# Assessing 1D Hydrodynamic Modeling of Júcar River Behavior in Mancha Oriental Aquifer Domain (SE Spain)

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}for both discharges and water depths over 0.96. The model validation results were obtained for a different gauge 08132 and the determination coefficients R

^{2}also perform very well with value of 0.90. The model developed might be useful for decision making in water resources management and can be used to generate simulated time series of water depths, levels, discharges, and velocities in reaches where gauging measurements are not available with a desired space-time resolution (from meter/second to kilometer/month). Estimation of critical discharge value (1.973 m

^{3}s

^{−1}) for system equilibrium, based on the balance between losing and gaining sub-reaches of the river, is also made with a statistical significance at 95% for hydrologic years 2007–2010, period influenced by restrictions in groundwater withdrawals. The results of the present research are important for the proper and objective management of the scarce water resources on a watershed scale in Júcar River Basin, a complex case study representing semiarid climate, growing anthropogenic pressures, and complex river–aquifer interactions. The used approach of dynamic representation of the river–aquifer interactions as distributed source boundary condition in the one-dimensional hydrodynamic model might be applied in another study case on similar scale.

## 1. Introduction

^{2}) in southwestern Europe). In this area, agriculture is currently (data from 2018) the largest water demands user (94.5%), followed by residential (3.8%) and industrial (1.6%) water supply. This demand is almost entirely supplied by groundwater which, due to the negative balance (for the river), has caused a decrease in groundwater levels that has caused Júcar River to experience a change from a gaining to a losing river in certain reaches [23,24]. The decrease in downstream discharges of Júcar River and the growing demand in the entire system are generating political disputes between stakeholders in the two main regions where Júcar River flows: Castilla-La Mancha (upper and middle sub-basins) and Valencia (low sub-basin) (Figure 1).

## 2. Study Area

^{−1}, varying from 280 mm year

^{−1}in the southern zone and 550 mm year

^{−1}in the northern zone. During dry years, the average precipitation is approximately 150 mm year

^{−1}(very common), while in the wet years 750 mm year

^{−1}can be reached. Potential evapotranspiration values exceed 1200 mm year

^{−1}, so the area is considered semi-arid to arid. Geomorphologically, the area is characterized by large depressions of intramiocene age filled with later materials (Tertiary–Plio–Quaternary) that conserve their horizontal disposition, causing the practically flat relief of the area. The high plateau is interrupted only by the valley excavated by Júcar River, the main fluvial course that crosses the MOA domain. The hydrological network is scarcely developed; therefore, the surface runoff (except for the Júcar River) is practically zero or insignificant, ranging between 0 and 5 mm year

^{−1}. The Alarcón reservoir, a basic element in the regulation of the Júcar River, is located upstream on its entrance into MOA domain (Figure 1).

^{3}. However, over the last 45 years, approximately 1000 km

^{2}of traditionally rain-fed land has been transformed into irrigated surface through the widespread use of groundwater for irrigation, which has led to significant socioeconomic development in the region. In recent decades, MOA has been in a quasi-equilibrium state with a stabilized annual balance. The annual volume extracted for irrigation was 320 hm

^{3}, while the estimated renewable resources were 389 hm

^{3}[28]. This stabilization is currently threatened due to the proliferation of wells with irrigation rights of up to 7000 m

^{3}year

^{−1}(treated differently in the concession process, without being subject to the same controls as the wells with bigger extraction volumes), used to irrigate crops in expansion such as almond and pistachio trees. This fact together with the volume of environmental restrictions set at 114 hm

^{3}by the last Júcar Basin water management plan [29] puts MOA in a state of quantitative overexploitation with the consequent negative effects on the interactions with Júcar River.

## 3. Materials and Methods

#### 3.1. Data Acquisition

^{3}s

^{−1})) and water depths (h, (m)) obtained from the four gauging stations used for modeling purposes can be found in Table 1. Furthermore, as complementary analysis to the descriptive statistics for the observed time series of discharge and depths, Hurst coefficient estimates [32,33,34,35,36,37] were used, since they present non-stationary component due to the increasing underground water extractions starting in mid-1970s, causing changes in the river-aquifer interactions. The Hurst coefficient H is a measure of self-similarity or a measure of the duration of the long-term dependence of a given process. Time series characterized by long-term dependence exhibit a slow decrease of the autocorrelation function. For a stationary process with long-term dependence H $\in \left(0.5,1\right]$, while H > 1 indicates a non-stationary unbounded process [33]. More comprehensive non-stationary analysis of the Jucar River–MOA interactions, their temporal evolution, and relation to climatic variables and drivers can be found in [24].

**Table 1.**General description and descriptive statistics of the observed daily time series with mean values for river discharge (Q, (m

^{3}s

^{−1})) and depths (h, (m)) obtained from four gauging stations with available information for the period 01.01.1974–30.09.2019 and used for the purposes of the modeling. The location of the gauging stations can be seen in Figure 1 and their cross sections in Figure 2. The Hurst coefficients H were estimated using regression on periodogram (RP), averaged wavelet coefficients (AWC) and the detrended fluctuation analysis (DFA) methods.

General Description | |||||||||
---|---|---|---|---|---|---|---|---|---|

CHJ Code | 08129 | 08132 | 08036 | 08144 | |||||

Location | El Picazo | Puente Carrasco | Los Frailes | Alcalá del Júcar | |||||

UTM ETRS89 H30 X | 578628 | 584728 | 608082 | 635980 | |||||

UTM ETRS89 H30 Y | 4368600 | 4341164 | 43327912 | 4339792 | |||||

Elevation, (m.a.s.l.) | 694 | 647 | 605 | 514 | |||||

Studied variables | Q_{Picazo} | h_{Picazo} | Q_{Carrasco} | h_{Carrasco} | Q_{Frailes} | h_{Frailes} | Q_{Alcalá} | h_{Alcalá} | |

(m^{3}s^{−1}) | (m) | (m^{3}s^{−1}) | (m) | (m^{3}s^{−1}) | (m) | (m^{3}s^{−1}) | (m) | ||

Time periods with data availability * | 01.01.1974– 30.09.2019 | 01.01.1974– 30.09.2019 | 01.01.1974– 30.09.1986 | 01.01.1974– 30.09.1986 | 01.01.1974– 30.09.1988 25.10.1991– 30.09.2019 | 01.01.1974– 30.09.1988 26.10.1991– 30.09.2019 | 01.10.1974– 30.09.1980 12.06.1984– 30.09.2019 | 13.06.1984– 18.04.2011 30.09.2015– 30.09.2019 | |

Data use in the model | Boundary cond. in | Calibration | Validation | Validation | Calibration | Calibration | Boundary cond. out | Boundary cond. out | |

Descriptive statistics | |||||||||

Mean (m^{3}s^{−1}) | 8.055 | 0.568 | 10.120 | 0.907 | 9.416 | 0.480 | 9.915 | 0.400 | |

Minimum (m^{3}s^{−1}) | 0.044 | 0.080 | 0.000 | 0.000 | 0.344 | 0.010 | 0.001 | 0.130 | |

Maximum (m^{3}s^{−1}) | 42.440 | 3.440 | 46.600 | 1.990 | 57.102 | 1.220 | 74.000 | 1.170 | |

Standard deviation (m^{3}s^{−1}) | 8.260 | 0.263 | 8.267 | 0.335 | 9.165 | 0.199 | 8.283 | 0.215 | |

Coefficient of variation | 1.025 | 0.463 | 0.770 | 0.369 | 0.973 | 0.4715 | 0.835 | 0.508 | |

Variance | 68.230 | 0.069 | 68.342 | 0.112 | 84.005 | 0.0395 | 68.606 | 0.046 | |

H—RP | 1.328 | 1.310 | 1.216 | 1.230 | 1.345 | 1.360 | 1.297 | 1.335 | |

H—AWC | 1.180 | 1.068 | 1.199 | 1.204 | 1.277 | 1.262 | 1.218 | 1.220 | |

H—DFA | 1.162 | 1.152 | 1.205 | 1.203 | 1.196 | 1.192 | 1.174 | 1.187 |

**Figure 2.**The geometries of Júcar River gauging stations are shown as introduced in the Cross Section file of MIKE11 for (

**a**) El Picazo, (

**b**) Puente Carrasco, (

**c**) Los Frailes, and (

**d**) Alcala del Júcar. Minimum and maximum water levels are indicated with green and red dashed lines, respectively, while intermediate water levels are drawn in blue. The rest of the cross sections with irregular geometries were also introduced but are not shown here. Their locations can be found on Figure 1.

#### 3.2. Model Setup

#### 3.2.1. Hydrodynamic Modeling Setting

^{3}s

^{−1}); A is the cross section flow area (m

^{2}); q is the lateral inflow (m

^{2}s

^{−1}); h is the water level above a reference datum (m); x is the downstream path (m); t is the time (s); n is the Manning coefficient (s m

^{−1/3}); R is the hydraulic or resistance radius (m); g is the gravity acceleration (m

^{2}s

^{−1}); and α is the momentum distribution coefficient [38]. The MIKE 11 HD module solves numerically the river networks and floodplains as a system of interconnected branches. Water levels and discharges are calculated at alternating points along the river branches as a function of time.

#### 3.2.2. Conceptual Model, Discretization, and Boundary Conditions

^{3}s

^{−1}) data from the El Picazo gauging station were used for the studied time period, which were entered as a time-varying (dynamic) open boundary condition upstream of the river. Observed discharge at the input varied from 0.04 m

^{3}s

^{−1}to 42.44 m

^{3}s

^{−1}during the study period, and the average discharge was 8.04 m

^{3}s

^{−1}(Table 1). Downstream of the river; (gauging station Alcalá del Júcar), the rating curve of the cross section is entered in table form as a boundary condition.

_{1}and Leakage

_{2}, expressed as follows:

_{1}(t

_{k}) = Q

_{LosFrailes}(t

_{k}) − 1/2 ((Q

_{Picazo}(t

_{k}) + Q

_{Picazo}(t

_{k+1}))

_{2}(t

_{k}) = Q

_{Alcalá}(t

_{k}) − 1/2 ((Q

_{LosFrailes}(t

_{k}) + Q

_{LosFrailes}(t

_{k+1}))

_{k}and (t

_{k}+ 1) are the kth and the ((k + 1)th) times of the observation. The obtained time series were introduced as distributed source boundary condition at the corresponding river reaches—Leakage1 is between El Picazo and Los Frailes gauging stations and Leakage2 is between Los Frailes and Alcalá del Júcar gauging stations.

#### 3.2.3. Calibration and Validation Model Evaluation Criteria

^{2}), Nash–Sutcliffe Efficiency (NSE) [51] and the root mean square error (RMSE). Their equations, ranges, and optimal values are given in Table 2.

^{2}) describe the degree of collinearity between simulated (S) and observed data (O). They are widely used in hydrological modeling; however, they are not sensitive to additive and proportional differences between model simulations and observed data [52]. The Nash–Sutcliffe Efficiency, NSE, accounts for the model’s ability to predict variables different from the mean and gives the magnitude of residual variation in comparison to observed data variance. The RMSE is suitable for continuous long-term simulations and is used in model performance evaluation as a measure of the difference between simulated and observed values.

^{2}, NSE, and RMSE. The performance criteria on daily, monthly, and annual temporal scales for watershed scale models can be considered “satisfactory” for flow simulations if R

^{2}> 0.60 and NSE > 0.50, “good” for 0.75 < R

^{2}≤ 0.85 and 0.70 < NSE ≤ 0.80, and “very good” for R

^{2}> 0.85 and NSE > 0.80 [53]. In regard to the water table depth (on a daily scale), the reported statistical evaluation criteria in [54] rate the model “acceptable” for NSE >0.40, “very good” for 0.60 < NSE ≤ 0.75, and “excellent” for NSE > 0.75.

## 4. Results and Discussion

#### 4.1. Calibration and Validation Results of HD Modeling

^{−1/3}). Observed and simulated Q y h at the Los Frailes gauging station (see Figure 1 and Figure 2) had a fit with an R

^{2}considerably lower than 0.80, therefore as suggested by the performance evaluation criteria reported for hydrodynamic models [42], a more precise calibration was needed, in this case, of the value of n along the river. Consequently, n was adjusted to a variable value that would produce the best match between observed and simulated values. The averaged values of n along the river vary from 0.027 (s m

^{−1/3}) to 0.042 (s m

^{−1/3}) and are introduced for each of the sections defined in the model. The characteristics of the riverbed, such as its geology, geomorphology, and surrounding vegetation, were taken into account [44]. The resulting values of n along the studied sub-reaches of the Júcar River, are shown in Figure 4a.

^{2}) for both periods are also performing very well. In practically more than 96% of the cases, the simulated discharges and water depths represent reality. The optimal value for RMSE is zero; therefore, the statistic indicates tolerable agreement between observed and simulated values for Q (0.30 m

^{3}s

^{−1}) and h (0.06 m).

^{3}s

^{−1}exists. The error performance statistics (see Table 3) also reflect this situation, the RMSE for the discharge departs from the optimal value zero, however the rest of statistics with optimal value 1 can be rated as very good (R and R

^{2}) and good (NSE). Considering that in Figure 6b the water depths adjustment is satisfactory, the reason for this shift could be the way MIKE HD module represents distributed sources (denominated leakage in our study) boundary condition which represents the interactions between the river and any type of inflow-outflow (e.g., aquifer–river interactions). Indeed, distributed sources can only be established between points where complete historical series are available. Therefore, although Leakeage1 is well defined in the El Picazo–Los Frailes reach, it should be different for the El Picazo–Puente de Carrasco and Puente de Carrasco–Los Frailes reaches. A highly probable explanation is that the model overestimates the leakage in the reach El Picazo–Puente de Carrasco and in the following reach Puente de Carrasco–Los Frailes it is underestimated; as a result, they compensate each other. This issue is interesting and serves to advertise to the water authority about the need for flow control at intermediate points.

^{3}s

^{−1}).

#### 4.2. Discussion (Implications for the Water Resources Management)

^{3}s

^{−1}the Júcar River may dry up between chainages 71,000 m and 80,000 m. This effect was observed during model calibration for the period influenced by OPAD measures. During this period, due to the environmental restrictions imposed by the river basin authorities (CHJ), no direct water abstractions were made from Júcar River and a perimeter of influence was established around it where groundwater pumping that could influence river flows was not allowed. In addition to this situation, and because of the scarcity of water in the headwaters of the system (Alarcón reservoir), the discharges released to Júcar river were relatively low, more specifically between 2 and 5 m

^{3}s

^{−1}at El Picazo gauging station (for a summary, see [23]). These are the cases when hydrodynamic modeling is considered essential to establish the minimum discharge’s stream flow so that the river would not dry up. As can be seen in the results of the model shown in Figure 9, for Reach 2 (net losing river), in 95% of the cases when the discharge at El Picazo gauging station was less than 1.97 m

^{3}s

^{−1}, the river would dry out close to Cuasiermas. In contrast, reach 3 in 90% of the cases the river would gain a base flow of 1.68 m

^{3}s

^{−1}.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Location of the study area. JRB: Júcar River Basin district, (

**b**) Júcar River hydrologic unit: The Upper, Middle, and Low sub-basins as defined within the JRB district; MOA: Mancha Oriental Aquifer (

**c**) Study area: Reach 1 is from Alarcon Reservoir exit to El Picazo gauge, Reach 2a—from El Picazo gauge to Villalgordo del Júcar location, Reach 2b—from Villalgordo del Júcar location to Los Frailes gauge, Reach 3—from Los Frailes gauge to Alcala del Júcar gauge, and Reach 4—from Alcala del Júcar gauge to the exit of Jucar River from MOA domain.

**Figure 4.**(

**a**) Averaged calibrated values of the variable Manning’s coefficient n along the studied reach of the Júcar River set in each cross section and the resulting values, as a function of the chainage. (

**b**) Graphical representation of Manning’s coefficient n as a function of water depth for Los Frailes gauging station cross section.

**Figure 5.**Simulated and observed time series. Daily mean observed (blue dots) and modeled (gray line) time series for water discharge (

**a**) and depths (

**b**) at Los Frailes gauging station within the time periods with available data, used for the model performance evaluation. The exact time periods can be found in Table 3.

**Figure 6.**Simulated and observed time series. Daily mean observed (gray diamonds) and modeled (black line) time series for discharge (

**a**) and water depths (

**b**) at Puente de Carrasco gauging station within time periods with available data, used for the model performance evaluation.

**Figure 7.**As an example, monthly mean values of discharge Q (

**a**) and depths h (

**b**) are represented with a spatial distribution of 1000 m for hydrologic year 10.2007–09.2008 when OPAD measures were applied.

**Figure 8.**Hurst coefficient estimates of the observed and simulated values of Q (

**a**,

**b**) and h (

**c**,

**d**). The three different estimation methods used are: regression on periodogram (RP), averaged wavelet coefficients (AWC), and detrended fluctuation analysis (DFA).

**Figure 9.**Scatterplots of mean monthly values obtained from the Jucar River model representing input discharge upstream vs. differential discharge between chainages 71,000 and 0 (m) (diamonds) and output discharge downstream vs. differential discharge between chainages 120,990 and 80,000 (m) (dots). Negative value for the constant term of the linear equation fit line indicates that the river is gaining, while positive values indicate that the river is losing.

**Table 2.**Model performance statistics, their equations, ranges, and optimal values, modified from [42]. O and S are observed and simulated values for a time series with length n and $\overline{\mathrm{O}}$ and $\overline{\mathrm{S}}$ are the mean values, respectively.

Statistic | Symbol | Equation | Range | Optimal Value | (Eq) |
---|---|---|---|---|---|

Coefficient of correlation | R | $\frac{{\sum}_{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{O}}_{\mathrm{k}}-\overline{\mathrm{O}})({\mathrm{S}}_{\mathrm{k}}-\overline{\mathrm{S}})}{\sqrt{{\sum}_{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{O}}_{\mathrm{k}}-\overline{\mathrm{O}})}\sqrt{{\sum}_{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{S}}_{\mathrm{k}}-\overline{\mathrm{S}})}}$ | −1 to 1 | −1(negative slope) 1(positive slope) | (7) |

Coefficient of determination | R^{2} | ${\left(\frac{{\sum}_{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{O}}_{\mathrm{k}}-\overline{\mathrm{O}})({\mathrm{S}}_{\mathrm{k}}-\overline{\mathrm{S}})}{\sqrt{{\sum}_{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{O}}_{\mathrm{k}}-\overline{\mathrm{O}})}\sqrt{{\sum}_{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{S}}_{\mathrm{k}}-\overline{\mathrm{S}})}}\right)}^{2}$ | 0 to 1 | 1 | (8) |

Nash–Sutcliffe Efficiency | NSE | $1-\frac{{\sum}_{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{O}}_{\mathrm{k}}-{\mathrm{S}}_{\mathrm{k}})}{{\sum}_{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{O}}_{\mathrm{k}}-\overline{\mathrm{O}})}$ | −∞ to1 | 1 | (9) |

Root mean square error | RMSE | $\sqrt{\frac{1}{\mathrm{n}}\sum _{\mathrm{k}=1}^{\mathrm{n}}({\mathrm{O}}_{\mathrm{k}}-{\mathrm{S}}_{\mathrm{k}})}$ | 0 to ∞ | 0 | (10) |

**Table 3.**Calibration and validation statistical performances at Los Frailes and Puente de Carrasco stations (simulated versus observed time series), represented by correlation coefficient (R), determination coefficient (R

^{2}), Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE) for discharge Q (m

^{3}s

^{−1}) and depths h (m) time series, calculated within periods with availability for observed data.

Error Statistics | R | R^{2} | NSE | RMSE |
---|---|---|---|---|

Calibration—08036 Los Frailes | ||||

Q (01.01.1974–30.09.1988) | 0.997 | 0.994 | 0.994 | 0.798 |

h (01.01.1974–30.09.1988) | 0.983 | 0.967 | 0.446 | 0.181 |

Q (25.10.1991–30.09.2019) | 0.998 | 0.996 | 0.997 | 0.375 |

h (25.10.1991–30.09.2019) | 0.998 | 0.995 | 0.812 | 0.064 |

Validation—08132 Puente Carrasco | ||||

Q (01.01.1974–30.09.1986) | 0.946 | 0.896 | 0.723 | 4.345 |

h (01.01.1974–30.09.1986) | 0.946 | 0.895 | 0.791 | 0.153 |

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## Share and Cite

**MDPI and ACS Style**

Dountcheva, I.; Sanz, D.; Penchev, P.; Cassiraga, E.; Galabov, V.; Gómez-Alday, J.J.
Assessing 1D Hydrodynamic Modeling of Júcar River Behavior in Mancha Oriental Aquifer Domain (SE Spain). *Water* **2023**, *15*, 485.
https://doi.org/10.3390/w15030485

**AMA Style**

Dountcheva I, Sanz D, Penchev P, Cassiraga E, Galabov V, Gómez-Alday JJ.
Assessing 1D Hydrodynamic Modeling of Júcar River Behavior in Mancha Oriental Aquifer Domain (SE Spain). *Water*. 2023; 15(3):485.
https://doi.org/10.3390/w15030485

**Chicago/Turabian Style**

Dountcheva, Iordanka, David Sanz, Philip Penchev, Eduardo Cassiraga, Vassil Galabov, and Juan José Gómez-Alday.
2023. "Assessing 1D Hydrodynamic Modeling of Júcar River Behavior in Mancha Oriental Aquifer Domain (SE Spain)" *Water* 15, no. 3: 485.
https://doi.org/10.3390/w15030485