Why is mathematics important when rain falls faster than streets and drains can carry it away? Urban flood drainage is a problem of rates, storage, geometry, probability and time. Rainfall arrives unevenly across a catchment. Some water infiltrates, some is stored on surfaces and some becomes runoff. That runoff travels through channels, pipes, detention systems and low points whose capacities change with depth and slope.
Mathematics helps engineers represent this changing system. It converts millimetres of rain into cubic metres of water, rainfall intensity into peak flow estimates, hydrographs into storage needs and pipe geometry into hydraulic capacity. It also makes uncertainty explicit: a design storm is not a prediction of the next storm, and no drainage system can remove every conceivable flood risk.
Singapore’s PUB publishes a Code of Practice on Surface Water Drainage. The current listing identifies the Seventh Edition of December 2018 with amendments through Addendum No. 3 dated April 2025. This article explains general mathematical mechanisms and uses simplified classroom examples. It does not reproduce the Code’s design procedure or replace a qualified professional’s assessment.
Flood safety comes first. Do not enter floodwater, drains, canals or construction sites to collect data. Use official rain, water-level and warning information, public maps, supervised school experiments and desk calculations.
Choose the drainage question you want to answer
- To convert rainfall depth into volume, begin with area and unit conversion.
- To estimate runoff, distinguish rainfall, loss, imperviousness and response time.
- To understand peak flow, connect intensity, area and a runoff coefficient carefully.
- To size temporary storage, compare inflow and outflow hydrographs.
- To understand pipes and channels, study continuity, velocity, slope and friction.
- To read risk language, separate annual exceedance probability from a timetable.
- To test a model, examine calibration, sensitivity and boundary conditions.
- To build skill safely, use public datasets or tabletop catchments rather than live drains.
The most useful habit is to draw a system boundary. Ask where water enters, where it can be stored, where it leaves and which quantities change with time.
Rainfall depth becomes volume through area
A rainfall depth of 1 mm spread over 1 m² equals 1 litre. This compact relationship is worth proving. One millimetre is 0.001 m, so volume is 0.001 m×1 m²=0.001 m³. Since 1 m³ is 1,000 litres, the result is 1 litre.
Therefore 25 mm over 2 hectares gives a gross water volume of 25 L/m²×20,000 m²=500,000 L, or 500 m³.
This is rain delivered to the plan area, not automatically runoff at one outlet. Infiltration, interception, depression storage, evaporation and spatial variation matter. The calculation establishes a volume budget before those pathways are modelled.
Intensity is a rate
Rainfall intensity describes depth per time, such as millimetres per hour. A 30 mm total can arrive gently over six hours or intensely over thirty minutes. The total depth is the same, but peak runoff can be very different.
If 18 mm falls in 20 minutes, the average intensity over that interval is 18÷(20/60)=54 mm/h. That does not mean every minute had the same intensity.
Short-interval peaks matter for small fast-responding catchments. Longer totals matter for storage and soil saturation. A report should state the averaging duration.
Hyetographs show rainfall through time
A hyetograph is a bar chart of rainfall intensity across consecutive intervals. The area of each bar—intensity multiplied by duration—is rainfall depth.
Suppose three 10-minute intervals have intensities 12, 60 and 18 mm/h. Depths are 12×1/6=2 mm, 60×1/6=10 mm and 18×1/6=3 mm. Total depth is 15 mm.
The order matters. A burst after the catchment is already wet may generate more runoff than the same burst at the start. A single total cannot preserve that sequence.
A catchment routes water to a common outlet
A drainage catchment is an area whose topography and drainage network direct runoff toward an outlet. Boundaries may follow ridges, kerbs, roof edges, pipes or constructed channels.
EPA’s Storm Water Management Model, SWMM, represents urban areas as subcatchments that receive precipitation and generate runoff, then routes flow through pipes, channels, storage devices, pumps and regulators.
Dividing a city into subcatchments is a modelling choice. Too few can hide spatial differences; too many increase data demands and computation. The chosen resolution should match the decision.
Impervious surfaces change the response
Roofs, roads and paved areas generally allow less infiltration than vegetated soil. They can produce faster and larger runoff for the same rain, although surface storage and drainage connections still matter.
A simple weighted runoff coefficient for two surface types is Cweighted=(C1A1+C2A2)/(A1+A2). If 60 per cent of an area has C=0.9 and 40 per cent has C=0.3, the weighted value is 0.6×0.9+0.4×0.3=0.66.
This average is only appropriate under the assumptions of the selected method. Real response changes with soil moisture, intensity, slope and connectivity.
The rational method is a peak-flow model
A common simplified expression is Q=CIA, with a unit-conversion factor when I and A are not in compatible units. Q is peak flow, C a runoff coefficient, I a design rainfall intensity associated with a chosen duration and frequency, and A catchment area.
In SI units with I in mm/h and A in hectares, Q≈0.00278CIA in m³/s. If C=0.7, I=100 mm/h and A=5 ha, Q≈0.00278×0.7×100×5=0.973 m³/s.
This is not a universal rainfall-to-flow law. It is used within defined ranges and local standards. Larger or more complex catchments usually need more detailed modelling.
The coefficient is not a magic property
A runoff coefficient compresses several physical effects into one number. It depends on land cover, slope, soil, storage and method conventions.
Using C=0.9 because a surface “looks paved” may ignore disconnected areas that drain onto grass. Conversely, compacted soil can generate more runoff than its green appearance suggests.
Coefficients should come from the governing guidance and project evidence. Sensitivity tests can show how much the result changes when C varies within a plausible range.
Time of concentration links duration to response
Time of concentration is a characteristic time for runoff from the hydraulically most remote relevant point to reach the outlet under a method’s definition.
In a rational-method application, design rainfall intensity is often selected for a duration related to this response time. A short time of concentration can imply a higher short-duration intensity on an intensity-duration-frequency curve.
The concept is more subtle than “walking time across the catchment”. Sheet flow, gutters, pipes, channels, slopes and depths affect travel. Local guidance specifies acceptable methods.
Intensity-duration-frequency curves summarise extremes
An intensity-duration-frequency, or IDF, relationship gives design rainfall intensity for combinations of duration and recurrence measure.
Shorter durations often have higher intensities. Rarer design events often have higher intensities for the same duration. The curve is estimated from historical rainfall records using statistical methods.
It does not predict that a specified storm will occur on schedule. It supplies a probabilistic design input, subject to record length, station coverage and changing climate.
Return period is not a calendar appointment
An event described as a 1-in-100 annual exceedance event has annual exceedance probability about 1 per cent under the model. It can occur in consecutive years.
The probability of at least one exceedance in N independent years is 1−(1−p)^N. With p=0.01 and N=30, the result is 1−0.99³⁰≈26.0 per cent.
Independence and stationarity are assumptions. The calculation corrects the common misconception that a “100-year storm” cannot recur for a century.
Climate change challenges stationarity
Traditional frequency analysis often assumes the statistical distribution is stable. Climate change and urban change can violate that assumption.
Nonstationary methods may allow parameters to vary with time or climate indicators. Scenario analysis tests multiple futures rather than selecting one timeless curve.
Uncertainty grows when extrapolating beyond historical experience. Good design combines updated official guidance, adaptation margins and consequences of failure.
Runoff is a hydrograph, not one number
A hydrograph plots flow against time. It rises, peaks and recedes as water moves through the catchment.
Two storms can have the same runoff volume but different peaks. A sharp hydrograph stresses conveyance capacity; a broad one stresses storage duration.
The area under the hydrograph is volume because flow rate integrated over time gives volume. This is the same rate-to-total idea seen in battery energy and traffic flow.
A triangular hydrograph gives a useful classroom model
Suppose a simplified hydrograph rises linearly from zero to 2 m³/s over 20 minutes and falls to zero over the next 40 minutes. Its area is a triangle:
Volume=0.5×base×height=0.5×3,600 s×2 m³/s=3,600 m³.
The example is not a professional design hydrograph, but it makes units visible. Seconds cancel with per-second flow, leaving cubic metres.
If a student used 60 minutes without converting to seconds, the result would be wrong by a factor of 60.
Continuity keeps the water budget honest
For a storage element, dS/dt=Qin−Qout, where S is stored volume. If inflow exceeds outflow, storage rises. If outflow exceeds inflow, storage falls.
In discrete intervals, ΔS≈(Qin−Qout)Δt. Start with an initial storage and update step by step.
Continuity is an accounting identity. It does not by itself tell us the outflow relation or maximum safe level. Those require geometry and hydraulics.
A worked detention-storage calculation
For ten minutes, average inflow is 1.4 m³/s and controlled outflow is 0.6 m³/s. Net inflow is 0.8 m³/s. Added storage is 0.8×600=480 m³.
For the next ten minutes, inflow is 0.9 m³/s and outflow 0.6 m³/s, adding 0.3×600=180 m³. Cumulative added storage is 660 m³ before considering initial water, later drainage and freeboard.
A real routing calculation updates water level and outflow together because outlet discharge often depends on head. The simple example shows why peak inflow alone does not equal storage volume.
Detention changes timing as well as amount
A detention facility temporarily stores runoff and releases it more slowly. It can lower the downstream peak by spreading volume over a longer period.
It does not necessarily remove the water from the system. Retention, infiltration and reuse have different water-balance effects.
PUB guidance notes that on-site detention can hold back or slow runoff before discharge to the public drainage system. The exact requirements belong to the current Code and professional design.
Storage geometry turns depth into volume
For vertical-sided storage with plan area A, a level rise Δh adds volume AΔh. If area changes with depth, volume is the integral of area with respect to height.
Suppose a basin’s plan area increases approximately linearly from 800 m² at the bottom to 1,200 m² one metre higher. A trapezoidal approximation gives (800+1,200)/2×1=1,000 m³.
Surveyed stage-storage curves are more reliable for irregular basins. Geometry is part of the hydraulic model, not a decorative drawing.
Freeboard is a safety margin, not storage to spend
Freeboard is vertical distance reserved above a design water level to reduce overtopping risk under uncertainty, waves, blockage or other effects as defined by the governing standard.
Counting freeboard volume as normal operating storage defeats its purpose. A model should distinguish active storage, dead storage, surcharge and emergency overflow.
Margins are not evidence that the calculation is careless. They acknowledge that models and future events are imperfect.
Flow rate equals area times velocity
Continuity in a full pipe or channel section gives Q=Av, where A is cross-sectional flow area and v is mean velocity.
A full circular pipe of diameter 0.8 m has area π(0.4)²≈0.503 m². At mean velocity 2 m/s, flow is about 1.01 m³/s.
Velocity is not chosen independently of slope, roughness, depth and energy. Q=Av is an identity; hydraulic equations determine which velocities are physically consistent.
Pipe area grows with diameter squared
For a full circular pipe, A=πD²/4. Increasing diameter from 0.8 m to 1.0 m multiplies area by (1.0/0.8)²=1.5625.
Capacity does not scale by area alone because hydraulic radius and friction also change. In common uniform-flow formulas, diameter can have a stronger exponent.
This is why “25 per cent wider” should not be casually translated to “25 per cent more capacity”. Geometry is nonlinear.
Manning’s equation relates flow, slope and roughness
For uniform open-channel flow in SI units, a common form is Q=(1/n)AR^(2/3)S^(1/2), where n is Manning roughness, A flow area, R hydraulic radius and S energy slope.
The formula is empirical and used under specific conditions. Roughness represents resistance from material, vegetation, irregularity and other features through a calibrated coefficient.
Doubling slope does not double Q in this formula; it multiplies Q by √2 if other terms stay fixed. Exponents encode sensitivity.
Hydraulic radius is not ordinary radius
Hydraulic radius is R=A/P, where P is wetted perimeter. For a full circular pipe, R equals D/4, not D/2.
For a 1 m wide rectangular channel with 0.5 m depth, A=0.5 m² and wetted perimeter is 1+0.5+0.5=2 m, so R=0.25 m.
The free surface is not part of the wetted perimeter. Confusing geometric radius with hydraulic radius produces major errors.
Open channels can change regime
The Froude number Fr=v/√(gD) compares flow speed with shallow-water wave speed, using an appropriate hydraulic depth D.
Fr below one is subcritical; above one is supercritical; near one is critical. Flow regime affects how disturbances travel and which boundary conditions control the solution.
This is one reason drainage cannot be reduced to “water goes downhill”. Depth and velocity interact dynamically.
Pipe flow may become pressurised
Storm sewers can flow partly full as open channels or become surcharged and pressurised. Manholes and storage nodes connect branches whose levels interact.
EPA SWMM includes dynamic wave routing for networks of conduits and nodes. Such models solve changing flow and depth across time rather than applying one steady equation everywhere.
Professional interpretation checks numerical stability, boundary conditions and whether the model structure matches the physical system.
Backwater connects downstream conditions upstream
If a downstream river, tide or channel level is high, it can reduce the head available for drainage and raise upstream water levels.
An outfall cannot always discharge at its free-flow capacity. Gates, pumps or storage may be used where gravity drainage is constrained.
This connects drainage with Why Mathematics? | Tides, Harmonic Cycles and Coastal Forecasting. The systems have different models, but they meet at a boundary condition.
Blockage is a scenario, not a coefficient to hide
Leaves, sediment, debris or maintenance issues can reduce inlet or conduit capacity. Instead of pretending the system is always clear, analysts can test partial blockage scenarios where relevant.
If an inlet’s effective open area falls by 30 per cent, flow may not fall by exactly 30 per cent because head and control regime change. A hydraulic model is needed.
Scenario analysis helps identify sensitive assets and maintenance priorities. It does not justify entering drains to inspect them without authority.
Inlets connect surface and underground networks
Street inlets capture surface flow into the drainage system. Their performance depends on geometry, spread, approach flow, blockage and local grade.
When inlet capacity is exceeded, water continues overland. A model that sends all runoff directly into pipes may miss surface pathways.
Modern urban modelling can couple one-dimensional pipe networks with two-dimensional surface flow. More detail demands more topographic and calibration data.
Topography decides where water can pond
Small elevation differences determine overland paths and depressions. Digital elevation models represent surface height on a grid or mesh.
Grid resolution matters. A coarse model may smooth out a kerb or underpass; a fine model increases data and computation.
Survey datums must match. Combining terrain and water levels from incompatible vertical references can create false flood depths.
Infiltration is time dependent
Dry soil may initially absorb water quickly, then slow as it becomes wet. Horton-type models use a decaying infiltration capacity. Green–Ampt models represent a wetting front using soil parameters.
EPA SWMM supports several infiltration methods and distinguishes pervious and impervious subareas.
Parameters should come from suitable data and calibration. A model name is not a guarantee that the soil behaves exactly as its idealisation.
Depression storage delays the first runoff
Small surface hollows store rainfall before runoff begins. Leaves and microtopography can increase or reduce this temporary storage.
If depression storage is 2 mm over 10,000 m², the corresponding volume is 20 m³. Once filled, later rainfall may generate runoff more directly.
This simple threshold creates nonlinear response: the first millimetres and later millimetres can have different effects.
Green infrastructure changes several terms
Bioretention, green roofs, swales and permeable surfaces can add storage, infiltration and evapotranspiration while slowing routing.
EPA’s SWMM documentation describes low-impact development controls and notes that bioretention cells provide storage, infiltration and evaporation for captured rainfall and runoff.
Performance depends on design, soil, maintenance and storm sequence. A percentage quoted from one site should not be copied blindly to another.
Calibration compares model and observation
Rain gauges, level sensors and flow measurements provide evidence. Calibration adjusts defensible parameters so simulated behaviour matches observed events.
Metrics such as root mean squared error, volume error and peak timing error describe different aspects. A model can match peak flow while missing volume, or match volume while shifting timing.
Calibration is not permission to force every parameter until one event looks perfect. Validation on other events tests transfer.
Root mean squared error emphasises larger misses
If observed flows are 1.0, 2.0 and 1.5 m³/s while modelled flows are 0.8, 2.4 and 1.3, residuals are 0.2, −0.4 and 0.2 under observed-minus-modelled convention.
RMSE is √((0.2²+0.4²+0.2²)/3)=√0.08≈0.283 m³/s.
RMSE hides timing and bias patterns, so plots and multiple metrics are needed. A single score cannot certify the model.
Sensitivity analysis finds influential assumptions
Vary rainfall, runoff coefficient, roughness, blockage or initial soil moisture within plausible ranges. Observe which outputs change most.
If a 10 per cent increase in rainfall intensity produces a much larger increase in maximum flood depth due to a threshold or bottleneck, the system is nonlinear.
Sensitivity analysis guides data collection and resilience planning. It does not assign probabilities unless the input variations have probabilistic meaning.
Scenario and probability are different
A scenario such as “outfall blocked by half” describes a condition. It does not say how likely that condition is.
Combining uncertain rainfall, sea level and blockage requires dependence assumptions. Treating them as independent can understate or overstate joint risk.
Reports should label deterministic scenarios, probabilistic events and safety factors separately.
Pumped systems have operating curves
A pump does not deliver one fixed flow in every condition. Its flow depends on head, speed and system resistance. A pump curve and system curve intersect at an operating point.
As downstream level rises, required head may increase and delivered flow may fall. Multiple pumps can interact with wet-well controls and power limits.
Storage must cover periods when inflow exceeds pumping. Backup power, maintenance and failure scenarios belong to professional design rather than a single nameplate capacity.
Culverts can be inlet-controlled or outlet-controlled
A culvert’s capacity may be controlled near the entrance or by conditions along and downstream of the barrel. Headwater, tailwater, slope, length, roughness and entrance shape matter.
Simply applying full-pipe area times a guessed velocity can miss the controlling regime. Hydraulic calculations compare relevant conditions.
This reinforces a general mathematical habit: before using an equation, identify which physical mechanism limits the system.
Travel time spreads the hydrograph
Runoff from different parts of a catchment arrives at different times. Routing translates and attenuates the hydrograph as water moves through channels and storage.
If two tributary peaks arrive together, their combined peak can be large. If one is delayed, the same total volume can produce a smaller combined maximum.
Synchronisation is therefore a design concern. Changing one branch may shift its peak into or away from another branch’s peak.
Numerical time step changes the simulation
A model updates rainfall, runoff, level and flow at discrete times. If the time step is too large, short rainfall bursts or rapid hydraulic changes can be missed.
Reducing the step should lead toward stable results within the method’s limits. If peak depth keeps changing greatly as the step shrinks, the solution is not numerically converged.
Smaller steps increase computation and do not repair wrong geometry or parameters. Numerical accuracy and model validity are separate.
Ensembles show a range of plausible futures
Instead of one rainfall input, an ensemble uses multiple plausible storms, forecasts or parameter sets. The resulting spread shows sensitivity to uncertain inputs.
An ensemble is not automatically a probability distribution. Members may not be equally likely or independent.
Communicators can report median, range and exceedance counts while explaining what the ensemble represents. One dramatic member should not be presented as the forecast.
Maintenance preserves modelled capacity
Drainage performance depends on inspection and maintenance. Sediment, vegetation, debris and damaged structures can reduce the effective geometry and roughness assumed in design.
A model calibrated to a clean system may overestimate neglected performance. Asset records and condition surveys connect mathematics to operations.
Maintenance decisions can be prioritised by consequence, likelihood and sensitivity. The best equation still needs a functioning physical system.
Unit checks catch silent errors
Rainfall may be in millimetres, area in hectares, time in minutes and flow in cubic metres per second. A correct formula with inconsistent units can be wrong by factors of 60, 1,000 or 10,000.
Write base units before substitution. In Q=CIA, C is dimensionless, I must be length per time and A area, producing volume per time after conversion.
Dimensional analysis cannot prove every equation is right, but it can quickly prove many are wrong.
Forecasting and design are different jobs
Design models ask what infrastructure should accommodate under specified standards and scenarios. Forecast models use current observations and weather predictions to estimate near-term conditions.
A design storm is not tomorrow’s forecast. A forecast warning is not a permanent design criterion.
The mathematics overlaps, but inputs, time horizons and decisions differ.
Residual risk remains after construction
Drainage reduces risk; it does not remove all risk. Events can exceed design assumptions, systems can be blocked, pumps can fail and downstream levels can be high.
Resilience includes safe overland flow paths, maintenance, warnings, emergency response and protection of critical assets.
Mathematics helps compare options, but communities also decide acceptable risk, land use and investment priorities.
Consequence changes the design question
The same probability can have very different consequences at a park, a basement electrical room or a hospital access route. Risk is often framed as a combination of likelihood and consequence, although the exact decision framework may be richer.
Expected annual loss multiplies event probabilities by associated losses and sums across events. It can compare strategies, but monetary totals do not fully capture injury, displacement, heritage, ecosystem damage or unequal impacts.
Multi-criteria analysis makes several objectives visible. Weights assigned to objectives represent values, not natural constants discovered by the model.
This is why flood engineering is both technical and civic. Mathematics organises evidence and trade-offs; affected communities and authorities decide acceptable protection and priorities.
Maps communicate model outputs with choices
A flood map may show depth, velocity, hazard category or probability. Colour bins and thresholds can make a continuous result appear to have sharp borders.
Map resolution, terrain data and scenario assumptions affect the displayed boundary. A property just outside a coloured polygon is not guaranteed to have zero risk.
Legends should name units, event, date, datum and model status. Interactive maps should not hide uncertainty behind smooth graphics. The visual is a model output, not a photograph of the future.
A safe tabletop investigation
Build a shallow tray catchment with clean materials under teacher supervision. Use a measuring cup to apply the same water volume over different durations. Compare peak outflow into a container.
Add a sponge or gravel area to represent temporary storage and infiltration, while stating that it is only an analogy. Record inflow timing, outflow timing and total volume.
Never use street drains or floodwater for this activity. The educational goal is continuity and hydrographs, not field exposure.
Common misconceptions to repair
- “Rainfall depth is already a volume.” Area is needed to convert it.
- “A 100-year event happens once per century.” It has an annual exceedance probability under a model.
- “Peak flow and total volume are the same.” One is a rate; the other is accumulated water.
- “A larger pipe gives proportionally larger capacity.” Geometry and friction create nonlinear scaling.
- “Storage removes water.” Detention often changes timing and release rate.
- “One calibrated event proves the model.” Validation across other events is required.
- “Flood protection means zero risk.” Residual risk always remains.
A practical learning path for students
Begin with millimetres, hectares, litres and cubic metres. Convert depth to volume. Next, calculate intensity and plot a hyetograph.
Then study weighted runoff coefficients, peak-flow estimates and hydrograph area. Use continuity to route a simple detention store. After that, learn geometry, Manning’s equation, probability and numerical time stepping.
Students interested in environmental or civil engineering can continue into differential equations, fluid mechanics, GIS and optimisation. The transferable core is rate, storage and uncertainty.
What parents can encourage
Use ordinary rain reports to practise units safely at home. Ask how many litres 10 mm of rain represents on a 20 m² roof, without suggesting that every litre can be captured.
Encourage the child to draw the water pathway and name assumptions. “Where can it store?” is often more useful than rushing to one formula.
Reinforce official safety advice. Floodwater depth, current, contamination and hidden openings make direct exploration dangerous.
Did you know? One millimetre of rain is one litre per square metre
This identity turns a small-looking depth into a city-scale volume. Ten millimetres over one square kilometre equals 10 million litres, or 10,000 m³, before losses.
Scale is why urban drainage mathematics matters. A number that seems tiny on a ruler becomes enormous across a catchment.
The benefits of learning mathematics include this ability to move between scales while keeping units and assumptions intact.
Frequently asked questions
What is rainfall intensity?
It is rainfall depth per unit time, such as millimetres per hour, over a stated averaging duration. A storm’s intensity can vary throughout the event.
What is the difference between runoff volume and peak flow?
Runoff volume is the total water that passes; peak flow is the highest rate. A hydrograph connects them through time.
Why store stormwater?
Temporary storage can reduce and delay downstream peak discharge. Other systems may also infiltrate, reuse or retain water. The design purpose must be stated.
Does a wider pipe always prevent flooding?
No. Inlets, upstream pipes, downstream levels, blockages, surface pathways and event size all matter. Changing one component can move the bottleneck.
What does a 1-in-100 event mean?
It usually describes about a 1 per cent annual exceedance probability under the stated statistical model, not a guaranteed 100-year gap.
Which school mathematics matters most?
Units, area, volume, rates, graphs and percentages come first. Algebra, trigonometry, calculus, probability and numerical methods support advanced modelling.
Does mathematics alone guarantee a drainage career?
No. Civil and environmental engineering also require science, design standards, field knowledge, software, teamwork, ethics and professional responsibility.
Useful next reading
Connect rainfall modelling to Why Mathematics? | Weather Forecasting, Differential Equations and Numerical Models. Strengthen everyday flow reasoning with Why Mathematics? | Water Conservation, Flow Rates and Everyday Choices and project quantities with Why Mathematics? | Construction Estimating, Quantity Take-Offs and Cost Control.
For authoritative practice, consult PUB’s Codes of Practice and Standard Drawings page and the listed Code of Practice on Surface Water Drainage. For modelling concepts, see the U.S. EPA’s Storm Water Management Model and SWMM 5.2 user manual.
Drainage mathematics is a hopeful form of engineering: it turns rainfall, land and infrastructure into a system we can measure, test and improve—while remaining honest that nature and cities contain uncertainty.