Distribution Models of Flow-Duration Quantiles for Streamgages

Dates

Start Date: 1950-01-01
End Date: 2009-12-31
Publication Date: 2021-02-25

Citation

Robinson, A.L., Asquith, W.H., Crowley-Ornelas, E.R., and Knight, R.R., 2021, Estimated quantiles of decadal flow-duration curves using selected probability distributions fit to no-flow fractions and L-moments predicted for streamgages and for pour points of level-12 hydrologic unit codes in the southeastern United States, 1950–2010: U.S. Geological Survey data release, https://doi.org/10.5066/P9MV8BYR.

Summary

Using previously published (Robinson and others, 2019) no-flow fractions and L-moments of nonzero streamflow from decadal streamflow flow-duration analysis (daily mean streamflow), probability distributions were fit to provide 27 estimated quantiles of decadal flow-duration curves, and hence the probability distributions are a form of parametric modeling that ensures monotonicity of the quantiles by non-exceedance probability (NEP). For both U.S. Geological Survey streamflow-gaging stations (streamgages) and level-12 hydrologic unit code (HUC12) catchments, as defined by Crowley-Ornelas and others (2019), the 27 quantiles were estimated and tabulated in this data release. Three probability distributions were used and are summarized [...]

Summary

Using previously published (Robinson and others, 2019) no-flow fractions and L-moments of nonzero streamflow from decadal streamflow flow-duration analysis (daily mean streamflow), probability distributions were fit to provide 27 estimated quantiles of decadal flow-duration curves, and hence the probability distributions are a form of parametric modeling that ensures monotonicity of the quantiles by non-exceedance probability (NEP). For both U.S. Geological Survey streamflow-gaging stations (streamgages) and level-12 hydrologic unit code (HUC12) catchments, as defined by Crowley-Ornelas and others (2019), the 27 quantiles were estimated and tabulated in this data release. Three probability distributions were used and are summarized by Asquith and others (2017): the asymmetric exponential power (AEP4) (4-parameter), generalized normal (GNO) (3-parameter log-normal), and kappa (KAP) (4-parameter). A summary of the mathematics for these distributions is provided in the README files within this data release and close consultation of the mathematical discussion in Asquith and others (2017) also is suggested. The lmomco R package (Asquith, 2020) was used for distribution fitting and the technically-demanding implementation for a single location is archived in the RESTORE/fdclmrpplo software release within file fdclmrpplo/scripts/pred_fdc_ref/pred_fdc_ref.R (Asquith and others, 2020). The implementation for the streamgages is archived in the RESTORE/fdclmrpplo software release within file fdclmrpplo/scripts/pred_fdc_gage/pred_fdc_gage.R, and the implementation for the HUC12s is archived file fdclmrpplo/scripts/pred_fdc_huc12/pred_fdc_huc12.R and README files therein. For a given data set of no-flow fraction and L-moments, the three distributions will have similar results in the central parts of NEP and differences will be largest in the far left (low flow) and far right (flood flow) tails. No opinion that a particular distribution is more suitable than another is provided with exception that the GNO is fit to the first three L-moments and the AEP4 and KAP are fit to the first four L-moments. As a result, it is logical to state that more information on the distribution of streamflow is retained by the AEP4 and KAP distributions than the GNO. The availability of three distributions with the data release is considered a feature because a semi-quantitative assessment of model error (uncertainty attributed to choice of model) can be made.

Asquith, W.H., 2020, lmomco—L-moments, censored L-moments, trimmed L-moments, L-comoments, and many distributions: R package version 2.3.6, https://CRAN.R-project.org/package=lmomco.

Asquith, W.H., Kiang, J.E., and Cohn, T.A., 2017, Application of at-site peak-streamflow frequency analyses for very low annual exceedance probabilities: U.S. Geological Survey Scientific Investigation Report 2017–5038, 93 p., https://doi.org/10.3133/sir20175038.

Asquith, W.H., Knight, R.R., and Crowley-Ornelas, E.R., 2020, RESTORE/fdclmrpplo—Source code for estimation of L-moments and percent no-flow conditions for decadal flow-duration curves and estimation at level-12 hydrologic unit codes along with other statistical computations: U.S. Geological Survey software release, Reston, Va., https://doi.org/10.5066/P93CKH92.

Crowley-Ornelas, E.R., Worland, S.C., Wieczorek, M.E., Asquith, W.H., Knight, R.R., 2019, Summary of basin characteristics for National Hydrography Dataset, version 2 catchments in the Southeastern United States, 1950–2010: U.S. Geological Survey data release, https://doi.org/10.5066/P9KXTDU4.

Robinson, A.L., Asquith, W.H., and Knight, R.R., 2019, Summary of decadal no-flow fractions and decadal L-moments of nonzero streamflow flow-duration curves for National Hydrography Dataset, version 2 catchments in the southeastern United States, 1950–2010: U.S. Geological Survey data release, https://doi.org/10.5066/P9Z4PM55.

Contacts

Originator :: Angela L Robinson, William H Asquith, Elena R Crowley-Ornelas, Rodney R Knight
Contact :: William H Asquith
Metadata Contact :: Angela L Robinson
Publisher :: U.S. Geological Survey - ScienceBase
Data Owner :: Lower Mississippi-Gulf Water Science Center
USGS Mission Area :: Water Resources
Distributor :: U.S. Geological Survey - ScienceBase

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Distribution Models of Flow-Duration Quantiles for Streamgages.xml Original FGDC Metadata	View	42.16 KB	application/fgdc+xml
all_gage_fdclmr_nnn.csv.zip		1.13 MB	application/zip
all_gage_fdclmr_nnn.feather.zip		1.55 MB	application/zip
README_gage_fdclmr.pdf		158.85 KB	application/pdf

Related External Resources

Type: Related Primary Publication

Crowley-Ornelas, E.R., Asquith, W.H., and Worland, S.C., 2023, Generalized additive model estimation of no-flow fractions and L-moments to support flow-duration curve quantile estimation using selected probability distributions for bay and estuary restoration in the Gulf States: U.S. Geological Survey Scientific Investigations Report 2022–5051, 35 p., https://doi.org/10.3133/sir20225051.	https://doi.org/10.3133/sir20225051

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The results are provided in two different formats— feather files and csv files— for the ease of the data user.

Distribution Models of Flow-Duration Quantiles for Streamgages

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