Cross-correlation analysis and information content of observed heads during pumping in unconfined aquifers


Corresponding author: D. Mao, Department of Hydrology and Water Resources, The University of Arizona, Tucson, AZ 85721, USA. (


[1] Using a first-order cross-correlation analysis, this paper investigates the relationship between observed heads and hydraulic properties in the saturated and vadose zones at different times and locations of three-dimensional unconfined aquifers during pumping tests. Cross-correlation analysis is a weighted sensitivity analysis casted into a stochastic framework. It determines the relative impact of each parameter with respect to others in time and space on the observed heads according to uncertainty or spatial variability of each parameter. It reveals the information content in measured drawdowns about heterogeneity during a pumping test in an unconfined aquifer, which is critical for aquifer parameter estimation. Based on a synthetic, numerical example, our cross-correlation analysis reveals that heads in the saturated zone at late times carry the greatest nonsymmetrically weighted information content about the hydraulic conductivity (KS) distribution within the cone of depression. On the other hand, heads in the saturated zone at early times contain the most information about the specific storage (SS) heterogeneity in a narrow region between the observation and pumping locations. During intermediate and late times, heads in the saturated zone largely reflect the effects of saturated water content (θS) and pore-size parameter (α) in the thin unsaturated region near the water table above the pumping and observation locations. At last, heads in the vadose zone at late times carry the greatest information about θS and α around the observation point.