The use of the pilot points method on groundwater modelling for a degraded aquifer with limited ﬁ eld data: the case of Lake Karla aquifer

Groundwater depletion poses a major threat to global groundwater resources with increasing trends due to natural and anthropogenic activities. This study presents a surface-groundwater framework for water resources modelling of ill-posed problems in hydrogeologically data-scarce areas. The proposed framework is based on the application of a conceptual water balance model and composed of surface hydrological (UTHBAL) and groundwater ﬂ ow simulation with the integration of a Newton formulation of the MODFLOW-2005 code (MODFLOW-NWT) and PEST suite modules. The groundwater simulation includes a preprocessor tool for automated calibration and a post-processor tool for automated validation. The methodology was applied to a rural region of Central Greece, Lake Karla Basin, which is degraded due to groundwater resources overexploitation to cover irrigation water demands. The aquifer is modelled focusing on a precise simulation – validation procedure of the conceptual model. The groundwater model was calibrated with the calibration preprocessor tool for spatially distributed hydraulic conductivity with the pilot points method. The calibration process achieved satisfactory results as validated by the post-process analysis of observed and simulated water levels. The ﬁ ndings for the groundwater budget indicate that the groundwater system is still under intense pressure even though farming activity in recent years has turned to less water-intensive crops. the pilot method on modelling in an area


GRAPHICAL ABSTRACT INTRODUCTION
Groundwater resources are vital in providing water for domestic, agricultural, and industrial use globally. Over two billion people rely on groundwater as their primary water source, while half or more of the irrigation water for agriculture is supplied from underground sources (Pisinaras et al. ; Famiglietti ). However, despite its critical importance to global water supplies, inadequate management practices are applied for monitoring groundwater resources. Furthermore, it is crucial to estimate the pressure on surface and groundwater systems due to groundwater depletion. Climate change and related changes on the components of the hydrological cycle complicate the task of sustaining groundwater supplies for the future. Hence, about 20% of the world's aquifers systems are estimated to be under over exploitation status and with increasing trends due to the climate change phenomenon and population growth (Upton et al. ).
Understanding why groundwater depletion has occurred may be the first step towards sustainable groundwater resources management. Numerical simulation models are effective and valuable tools for computing water budgets of regional groundwater systems and the planning and policy making for groundwater resources management (Konikow & Kendy ). The analysis of groundwater system through simulation is the main process before a researcher/modeller deals with the management of groundwater resources (Doherty & Hunt ). The simulation problems in groundwater hydrology are part of the complex environmental issues that are difficult to solve.
These problems in groundwater modelling become extremely difficult when in addition to the lack of field data problems also meet a lack of quality data (Singh ).
One of the most important issues for water resources management is developing strategies for groundwater modelling that are adaptable to data scarcity and field measurements and so begins the difficulty of the inverse problem. According to Zhou and her associates () many approaches have been proposed to resolve the inverse problem in hydrogeological modelling. Inverse methods are categorized as direct and indirect ones. The inverse problem in hydrogeological fields is difficult to solve because it is ill posed and the calibration parameters are more than the observations (Anderson et al. ).
Common indirect methods used to solve the inverse problem are the geostatistical approach, the maximum likelihood method where zonation is employed, and pilot points. The most advanced methods where the stochastic approach is introduced are the self-calibrated method, the Markov chain Monte Carlo method, the gradual deformation method, the probability perturbation method, and the ensemble Kalman filter. The geostatistical approach has several advantages, however it is not appropriate for use in the inverse model where the hydraulic conductivity variable poses spatial distributions with significant heterogeneity, forcing the transition from linearized to nonlinearized approaches (Zhou et al. ).
Zonation assumes an abrupt spatial change in parameter values, whereas the pilot points method produces smoothly distributed parameters and flexibility compared to the zonation approach (Anderson et al. ; Rajabi et al. ). These strategies are particularly important in arid and semi-arid areas where access to data is poor and data collection is difficult, such as the Lake Karla aquifer, Greece. This study analyzes the groundwater resources status of the Lake Karla aquifer focusing on a precise simulation-validation procedure of the groundwater model. A surface hydrological simulation tool was applied to calculate the groundwater recharge while the MODFLOW with a Newton formulation was employed to simulate groundwater flow. The groundwater model was calibrated for spatial distributed hydraulic conductivity based on the pilot points method, since there are limited data for this parameter.
This paper presents a new framework for calibrating and validating the groundwater flow simulation applying two automated tools with the use of pilot points. The first relates to calibration post-process analysis and is called PLPROC and the second one deals with the post-process analysis of the results and is called mod2obs (Doherty , ).

Study area
The study area of about 500 km 2 is located at Eastern Thessaly, Greece and occupies the plain zone of Lake

METHODS AND APPLICATION
The methodology is described in Figure 2  When there is no observed decrease, we can conclude that the groundwater hydrology model is unstable and needs to be re-evaluated.  acceptable criterion for the successful completion of calibration is a RMSE deviance of 10% of the water levels' total range. MAE is more robust in estimating the effects of outlier values of the spatial distribution than the RMSE, and therefore it is usually smaller than RMSE. However, if the calibration procedure should be continued, depends on score of the Nash-Sutcliffe Efficiency (E f ) (Anderson et al.

).
Estimation of groundwater recharge and irrigation demands covered by the groundwater system The surface hydrological model (UTHBAL), is a surface hydrological simulation tool that gives a representation of the rainfall-runoff interactions of a catchment area.
UTHBAL uses the components of the hydrological cycle, monthly time series of precipitation (P), mean temperature (T) and potential evapotranspiration (Ep) as inputs. The surface hydrological simulation tool disaggregates the total precipitation into rainfall and snowfall. UTHBAL distinguishes the total watershed runoff (Qsim), between the surface runoff (SR), the interflow (MR), and the baseflow (Qg) utilizing a soil moisture mechanism (Nmoist) and finally estimates the groundwater recharge to the subsurface systems (Loukas et al. ). In this study, UTHBAL has been applied in semi-distributed mode because the aquifer system covers the lower zone of the Karla watershed (e.g.   Table 2 shows the pumping rates for each zone and the respective irrigation area. It is worth noting that although the reservoir exists at present, it does not participate in the current study. The former natural Lake Karla had been drained in the 1960s, causing serious environmental problems in the area. A reservoir for the restoration of Lake Karla has been recently constructed to reverse the bad environmental status. The Lake Karla reservoir project construction has been completed in 2018 (Sidiropoulos et al. ). Thus, its contribution to the groundwater system is not considered during the simulation.

Groundwater simulation
Groundwater flow simulation is achieved with the use of the

Calibration and validation process
The calibration process attempts to bring the model response as close to the observed ones as possible. In the first stage, a trial-and-error method is employed whereas, in the next stage, the pilot points approach was chosen. The pilot point approach is followed due to the lack of field measurements of hydraulic conductivity. input files to be in a predefined format (Doherty ). Upon completion of the calibration preprocess, the template files of hydraulic conductivity are created automatically and then used during the PEST run. PEST tool is used in the model optimization process in the regularization mode.
The general form of the measurement objective function (Equation (1)) is shown in Figure 2 Φ where (h obs indicates the observation hydraulic head, h sim is the simulated hydraulic head, and w the weight that has been applied to the measurement. In this study, we followed

Post-processing analysis
Post-processing data were analyzed using mod2obs (Doherty

RESULTS
The model calibration was carried out based on hydraulic head data for the period between 2/11/1987 and 12/ 11/2015. Data were validated for the period between  (2)), the RMSE (Equation (3)), and the Coefficient of Determination (R 2 ). The statistical results are presented in Table 3: where, Y O is the mean observed value, Y m is the simulated value and Y o is the observed one at time t: where, Y m is the simulated value, Y o is the observed one, i is the code number of observation points, and n is the number of observation points.
Figures 5-7 demonstrate two types of results. The calibration and the validation using the pilot points

CONCLUSIONS
This study analyzes the groundwater resources status of the Lake Karla aquifer focusing on a precise simulation-validation procedure of groundwater model based upon new and innovative methodologies. The simulated annual decrease in groundwater levels verify the groundwater depletion and shows that the groundwater system is still under intense pressure even though farming activity in recent years has turned to less water-intensive crops. Moreover, the enduring water balance deficit indicates the necessity for the construction of collective irrigation networks that will eliminate the extravagant number of private own wells, and the need for sustainable water

DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.