Storm Hydrographs and River Discharge Factors

A storm hydrograph is a graph that shows how river discharge changes over time in response to a rainfall event, and the factors that affect river discharge, such as rainfall, slope, rock type, land use and basin shape, decide whether the response is quick and flashy or slow and gentle. In brief: the main parts of a hydrograph are the baseflow, the rising limb, the peak discharge, the falling (recessional) limb and the lag time, which is the time between the peak of the rainfall and the peak of the discharge. Short lag times and high peaks mean a high flood risk, and they are typical of steep, impermeable, urban or circular basins.

Hydrographs are used by engineers and planners to predict floods and design defenses. This guide explains the parts of a hydrograph, the factors that change its shape, how human activity alters it, compares flashy and subdued responses in a table, works through a numerical example, outlines the history and corrects common mistakes.

What are the parts of a storm hydrograph?

The horizontal axis shows time (hours or days) and the vertical axis shows discharge (m³/s). Rainfall is often shown as bars at the top. The graph has these parts:

• Baseflow: the normal flow fed by groundwater before the storm.
• Rising limb: the steep increase in discharge as runoff reaches the river from overland flow and throughflow.
• Peak discharge: the highest discharge during the event.
• Falling (recessional) limb: the decline in discharge as the runoff ends and flow returns to baseflow, usually gentler than the rising limb.
• Lag time: the time from the peak rainfall to the peak discharge.
• Bankfull discharge: the discharge that fills the channel. Above this, the river floods.

A “flashy” hydrograph has a short lag time, a steep rising limb and a high peak. A “subdued” one has a long lag time, a gentle rising limb and a low peak.

What factors affect river discharge?

Precipitation factors

• Intensity and duration: intense rain can exceed the soil’s infiltration capacity, creating overland flow, and long rain saturates the soil.
• Type and timing: snowmelt, rain falling on snow, or storms moving downstream with the river flow increase peaks.
• Antecedent moisture: previous rain leaves the soil saturated, so a new storm runs off quickly. Frozen ground behaves in a similar way.

Basin characteristics

• Basin shape: circular basins deliver water from all parts to the outlet at about the same time, which gives a high peak, while long, thin basins spread the arrival over time.
• Basin size: small basins respond more rapidly.
• Slope: steep slopes speed up runoff and shorten lag times.
• Drainage density: a high density of streams (length of channels per km²) moves water quickly to the main channel.
• Geology and soil: permeable rocks such as chalk and sand allow infiltration and give subdued responses, while impermeable rocks such as clay and granite lead to fast runoff.

How do people change the response?

Urbanization replaces soil with roofs, roads and pavements, which prevents infiltration and sends water along drains to rivers rapidly, so lag times fall and peaks rise, a pattern shown in urban hydrographs. Deforestation reduces interception and evapotranspiration and exposes soil. Agriculture with compacted soils, drainage ditches and straightened channels speeds up the flow. Conversely, afforestation, restoring wetlands and meanders, building ponds and “sustainable drainage systems” in cities, and reservoirs can flatten the hydrograph and delay peaks. Climate change is expected to increase the intensity of heavy rain in many regions, which will raise flood peaks.

Flashy and subdued hydrographs compared

Worked example: reading a hydrograph

The data are hypothetical. Consider a river after a storm that has its peak rainfall at hour 2.

1. Baseflow: the discharge before the storm is 5 m³/s.
2. Peak discharge: the highest value is 62 m³/s at hour 6.
3. Lag time: the peak rainfall was at hour 2 and the peak discharge at hour 6, so the lag time is 6 − 2 = 4 hours.
4. Rise above baseflow: the peak is 62 − 5 = 57 m³/s above baseflow, which is 62 ÷ 5 = 12.4 times the baseflow.
5. Rising limb gradient: from hour 2 to hour 6, discharge rises by 62 − 8 = 54 m³/s in 4 hours, which is 13.5 m³/s per hour. The falling limb from hour 6 to hour 12 drops by 62 − 12 = 50 in 6 hours, which is 8.3 per hour, so the falling limb is gentler.
6. Urban comparison: after urbanization, the lag time is cut to 1.5 hours and the peak rises to 95 m³/s. The peak is 95 ÷ 62 = 1.53 times higher, which is 53% more, and the warning time is 2.5 hours shorter.
7. Bankfull: if the channel can carry 55 m³/s, the river exceeds bankfull when the discharge is above 55, which happens close to the peak at hour 6.

How did hydrograph analysis develop?

Early flood forecasting was based on records of river levels. In 1932, LeRoy Sherman, an American engineer, introduced the unit hydrograph, which describes the response of a basin to a standard unit of rainfall, and allows predictions of discharge for any storm by adding together the responses. Robert Horton’s work on drainage density and infiltration in the 1930s and 1940s supported the approach. Computer models, radar rainfall measurements and satellite data now allow hydrographs to be forecast in real time. Studies of urban and land-use effects since the 1960s have helped planners to design drainage that limits flood peaks.

Which mistakes are common?

Mistake 1: Measuring lag time from the start of the rain

Lag time is the interval between peak rainfall and peak discharge, not between the first drop and the peak.

Mistake 2: Thinking that a high peak always means more total water

A flashy basin may produce a high peak but a short event. The total volume depends on the area under the curve and the rainfall.

Mistake 3: Ignoring antecedent conditions

The same storm can have a small effect on dry soil and a severe effect on saturated soil.

Mistake 4: Assuming that deforestation is the only cause of floods downstream

Rainfall, geology and drainage and, in cities, paved surfaces also matter, and the effect of forest cover is strongest for smaller storms and smaller basins.