Refinement of a regression-based method for prediction of flow-duration curves of daily streamflow in the conterminous United States

The probability distribution of daily streamflow in the conterminous United States

10.5194/hess-2016-460 ◽

2016 ◽

Author(s):

Annalise G. Blum ◽

Richard M. Vogel ◽

Stacey A. Archfield

Keyword(s):

United States ◽

Probability Distribution ◽

Regression Models ◽

Probability Distributions ◽

Practical Method ◽

Daily Streamflow ◽

Flow Duration ◽

Generalized Pareto ◽

Flow Duration Curves

Abstract. One of the most commonly used tools in hydrology, empirical flow duration curves (FDCs) characterize the frequency with which streamflows are equaled or exceeded. Finding a suitable probability distribution to approximate a FDC enables regionalization and prediction of FDCs in basins that lack streamflow measurements. FDCs constructed from daily streamflow observations can be computed as the period-of-record FDC (POR-FDC) to represent long-term streamflow conditions or as the median annual FDC (MA-FDC) to represent streamflows in a typical year. The goal of this study is to identify suitable probability distributions for both POR-FDCs and MA-FDCs of daily streamflow for unregulated and perennial streams. Comparisons of modeled and empirical FDCs at over 400 unregulated stream gages across the conterminous United States reveal that both the four-parameter kappa (KAP) and three-parameter generalized Pareto (GPA3) distributions can provide reasonable approximations to MA-FDCs; however, even four and five-parameter distributions are unable to capture the complexity of the POR-FDC behavior for which flows often range over five or more orders of magnitude. Regional regression models developed for the mid-Atlantic and Missouri regions as case studies present a simple and practical method to predict MA-FDCs at ungaged sites, which can be accurately predicted more consistently compared to POR-FDCs.

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On the probability distribution of daily streamflow in the United States

Hydrology and Earth System Sciences ◽

10.5194/hess-21-3093-2017 ◽

2017 ◽

Vol 21 (6) ◽

pp. 3093-3103 ◽

Cited By ~ 26

Author(s):

Annalise G. Blum ◽

Stacey A. Archfield ◽

Richard M. Vogel

Keyword(s):

United States ◽

Probability Distribution ◽

The United States ◽

Good Representation ◽

Lognormal Distributions ◽

Daily Streamflow ◽

The Us ◽

Flow Duration Curves ◽

A Site ◽

Physiographic Regions

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.

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Bias correction of simulated historical daily streamflow at ungauged locations by using independently estimated flow duration curves

Hydrology and Earth System Sciences ◽

10.5194/hess-22-5741-2018 ◽

2018 ◽

Vol 22 (11) ◽

pp. 5741-5758 ◽

Cited By ~ 3

Author(s):

William H. Farmer ◽

Thomas M. Over ◽

Julie E. Kiang

Keyword(s):

Bias Correction ◽

Temporal Structure ◽

Daily Streamflow ◽

Flow Duration ◽

Regional Regression ◽

Daily Data ◽

Potential Efficacy ◽

Flow Duration Curves ◽

Future Work ◽

Streamflow Timing

Abstract. In many simulations of historical daily streamflow distributional bias arising from the distributional properties of residuals has been noted. This bias often presents itself as an underestimation of high streamflow and an overestimation of low streamflow. Here, 1168 streamgages across the conterminous USA, having at least 14 complete water years of daily data between 1 October 1980 and 30 September 2013, are used to explore a method for rescaling simulated streamflow to correct the distributional bias. Based on an existing approach that separates the simulated streamflow into components of temporal structure and magnitude, the temporal structure is converted to simulated nonexceedance probabilities and the magnitudes are rescaled using an independently estimated flow duration curve (FDC) derived from regional regression. In this study, this method is applied to a pooled ordinary kriging simulation of daily streamflow coupled with FDCs estimated by regional regression on basin characteristics. The improvement in the representation of high and low streamflows is correlated with the accuracy and unbiasedness of the estimated FDC. The method is verified by using an idealized case; however, with the introduction of regionally regressed FDCs developed for this study, the method is only useful overall for the upper tails, which are more accurately and unbiasedly estimated than the lower tails. It remains for future work to determine how accurate the estimated FDCs need to be to be useful for bias correction without unduly reducing accuracy. In addition to its potential efficacy for distributional bias correction, this particular instance of the methodology also represents a generalization of nonlinear spatial interpolation of daily streamflow using FDCs. Rather than relying on single index stations, as is commonly done to reflect streamflow timing, this approach to simulation leverages geostatistical tools to allow a region of neighbors to reflect streamflow timing.

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Comments on "Bias correction of simulated historical daily streamflow at ungauged locations by using independently estimated flow-duration curves"

10.5194/hess-2018-30-rc3 ◽

2018 ◽

Author(s):

Anonymous

Keyword(s):

Bias Correction ◽

Daily Streamflow ◽

Flow Duration ◽

Flow Duration Curves

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Climate and Landscape Controls of Regional Patterns of Flow Duration Curves Across the Continental United States: Statistical Approach

Water Resources Research ◽

10.1029/2020wr028041 ◽

2020 ◽

Vol 56 (11) ◽

Author(s):

Saba Ghotbi ◽

Dingbao Wang ◽

Arvind Singh ◽

Talea Mayo ◽

Murugesu Sivapalan

Keyword(s):

United States ◽

Statistical Approach ◽

Regional Patterns ◽

Flow Duration ◽

Flow Duration Curves

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Bias correction of Simulated Historical Daily Streamflow at Ungauged Locations by Using Independently Estimated Flow-Duration Curves

10.5194/hess-2018-30 ◽

2018 ◽

Author(s):

William H. Farmer ◽

Thomas M. Over ◽

Julie E. Kiang

Keyword(s):

Bias Correction ◽

Spatial Interpolation ◽

Daily Streamflow ◽

Flow Duration ◽

Distributional Properties ◽

Daily Data ◽

Potential Efficacy ◽

Flow Duration Curves ◽

Future Work ◽

Streamflow Timing

Abstract. In many simulations of historical daily streamflow distributional bias arising from the distributional properties of residuals, however small, has been noted. This bias often presents itself as an underestimation of high streamflow and an overestimation of low streamflow. Here, 1168 streamgages across the conterminous United States having at least 14 complete water years of daily data between October 01, 1980, and September 30, 2013, are used to explore a method for rescaling simulated streamflow to correct the distributional bias. Based on an existing approach that separates the simulated streamflow into components of timing and magnitude, the timing component is converted into simulated nonexceedance probabilities and rescaled to new volumes using an independently estimated flow-duration curve (FDC). In this study, this method is applied to a pooled ordinary kriging simulation of daily streamflow coupled with FDCs estimated by regional regression on basin characteristics. The improvement in the representation of high and low streamflows is correlated with the accuracy and unbiasedness of the estimated FDC. The method is verified by using an idealized case, though, with the introduction of regionally regressed FDCs developed for this study, the method is only useful overall for the upper tails, which are more accurately and unbiasedly estimated than the lower tails. It remains for future work to determine how accurate the estimated FDCs need to be to be useful for bias correction without unduly reducing accuracy. In addition to its potential efficacy for distributional bias correction, this methodology also represents a generalization of nonlinear spatial interpolation of daily streamflow using FDCs. Rather than relying on single index stations as is commonly done to reflect streamflow timing, this approach leverages geostatistical tools to allow a region of neighbors to reflect streamflow timing.

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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 2: Role of seasonality and associated process controls

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-9-7035-2012 ◽

2012 ◽

Vol 9 (6) ◽

pp. 7035-7084 ◽

Cited By ~ 6

Author(s):

S. Ye ◽

M. A. Yaeger ◽

E. Coopersmith ◽

L. Cheng ◽

M. Sivapalan

Keyword(s):

United States ◽

Vegetation Cover ◽

Model Complexity ◽

Mountain Range ◽

Regional Patterns ◽

Flow Duration ◽

The North ◽

Physical Controls ◽

Flow Duration Curves ◽

Process Controls

Abstract. The goal of this paper is to explore the process controls underpinning regional patterns of variations of runoff regime behavior, i.e., the mean seasonal variation of runoff within the year, across the continental United States. The ultimate motivation is to use the resulting process understanding to generate insights into the physical controls of Flow Duration Curves, in view of the close connection between these two alternative signatures of runoff variability. To achieve these aims a top-down modeling approach is adopted; we start with a simple two-stage bucket model, which is systematically enhanced through addition of new processes on the basis of model performance assessment in relation to observations, using rainfall-runoff data from 197 United States catchments belonging to the MOPEX dataset. Exploration of dominant processes and the determination of required model complexity are carried out through model-based sensitivity analyses, guided by a performance metric. Results indicated systematic regional trends in dominant processes: snowmelt was a key process control in cold mountainous catchments in the north and north-west, whereas snowmelt and vegetation cover dynamics were key controls in the north-east; seasonal vegetation cover dynamics (phenology and interception) were important along the Appalachian mountain range in the east. A simple two-bucket model (with no other additions) was found to be adequate in warm humid catchments along the west coast and in the south-east, with both regions exhibiting strong seasonality, whereas much more complex models are needed in the dry south and south-west. Agricultural catchments in the mid-west were found to be difficult to predict with the use of simple lumped models, due to the strong influence of human activities. Overall, these process controls arose from general east-west (seasonality) and north-south (aridity, temperature) trends in climate (with some exceptions), compounded by complex dynamics of vegetation cover and to a less extent by landscape factors (soils, geology and topography).

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