# Coupling SWAT Model and CMB Method for Modeling of High-Permeability Bedrock Basins Receiving Interbasin Groundwater Flow

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, and flows southward among the Sierra de Castril (west) and Sierra Seca (east) Mountains [43] (Figure 1b).

#### 2.2. Overall Model Description

#### 2.3. CMB Method

#### 2.3.1. CMB Method Application for Aquifer Recharge over Continental Spain

#### 2.3.2. IGF Series Generation

_{i}is i–year P and Ps

_{i}is its normalized value, $\overline{P}$ is mean P, and ${\sigma}_{R}$ is standard deviation of mean R.

_{i}is i–year R, and ${\mathrm{m}}_{C}$ and ${\sigma}_{C}$ are expressed as:

#### 2.4. BFLOW Program

#### 2.5. SWAT Model

#### 2.5.1. Description of the SWAT Model

_{2}O), ${\mathrm{SW}}_{0}$ is initial soil–water content (mm H

_{2}O), t is time (days), ${\mathrm{P}}_{\mathrm{day}}$ is precipitation on day i (mm H

_{2}O), ${\mathrm{ET}}_{\mathrm{day}}$ is evapotranspiration on day i (mm H

_{2}O), ${\mathrm{Q}}_{\mathrm{surf}}$ is surface runoff on day i (mm H

_{2}O), ${\mathrm{W}}_{\mathrm{seep}}$ is water amount that enters the vadose zone from the soil profile on day i (mm H

_{2}O), and ${\mathrm{Q}}_{\mathrm{gw}}$ is groundwater return flow on day i (mm H

_{2}O).

#### 2.5.2. Data, Model Set-Up, Calibration, and Validation

^{2}), percent bias (PBIAS), Root Mean Square Error (RMSE), and RMSE relative to standard deviation of the observed data (RSR) were used (Table 1).

## 3. Results and Discussion

#### 3.1. Using the CMB Datasets to Estimate IGF

^{–1}, which means recharge–precipitation ratios were in the 0.29–0.37 range; the standard deviation of mean R varied within the 39–90 mm year

^{–1}range, which placed the given coefficients of variation of mean annual R (mean value-to-standard deviation ratio) in the 0.27–0.30 range (Table 2). For the control period (1996–2005), fitting parameters were calculated to generate the yearly R data series in the CRB and upstream GRW and SRW contributing areas, which are in Table 3, whereas the generated surface-weighted yearly P and R series are in Table 4. In each area, yearly R and P series for the control period (1996–2005) were compared. The resulting parametric functions allowed for the extension of the calculated yearly R series to cover the yearly P full record (1951–2016) (Figure 4). Figure 5 shows the full yearly baseflow series generated within the CBR, as well as the yearly surface-weighted IGF series contributed by upstream GRW and SRW areas. As observed, IGF is somewhat higher than baseflow, generated within the CRB. IGF is about 51% of total CRB baseflow.

#### 3.2. Comparison of SWAT Model Results with and without IGF

#### 3.3. Calibration and Validation of SWAT Model Including IGF

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Location of the Castril River basin (CRB) within the Guadalquivir River watershed (GRW) in southern Spain, adjacent to the Segura River watershed (SRW). (

**b**) Discretization of the CRB and 29 sub-basins using the 25 m resolution Digital Elevation Model (DEM) from the Spanish National Geographic Institute, showing other features cited in the text. (

**c**) After the Geological Survey of Spain (IGME) (1988, 1995, 2001) [50,51,52] and direct field observations, a hydrogeological map of the CRB (scale 1:200,000), the schematic hydrogeological functioning of the CRB and the hydraulically connected upstream GRW and SRW contributing areas, a hydrogeological cross-section A–A′ showing aquifer dimensions, CBR location, groundwater divides and flow paths, and the 10 km x 10 km cells for distributed net aquifer recharge (R) in the part of continental Spain [34,42] covered in the study area was developed.

**Figure 2.**Land-use map (scale 1:25,000) from the Andalusian Environmental Information Network (REDIAM).

**Figure 3.**Flow diagram for the coupled Soil and Water Assessment Tool (SWAT) model and chloride mass balance (CMB) method application to model streamflow of hydrological basins subjected to interbasin groundwater flow (IGF).

**Figure 4.**For the control period (1996–2005), parameterization of yearly P–R functions in the CRB and upstream GRW and SRW contributing areas; yearly R equals yearly baseflow. Yearly IGF series refers to the surface-weighed sum of upstream R = baseflow from GRW and SRW areas contributing to the CRB streamflow. In all cases, the Pearson coefficient of correlation is 1.

**Figure 5.**For the full period (1951–2016), (

**a**) surface-weighted yearly P series in the area compiled from the Spanish National Weather Service (AEMET) grid version 1.0 and cumulative deviation (CD) from mean yearly P in mm year

^{−1}; and (

**b**) generated yearly baseflow series in the CRB and yearly surface-weighed IGF series from upstream GRW and SRW contributing areas in mm year

^{−1}, and IGF fraction relative to total CRB baseflow (IGF–CRB) dimensionless ratio. The control period (1996–2005) is grey shallowed (CP). Vertical dotted lines indicate selected time intervals for the SWAT model warm-up (W), calibration (C), and validation (V) phases.

**Figure 6.**For the selected calibration period (1995−1997) and on a monthly scale, observed streamflow compared to (i) initial simulated streamflow without IGF and (ii) corrected simulated streamflow with IGF. The statistics NSE and PBIAS show the model performance achieved in each simulation.

**Figure 7.**On a monthly scale, observed streamflow compared to corrected simulated streamflow with SWAT model for the (

**a**) calibration and (

**b**) validation phases.

**Figure 8.**On a daily scale, observed streamflow compared to corrected simulated streamflow with SWAT model for the (

**a**) calibration and (

**b**) validation phases.

**Table 1.**Equations, ranges, and optimal values for SWAT model performance statistics, after Moriasi et al. (2012) [67].

Statistic and Equation ^{1} | Description |
---|---|

$\mathrm{NSE}:\text{}\mathrm{Nash}\u2013\mathrm{Sutcliffe}\text{}\mathrm{Ef}\mathrm{fi}\mathrm{ciency}\text{}\mathrm{Coef}\mathrm{fi}\mathrm{cient}$ $=1-\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Q}}_{\mathrm{obs}\text{}\mathrm{i}}-{\mathrm{Q}}_{\mathrm{sim}\text{}\mathrm{i}}\right)}^{2}}{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Q}}_{\mathrm{obs}\text{}\mathrm{i}}-\mathrm{Q}\text{\xaf}\right)}^{2}}$ | NSE indicates a perfect match between observed and simulated data, and ranges from −∞ to 1. Higher than 0.5 is considered satisfactory. |

$\mathrm{lnNSE}$$=1-\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left(\mathrm{ln}({\mathrm{Q}}_{\mathrm{obs}\text{}\mathrm{i}})-ln({\mathrm{Q}}_{\mathrm{sim}\text{}\mathrm{i}})\right)}^{2}}{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left(\mathrm{ln}({\mathrm{Q}}_{\mathrm{obs}\text{}\mathrm{i}})-\overline{\mathrm{ln}\left(\mathrm{Q}\right)}\right)}^{2}}$ | lnNSE is the logarithmic form of the model efficiency coefficient. NSE emphasizes the high flows, and lnNSE emphasizes the low flows. |

${R}^{2}:Coef\mathrm{fi}cientofDetermination$ $=\left(\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({Q}_{obsi}-\overline{Q}\right)\left({Q}_{simi}-\overline{{Q}_{simi}}\right)}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({Q}_{obsi}-\overline{Q}\right)}^{2}}\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({Q}_{simi}-\overline{{Q}_{simi}}\right)}^{2}}}\right)\xb2$ | R^{2} indicates the degree of linear relationship between simulated and observed data, and ranges from 0 to 1. Higher than 0.5 is considered a satisfactory result. |

$\mathrm{PBIAS}:\text{}\mathrm{Percent}\text{}\mathrm{Bias}$ $=\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{Q}}_{\mathrm{obs}\text{}\mathrm{i}}-{\mathrm{Q}}_{\mathrm{sim}\text{}\mathrm{i}}\right)\Delta 100}{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{Q}}_{\mathrm{obs}\text{}\mathrm{i}}\right)}$ | PBIAS calculates the average tendency of the simulated data to be higher or lower than their observed counterparts. The optimal value is 0, and an acceptable one is between ±25. |

$\mathrm{RMSE}:\text{}\mathrm{Root}\text{}\mathrm{Mean}\text{}\mathrm{Square}\text{}\mathrm{Error}$ $=\sqrt{{\displaystyle \sum}_{i=1}^{n}{\left({Q}_{\mathrm{obs}\text{}i}-{Q}_{\mathrm{sim}\text{}i}\right)}^{2}}$ | RMSE = 0 indicates a perfect match between observed and simulated data. Increasing RMSE values indicate that matching is getting worse. |

$RSR:\mathrm{Root}\text{}\mathrm{Mean}\text{}\mathrm{Square}\text{}\mathrm{Error}\text{}\mathrm{relative}\text{}\mathrm{to}\text{}\mathrm{standard}$ $\mathrm{deviation}\text{}\mathrm{of}\text{}\mathrm{the}\text{}\mathrm{observed}\text{}\mathrm{data}$ $=\frac{RMSE}{STDE{V}_{obs}}=\frac{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({Q}_{\mathrm{obs}\text{}i}-{Q}_{\mathrm{sim}\text{}i}\right)}^{2}}}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({Q}_{obsi}-\overline{{\mathrm{Q}}_{simi}}\right)}^{2}}}$ | RSR is RMSE relative to standard deviation of the observed data, and ranges from 0 to ∞. The lower the RSR, the lower the RMSE and the better the model performance. Lower than 0.7 is acceptable. |

^{1}n is the total number of observations, ${Q}_{obsi}$ and ${Q}_{simi}$ are observed and simulated streamflow at observation i, $\overline{Q}$ is the mean of the observed data over the simulation period, and $\overline{{Q}_{simi}}$ is the mean of the simulated data over the simulation period.

Cell ^{1} | CRB | GRW | SRW | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

S | P ^{2} | CVP | R | CVR | S | P | CVP | R | CVR | S | P | CVP | R | CVR | |

3200 | 3.2 | 894 | 0.31 | 315 | 0.27 | 0.8 | 894 | 0.31 | 315 | 0.27 | |||||

3201 | 10.4 | 909 | 0.33 | 332 | 0.27 | 20.2 | 909 | 0.33 | 332 | 0.27 | |||||

3202 | 60.6 | 693 | 0.34 | 229 | 0.28 | 4.8 | 693 | 0.34 | 229 | 0.28 | |||||

3203 | 7.1 | 486 | 0.35 | 143 | 0.27 | ||||||||||

3275 | 1.0 | 813 | 0.32 | 276 | 0.27 | 21.7 | 813 | 0.32 | 276 | 0.27 | |||||

3276 | 22.0 | 668 | 0.33 | 206 | 0.29 | 14.5 | 668 | 0.33 | 206 | 0.29 | 25.0 | 668 | 0.33 | 206 | 0.29 |

3277 | 1.8 | 517 | 0.35 | 153 | 0.30 | 1.1 | 517 | 0.35 | 153 | 0.30 | |||||

3349 | 0.1 | 687 | 0.32 | 212 | 0.27 | 0.5 | 687 | 0.32 | 212 | 0.27 | |||||

3350 | 2.0 | 612 | 0.33 | 186 | 0.28 | 0.5 | 612 | 0.33 | 186 | 0.28 | |||||

Sum | 101.9 | 46.9 | 48.4 | ||||||||||||

SWA ^{3} | 692 | 0.34 | 227 | 0.28 | 787 | 0.33 | 269 | 0.28 | 736 | 0.32 | 239 | 0.28 |

^{1}Cell ID as in Figure 1c.

^{2}S is surface in km

^{2}, P and R are, respectively, mean precipitation and mean net aquifer recharge over the control period (1996–2005) in mm year

^{–1}; and CVP and CVR are the dimensionless coefficients of variation of mean P and R over the control period (1996–2005) as fractions.

^{3}SWA is surface-weighted average.

Parameter ^{1} | CRB | GRW | SRW |
---|---|---|---|

Δm | −0.67 | −0.66 | −0.67 |

Δσ | −0.73 | −0.71 | −0.72 |

m_{C} | 227 | 269 | 239 |

σ_{C} | 63.1 | 74.9 | 66.8 |

^{1}Δm and Δσ are dimensionless, and m

_{C}and σ

_{C}are in mm year

^{–1}.

**Table 4.**For the control period (1996–2005), surface-weighted yearly series of (i) P and R in the CRB and in upstream GRW and SRW areas, and (ii) IGF from the GRW and SRW area contributing to CRB.

Year | P ^{1} | Psi ^{1} | R, CRB ^{1} | R, GRW | R, SRW | IGF, GRW+SRW ^{2} |
---|---|---|---|---|---|---|

1996 | 1037.9 | 1.76 | 338.5 | 401.4 | 357.1 | 378.9 |

1997 | 978.9 | 1.47 | 319.8 | 379.2 | 337.3 | 357.9 |

1998 | 472.3 | −1.08 | 159.2 | 188.7 | 167.4 | 177.9 |

1999 | 575.4 | −0.56 | 191.9 | 227.5 | 202.0 | 214.6 |

2000 | 669.5 | −0.09 | 221.7 | 262.9 | 233.6 | 248.0 |

2001 | 742.6 | 0.28 | 244.9 | 290.4 | 258.1 | 274.0 |

2002 | 616.8 | −0.35 | 205.0 | 243.1 | 215.9 | 229.3 |

2003 | 723.7 | 0.19 | 238.9 | 283.3 | 251.8 | 267.3 |

2004 | 641.5 | −0.23 | 212.9 | 252.4 | 224.2 | 238.1 |

2005 | 406.9 | −1.40 | 138.5 | 164.1 | 145.5 | 154.7 |

Mean ^{3} | 686.6 | 227.1 | 269.3 | 239.3 | 240.1 | |

SD | 199.2 | 63.1 | 74.9 | 66.8 | 66.8 | |

CV | 0.29 | 0.28 | 0.28 | 0.28 | 0.28 |

^{1}P and R are, respectively, annual precipitation and net aquifer recharge in mm year

^{−1}, and Psi is dimensionless normalized yearly P.

^{2}IGF is interbasin groundwater flow in mm year

^{−1}.

^{3}Mean and SD are mean and standard deviation over the control period (1996–2005) in mm year

^{−1}, and CV is dimensionless coefficient of variation as a fraction.

Parameter ^{1} | Description | Range Used in Calibration | Fitted Value |
---|---|---|---|

r_CN2.mgt | Soil Conservation Service (SCS) runoff curve number | −0.1 to 0.1 | 0.08 |

v_ALPHA_BF.gw | Baseflow alpha factor (day^{−1}) | 0 to 1 | 0.11 |

a_GW_DELAY.gw | Groundwater delay time (day) | 0 to 60 | 2.82 |

a_GWQMN.gw | Threshold depth of water in the shallow aquifer for return flow to occur (mm) | −200 to 1000 | 898.00 |

v_GW_REVAP.gw | Groundwater revap coefficient | 0.02 to 0.1 | 0.09 |

a_RCHRG_DP.gw | Deep aquifer percolation fraction | −0.05 to 0.05 | 0.04 |

a_REVAPMN.gw | Threshold depth of water in shallow aquifer for revap or percolation to deep aquifer to occur (mm) | −500 to 500 | −61.00 |

v_CANMX.hru | Maximum canopy storage (mm) | 0 to 8 | 0.47 |

v_EPCO.bsn | Plant uptake compensation factor | 0.5 to 1 | 0.56 |

v_ESCO.bsn | Soil evaporation compensation factor | 0.3 to 0.8 | 0.61 |

r_SOL_AWC.sol | Available water capacity of the soil layer (mm H_{2}O/mm soil) | −0.02 to 0.02 | −0.02 |

v_LAT_TTIME.hru | Lateral flow travel time (day) | 0 to 180 | 76.50 |

v_SLSOIL.hru | Slope length for lateral subsurface flow (m) | 0 to 150 | 1.35 |

r_SLSUBBSN.hru | Average slope length (m) | −0.5 to 0.5 | 0.08 |

r_HRU_SLP.hru | Average slope steepness (m/m) | −0.5 to 0.5 | 0.40 |

v_OV_N.hru | Manning’s ‘n’ value for overland flow | 0.01 to 1 | 0.61 |

r_CH_S1.sub | Average slope of tributary channels (m/m). | −0.5 to 0.5 | 0.26 |

v_CH_N1.sub | Manning’s ‘n’ value for the tributary channels | 0.01 to 30 | 1.68 |

r_CH_S2.rte | Average slope of main channel along the channel length (m/m) | −0.5 to 0.5 | −0.04 |

v_CH_N2.rte | Manning’s ‘n’ value for the main channel | 0.01 to 0.3 | 0.04 |

v_SURLAG.bsn | Surface runoff lag coefficient | 0.05 to 24 | 20.71 |

^{1}(r_) refers to relative change, i.e., the current parameter must be multiplied by (1 + the value obtained in calibration), (v_) means that the existing parameter value must be replaced by the value obtained in calibration, and (a_) refers to absolute change, i.e., the fitted value must be added to the existing value of the parameter.

**Table 6.**SWAT model performance statistics for corrected simulated monthly and daily streamflow during calibration and validation phases.

Statistic | Time Step | Calibration | Validation |
---|---|---|---|

NSE | Monthly | 0.77 | 0.8 |

R^{2} | Monthly | 0.92 | 0.89 |

PBIAS | Monthly | 19.82 | 17.25 |

RSR | Monthly | 0.48 | 0.44 |

lnNSE | Daily | 0.81 | 0.64 |

© 2020 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**

Senent-Aparicio, J.; Alcalá, F.J.; Liu, S.; Jimeno-Sáez, P. Coupling SWAT Model and CMB Method for Modeling of High-Permeability Bedrock Basins Receiving Interbasin Groundwater Flow. *Water* **2020**, *12*, 657.
https://doi.org/10.3390/w12030657

**AMA Style**

Senent-Aparicio J, Alcalá FJ, Liu S, Jimeno-Sáez P. Coupling SWAT Model and CMB Method for Modeling of High-Permeability Bedrock Basins Receiving Interbasin Groundwater Flow. *Water*. 2020; 12(3):657.
https://doi.org/10.3390/w12030657

**Chicago/Turabian Style**

Senent-Aparicio, Javier, Francisco J. Alcalá, Sitian Liu, and Patricia Jimeno-Sáez. 2020. "Coupling SWAT Model and CMB Method for Modeling of High-Permeability Bedrock Basins Receiving Interbasin Groundwater Flow" *Water* 12, no. 3: 657.
https://doi.org/10.3390/w12030657