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

Abstract. The paper reports on a four-pronged study of the physical controls on regional patterns of the flow duration curve (FDC). This involved a comparative analysis of long-term continuous data from nearly 200 catchments around the US, encompassing a wide range of climates, geology, and ecology. The analysis was done from three different perspectives – statistical analysis, process-based modeling, and data-based classification – followed by a synthesis, which is the focus of this paper. Streamflow data were separated into fast and slow flow responses, and associated signatures, and both total flow and its components were analyzed to generate patterns. Regional patterns emerged in all aspects of the study. The mixed gamma distribution described well the shape of the FDC; regression analysis indicated that certain climate and catchment properties were first-order controls on the shape of the FDC. In order to understand the spatial patterns revealed by the statistical study, and guided by the hypothesis that the middle portion of the FDC is a function of the regime curve (RC, mean within-year variation of flow), we set out to classify these catchments, both empirically and through process-based modeling, in terms of their regime behavior. The classification analysis showed that climate seasonality and aridity, either directly (empirical classes) or through phenology (vegetation processes), were the dominant controls on the RC. Quantitative synthesis of these results determined that these classes were indeed related to the FDC through its slope and related statistical parameters. Qualitative synthesis revealed much diversity in the shapes of the FDCs even within each climate-based homogeneous class, especially in the low-flow tails, suggesting that catchment properties may have become the dominant controls. Thus, while the middle portion of the FDC contains the average response of the catchment, and is mainly controlled by climate, the tails of the FDC, notably the low-flow tails, are mainly controlled by catchment properties such as geology and soils. The regime behavior explains only part of the FDC; to gain a deeper understanding of the physical controls on the FDC, these extremes must be analyzed as well. Thus, to completely separate the climate controls from the catchment controls, the roles of catchment properties such as soils, geology, topography etc. must be explored in detail.

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Classifying low flow hydrological regimes at a regional scale

Hydrology and Earth System Sciences ◽

10.5194/hess-15-3741-2011 ◽

2011 ◽

Vol 15 (12) ◽

pp. 3741-3750 ◽

Cited By ~ 21

Author(s):

M. J. Kirkby ◽

F. Gallart ◽

T. R. Kjeldsen ◽

B. J. Irvine ◽

J. Froebrich ◽

...

Keyword(s):

Regional Scale ◽

Low Flow ◽

Balance Model ◽

Hydraulic Geometry ◽

Climate Data ◽

Cross Sectional ◽

Flow Duration ◽

River Bed ◽

Climatic Scenarios ◽

Flow Duration Curves

Abstract. The paper uses a simple water balance model that partitions the precipitation between actual evapotranspiration, quick flow and delayed flow, and has sufficient complexity to capture the essence of climate and vegetation controls on this partitioning. Using this model, monthly flow duration curves have been constructed from climate data across Europe to address the relative frequency of ecologically critical low flow stages in semi-arid rivers, when flow commonly persists only in disconnected pools in the river bed. The hydrological model is based on a dynamic partitioning of precipitation to estimate water available for evapotranspiration and plant growth and for residual runoff. The duration curve for monthly flows has then been analysed to give an estimate of bankfull flow based on recurrence interval. Arguing from observed ratios of cross-sectional areas at flood and low flows, hydraulic geometry suggests that disconnected flow under "pool" conditions is approximately 0.1% of bankfull flow. Flow duration curves define a measure of bankfull discharge on the basis of frequency. The corresponding frequency for pools is then read from the duration curve, using this (0.1%) ratio to estimate pool discharge from bank full discharge. The flow duration curve then provides an estimate of the frequency of poorly connected pool conditions, corresponding to this discharge, that constrain survival of river-dwelling arthropods and fish. The methodology has here been applied across Europe at 15 km resolution, and the potential is demonstrated for applying the methodology under alternative climatic scenarios.

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Geostatistical prediction of flow-duration curves

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-10-13053-2013 ◽

2013 ◽

Vol 10 (11) ◽

pp. 13053-13091 ◽

Cited By ~ 3

Author(s):

A. Pugliese ◽

A. Castellarin ◽

A. Brath

Keyword(s):

Cross Validation ◽

Central Italy ◽

Weighted Average ◽

Low Flow ◽

Mean Annual Precipitation ◽

Ungauged Catchments ◽

Study Region ◽

Daily Streamflow ◽

Flow Duration ◽

Flow Duration Curves

Abstract. We present in this study an adaptation of Topological kriging (or Top-kriging), which makes the geostatistical procedure capable of predicting flow-duration curves (FDCs) in ungauged catchments. Previous applications of Top-kriging mainly focused on the prediction of point streamflow indices (e.g. flood quantiles, low-flow indices, etc.). In this study Top-kriging is used to predict FDCs in ungauged sites as a weighted average of standardised empirical FDCs through the traditional linear-weighting scheme of kriging methods. Our study focuses on the prediction of period-of-record FDCs for 18 unregulated catchments located in Central Italy, for which daily streamflow series with length from 5 to 40 yr are available, together with information on climate referring to the same time-span of each daily streamflow sequence. Empirical FDCs are standardised by a reference streamflow value (i.e. mean annual flow, or mean annual precipitation times the catchment drainage area) and the overall deviation of the curves from this reference value is then used for expressing the hydrological similarity between catchments and for deriving the geostatistical weights. We performed an extensive leave-one-out cross-validation to quantify the accuracy of the proposed technique, and to compare it to traditional regionalisation models that were recently developed for the same study region. The cross-validation points out that Top-kriging is a reliable approach for predicting FDCs, which can significantly outperform traditional regional models in ungauged basins.

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Exploring the physical controls of regional patterns of flow duration curves – Part 4: A synthesis of empirical analysis, process modeling and catchment classification

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-9-7131-2012 ◽

2012 ◽

Vol 9 (6) ◽

pp. 7131-7180 ◽

Cited By ~ 5

Author(s):

M. Yaeger ◽

E. Coopersmith ◽

S. Ye ◽

L. Cheng ◽

A. Viglione ◽

...

Keyword(s):

Low Flow ◽

Middle Portion ◽

Qualitative Synthesis ◽

Statistical Parameters ◽

Regional Patterns ◽

Flow Duration ◽

Analysis Process ◽

Wide Range ◽

Physical Controls ◽

Flow Duration Curves

Abstract. The paper reports on a four-pronged study of the physical controls on regional patterns of the Flow Duration Curve (FDC). This involved a comparative analysis of long-term continuous data from nearly 200 catchments around the US, encompassing a wide range of climates, geology and ecology. The analysis was done from three different perspectives – statistical analysis, process-based modeling, and data-based classification, followed by a synthesis, which is the focus of this paper. Streamflow data was separated into fast and slow flow responses, and associated signatures, and both total flow and its components were analyzed to generate patterns. Regional patterns emerged in all aspects of the study. The mixed gamma distribution described well the shape of the FDC; regression analysis indicated that certain climate and catchment properties were first order controls on the shape of the FDC. In order to understand the spatial patterns revealed by the statistical study, and guided by the hypothesis that the middle portion of the FDC is a function of the regime curve (RC, mean within year variation of flow), we set out to classify these catchments, both empirically and through process-based modeling, in terms of their regime behavior. The classification analysis showed that climate seasonality and aridity, either directly (empirical classes) or through phenology (vegetation processes), were the dominant controls on the RC. Quantitative synthesis of these results determined that these classes were indeed related to the FDC through its slope and related statistical parameters. Qualitative synthesis revealed much diversity in the shapes of the FDCs even within each climate-based homogeneous class, especially in the low-flow tails, suggesting that catchment properties may have become the dominant controls. Thus, while the middle portion of the FDC contains the average response of the catchment, and is mainly controlled by climate, the tails of the FDC, notably the low-flow tails, are mainly controlled by catchment properties such as geology and soils. The regime behavior explains only part of the FDC; to gain a deeper understanding of the physical controls on the FDC, these extremes must be analyzed as well. Thus, to completely separate the climate controls from the catchment controls, the roles of catchment properties such as soils, geology, topography etc., must be explored in detail.

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Analytical model for flow duration curves in seasonally dry climates

Water Resources Research ◽

10.1002/2014wr015301 ◽

2014 ◽

Vol 50 (7) ◽

pp. 5510-5531 ◽

Cited By ~ 45

Author(s):

Marc F. Müller ◽

David N. Dralle ◽

Sally E. Thompson

Keyword(s):

Analytical Model ◽

Seasonally Dry ◽

Flow Duration ◽

Flow Duration Curves ◽

Dry Climates

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Analytical flow duration curves for summer streamflow in Switzerland

Hydrology and Earth System Sciences ◽

10.5194/hess-22-2377-2018 ◽

2018 ◽

Vol 22 (4) ◽

pp. 2377-2389 ◽

Cited By ~ 6

Author(s):

Ana Clara Santos ◽

Maria Manuela Portela ◽

Andrea Rinaldo ◽

Bettina Schaefli

Keyword(s):

Linear Model ◽

Nonlinear Model ◽

Low Flow ◽

Model Parameters ◽

Modeling Framework ◽

Data Set ◽

Flow Duration ◽

Daily Precipitation Data ◽

Wide Range ◽

Flow Duration Curves

Abstract. This paper proposes a systematic assessment of the performance of an analytical modeling framework for streamflow probability distributions for a set of 25 Swiss catchments. These catchments show a wide range of hydroclimatic regimes, including namely snow-influenced streamflows. The model parameters are calculated from a spatially averaged gridded daily precipitation data set and from observed daily discharge time series, both in a forward estimation mode (direct parameter calculation from observed data) and in an inverse estimation mode (maximum likelihood estimation). The performance of the linear and the nonlinear model versions is assessed in terms of reproducing observed flow duration curves and their natural variability. Overall, the nonlinear model version outperforms the linear model for all regimes, but the linear model shows a notable performance increase with catchment elevation. More importantly, the obtained results demonstrate that the analytical model performs well for summer discharge for all analyzed streamflow regimes, ranging from rainfall-driven regimes with summer low flow to snow and glacier regimes with summer high flow. These results suggest that the model's encoding of discharge-generating events based on stochastic soil moisture dynamics is more flexible than previously thought. As shown in this paper, the presence of snowmelt or ice melt is accommodated by a relative increase in the discharge-generating frequency, a key parameter of the model. Explicit quantification of this frequency increase as a function of mean catchment meteorological conditions is left for future research.

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Applying Weibull distribution and Low Flow Frequency Curves for minimum flow prediction in an ungagged stream in Connecticut, New England

10.53902/gsres.2021.01.000520 ◽

2021 ◽

Vol 1 (4) ◽

Author(s):

Juan M Stella

Keyword(s):

Weibull Distribution ◽

New England ◽

Low Flow ◽

Distribution Model ◽

Flow Duration ◽

Low Flows ◽

Flow Prediction ◽

Flow Duration Curves ◽

Three Rivers ◽

Thames River

The necessity to conduct hydrological studies for water resources management, infrastructure design and, ecosystems protection can help mitigate flood and drought hazards. Prediction of low flows remains an important task for water management and ecosystems protection that can affect streams during low-flow periods. There have been many approaches to low flow prediction applying either statistical or deterministic methods, but there has not been any successful approach to link low flows between similar watersheds yet. The Fenton, Natchaug and Mount Hope Rivers watersheds are neighbors and are the major streams that discharge into the Mansfield Hollow Lake that belongs to the Thames River watershed, located in Northeast of the State of Connecticut in USA. A study to determine whether and how water withdrawals from the University’s Fenton River water supply wells affect the fisheries habitat of the Fenton River adjacent to the well field was conducted for four years at the beginning of 2002. The Mount Hope River was the only river with a long record of daily discharges available since the year 1940, meanwhile the Fenton and Natchaug River remained ungagged until the year 2006. This research developed and tested two mathematical models for the prediction of minimum discharges in the Fenton and Natchaug Rivers with the discharges available from the Mount Hope River. Yearly Low Flow Duration Curves (LFFC) and Weibull distribution methods were applied to the three rivers to predict the low flows in the Fenton and Natchaug Rivers taking as input the minimum flows and dates in the Mount Hope River. The results found that the Weibull distribution model showed a much better accuracy than the Low Flow Duration Curve method for the prediction of low flows discharges in the Fenton and Natchaug Rivers.

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