Methods Note/ On Simulation and Analysis of Variable-Rate Pumping Tests by Phoolendra Kumar Mishra 1 , Velimir Vessilinov 2 , and Hoshin Gupta 3 Abstract Analytical solutions for constant-rate pumping tests are widely used to infer aquifer properties. In this note, we implement a methodology that approximates the time-varying pumping record as a series of segments with linearly varying pumping rates. We validate our approach using an analytical solution for a sinusoidally varying pumping test. We also apply our methodology to analyze synthetic test data and compare the results with those from a commonly used method where rate variations are represented by a series of constant-rate steps. Introduction Hydraulic properties of an aquifer are commonly inferred by fitting drawdown and/or recovery data recorded from pumping tests to analytical solutions for radial flow toward a pumping well. For mathematical sim- plicity, such analytical solutions are commonly derived for constant-rate conditions. However, the pumping rate may vary either intentionally or because of technical difficulties during the test. The most common approach to analyze pumping tests with variable pumping rates is based on superpo- sition of piecewise constant rates. Considering a confined aquifer as a linear system with time-invariant boundary conditions, Cooper and Jacob (1946) applied the superpo- sition principle to account for stepwise changes in pump- ing rates. Abu-Zeid and Scott (1963), Abu-Zeid et al. (1964) and Hantush (1964) proposed analytical solutions 1 Corresponding author: Computational Earth Sciences Group, Los Alamos National Laboratory, MS T003, Los Alamos, NM 87545. He is now at the Department of Civil and Environmental Engineering, California State University, Fullerton, CA 92832; pkmishra@fullerton.edu 2 Computational Earth Sciences Group, Los Alamos National Laboratory, MS T003, Los Alamos, NM 87545. 3 Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 87521. Received September 2011, accepted June 2012.  2012, The Author(s) Ground Water  2012, National Ground Water Association. doi: 10.1111/j.1745-6584.2012.00961.x for variable-rate pumping tests assuming exponentially decreasing pumping rates. Lai et al. (1973) and Lai and Su (1974) extended the solution of Papadopulos and Cooper (1967) to include leakage from the semi-confining lay- ers when the pumping rates are exponentially and linearly varying. Black and Kipp (1981) provided a solution to an aquifer borehole test for sinusoidal perturbation in a con- fined non-leaky aquifer. Rasmussen et al. (2003) extended the Hantush (1964) solution to include sinusoidal variation of pumping rates. In some field applications, the pumping rates are varied intentionally. Butler and McElwee (1990) sug- gested that variable pumping rates can be used to increase the sensitivity of parameters to observed drawdown, and hence improve parameter identifiably; each time the pumping rate is increased, a new cone of depression (superimposed upon the original one) propagates out from the pumping well, producing an increase in sensitivity and a new interval of time during which the aquifer zone influences drawdown. Adequate representation of variable pumping rates can be important when various natural phenomena unac- counted for in the analytical solution are causing tran- sients in the observed drawdown records (e.g., barometric effects, infiltration events). In these cases, the analysis of the observed drawdown transients is difficult, if tran- sients caused by variable pumping rates are not accurately captured. The commonly used approach of constant-rate step changes to represent pumping variability may not always NGWA.org GROUND WATER 1