Fitting and reading the results

Automatic and visual matching, holding parameters fixed, and what the standard errors, RMSE, AICc and the cautions mean.

Automatic fit

Press Automatic fit on the right, Fit on the toolbar or F5, or choose Match > Automatic fit. PumpPilot finds the parameters that minimise the squared differences between the readings and the solution, over every reading of every included well at once, starting from several points to avoid a local minimum. Most fits take well under a second; a Neuman fit usually takes 15 to 40 seconds and can be stopped with Stop.

Every reading counts equally, so a well with thousands of logger readings weighs more in a joint fit than a well read by hand thirty times. To see what each well says on its own, untick the others and fit again.

Visual match and fixed parameters

Type a value into a parameter and press Enter: the curves are redrawn at once, which is a visual match. Tick Fix beside a parameter to hold it at its value during the next automatic fit, for example a storativity known from another test, or a specific yield the readings cannot determine.

The results

Parameter values with a ± value under each: one standard error, from the curvature of the fit at its optimum.
Readings: the number fitted. RMSE: the root mean square difference between readings and solution, in the length unit of the test.
AICc: the corrected Akaike information criterion, for comparing solutions on the same readings.
Derived values that follow from the fit and the thickness: hydraulic conductivity K = T / b, specific storage Ss = S / b, and for Hantush-Jacob the aquitard resistance c = B squared / T and the leakance 1 / c; for Neuman the vertical conductivity Kz.
For an example test, the published parameters, to compare with.

The cautions

Under the results PumpPilot lists what a careful reviewer would raise about the fit. Each rests on something the fit itself reports:

The optimiser stopped before converging. Try other starting values by typing them in, or fix a parameter.
A parameter ended at its limit (for example Sy at 0.6). The readings do not determine it. Fix it at a value you can justify, or use a solution without it.
The residuals are correlated in time. The differences between readings and solution run in long stretches of one sign, so the ± values, which assume independent differences, are too small. On synthetic tests with a lag-1 correlation of 0.9 they were 3 to 4 times too small. Read them as lower bounds.
The pumped well is in a joint fit with a solution that has no losses at the well face (Theis or Hantush-Jacob). The pumped well's drawdown includes those losses and pulls the fit. Fit it alone, or use Papadopulos-Cooper with skin.

A good fit shows that the solution can describe the readings, not that its assumptions hold at the site. At Gridley, for example, one Theis solution fitted to both wells misses them by 0.18 to 0.32 m; fitted alone, each well gives a different transmissivity.