scholarly journals The probability distribution of daily streamflow in the conterminous United States

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.

scholarly journals On the probability distribution of daily streamflow in the United States

2017 ◽  
Vol 21 (6) ◽  
pp. 3093-3103 ◽  
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.

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

2007 ◽  
Vol 30 (4) ◽  
pp. 937-953 ◽  
Author(s):  
Attilio Castellarin ◽  
Giorgio Camorani ◽  
Armando Brath
Keyword(s):  
Ungauged Basins ◽  
Flow Duration ◽  
Flow Duration Curves

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

2018 ◽  
Vol 22 (11) ◽  
pp. 5741-5758 ◽  
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.

A Method Based on Taking the Average of Probabilities to Compute the Flow Duration Curve

2000 ◽  
Vol 31 (3) ◽  
pp. 187-206 ◽  
Author(s):  
Hikmet Kerem Cigizoglu
Keyword(s):  
Probability Distributions ◽  
Maximum Flow ◽  
Exceedance Probability ◽  
Flow Duration Curve ◽  
Marginal Probability ◽  
Lognormal Distributions ◽  
Type Iii ◽  
Flow Duration ◽  
Pearson Type ◽  
Flow Duration Curves

In this study a method based on taking the average of the probabilities is presented to obtain flow duration curve. In this method the exceedance probability for each flow value is computed repeatedly for all time periods within a year. The final representing exceedance is just simply the average of all these probabilities. The applicability of the method to daily mean flows is tested assuming various marginal probability distributions like normal, Pearson type III, log-Pearson type III, 2-parameter lognormal and 3-parameter lognormal distributions. It is seen that the observed flow duration curves were quite well approximated by the 2-parameter lognormal average of probabilities curves. In that case the method requires the computation of the daily mean and standard deviation values of the observed flow data. The method curve enables extrapolation of the available data providing the exceedance probabilities for the flows higher than the observed maximum flow. The method is applied to the missing data and ungauged site problems and the results are quite satisfactory.

Safety factors and the probability distribution of soil strength

1970 ◽  
Vol 7 (3) ◽  
pp. 225-242 ◽  
Author(s):  
Peter Lumb
Keyword(s):  
Probability Distribution ◽  
Beta Distribution ◽  
Probability Distributions ◽  
Earth Dams ◽  
Safety Factors ◽  
Independent Variables ◽  
Long Term Stability ◽  
Undrained Strength ◽  
Partial Safety Factors

For soils exhibiting both cohesive and frictional components of strength, the natural variabilities of the components are compared for soil in the undisturbed state and as compacted in earth dams. The probability distributions of the components are shown to agree more closely with a theoretical beta distribution than with the commonly assumed normal distribution.The cohesive and frictional components can be regarded as independent variables and the design safety factor interpreted in terms of probabilities. Assuming equal probabilities for each component leads to the use of partial safety factors which are larger for the cohesive part than for the frictional part. For long-term stability problems limiting partial safety factors corresponding to zero probability can be obtained.The undrained strength of clays also agrees with a beta distribution but in this case there are no limiting safety factors, and some non-zero probability must be associated with the design.

scholarly journals Predicting Major Storm Surge Levels

Atmosphere ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 756
Author(s):  
Robert Mendelsohn
Keyword(s):  
United States ◽  
Probability Distribution ◽  
Storm Surge ◽  
East Coast ◽  
The United States ◽  
Coastal Flooding ◽  
Southeast United States ◽  
Tidal Data ◽  
Major Hurricane

The National Atmospheric and Oceanic Administration (NOAA) calculates the surge probability distribution along the coast from their long-term tidal stations. This process is sufficient for predicting the surge from common storms but tends to underestimate large surges. Across 23 long-term tidal stations along the East Coast of the United States, 100-year surges were observed 49 times, although they should have occurred only 23 times. We hypothesize that these 100-year surges are not the tail outcome from common storms but are actually caused by major hurricanes. Matching these 100-year surges with major hurricanes revealed that major hurricanes caused 43 of the 49 surges. We consequently suggest a revised approach to estimating the surge probability distribution. We used tidal data to estimate the probability of common surges but analyzed major hurricane surges separately, using the return rate of major hurricanes and the observed surge from each major hurricane to predict hurricane surges. The revision reveals that expected coastal flooding damage is higher than we thought, especially in the southeast United States.

scholarly journals Best fitting probability distributions for annual maximum discharge data of the river Kopili, Assam

2009 ◽  
Vol 1 (1) ◽  
pp. 50-52
Author(s):  
Abhijit Bhuyan ◽  
Munindra Borah
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Annual Maximum ◽  
Discharge Data ◽  
Generalized Pareto ◽  
Maximum Discharge ◽  
Pearson Type ◽  
Best Fitting ◽  
Log Normal

In this study our main objective is to determine the best fitting probability distribution for annual maximum flood discharge data of river Kopili, Assam. Various probability distributions i.e. Gumbel (G), generalized extreme value (GEV), normal (N), log-normal (LN3), generalized logistic (GLO), generalized pareto (GPA) and Pearson type-III (PE3) have been used for our study. The L-moments methods have been used for estimating the parameters of all the distributions. The root mean square error (RMSE), model efficiency and D-index (fit in the top six values) together with L-moment ratio diagram is used for goodness of fit measure. It has been observed that Generalized Pareto is the best fitting probability distribution for annual maximum discharge data of river Kopili.

Sign in / Sign up

Export Citation Format

Share Document