A MATLAB Toolbox of Parametric Expressions of the Flow Duration Curve

The flow duration curve (FDC) is a signature catchment characteristic that depicts graphically the relationship between the exceedance probability of streamflow and its magnitude. This curve is used widely for flood risk analysis, water quality management, and the design of hydroelectric power plants (among others). Several mathematical formulations have been proposed to mimic the FDC. Yet, these functions are often not flexible enough to portray accurately the functional shape of the FDC for a large range of catchments. Vrugt and Sadegh (2013) introduced the soil water characteristic (SWC) of van Genuchten (van Genuchten, 1980) as new parametric expression of the FDC for diagnostic model evaluation with DREAM(ABC). Sadegh et al. (2016) build on the work of Vrugt and Sadegh (2013) and compared several models of the SWC against their counterparts published in the literature. These new expressions were shown to fit well the empirical FDCs of the 438 watersheds of the MOPEX data set. Here, we present a MATLAB toolbox, called FDCFIT which contains the fifteen different FDC functions described in Sadegh et al. (2016) and returns the values of their coefficients for a given discharge record, along with graphical output of the fit. Two case studies are used to illustrate the main capabilities and functionalities of the FDCFIT toolbox.

[1]  Jasper A. Vrugt,et al.  Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation , 2016, Environ. Model. Softw..

[2]  Richard M. Vogel,et al.  Closure of "Regional Flow-Duration Curves for Ungauged Sites in Massachusetts" , 1990 .

[4]  Jasper A. Vrugt,et al.  Multi-criteria Optimization Using the AMALGAM Software Package: Theory, Concepts, and MATLAB Implementation , 2016 .

[5]  Leonardo Noto,et al.  Regional flow duration curves for ungauged sites in Sicily , 2010 .

[6]  J. Vrugt,et al.  Approximate Bayesian Computation using Markov Chain Monte Carlo simulation: DREAM(ABC) , 2014 .

[7]  Hoshin Vijai Gupta,et al.  The soil water characteristic as new class of closed-form parametric expressions for the flow duration curve , 2016 .

[8]  Marco Franchini,et al.  Regional analysis of flow duration curves for a limestone region , 1996 .

[9]  Richard M. Vogel,et al.  Flow duration curves II : a review of applications in water resources planning , 1995 .

[10]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[11]  Eric Sauquet,et al.  Comparison of catchment grouping methods for flow duration curve estimation at ungauged sites in France , 2011 .

[12]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[13]  M. Parlange,et al.  Statistics of extremes in hydrology , 2002 .

[14]  J. A. Vrugt,et al.  Approximate Bayesian Computation in hydrologic modeling: equifinality of formal and informal approaches , 2013 .

[15]  K. Kosugi.  Lognormal Distribution Model for Unsaturated Soil Hydraulic Properties , 1996 .

[16]  Richard M. Vogel,et al.  Flow‐Duration Curves. I: New Interpretation and Confidence Intervals , 1994 .

[17]  Q. Duana,et al.  Model Parameter Estimation Experiment (MOPEX): An overview of science strategy and major results from the second and third workshops , 2006 .

[18]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[19]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[20]  J. Vrugt,et al.  A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors , 2010 .

[21]  Ton H. Snelder,et al.  Comparing methods for estimating flow duration curves at ungauged sites , 2012 .

[22]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[23]  J. Vrugt,et al.  Toward diagnostic model calibration and evaluation: Approximate Bayesian computation , 2013 .

[24]  Ken'ichirou Kosugi,et al.  Three‐parameter lognormal distribution model for soil water retention , 1994 .