## 1. Introduction

[2] The Rhine valley aquifer is a privileged object of study for several reasons: (1) The aquifer is a huge alluvial reservoir containing the largest European groundwater resource. (2) The aquifer is well known, instrumented, and monitored; many hydrological studies have already been carried out, providing abundant additional data. (3) the alluvial aquifer is not bound to a single river, but receives various inflows: Periodic rainfall due to the semicontinental climate of the region, summer inflow from the Rhine River due to snow melting in the Alps and spring river floods from the Vosges and the Black Forest mountains.

[3] We needed to extract smoothed regional information from these point data in order to solve other problems such as the calculation of the geodetic effect of hydrological loading. We therefore decide to find out the main common source signals, which combine differently in the local measurements. The smoothing problem is then expressed as finding a mean behavior for the local combinations of these source signals. In this paper, the variation of the piezometric head of an aquifer Δ*H* is considered as the linear superposition of several contributions *H*_{k} due to various sources with associated weight *α*_{k}: Δ*H* = Σ_{k}*α*_{k}*H*_{k}. The blind separation of the sources refers to the problem of reproducing the contribution of source signals from piezometric head values, without making any assumption or exploiting any external knowledge, except for some mathematical considerations. “Blind” means that the statistics of the source signals and the way they mix are unknown. Several mathematical or physical models are used to mix contributions, for different purposes: e.g., immediate, convolution-based, or spectral-based models.

[4] In this work, the temporal contributions *H*_{k} and associated weights *α*_{k} are determined using immediate mix model. As a consequence, the method neglect the propagation effects of the physical processes involved.

[5] The source processes are represented by a set of piezometric head time series sampled at various locations within the system. Here, we use a statistical multivariate analysis, the Karhunen-Loève transform (KLT), to sum up the observations into a set of a minimum number of temporal characteristic signals.

[6] The principle of KLT has frequently been used under different names depending on the applications and fields of study: singular value decomposition (SVD) in geomagnetics to search for particular temporal signals [*Pereira*, 2004] and empirical orthogonal function (EOF) analysis in meteorology in order to analyze spatial structure of atmospheric fields [*Grimmer*, 1963]. The link between both methods is given by [*Gerbrands*, 1981]. The method has also been applied on hydrological purpose, for example, by *Gottschalk* [1985], for the interpolation of water balance elements. An evolution of KLT method, multichannel singular spectrum analysis (MSSA) has also been used by *Shun and Duffy* [1999] in order to highlight space-time patterns of precipitation, temperature and runoff.

[7] In this work, the Karhunen-Loève transform is first used to separate space and time and define a new orthogonal basis where each observed piezometric head time series can be expressed as the sum of a small number of characteristic temporal signals *H*_{k} calculated for the whole aquifer and associated with spatial information *a*_{k} for each piezometric head. This spatial information is then interpreted and regionalized by geostatistical methods in order to make a statistical reconstruction model of the model of the aquifer containing only sound information.