Groundwater — Thirty years of a basin you cannot see into.

You are the basin water manager. You manage the water under a 60-by-40-kilometre valley: wells for a growing town, irrigation for the farms, a stream that only flows while the water table stays above its bed, and clay layers that compact permanently once you draw the head below the level they were last squeezed to. Thirty years pass in a couple of minutes, and almost nothing you do is visible from the surface until it is too late.

Timescale: 30 years. Model: 2-D finite-difference groundwater flow (Boussinesq), ADI, with Terzaghi-style compaction

What you will learn

• Why a cone of depression spreads for kilometres and takes decades to refill.
• How pumping a basin dry shows up first in the stream, not in the wells.
• Why land subsidence from over-pumping is permanent even when the water comes back.

Scenarios

• Sandbox — Thirty years, every control unlocked, no objectives.
• The Lull — Ten easy years, then seven dry ones. Meet demand and keep subsidence under 30 cm.
• Coastal Town — The sea is at the east edge. Keep the wells fresh.
• Recovery — You inherit an overdrafted basin. Rebuild storage in twenty years.

What you control

• Mean precipitation (mm/yr) — The long-run average. Individual years vary around it; droughts are years strung together.
• Infiltration fraction — How much rain reaches the water table instead of evaporating or running off.
• Climate sequence — The pattern of wet and dry years the basin will actually get.
• Drought severity — How far below normal a drought year falls. At 1.0 a drought year gets a third of normal rain.
• Basin fill — What the valley is filled with — this sets where water moves easily and where the ground can compact.
• Hydraulic conductivity (m/d) — How fast water moves through the main sand unit. Ten times higher spreads a cone of depression ten times further.
• Specific yield — The fraction of the rock volume that actually drains — the size of the basin’s bank account.
• Aquifer thickness (m) — Saturated thickness sets transmissivity: a thin aquifer draws down far faster.
• Clay compressibility (1/m) — Inelastic skeletal storativity of the clay: metres of permanent settlement per metre of head decline.
• Irrigated area (ha) — The single biggest lever in most real basins. Every hectare is a standing annual demand.

Questions

What does the head contour map actually show?

Hydraulic head: the elevation water would stand at in a well screened in the aquifer. Water flows down the head gradient, at right angles to the contours, and the closer the contours, the steeper the gradient and the faster the flow.

Why does my well go dry before the aquifer is empty?

A well only produces while the water table is above its screen. Long before an aquifer is exhausted, the cone of depression around a heavily pumped well drops below shallow screens, and those wells fail while deeper ones nearby keep pumping.

Is the subsidence really permanent?

The inelastic part is. When head in a clay layer falls below the lowest value it has ever seen (its pre-consolidation head), the clay grains rearrange irreversibly. Recovering head recovers only the small elastic component.

What this model cannot do

• One layer. Real basins are stacks of aquifers and aquitards with different heads; a two-layer basin can be pumped in ways this model cannot represent.
• The unsaturated zone is instantaneous. Real recharge takes months to years to arrive at the water table, so this model responds to a wet winter too quickly.
• Solute transport is not simulated. The sea-water interface is a sharp Ghyben–Herzberg surface, not a mixing zone, and it cannot represent the slow salinisation of a well field.
• Compaction is instantaneous. Thick clays take decades to drain and settle; here the settlement arrives with the head change that causes it.
• The stream has a fixed stage. A real river’s stage falls as its flow falls, which makes the losing-stream feedback worse than shown.
• This is a fictional basin. It is not a model of any real aquifer and cannot be used to plan one.

Sources

• Freeze, R. A. & Cherry, J. A. (1979), Groundwater — the standard text for everything above
• Harbaugh, A. W. (2005), MODFLOW-2005 — the reference implementation of this class of model
• Peaceman, D. W. & Rachford, H. H. (1955), The numerical solution of parabolic and elliptic differential equations — the ADI scheme used here
• Riley, F. S. (1969), Analysis of borehole extensometer data from central California — the aquitard-compaction formulation
• Theis, C. V. (1935), The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well — the transient solution the tests check against
• Konikow, L. F. & Kendy, E. (2005), Groundwater depletion: a global problem