## 2 Materials and Methods
### Description of the Numerical Model
#### 2.2.2 Characteristics of the Model
The value of the pumping and discharge rates were 5.94 m\({}^{3}\)/s, which is  
Figure 3: A detailed view of the modelled mine is shown on the right while a general view of the numerical model is shown on the left side of the figure. It is possible to observe how the bottom of the chambers increases progressively from west to east. the required flow rate to fill or empty 10% of the underground reservoir in 2 hours. The frequency of pumping and discharge (operation scenario) was generated randomly since it is difficult to predict how the electrical generation and demand will evolve during a year. Every two hours, a choice was made between three options (discharge, pumping, or no-operation), and thus, the minimum duration of pumping or discharge operations was 2 hours. No limitation was adopted concerning the duration of pumping, discharge, or no-operation phases. Figure 4 displays the operation scenarios randomly computed for the TOP and MIDDLE hypotheses during the 10 first days and assuming no-groundwater exchanges. Positive values indicate that water was discharged while negative values indicate that the water was pumped. The same pumping-discharge function was used for all scenarios within the same hypothesis concerning the position of the piezometric head (i.e., TOP or MIDDLE). Later, during the simulation process, the virtual connections (the internal boundary conditions explained in Section 2.2.1) constrained the pumping and discharge when the underground reservoir was filled or emptied faster than expected. This occurred because water exchanges cannot be anticipated and, thus, cannot be taken into account when defining the operation scenarios. Figure 4 shows that the pumping-discharge frequencies were very similar for the TOP and MIDDLE scenarios. Differences were observed only during the first and third days. In the first day, we observed that the discharged water was higher for the MIDDLE scenario (red dotted line), and this occurred due to the BCs and the initial conditions. Initially, the underground reservoir was full in the scenario TOP, and, therefore, pumping was needed before any discharge. There was a short pumping at the beginning, and then the underground reservoir was quickly filled by a short subsequent discharge; therefore, no more water could be introduced in the underground reservoir until the next pumping. However, in the scenario MIDDLE, the initial head was located at the half depth of the mine; therefore, more water could be discharged without the need for previous pumping. In contrast, during the third day, more water could be pumped in the scenario TOP than in the scenario MIDDLE. In this case, the natural piezometric head in the scenario MIDDLE was lower than in the TOP one; therefore, the underground reservoir was empty faster in the MIDDLE than in the TOP scenario, and the pumping was stopped earlier. Figure 4: Operation scenarios during the first 10 days for the TOP (blue continuous line) and MIDDLE (red dotted line) scenarios. For the initial conditions, we assumed that the piezometric head distribution matched with that in natural conditions. Therefore, no previous pumping was considered before the start of the activity of the plant. Certain authors considered that, initially, the underground reservoir must be empty [50] because previous works needed to adapt the mine to be used as an underground reservoir, and this adaptation requires dewatering it. However, it was proven in a previous investigation that the differences between considering a previous pumping or not are negligible and only occur during the early periods [33]. This justifies the adopted hypothesis for constructing the numerical model used here. In addition, after any long shutdown of the plant activity, the piezometric head would reach its natural position. As a result, the initial conditions when the activity of the plant would be resumed are the same as those considered in the numerical model.