Choosing a solution
What each of the four solutions assumes, how the derivative on the plot points to one, and how Compare solutions ranks them.
Choose the solution in the Solution box on the right or from the Solution menu. Each describes drawdown around a well pumped at the rates of the schedule, in an aquifer of infinite extent.
| Solution | Aquifer and well | Parameters |
|---|---|---|
| Theis (confined) | Confined, uniform, fully penetrating line-source well, no storage in the well | T, S |
| Hantush-Jacob (leaky) | Confined, with leakage through an aquitard that stores no water | T, S, B (leakage factor) |
| Papadopulos-Cooper (large well) | Confined, well of finite diameter that stores water; optional skin at the well face | T, S, and optionally Sk (skin) and rc (effective casing radius) |
| Neuman (unconfined) | Unconfined, with delayed response of the water table; anisotropic | T, S, Sy (specific yield), Kd (Kz/Kr) |
The Neuman solution needs the saturated thickness. The Papadopulos-Cooper solution uses the well and casing radii, so it is the one to use with readings from the pumping well, where the water stored in the casing and losses at the well face show at early time.
Reading the derivative
The hollow markers are the derivative of drawdown with respect to the logarithm of time (Bourdet et al. 1989), and the dashed lines the same derivative of the solution. On log-log axes the derivative separates flow regimes that look alike in the drawdown (Renard et al. 2009):
- Flat at late time: radial flow in a confined aquifer, as the Theis solution assumes. The level of the flat part is Q / (4 pi T).
- Rising, then falling towards zero: the drawdown is stabilising because water is arriving from outside the aquifer, as through a leaky aquitard (Hantush-Jacob).
- Flat, then a dip, then back to the same level: delayed yield from the water table in an unconfined aquifer (Neuman).
- A slope of one at early time, in drawdown and derivative together: water coming out of the well's own casing (Papadopulos-Cooper).
The derivative of noisy readings is noisy. It is computed over neighbours at least 0.2 natural-log units of time apart; the readings themselves are not smoothed.
Compare solutions
Match > Compare solutions... fits several solutions to the same readings and ranks them by AICc, the corrected Akaike information criterion, which weighs the fit against the number of parameters. Tick the solutions, press Fit and rank, and press Use on a row to take that fit.
- Lower AICc is a better balance of fit and parameter count on this record. A difference under about 2 carries little weight.
- AICc assumes independent residuals, which field records rarely have (see Fitting), so read small differences with care.
- A better AICc does not say which process caused the departure from the Theis curve. Check the derivative and what is known of the site before choosing.