## 1. Introduction

[2] Estimating the current hydrodynamic state of aquifers is crucial for modeling them accurately. One requires knowledge of whether an aquifer system is in steady state with respect to recharge and discharge or if it is in a transient state where recharge does not equal discharge.

[3] Changes in recharge, discharge, or hydraulic parameters can result in the groundwater system being in disequilibrium which will initiate some transient groundwater behavior. Different mechanisms such as geologic processes [*Luo*, 1994; *Neuzil*, 1995; *Gonçalvès et al*., 2004], or morphologic and climatic variations [*Love et al*., 1994; *Gonçalvès et al*., 2004; *Jost et al*., 2007] can lead to hydrodynamic changes. Transient behaviors of groundwater systems are related to a balance between the origin of the perturbation and the resulting flows, which tend to dissipate it. A major control of this dissipation is the aquifer diffusivity, the ratio of aquifer transmissivity to storativity.

[4] In aquitards with low permeability, long-term transient behavior can occur due to their low hydraulic diffusivity [*de Marsily*, 1986; *Neuzil*, 1995]. Conversely, in aquifers with higher hydraulic diffusivity, one would expect the transient behavior to occur over shorter time periods as they adjust more rapidly to any hydraulic perturbation [*Neuzil*, 1995]. However, several studies, based on numerical models, have examined the effect of past climatic conditions on present-day hydrodynamics [*Burdon*, 1977; *Lloyd and Farag*, 1978; *Dieng et al*., 1990; *Love et al*., 1994; *de Vries*, 1997; *Coudrain et al*., 2001; *Houston and Hart*, 2004; *Jost et al*., 2007; *Sy and Besbes*, 2008] showing that aquifers may present long-term transient behaviors due to past-climatic variations.

[5] Transient behavior, such as occurs after any sudden change of hydraulic conditions, results in a nearly exponential relaxation toward a new steady state. This exponential relaxation is characterized by a time constant *τ*, which is a function of the storativity, transmissivity, and length of the aquifer, as will be shown later, or as shown by *Domenico and Schwartz* [1998]. After a hydraulic perturbation, such as the cessation of recharge, the time to reach a near-steady state or near-equilibrium (*t _{NE}*) can be estimated from the knowledge of

*τ*. The knowledge of

*t*is important to assess the hydrodynamic state of aquifers, i.e., steady state versus transient, and therefore to model them appropriately. Solution formulae exist to estimate the time constant for fully confined [

_{NE}*Domenico and Schwartz*, 1998] or fully unconfined aquifers [

*Reilly and Harbaugh*, 2004]. We are unaware of any solution formula that has been proposed to estimate this time constant in mixed aquifers, i.e., hydrogeologic systems which are partly unconfined and partly confined. Although, the estimation of

*t*is crucial to assess the hydrodynamic state of aquifers, only a few studies have applied this methodology [

_{NE}*York et al*., 2002;

*Schwartz et al*., 2009]. These previous studies have examined small-size to medium-size aquifers (40–70 km) in length. This study focuses on the estimation of

*t*for large mixed aquifers, i.e., with a size of several hundreds of kilometers.

_{NE}[6] The purpose of this work is to develop and test a new time constant, *τ _{m}*, for mixed aquifers in order to assess their hydrodynamic state as a simple first approximation avoiding the use of numerical models, which could be time consuming. This new solution has been obtained using a Laplace transform analysis of the equation describing flow in a conceptual model of an unconfined-confined aquifer submitted to an initial disequilibrium with a long-term disturbance. This new formulation has been tested by comparison with a numerical model whose geometry and hydrogeological characteristics were loosely based on the western margin of the Great Artesian Basin (GAB, Australia). Here we use the western GAB purely as a demonstration aquifer to validate the new time constant solution for mixed aquifers (other similar aquifers could also have been chosen). Finally,

*t*values of 13 worldwide large aquifers have been estimated by using the solutions for mixed, fully confined and fully unconfined aquifers, depending on their characteristics.

_{NE}