# Comparison of Three Daily Rainfall-Runoff Hydrological Models Using Four Evapotranspiration Models in Four Small Forested Watersheds with Different Land Cover in South-Central Chile

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{−1}; no forest management was performed in these catchments [3].

#### 2.2. Hydrometeorological Data

#### 2.3. Hydrological Models

_{1}: maximum storage capacity (mm); X

_{2}: groundwater exchange coefficient (mm); X

_{3}: maximum channel transit capacity (mm); and X

_{4}: base time of unit hydrograph (days) [22] (Figure 3).

_{5}, is an exchange threshold between precipitation capture (dimensionless) [74].

_{6}parameter corresponds to the exponential storage vacuum coefficient and can only take values greater than or equal to 0 [24,74]. A better understanding of the methodological steps followed for this research work is shown in Figure 4.

#### 2.4. Evapotranspiration Models

_{O}) model [48] (Equations (1) and (2)) is defined as a physically based daily potential model in which potential evapotranspiration depends exclusively on temperature and extraterrestrial solar radiation.

_{O}= Oudin’s model estimate for potential evapotranspiration (mm day

^{−1}); ${\mathrm{R}}_{\mathrm{e}}$ = extraterrestrial radiation (Mj m

^{2}day

^{−1}); $\mathrm{t}$ = temperature (°C); $\mathsf{\lambda}$ = latent heat flux (Mj kg

^{−1}); $\mathsf{\rho}$ = water density (kg m

^{−3}).

_{H}) model (Equation (3)) is a daily potential evapotranspiration model, also physics-based, which, unlike the one proposed by Oudin, depends on temperature and incident solar radiation [76].

_{H}= Hargreaves’ model estimate for potential evapotranspiration (mm day

^{−1}); R

_{S}= incident radiation (mm day

^{−1}); t = temperature (°C).

_{PTp}) [55] (Equation (4)) defines potential evaporation as the evaporation that would occur from a hypothetical saturated surface, with similar radiative properties throughout the study area. This area is small enough so that excess moisture flux does not change the characteristics of the convective boundary layer.

_{PTp}= equilibrium rate of evapotranspiration (mm day

^{−1}), which assumes no aerodynamic transfer; Δ = slope of the saturated steam heat curve (Pa °C

^{−1}); Υ = psychometric constant (Pa °C

^{−1}); λ = latent heat flux (Mj kg

^{−1}).

_{PTp}[77]. The parameter “α” is related to the vegetation land cover and corresponds to the relationship between the rate of evapotranspiration and the rate of limiting evapotranspiration observed in the study area [55].

_{PTa}) (Equation (5)). The parameter “α” has been studied by several authors and calculated for different types of ecosystems (e.g., [77,78]). In our case, it was estimated from the values proposed by [79,80,81] for coniferous and broad-leaved temperate forests (0.77 for native forest in Q2, 0.73 for coniferous and native forest in Q3 and 0.83 for broad-leaved eucalyptus in BLQ1 and BLQ2). For more details of E

_{O}, E

_{H}, E

_{PTp}and E

_{PTa}, see [48,76,79,80,81].

_{PTa}= Priestley–Taylor’s model estimate for actual evapotranspiration (mm day

^{−1}); Δ = slope of the saturated steam heat curve (Pa °C

^{−1}); Υ = psychometric constant (Pa °C

^{−1}); λ = latent heat flux (Mj kg

^{−1}); α = coefficient related to vegetation land cover.

#### 2.5. Model Calibration and Validation

#### 2.6. Model Efficiency

_{PTa}).

#### 2.7. Sensitivity Analysis

## 3. Results

#### 3.1. Best Evapotranspiration Model That Maximizes Model Performance

_{1}-X

_{2}-X

_{4}parameter values and higher X

_{3}parameter values. The X

_{5}parameter was in general lower in catchment Q2 and the X

_{6}parameter was higher in wetter catchments (BLQ1 and 2).

_{PTp}(Priestley–Taylor), E

_{PTa}(Actual Priestley–Taylor) and E

_{H}(Hargreaves–Samani) methods, which in summer months are on average four and three times higher than Oudin evapotranspiration methods, respectively. On the contrary, the minimum values in summer months are reached by the E

_{o}(Oudin) method. During the winter months, all models achieved similar evapotranspiration values (Figure 6).

_{O}model, and in BLQ1 with the E

_{H}method. In the GR5J model, the highest efficiency was obtained in catchments Q3, BLQ1 and BLQ2 with the E

_{O}method, and in Q2 with E

_{H}. Finally, the GR6J model reached its highest efficiency in catchments Q3, BLQ1 and BLQ2 when the E

_{O}method was used, and in Q2 when E

_{PTp}was used.

#### 3.2. Peak Flows and Summer Flow

#### 3.3. Sensitivity Analysis

_{1}and X

_{4}showed low sensitivity because a given value of the parameters could be associated with high or low efficiency values. On the contrary, parameters X

_{2}and X

_{3}showed high sensitivity since the distribution of the parameter values, and the efficiency statistic RMSE, reflected a clear efficiency trend in both. This means that negative values close to 0 in X

_{2}, and values higher than 2000 in X

_{3}, allowed higher efficiency in the flow simulation (Figure A1 in Appendix A).

_{1}, X

_{3}and X

_{4}showed low sensitivity. In the GR6J model, the parameter X

_{6}also showed low sensitivity, since a given value of the parameters can be associated with high or low efficiency values. On the contrary, parameters X

_{2}and X

_{5}were very sensitive and values close to 0 reached the lowest RMSE values, i.e., higher efficiency. As the parameters moved away from 0, efficiency decreased and RMSE increased (Figure A2 and Figure A3 in Appendix A).

## 4. Discussion

_{O}) in the dry mixed land cover (Q3) and in both wet southern catchments (BLQ1 and BLQ2) with E. nitens land cover. Consistently, Oudin’s potential evapotranspiration model yielded better results in all models and in all catchments. Therefore, our study validated the hypothesis (i) that increasing model complexity will allow for greater efficiency in simulating streamflow in small catchments, and a simpler PET approach also achieved better results, as also showed by Kannan et al. [59] in a small catchment in England and Oudin et al. [48,90].

_{O}yields less ET rates.

#### 4.1. Annual Streamflow

_{O}reaches the lowest value in the evapotranspiration models. However, as pointed out by [97], the Hargreaves–Samani model underestimates the values observed in meteorological stations, while Priestley–Taylor reaches evapotranspiration values that are closer to the observed values.

_{O}and E

_{H}model. We also observed that the Priestley–Taylor evapotranspiration model in its potential form (EPTp) yielded similar results in both BLQ1 and 2 paired catchments, with differences around 1.8%. Unlike what is reported by [51] for the GR4J model across the USA, in our study catchments, this model was affected by differences in PET inputs on drier catchments (Q2 and Q3), even though there were water limitations due to lower rainfall and probably less soil water availability.

#### 4.2. Peak Flows

#### 4.3. Summer Flows

_{6}) in the GR6J model. This gave a more accurate simulation of low flows in summer in most of the studied scenarios and does not decrease efficiency in the simulation of maximum flows [24,74]. One possible explanation is that the GR6J exponential routing store is capable of dealing with positive and negative values, so it has the capability to represent water levels even though no water reaches this storage (no precipitation or drainage), and it can therefore simulate the recession stage more efficiently [111].

_{2}and X

_{5}in Q2 and BLQ1, is given by using different evapotranspiration methods. Additionally, the parameters x1, X

_{2}and X

_{3}are more sensitive than the parameter x4 to the precipitation input data, while X

_{3}is more sensitive to the size of the catchment and the length of the water network [112]. For instance, X

_{1}in BLQ1 changes from 979 to 671 when passing from GR4J to GR5J, while it drops to 323 in GR6J. This means that hydrological processes represented by parameters are re-arranged by the model. Thus, as the variability of the parameter X

_{1}among the catchments may be related to the variations in the input values of precipitation and not to PET, further analyses are required to accurately identify the sources of variability for parameter X

_{1}.

_{2}and X

_{3}in the GR4J model (similar results to those obtained by [113]) and X

_{2}and X

_{5}in the GR5J and GR6J models are the most sensitive parameters, explaining its greater variability when using different evapotranspiration input data for the same catchment. So, when a more efficient discharge simulation is needed, they must be calibrated before any other parameters.

## 5. Conclusions

_{5}and X

_{6}indicates the importance of below-ground processes such as infiltration, vadose zone storage and groundwater recharge. Additionally, lower ET amounts yield better model performance, which links to plant-related hydrological processes such as root depth, canopy density and orientation. Our results highlight the importance of a better representation of the water movement in the soil–plant–atmosphere continuum. We also note that current soil–water information for the sites does not suffice to improve model efficiency. Detailed simulations of small-scale catchments (less than 1 km

^{2}) would also require parameterizing the within-catchment variability of soil–water relationships. Even though variability could be small, it could lead to differences in outputs or switching the prevalence of different hydrological processes. Another limitation lies in the difficulty of giving physical meaning to lumped parameters. Differences in the performance of GRxJ models among catchments also highlight the importance of the hydrological setting.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Scatter plots between the RMSE efficiency statistic (Y-axis) and the parameter values: (

**A**) X

_{1}, (

**B**) X

_{2}, (

**C**) X

_{3}and (

**D**) X

_{4}, for the GR4J hydrological model.

**Figure A2.**Scatter plots between the RMSE efficiency statistic (Y-axis) and the parameter values: (

**A**) X

_{1}, (

**B**) X

_{2}, (

**C**) X

_{3}, (

**D**) X

_{4}and (

**E**) X

_{5}, for the GR5J hydrological model.

**Figure A3.**Scatter graphs between RMSE efficiency statistic (Y-axis) and parameter values: (

**A**) X

_{1}, (

**B**) X

_{2}, (

**C**) X

_{3}, (

**D**) X

_{4}, (

**E**) X

_{5}and (

**F**) X

_{6}, for hydrological model GR6J.

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**Figure 2.**Ombrothermic diagram for the catchments: (

**A**) Quivolgo (Q1 and Q2) and (

**B**) Bajo las Quemas (BLQ1 and BLQ2), in south-central Chile [68]; and (

**C**) mean monthly streamflow for the four catchments.

**Figure 3.**GR4J rainfall–runoff model diagram (modified from [73]).

**Figure 5.**Simulated and observed discharge for (

**A**) Q1, (

**B**) Q2, (C) BLQ 1 and (

**D**) BLQ2 using the GR4J, GR5J and GR6J models for the calibration and validation period. Vertical line represents the end of calibration period and start of the validation period (1 January 2015).

**Figure 6.**Daily potential/actual evapotranspiration for: Q2 (

**A**), Q3 (

**B**), BLQ1 (

**C**) and BLQ2 (

**D**) using Oudin model (E

_{O}), Hargreaves–Samani (E

_{H}) model, potential Priestley–Taylor (E

_{TPp}) model and actual Priestley–Taylor (E

_{TPa}) model, in the calibration and validation period. Vertical lines represent the end of calibration period (right) and beginning of validation period (left).

**Figure 7.**Streamflow simulation efficiency for models GR4J, GR5J and GR6J for summer flows in catchments Q2, Q3, BLQ1 and BLQ2 using NSElog criteria for calibration (C) and validation period (V).

**Figure 8.**Low-flow exceedance probability curves for observed and simulated values by the GR4J, GR5J and GR6J hydrological models in the calibration period for: Q2 (

**A**), Q3 (

**B**), BlQ1 (

**C**) and BLQ2 (

**D**), in south-central Chile.

**Figure 9.**Low-flow exceedance probability curves for observed and simulated values by the GR4J, GR5J and GR6J hydrological models in the validation period for: Q2 (

**A**), Q3 (

**B**), BLQ1 (

**C**) and BLQ2 (

**D**), in south-central Chile.

**Table 1.**Vegetation cover and geomorphological data of surface (ha), exposure (°) and slope (°) in the catchments.

Catchment | Area | Land Cover | Aspect | Slope |
---|---|---|---|---|

(ha) | (Grade) | (%) | ||

Q2 | 33.02 | Native forest | 135.61 | 27.33 |

Q3 | 40.14 | Native forest and P. radiata plantation (Mixed) | 179.38 | 24.13 |

BLQ1 | 22.63 | E. nitens plantation | 309.88 | 14.71 |

BLQ2 | 22.21 | E. nitens plantation | 285.11 | 14.15 |

N° | Equation | Values | Reference |
---|---|---|---|

1 | $KGE=1-\sqrt{{\left(1-\alpha \right)}^{2}+{\left(1-\beta \right)}^{2}+{\left(1-\rho \right)}^{2}}$ $\alpha =\frac{{\sigma}_{obs}}{{\sigma}_{sim}}$$;\text{}\beta =\frac{{\mu}_{obs}}{{\mu}_{sim}}$ | ${\sigma}_{obs}=STobservedstreamflow$ ${\sigma}_{sim}=STsimulatedstreamflow$ ${\mu}_{obs}=Meanobservedstreamflos$ ${\mu}_{sim}=Meansimulatedstreamflow$ $\rho =Pearsoncorrelation$ | [84] |

2 | $KGE=1-\sqrt{{\left(1-\alpha \right)}^{2}+{\left(1-\beta \right)}^{2}+{\left(1-\rho \right)}^{2}}$ $\alpha =\frac{C{V}_{obs}}{C{V}_{sim}}$$;\text{}\beta =\frac{{\mu}_{obs}}{{\mu}_{sim}}$ | $C{V}_{obs}=Coefficientofvariationobservedstreamflow$ $C{V}_{sim}=Coefficientofvariationsimulatedstreamflow$ ${\mu}_{obs}=Meanobservedstreamflow$ ${\mu}_{sim}=Meansimulatedstreamflow$ $\rho =Pearsoncorrelation$ | [84] |

3 | $RMSE=\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({\widehat{Q}}_{i}-{Q}_{i}\right)}^{2}}{n}}$ | ${Q}_{i}=Observedstreamflow$ ${\widehat{Q}}_{i}=Simulatedstreamflow$ $n=Datanumber$ | [71] |

4 | $NSE=1-\left[\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({\widehat{Q}}_{i}-{Q}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left(\overline{Q}-{Q}_{i}\right)}^{2}}\right]$ | ${Q}_{i}=Observedstreamflow$ ${\widehat{Q}}_{i}=Simulatedstreamflow$ $\overline{Q}=Meanobservedstreamflow$ | [85] |

5 | $IOA=1-\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({\widehat{Q}}_{i}-{Q}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left(\left|\overline{Q}-{Q}_{i}\right|+\left|\overline{Q}-{\widehat{Q}}_{i}\right|\right)}^{2}}$ | ${Q}_{i}=Observedstreamflow$ ${\widehat{Q}}_{i}=Simulatedstreamflow$ $\overline{Q}=Meanobservedstreamflow$ $n=Datanumber$ | [86,87] |

6 | $MAE=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left|{\widehat{Q}}_{i}-{Q}_{i}\right|}{n}$ | ${Q}_{i}=Observedstreamflow$ ${\widehat{Q}}_{i}=Simulatedstreamflow$ $n=Datanumber$ | [86] |

7 | $MAPE=\frac{100\ast {{\displaystyle \sum}}_{i=1}^{n}\left|\frac{{\widehat{Q}}_{i}-{Q}_{i}}{{Q}_{i}}\right|}{n}$ | ${Q}_{i}=Observedstreamflow$ ${\widehat{Q}}_{i}=Simulatedstreamflow$ $n=Datanumber$ | [87] |

8 | $SI=\frac{\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left(\left({\widehat{Q}}_{i}-{\overline{Q}}_{i}\right)-\left({Q}_{i}-\overline{Q}\right)\right)}^{2}}{n}}}{\frac{{{\displaystyle \sum}}_{i=1}^{n}{Q}_{i}}{n}}$ | ${Q}_{i}=Observedstreamflow$ ${\widehat{Q}}_{i}=Simulatedstreamflow$ $\overline{Q}=Meanobservedstreamflow$ $\overline{{Q}_{i}}=Meansimulatedstreamflow$ $n=Datanumber$ | [88] |

9 | $BIAS=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({\widehat{Q}}_{i}-{Q}_{i}\right)}{n}$ | ${Q}_{i}=Observedstreamflow$ ${\widehat{Q}}_{i}=Simulatedstreamflow$ $n=Datanumber$ | [86,89] |

8 | $NSElog=1-\left[\frac{{{\displaystyle \sum}}_{i=1}^{n}\left(log({\widehat{Q}}_{i}\right)-log\left({Q}_{i}\right){)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}\left(\overline{log(Q}\right)-log({Q}_{i}){)}^{2}}\right]$ | $\mathrm{log}\left({Q}_{i}\right)=Logaritmicobservedstreamflow$ $log({\widehat{Q}}_{i})=Logarithmicsimulatedstreamflow$ $\overline{log\left(Q\right)}=Meanoflogarithmicobservedstreamflow$ | [90,91] |

**Table 3.**Parameter sets that maximize flow simulation efficiency in each basin for GR4J, GR5J and GR6J hydrologic models in calibration period.

Catchment | |||||
---|---|---|---|---|---|

Model | Parameter | Q2 | Q3 | BLQ1 | BLQ2 |

GR4J | X_{1} | 109.94 | 8690.62 | 979.30 | 1577.47 |

X_{2} | −146.91 | −1.62 | 7.19 | 2.62 | |

X_{3} | 7500.22 | 25.79 | 62.98 | 197.93 | |

X_{4} | 0.98 | 1.10 | 1.41 | 1.42 | |

GR5J | X_{1} | 122.81 | 10114.94 | 671.08 | 1314.74 |

X_{2} | −9.21 | −1.20 | −1.90 | 0.78 | |

X_{3} | 7598.89 | 24.74 | 235.18 | 212.79 | |

X_{4} | 0.98 | 0.78 | 1.15 | 1.16 | |

X_{5} | 0.13 | 0.35 | 1.00 | 0.00 | |

GR6J | X_{1} | 139.10 | 104.57 | 323.76 | 509.16 |

X_{2} | −1.18 | −2.66 | 0.52 | 0.17 | |

X_{3} | 6276.71 | 2554.09 | 112.17 | 123.36 | |

X_{4} | 0.98 | 1.04 | 1.48 | 1.48 | |

X_{5} | −0.11 | −0.03 | −0.41 | −0.73 | |

X_{6} | 64.39 | 1.52 | 96.54 | 92.45 |

**Table 4.**Best evapotranspiration models (PET) that maximize hydrological model performance for the calibration period.

Catchment | |||||
---|---|---|---|---|---|

Q2 | Q3 | BLQ1 | BLQ2 | ||

GR4J | PET | E_{O} | E_{O} | E_{H} | E_{O} |

KGE | 0.569 | 0.725 | 0.766 | 0.81 | |

KGE’ | 0.456 | 0.704 | 0.813 | 0.815 | |

NSE | 0.495 | 0.569 | 0.72 | 0.673 | |

RMSE (mm) | 0.525 | 0.342 | 2.347 | 2.016 | |

IOA | 0.84 | 0.861 | 0.912 | 0.904 | |

MAE (mm) | 0.261 | 0.235 | 1.182 | 1.181 | |

MAPE (%) | 34.6 | 225.1 | 28.3 | 43.5 | |

SI | 0.67 | 0.84 | 0.49 | 0.55 | |

BIAS (mm) | 0.073 | −0.013 | 0.39 | −0.054 | |

GR5J | PET | E_{H} | E_{O} | E_{O} | E_{O} |

KGE | 0.561 | 0.748 | 0.753 | 0.8 | |

KGE’ | 0.448 | 0.721 | 0.734 | 0.772 | |

NSE | 0.471 | 0.553 | 0.712 | 0.68 | |

RMSE (mm) | 0.537 | 0.348 | 2.38 | 1.995 | |

IOA | 0.84 | 0.857 | 0.905 | 0.905 | |

MAE (mm) | 0.243 | 0.234 | 1.387 | 1.151 | |

MAPE (%) | 32.5 | 220.3 | 37.3 | 41.8 | |

SI | 0.61 | 0.89 | 0.37 | 0.44 | |

BIAS (mm) | 0.019 | −0.028 | −0.087 | −0.069 | |

GR6J | PET | E_{PTp} | E_{O} | E_{O} | E_{O} |

KGE | 0.574 | 0.818 | 0.801 | 0.808 | |

KGE’ | 0.471 | 0.804 | 0.798 | 0.781 | |

NSE | 0.395 | 0.724 | 0.733 | 0.683 | |

RMSE (mm) | 0.575 | 0.273 | 2.292 | 1.985 | |

IOA | 0.862 | 0.824 | 0.917 | 0.907 | |

MAE (mm) | 0.229 | 0.188 | 1.273 | 1.093 | |

MAPE (%) | 28.4 | 192.7 | 30.4 | 38 | |

SI | 0.57 | 0.77 | 0.37 | 0.46 | |

BIAS (mm) | −0.029 | −0.0014 | −0.0057 | 0.06 |

_{H}is the Hargreaves–Samani model; E

_{O}is the Oudin model; E

_{PTp}is the potential evapotranspiration according to Priestley–Taylor; E

_{PTa}is the actual evapotranspiration according to Priestley–Taylor.

**Table 5.**Efficiency criteria for the validation period in all basins using the GR4J, GR5J and GR6J hydrological models.

Catchment | |||||
---|---|---|---|---|---|

Q2 | Q3 | BLQ1 | BLQ2 | ||

GR4J | KGE | 0.569 | 0.725 | 0.766 | 0.810 |

KGE’ | 0.456 | 0.704 | 0.813 | 0.815 | |

NSE | 0.495 | 0.569 | 0.720 | 0.673 | |

RMSE (mm) | 0.525 | 0.342 | 2.347 | 2.016 | |

IOA | 0.840 | 0.861 | 0.912 | 0.904 | |

MAE (mm) | 0.261 | 0.235 | 1.182 | 1.181 | |

MAPE (%) | 34.6 | 225.1 | 28.3 | 43.5 | |

SI | 0.59 | 0.74 | 0.54 | 0.65 | |

BIAS (mm) | 0.058 | −0.0051 | 0.058 | −0.098 | |

GR5J | KGE | 0.561 | 0.748 | 0.753 | 0.800 |

KGE’ | 0.448 | 0.721 | 0.734 | 0.772 | |

NSE | 0.471 | 0.553 | 0.712 | 0.680 | |

RMSE (mm) | 0.537 | 0.348 | 2.380 | 1.995 | |

IOA | 0.840 | 0.857 | 0.905 | 0.905 | |

MAE (mm) | 0.243 | 0.234 | 1.387 | 1.151 | |

MAPE (%) | 32.5 | 220.3 | 37.3 | 41.8 | |

SI | 0.63 | 0.74 | 0.58 | 0.64 | |

BIAS (mm) | 0.026 | 0.0088 | 0.18 | 0.41 | |

GR6J | KGE | 0.574 | 0.818 | 0.801 | 0.808 |

KGE’ | 0.471 | 0.804 | 0.798 | 0.781 | |

NSE | 0.395 | 0.724 | 0.733 | 0.683 | |

RMSE (mm) | 0.575 | 0.273 | 2.292 | 1.985 | |

IOA | 0.862 | 0.824 | 0.917 | 0.907 | |

MAE (mm) | 0.229 | 0.188 | 1.273 | 1.093 | |

MAPE (%) | 28.4 | 192.7 | 30.4 | 38.0 | |

SI | 0.54 | 0.60 | 0.56 | 0.64 | |

BIAS (mm) | 0.0061 | −0.10 | 0.12 | 0.41 |

**Table 6.**Low and upper limit of the parameters of the GR4J, GR5J and GR6J hydrological models for the sensitivity analysis.

GR4J | GR5J | GR6J | ||
---|---|---|---|---|

X_{1} | Lower limit | 0 | 0 | 0 |

Upper limit | 10,000 | 10,000 | 10,000 | |

X_{2} | Lower limit | −100 | −100 | −100 |

Upper limit | 100 | 100 | 100 | |

X_{3} | Lower limit | 0 | 0 | 0 |

Upper limit | 4000 | 4000 | 4000 | |

X_{4} | Lower limit | 0.5 | 0.5 | 0.5 |

Upper limit | 3 | 3 | 3 | |

X_{5} | Lower limit | - | −100 | −100 |

Upper limit | - | 100 | 100 | |

X_{6} | Lower limit | - | - | 0 |

Upper limit | - | - | 500 |

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Flores, N.; Rodríguez, R.; Yépez, S.; Osores, V.; Rau, P.; Rivera, D.; Balocchi, F.
Comparison of Three Daily Rainfall-Runoff Hydrological Models Using Four Evapotranspiration Models in Four Small Forested Watersheds with Different Land Cover in South-Central Chile. *Water* **2021**, *13*, 3191.
https://doi.org/10.3390/w13223191

**AMA Style**

Flores N, Rodríguez R, Yépez S, Osores V, Rau P, Rivera D, Balocchi F.
Comparison of Three Daily Rainfall-Runoff Hydrological Models Using Four Evapotranspiration Models in Four Small Forested Watersheds with Different Land Cover in South-Central Chile. *Water*. 2021; 13(22):3191.
https://doi.org/10.3390/w13223191

**Chicago/Turabian Style**

Flores, Neftali, Rolando Rodríguez, Santiago Yépez, Victor Osores, Pedro Rau, Diego Rivera, and Francisco Balocchi.
2021. "Comparison of Three Daily Rainfall-Runoff Hydrological Models Using Four Evapotranspiration Models in Four Small Forested Watersheds with Different Land Cover in South-Central Chile" *Water* 13, no. 22: 3191.
https://doi.org/10.3390/w13223191