reduction is 25 % for high-flow regimes. In contrast, the maximum discharge of low- and high-flow regimes increases by up to 50 %. In melt-dominated regions, the changes point in the other direction than those in rainfall-dominated regions. The minimum and maximum discharges of extreme regimes increase by up to 100 % and decrease by less than 50 %, respectively. Our findings provide guidance in water resource planning and management and the extreme regime estimates are a valuable basis for climate impact studies. Highlights Estimation of 100-year low- and high-flow regimes using annual flow duration curves and stochastically simulated discharge time series Both mean and extreme regimes will change under future climate conditions. The minimum discharge of extreme regimes will decrease in rainfall-dominated regions but increase in melt-dominated regions. The maximum discharge of extreme regimes will increase and decrease in rainfall-dominated and melt-dominated regions, respectively.

On the Effect of Nonlinear Recessions on Low Flow Variability: Diagnostic of an Analytical Model for Annual Flow Duration Curves

AbstractPredicting the proportion of the water year a given stream will remain at or above various flow thresholds is critically important for making sound water management decisions. Flow duration curves (FDCs) succinctly capture this information using all data available over some historical period, while annual flow duration curves (AFDCs) instead use data from each individual water year. Analyzing the population of AFDCs, and in particular the tails of this distribution, can allow water managers to better prepare for years with extreme streamflow conditions. However, long time series of observations are necessary to capture interannual streamflow variations and are problematic to obtain in rapidly changing and poorly gauged catchments. By incorporating a process‐based model to construct AFDCs based on daily rainfall statistics and flow recession characteristics, the proposed approach is a first step toward addressing this challenge. Results indicate that prediction performance varies substantially across flow quantiles and that the current model fails to properly capture the interannual variability of low flows. Numerical analyses attributed these errors to nonlinearity in storage‐discharge relation, rather than cross‐scale streamflow correlations and non‐Poissonian rainfall, explaining the origin of commonly observed heavy‐tailed behavior in low flow quantiles. We present a case study on hydroelectric power generation, showing that faithfully capturing both interannual streamflow variability and recession nonlinearity has important implications for installation profitability.

Annual flow duration curve model for ungauged basins

AbstractA flow duration curve (FDC) plots the percentage of time that flow in a stream is equal to or exceeding a given value. In a gauged basin, it is obtained by sorting the observed flow from the largest to the smallest, and plotting against the corresponding exceedance probability. At ungauged basins where no data exist, the need for developing empirical methods emerges. This study aims at developing an FDC model for ungauged basins. The model is based on the normalized nondimensional annual mean flow quantiles. The annual mean flow is empirically calculated by a regression equation that takes drainage area and annual precipitation as input. Slope of the channel is additionally considered in the regression, however no better performance is achieved. Seyhan and Ceyhan basins in the Mediterranean region in southern Turkey are chosen as the study area. Data from 109 gauging stations are used for the calibration and validation of the model. Gauging stations on the tributaries are studied with a view to limiting anthropogenic activities on the rivers. Results of the application are found so promising that the model can be considered a good foundation for the development of FDCs at ungauged basins.

On the probability distribution of daily streamflow in the United States

Abstract. Daily streamflows are often represented by flow duration curves (FDCs), which illustrate the frequency with which flows are equaled or exceeded. FDCs have had broad applications across both operational and research hydrology for decades; however, modeling FDCs has proven elusive. Daily streamflow is a complex time series with flow values ranging over many orders of magnitude. The identification of a probability distribution that can approximate daily streamflow would improve understanding of the behavior of daily flows and the ability to estimate FDCs at ungaged river locations. Comparisons of modeled and empirical FDCs at nearly 400 unregulated, perennial streams illustrate that the four-parameter kappa distribution provides a very good representation of daily streamflow across the majority of physiographic regions in the conterminous United States (US). Further, for some regions of the US, the three-parameter generalized Pareto and lognormal distributions also provide a good approximation to FDCs. Similar results are found for the period of record FDCs, representing the long-term hydrologic regime at a site, and median annual FDCs, representing the behavior of flows in a typical year.

Spatially-smooth regionalization of flow duration curves in non-pristine basins

Abstract. The flow duration curve (FDC) is a fundamental signature of the hydrological cycle to support water management strategies. Despite many studies on this topic, its estimation in ungauged basins is still a relevant issue as the FDC is controlled by different types of processes at different time-space scales, thus resulting quite sensitive to the specific case study. In this work, a regional spatially-smooth procedure to evaluate the annual FDC in ungauged basins is proposed, based on the estimation of the L-moments (mean, L-CV and L-skewness) through regression models valid for the whole case study area. In this approach, homogeneous regions are no longer required and the L-moments are allowed to continuously vary along the river network, thus providing a final FDC smoothly evolving for different locations on the river. Regressions are based on a set of topographic, climatic, land use and vegetation descriptors at the basin scale. Moreover, the model ensures that the mean annual runoff is preserved at the river confluences, i.e. the sum of annual flows of the upstream reaches is equal to the predicted annual downstream flow. The proposed model is adapted to incorporate different "sub-models" to account for local information within the regional framework, where man-induced alterations are known, as common in non-pristine catchments. In particular, we propose a module to consider the impact of existing/designed water withdrawals on the L-moments of the FDC. The procedure has been applied to a dataset of daily observation of about 120 gauged basins on the upper Po river basin in North-Western Italy.

Hypothesis tests for hydrologic alteration

Summary Hydrologic systems can be altered by anthropogenic and climatic influences. While there are a number of statistical frameworks for describing and evaluating the extent of hydrologic alteration, here we present a new framework for assessing whether statistically significant hydrologic alteration has occurred, or whether the shift in the hydrologic regime is consistent with the natural variability of the system. Four hypothesis tests based on shifts of flow duration curves (FDCs) are developed and tested using three different experimental designs based on different strategies for resampling of annual FDCs. The four hypothesis tests examined are the Kolmogorov–Smirnov (KS), Kuiper (K), confidence interval (CI), and ecosurplus and ecodeficit (Eco). Here 117 streamflow sites that have potentially undergone hydrologic alteration due to reservoir construction are examined. 20 years of pre-reservoir record is used to develop the critical value of the test statistic for type I errors of 5% and 10%, while 10 years of post-alteration record is used to examine the power of each test. The best experimental design, based on calculating the mean annual FDC from an exhaustive jackknife resampling regime, provided a larger number of unique values of each test statistic and properly reproduced type I errors. Of the four tests, the CI test consistently had the highest power, while the K test had the second highest power; KS and Eco always had the lowest power. The power of the CI test appeared related to the storage ratio of the reservoir, a rough measure of the hydrologic alteration of the system.

Increased dry season water yield in burned watersheds in Southern California

The current work evaluates the effects of the 2003 Old Fire on semi-arid systems in the San Bernardino Mountains, California. Pre- and post-fire daily streamflow are used to analyze flow regimes in two burned watersheds. The average pre-fire runoff ratios in Devil Canyon and City Creek are 0.14 and 0.26, respectively, and both increase to 0.34 post-fire. Annual flow duration curves are developed for each watershed and the low flow is characterized by a 90% exceedance probability threshold. Post-fire low flow is statistically different from the pre-fire values (α = 0.05). In Devil Canyon the annual volume of pre-fire low flow increases on average from 2.6E + 02 to 3.1E + 03 m3 (1090% increase) and in City Creek the annual low flow volume increases from 2.3E + 03 to 5.0E + 03 m3 (118% increase). Predicting burn system resilience to disturbance (anthropogenic and natural) has significant implications for water sustainability and ultimately may provide an opportunity to utilize extended and increased water yield.

Annual flow duration curves assessment in ephemeral small basins

Flow duration curve (FDC) represents a comprehensive signature of temporal runoff variability often used to synthesize catchment rainfall–runoff responses. A new model, the ModABa (MODel for Annual flow duration curves assessment in ephemeral small BAsins), is here introduced. It can be thought as a wide mosaic whose tesserae are frameworks, models or conceptual schemes separately developed in different studies and harmoniously interconnected with the final aim of reproducing the annual FDC in intermittent small catchments. Two separated seasons within the hydrological year are distinguished: a dry season, characterized by absence of streamflow, and a non-zero season. Streamflow is disaggregated into a subsurface component and a surface component that, in turn, is considered formed by two different contributions: impervious runoff and surface runoff from permeable areas induced by heavy rains. The FDCs of the two streamflow components are first separately and differently computed, and then combined to obtain the non-zero FDC. This last, together with the estimated probability of null streamflow, allows the annual FDC assessment through the theory of total probability. The ModABa is here tested on a small Italian catchment and the results show how the model, once calibrated, is able to accurately reproduce the empirical FDC for the analyzed case, starting from easily derivable parameters and commonly available climatic data. In this sense, the model reveals itself as a valid tool, potentially suitable for predictions at ungauged basins in a regionalization framework.

A New Application of Flow Duration Curve (FDC) in Designing Run-of-River Power Plants

The present study evaluates the effects of river run-off regime and hydrological uncertainty on the hydroelectric production of a run-of-river power plant. The mean annual energy from a plant was modeled as a function of run-off regime and design flow, by means of a procedure developed on the mean annual Flow Duration Curves (FDCs) of 15 sample basins in the Umbria Region (Central Italy). Results show that energy output decreases from constant to torrential regimes, following a potential function, and that, the greater the design flow, the greater the rate of decrease. The treatment and validation of these results provided a useful tool for easy identification of optimal design flow, according to the hydrological features of the basin and the target hydroelectric production at the station. Analyses of FDCs with a 20-year return period also showed that the decrease in energy production in dry years and its increase in wet years, compared with the mean annual value, are linearly linked to the design flow. In the present context of possible climate change, this result is presented as the possibility of partially controlling the effects of positive or negative flow rate trends. The results reported here can be applied to any kind of river and hydraulic technology at the power station.

A STOCHASTIC INDEX METHOD FOR CALCULATING ANNUAL FLOW DURATION CURVES IN INTERMITTENT RIVERS

ABSTRACTFlow duration curves are useful tools to estimate available surface water resources, at the basin scale. These represent the percentage of time during which discharge values are exceeded, irrespective of their temporal sequence. Annual flow duration curves are useful tools for evaluating all flow quantiles of a river and their confidence intervals, by removing the effects of variability from year to year. However, these tools fail to represent the hydrological regime of ephemeral rivers, since they cannot account for zero flows. In this work we propose a technique for calculating annual flow duration curves and their standard deviation in the case of intermittent rivers. In particular, we propose a generalization of the stochastic index method, in which we use the concept of total probability and order statistics. The method is proposed to determine the conditional distribution of positive flows, for given probability of dryness, and is implemented on three catchments in Italy and Greece, with low (<5%) and high (>40%) frequency of zero flows, respectively. Copyright © 2013 John Wiley & Sons, Ltd.

Research Spotlight: New analysis can better anticipate the likelihood of flood occurrence

To manage freshwater resources, communities need information on how likely the volume of flow for a river or stream will equal or exceed a certain value of interest. Such information, for example, helps engineers know how much water to release into dams' spillways, guides urban planners in anticipating flash floods, and provides scientists with information on how changing precipitation patterns may influence flood frequency. Central to gaining these insights are flow duration curves (FDCs), which help to quantify the likelihood that streamflow will be greater than a specific level. Traditional period‐of‐record FDCs are a representation of the entire record of observation of a particular stream, whereas annual FDCs yield a picture on an annual basis. Serinaldi shows that both FDCs and annual FDCs can be complemented with confidence intervals based on a unique theoretical framework, which confirms the dual nature of the two approaches.

Analytical confidence intervals for index flow flow duration curves

This study illustrates how analytical period‐of‐record flow duration curves (FDCs) and annual FDCs (AFDCs) of daily streamflow series developed in an index flow framework can be complemented by theoretical confidence intervals (CIs) deduced from the theory of nonparametric CIs for quantiles and fractional order statistics. By focusing on AFDCs, the proposed approach yields results very close to CIs for order statistics which are commonly used to construct AFDCs and CIs for AFDCs. When the method is applied to index flow FDCs, the comparison with Monte Carlo techniques allows the elucidation of some properties of FDCs which have not been previously explored in depth. The approach helps to overcome the problem of lack of CIs for index flow FDCs by introducing approximate analytical CIs based on an effective sample size. Thus, the underlying idea is emphasized that CIs of index flow FDCs and AFDCs can be coherently obtained by reasoning in terms of distribution of quantiles rather than distribution of order statistics. Moreover, a few results taken from nonparametric statistics allow the introduction of semiparametric index flow FDCs and AFDCs which are potentially useful for parsimonious regionalization procedures.

The uncertainty effects of design flow on water quality management

In water quality management, pollution control strategies have been sought to accord with the assimilative capacity of water bodies so as to preserve water quality. The waste load allocation (WLA) is a useful approach to determine the allowable loading of pollution sources in water quality management. For any WLA, a particular water body condition is needed as a basic scenario under which the relevant parameters are fixed. The particular flow rate is known as design flow and usually set at low flow in order to be protective. The design flow is traditionally a particular deterministic value, such as Q (75), implying that it is expected that the probability of water quality violation is 25% in the long run. However, this long-term expectation might not be realized in individual years due to variability of natural flow. The flow variability will make a WLA plan overoptimistic or over-conservative in different years, suggesting that the deterministic design flow without uncertainty consideration might lead to an ineffective or inefficient decision-making. To address the problem, we explicate the relationship between flow variability, design flow and water quality with different flow distributions to facilitate the understanding of the process of a WLA. In order to manifest the uncertainty effects of design flow, the results from the annual flow duration curve (AFDC) is compared with the conventional flow duration curve (FDC). The AFDC approach is capable of obtaining the uncertainty level of the design flow by generating the confidence interval rather than a fixed value. The effect of different record lengths on design flow determination is estimated as well. Finally, a refined WLA process is proposed with a re-examination of water quality violation to improve the allocation decision under uncertainty. TaHan River Basin in northern Taiwan is used as a case study.

Predicting annual and long-term flow-duration curves in ungauged basins

The construction of flow-duration curves is a fundamental task for several activities related to water resources management. The scarcity of observed streamflow data is a diffuse problem in the real world, and flow-duration curves often need to be constructed for ungauged basins. We address this problem by regionalising the stochastic index-flow model of flow-duration curves proposed by Castellarin et al. [Castellarin A, Vogel RM, Brath A. A stochastic index flow model of flow-duration curves. Water Resour Res 2004;40:W03104. doi:10.1029/2003WR002524]. The index-flow model differs from any other stochastic model of flow-duration curves proposed in the literature because it can be used for deriving long-term as well as annual flow-duration curves. The former are constructed on the basis of several years of streamflow data, whereas the latter refer to a given water or calendar year (a typical hydrologic year or a particularly wet or dry year). We apply an extensive cross-validation procedure to quantify the uncertainty of the proposed regional model and to compare it with the uncertainty of traditional regional models of flow-duration curves proposed in the literature. The results of the study indicate that the regional index-flow model is as reliable as or more reliable than traditional regional models for estimating long-term flow-duration curves. Also, the proposed model is more versatile than previous regional models as it can be used for estimating long-term and annual flow-duration curves and for reproducing the variance of annual flow-duration curves.