Hydrology Lab: learn by changing things
Two short, guided lessons. Each step shows one idea, lets you change one thing, and explains what happened and why.
- One idea per chapterEach chapter explains one concept in plain words, then lets you test it.
- Change one thingClick the map or move a single slider. Everything else stays fixed.
- See cause → effectThe lab tells you what your change caused, with the numbers before and after.
Terrain: a grid of heights
A digital elevation model (DEM) stores the ground height of every cell in a grid. Here each cell is 1 km × 1 km and its number is the height above sea level in metres.
Water always flows downhill — so the heights alone decide where rain will go.
- 1.Click a cell on the high ridge at the top (≈ 480 m).
- 2.Click a cell in a valley and compare its neighbours.
- 3.Find the lake (west) and the bay (east) at 0 m — every raindrop ends up there.
Click any cell on the map to begin.
Short manual & glossary — Watershed labShow ▾
- Work through the chapters in order; each one adds a single idea to the previous one.
- Read “The idea”, then do the “Try this” steps on the map.
- “What you see” explains the result of your last click or change in words.
- When you move a slider, the grey box reports cause → effect with the numbers before and after.
- The terrain is synthetic and simplified (15 × 12 cells of 1 km). It is built for learning, not for design.
- DEM:
- Digital elevation model — a grid of ground heights.
- D8:
- Flow-direction rule: water goes to the steepest of the 8 neighbours.
- Flow accumulation:
- Number of cells that drain through a cell (its upstream area).
- Pour point:
- The point where a watershed's water leaves it.
- Watershed / catchment:
- All land that drains to one pour point.
- Drainage divide:
- The ridge line that separates two watersheds.
- Runoff coefficient C:
- Share of rain that becomes surface runoff (0 = none, 1 = all).
Show data table
| Time (h) | Inflow I (m³/s) |
|---|---|
| 0.0 | 5.0 |
| 4.0 | 127.0 |
| 8.0 | 135.0 |
| 12.0 | 74.4 |
| 16.0 | 33.0 |
| 20.0 | 14.6 |
| 24.0 | 8.0 |
| 28.0 | 5.9 |
| 32.0 | 5.2 |
| 36.0 | 5.1 |
| 40.0 | 5.0 |
| 44.0 | 5.0 |
| 48.0 | 5.0 |
The flood: a hydrograph
A hydrograph shows river flow over time. During a flood the flow rises (rising limb), reaches a peak, and slowly falls again (falling limb).
The area under the curve is the flood volume — the amount of water the dam will have to deal with.
Change a setting — this box will show what your change caused.
- 1.Double the peak: what happens to the volume?
- 2.Keep the peak, make the time to peak longer: same peak, but more water.
- 3.Hover the chart to read the flow at any hour.
The river peaks at 150 m³/s after 6 h. In total the flood brings 5.25 million m³ of extra water — about 2098 Olympic swimming pools.
The math behind it▾
- Ip
- peak inflow (m³/s)
- Ib
- base flow, 5 m³/s
- Tp
- time to peak (h); at t = Tp the curve equals Ip exactly
- V
- flood volume above base flow (m³)
Short manual & glossary — Reservoir labShow ▾
- Go through the chapters in order: flood → bucket → outlets → routing → challenge.
- Change one slider at a time. The grey box reports cause → effect with numbers before and after.
- Hover (or focus and use the arrow keys on) a chart to read exact values; each chart also has a data table.
- In “Flood routing”, grey dashed lines show your reference design — set a new reference any time.
- The dam and flood are idealized (level-pool routing, solved with a fixed-step RK4 method). Built for learning, not for design.
- Hydrograph:
- Graph of river flow over time.
- Inflow I / outflow Q:
- Water entering / leaving the reservoir (m³/s).
- Bottom outlet:
- Pipe near the reservoir bed that always releases water.
- Spillway:
- Overflow channel that works once the water passes its crest.
- Attenuation:
- How much lower the outflow peak is than the inflow peak.
- Delay (lag):
- Time between the inflow peak and the outflow peak.
- Freeboard:
- Distance between the highest water level and the dam crest.
- Level-pool routing:
- Routing that assumes a flat water surface in the reservoir.
∑Governing equations — reservoir flood routingShow ▾
1. Inflow hydrograph
- Ip
- peak inflow (m³/s)
- Ib
- base flow, 5 m³/s
- Tp
- time to peak (h); at t = Tp the curve equals Ip exactly
- V
- flood volume above base flow (m³)
2. Continuity (mass balance)
- S
- stored volume (m³)
- h
- water level above the reservoir bed (m)
- A(h)
- water-surface area at level h (m²); a large lake rises slowly
“Level-pool” routing assumes the lake surface stays flat, so a single level h describes the whole reservoir. The level peaks when dh/dt = 0, i.e. when I = Q.
3. Stage–storage and stage–area
- Smax
- reservoir volume when full to the crest (the “reservoir size” slider)
- Hc
- dam crest level, 20 m
An idealized valley that widens with height (instead of surveyed bathymetry): the higher the water, the larger the lake surface.
4. Outlet equations (rating curve)
- c1
- outlet discharge coefficient, 0.62
- c2
- weir coefficient, 2.0 m½/s
- g
- gravity, 9.81 m/s²
- d
- bottom outlet diameter (m)
- Aw
- wetted area of a partly full circular pipe (m²)
- Ls
- spillway width (m)
- Hs
- spillway crest level (m)
- Lc
- dam crest length, 150 m
- Hc
- dam crest level, 20 m
Heads are measured from the reservoir bed and the weir heads are divided by a reference head of 1 m, so the units work out. Real outlets are calibrated in the field; these coefficients are typical textbook values.
5. Numerical solution (RK4)
The equation cannot be solved by hand because Q and A both depend on h, so the computer steps forward in time. Runge–Kutta (RK4) takes four slope samples inside each step and averages them, which is far more accurate than a single slope (Euler's method).