The soil water characteristic as new class of closed-form parametric expressions for the flow duration curve

Abstract

Keywords:Closed-form expression for FDC Soil water characteristic Regionalization of FDC s u m m a r yThe flow duration curve is a signature catchment characteristic that depicts graphically the relationship between the exceedance probability of streamflow and its magnitude. This curve is relatively easy to create and interpret, and is used widely for hydrologic analysis, water quality management, and the design of hydroelectric power plants (among others). Several mathematical expressions have been proposed to mimic the FDC. Yet, these efforts have not been particularly successful, in large part because available functions are not flexible enough to portray accurately the functional shape of the FDC for a large range of catchments and contrasting hydrologic behaviors. Here, we extend the work of Vrugt and Sadegh (2013) and introduce several commonly used models of the soil water characteristic as new class of closed-form parametric expressions for the flow duration curve. These soil water retention functions are relatively simple to use, contain between two to three parameters, and mimic closely the empirical FDCs of 430 catchments of the MOPEX data set. We then relate the calibrated parameter values of these models to physical and climatological characteristics of the watershed using multivariate linear regression analysis, and evaluate the regionalization potential of our proposed models against those of the literature. If quality of fit is of main importance then the 3-parameter van Genuchten model is preferred, whereas the 2-parameter lognormal, 3-parameter GEV and generalized Pareto models show greater promise for regionalization.

Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

“…If this were not the case then many accepted samples are required to approximate closely the distribution of the probability mass within the posterior distribution. Indeed, methods such as the generalized likelihood uncertainty estimation (GLUE) that rely on uniform sampling (such as rejection sampling) can produce questionable results if the target distribution is somewhat complex and/or comprises only a relatively small part of the prior distribution (Vrugt, 2015a). In summary, standard Monte Carlo simulation methods are computationally inefficient for anything but very low dimensional problems.…”

“…Sadegh and Vrugt, 2014; Vrugt, submitted for publication). Finally, likelihood function 23 enables use of the limits of acceptability framework (Beven, 2006;Beven and Binley, 2014;Vrugt, 2015a). Section 5 presents the application of different likelihood functions and provides templates for their use.…”

“…Four different summary metrics of the discharge data are used for ABC inference (activated with likelihood function 22), including S 1 (-) the annual runoff coefficient, S 2 (-) the annual baseflow coefficient, and S 3 (day/mm) and S 4 (-) two coefficients of the flow duration curve Sadegh et al, 2015a). The following setup is used in the MATLAB package of DREAM.…”

“…I refer to and Scharnagl et al (2015) for an exact derivation and detailed analysis of likelihood functions 14 and 17, respectively, and Whittle (1953) for an introduction to likelihood 15. The ABC likelihood functions 21 and 22 are described and discussed in detail by Turner and Sederberg (2012) and Sadegh and Vrugt (2014), whereas the limits of acceptability function 23 is introduced and tested in Vrugt (2015a). The pseudo-likelihoods in 31, 32, 33 and 34 are explicated in the GLUE papers of Beven and coworkers (Beven and Binley, 1992;Freer et al, 1996;Beven and Freer, 2001;Beven, 2006).…”

“…The present code differs from its earlier versions in that it contains a suite of new options and new methodological developments Sadegh and Vrugt, 2014;Vrugt, 2015a,submitted for publication).…”