# Identifying a Suitable Model for Low-Flow Simulation in Watersheds of South-Central Chile: A Study Based on a Sensitivity Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Study Area and Hydrometeorological Data

#### 2.2. HBV Hydrological Model Description

_{f}). All the snow contributed directly to snow storage (SS). If the actual temperature was greater than TT, there was snowmelt. Snowmelt water was controlled by a degree-day factor (C

_{melt}), which determines the daily amount of melted snow depending on the difference between the actual and threshold temperatures. Subsequently, the sum of precipitation and snowmelt (∆P) passed to the soil routine, which included two modules. The first module calculated the actual evapotranspiration (E

_{a}), which was equal to potential evapotranspiration (PET) if the relationship between soil moisture and maximum soil moisture (SM/FC) was above a threshold value for potential evapotranspiration (LP). On the other hand, for soil moisture values below LP, the actual evapotranspiration will be linearly reduced, as shown in Figure 2 (upper left corner).

_{m}) obtained from the Thornthwaite method, long-term monthly temperature averages (T

_{m}) and daily mean air temperature (Td). The daily evapotranspiration was calculated by transforming (adjusting) the PET

_{m}through the difference between the T

_{d}and T

_{m}and a coefficient C (see Equation (1)). Bergström [34] mentioned that the adjusted potential evapotranspiration is limited to positive values and is not allowed to exceed twice the monthly average.

_{perc}). The upper deposit had two outlets (Q

_{0}and Q

_{1}), while the lower deposit had one (Q

_{2}). When the water level in the upper deposit exceeded a threshold value (L), runoff was produced quickly in its upper part (Q

_{0}). The response of the other outlets was relatively slow. The streamflows were controlled by recession coefficients k

_{0}, k

_{1}and k

_{2}, which represented the response functions of the upper and lower deposits. The constant infiltration rate (Q

_{perc}) was controlled by a coefficient k

_{p}.

_{0}must always be greater than k

_{1}. In addition, the response of the third outlet (groundwater runoff) (Q

_{2}) must be slower than that of the second one (Q

_{1}); therefore, k

_{2}must be lower than k

_{1}[33]. For a better understanding of the model, see Bergström [34] and Kollat et al. [35].

#### 2.3. Analyzed Groundwater Storage Structures

_{0}and Q

_{1}). Outlet Q

_{0}represented surface runoff that was produced if the water level of the reservoir surpassed a threshold value (L). Outlet Q

_{1}represented groundwater release from the aquifer with a linear relationship. Both outlets were controlled by recession coefficients k

_{0}and k

_{1}(Figure 3a).

_{NSE}function (described in the following section), which focused on the simulation of low flows, was used.

#### 2.4. Sensitivity Analysis and Calibration

_{NSE}) since it has been used in several studies to evaluate the performance in the low flow simulation [44,45,46,47,48,49,50]. The logarithmic transformation is similar to the Box-Cox transformation used in the transformed root mean squared error (TRMSE) (see Kollat et al. [35]; van Werkhoven et al. [51]), but these transformations penalize the errors of high flows, placing increasing emphasis on low flows [52]. Therefore, the calibration was restricted to the lower part of the hydrograph [11].

_{NSE}varies between −$\infty $ and 1, with a value equal to 1 indicating a perfect fit and values less than 1 indicating that there are differences between the simulated (${\mathrm{Q}}_{\mathrm{sim}}$) and observed streamflows (${\mathrm{Q}}_{\mathrm{o}}$).

_{NSE}values over 0.5 were considered “good” simulations; therefore, this value was set as the threshold value. Models with LOG

_{NSE}greater than (or equal to) 0.5 were considered behavioral, while models with values below 0.5 were considered non-behavioral.

## 3. Results and Discussion

_{NSE}values for all the implemented models. Figure 4 shows boxplots of the simulated and observed streamflows for low flows (streamflows between the 70th and 99th percentile of the duration curve) and Figure 5 shows the MVD values for the parameters associated with the response structure of each model.

#### 3.1. Groundwater Storage Structures Performance

_{NSE}> 0.79). Meanwhile, model M2 presented good performance (LOG

_{NSE}> 0.77) only in watersheds with sedimentary influence and topography with gentle slopes (e.g., CHC, DL, QL, CA), while in watersheds with volcanic influence and steep topography (e.g., CHE, DSL, CR, ALL) deficient performance was observed (LOG

_{NSE}< 0.5). Model M3, which had two reservoirs (one with a quick response and one slow) presented a performance similar to M2 in volcanic watersheds, with similar LOG

_{NSE}values (LOG

_{NSE}< 0.5). The deficient performance of M3 in volcanic watersheds and rugged topography can be attributed to the fact that quick response predominated in the storage-release structures of these watersheds; therefore, M3 was unable to correctly represent the hydrological processes that occurred in the mountain block system [54]. Similarly, the M4 structure did not exhibit good performance in volcanic watersheds, except in DSL, with a LOG

_{NSE}value of ~0.62. Its better performance in DSL could be associated with the volcano-sedimentary influence in the watershed [27], which could influence the runoff generation responses that a model with a nonlinear response is able to identify better than a model with a linear storage-release response.

#### 3.2. Sensitivity of the Parameters Associated to Runoff Response Sub-Models

_{NSE}> 0.5). In general, for volcanic watersheds and steep topography, behavioral models with M2, M3 and M4 were not observed. This indicates that these structures do not suitably represent or simulate the hydrological processes of groundwater storage and release in watersheds with such characteristics. Therefore, in Figure 4 only the results associated with behavioral models are shown. In addition, it is observed in the figure that the MVD values of the watersheds with volcanic influence and steep topography are higher than those of watersheds with sedimentary influence and flat topography (Figure 4). This indicates the importance of correctly representing the processes related to groundwater storage-release in watersheds with volcanic influence and topography with steep slopes.

_{p}, which connects/controls the flow between slow and quick reservoirs. A similar result was obtained for M3, in which the parameter that distributes water between quick and slow reservoirs ($\alpha $) has high sensitivity (MVD~0.9). The greater model sensitivity to parameters could be a result of the combined effect of the fractured rock characteristics [8,27,28] and steep topography (slopes mostly greater than 50°) that these watersheds present (Figure 1b,c). Fractures can act as paths or routes [55] that allow groundwater infiltration, storage and release [22] through quick or slow runoff generation processes. Similar results were found by Rusli et al. [56], who analyzed parameter sensitivity in the Jiangwan basin in China, which has fractured geological characteristics, including cracks and faults, like those of the watersheds in this study.

_{1}and k

_{2}of M1, k

_{1}of M2 or k

_{01}and k

_{02}of M3) presented greater sensitivity (MVD > 0.5) than the direct runoff parameter (k

_{0}). This greater MVD (sensitivity) was a result of these parameters being directly related to low-flow generation. Abebe et al. [57] mention that the greater sensitivity of the k

_{2}and k

_{p}parameters in M1 is due to the relationship between slow groundwater release processes and percolation.

_{70}streamflows was seen. Models M1 and M2 presented a median near the observed values in watersheds with greater sedimentary influence and topography with gentle slopes.

#### 3.3. Influence of the Hydrological Characteristics

^{3}/s against 13.1 m

^{3}/s), which was related to differences in size. In addition, CA and QL showed similar topography, with average slopes of 2.4° and 6.0°, respectively. According to the above, hydro-meteorological patterns were also related to the model performance findings, with basins with similar topographical and meteorological characteristics presenting similar hydrological model patterns (performance and low-flow model fit).

#### 3.4. M1 Model Analysis

_{0}(surface runoff), k

_{1}(subsoil surface or subsurface) and k

_{2}(baseflow), as well as parameter k

_{p}, which connected the two storage reservoirs. The three responses represented processes during and after rainfall periods [61] and were related to the three theoretical breakpoints (points A, B and C in Figure 7) of the recession curve of the hydrograph of a watershed mentioned in the literature [62,63]. Point B (Figure 7) indicated the start of recession flows; therefore, most streamflow input to runoff came from the aquifer. Thus, the second outlet (Q

_{1}) of M1 represented primary or quick groundwater storage and release response generated by bed drainage (quick interflow, [57]). Finally, in long periods without rainfall, the surface streamflow or quick interflow ceased [61]. This resulted in greater groundwater release from deep storage (represented by k

_{2}, the third breakpoint in Figure 7). Hence, M1 represented a structure with greater flexibility to reproduce streamflow generation processes compared to other models (considering different watershed types) without under- or overparameterization that may produce an unsuitable representation of processes.

_{1}and k

_{2}in M1 (associated with quick and slow runoff responses) took on greater importance (sensitivity). In contrast, in watersheds of the Central Valley (sedimentary, relief with gentle slopes), parameters associated with slow runoff took on greater importance (sensitivity) (e.g., parameter k

_{2}in M2). This suggests that in watersheds characterized by both volcanic geology and rugged relief, greater emphasis on the suitable representation of streamflow generation processes is needed.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study area and elevation map (

**a**). Yellow circles correspond to volcanic watersheds and red triangles to sedimentary watersheds. Additionally, a slope map of watersheds (

**b**,

**c**) is shown.

**Figure 2.**General conceptual diagram of the simplified HBV model, including a description of its parameters and main equations.

**Figure 3.**Additional adapted configurations of conceptual groundwater models, including a description of their parameters and main equations. (

**a**) M2 model: one reservoir with two outlets; (

**b**) M3 model: combination of two parallel reservoir with two outlets each one; (

**c**) M4 model: one reservoir with two non-linear outlets.

**Figure 4.**MVD variation in watersheds with (i) volcanic influence in red boxplots (CHE, DSL, CR, ALL); (ii) sedimentary influence in blue boxplots (CHC, DL, QL, CA). With models M2 and M3, no behavioral models were obtained in volcanic watersheds; therefore, no sensitivity analysis was carried out.

**Figure 6.**Comparison of observed and simulated streamflows for (

**a**) CHC (sedimentary and flat watershed) and (

**b**) in DSL (volcanic and steep watershed) (period April 2001–March 2003).

**Table 1.**Monitoring stations, availability, geological formation and hydro-meteorological information in study watersheds.

Station (ID) | Area | Geological Formation (%) | Relief (°) | Hydro-Meteorological Information | ||||||
---|---|---|---|---|---|---|---|---|---|---|

ID | Station | (km^{2}) | V | S | O | AS | MAP | MAD | MAT | MAE |

CHE | Chillan at Esperanza | 210 | 90.4 | 0 | 9.6 | 17.8 | 2200 | 15.6 | 9.3 | 964 |

DSL | Diguillín at San Lorenzo | 207 | 85.1 | 0 | 14.9 | 23.6 | 2300 | 16.4 | 9.2 | 920 |

CR | Cautin at Rari-Ruca | 1255 | 96.6 | 1.2 | 2.2 | 14.4 | 2330 | 102.7 | 8.2 | 1006 |

ALL | Río Allipen at Laureles | 1652 | 56.3 | 21.9 | 21.8 | 13 | 2294 | 139.4 | 8.7 | 1023 |

QL | Quino at Longitudinal | 298 | 31 | 69 | 0 | 2.4 | 1850 | 13.1 | 12.5 | 1066 |

CHC | Chillán to Confluencia | 754 | 25.3 | 70.4 | 4.3 | 8.1 | 1500 | 29.9 | 12.1 | 1163 |

DL | Diguillin at Longitudinal | 1239 | 26.5 | 69.7 | 3.8 | 10 | 1736 | 46.9 | 10.9 | 1103 |

CA | Cautin at Almagro | 5470 | 58.1 | 40.1 | 1.8 | 6 | 1838 | 261 | 10.5 | 1052 |

^{3}/s); MAT: Mean annual temperature (°C); MAE: Mean annual evapotranspiration (mm). The statistics of hydro-meteorological data were obtained from the historical database of stations controlled by the DGA.

Parameter (Units) | M1 | M2 | M3 | M4 |
---|---|---|---|---|

Mass Balance | ||||

A | 0.8–2.5 | 0.8–2.5 | 0.8–2.5 | 0.8–2.5 |

Snow Routine | ||||

C_{melt} $\left(mm\xb0{C}^{-1}{d}^{-1}\right)$ | 0.5–7 | 0.5–7 | 0.5–7 | 0.5–7 |

${S}_{f}$ | 0.5–1.2 | 0.5–1.2 | 0.5–1.2 | 0.5–1.2 |

Soil Routine | ||||

FC (mm) | 0–2000 | 1–2000 | 0–2000 | 1–2000 |

$\beta $ | 0–7 | 0–7 | 0–7 | 0–7 |

$a$ | - | - | 0–0.5 | - |

LP | 0.3–1 | 0.3–1 | 0.3–1 | 0.3–1 |

C ($\xb0{C}^{-1}$) | 0.01–0.3 | 0.01–0.3 | 0.01–0.3 | 0.01–0.3 |

Response Routine | ||||

L (mm) | 0–100 | 0–100 | 0–100 | 0–100 |

L2 (mm) | - | - | 0–100 | - |

${k}_{0}$ (${d}^{-1}$) | 0.3–0.6 | 0.3–0.6 | 0.3–0.6 | 0.3–0.6 |

${k}_{1}$ (${d}^{-1}$) | 0.1–0.2 | 0.1–0.2 | 0.1–0.2 | 0.1–0.2 |

${k}_{2}$ (${d}^{-1}$) | 0.01–0.1 | - | - | - |

${k}_{p}$ (${d}^{-1}$) | 0.01–0.1 | - | - | - |

${K}_{02}$ (${d}^{-1}$) | - | - | 0.3–0.1 | - |

${K}_{12}$ (${d}^{-1}$) | - | - | 0.2–0.05 | - |

b | - | - | - | 1–0.33 |

**Table 3.**Model performance in the calibration and validation periods. The blue bars represent behavioral models (LOG

_{NSE}> 0.5) and the red bars non-behavioral models.

**Table 4.**Streamflow and corrected precipitation (corrected precipitation by a factor) statistics for the calibration and validation periods in the studied watersheds.

Watershed | Period | MAP (mm) | MAD (m^{3}/s) | Q_{50} (m^{3}/s) | Q_{70} (m^{3}/s) |
---|---|---|---|---|---|

CHE | Calibration | 2950 | 16.3 | 10.5 | 6.6 |

Validation | 2478 | 13.2 | 7.2 | 5.7 | |

DSL | Calibration | 3091 | 18.3 | 10.1 | 5.6 |

Validation | 2534 | 16.2 | 9.0 | 4.1 | |

CR | Calibration | 2417 | 95.7 | 79.4 | 50.6 |

Validation | 2029 | 85.5 | 66.3 | 40.0 | |

ALL | Calibration | 2901 | 139.9 | 114.0 | 74.1 |

Validation | 2774 | 127.9 | 105.0 | 74.8 | |

QL | Calibration | 2652 | 13.3 | 6.1 | 2.0 |

Validation | 2314 | 12.2 | 5.7 | 2.1 | |

CHC | Calibration | 1681 | 26.3 | 8.7 | 2.8 |

Validation | 1379 | 22.2 | 8.3 | 2.5 | |

DL | Calibration | 2320 | 57.0 | 22.5 | 7.7 |

Validation | 1891 | 46.0 | 14.5 | 5.1 | |

CA | Calibration | 1966 | 270.0 | 167.0 | 81.1 |

Validation | 1822 | 305.0 | 163.0 | 95.5 |

_{70}: 70th percentiles of the duration curve; Q

_{50}: 50th percentiles of the duration curve.

© 2019 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/).

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**MDPI and ACS Style**

Parra, V.; Arumí, J.L.; Muñoz, E.
Identifying a Suitable Model for Low-Flow Simulation in Watersheds of South-Central Chile: A Study Based on a Sensitivity Analysis. *Water* **2019**, *11*, 1506.
https://doi.org/10.3390/w11071506

**AMA Style**

Parra V, Arumí JL, Muñoz E.
Identifying a Suitable Model for Low-Flow Simulation in Watersheds of South-Central Chile: A Study Based on a Sensitivity Analysis. *Water*. 2019; 11(7):1506.
https://doi.org/10.3390/w11071506

**Chicago/Turabian Style**

Parra, Víctor, Jose Luis Arumí, and Enrique Muñoz.
2019. "Identifying a Suitable Model for Low-Flow Simulation in Watersheds of South-Central Chile: A Study Based on a Sensitivity Analysis" *Water* 11, no. 7: 1506.
https://doi.org/10.3390/w11071506