Basic Concepts for the Linear Model of Ground Water Level Recession

Abstract

Basic concepts are illustrated for the display of ground water level recession as a linear plot on a semilog graph, as first described by Rorabaugh. This exponential decay function can be achieved if there is a definable outflow boundary such as a lake or river and if water levels are expressed relative to the altitude of the boundary. The model can be used to estimate aquifer hydraulic diffusivity. Concepts are illustrated using three finite-difference simulations. One represents the ideal case as described by Rorabaugh, in which the altitude of the outflow boundary is uniform along its length. Another simulation includes a sloping boundary with simple geometry and demonstrates that the model can be used accurately. Based on this simulation, it appears that the ground water level must be expressed relative to the closest point on the outflow boundary. The third simulation includes a sloping boundary and complex boundary shape, and demonstrates departures from the linear model of recession and errors in the estimate of hydraulic diffusivity. Another cause of nonlinearity is the instability of the ground water head profile soon after a recharge event. The nature of these early-time departures will vary depending on the location of the water level observation site relative to the outflow boundary and the hydrologic divide of the ground water flow system.

Straight thinking about groundwater recession

“…Venetis [1969] even explicitly states that t crit will be less than one month most of the time, but without giving any justification for that assertion, and Venetis [1971] suggests ''experience often shows that this (i.e., critical time is reached) occurs after the first week.' ' Rutledge [2006] notes that departures from the exponential form will occur prior to the critical time but does not go further to present a range of critical times for typical aquifer conditions. Second, the popularity, simplicity and intuitively appealing idea of aquifers acting as ''linear stores'' has become standard modeling practice in both hydrogeology [e.g., Schoeller, 1959;Gehrels and Gieske, 2003] and hydrology [e.g., Nash, 1959].…”

“…I propose that this may be for a number of reasons. First, the literature describing groundwater recession from a hydraulic perspective generally report case studies based on small and highly diffusive aquifers where t crit is small in any case [Rorabaugh, 1960;Venetis, 1969Venetis, , 1971Olin, 1992;Crosbie, 2005;Rutledge, 2006;Park and Parker, 2008;Jie et al, 2011;Liang and Zhang, 2012]. Venetis [1969] even explicitly states that t crit will be less than one month most of the time, but without giving any justification for that assertion, and Venetis [1971] suggests ''experience often shows that this (i.e., critical time is reached) occurs after the first week.'…”

“…Real world examples are shown by Rorabaugh [1960] and more recently in Nimmo [2010] and Cuthbert et al [2013]. For such cases, it should be noted that Rutledge [2006] tested the Rorabaugh [1960] model for some nonidealized scenarios using numerical models and showed that significant deviations from an exponential form may occur, for example, in cases of sloping boundaries or those with complex geometry.…”

Use of Groundwater Levels with the PULSE Analytical Model

“…As indicated diagrammatically (Rorabaugh 1960, Figure 1), water levels are expressed relative to the level of the outflow boundary. More information about Rorabaugh's (1960) method was published by Rutledge (2006), including the effect of a sloping outflow boundary. Risser et al (2005) noted there can be considerable ambiguity about the level of the outflow boundary.…”

“…This was observed for wells that are exposed to a fractured-rock aquifer, a condition that might be considered favorable for the hydraulic connection between well and aquifer. More information about Rorabaugh's (1960) method was published by Rutledge (2006), including the effect of a sloping outflow boundary. The author encourages the program user to review these two publications if groundwater levels are used to evaluate the recession index.…”