The outcome of a dimensionless characterization study in a two-dimensional porous media domain in which groundwater flows at a constant horizontal velocity is presented in this report. Using spatial discrimination, the dimensionless groups that govern the solution patterns are determined from dimensionless governing equations. As a boundary condition on the surface, the case of constant temperature is studied. From the mathematical deduction of the groups, a characteristic horizontal length emerges. This length determines the region in which temperature–depth profiles are affected by flow. Existing analytical solutions have been shown to be invalid due to the severe assumption that the horizontal thermal gradient has a constant value. Therefore, universal solutions based on pi theorem have been obtained for the characteristic horizontal length, temperature field, temperature–depth profiles and horizontal temperature profiles. Dependencies between dimensionless groups have been depicted by universal curves, abacuses and surfaces. These graphical solutions are used in an easy way to estimate groundwater velocity from experimental temperature measurements in the form of an inverse problem. In addition, an easy and fast protocol for estimating fluid flow velocity and groundwater inlet temperature from temperature profile measurements is proposed. This protocol is applied in a scenario of groundwater discharge from a quaternary aquifer to a salty lagoon located in the southeast of Spain.

The Agua Amarga coastal aquifer has experienced different anthropic interventions over the last 100 years. Since 2008, groundwater abstractions along the coastline to supply the Alicante I and II desalination plants have been combined with artificial recharge. This measure, consisting of seawater irrigation over the salt marsh, has reduced the impact on the piezometry and surface ecosystems. The study of the effect of this measure on groundwater flow is addressed by applying an inverse problem protocol to temperature profiles monitored in a piezometer located inside the recharge area. Information on monthly seawater irrigation volumes, rainfall, and average air and seawater temperatures have also been gathered as input data to quantify vertical flow. An upward flow component for the period 2010–2022 that varies between 2 × 10−9 and 7.5 × 10−7 m/s has been found. These values decrease near the surface, where the flow is mainly horizontal.

In the present work, a network model for the numerical resolution of the heat transport problem in porous media coupled with a water flow is presented. Starting from the governing equations, both for 1D and 2D geometries, an equivalent electrical circuit is obtained after their spatial discretization, so that each term or addend of the differential equation is represented by an electrical device: voltage source, capacitor, resistor or voltage-controlled current source. To make this possible, it is necessary to establish an analogy between the real physical variables of the problem and the electrical ones, that is: temperature of the medium and voltage at the nodes of the network model. The resolution of the electrical circuit, by means of the different circuit resolution codes available today, provides, in a fast, simple and precise way, the exact solution of the temperature field in the medium, which is usually represented by abaci with temperature-depth profiles. At the end of the article, a series of applications allow, on the one hand, to verify the precision of the numerical tool by comparison with existing analytical solutions and, on the other, to show the power of calculation and representation of solutions of the network models presented, both for problems in 1D domains, typical of scenarios with vertical flows, and for 2D scenarios with regional flow.

A dimensional study of two problems in which groundwater flow is oblique has been carried out in order to characterize the vertical profiles of temperature along the domain affected by the flow, determining an input region in which the profiles depend on the horizontal position followed by a region in which profiles only depend on the vertical component of the flow. In the first problem, the horizontal and vertical components of velocity are constant. In the second scenario, the oblique flow of groundwater is generated because in the boundary conditions, the hydraulic potentials present a constant value. From the discriminated dimensional analysis of the mathematical model (governing equations and boundary conditions), the dependencies of the unknowns of greatest interest, characteristic lengths for the development of temperature‐depth profiles, velocity profiles and the temperature field, with the dimensionless groups deduced are established. Once these dependencies have been verified, they are graphically represented by means of curves and surfaces as universal solutions to these problems. Based on these universal solutions an inverse problem protocol for estimating water flows from temperature measurements is proposed. The use of universal graphs of the two proposed scenarios avoids the large number of numerical simulations that this type of problem required.

In the present investigation, a numerical model based on the network simulation method has been designed and applied in order to obtain correlation between temperature patterns and profiles in large 2-D groundwater real scenarios, with horizontal or vertical regional flow and thermal conditions that reproduce approximately real cases, such as the daily or seasonal variation of the soil surface temperature. The illustrated applications show the power and capacity of the numerical tool, which is based on the analogy between electrical and physical variables of the problem to design an equivalent electrical circuit, from whose resolution the values of the real variables temperature and transferred heat flow are inferred.