Toward Improved Understanding of Aquifer Response Time Scales

Abstract

Several methods are available in the published literature to analyze transient groundwater flow processes. These methods include both numerical and analytical approaches which describe how groundwater heads would transition from an initial unsteady state to a final steady state. The primary objective of this study is to quantify the time scale required for transient groundwater systems to approach its steady state conditions. Understanding these response time scales is important for managing different types of groundwater resources management problems. Since, in many cases, the governing equation for groundwater flow is identical to the well-known diffusion equation, the knowledge gained from this study is applicable for managing other systems that can be modeled using the diffusion equation. The diffusion equation is one of the most commonly used models for describing a variety of problems involving heat, solute, and water transport processes. When a diffusive system is transient, the dependent variable (e.g., temperature, concentration, or hydraulic head) varies with time; whereas at steady state, the temporal variations becomes negligible. In this work we generalize our steady state analyze and propose an intermediate state, called steady-shape state, which corresponds to situations where temporal variations in diffusive fluxes becomes negligible; however, the dependent variable might still remain transient. We present a general theoretical framework for quantifying the times scale needed for a diffusive system to approach both steady shape and steady state conditions.