## 6 Contributions and Conclusions  
The SW-GW interaction problem has been dealt with using the interdependences of the mechanical (flow) and thermal (heat transport) equations. To date, this issue has not been accurately addressed from a quantitative theoretical and dimensional point of view. Firstly, the application of the non-dimensionalization technique to the governing equations, a protocol that invariably leads to the most accurate solution, resulted in new dimensionless groups. Secondly, the pi theorem was applied to establish the functions of the unknowns. Finally, numerical simulations were used to check the monomials and to depict new user-friendly type curves. These can be applied to quantify flow or parameter values without resorting to new analytical calculus or numerical simulations and to general cases of SW-GW interactions (rivers and lakes), and they are not limited to the specific boundary conditions defined using other solutions. The special dimensionless group, \(\rm\pi_{1}=\frac{K_{x}}{L^{2}}\frac{H^{2}}{K_{y}}\), which is a ratio of hydraulic conductivities corrected using an aspect ratio, simplifies the representation of the dimensionless discharge flows and hydraulic potentials in the whole domain. The solution for the recharge from the river to the aquifer is a single abacus (set of type curves); the dimensionless flow is \(\rm\frac{Q}{(h_{2}-h_{1})\sqrt{K_{x}K_{y}}}\), and \(\rm Q\) is the real flow in the cross-section. The abacus represents the dependence of this dimensionless quantity versus \(\rm\frac{K_{x}}{L^{2}}\frac{H^{2}}{K_{y}}\) and \(\rm\frac{I_{L}}{L}\). In the same way, the representation of the dimensionless type curves of the hydraulic potentials corresponding to a specific horizontal location \(\rm x=x_{o}\) would depend on the same two previous dimensionless groups. The position \(\rm x=I_{r}\) was chosen to qualitatively illustrate the flow lines at this position and to determine whether the region in which the velocity had vertical and horizontal components was close to or far from the edge of the surface water recharge. In scenarios in which the total length of the domain (L) is far away from the recharge area, a region bounded by a thermal length (\(\rm I_{T}\)) appears, which is defined as the length in which thermal changes due to changes in water velocity are appreciable. The dimensionless value of this length depends on three lumped parameters: \(\rm\frac{K_{x}}{K_{y}}\frac{k_{m}}{\rho_{\rm e,vac}c_{\rm w}K_{y}(h_{2}-h_{1})}\), and \(\rm\frac{I_{L}}{H}\). From the dimensionless temperature-depth profiles and the set of type curves of the thermal length, the value of the thermal conductivity of the porous media can be estimated. For this estimation, the hydraulic parameters and the geometry of the domain are assumed to be known and are used as input data. For general scenarios in which it is not known whether the thermal characteristic length is greater than the total length of the domain (distance between \(\rm h_{2}\) and \(\rm h_{1}\)) or it is known that the total length of the domain is equal to or less than the thermal one, the dimensionless field of temperatures depends on the same three monomials as the thermal length, as well as on the position in the domain and on \(\rm L/H\). Two real case studies were used to assess the reliability of the type curves. The recharge volumes calculated differed by 13-20% from the estimated or real values; this was due to the fact that the hydrogeological features contained uncertainties and an assumption was made regarding the main factors influencing the errors. Further studies should consider extended scenarios such as those of pure horizontal flow or unconfined aquifers with a high piezometric gradient. The extended compendium would be applied according to the same methods used in this study. Conceptualization, J.A.J.-V. and I.A. ; methodology, J.A.J.-V., I.A. and C.D. ; software, J.A.J.-V. and I.A. ; validation, J.A.J.-V., I.A., C.D. and D.L. ; formal analysis, J.A.J.-V., I.A., C.D. and D.L.