Example 13

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Case-Study XIII: Nash-Cascade model of hydrograph

The thirteenth case study considers the modeling of the instantaneous unit hydrograph using the ordinates of Nash (1960) defined as


where (mm/day) is the simulated streamflow at time t (days), g (-) denotes the number of reservoirs, α (days) signifies the recession constant, and is the gamma function


which satisfies the recursion .

A n = 25-day period with synthetic daily streamflow data was generated by driving Equation (13.01) with an artificial precipitation record using g = 2 reservoirs, and a recession constant of α=4 days. This artificial data set is subsequently perturbed with a heteroscedastic measurement error (non-constant variance) with standard deviation equal to 10% of the original simulated discharge values. The DREAM algorithm is now used to derive the posterior distribution of both parameters g and α using a bivariate uniform prior distribution, [1,10] and Gaussian likelihood function



where and are the observed and simulate discharge record, respectively, and n denotes the number of measurements. The initial population is drawn from the prior distribution using Latin hypercube sampling. We use N = 8 chains with DREAM to generate samples and use standard settings for the algorithmic variables.

Implementation of plugin functions

The complete source code can be found in DREAM SDK - Examples\D3\Drm_Example13\Plugin\Src_Cpp