## 5 Application to a Real Aquifer  
The above protocol has been applied to the Agua Amarga coastal aquifer (Alicante, SE of Spain) to estimate lateral groundwater velocity. It is a very controlled aquifer due to environmental issues related to the salt marsh ecosystem developed on its surface [27]. This ecosystem interferes with the extraction wells that supply the Alicante I and II desalination plants [28] and the existence of an old salt industry in the coastal region. Agua Amarga is a depressed natural brackish water lagoon separated from the Mediterranean Sea by a sand bar with a length of 2 km and a width of 50-200 m. This Quaternary-Neogene aquifer,  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**y (m)**} & \multicolumn{3}{c}{\(T_{x_{a}}\) (\({}^{\mathrm{e}}\)C)} & \multicolumn{3}{c}{\(T_{x_{b}}\) (\({}^{\mathrm{e}}\)C)} \\ \cline{2-7}  & **Real** & **e = 1\%** & **e = 2\%** & **Real** & **e = 1\%** & **e = 2\%** \\ \hline
0.11 & 0.797 & 0.798 & 0.790 & 0.868 & 0.876 & 0.863 \\
0.23 & 0.59  
connected to the sea, has an average hydraulic gradient between 0.1 and 1.5%. The aquifer has an approximate extension of 1700 hectares, of which 150 hectares are occupied by plots of land where a salt industry was developed, whose activity took place approximately between 1925 and 1975 [29]. Figure 3 shows the aquifer location, its limits, and the position of the measurement wells, P-3 and P-4, separated by a distance of 300 m and far away from the salt marsh and the extraction wells of the desalination plants. The piezometric isolines derived from the aquifer control well network, also shown in Figure 3, allow us to ensure that the groundwater flow between the P-3 and P-4 boreholes is horizontal and directed towards the coastline. A thermal diffusivity of 3.6 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s has been estimated [30]. Figure 4 shows the geologic cross-section through the P-3 and P-4 well line to the sea. The aquifer, formed by an approximately 20 m thick layer of silty sands and conglomerates from the Pliocene-Pleistocene, is located under a thin layer of clayey mud with gypsum and salt (Quaternary). Beneath the aquifer, a limestone marl formation (Upper Messinian) acts as an impermeable barrier. Figure 4: Cross-section of the aquifer on the line defined by wells P-3 and P-4. Figure 3: Location and limits of Agua Amarga coastal aquifer with wells P-3 and P-4 (Google Earth Pro). The temperature profiles of these wells, corresponding to March 2019, are shown in Figure 5. Six temperatures have been taken at positions separated by 1 m, between depths y = 3.0 to y = 8.0 m measured from the water table, thus avoiding the influence on temperature profiles due to changes in ambient temperature during the day. According to Figure 5, temperatures in the upper and lower boundary conditions at the domain are 18.2 and 20.2 \({}^{\circ}\)C, respectively. The simulated domain is 900 m, an extension large enough to ensure that, at the right edge, the profiles are fully developed and not dependent on the horizontal position. Partial results of the application of the protocol for successive iterations in velocity are as follows: functionals, \(\Psi_{\text{b,min,j}}\), \(\Psi_{\text{a,j}}\) and its sum \(\Psi_{\text{b,min,j}}+\Psi_{\text{a,j}}\). Estimated positions of the wells, in relation to the water inlet source, \(\text{x}_{\text{a,j}}\) and \(\text{x}_{\text{b,j}}\), are shown in Table 4. The convergence of these results provides the following estimates for velocity and well positions: \(\text{v}_{\text{o}}\) = 8.0 \(\times\) 10\({}^{-5}\) m/s, \(\text{x}_{\text{a}}\) = 487.5 m (P-3) and \(\text{x}_{\text{b}}\) = 187.5 m (P-4). The protocol for estimating the temperature of the inlet groundwater flow, the partial results of which are shown in Table 5, gives a value of \(\text{T}_{\text{w}}\) = 20.0 (\({}^{\circ}\)C). This value corrects the positions of wells P-3 and P-4 to \(\text{x}_{\text{a}}\) = 424.5 m and \(\text{x}_{\text{b}}\) = 124.5 m, respectively.