Infer stream exchange from a shared hydraulic-head datum

1. Define the process and evidence

A stream may gain water from an aquifer or lose water into it. The direction depends on hydraulic heads and hydraulic connection, not on comparing water depths measured from unrelated ground surfaces. Elevation and pressure must be referred to a common datum.

2. Connect mechanism and boundary

The original saturated streambed has conductivity 0.1 m/day, area 100 m² and thickness 2 m. Positive flow from aquifer to river is Q=5(ha−hr) m³/day. Equal heads produce zero exchange in this model; higher aquifer head gives a gaining stream, while higher river head gives a losing stream.

Water-table contours and nested head observations can reveal flow directions, but an unsaturated gap beneath a disconnected stream changes the boundary problem. A perched stream, seasonal stage change or pumping influence may therefore require more than the saturated-bed formula. Streambed sediment can also create a low-conductivity barrier.

Changing river stage can reverse exchange without changing the bed material. Conversely, changing bed conductivity affects magnitude without necessarily changing direction. Separate a geometric/head explanation from a material-property explanation and retain what observation would discriminate them.

3. Reconstruct the worked packet

Aquifer head 102 m and river head 99 m give +15 m³/day into the river. If river head rises to 102 m with the same aquifer head, this model gives zero exchange, not a permanently fixed gaining classification.

4. Predict and investigate

Predict first: Can a stream switch from gaining to losing without changing its sediment conductivity?

Vary each head independently, keeping their common datum explicit. Identify the sign change and distinguish a lower flux caused by smaller gradient from one caused by lower conductivity outside this slider.

5. Test a changed case

Apply the evidence to a changed case

Aquifer head 98 m and river head 101 m imply what exchange?

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Q=5(98−101)=−15 m³/day: water moves from river toward aquifer under the stipulated saturated connection. The minus sign records direction, not a negative water volume.

6. Retain a defensible process notebook

Preserve first predictions, complete source/units, geometry, flux and storage boundaries, calculations and competing interpretations. Only the explicitly labeled USGS discharge archive is actual measured-derived source data; all other numerical packets and diagrams are invented. Public practice does not certify independent reasoning, actual field competence or a safe environmental decision.

Mechanism or dataset reference, checked 30 October 2026. Original prose, calculations, diagrams and questions; source observations retain agency and provenance.