Clepsydra

https://aquiferpumpingtest.org/

Clepsydra - the water clock

Aquifer pumping-test analysis that runs entirely in a browser tab. Paste time and drawdown readings, match a type curve, read off transmissivity and storativity with an honest uncertainty on each.

Theis, Cooper–Jacob, Hantush–Jacob and Theis recovery. Nothing is uploaded, nothing is installed, and there is no account.

Free software under the GNU AGPL v3. Not certified or approved by anybody.

The mathematics of aquifer test interpretation has been public and unencumbered since 1935. Theis derived the well function from the heat conduction analogy; Cooper and Jacob published the logarithmic approximation in 1946; Hantush and Jacob published the leaky solution in 1955. None of it is anyone's intellectual property.

What is charged for is the interface.

Before building this I went looking for a free tool that would take a column of drawdown readings and fit a curve to them in a browser. Every free option I found fails in the same specific way: the engine exists but there is no interface. The maths is available in R and Python packages that need a language runtime and a toolchain before they compute anything, or in Windows desktop programs, or in a spreadsheet. Nothing does it in a browser tab.

This is that missing interface, and nothing more. The solutions it implements are the ones any hydrogeology textbook contains.

Verified by searching in July 2026. Prices and capabilities change; check them before relying on this table. If any of it has gone stale, please open an issue.

Clepsydra is listed last on purpose. Read the row above it first.

If you can install R, use pumpingtest instead of this. It is more capable. Clepsydra's only real advantage over it is that it needs nothing installed.

If you need a report a regulator will accept, buy AQTESOLV. This project has no standing with anyone.

• Not certified, accredited or approved by any agency, regulator, standards body or trade association. No one has reviewed it.
• Not a substitute for a hydrogeologist. It will fit a curve to nonsense without complaint. Reading the diagnostic plot is the actual skill and the software cannot do it for you.
• No slug tests, no constant-head tests, no step-drawdown tests.
• No bounded aquifers, image wells or barriers. Every solution here assumes an aquifer of infinite lateral extent.
• No partial penetration, wellbore storage or skin effect. All wells are assumed fully penetrating with negligible storage.
• No unconfined-specific solution. Neuman's delayed-yield solution is not implemented. Applying Theis to a water-table aquifer, as this would let you do, ignores delayed gravity drainage and will mislead you at intermediate times.
• No variable discharge. Constant rate only.
• No printed report output.

npm run test runs 76 tests. The ones that matter:

The well function is checked three independent ways. Against reference values of the exponential integral computed with mpmath at 25 decimal digits (agreement to 1 part in 10¹¹); against a Gauss–Legendre quadrature written separately from the integral definition, sharing no code with the implementation; and against identities it must satisfy regardless of either, including W(u,0) = W(u) exactly, W(0,b) = 2K₀(b), and monotonicity in both arguments.

The fit is checked against the commercial incumbent on public field data. The Oude Korendijk test (de Wit 1963, published in Kruseman & de Ridder, ILRI Publication 47) is the standard worked example in the field. Fitting both piezometers simultaneously, AQTESOLV, MLU and TTim all report hydraulic conductivity near 66 m/d and specific storage near 2.54 × 10⁻⁵ /m, which for a 7 m aquifer is T = 462.6 m²/d and S = 1.779 × 10⁻⁴, with RMSE 0.0501 m.

Clepsydra returns T = 462.6 m²/d, S = 1.779 × 10⁻⁴, RMSE 0.0501 m.

The drag interaction is checked against physics, not against its own formula. Sliding a type curve on log-log paper is exactly equivalent to changing T and S. A test shifts a point on the curve by a given number of decades and compares it against the model evaluated at the translated parameters, requiring agreement to 1 part in 10⁹.

Two paths to transmissivity that share no arithmetic. The Bourdet log-derivative plateau gives T = Q/4πT′ without any curve fitting at all. It is printed next to the fitted value so a disagreement is visible.

Degenerate input is tested, not assumed. Empty records, fewer readings than parameters, zero and negative discharge, zero radial distance, NaN and Infinity in the readings, non-positive times, all-zero drawdown, recovery without a pumping duration, truncated and corrupt share links, malformed pasted data.

Recorded because a test suite that never found anything is not evidence of anything:

1. The optimiser returned a confident wrong answer on leaky aquifers. It reported T = 1599 m²/d where the true value was 300. Sum of squared residuals at the true parameters was exactly zero; at the "converged" answer it was 0.53. The cause was a straight-line seed for storativity that is five orders of magnitude wrong on a response approaching steady state. Fixed by scanning absolute physical grids for S and r/B rather than grids relative to a seed.
2. The plot was ruled in SI seconds while its axis said minutes. Every reading sat two decades from where the label claimed. Every number in the readout was correct and the picture was wrong. Caught by rendering the component and looking at it, not by any engine test. There is now a regression test on that boundary.
3. A reference value was wrong, not the code. W(0.05) failed at 1.4 × 10⁻⁸. The transcribed table value was bad; the implementation was fine. Reference values now come from mpmath rather than from a printed table, and the tolerance was tightened rather than loosened.
4. A screen reader would have announced "Transmissivity NaN."
5. The type curve drew straight out of the bottom of the plot and over the axis labels. Theis drawdown tends to zero as time tends to zero, so on log paper the curve descends without limit and there was no clip region. Reported from a screenshot of the deployed site, not caught here — my own rasterised images showed it and I did not see it. There is now a clip on the ruled rectangle, a test asserting the clip covers exactly that rectangle, and a second test asserting the curve genuinely does run past the edge so the clip is not decorative.
6. A number input collapsed to nothing but its spinner arrows, squeezed out by a unit label that took its content width while the input had no minimum.

There was no browser available in the environment this was built in. The components were rendered with react-dom/server and the resulting SVG rasterised and inspected, which verifies scales, ruling, curve geometry, marker placement and colour assignment — but not the HTML layout, the CSS grid, the responsive breakpoint, focus rings, or any pointer interaction.

Check these first after deploying:

1. Dragging the curve. Pointer capture and the touch path are entirely unexercised. Press on the curve, drag, confirm T and S move the right way: dragging up should decrease T.
2. Arrow-key nudging after tabbing to the curve, and whether the focus ring is visible on it.
3. The mobile breakpoint at 860px, where the rail moves below the plot.
4. Clipboard access for share links, which browsers restrict differently. There is a fallback that writes the link to the address bar; confirm it fires rather than failing silently.
5. CompressionStream('deflate-raw'), which older Safari lacks. There is an uncompressed fallback path that has been unit-tested but never exercised in a real browser that actually lacks the API.
6. localStorage in private browsing, where writes throw. The failure is swallowed on purpose; confirm the app still works rather than blanking.

• Oude Korendijk dataset. Field measurements from a 1963 test in a polder south of Rotterdam (de Wit 1963), published in Kruseman & de Ridder, Analysis and Evaluation of Pumping Test Data, ILRI Publication 47. The time–drawdown values were transcribed from the TTim project (MIT licensed, Mark Bakker, https://github.com/mbakker7/ttim), which distributes them as docs/03pumpingtests/data/piezometer_h30.txt and piezometer_h90.txt. The published comparison against AQTESOLV, MLU and TTim comes from TTim's documentation.
• The second built-in dataset is synthetic, generated by this repository at stated parameters with seeded pseudo-random noise. It is labelled as such in the interface. It proves nothing about real aquifers.

Colour means one thing and one thing only:

Which piezometer is encoded by shape — circle, square, triangle, diamond — so that the colour channel stays free to carry meaning. Nothing in the interface chrome is coloured.

The two strips under the plot both answer "should I believe this?" The derivative flattens onto a plateau at Q/4πT once radial flow is established; if your late data are not flat, the aquifer is not doing what the model assumes and curve fitting will not fix that. Structure in the misfit strip — a run of same-sign residuals — means the wrong model, not noisy data.

• T, S and r/B are fitted in log₁₀ space by Levenberg–Marquardt with a numeric Jacobian. Uncertainty comes from the covariance matrix and is reported as a multiplicative 95% factor, because a storativity is uncertain by a factor of two, not by ±0.0001. The 95% interval uses 1.96 standard errors rather than a t-distribution.
• The optimiser is started from a Cooper–Jacob straight-line seed plus the four best corners of a coarse grid scan, and the lowest sum of squares wins.
• W(u) uses a series expansion below u = 1 and a modified Lentz continued fraction above it. The leaky well function uses composite 8-point Gauss–Legendre over the window where the integrand is above e⁻⁵⁰.
• The derivative uses the Bourdet weighted-window scheme with a smoothing width of 0.25 in ln t.
• Everything crossing an engine boundary is metres and seconds. Unit conversion happens in exactly one file.

npm install
npm run dev      # development server
npm run test     # 76 tests
npm run build    # static output in dist/

Vite, React and TypeScript are pinned to conservative versions so this runs in WebContainer environments such as bolt.new. base is ./ and the build target is es2021. There are no runtime dependencies beyond React; the charts are hand-rolled SVG.

GNU Affero General Public License v3.0 only. See LICENSE.

The AGPL is deliberate: if you run a modified version of this as a network service, the people using it are entitled to your source.

== We're Using GitHub Under Protest ==

This project is currently hosted on GitHub. This is not ideal; GitHub is a proprietary, trade-secret system that is not Free and Open Source Software (FOSS). We are deeply concerned about using a proprietary system like GitHub to develop our FOSS project. I have a website where the project contributors are actively discussing how we can move away from GitHub in the long term. We urge you to read about the Give up GitHub campaign from the Software Freedom Conservancy to understand some of the reasons why GitHub is not a good place to host FOSS projects.

If you are a contributor who personally has already quit using GitHub, please email me at kevinBell@Linux.com for how to send us contributions without using GitHub directly.

Any use of this project's code by GitHub Copilot, past or present, is done without our permission. We do not consent to GitHub's use of this project's code in Copilot.

https://aquiferpumpingtest.org/

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