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The Cobres basin is discretized into 175 grid squares of 2 × 2 km2 (Figure 1), to each of which are assigned parameters with unique values. The SHETRAN calibration parameters are the Strickler overland flow resistance coefficient and AET/PET ratio for the grid squares with two main types of land-use and the top soil depth, saturated hydraulic conductivity, saturated water content, residual water content and van Genuchten n and α parameters for those with three main types of soil. As shown in Table 1, the parameter values are constrained within physically realistic ranges according to field measurements of Cardoso (1965) and literature data (Bathurst et al. 1996, 2002; Saxton & Rawls 2006). Details of the SHETRAN model set-up and parameter ranges can be found in Zhang et al. (2013). As for the configuration of MOEAs, the population size is set to 50, the maximum number of generations is 30, and the (ηc, ηm) parameters are given three alternative sets (0.5, 0.5), (2.0, 0.5) and (20., 20.), based on the recommended value of (20., 20.) by Deb et al. (2002) and the values previously applied to hydrological applications (Bekele & Nicklow 2007; Tang 2007; Zeng et al. 2010), for all three algorithms NSGA-II, R-NSGA-II and ER-NSGA-II; three reference points with (RMSE, LOGE) of (1.50, 2.50), (1.25, 2.65) and (1.00, 2.80) are set for the R-NSGA-II and ER-NSGA-II, based on the possible ranges of results obtained from a trial run by NSGA-II and as explained in Zhang et al. (2013). For R-NSGA-II, the ɛ is set to 0.001, according to Deb et al. (2006) and Siegmund et al. (2012). For ER-NSGA-II, the a, and are set as 0.5, 0.001 and 0.5 to allow for a variation of ɛ in the range of [0.001, 0.026]; the constraint of the Pareto-fitness approach recommended by Siegmund et al. (2012) is used, and, for step (e) in the section ‘Similarities and differences between NSGA-II, R-NSGA-II and ER-NSGA-II’, the best five non-dominated levels of are supposed to provide 28, 12, 6, 3 and 1 solutions as new populations. A Matlab code was developed for the above-mentioned optimizations based on Seshadri (2009) and Lin (2011).

Table 1

The SHETRAN calibration parameters' description, feasible ranges and values derived from automatic calibrations

Parameters (unit)DescriptionRangeAutomatic calibration resultsa,b
Sim1aSim1bSim1Sim2Sim3Sim4
K1 (m1/3s–1Strickler overland flow resistance coefficient for crops 2.5–10.0 9.6 9.7 10.0 10.0 9.1 3.2 
K2 (m1/3s–1Strickler overland flow resistance coefficient for agroforestry 0.5–5.0 5.0 5.0 5.0 0.5 0.5 0.5 
Ks1 (m/day) Saturated hydraulic conductivity of Vx soil 0.110–0.192 0.174 0.190 0.184 0.192 0.192 0.188 
θs1 (m3/m3Saturated water content of Vx soil 0.506–0.517 0.517 0.517 0.511 0.517 0.506 0.513 
θr1 (m3/m3Residual water content of Vx soil 0.065–0.073 0.067 0.066 0.068 0.073 0.071 0.069 
n1 (-) van Genuchten n of Vx soil 1.221–1.403 1.221 1.221 1.221 1.221 1.224 1.226 
α1 (cm−1van Genuchten α of Vx soil 0.0055–0.0250 0.0056 0.0055 0.0057 0.0055 0.0055 0.0055 
h1 (m) Top soil depth of Vx soil 0.30–0.65 0.30 0.30 0.33 0.65 0.65 0.65 
Ks2 (m/day) Saturated hydraulic conductivity of Px soil 0.191–0.425 0.424 0.423 0.425 0.423 0.423 0.425 
θs2 (m3/m3Saturated water content of Px soil 0.418–0.519 0.418 0.418 0.418 0.418 0.493 0.418 
θr2 (m3/m3Residual water content of Px soil 0.041–0.053 0.053 0.053 0.053 0.042 0.051 0.048 
n2 (-) van Genuchten n of Px soil 1.345–1.422 1.347 1.347 1.347 1.345 1.345 1.358 
α2 (cm−1van Genuchten α of Px soil 0.0075–0.0225 0.0075 0.0075 0.0075 0.0075 0.0076 0.0088 
h2 (m) Top soil depth of Px soil 0.30–0.40 0.33 0.33 0.33 0.30 0.35 0.4 
Ks3 (m/day) Saturated hydraulic conductivity of Ex soil 0.233–2.221 2.019 1.786 1.987 1.987 2.043 2.221 
θs3 (m3/m3Saturated water content of Ex soil 0.446–0.457 0.446 0.446 0.446 0.446 0.452 0.446 
θr3 (m3/m3Residual water content of Ex soil 0.051–0.120 0.082 0.065 0.073 0.120 0.083 0.051 
n3 (-) van Genuchten n of Ex soil 1.311–1.557 1.488 1.381 1.557 1.544 1.321 1.311 
α3 (cm−1van Genuchten α of Ex soil 0.0250–0.0690 0.0252 0.0250 0.0275 0.0670 0.028 0.025 
h3 (m) Top soil depth of Ex soil 0.05–0.10 0.05 0.05 0.05 0.10 0.06 0.05 
AETPETFC1 (-) The AET/PET ratio at field capacity for crop 0.50–0.90 0.500 0.500 0.500 0.500 0.502 0.501 
AETPETFC2 (-) The AET/PET ratio at field capacity for agroforestry 0.60–0.80 0.612 0.617 0.622 0.600 0.600 0.607 
Parameters (unit)DescriptionRangeAutomatic calibration resultsa,b
Sim1aSim1bSim1Sim2Sim3Sim4
K1 (m1/3s–1Strickler overland flow resistance coefficient for crops 2.5–10.0 9.6 9.7 10.0 10.0 9.1 3.2 
K2 (m1/3s–1Strickler overland flow resistance coefficient for agroforestry 0.5–5.0 5.0 5.0 5.0 0.5 0.5 0.5 
Ks1 (m/day) Saturated hydraulic conductivity of Vx soil 0.110–0.192 0.174 0.190 0.184 0.192 0.192 0.188 
θs1 (m3/m3Saturated water content of Vx soil 0.506–0.517 0.517 0.517 0.511 0.517 0.506 0.513 
θr1 (m3/m3Residual water content of Vx soil 0.065–0.073 0.067 0.066 0.068 0.073 0.071 0.069 
n1 (-) van Genuchten n of Vx soil 1.221–1.403 1.221 1.221 1.221 1.221 1.224 1.226 
α1 (cm−1van Genuchten α of Vx soil 0.0055–0.0250 0.0056 0.0055 0.0057 0.0055 0.0055 0.0055 
h1 (m) Top soil depth of Vx soil 0.30–0.65 0.30 0.30 0.33 0.65 0.65 0.65 
Ks2 (m/day) Saturated hydraulic conductivity of Px soil 0.191–0.425 0.424 0.423 0.425 0.423 0.423 0.425 
θs2 (m3/m3Saturated water content of Px soil 0.418–0.519 0.418 0.418 0.418 0.418 0.493 0.418 
θr2 (m3/m3Residual water content of Px soil 0.041–0.053 0.053 0.053 0.053 0.042 0.051 0.048 
n2 (-) van Genuchten n of Px soil 1.345–1.422 1.347 1.347 1.347 1.345 1.345 1.358 
α2 (cm−1van Genuchten α of Px soil 0.0075–0.0225 0.0075 0.0075 0.0075 0.0075 0.0076 0.0088 
h2 (m) Top soil depth of Px soil 0.30–0.40 0.33 0.33 0.33 0.30 0.35 0.4 
Ks3 (m/day) Saturated hydraulic conductivity of Ex soil 0.233–2.221 2.019 1.786 1.987 1.987 2.043 2.221 
θs3 (m3/m3Saturated water content of Ex soil 0.446–0.457 0.446 0.446 0.446 0.446 0.452 0.446 
θr3 (m3/m3Residual water content of Ex soil 0.051–0.120 0.082 0.065 0.073 0.120 0.083 0.051 
n3 (-) van Genuchten n of Ex soil 1.311–1.557 1.488 1.381 1.557 1.544 1.321 1.311 
α3 (cm−1van Genuchten α of Ex soil 0.0250–0.0690 0.0252 0.0250 0.0275 0.0670 0.028 0.025 
h3 (m) Top soil depth of Ex soil 0.05–0.10 0.05 0.05 0.05 0.10 0.06 0.05 
AETPETFC1 (-) The AET/PET ratio at field capacity for crop 0.50–0.90 0.500 0.500 0.500 0.500 0.502 0.501 
AETPETFC2 (-) The AET/PET ratio at field capacity for agroforestry 0.60–0.80 0.612 0.617 0.622 0.600 0.600 0.607 

a’sim1a’, ‘sim1b’, ‘sim1’, ‘sim2’, ‘sim3’ and ‘sim4’ are SHETRAN simulations with (RMSE, LOGE, NSE) of respectively (2.82, 2.73, 0.87), (2.83, 2.73, 0.87), (2.81, 2.74, 0.87), (3.81, 2.53, 0.77), (4.85, 2.49, 0.63) and (5.85, 2.46, 0.46) at basin outlet, for the calibration period (2004–2006).

b’sim1a’, ‘sim1b’ and ‘sim1'are equivalently good; the hydrograph comparisons are shown in Figure 8 for the simulations ‘sim1’, ‘sim2’, ‘sim3’ and ‘sim4’.

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