Methodology

Stormwater, Runoff and the Water Balance

Why a small catchment is designed for a more intense rainfall than a large one, why a detention basin can make things worse downstream, and why a rainwater tank delivers far less than annual rainfall times roof area.
  • 9Sections
  • 1Equations
  • 13Calculators

Rate and volume are different questions

A drainage design asks two things that look similar and are not. How FAST does water arrive at its peak — which sizes pipes, inlets, channels and outfalls. And how MUCH arrives in total — which sizes tanks, basins, soakaways and harvesting systems.

They need different rainfall. The peak comes from a short, intense storm; the volume comes from a longer, gentler one that delivers more water overall. A site's critical storm for pipe sizing and its critical storm for storage sizing are usually not the same event, and a storage volume derived from the pipe-sizing storm is undersized — often badly.

This is the single most common conceptual error in small-site drainage, and it is easy to make because the same rainfall data serves both. The pages here state which question they are answering, because a peak flow in litres per second and a storage volume in cubic metres are not two views of one calculation.

Q=C⁢i⁢A,V=P⁢A⁢C⁢η
The rational method for peak flow, and the volume form beside it. Same coefficient, same area, entirely different rainfall input and entirely different answer.
Q
peak flow rate
i
rainfall INTENSITY at a duration equal to the time of concentration
P
rainfall DEPTH over the period of interest — a storm, a month, a year
C
runoff coefficient: the fraction that runs off rather than soaking in or evaporating
η
collection efficiency — filter losses, first flush diverted, overflow

Time of concentration, and why small catchments get worse rainfall

The rational method chooses its rainfall intensity at a duration equal to the TIME OF CONCENTRATION — the time for runoff from the most remote point of a catchment to reach the outlet. The reasoning is that only a storm lasting at least that long has the whole catchment contributing at once.

Because rainfall intensity falls as duration rises, this produces a result that reads backwards at first: a small catchment with a short time of concentration is designed against a MORE intense rainfall than a large one. The small site is not being treated harshly; it is simply capable of responding to a cloudburst that a large catchment would average out.

Development changes the same term and raises the peak without changing the area at all. Replacing grass and overland flow with smooth paving and pipes shortens the time of concentration, so the runoff arrives sooner and more of it arrives together. A site that is no larger and no less permeable than before can still produce a higher peak simply because it drains faster.

The method's limits follow from its assumptions. It presumes rainfall steady and uniform over the catchment, a constant runoff coefficient, and no storage anywhere in the system, all of which hold reasonably on small sites and progressively less well as area grows. It also returns a single peak rather than a HYDROGRAPH, which means it cannot size a detention basin — routing a flood through storage needs the shape of the flow over time, not its maximum.

The runoff coefficient is not a property of the surface alone

Published runoff coefficients are quoted per surface type — roof, asphalt, gravel, grass — which encourages the idea that each surface has one. They also depend on the slope, on the soil beneath, on how wet the ground already is, and on how severe the storm is.

Severity matters most. In a rare, intense event a pervious surface saturates and then behaves much more like a paved one, so the coefficient rises with return period. Design guidance handles this with a frequency adjustment applied to the tabulated value, and omitting it under-predicts exactly the events the design exists to handle.

Antecedent conditions do the same on a shorter timescale. The same lawn absorbs a summer shower and sheds a winter one, because it is already full. Any design relying on infiltration has to be assessed on WET ground rather than on an average, and that is the assumption the calculators here state.

For a composite site the coefficients are area-weighted, and the weighting is worth doing carefully: a small paved area within a large green one can contribute most of the runoff, so an average taken by eye rather than by area is usually optimistic.

Detention delays; only retention and infiltration remove

Three things are commonly called attenuation and only two of them reduce the amount of water leaving a site. DETENTION holds water and releases it more slowly: the peak falls, the volume is unchanged. RETENTION keeps it — for use, for evaporation, or until it is transpired. INFILTRATION returns it to the ground.

Getting this distinction wrong produces a specific downstream failure. Detention spreads each site's discharge over a longer period, and where many sites do this along one watercourse their extended outflows can arrive together and coincide with the catchment's own slower response. The peak that each site individually reduced can be reassembled downstream, larger than before. This is why catchment-scale drainage strategies exist and why site-by-site compliance is not equivalent to them.

It is also why infiltration is preferred wherever the ground and the groundwater allow it, and why the surface water hierarchy in most modern guidance puts infiltration and reuse above discharge to a sewer. An infiltration design needs a measured soil infiltration rate, a check on groundwater level and a half-drain-time requirement so the system recovers before the next storm — none of which a runoff calculation can supply.

Green roofs and permeable paving: the storage is in the voids, and it fills

A green roof's retention is the water its growing medium and drainage layer can hold, and its value is entirely dependent on ANTECEDENT conditions. A saturated roof retains nothing — it is a roof. Annual retention figures of half the rainfall or more are genuine and are achieved by holding many small events, while the design storm that the drainage below must handle should be assessed on a roof that is already wet.

The medium is also not soil. It is a lightweight engineered substrate whose water-holding capacity, weight when saturated and drainage rate are declared properties, and the saturated weight is a structural load that has to be carried rather than a hydrological input.

Permeable paving stores water in the VOIDS of its sub-base, typically around a third of the layer's bulk volume for open-graded aggregate. So the storage available is the layer thickness times the area times the void ratio, less whatever has not drained since the last storm, and a design that treats the sub-base as solid storage overstates it threefold.

Its failure mode is not structural but a maintenance one: the surface CLOGS with fines, and infiltration rate falls over years from an initial value that is far higher than anything the design needs. This is why permeable paving is specified with a large initial margin, why its infiltration rate is measured in service rather than assumed, and why sweeping is a design assumption rather than a housekeeping preference.

Harvesting: yield is the lesser of supply and demand, meeting in time

Annual rainfall multiplied by roof area, a runoff coefficient and a filter efficiency gives the water a roof COLLECTS. It is not the water a tank supplies, and the gap between the two is large.

The reason is timing. Rain arrives in events; demand occurs continuously. When the tank is full, additional rain overflows and is lost; when it is empty, demand goes unmet regardless of how much fell last month. The yield is therefore the lesser of supply and demand AT EACH MOMENT, accumulated — which is a simulation over a time series, not a multiplication.

Tank size then shows strongly diminishing returns. A small tank captures the frequent small events that make up most of the annual total, and each further increment of volume only captures rarer, larger ones. Doubling a tank rarely doubles the water it delivers, and the standards for these systems specify a daily or finer time-step calculation for exactly this reason.

So an annual-average figure is useful for a first screen and misleading as a design. Where the water matters — irrigation through a dry season, a non-potable supply with a guaranteed availability — the honest method is a continuous simulation against a real rainfall record, and these pages say so rather than presenting a yearly total as a yield.

Emptying, and matching a zone to what the supply can give

Water draining from a tank, a basin or a reservoir through an outlet leaves more slowly as the level falls, because the head driving it falls too. Flow through an orifice goes with the square root of head, so a vessel does not empty at a steady rate and the last portion takes disproportionately long — which is why a drawdown time is not the volume divided by the initial flow.

That non-linearity is what makes half-drain-time a design criterion rather than a curiosity: a system that empties fully in a specified period is available for the next storm, and one sized on its initial discharge rate is not.

Irrigation zoning runs into the same constraint from the supply side. A zone is limited by the FLOW available, not by the area to be watered, so zones are sized by adding up head demands until the supply is used and then starting another. Two further points decide whether the result waters evenly: every head in one zone should have a matched precipitation rate, because mixing types in a zone waters some of it correctly and the rest badly; and areas with different sun, slope or planting belong in different zones whatever the flow allows, because they need different run times.

What has to be measured, and what has to be agreed

Rainfall data is the input that most changes the answer, and it is regional and dated. Intensity-duration-frequency relationships are published by national meteorological services and are periodically revised as records lengthen and climate change is incorporated — and a design using an old dataset is designing for a climate that has been superseded on paper as well as in fact.

Infiltration rates must be measured on site rather than taken from a soil description, because they vary by orders of magnitude and because the value that matters is the one at the depth and location of the proposed system. A single trial pit is the minimum and is itself a sample of one.

Discharge rates, connection points and the acceptability of any strategy are matters for the drainage authority, the sewerage undertaker and the environmental regulator, and they differ between jurisdictions and between catchments within one. The calculators here produce the quantities those conversations start from — a peak flow, a storage volume, a retained depth, a drawdown time — and none of them is an approval or a substitute for a drainage design.

Soakaways: the critical storm is found, and the shape empties it

BRE Digest 365 sizes a soakaway from a trial pit dug where it will go. The pit is filled three times and the fall from 75 to 25 per cent of its depth is timed; the infiltration rate is the water lost, over the pit's wetted area to half depth and the time it took, from the slowest fill.

Storage is then a search rather than a single sum: for each storm duration, the inflow from the impermeable area less the outflow through the soakaway's sides, and the largest difference is what it must hold — on slow ground, the storm that lasts most of a day. The Digest also asks the store to empty to half within 24 hours, and because the stored volume and the side area both grow with depth, only the plan shape changes that time: plan area over perimeter, times the void ratio, over the infiltration rate.

Calculators that use this method

Basis

  • Kuichling, E. (1889), The Relation Between the Rainfall and the Discharge of Sewers in Populous Districts — the origin of the rational method.
  • NRCS Technical Release 55, Urban Hydrology for Small Watersheds — time of concentration, curve numbers and the hydrograph methods the rational method cannot provide.
  • ASCE/EWRI Manual of Practice 77, Design and Construction of Urban Stormwater Management Systems, including the frequency adjustment applied to runoff coefficients.
  • CIRIA C753, The SuDS Manual — the surface water hierarchy, half-drain-time criteria, infiltration testing and catchment-scale effects of detention.
  • FLL Green Roof Guidelines and ASTM E2397 / E2398 for substrate water retention and saturated weight.
  • ASTM C1781, Surface Infiltration Rate of Permeable Unit Pavement Systems, and ASTM C1701 for pervious concrete — the in-service measurement that clogging makes necessary.
  • BS 8515, rainwater harvesting systems, withdrawn in 2018 and replaced by BS EN 16941-1: an intermediate approach, which BS EN 16941-1 keeps as its basic approach, sizes the store from annual yield and annual demand, and a detailed approach follows it day by day through a rainfall record.
  • National intensity-duration-frequency data (for example NOAA Atlas 14, or the FEH rainfall model in the UK), including their revision history.
  • BRE Digest 365 Soakaway design — the trial pit infiltration rate, the duration search for storage, and the half-emptying time.
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