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Weather, pond and shaft
Runoff is rain plus degree-day melt times the runoff coefficient. A weir passes pond water into the shaft; the outlet obeys Torricelli flow, so a blocked outlet needs a much higher head to pass the same inflow.
Operation
Model checks
The science
What is modelled
A two-reservoir mass balance: a shallow surface pond fed by runoff, and a deep cylindrical moulin shaft fed through a weir and drained by an orifice at the bottom. Snow can store precipitation below freezing, and a full shaft pushes water back to the pond.
Equations
- Degree-day melt:
M = k T A(5.5 mm per degree per day); runoff = (rain + melt) x runoff coefficient. - Weir intake
K h^1.5with backpressure as the shaft fills; outletCd A (1 - b) sqrt(2 g h). - Mass balance
dV/dt = in - out - overflow, integrated in 0.4 s sub-steps.
Checks run in the page
- Water balance after a rainstorm.
- Steady-state head against the Torricelli solution.
- Degree-day melt arithmetic.
- Snow storage below freezing.
Honest simplifications
No ice-flow, conduit growth by melting, R-channel or pressure-dependent closure, no diurnal cycle and a fixed ice fraction. A teaching model, not a calibrated glacier hydrology solver.
What to try
- Press Blocked outlet: the shaft fills and the pond overflows.
- Press Snowfall: precipitation is stored as snow and no water drains.
- Press Cloudburst and watch the pond and the shaft respond with different delays.