SCIENCE · INVESTIGATE AND EXPLAIN

Balance a watershed water budget

Account for monthly inputs, outputs and storage using basin-equivalent depths and volumes.

Learning outcome: Construct a consistent water ledger and convert a basin-equivalent depth into volume.

Starting recap

A budget tracks material entering, leaving and remaining inside a chosen boundary. All monthly amounts must refer to the same area and interval.

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Try

For P = 100 mm, actual ET = 60 mm and stream outflow Q = 40 mm, storage change is zero and ending storage remains 100 mm.

Open the experiment

Predict

If precipitation increases by 20 mm while the supplied outputs stay fixed, how much does ending storage change?

Your prediction and reason

Experiment

Capture the default budget, then raise precipitation to 120 mm while keeping actual ET at 60 mm. Check the depth ledger and independently convert the added water to cubic meters.

Balance a monthly watershed budget

Worked teaching model · synthetic values · Fictional one-month totals over a 2 km² watershed. Initial total storage is 100 mm of basin-equivalent water; stream outflow at the outlet is fixed at 40 mm. No other boundary inflow or outflow is included. P and actual ET are proposed totals, not weather forecasts or potential ET. Surface water, soil water and groundwater are inside this accounting boundary. A negative arithmetic endpoint rejects the supplied budget; water is not clamped or allowed to become physically negative. Timing, maximum capacity and partition among stores are not modeled.

Monthly precipitation: 100 mm Monthly actual evapotranspiration: 60 mm

Reset keeps your prediction, captures and practice history.

Nonnegative endpoint: necessary total-water constraint satisfied. This does not prove that water was available at every moment or that the supplied quantities were measured correctly.

One-month balance in basin depth and volume
Quantity	Depth equivalent (mm)	Volume (m³)
Initial stored water	100	200,000
Precipitation input P	100	200,000
Actual ET output	60	120,000
Outlet streamflow Q	40	80,000
Storage change ΔS = P − ET − Q	0	0
End stored water	100	200,000

The same-month identity is initial storage + precipitation = ET + outlet flow + arithmetic endpoint. Internal infiltration and recharge move water between included stores; adding them again as basin losses double-counts transfers. No claim of safe withdrawal, flood timing or groundwater level follows from this ledger.

Storage change: 0 mm. End storage: 100 mm.

ΔS = P − ET − Q = 100 − 60 − 40 = 0 mm. Arithmetic endpoint = 100 mm. One millimeter over 2 km² equals 2,000 m³. A nonnegative endpoint passes only this total-water constraint; it does not verify observations or within-month timing.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Draw a box around the water being counted

A water budget records water entering, leaving and remaining in a defined system. This investigation follows a fictional 2 km² watershed for one month. Starting storage is 100 mm of basin-equivalent water. Precipitation P and actual evapotranspiration ET are adjustable supplied amounts; total stream outflow Q is fixed at 40 mm. These are synthetic teaching values, not measurements of a named basin.

The selected system includes its surface, soil and groundwater stores. The model assumes no groundwater exchange across its outer boundary and no water imports or exports beyond the stated precipitation, ET and stream outflow. Real budgets must identify their own boundary and relevant fluxes. The conservation principle behind water budgets relates storage change to inflow minus outflow. USGS Circular 1308 on water budgets.

Write one ledger for one month

Let ΔS mean the change in storage during the month, measured in basin-equivalent millimeters. Then ΔS = P − ET − Q. Ending storage equals starting storage plus that change: S_end = 100 + P − ET − 40. The numbers 100 and 40 have the same millimeter unit as the control settings.

At the default P = 100 and ET = 60, the calculation is ΔS = 100 − 60 − 40 = 0 mm. Ending storage is 100 mm. Zero change does not mean no water moved: 100 mm entered and 100 mm left. Draw separate arrows for those exchanges rather than representing this case as an inactive basin.

Actual ET combines water returned to the atmosphere through evaporation and plant transpiration. Here it is an assigned monthly total, not a prediction from sunlight, temperature or vegetation. The controls can request an inconsistent combination; the model checks the resulting accounting rather than silently restricting ET to an available-water estimate.

Give millimeters their area meaning

A basin-equivalent depth expresses a volume spread uniformly over the whole basin area for accounting. It does not claim that a uniform sheet of water physically covers the ground. Nor is 100 mm of total storage a measurement of lake level, water-table depth or soil wetness at every point.

The area is 2 km² = 2,000,000 m². A depth of 1 mm is 0.001 m, so its volume is 0.001 m × 2,000,000 m² = 2,000 m³. Thus the starting 100 mm represents 200,000 m³. Keep the square on the area unit: confusing square kilometers with kilometers would invalidate the conversion.

Convert each default ledger entry independently. Precipitation is 200,000 m³, ET is 120,000 m³ and stream outflow is 80,000 m³. Their volume balance gives the same zero storage change as the depth calculation. This agreement checks units and arithmetic, not the truth of the supplied values.

Change one input and explain the result

Increase precipitation to 120 mm while leaving ET at 60 mm. The added 20 mm is 40,000 m³. With the supplied outputs fixed, ΔS becomes +20 mm and ending storage becomes 120 mm. Record the before-and-after cases and show both unit systems.

This controlled comparison does not claim that real ET and streamflow would remain unchanged after more rain. They are held fixed to expose the accounting relationship. No timing within the month, runoff mechanism, storage capacity or saturation threshold is calculated. A positive endpoint is an arithmetic result, not a flood forecast.

For a paper activity, make cards for starting storage, precipitation, ET, stream outflow and ending storage. Use one drawn token for 10 mm and annotate its volume as 20,000 m³. Move tokens across the boundary only for the named input and outputs, and compare the remaining tokens with the equation.

Transfer to a new monthly ledger

Set P = 80 mm and actual ET = 50 mm, keeping the supplied start and stream outflow. Predict storage change, ending storage and ending volume before checking.

Check the water-budget transfer

ΔS = 80 − 50 − 40 = −10 mm. Ending storage is 90 mm, equivalent to 180,000 m³ over 2 km². The outputs exceed precipitation by 10 mm, supplied by declining storage. All terms refer to the same month and basin.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

State the watershed area, month and boundary assumptions; show the conservation equation and explain why basin-equivalent millimeters are not a lake-level reading.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Separate magnitude, shaking intensity and damage Next: Interpret declining storage and infeasible budgets

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