Reading a Hydrograph
A storm. A stream. A wiggly line. Learn how to read the shape — rising limb, peak, recession — and pull baseflow apart from quickflow with a slider you control.
The seven-step tour — click to jump
1 · What is a hydrograph?
A hydrograph is a time-series of discharge — usually m³/s on the y-axis and hours or days on the x-axis. Scroll the panel on the right to walk through the three named regions.
Step 1 · Rising limb
After rain falls, the channel doesn't respond instantly — water has to reach the stream. The discharge climbs steeply: this is the rising limb. Steeper limb → flashier catchment (small, urban, saturated).
Step 2 · Peak
The flow tops out at the peak discharge — the largest instantaneous flow during the event. Lag time is the delay between the rainfall centroid and this peak. For flood design, the peak is everything.
Step 3 · Falling limb (recession)
Once rain stops, the channel drains. The falling limb, or recession, often follows a near-exponential decay set by catchment storage. Slow recession → big groundwater reservoir; fast recession → little storage.
2 · Anatomy of a single storm event
A 96-hour event: a 4-hour pulse drives a gamma-shaped response. Hover for hourly values. The dashed line is a straight-line baseflow separation (event start → recession inflection).
Probe by dragging: at hour the discharge is —.
3 · Baseflow separation — the Lyne–Hollick filter
Real baseflow isn't a straight line. The Lyne–Hollick filter [1] runs three forward/backward passes of a one-parameter recursion:
bt = Qt − max(ft, 0)
Drag α inline: → higher values strip more quickflow, giving a smoother, lower baseflow line. BFI = baseflow volume ÷ total volume.
Filtered baseflow
Drag the slider — both lines update at ~60 fps.
α = 0.925 with 3 passes (forward, backward, forward) is the published Lyne–Hollick default.
Move the slider above to 0.99 and see baseflow approach a near-flat line.
4 · Doubling rainfall ≠ doubling peak
Two storms on the same catchment. Drag the number: drop as much rain on the right panel as the left, and the peak grows faster than linearly. That's saturated soil at work.
Small storm (10 mm)
Large storm (20 mm)
Q_runoff = P · (P − Ia)² / (P − Ia + S), scaled and convolved with a gamma unit-hydrograph kernel.
5 · Checkpoint
Answer all three questions correctly to mark this module complete.
A small headwater catchment after a brief storm shows a steep, narrow hydrograph that peaks in 2 hours and is back to baseflow within 6. What does that shape tell you?
You raise the Lyne–Hollick filter parameter from α = 0.925 to α = 0.985. What happens to the computed BFI?
If you double the rainfall on an already-wet catchment, what's the most likely outcome for the peak discharge?
6 · Pull it together with real-shape data
Pick a gauge. The cell synthesises a year of daily streamflow shaped to mimic that catchment's character (snowmelt, flashy, or baseflow-dominated), then overlays the Lyne–Hollick baseflow. The source regenerates each time you change the gauge.
fetch_streamflow_data and extract_hydrological_signatures.
References
- Lyne, V. & Hollick, M. (1979). Stochastic time-variable rainfall-runoff modelling. Institute of Engineers Australia National Conference, Publ. 79/10, 89–93.
- Nathan, R.J. & McMahon, T.A. (1990). Evaluation of automated techniques for base flow and recession analyses. Water Resources Research, 26(7), 1465–1473. DOI: 10.1029/WR026i007p01465
- Eckhardt, K. (2005). How to construct recursive digital filters for baseflow separation. Hydrological Processes, 19(2), 507–515. DOI: 10.1002/hyp.5675
- Addor, N., Newman, A.J., Mizukami, N. & Clark, M.P. (2017). The CAMELS data set: catchment attributes and meteorology for large-sample studies. Hydrology and Earth System Sciences, 21, 5293–5313. DOI: 10.5194/hess-21-5293-2017
- USDA-SCS (1972). National Engineering Handbook, Section 4: Hydrology. Runoff curve-number method.
fetch_streamflow_data for real CAMELS.