# The Impact of Groundwater Model Parametrization on Calibration Fit and Prediction Accuracy—Assessment in the Form of a Post-Audit at the SLOVNAFT Oil Refinery Site, in Slovakia

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}and is situated on the northernmost part of a river island bordered by the Danube’s main course (SW border of the island) and its branch—the Little Danube River (NE border of the island). There are fluvial sand and gravel deposits form the main and most significant part of the investigated aquifer. The thickness of these deposits ranges between 12 m on the NW and 45 m on the east part of the modeled area. Under the sand and gravel Quaternary layers, Neogene fine sand occurs with significantly lower hydraulic conductivity. The base of these permeable units consists of Neogene clays (Figure 2 and Figure 3). In the central part of the model domain, the SLOVNAFT refinery area is situated with the pumping wells of its groundwater hydraulic protection system (GWHP) operated by the VÚRUP company. The GWHP system prevents the spreading of polluted groundwater outside the refinery area [27] and represents an important model stressor. The number of pumping wells vary depending on the actual conditions but is usually around 70 (Figure 4). Additionally, the actual pumping rates of individual wells vary depending on actual conditions and are measured daily. The refinery area and its surroundings are highly populated by observation wells (875 at the end of 2019). The monitored parameters consist of a hydraulic head as well as the groundwater quality. The head observation frequency depends on the position of a particular observation well. Inside the refinery area, monitoring is conducted either once a day or once a week, depending on the occurrence of GW pollution in a given well. In the vicinity of the refinery area, it is four times a year, while in the more distant surroundings of the refinery, it is twice a year.

#### 2.1. Model Settings

^{−2}m·s

^{−1}, and horizontal hydraulic conductivity is regarded as isotropic (Kx = Ky). The vertical hydraulic conductivity is computed by the formula Kz = Kxy/5. Groundwater within the modeled area is under unconfined conditions. Model hydrological settings are represented by the long-term (1961–1990) annual precipitation, which averages around 600 mm [28], as well as the long-term (1961–1990) annual actual evapotranspiration, which averages around 450 mm [28]. Therefore, around 150 mm of precipitation is left annually for infiltration on average. Recharge of the modeled aquifer is predominantly secured by water infiltration from the Danube River. This river also defines the western border of the model domain, and with its average discharge of around 2000 m

^{3}·s

^{−1}, it represents one of the model’s constant head boundary conditions. Its branch, the Little Danube River, is represented as a 3rd type boundary condition and is situated on the northern part of the model domain (Figure 4). Groundwater within the study area is intensively extracted by the pumping wells of the GWHP system and is discharged outside of the model domain after treatment. The overall pumping rate varies based on the GWHP system dynamic operation. Throughout the years, new pumping wells have also been introduced, since some of the old ones have been deactivated.

#### 2.2. Model Calibration and Prediction

- OF: objective function (sum of squared residuals),
- HOB: groundwater head observations number,
- nPAR: number of adjusted parameters.

#### 2.3. Conceptual Approach in Individual Model Scenarios

^{−1}) is the value of 4.76 × 10

^{−9}m·s

^{−1}.

## 3. Results

**V1 calibration**, the resulting K values are shown in Figure 6a. They range from 0.005 m·s

^{−1}to 1 × 10

^{−8}m·s

^{−1}. The variant V1 can be characterized as the worst one among all variants in each of the evaluated criteria listed in Table 2. In the scatter plot of OBS vs. SIM (Figure 10), the V1 variant performed relatively poorly within the calibration. The spatial distribution of residuals is not random (Figure 11) and the ratio of RMSE and OBS dispersion is 4.0% (Figure 12). The lowest value of AIC, AICc, and BIC criteria (Table 2) is achieved due to the extremely low number of calibrated parameters. Regarding the mentioned information criteria, the V1 scenario is assumed to provide the best prediction accuracy.

**V1 prediction**performance, the value of all evaluated characteristics, which are introduced in Table 3, are the worst from all evaluated variants. In the scatterplot of OBS vs. SIM (Figure 10), the V1 variant performed relatively poorly within calibration for 2008, and even worse in the prediction for 2019. Residual distribution maps (Figure 13) show significant grouping of negative and positive residuals. The residual spatial distribution cannot be classified as random. The ratio of RMSE and OBS dispersion is 6.4% (Table 3, Figure 12). In all evaluated characteristics, the V1 model performed significantly worse in prediction compared to its calibration fit. Despite the best values of AIC, AICc, and BIC information criteria, the V1 prediction performance is the worst among evaluated scenarios. Considering the results, the V1 variant can be considered an example of conceptual oversimplification.

**V2 calibration**, the resulting distribution of K values is shown in Figure 6b. They range from 0.05 m·s

^{−1}to 1 × 10

^{−8}m·s

^{−1}. The resulting EVT values are shown in Figure 7. EVT in urbanized areas reached the highest value of 567 mm·y

^{−1}. Here, it is likely that a significant effect of the interception and drainage of precipitation from the artificial surfaces of the area takes place. In the forests, the EVT reached a calibrated value of 473 mm·y

^{−1}. In agriculture fields, the EVT had the lowest value of 378 mm·y

^{−1}. OF and RMSE values are significantly lower compared to V1 (Table 2). This result represents a significantly better overall fit of the higher parametrized scenario V2 over V1 within the calibration. In the scatterplot of OBS vs. SIM (Figure 10), the V2 variant performs significantly better than V1. The spatial distribution of residuals is partly random and partly grouped (Figure 11). The ratio of RMSE and OBS dispersion is 2.6% (Figure 12). The relatively favorable values of AIC, AICc, and BIC criteria (Table 2) are achieved due to the relatively low number of calibrated parameters at a relatively low value of OF. From the V1 and V2 comparison, where the conceptual difference lies in the zonal calibration of the Quaternary aquifer K and zonal calibration of EVT, it can be concluded that the effect of higher parametrization has a significant impact on the overall model fit. Regarding the AIC, AICc, and BIC evaluation results, V2 is the second most successful calibration scenario.

**V2 prediction**performance is significantly better than the V1 model (Table 3), but still worse than its calibration fit. This is evident from the scatterplot of OBS vs. SIM (Figure 10). Residual distribution maps (Figure 13) show significant grouping of negative and positive residuals. The residual spatial distribution is not random and is worse in the prediction than in the calibration. The ratio of RMSE and OBS dispersion is 2.9%, which is slightly higher than for the calibration (Figure 12). In all the evaluated characteristics, the V2 model performs worse in prediction compared to its calibration fit.

**V3 calibration**, the resulting distribution of K values is shown in Figure 6c. They range from 0.05 m·s

^{−1}to 1 × 10

^{−11}m·s

^{−1}. The overall improvement in the calibration fit against the V1 and V2 models was indicated by the statistics introduced in Table 2. In the scatterplot of OBS vs. SIM (Figure 10), the V3 variant performs slightly better than the V2 variant. The spatial distribution of residuals is still not random (Figure 11) and is even worse than in the case of the V2 scenario. The V3 solution represents a ratio of RMSE and OBS dispersion of 1.6% (Table 2, Figure 12). This is the best value among the evaluated variants so far. The calibrated riverbed conductance of the Little Danube River is shown in Figure 8a. It ranges between the values 0.075 m·s

^{−1}and 2.12 × 10

^{−12}m·s

^{−1}. From the AIC, AICc, and BIC evaluation, it follows that the V3 calibration variant is significantly less accurate for prediction than the V2 and V1 scenarios, due to the increased number of parameters and less significant OF value reduction (Table 2). Despite a reduction in the computation grid density, the value of RMSE, OF, and other related criteria are better than in the previous scenarios. The input precipitation and evapotranspiration difference of 4.76 × 10

^{−9}m·s

^{−1}(150 mm·y

^{−1}), which was applied as one parameter for the whole model domain (the initial value is regional, not exact for local areas), has been optimized to 4.6 × 10

^{−9}m·s

^{−1}(145 mm·y

^{−1}).

**V3 prediction**performance, all evaluated statistics are slightly better than in the case of the V2 scenario; however, from a practical point of view, the prediction accuracies of V2 and V3 are very similar. The prediction performance of V3 is worse than its calibration fit. In the scatter plot of OBS vs. SIM (Figure 10), V3 performs similar to the V2 variant. Residual distribution maps (Figure 13) show a significant grouping of negative and positive residuals, as well as in the V2 case. The ratio of RMSE and OBS dispersion is 2.7% (Figure 12).

**V4 calibration**, the resulting distribution of K values is shown in Figure 6d. They range from 0.05 m·s

^{−1}to 1 × 10

^{−11}m·s

^{−1}. The increased parametrization leads to increased calibration accuracy, which is the best among the evaluated scenarios. The improvement was recorded in all the evaluated characteristics (Table 2), and the RMSE reaches 0.1 m. In the scatterplot of OBS vs. SIM (Figure 10), V4 provides the best solution. Spatial distribution of residuals is close to random (Figure 11). The ratio of RMSE and OBS dispersion is 1.2% (Table 2, Figure 12). The resulting riverbed conductance of the Little Danube is shown in Figure 8b. From the AIC, AICc, and BIC evaluation point of view, the V4 variant is the least probable (Table 2) due to a significant increase in the number of parameters and a relatively slight decrease in OF and RMSE.

**V4 prediction**performance is the best, but is similar to V2 and V3 (Table 3). In the scatterplots of OBS vs. SIM (Figure 10), the V4 scenario prediction performs the best, as well as in the calibration stage. Residual distribution randomness (Figure 13) is worse than in V2 and quite similar to V3. The V4 model performs significantly worse in prediction compared to the calibration stage.

## 4. Discussion

## 5. Conclusions

- -
- the K-field zonation based on groundwater level residuals’ distribution can be valuable in the calibration process if there are only limited K data from the field survey;
- -
- higher parametrization does not necessarily lead to a more effective solution regarding prediction accuracy and several variants of a solution with continual post-audit evaluation should be used whenever possible;
- -
- different model variants with similar prediction accuracy in terms of groundwater level fit can produce different groundwater pathlines; and, finally,
- -
- the information criteria AIC, AICc, and BIC can be inaccurate in the evaluation of model prediction accuracy.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AIC | Akaike Information Criterion |

AICc | Corrected Akaike Information Criterion |

AVG | average |

AVG ABS RES | averaged absolute residuals |

BIC | Bayesian Information Criterion |

E, W, N, S | east, west, north, south |

EVT | evapotranspiration or evapotranspiration package/module in MODFLOW-2005 program |

f | function |

GLUE-MBA | Generalized Likelihood Uncertainty Estimation–Bayesian Model Averaging methods |

GW | groundwater |

GWHP | Groundwater Hydraulic Protection System |

H | hydraulic head |

CHD | Time-Variant Specified-Head package/module in MODFLOW-2005 program |

K | hydraulic conductivity (m·s^{−1}) |

Kx, Ky | horizontal hydraulic conductivity (m·s^{−1}) in “x” and “y” direction, respectively |

Kz | vertical hydraulic conductivity (m·s^{−1}) |

LPF | layer property flow package/module in MODFLOW-2005 program |

nPAR | number of adjusted parameters during calibration |

OBS | observed groundwater head |

OF | sum of squared residuals or objective function |

PCG | preconditioned conjugate gradient package (solver) in MODFLOW-2005 program |

Q | discharge or pumping rate (m^{3}.s^{−1}) |

Q pump | overall pumping rate at modeled site |

RES | groundwater head residual (difference between observed and simulated head) |

RCH | recharge or recharge package/module in MODFLOW-2005 program |

RIV | river package/module in MODFLOW-2005 program |

RMSE | root mean square error |

SIM | calculated (simulated) groundwater head |

V1–V4 | model scenarios (variants) |

WEL | well package/module in MODFLOW-2005 program |

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**Figure 2.**Block diagram of geological settings with the principal aquifer layers and pumping wells depiction (vertical exaggeration 1:20).

**Figure 4.**Constant head boundary level, pumping wells, surface water bodies and situation of the geological section 1–2 in the model domain.

**Figure 5.**Differences in averaged observed groundwater head (contours) and averaged pumping rates (proportional dots), respectively, between the period of prediction (2019) and the calibration period (2008) (2019 minus 2008). The whole model domain view (

**left**) and detail view on the central model area (

**right**).

**Figure 6.**Horizontal hydraulic conductivity (Kxy) zonation within individual model variants ((

**a**)—V1, (

**b**)—V2, (

**c**)—V3, (

**d**)—V4) with the optimized Kxy values after calibration (planar view and vertical cross sections along the blue and green double lines).

**Figure 7.**Evapotranspiration zonation with the optimized values within V2 model variant (planar view and vertical cross sections along the blue and green lines).

**Figure 9.**Resulting groundwater table of the V4 model variant, hydroizohypses, bodies of surface water, refinery area border, and pumping wells’ location in the 3D modeled site view.

**Figure 10.**Scatterplots of observed and simulated groundwater heads within individual model variants (V1–V4) after calibration (2008) and within prediction (2019).

**Figure 11.**Groundwater head residuals within individual model variants (V1–V4) after calibration; blue: simulated heads too high, red: simulated heads too low.

**Figure 12.**RMSE of groundwater head residuals and observed head dispersion (HOBdisp%) ratio of model variants (V1–V4) for calibration and prediction.

**Figure 13.**Groundwater head residuals within individual model variants (V1–V4) for prediction; blue: simulated heads too high, red: simulated heads too low.

**Figure 14.**Groundwater pathlines prediction of individual model variants with the stop and pass-through weak sinks setting in the MODPATH 6 software.

**Table 1.**Comparison of the values of main features influencing modeled conditions between the years 2008 and 2019.

Feature | Units | 2008 | 2019 | ABS Delta |
---|---|---|---|---|

AVG OBS | m a.s.l. | 124.27 | 123.69 | 0.58 |

AVG RIV 1 | m a.s.l. | 131.83 | 131.99 | 0.16 |

AVG RIV 2 | m a.s.l. | 130.91 | 130.87 | 0.04 |

AVG Q _{pumping} | m^{3}·s^{−1} | 0.916 | 1.009 | 0.093 |

Model Variant | nPAR | OF | AVG RES (m) | AVG ABS RES (m) | RMSE (m) | AIC | AICc | BIC | RMSE and OBS Dispersion Ratio (%) |
---|---|---|---|---|---|---|---|---|---|

V1 | 2 | 64.5 | 0.04 | 0.25 | 0.34 | 69 | 69 | 77 | 4.0 |

V2 | 43 | 26.5 | −0.05 | 0.14 | 0.22 | 113 | 121 | 298 | 2.6 |

V3 | 139 | 11.0 | 0.05 | 0.11 | 0.14 | 289 | 389 | 885 | 1.6 |

V4 | 255 | 5.8 | −0.01 | 0.07 | 0.1 | 516 | 977 | 1611 | 1.2 |

Model Variant | OF | AVG RES (m) | AVG ABS RES (m) | RMSE (m) | RMSE and OBS Dispersion Ratio (%) |
---|---|---|---|---|---|

V1_2019 | 205.7 | −0.29 | 0.45 | 0.62 | 6.4 |

V2_2019 | 44.2 | −0.05 | 0.20 | 0.28 | 2.9 |

V3_2019 | 35.7 | 0.03 | 0.17 | 0.26 | 2.7 |

V4_2019 | 31.4 | −0.06 | 0.17 | 0.24 | 2.5 |

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## Share and Cite

**MDPI and ACS Style**

Zatlakovič, M.; Krčmář, D.; Hodasová, K.; Sracek, O.; Marenčák, Š.; Durdiaková, Ľ.; Bugár, A.
The Impact of Groundwater Model Parametrization on Calibration Fit and Prediction Accuracy—Assessment in the Form of a Post-Audit at the SLOVNAFT Oil Refinery Site, in Slovakia. *Water* **2023**, *15*, 839.
https://doi.org/10.3390/w15050839

**AMA Style**

Zatlakovič M, Krčmář D, Hodasová K, Sracek O, Marenčák Š, Durdiaková Ľ, Bugár A.
The Impact of Groundwater Model Parametrization on Calibration Fit and Prediction Accuracy—Assessment in the Form of a Post-Audit at the SLOVNAFT Oil Refinery Site, in Slovakia. *Water*. 2023; 15(5):839.
https://doi.org/10.3390/w15050839

**Chicago/Turabian Style**

Zatlakovič, Martin, Dávid Krčmář, Kamila Hodasová, Ondra Sracek, Štefan Marenčák, Ľubica Durdiaková, and Alexander Bugár.
2023. "The Impact of Groundwater Model Parametrization on Calibration Fit and Prediction Accuracy—Assessment in the Form of a Post-Audit at the SLOVNAFT Oil Refinery Site, in Slovakia" *Water* 15, no. 5: 839.
https://doi.org/10.3390/w15050839