Applications of the time-naught term in the Cooper and Jacob (1946) equation

The ability to manipulate analytical expressions for aquifer drawdown can provide insights into groundwater flow processes and assist with assessing strengths and weaknesses of aquifer parameter estimation methods. In the Cooper and Jacob (1946) parameter estimation method, the antilog of the horizontal-axis intercept in a plot of drawdown vs. log(time) is referred to as time naught (t(0)), which is used for estimating storativity. This article briefly reviews traditional uses of the time-naught concept and then spends time introducing new insights and applications involving (1) time-naught/distance relationships, including ways to compensate for certain missing data; (2) use of time naught in a simple method providing a quick visual check of which data in a Cooper-Jacob plot are suitable for use in linear regression; (3) application of time naught, as determined for one well, in estimating the later minimum time for which data from a distant well can be used in the Cooper-Jacob method; (4) development of relationships between drawdown and time naught; (5) use of time naught in a simple algebraic equation to estimate drawdown at smaller times than feasible using the Cooper-Jacob method; and (6) employment of time naught and a vertical-axis intercept on a plot of drawdown vs. log(time) for evaluating storativity. This information may be useful to new hydrogeologists or others interested in further developing their analytical well hydraulics skills.