# Does the Complexity of Evapotranspiration and Hydrological Models Enhance Robustness?

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}) statistical indicator is also often used as an alternative criterion for comparing different model structures [39]. The AIC basically assumes the Kullback-Leibler’s information and the BIC uses Bayesian approaches to estimate the variations between the observed and simulated models. The AIC, BIC, and Ra

^{2}statistical indicators are able to balance performance against model complexity (the number of parameters). After the computation of the statistical indicators, the model with a minimum value of AIC, BIC, and the maximum value of Ra

^{2}can be adopted for practical application [45,46].

^{2}) were used to select the most appropriate model structure among the applied five hydrological models of increasing complexity and 12 PET estimation methods. Similarly, the model robustness was evaluated by comparing the Dimensionless Bias of five hydrological models for 12 PET inputs.

^{2}). The five hydrological models and 12 PET estimation methods had different levels of complexity. The GR4J (four parameters), SIMHYD (seven parameters), CAT (eight parameters), TANK (12 parameters), and SAC-SMA (16 parameters) models were selected when considering their wide applications in several basins. Similarly, the 12 PET estimation methods required different climatic variables including mean Temperature (T), Wind Speed (u), Relative Humidity (RH), and Solar Radiation (R

_{S}) data depending on the level of complexity. The available hydro-meteorological data obtained from 10 catchments were used to set up and calibrate five hydrological models for 12 PET inputs. The Thiessen polygon method was used for estimating the mean areal precipitation. There exist several kinds of optimization methods for calibrating hydrological models and the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm is often adopted by researchers due to its broad applications, efficiency, and robustness [49,50,51,52]. In this study, the SCE-UA algorithm was used to optimize the hydrological model parameters for each PET input by setting a similar objective function: NSE, LogNSE, KGE, and RSR. The detailed description of the 10 catchments hydrological characteristics, the dataset used, the methodology adopted, the result, and discussions are presented in the next sections.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The main hydrological characteristics of the catchments are concentrated in summer (June to September), contributing to 70% of the precipitation that leads to peak flow. However, the snowmelt effect is not significant in these regions due to the limited amount of winter precipitation (December to February). The location of the 10 catchments, major rivers, and streamflow gauging stations are shown in Figure 1.

#### 2.2. Data

_{S}(MJ/m

^{2}d) estimated from the daily sunshine hours (n) while using the Ångström-Prescott equation [53]. The major hydrological characteristics and hydro-climate conditions of the catchments are summarized in Table 1. The mean annual PET was estimated using the Penman-Monteith method.

#### 2.3. PET Estimation Methods

#### 2.4. Overview of Hydrological Model Structure

#### 2.4.1. GR4J

#### 2.4.2. SIMHYD

#### 2.4.3. CAT

#### 2.4.4. TANK

#### 2.4.5. SAC-SMA

#### 2.5. Model Calibration and Validation

_{obs}, Q

_{sim}, and Q

_{mean}are the observed, simulated, and mean observed streamflow, respectively. R

^{2}, SD, and M are the Pearson Correlation Coefficient, standard deviation, and mean, respectively.

#### 2.6. Model Complexity Comparison Criteria and Robustness

#### 2.6.1. Model Complexity Comparison Criteria

^{2}for each PET input. The AIC, BIC, and Ra

^{2}are the statistical indicators commonly used to compare a model structure of different complexity in various subject areas. The three statistical indicators’ model comparison criteria are able to penalize the number of estimated parameters depending on the model complexity. The model comparison criteria have been applied for frequency analysis of hydrological extremes [46,102] and for predictions of groundwater models [103]. Other studies have also applied the criteria to compare conceptual rainfall-runoff models with artificial neural network models [45,104,105]. Akaike [43] proposed the AIC for the first time based on Kullback-Leibler’s information as the discrepancies between the observed and simulated models. Similarly, Schwarz [44] proposed a more parsimonious method, called the BIC, which considers the Bayesian approaches. The Adjusted R-square Ra

^{2}has also been used as an alternative method to compare model structures of different complexity [45]. The AIC, BIC, and Ra

^{2}statistical indicators were calculated for the five hydrological models of increasing complexity for each PET input. The model with a minimum AIC, BIC, and maximum Ra

^{2}was considered to be the better performing and with greater parsimony. In this study, similar model comparison criteria were adopted to evaluate the five hydrological models for each PET input. The three statistical indicators, AIC, BIC, and Ra

^{2}were calculated, as follows:

^{2}are the number of data points, root mean squared error of the model output, the number of model parameters, and Pearson Correlation Coefficient, respectively.

#### 2.6.2. Model Robustness

## 3. Results

#### 3.1. Calibration and Validation

^{2}assessment criterion showed relatively higher values when compared to the SIMHYD and TANK models in most of the tested catchments in the calibration as well as the validation periods. However, it would be naive to identify one best hydrological model because of the minor differences in the index values (NSE < 0.2, RSR < 0.15, KGE < 0.2, and R

^{2}< 0.15) in most of the tested catchments, except for the Imha and Andong catchments. The five hydrological models’ performance was observed to be higher and more insensitive for the Seolmacheon experimental catchment for the 12 PET inputs in the calibration and validation periods (Figure 4 and Figure 5). The scatterplot of the five hydrological models’ performance simulated over the application period (2002–2012) for four selected catchments when considering the Penman-Monteith PET input also showed a small variation (R

^{2}< 0.15), as presented in Figure 7.

#### 3.2. Effect of Model Structure Complexity on Model Performance

#### 3.3. Effect of PET Complexity on Model Parameters

#### 3.4. Effect of PET and Model Structure Complexity on Model Robustness

^{2}values, calculated to compare a model structure also showed similar results with the model performance evaluation index values (NSE, LogNSE, RSR, and KGE). The GR4J, CAT, and SAC-SMA models’ statistical indicator showed a minimum AIC, BIC, and maximum Ra

^{2}value in all of the tested catchments, both in the calibration and validation periods. The minimum AIC, BIC, and maximum Ra

^{2}value showed that the GR4J, CAT, and SAC-SMA had better model performance for simulating streamflow (Figure 10). However, the SIMHYD and TANK models showed a higher AIC, BIC, and lower Ra

^{2}for most of the tested catchments when compared with the GR4J, CAT, and SAC-SMA models’ statistical indicator values. Moreover, the effect of the 12 PET complexity was more captured by the three statistical indicators, and higher AIC, BIC, and lower Ra

^{2}values were also observed for the Hamon PET input values, as shown in Figure 10. Similar responses were also observed in all of the tested catchments and Figure 10 shows the AIC, BIC, and Ra

^{2}values of four selected catchments for the 12 PET input values in the validation periods.

## 4. Discussion

_{S}, n, and u). The five hydrological models’ performance was relatively low in the Imha and Andong catchments when compared to the other tested catchments in the validation periods. The Hamon PET estimation method was the only input that clearly showed a decreasing model performance in all of the tested catchments, except for Seolmacheon. This decrease in model performance was likely due to the underestimated values of the Hamon PET estimation method in all of the tested catchments. The better model performance and stable parameters observed in the smallest Seolmacheon experimental catchment were probably related to the size or the availability of high-quality hydro-meteorological data when compared to other study sites. The complexity of the PET estimation method and hydrological model structure did not affect the model performance significantly because of the efficiency of the SCE-UA algorithm to optimize the model parameters for each PET input in the calibration process.

^{2}) also agreed with the computed model evaluation index values (NSE, LogNSE, RSR, and KGE). The results of the three statistical indicator showed higher AIC, BIC, and lower Ra

^{2}values for the Hamon PET estimation method in all of the tested catchments. The lower performance for the Hamon PET input was most likely due to the underestimated value of the PET. The 12 PET estimation methods and five hydrological models’ structure complexity effect were better captured by the three statistical indicators. Although the model complexity comparison criteria (AIC, BIC, and Ra

^{2}) results revealed that the GR4J, CAT, and SAC-SMA models had a better capability to simulate streamflow, it would be naive to identify the best hydrological model. The GR4J, CAT, and SAC-SMA models’ behavioral similarities and lower Dimensionless Bias were observed in all of the tested catchments. The five hydrological models lacked robustness, particularly for extreme hydrological conditions (high and low flow) and for the Hamon PET input value, which was observed in all of the tested catchments, except the Seolmacheon. Perrin et al. [7] also discussed the difficulty of identifying the best hydrological model. Furthermore, a previous study conducted on the frequency analysis of hydrological extremes also addressed the limitations and difficulties of completely concluding the superiority of one model for practical applications [46].

## 5. Conclusions

^{2}) captured the PET and hydrological model structure complexity. The model complexity comparison criteria results showed minimum AIC, BIC, and maximum Ra

^{2}values for the GR4J, CAT, and SAC-SMA, which is in agreement with the computed model evaluation index values (NSE, RSR and KGE). In addition, the three hydrological models showed lower Dimensionless Bias, and identical behavioral similarities were observed in all of the tested catchments. However, the five hydrological models’ lack of robustness were observed for high and low flow, as well as the Hamon PET input values in all of the tested catchments.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

PET Estimation Methods | Formula | Required Data | Reference |
---|---|---|---|

Abtew | $PET=0.52\frac{{R}_{s}}{\lambda}$ | T, R_{s} | [112] |

Blaney Criddle | $PET=\left(0.0043R{H}_{min}-\frac{n}{N}-1.41\right)+{b}_{var}{p}_{y}\left(0.46{T}_{a}+8.13\right)$ | T, RH, n | [113] |

Chapman Australian | $PET={A}_{p}{E}_{pan}+{B}_{p}$ | T, RH, R_{s} | [114] |

${E}_{pan}=\frac{\Delta}{\Delta +{a}_{p}\gamma}\frac{{R}_{Npan}}{\lambda}+\frac{{a}_{p}\gamma}{\Delta +{a}_{p}\gamma}{f}_{pan}\left(u\right)({v}_{a}{}^{*}-{v}_{a)}$ | |||

Granger Gray | $PET=\frac{\Delta {G}_{g}}{\Delta {G}_{g}+\gamma}\frac{{R}_{n}-G}{\lambda}+\frac{\gamma {G}_{g}}{\Delta {G}_{g}+\gamma}{E}_{a}$ | T, RH, R_{s} | [115] |

Hamon | $PET=0.55{(\frac{n}{12})}^{2}(\frac{SVD}{100})\left(25.4\right)$ | T, n | [116] |

Hargreaves Samani | $PET=0.0135{C}_{HS}\frac{{R}_{a}}{\lambda}\left({T}_{max}-{T}_{min}{)}^{2}({T}_{a}+17.8\right)$ | T | [117] |

Makkink | $PET=0.61(\frac{\Delta}{\Delta +\gamma}-\frac{{R}_{a}}{2.45})-0.12$ | T, R_{s} | [118] |

Matt Shuttleworth | $PET=\frac{1}{\lambda}\frac{\Delta {R}_{n}+\frac{{\rho}_{a}{c}_{a}{u}_{2}(VP{D}_{2})}{{r}_{c}{}^{50}}(\frac{VP{D}_{50}}{VP{D}_{2}})}{\Delta +\gamma (1+\frac{{({r}_{s})}_{c}{u}_{2}}{{r}_{c}{}^{50}})}$ | T, RH, R_{s}, u | [119] |

Penman | $PET\approx 0.047{R}_{S}({T}_{a}+9.5{)}^{0.5}-2.4{(\frac{{R}_{S}}{{R}_{a}})}^{2}+0.09({T}_{a}+20)(1-\frac{R{H}_{mean}}{100})$ | T, RH, R_{s} | [120] |

Penman-Monteith | $PET=\frac{0.408\Delta \left({R}_{n}-G\right)+\gamma \frac{900}{{T}_{a}+273}{u}_{2}({v}_{a}{}^{*}-{v}_{a)}}{\Delta +\gamma \left(1+0.34{u}_{2}\right)}$ | T, RH, R_{s}, n, u | [121] |

Priestley Taylor | $PET=\frac{1.26\Delta {R}_{n}}{\lambda \rho \left(\Delta +\gamma \right)}$ | T, RH, R_{s} | [122] |

Turc | $PET=0.013\left(23.88{R}_{s}+50\right)\left(\frac{{T}_{a}}{{T}_{a}+15}\right)$, for RH > 50% | T, RH, R_{s} | [123] |

$PET=0.013\left(23.88{R}_{s}+50\right)\left(\frac{{T}_{a}}{{T}_{a}+15}\right)\left(1+\frac{50-RH}{70}\right)$, for RH < 50% |

_{a}is the aerodynamic component of Penman’s equation (mm/d); rc

^{50}is the aerodynamic resistance for crop height, h(s/m); r

_{s}is the surface resistance (s/m); (r

_{s})

_{c}is the surface resistance of a well-watered crop equivalent to FAO crop coefficient (s/m); ρ is the water density (kg/m

^{3}); ρ

_{a}is the mean air density at constant pressure (kg/m

^{3}), SVD is the saturated vapor density at mean air temperature (g/m

^{3}); G is the soil heat flux (MJ/m

^{2}d); R

_{n}is the net radiation at evaporating surface at air temperature ((MJ/m

^{2}d); R

_{s}is the incoming solar radiation ((MJ/m

^{2}d); R

_{a}is the extraterrestrial radiation ((MJ/m

^{2}d); R

_{NPan}is the net radiation at Class-A pan ((MJ/m

^{2}d); λ is the latent heat of vaporization (MJ/kg); c

_{a}is the specific heat of air (MJ/kg °C); Ta, ${T}_{max},{T}_{min}$ are the mean, maximum, and minimum temperature (°C), respectively; b

_{var}is the working variable (-); G

_{g}is the dimensionless relative evaporation parameter (-); C

_{HS}is the Hargreaves-Samani working coefficient (-); a

_{p}is the constant in PenPan equation (-); A

_{p}is the gradient (-); B

_{p}is the intercept (-); $RH$, $R{H}_{mean},R{H}_{min}$ are the daily, mean, minimum relative humidity(%), respectively; p

_{y}is the percentage of actual daytime hours for the specific day compared to the day-light hours for the entire year (%); N is the total day length (h); n is the duration of sunshine hours in a day (h); Δ is the slope of the saturation vapor pressure curve (kPa/°C); γ is the psychrometric constant (kPa/°C); VPD

_{2,}VPD

_{50}are the vapor pressure deficit at 2 m and 50 m, respectively (kPa); (v

_{a}

^{∗}− v

_{a}) is the vapor pressure deficit at air temperature (kPa); f

_{Pan}(u) is the wind function for Class-A pan (ms

^{−1}); ${u}_{2}$ is the average daily wind speed at 2 m height (m/s); and u is the mean daily wind speed (m/s).

Seolmacheon | NSE | LogNSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

PET Methods | GR4J | SIMHYD | CAT | TANK | SAC-SAM | GR4J | SIMHYD | CAT | TANK | SAC-SAM |

Abtew | 0.85 | 0.87 | 0.80 | 0.89 | 0.87 | 0.71 | 0.18 | 0.85 | 0.91 | 0.87 |

Blaney Criddle | 0.87 | 0.87 | 0.79 | 0.89 | 0.87 | 0.87 | 0.29 | 0.88 | 0.62 | 0.87 |

Chapman Australian | 0.86 | 0.87 | 0.78 | 0.90 | 0.87 | 0.83 | 0.38 | 0.89 | 0.57 | 0.89 |

Granger Gray | 0.90 | 0.84 | 0.80 | 0.89 | 0.84 | 0.87 | 0.31 | 0.88 | 0.47 | 0.89 |

Hamon | 0.87 | 0.86 | 0.80 | 0.89 | 0.86 | 0.88 | 0.37 | 0.89 | 0.62 | 0.89 |

Hargreaves Samani | 0.87 | 0.86 | 0.77 | 0.88 | 0.86 | 0.88 | 0.03 | 0.90 | 0.49 | 0.89 |

Makkink | 0.85 | 0.85 | 0.80 | 0.90 | 0.85 | 0.81 | 0.34 | 0.88 | 0.32 | 0.88 |

Matt Shuttleworth | 0.87 | 0.86 | 0.78 | 0.90 | 0.86 | 0.89 | 0.39 | 0.90 | 0.63 | 0.89 |

Penman | 0.87 | 0.88 | 0.79 | 0.88 | 0.88 | 0.83 | 0.35 | 0.88 | 0.55 | 0.88 |

Penman-Monteith | 0.86 | 0.87 | 0.79 | 0.89 | 0.87 | 0.84 | 0.38 | 0.89 | 0.45 | 0.88 |

Priestley Taylor | 0.85 | 0.86 | 0.78 | 0.87 | 0.86 | 0.73 | 0.25 | 0.85 | 0.76 | 0.87 |

Turc | 0.88 | 0.86 | 0.80 | 0.89 | 0.86 | 0.90 | 0.39 | 0.90 | 0.65 | 0.88 |

Boryeong | ||||||||||

Abtew | 0.85 | 0.66 | 0.79 | 0.77 | 0.79 | 0.82 | 0.46 | 0.81 | 0.24 | 0.15 |

Blaney Criddle | 0.85 | 0.72 | 0.79 | 0.77 | 0.79 | 0.80 | 0.75 | 0.83 | 0.72 | −1.33 |

Chapman Australian | 0.86 | 0.76 | 0.76 | 0.82 | 0.76 | 0.84 | 0.46 | 0.84 | 0.25 | −0.71 |

Granger Gray | 0.85 | 0.74 | 0.79 | 0.77 | 0.79 | 0.81 | 0.72 | 0.83 | 0.62 | −1.00 |

Hamon | 0.83 | 0.64 | 0.79 | 0.70 | 0.79 | 0.68 | 0.65 | 0.73 | 0.42 | 0.29 |

Hargreaves Samani | 0.74 | 0.74 | 0.79 | 0.79 | 0.79 | 0.82 | 0.23 | 0.84 | 0.31 | 0.34 |

Makkink | 0.85 | 0.72 | 0.81 | 0.76 | 0.81 | 0.84 | 0.63 | 0.85 | 0.66 | −0.82 |

Matt Shuttleworth | 0.85 | 0.70 | 0.81 | 0.79 | 0.81 | 0.80 | 0.74 | 0.82 | 0.83 | −1.03 |

Penman | 0.85 | 0.75 | 0.78 | 0.72 | 0.78 | 0.83 | −0.09 | 0.82 | 0.59 | 0.27 |

Penman-Monteith | 0.86 | 0.74 | 0.80 | 0.80 | 0.80 | 0.84 | 0.40 | 0.82 | 0.74 | −0.40 |

Priestley Taylor | 0.85 | 0.73 | 0.79 | 0.79 | 0.79 | 0.83 | 0.38 | 0.84 | 0.77 | −1.07 |

Turc | 0.73 | 0.71 | 0.77 | 0.77 | 0.77 | 0.80 | 0.57 | 0.85 | 0.75 | −0.87 |

Kyeongan | ||||||||||

Abtew | 0.85 | 0.79 | 0.78 | 0.87 | 0.85 | 0.65 | −2.15 | 0.73 | 0.77 | 0.70 |

Blaney Criddle | 0.86 | 0.75 | 0.82 | 0.87 | 0.86 | 0.76 | 0.16 | 0.77 | 0.49 | 0.70 |

Chapman Australian | 0.86 | 0.72 | 0.80 | 0.87 | 0.86 | 0.70 | −2.09 | 0.74 | 0.66 | 0.68 |

Granger Gray | 0.87 | 0.72 | 0.80 | 0.88 | 0.87 | 0.75 | −0.43 | 0.75 | 0.55 | 0.68 |

Hamon | 0.86 | 0.70 | 0.82 | 0.82 | 0.86 | 0.77 | 0.15 | 0.79 | 0.60 | 0.75 |

Hargreaves Samani | 0.86 | 0.72 | 0.78 | 0.86 | 0.86 | 0.68 | −1.54 | 0.74 | −0.45 | 0.71 |

Makkink | 0.86 | 0.71 | 0.80 | 0.87 | 0.86 | 0.72 | −1.00 | 0.74 | −0.03 | 0.67 |

Matt Shuttleworth | 0.87 | 0.76 | 0.80 | 0.88 | 0.87 | 0.76 | −0.52 | 0.78 | 0.42 | 0.72 |

Penman | 0.83 | 0.69 | 0.78 | 0.86 | 0.83 | 0.53 | −1.64 | 0.69 | −0.14 | 0.72 |

Penman-Monteith | 0.86 | 0.71 | 0.79 | 0.87 | 0.86 | 0.68 | −2.97 | 0.75 | 0.05 | 0.72 |

Priestley Taylor | 0.86 | 0.67 | 0.81 | 0.87 | 0.86 | 0.72 | −1.11 | 0.76 | 0.27 | 0.72 |

Turc | 0.87 | 0.68 | 0.81 | 0.87 | 0.87 | 0.76 | −0.50 | 0.79 | −0.18 | 0.73 |

Seomjingang | ||||||||||

Abtew | 0.91 | 0.81 | 0.80 | 0.90 | 0.81 | 0.83 | −0.72 | 0.83 | −0.32 | 0.79 |

Blaney Criddle | 0.90 | 0.79 | 0.79 | 0.86 | 0.79 | 0.79 | 0.66 | 0.80 | 0.57 | 0.68 |

Chapman Australian | 0.91 | 0.79 | 0.79 | 0.90 | 0.79 | 0.84 | −0.02 | 0.84 | 0.37 | 0.78 |

Granger Gray | 0.91 | 0.80 | 0.79 | 0.90 | 0.80 | 0.83 | 0.05 | 0.83 | 0.51 | 0.76 |

Hamon | 0.88 | 0.76 | 0.77 | 0.83 | 0.76 | 0.73 | 0.64 | 0.73 | 0.42 | 0.70 |

Hargreaves Samani | 0.92 | 0.79 | 0.78 | 0.89 | 0.79 | 0.84 | −0.50 | 0.83 | −0.16 | 0.76 |

Makkink | 0.91 | 0.81 | 0.79 | 0.90 | 0.81 | 0.84 | 0.20 | 0.84 | 0.44 | 0.79 |

Matt Shuttleworth | 0.91 | 0.80 | 0.79 | 0.91 | 0.80 | 0.80 | −0.13 | 0.83 | 0.57 | 0.80 |

Penman | 0.92 | 0.82 | 0.79 | 0.90 | 0.82 | 0.84 | −1.25 | 0.84 | −0.42 | 0.78 |

Penman-Monteith | 0.91 | 0.79 | 0.79 | 0.90 | 0.79 | 0.84 | −0.93 | 0.84 | 0.10 | 0.77 |

Priestley Taylor | 0.91 | 0.79 | 0.79 | 0.89 | 0.79 | 0.84 | −0.55 | 0.83 | 0.29 | 0.75 |

Turc | 0.91 | 0.80 | 0.79 | 0.90 | 0.80 | 0.82 | −0.36 | 0.82 | 0.47 | 0.76 |

Yongdam | ||||||||||

Abtew | 0.91 | 0.79 | 0.89 | 0.89 | 0.89 | 0.85 | −2.80 | 0.86 | 0.49 | 0.46 |

Blaney Criddle | 0.90 | 0.73 | 0.87 | 0.82 | 0.87 | 0.81 | 0.47 | 0.86 | 0.55 | 0.32 |

Chapman Australian | 0.91 | 0.78 | 0.89 | 0.89 | 0.89 | 0.85 | −0.87 | 0.86 | 0.19 | 0.18 |

Granger Gray | 0.90 | 0.78 | 0.88 | 0.89 | 0.88 | 0.84 | −0.09 | 0.84 | 0.64 | 0.46 |

Hamon | 0.84 | 0.68 | 0.85 | 0.78 | 0.85 | 0.75 | 0.59 | 0.77 | 0.29 | 0.33 |

Hargreaves Samani | 0.91 | 0.75 | 0.86 | 0.88 | 0.86 | 0.86 | −0.76 | 0.86 | −0.57 | 0.55 |

Makkink | 0.90 | 0.77 | 0.88 | 0.89 | 0.88 | 0.85 | 0.23 | 0.86 | 0.63 | 0.33 |

Matt Shuttleworth | 0.90 | 0.76 | 0.88 | 0.88 | 0.88 | 0.84 | 0.17 | 0.85 | 0.67 | 0.33 |

Penman | 0.91 | 0.78 | 0.86 | 0.88 | 0.86 | 0.86 | −2.34 | 0.85 | 0.73 | 0.64 |

Penman-Monteith | 0.91 | 0.77 | 0.88 | 0.88 | 0.88 | 0.86 | −0.67 | 0.86 | 0.46 | 0.56 |

Priestley Taylor | 0.91 | 0.81 | 0.87 | 0.88 | 0.87 | 0.85 | −0.88 | 0.85 | 0.68 | 0.52 |

Turc | 0.87 | 0.79 | 0.87 | 0.89 | 0.87 | 0.83 | 0.10 | 0.84 | 0.34 | 0.46 |

Juam | ||||||||||

Abtew | 0.90 | 0.66 | 0.84 | 0.88 | 0.84 | 0.88 | −0.46 | 0.90 | 0.85 | 0.86 |

Blaney Criddle | 0.90 | 0.57 | 0.83 | 0.81 | 0.83 | 0.82 | 0.72 | 0.87 | 0.67 | 0.70 |

Chapman Australian | 0.91 | 0.67 | 0.81 | 0.88 | 0.81 | 0.89 | 0.37 | 0.90 | 0.79 | 0.80 |

Granger Gray | 0.90 | 0.70 | 0.81 | 0.84 | 0.81 | 0.81 | 0.41 | 0.86 | 0.56 | 0.84 |

Hamon | 0.84 | 0.57 | 0.82 | 0.78 | 0.82 | 0.61 | 0.20 | 0.60 | 0.73 | 0.52 |

Hargreaves Samani | 0.89 | 0.74 | 0.83 | 0.90 | 0.83 | 0.89 | −0.07 | 0.90 | 0.03 | 0.75 |

Makkink | 0.91 | 0.60 | 0.85 | 0.84 | 0.85 | 0.86 | 0.54 | 0.90 | 0.87 | 0.85 |

Matt Shuttleworth | 0.90 | 0.60 | 0.85 | 0.82 | 0.85 | 0.80 | 0.56 | 0.86 | 0.85 | 0.77 |

Penman | 0.90 | 0.72 | 0.84 | 0.89 | 0.84 | 0.86 | 0.00 | 0.87 | 0.67 | 0.80 |

Penman-Monteith | 0.91 | 0.69 | 0.84 | 0.88 | 0.84 | 0.90 | 0.15 | 0.89 | 0.08 | 0.85 |

Priestley Taylor | 0.91 | 0.63 | 0.84 | 0.88 | 0.84 | 0.88 | 0.40 | 0.89 | 0.34 | 0.82 |

Turc | 0.83 | 0.66 | 0.83 | 0.88 | 0.83 | 0.85 | 0.35 | 0.87 | 0.81 | 0.81 |

Imha | ||||||||||

Abtew | 0.69 | 0.61 | 0.64 | 0.67 | 0.69 | 0.70 | −1.53 | 0.73 | 0.89 | 0.70 |

Blaney Criddle | 0.65 | 0.58 | 0.67 | 0.71 | 0.65 | 0.83 | 0.41 | 0.83 | 0.74 | 0.70 |

Chapman Australian | 0.72 | 0.65 | 0.65 | 0.71 | 0.72 | 0.78 | −1.35 | 0.80 | −1.00 | 0.78 |

Granger Gray | 0.67 | 0.62 | 0.60 | 0.66 | 0.67 | 0.82 | −0.44 | 0.80 | −0.03 | 0.71 |

Hamon | 0.61 | 0.55 | 0.58 | 0.55 | 0.61 | 0.67 | 0.37 | 0.70 | 0.61 | 0.67 |

Hargreaves Samani | 0.65 | 0.63 | 0.62 | 0.67 | 0.65 | 0.80 | −1.11 | 0.79 | 0.76 | 0.71 |

Makkink | 0.70 | 0.62 | 0.64 | 0.72 | 0.70 | 0.80 | −0.63 | 0.78 | −0.61 | 0.65 |

Matt Shuttleworth | 0.69 | 0.65 | 0.69 | 0.75 | 0.69 | 0.84 | −1.76 | 0.81 | 0.59 | 0.50 |

Penman | 0.65 | 0.65 | 0.61 | 0.65 | 0.65 | 0.79 | −0.77 | 0.78 | 0.59 | 0.71 |

Penman-Monteith | 0.72 | 0.65 | 0.68 | 0.67 | 0.72 | 0.76 | −2.05 | 0.75 | 0.86 | 0.60 |

Priestley Taylor | 0.70 | 0.63 | 0.62 | 0.72 | 0.70 | 0.82 | −1.03 | 0.80 | −0.42 | 0.56 |

Turc | 0.72 | 0.63 | 0.67 | 0.72 | 0.72 | 0.86 | −0.76 | 0.84 | −0.30 | 0.71 |

Andong | ||||||||||

Abtew | 0.83 | 0.69 | 0.74 | 0.84 | 0.83 | 0.79 | −1.63 | 0.80 | 0.78 | 0.51 |

Blaney Criddle | 0.70 | 0.68 | 0.73 | 0.86 | 0.70 | 0.76 | 0.46 | 0.80 | 0.61 | 0.57 |

Chapman Australian | 0.84 | 0.69 | 0.75 | 0.88 | 0.84 | 0.80 | −0.88 | 0.81 | −0.38 | 0.35 |

Granger Gray | 0.82 | 0.69 | 0.73 | 0.86 | 0.82 | 0.76 | −0.18 | 0.79 | 0.30 | 0.29 |

Hamon | 0.75 | 0.52 | 0.75 | 0.71 | 0.75 | 0.67 | 0.43 | 0.71 | 0.72 | 0.39 |

Hargreaves Samani | 0.85 | 0.69 | 0.71 | 0.81 | 0.85 | 0.80 | −0.88 | 0.79 | −0.74 | 0.40 |

Makkink | 0.83 | 0.71 | 0.73 | 0.89 | 0.83 | 0.78 | −0.45 | 0.81 | −0.42 | 0.33 |

Matt Shuttleworth | 0.83 | 0.70 | 0.77 | 0.89 | 0.83 | 0.76 | 0.14 | 0.79 | 0.68 | 0.03 |

Penman | 0.84 | 0.67 | 0.75 | 0.84 | 0.84 | 0.80 | −0.93 | 0.80 | 0.11 | 0.51 |

Penman-Monteith | 0.84 | 0.69 | 0.74 | 0.88 | 0.84 | 0.80 | −0.81 | 0.81 | −0.57 | 0.48 |

Priestley Taylor | 0.83 | 0.70 | 0.74 | 0.86 | 0.83 | 0.78 | −0.61 | 0.80 | 0.73 | 0.52 |

Turc | 0.76 | 0.68 | 0.76 | 0.80 | 0.76 | 0.76 | −0.08 | 0.79 | 0.66 | 0.45 |

Soyanggang | ||||||||||

Abtew | 0.91 | 0.77 | 0.86 | 0.92 | 0.86 | 0.84 | −1.47 | 0.82 | −1.66 | 0.71 |

Blaney Criddle | 0.91 | 0.75 | 0.88 | 0.92 | 0.88 | 0.80 | 0.55 | 0.84 | 0.69 | 0.79 |

Chapman Australian | 0.91 | 0.76 | 0.87 | 0.93 | 0.87 | 0.84 | −0.52 | 0.84 | 0.66 | 0.73 |

Granger Gray | 0.91 | 0.76 | 0.86 | 0.92 | 0.86 | 0.83 | −0.15 | 0.83 | 0.65 | 0.63 |

Hamon | 0.90 | 0.77 | 0.88 | 0.90 | 0.88 | 0.79 | 0.66 | 0.80 | 0.77 | 0.72 |

Hargreaves Samani | 0.91 | 0.75 | 0.84 | 0.92 | 0.84 | 0.84 | −1.68 | 0.83 | 0.03 | 0.66 |

Makkink | 0.91 | 0.73 | 0.86 | 0.92 | 0.86 | 0.84 | −1.78 | 0.84 | 0.68 | 0.71 |

Matt Shuttleworth | 0.91 | 0.69 | 0.86 | 0.92 | 0.86 | 0.83 | −0.80 | 0.83 | 0.68 | 0.67 |

Penman | 0.92 | 0.62 | 0.87 | 0.91 | 0.87 | 0.84 | −4.15 | 0.82 | −0.04 | 0.71 |

Penman-Monteith | 0.91 | 0.76 | 0.87 | 0.92 | 0.87 | 0.84 | −1.06 | 0.83 | 0.46 | 0.71 |

Priestley Taylor | 0.91 | 0.78 | 0.87 | 0.92 | 0.87 | 0.83 | −0.45 | 0.82 | 0.62 | 0.68 |

Turc | 0.92 | 0.78 | 0.87 | 0.92 | 0.87 | 0.82 | 0.13 | 0.82 | 0.47 | 0.73 |

Chungju | ||||||||||

Abtew | 0.79 | 0.66 | 0.60 | 0.84 | 0.79 | 0.86 | −1.67 | 0.86 | 0.80 | 0.83 |

Blaney Criddle | 0.82 | 0.64 | 0.65 | 0.85 | 0.82 | 0.79 | 0.65 | 0.85 | 0.73 | 0.86 |

Chapman Australian | 0.80 | 0.65 | 0.59 | 0.86 | 0.80 | 0.86 | −0.87 | 0.87 | −0.09 | 0.86 |

Granger Gray | 0.81 | 0.66 | 0.66 | 0.85 | 0.85 | 0.85 | 0.33 | 0.86 | 0.44 | 0.86 |

Hamon | 0.80 | 0.68 | 0.62 | 0.81 | 0.80 | 0.77 | 0.65 | 0.78 | 0.80 | 0.78 |

Hargreaves Samani | 0.80 | 0.68 | 0.56 | 0.82 | 0.80 | 0.86 | −1.56 | 0.86 | 0.70 | 0.85 |

Makkink | 0.81 | 0.66 | 0.59 | 0.85 | 0.81 | 0.86 | −0.23 | 0.87 | 0.68 | 0.87 |

Matt Shuttleworth | 0.81 | 0.68 | 0.64 | 0.85 | 0.81 | 0.84 | 0.32 | 0.86 | 0.58 | 0.86 |

Penman | 0.79 | 0.64 | 0.61 | 0.84 | 0.79 | 0.86 | −2.55 | 0.86 | 0.79 | 0.85 |

Penman-Monteith | 0.80 | 0.64 | 0.62 | 0.82 | 0.80 | 0.86 | −1.09 | 0.86 | −0.92 | 0.84 |

Priestley Taylor | 0.81 | 0.64 | 0.58 | 0.81 | 0.81 | 0.85 | −0.28 | 0.86 | 0.64 | 0.82 |

Turc | 0.83 | 0.68 | 0.60 | 0.85 | 0.83 | 0.83 | 0.14 | 0.85 | 0.51 | 0.86 |

## Appendix B

**Figure A1.**The GR4J model structure and feasible parameter ranges [15].

**Figure A2.**The SIMHYD model structure and feasible parameter ranges [65].

**Figure A3.**The CAT model structure and feasible parameter ranges [74].

**Figure A4.**The TANK model structure and feasible parameter ranges [80].

**Figure A5.**The SAC-SAM model structure and feasible parameter ranges [88].

**Figure A6.**The five hydrological models’ performance percentage variations calculated considering the Penman-Monteith PET input Nash-Sutcliffe Efficiency (NSE) index values as a benchmark for the calibration periods. (

**a**) Boryeong; (

**b**) Seomjingang; (

**c**) Soyanggang, and (

**d**) Chungju catchments.

## References

- Hrachowitz, M.; Clark, M.P. HESS Opinions: The complementary merits of competing modelling philosophies in hydrology. Hydrol. Earth Syst. Sci.
**2017**, 21, 3953–3973. [Google Scholar] [CrossRef] [Green Version] - Brown, C.M.; Lund, J.R.; Cai, X.; Reed, P.M.; Zagona, E.A.; Ostfeld, A.; Hall, J.; Characklis, G.W.; Yu, W.; Brekke, L. The future of water resources systems analysis: Toward a scientific framework for sustainable water management. Water Resour. Res.
**2015**, 51, 6110–6124. [Google Scholar] [CrossRef] [Green Version] - Casadei, S.; Pierleoni, A.; Bellezza, M. Sustainability of Water Withdrawals in the Tiber River Basin (Central Italy). Sustainability
**2018**, 10, 485. [Google Scholar] [CrossRef] - Park, D.; Kim, Y.; Um, M.-J.; Choi, S.-U. Robust Priority for Strategic Environmental Assessment with Incomplete Information Using Multi-Criteria Decision Making Analysis. Sustainability
**2015**, 7, 10233–10249. [Google Scholar] [CrossRef] [Green Version] - Horne, J. Water Information as a Tool to Enhance Sustainable Water Management—The Australian Experience. Water
**2015**, 7, 2161–2183. [Google Scholar] [CrossRef] [Green Version] - Chung, E.-S.; Abdulai, P.J.; Park, H.; Kim, Y.; Ahn, S.R.; Kim, S.J. Multi-Criteria Assessment of Spatial Robust Water Resource Vulnerability Using the TOPSIS Method Coupled with Objective and Subjective Weights in the Han River Basin. Sustainability
**2016**, 9, 29. [Google Scholar] [CrossRef] - Perrin, C.; Michel, C.; Andréassian, V. Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments. J. Hydrol.
**2001**, 242, 275–301. [Google Scholar] [CrossRef] - Beck, H.E.; van Dijk, A.I.; de Roo, A.; Dutra, E.; Fink, G.; Orth, R.; Schellekens, J. Global evaluation of runoff from 10 state-of-the-art hydrological models. Hydrol. Earth Syst. Sci.
**2017**, 21, 2881–2903. [Google Scholar] [CrossRef] [Green Version] - Beven, K.J. Rainfall-Runoff Modelling: The Primer, 2nd ed.; Wiley-Blackwell: Chichester, UK; Hoboken, NJ, USA, 2012; ISBN 978-0-47-071459-1. [Google Scholar]
- Beven, K. How far can we go in distributed hydrological modelling? Hydrol. Earth Syst. Sci. Discuss.
**2001**, 5, 1–12. [Google Scholar] [CrossRef] [Green Version] - Goderniaux, P.; Brouyère, S.; Fowler, H.J.; Blenkinsop, S.; Therrien, R.; Orban, P.; Dassargues, A. Large scale surface–subsurface hydrological model to assess climate change impacts on groundwater reserves. J. Hydrol.
**2009**, 373, 122–138. [Google Scholar] [CrossRef] - Kim, N.W.; Chung, I.M.; Won, Y.S.; Arnold, J.G. Development and application of the integrated SWAT–MODFLOW model. J. Hydrol.
**2008**, 356, 1–16. [Google Scholar] [CrossRef] - Butts, M.B.; Payne, J.T.; Kristensen, M.; Madsen, H. An evaluation of the impact of model structure on hydrological modelling uncertainty for streamflow simulation. J. Hydrol.
**2004**, 298, 242–266. [Google Scholar] [CrossRef] - Bennett, J.C.; Robertson, D.E.; Ward, P.G.D.; Hapuarachchi, H.A.P.; Wang, Q.J. Calibrating hourly rainfall-runoff models with daily forcings for streamflow forecasting applications in meso-scale catchments. Environ. Model. Softw.
**2016**, 76, 20–36. [Google Scholar] [CrossRef] - Perrin, C.; Michel, C.; Andréassian, V. Improvement of a parsimonious model for streamflow simulation. J. Hydrol.
**2003**, 279, 275–289. [Google Scholar] [CrossRef] - Jung, D.; Choi, Y.H.; Kim, J.H. Multiobjective Automatic Parameter Calibration of a Hydrological Model. Water
**2017**, 9, 187. [Google Scholar] [CrossRef] - Andréassian, V.; Perrin, C.; Michel, C. Impact of imperfect potential evapotranspiration knowledge on the efficiency and parameters of watershed models. J. Hydrol.
**2004**, 286, 19–35. [Google Scholar] [CrossRef] - Ficchì, A.; Perrin, C.; Andréassian, V. Impact of temporal resolution of inputs on hydrological model performance: An analysis based on 2400 flood events. J. Hydrol.
**2016**, 538, 454–470. [Google Scholar] [CrossRef] - Oudin, L.; Michel, C.; Anctil, F. Which potential evapotranspiration input for a lumped rainfall-runoff model? Part 1—Can rainfall-runoff models effectively handle detailed potential evapotranspiration inputs? J. Hydrol.
**2005**, 303, 275–289. [Google Scholar] [CrossRef] - Oudin, L.; Hervieu, F.; Michel, C.; Perrin, C.; Andréassian, V.; Anctil, F.; Loumagne, C. Which potential evapotranspiration input for a lumped rainfall-runoff model? Part 2—Towards a simple and efficient potential evapotranspiration model for rainfall–runoff modelling. J. Hydrol.
**2005**, 303, 290–306. [Google Scholar] [CrossRef] - Knipper, K.; Hogue, T.; Scott, R.; Franz, K. Evapotranspiration Estimates Derived Using Multi-Platform Remote Sensing in a Semiarid Region. Remote Sens.
**2017**, 9, 184. [Google Scholar] [CrossRef] - Harrigan, S.; Berghuijs, W. The Mystery of Evaporation. Streams of Thought. Young Hydrol. Soc.
**2016**, 10. [Google Scholar] [CrossRef] - Guo, D.; Westra, S.; Maier, H.R. An R package for modelling actual, potential and reference evapotranspiration. Environ. Model. Softw.
**2016**, 78, 216–224. [Google Scholar] [CrossRef] - Parmele, L.H. Errors in output of hydrologic models due to errors in input potential evapotranspiration. Water Resour. Res.
**1972**, 8, 348–359. [Google Scholar] [CrossRef] - Nandakumar, N.; Mein, R.G. Uncertainty in rainfall-runoff model simulations and the implications for predicting the hydrologic effects of land-use change. J. Hydrol.
**1997**, 192, 211–232. [Google Scholar] [CrossRef] - Paturel, J.E.; Servat, E.; Vassiliadis, A. Sensitivity of conceptual rainfall-runoff algorithms to errors in input data—Case of the GR2M model. J. Hydrol.
**1995**, 168, 111–125. [Google Scholar] [CrossRef] - Xu, C.-Y.; Vandewiele, G.L. Sensitivity of monthly rainfall-runoff models to input errors and data length. Hydrol. Sci. J.
**1994**, 39, 157–176. [Google Scholar] [CrossRef] [Green Version] - Xu, C.; Tunemar, L.; Chen, Y.D.; Singh, V.P. Evaluation of seasonal and spatial variations of lumped water balance model sensitivity to precipitation data errors. J. Hydrol.
**2006**, 324, 80–93. [Google Scholar] [CrossRef] - Barella-Ortiz, A.; Polcher, J.; Tuzet, A.; Laval, K. Potential evaporation estimation through an unstressed surface-energy balance and its sensitivity to climate change. Hydrol. Earth Syst. Sci.
**2013**, 17, 4625–4639. [Google Scholar] [CrossRef] [Green Version] - McVicar, T.R.; Roderick, M.L.; Donohue, R.J.; Li, L.T.; Van Niel, T.G.; Thomas, A.; Grieser, J.; Jhajharia, D.; Himri, Y.; Mahowald, N.M.; et al. Global review and synthesis of trends in observed terrestrial near-surface wind speeds: Implications for evaporation. J. Hydrol.
**2012**, 416–417, 182–205. [Google Scholar] [CrossRef] - Andersson, L. Improvements of runoff models what way to go? Hydrol. Res.
**1992**, 23, 315–332. [Google Scholar] [CrossRef] - Lindroth, A. Potential Evaporation—A Matter of Definition: A Comment on ‘Improvements of Runoff Models—What Way to Go’? Hydrol. Res.
**1993**, 24, 359–364. [Google Scholar] [CrossRef] - Morton, F.I. Evaporation research—A critical review and its lessons for the environmental sciences. Crit. Rev. Environ. Sci. Technol.
**1994**, 24, 237–280. [Google Scholar] [CrossRef] - Evans, J.P. Improving the characteristics of streamflow modeled by regional climate models. J. Hydrol.
**2003**, 284, 211–227. [Google Scholar] [CrossRef] - Oudin, L.; Andréassian, V.; Perrin, C.; Anctil, F. Locating the sources of low-pass behavior within rainfall-runoff models: Low-pass behavior of rainfall-runoff models. Water Resour. Res.
**2004**, 40. [Google Scholar] [CrossRef] - Oudin, L.; Perrin, C.; Mathevet, T.; Andréassian, V.; Michel, C. Impact of biased and randomly corrupted inputs on the efficiency and the parameters of watershed models. J. Hydrol.
**2006**, 320, 62–83. [Google Scholar] [CrossRef] - Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models. Part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Beven, K.; Binley, A. GLUE: 20 years on. Hydrol. Process.
**2014**, 28, 5897–5918. [Google Scholar] [CrossRef] - Moussa, R.; Chahinian, N. Comparison of different multi-objective calibration criteria using a conceptual rainfall-runoff model of flood events. Hydrol. Earth Syst. Sci.
**2009**, 13, 519–535. [Google Scholar] [CrossRef] [Green Version] - Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Gupta, H.V.; Kling, H.; Yilmaz, K.K.; Martinez, G.F. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. J. Hydrol.
**2009**, 377, 80–91. [Google Scholar] [CrossRef] [Green Version] - Clark, M.P.; Slater, A.G.; Rupp, D.E.; Woods, R.A.; Vrugt, J.A.; Gupta, H.V.; Wagener, T.; Hay, L.E. Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resour. Res.
**2008**, 44, W00B02. [Google Scholar] [CrossRef] - Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control
**1974**, 19, 716–723. [Google Scholar] [CrossRef] - Schwarz, G. Estimating the Dimension of a Model. Ann. Stat.
**1978**, 6, 461–464. [Google Scholar] [CrossRef] - Qi, M.; Zhang, G.P. An investigation of model selection criteria for neural network time series forecasting. Eur. J. Oper. Res.
**2001**, 132, 666–680. [Google Scholar] [CrossRef] - Laio, F.; Di Baldassarre, G.; Montanari, A. Model selection techniques for the frequency analysis of hydrological extremes. Water Resour. Res.
**2009**, 45, W07416. [Google Scholar] [CrossRef] - Merz, R.; Parajka, J.; Blöschl, G. Time stability of catchment model parameters: Implications for climate impact analyses. Water Resour. Res.
**2011**, 47, W02531. [Google Scholar] [CrossRef] - Coron, L.; Andréassian, V.; Perrin, C.; Bourqui, M.; Hendrickx, F. On the lack of robustness of hydrologic models regarding water balance simulation: A diagnostic approach applied to three models of increasing complexity on 20 mountainous catchments. Hydrol. Earth Syst. Sci.
**2014**, 18, 727–746. [Google Scholar] [CrossRef] - Duan, Q.; Sorooshian, S.; Gupta, V.K. Optimal use of the SCE-UA global optimization method for calibrating watershed models. J. Hydrol.
**1994**, 158, 265–284. [Google Scholar] [CrossRef] [Green Version] - Ajami, N.K.; Gupta, H.; Wagener, T.; Sorooshian, S. Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system. J. Hydrol.
**2004**, 298, 112–135. [Google Scholar] [CrossRef] - Madsen, H. Automatic calibration of a conceptual rainfall–runoff model using multiple objectives. J. Hydrol.
**2000**, 235, 276–288. [Google Scholar] [CrossRef] - Roy, T.; Gupta, H.V.; Serrat-Capdevila, A.; Valdes, J.B. Using satellite-based evapotranspiration estimates to improve the structure of a simple conceptual rainfall–runoff model. Hydrol. Earth Syst. Sci.
**2017**, 21, 879–896. [Google Scholar] [CrossRef] [Green Version] - McMahon, T.A.; Peel, M.C.; Lowe, L.; Srikanthan, R.; McVicar, T.R. Estimating actual, potential, reference crop and pan evaporation using standard meteorological data: A pragmatic synthesis. Hydrol. Earth Syst. Sci.
**2013**, 17, 1331–1363. [Google Scholar] [CrossRef] - Xu, C.-Y.; Singh, V.P. Cross Comparison of Empirical Equations for Calculating Potential Evapotranspiration with Data from Switzerland. Water Resour. Manag.
**2002**, 16, 197–219. [Google Scholar] [CrossRef] - Brutsaert, W. Evaporation into the Atmosphere: Theory, History and Applications; Springer: Dordrecht, The Netherlands, 1982; ISBN 978-9-40-171497-6. [Google Scholar]
- Zhao, L.; Xia, J.; Xu, C.; Wang, Z.; Sobkowiak, L.; Long, C. Evapotranspiration estimation methods in hydrological models. J. Geogr. Sci.
**2013**, 23, 359–369. [Google Scholar] [CrossRef] - García Hernández, J.; Claude, A.; Paredes Arquiola, J.; Roquier, B.; Boillat, J.-L. Integrated flood forecasting and management system in a complex catchment area in the Alps—Implementation of the MINERVE project in the Canton of Valais. In Special Session on Swiss Competences in River Engineering and Restoration, Proceedings of the River Flow 2014, Lausanne, Switzerland, 3–5 September 2014; EPFL: Leiden, Switzerland, 2014; pp. 87–97. [Google Scholar]
- Demirel, M.C.; Booij, M.J.; Hoekstra, A.Y. The skill of seasonal ensemble low-flow forecasts in the Moselle River for three different hydrological models. Hydrol. Earth Syst. Sci.
**2015**, 19, 275–291. [Google Scholar] [CrossRef] [Green Version] - Kim, D.; Jung, I.W.; Chun, J.A. A comparative assessment of rainfall–runoff modelling against regional flow duration curves for ungauged catchments. Hydrol. Earth Syst. Sci.
**2017**, 21, 5647–5661. [Google Scholar] [CrossRef] [Green Version] - Nepal, S.; Chen, J.; Penton, D.J.; Neumann, L.E.; Zheng, H.; Wahid, S. Spatial GR4J conceptualization of the Tamor glaciated alpine catchment in Eastern Nepal: Evaluation of GR4JSG against streamflow and MODIS snow extent: Hydrological Modelling in Tamor Catchment. Hydrol. Process.
**2017**, 31, 51–68. [Google Scholar] [CrossRef] - Velázquez, J.A.; Anctil, F.; Ramos, M.H.; Perrin, C. Can a multi-model approach improve hydrological ensemble forecasting? A study on 29 French catchments using 16 hydrological model structures. Adv. Geosci.
**2011**, 29, 33–42. [Google Scholar] [CrossRef] [Green Version] - Ajmal, M.; Khan, T.A.; Kim, T.-W. A CN-Based Ensembled Hydrological Model for Enhanced Watershed Runoff Prediction. Water
**2016**, 8, 20. [Google Scholar] [CrossRef] - Tian, Y.; Booij, M.J.; Xu, Y.-P. Uncertainty in high and low flows due to model structure and parameter errors. Stoch. Environ. Res. Risk Assess.
**2014**, 28, 319–332. [Google Scholar] [CrossRef] - Porter, J.W.; McMahon, T.A. Application of a catchment model in southeastern Australia. J. Hydrol.
**1975**, 24, 121–134. [Google Scholar] [CrossRef] - Chiew, F.H.S.; Peel, M.C.; Western, A.W. Application and testing of the simple rainfall-runoff model SIMHYD. In Mathematical Models of Small Watershed Hydrology and Applications; Singh, V.P., Frevert, D.K., Eds.; Water Resources Publications: Littleton, CO, USA, 2002; pp. 335–367. [Google Scholar]
- Chiew, F.H.S.; Kirono, D.G.C.; Kent, D.M.; Frost, A.J.; Charles, S.P.; Timbal, B.; Nguyen, K.C.; Fu, G. Comparison of runoff modelled using rainfall from different downscaling methods for historical and future climates. J. Hydrol.
**2010**, 387, 10–23. [Google Scholar] [CrossRef] - Li, C.Z.; Zhang, L.; Wang, H.; Zhang, Y.Q.; Yu, F.L.; Yan, D.H. The transferability of hydrological models under nonstationary climatic conditions. Hydrol. Earth Syst. Sci.
**2012**, 16, 1239–1254. [Google Scholar] [CrossRef] [Green Version] - Li, H.; Zhang, Y. Regionalising rainfall-runoff modelling for predicting daily runoff: Comparing gridded spatial proximity and gridded integrated similarity approaches against their lumped counterparts. J. Hydrol.
**2017**, 550, 279–293. [Google Scholar] [CrossRef] - Vaze, J.; Post, D.A.; Chiew, F.H.S.; Perraud, J.-M.; Teng, J.; Viney, N.R. Conceptual Rainfall–Runoff Model Performance with Different Spatial Rainfall Inputs. J. Hydrometeorol.
**2011**, 12, 1100–1112. [Google Scholar] [CrossRef] - Yu, B.; Zhu, Z. A comparative assessment of AWBM and SimHyd for forested watersheds. Hydrol. Sci. J.
**2015**, 60, 1200–1212. [Google Scholar] [CrossRef] - Peel, M.C.; Chiew, F.H.; Western, A.W.; McMahon, T.A. Extension of Unimpaired Monthly Streamflow Data and Regionalisation of Parameter Values to Estimate Streamflow in Ungauged Catchments; Australian Natural Resources Atlas: Melbourne, Australia, 2000. [Google Scholar]
- Kim, H.-J.; Jang, C.-H. Catchment Hydrologic Cycle Assessment Tool—A User Guide; Korea Institute of Civil Engineering and Building Technology: Goyang, Korea, 2017. [Google Scholar]
- Miller, J.D.; Kim, H.; Kjeldsen, T.R.; Packman, J.; Grebby, S.; Dearden, R. Assessing the impact of urbanization on storm runoff in a peri-urban catchment using historical change in impervious cover. J. Hydrol.
**2014**, 515, 59–70. [Google Scholar] [CrossRef] [Green Version] - Kim, H.-J.; Jang, C.-H.; Noh, S.-J. Development and application of the catchment hydrologic cycle assessment tool considering urbanization (I)-Model development. J. Korea Water Resour. Assoc.
**2012**, 45, 203–215. [Google Scholar] [CrossRef] - Green, W.H.; Ampt, G.A. Studies on Soil Phyics. J. Agric. Sci.
**1911**, 4, 1–24. [Google Scholar] [CrossRef] - Jang, C.H.; Kim, H.J.; Ahn, S.R.; Kim, S.J. Assessment of hydrological changes in a river basin as affected by climate change and water management practices, by using the cat model. Irrig. Drain.
**2016**, 65, 26–35. [Google Scholar] [CrossRef] - Jang, C.-H.; Kim, H.-J.; Kim, J.-T. Prediction of Reservoir Water Level using CAT. J. Korean Soc. Agric. Eng.
**2012**, 54, 27–38. [Google Scholar] [CrossRef] [Green Version] - Choi, S.; Jang, C.; Kim, H. Analysis of Short-term Runoff Characteristics of CAT-PEST Connected Model using Different Infiltration Analysis Methods. J. Korea Acad. Ind. Coop. Soc.
**2016**, 17, 26–41. [Google Scholar] [CrossRef] - Hwang, S.; Kang, M.-S. Evaluation of the CAT Model in hydrological simulation for a small watershed. In Proceedings of the 2012 ASABE Annual International Meeting, Dallas, TX, USA, 29 July–1 August 2012; American Society of Agricultural and Biological Engineers: St. Joseph, MI, USA, 2012; p. 1. [Google Scholar]
- Sugawara, M. Automatic calibration of the tank model/L’étalonnage automatique d’un modèle à cisterne. Hydrol. Sci. Bull.
**1979**, 24, 375–388. [Google Scholar] [CrossRef] - Chadalawada, J.; Havlicek, V.; Babovic, V. A Genetic Programming Approach to System Identification of Rainfall-Runoff Models. Water Resour. Manag.
**2017**, 31, 3975–3992. [Google Scholar] [CrossRef] - Sugawara, M. Tank model. In Computer Models of Watershed Hydrology; Singh, V.P., Ed.; Water Resources Publications: Littleton, CO, USA, 1995; ISBN 0-918334-91-8. [Google Scholar]
- Lee, Y.H.; Singh, V.P. Tank Model for Sediment Yield. Water Resour. Manag.
**2005**, 19, 349–362. [Google Scholar] [CrossRef] - Sung, Y.-K.; Kim, S.-H.; Kim, H.-J.; Kim, N.-W. The Applicability Study of SYMHYD and TANK Model Using Different Type of Objective Functions and Optimization Methods. J. Korea Water Resour. Assoc.
**2004**, 37, 121–131. [Google Scholar] [CrossRef] - Yokoo, Y.; Chiba, T.; Shikano, Y.; Leong, C. Identifying dominant runoff mechanisms and their lumped modeling: A data-based modeling approach. Hydrol. Res. Lett.
**2017**, 11, 128–133. [Google Scholar] [CrossRef] - Song, J.-H.; Her, Y.; Park, J.; Lee, K.-D.; Kang, M.-S. Simulink Implementation of a Hydrologic Model: A Tank Model Case Study. Water
**2017**, 9, 639. [Google Scholar] [CrossRef] - Chen, R.-S.; Pi, L.-C.; Hsieh, C.-C. Application of Parameter Optimization Method for Calibrating Tank Model1. J. Am. Water Resour. Assoc.
**2005**, 41, 389–402. [Google Scholar] [CrossRef] - Burnash, R.J.C. The NWS river forecast system-catchment modeling. In Computer Models of Watershed Hydrology; Singh, V.P., Ed.; Water Resources Publications: Littleton, CO, USA, 1995; ISBN 0-918334-91-8. [Google Scholar]
- Wright, A.J.; Walker, J.P.; Pauwels, V.R.N. Estimating rainfall time series and model parameter distributions using model data reduction and inversion techniques. Water Resour. Res.
**2017**, 53, 6407–6424. [Google Scholar] [CrossRef] - Bowman, A.L.; Franz, K.J.; Hogue, T.S. Case Studies of a MODIS-Based Potential Evapotranspiration Input to the Sacramento Soil Moisture Accounting Model. J. Hydrometeorol.
**2016**, 18, 151–158. [Google Scholar] [CrossRef] - Heřmanovský, M.; Havlíček, V.; Hanel, M.; Pech, P. Regionalization of runoff models derived by genetic programming. J. Hydrol.
**2017**, 547, 544–556. [Google Scholar] [CrossRef] - Huang, C.; Newman, A.J.; Clark, M.P.; Wood, A.W.; Zheng, X. Evaluation of snow data assimilation using the ensemble Kalman filter for seasonal streamflow prediction in the western United States. Hydrol. Earth Syst. Sci.
**2017**, 21, 635–650. [Google Scholar] [CrossRef] - Katsanou, K.; Lambrakis, N. Modeling the Hellenic karst catchments with the Sacramento Soil Moisture Accounting model. Hydrogeol. J.
**2017**, 25, 757–769. [Google Scholar] [CrossRef] - Shin, M.-J.; Guillaume, J.H.A.; Croke, B.F.W.; Jakeman, A.J. Addressing ten questions about conceptual rainfall–runoff models with global sensitivity analyses in R. J. Hydrol.
**2013**, 503, 135–152. [Google Scholar] [CrossRef] - Vrugt, J.A.; Gupta, H.V.; Dekker, S.C.; Sorooshian, S.; Wagener, T.; Bouten, W. Application of stochastic parameter optimization to the Sacramento Soil Moisture Accounting model. J. Hydrol.
**2006**, 325, 288–307. [Google Scholar] [CrossRef] - Anderson, R.M.; Koren, V.I.; Reed, S.M. Using SSURGO data to improve Sacramento Model a priori parameter estimates. J. Hydrol.
**2006**, 320, 103–116. [Google Scholar] [CrossRef] - Khu, S.-T.; Werner, M.G. Reduction of Monte-Carlo simulation runs for uncertainty estimation in hydrological modelling. Hydrol. Earth Syst. Sci. Discuss.
**2003**, 7, 680–692. [Google Scholar] [CrossRef] [Green Version] - Lee, S.; Kang, T. Analysis of Constrained Optimization Problems by the SCE-UA with an Adaptive Penalty Function. J. Comput. Civ. Eng.
**2016**, 30, 04015035. [Google Scholar] [CrossRef] - Van Griensven, A.; Meixner, T.; Grunwald, S.; Bishop, T.; Diluzio, M.; Srinivasan, R. A global sensitivity analysis tool for the parameters of multi-variable catchment models. J. Hydrol.
**2006**, 324, 10–23. [Google Scholar] [CrossRef] - Rosenbrock, H. An automatic method for finding the greatest or least value of a function. Comput. J.
**1960**, 3, 175–184. [Google Scholar] [CrossRef] - Liu, X.; Yang, T.; Hsu, K.; Liu, C.; Sorooshian, S. Evaluating the streamflow simulation capability of PERSIANN-CDR daily rainfall products in two river basins on the Tibetan Plateau. Hydrol. Earth Syst. Sci.
**2017**, 21, 169–181. [Google Scholar] [CrossRef] [Green Version] - Kim, H.; Kim, S.; Shin, H.; Heo, J.-H. Appropriate model selection methods for nonstationary generalized extreme value models. J. Hydrol.
**2017**, 547, 557–574. [Google Scholar] [CrossRef] - Gaganis, P.; Smith, L. A Bayesian Approach to the quantification of the effect of model error on the predictions of groundwater models. Water Resour. Res.
**2001**, 37, 2309–2322. [Google Scholar] [CrossRef] [Green Version] - Kamruzzaman, M.; Shahriar, M.S.; Beecham, S. Assessment of Short Term Rainfall and Stream Flows in South Australia. Water
**2014**, 6, 3528–3544. [Google Scholar] [CrossRef] [Green Version] - Wilby, R.L.; Abrahart, R.J.; Dawson, C.W. Detection of conceptual model rainfall-runoff processes inside an artificial neural network. Hydrol. Sci. J.
**2003**, 48, 163–181. [Google Scholar] [CrossRef] - Coron, L.; Andréassian, V.; Perrin, C.; Lerat, J.; Vaze, J.; Bourqui, M.; Hendrickx, F. Crash testing hydrological models in contrasted climate conditions: An experiment on 216 Australian catchments. Water Resour. Res.
**2012**, 48, W05552. [Google Scholar] [CrossRef] - Hornberger, G.M.; Beven, K.J.; Cosby, B.J.; Sappington, D.E. Shenandoah Watershed Study: Calibration of a Topography-Based, Variable Contributing Area Hydrological Model to a Small Forested Catchment. Water Resour. Res.
**1985**, 21, 1841–1850. [Google Scholar] [CrossRef] - Loague, K.M.; Freeze, R.A. A Comparison of Rainfall-Runoff Modeling Techniques on Small Upland Catchments. Water Resour. Res.
**1985**, 21, 229–248. [Google Scholar] [CrossRef] - Beven, K. Changing ideas in hydrology -The case of physically-based models. J. Hydrol.
**1989**, 105, 157–172. [Google Scholar] [CrossRef] - Orth, R.; Staudinger, M.; Seneviratne, S.I.; Seibert, J.; Zappa, M. Does model performance improve with complexity? A case study with three hydrological models. J. Hydrol.
**2015**, 523, 147–159. [Google Scholar] [CrossRef] [Green Version] - Gan, T.Y.; Dlamini, E.M.; Biftu, G.F. Effects of model complexity and structure, data quality, and objective functions on hydrologic modeling. J. Hydrol.
**1997**, 192, 81–103. [Google Scholar] [CrossRef] - Abtew, W. Evapotranspiration Measurements and Modeling for Three Wetland Systems in South Florida1. J. Am. Water Resour. Assoc.
**1996**, 32, 465–473. [Google Scholar] [CrossRef] - Allen, R.G.; Pruitt, W.O. Rational Use of the FAO Blaney-Criddle Formula. J. Irrig. Drain. Eng.
**1986**, 112, 139–155. [Google Scholar] [CrossRef] - Chapman, T.G. Estimation of evaporation in rainfall-runoff models. In Proceedings of the MODSIM 2003 International Congress on Modelling and Simulation, Townsville, Australia, 14–17 July 2003; Volume 1, pp. 148–153. [Google Scholar]
- Granger, R.J.; Gray, D.M. Evaporation from natural nonsaturated surfaces. J. Hydrol.
**1989**, 111, 21–29. [Google Scholar] [CrossRef] - Hamon, W.R. Estimating Potential Evapotranspiration. J. Hydraul. Div.
**1961**, 87, 107–120. [Google Scholar] - Hargreaves, G.H.; Samani, Z.A. Reference crop evapotranspiration from temperature. Appl. Eng. Agric.
**1985**, 1, 96–99. [Google Scholar] [CrossRef] - De Bruin, H.A.R.; Lablans, W.N. Reference crop evapotranspiration determined with a modified Makkink equation. Hydrol. Process.
**1998**, 12, 1053–1062. [Google Scholar] [CrossRef] - Shuttleworth, W.J.; Wallace, J.S. Calculating the water requirements of irrigated crops in Australia using the Matt-Shuttleworth approach. Trans. ASABE
**2009**, 52, 1895–1906. [Google Scholar] [CrossRef] - Penman, H.L. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. Lond. A
**1948**, 193, 120–145. [Google Scholar] [CrossRef] - Allen, R.G.; Pereira, L.S.; Raes, D.; Smith, M. FAO Irrigation and Drainage Paper No. 56; Food and Agriculture Organization of the United Nations: Rome, Italy, 1998; Volume 56, pp. 97–156. [Google Scholar]
- Priestley, C.H.B.; Taylor, R.J. On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters. Mon. Weather Rev.
**1972**, 100, 81–92. [Google Scholar] [CrossRef] [Green Version] - Turc, L. Estimation of irrigation water requirements, potential evapotranspiration: A simple climatic formula evolved up to date. Ann. Agron.
**1961**, 12, 13–49. [Google Scholar]

**Figure 2.**Land use and the soil texture map of the 10 gauged catchments. (

**a**) Land use and (

**b**) Soil texture.

**Figure 3.**Daily Potential Evapotranspiration (PET). (

**a**) Daily PET of Seolmacheon, Boryeong, Kyeongan, Seomjingang, and Yongdam catchments (

**b**) Daily PET of Juam, Imha, Andong, Soyanggang, and Chungju catchments.

**Figure 4.**The performances of the five hydrological models for the 12 Potential Evapotranspiration (PET) input values in the calibration periods. (

**a**) Nash-Sutcliffe Efficiency (NSE); (

**b**) Logarithmic Nash-Sutcliffe Efficiency (LogNSE); (

**c**) Ratio of the root mean square error to the standard deviation of measured data (RSR); and, (

**d**) Kling-Gupta Efficiency (KGE) corresponding to the catchment No. 1–10. The vertical axis corresponds to the model performances of the 12 PET inputs.

**Figure 5.**The performances of the five hydrological models for the 12 Potential Evapotranspiration (PET) input values in the validation periods. (

**a**) Nash-Sutcliffe Efficiency (NSE); (

**b**) Logarithmic Nash-Sutcliffe Efficiency (LogNSE); (

**c**) Ratio of the root mean square error to the standard deviation of measured data (RSR); and, (

**d**) Kling-Gupta Efficiency (KGE) corresponding to the catchment No. 1–10. The vertical axis corresponds to the model performances of the 12 PET inputs.

**Figure 6.**The five hydrological models’ performance percentage variations calculated considering the Penman-Monteith PET input Nash-Sutcliffe Efficiency (NSE) index values as a benchmark for the validation periods. (

**a**) Boryeong; (

**b**) Seomjingang; (

**c**) Soyanggang; and, (

**d**) Chungju catchments.

**Figure 7.**Scatterplot of the five hydrological models’ performance (Nash-Sutcliffe Efficiency (NSE)) for the Penman-Monteith Potential Evapotranspiration (PET) input. (

**a**) Boryeong; (

**b**) Seomjingang; (

**c**) Soyanggang; and, (

**d**) Chungju catchments.

**Figure 8.**Five hydrological models‘ performance (Nash-Sutcliffe Efficiency (NSE)) for the 12 PET inputs. (

**a**) Boryeong; (

**b**) Seomjingang; (

**c**) Soyanggang; and, (

**d**) Chungju catchments.

**Figure 9.**Five hydrological models’ parameters response to the 12 PET input for the Boryeong catchment. (

**a**) Génie Rural à 4 paramètres Journalier (GR4J); (

**b**) Simplified Hydrolog (SIMHYD); (

**c**) Catchment Hydrological Cycle Assessment Tool (CAT); (

**d**) TANK, and (

**e**) Sacramento Soil Moisture Accounting (SAC-SMA). The letters correspond to the five hydrological models’ parameters.

**Figure 10.**Five hydrological models’ statistical indicator values for the 12 PET inputs in the validation periods. (

**a**) Boryeong; (

**b**) Seomjingang; (

**c**) Soyanggang; and, (

**d**) Chungju catchments. The black color is the Akaike Information Criterion (AIC), the green color is the Bayesian Information Criterion (BIC), and the blue black color is the Adjusted R-square (Ra

^{2}).

**Figure 11.**Five hydrological models’ Dimensionless Bias and behavioral similarities for the 12 PET inputs values in the Boryeong catchment. (

**a**) Hydro-meteorological data; (

**b**) GR4J; (

**c**) SIMHYD; (

**d**) CAT; (

**e**) TANK; and, (

**f**) SAC-SMA models.

No | ^{1} Catchment | Area (km^{2}) | Mean Annual T (°C) | Mean Annual P (mm) | Mean Annual PET (mm) | Mean Annual Q (mm) | PET/P | Q/P |
---|---|---|---|---|---|---|---|---|

1 | Seolmacheon | 8.50 | 11.19 | 1542.30 | 1226.65 | 1064.40 | 0.80 | 0.69 |

2 | Boryeong | 163.70 | 12.77 | 1425.43 | 1012.27 | 882.52 | 0.71 | 0.62 |

3 | Kyeongan | 262.40 | 12.76 | 1400.28 | 1326.09 | 937.12 | 0.95 | 0.67 |

4 | Seomjingang | 763 | 11.91 | 1466.98 | 815.19 | 883.34 | 0.56 | 0.60 |

5 | Yongdam | 930 | 11.11 | 1477.57 | 883.27 | 904.69 | 0.60 | 0.61 |

6 | Juam | 1010 | 14.61 | 1595.86 | 1017.39 | 776.18 | 0.64 | 0.49 |

7 | Imha | 1361 | 12.52 | 1073.55 | 940.98 | 575.06 | 0.88 | 0.54 |

8 | Andong | 1584 | 11.82 | 1302.23 | 1032.93 | 728.20 | 0.79 | 0.56 |

9 | Soyanggang | 2703 | 11.78 | 1394.90 | 840.89 | 915.85 | 0.60 | 0.66 |

10 | Chungju | 6648 | 12.10 | 1406.93 | 922.96 | 930.96 | 0.66 | 0.66 |

^{1}The analysis period (2002–2012) was the same for all catchments except Kyeongan (2000–2008). Mean Temperature (T), Potential Evapotranspiration (PET), Precipitation (P), and Streamflow (Q).

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Birhanu, D.; Kim, H.; Jang, C.; Park, S.
Does the Complexity of Evapotranspiration and Hydrological Models Enhance Robustness? *Sustainability* **2018**, *10*, 2837.
https://doi.org/10.3390/su10082837

**AMA Style**

Birhanu D, Kim H, Jang C, Park S.
Does the Complexity of Evapotranspiration and Hydrological Models Enhance Robustness? *Sustainability*. 2018; 10(8):2837.
https://doi.org/10.3390/su10082837

**Chicago/Turabian Style**

Birhanu, Dereje, Hyeonjun Kim, Cheolhee Jang, and Sanghyun Park.
2018. "Does the Complexity of Evapotranspiration and Hydrological Models Enhance Robustness?" *Sustainability* 10, no. 8: 2837.
https://doi.org/10.3390/su10082837