Flood Routing

Open Flood Routing

Route inflow hydrographs through detention basins, stormwater ponds, and small dams using the modified-Puls (storage-indication) method. This guide covers the routing mathematics, stage-storage and stage-discharge relationships, composite outlet design (weirs, orifices, standpipes, culverts, spillways), timestep guidance, auto-sizing for target attenuation, and a complete worked example.

Overview

Flood routing is the process of computing how an inflow hydrograph is transformed as it passes through a storage element — a detention basin, stormwater pond, small dam, or any reservoir-like feature where water is temporarily held and released in a controlled manner. The storage acts as a low-pass filter: high-frequency variations (the sharp peak of the inflow) are absorbed into the pool and released more gradually, producing an outflow hydrograph that is lower in peak magnitude and delayed in time.

The HydroDesign Flood Routing tool implements level-pool (reservoir) routing using the modified-Puls — also called storage-indication — method. Given an inflow hydrograph, a stage-storage curve describing the basin’s volumetric capacity, and a stage-discharge relationship describing how the outlet works release water, the tool produces the outflow hydrograph together with the time history of water surface elevation, stored volume, and individual outlet contributions.

When to use this tool

Use Flood Routing whenever you need to evaluate the time-varying performance of a storage element — sizing a detention basin to meet a discharge permit, checking spillway adequacy for a small dam, analysing the attenuation provided by an existing pond, or verifying that post-development peaks are attenuated to pre-development rates. For full-hydrograph transformation along a river channel, use the Hydrologic Routing tool (Muskingum, kinematic wave); this tool is specifically for reservoir-type storage with a horizontal pool surface.

The method was previously bundled as the “Detention Basin Designer.” It has been renamed to Flood Routing because the same engine serves a broader range of applications: retention ponds, offline storage cells, roadside swales with outlet weirs, small earthen dams, and attenuation tanks — any situation where an inflow hydrograph, a storage-elevation relationship, and an outlet rating curve define the problem.

Storage-indication method theory

All reservoir routing methods are derived from the continuity equation — the mass balance between inflow, outflow, and storage change in a control volume:

$$I(t) - O(t) \;=\; \frac{dS}{dt}$$

Continuity equation — instantaneous mass balance

Where $I(t)$ is the inflow rate (m³/s), $O(t)$ is the outflow rate (m³/s), and $S(t)$ is the stored volume (m³). Integrating over a small time step $\Delta t$ and averaging inflow and outflow linearly over that interval gives the finite-difference continuity form:

$$\bar{I} \;-\; \bar{O} \;=\; \frac{\Delta S}{\Delta t}$$

Continuity equation — finite-difference form (average inflow minus average outflow equals storage change)

Expanding the averages and rearranging produces the form that underlies the modified-Puls algorithm:

$$\frac{I_1 + I_2}{2} \;-\; \frac{O_1 + O_2}{2} \;=\; \frac{S_2 - S_1}{\Delta t}$$

Modified-Puls form — raw statement of the time-stepped balance

The clever step is to rearrange all quantities at the new time level ($S_2$, $O_2$) to the left-hand side and everything at the known time level ($S_1$, $O_1$, $I_1$, $I_2$) to the right:

$$\left( \frac{2 S_2}{\Delta t} + O_2 \right) \;=\; \left( I_1 + I_2 \right) \;+\; \left( \frac{2 S_1}{\Delta t} - O_1 \right)$$

Storage-indication form — all unknowns on the left, all knowns on the right

The left-hand side contains two unknowns ($S_2$ and $O_2$), but because both depend uniquely on the water surface elevation $h_2$ at the end of the step, they can be combined into a single quantity — the storage-indication value $\Phi = 2S/\Delta t + O$. Pre-computing $\Phi$ as a function of elevation converts the routing problem into a simple table lookup at every time step:

1. Evaluate the right-hand side from known quantities at time step $n$.
2. Look up the resulting $\Phi$ value on the pre-computed $\Phi(h)$ curve to obtain $h_2$.
3. Interpolate $S_2$ from the stage-storage curve at $h_2$, and $O_2$ from the stage-discharge curve at $h_2$.
4. Record and advance to the next step.

Why the storage-indication transformation matters

Without the transformation, each time step would require an iterative solution of a non-linear equation (because outflow is a non-linear function of storage through the stage-discharge curve). The $\Phi$ substitution makes every step a single lookup, producing a fast, stable, and non-iterative algorithm. This is why the method is sometimes simply called “the storage-indication method.”

The modified-Puls method assumes a horizontal water surface in the basin (the “level-pool” assumption). This is accurate when the basin is short relative to the wavelength of the routed hydrograph — the usual case for detention basins, small ponds, and compact reservoirs. For long, narrow reservoirs where the water surface slopes significantly during the passage of a flood, more elaborate dynamic routing is required.

Basin geometry and storage

The first half of the routing problem is describing how the basin stores water — the relationship between water surface elevation and the volume contained below it. This is the stage-storage curve $S(h)$.

Basin definition methods

The tool accepts the storage-elevation relationship in three equivalent forms, selected according to the data available.

Method	Input	Best for
Known geometry	Shape, length/width or diameter, depth, side slope	Preliminary design of new basins; parametric studies
Known volume	Elevation-volume table (≥3 rows)	Existing basins from survey; irregular shapes
Known area	Elevation-area table (≥3 rows)	Working from contour plans; footprint-driven design

For the known-area method, the stage-storage curve is derived by integrating the area curve using the trapezoidal rule:

$$S(h_i) \;=\; S(h_{i-1}) \;+\; \frac{A(h_i) + A(h_{i-1})}{2} \cdot (h_i - h_{i-1})$$

Integrating an elevation-area table to produce cumulative storage

Basin shapes

Three regular shapes are available when using the known-geometry method. Each has a closed-form expression for the plan area at depth $h$ above the basin floor:

Shape	Plan area at depth h	Notes
Rectangular	$(L + 2zh)(W + 2zh)$	Simplest; use $z = 0$ for vertical walls (concrete vaults)
Trapezoidal	$(L + 2zh)(W + 2zh)$	Same formula, typically with $z > 0$; standard earthen basin shape
Circular	$\pi (D/2 + zh)^2$	Round basins or tanks; defined by base diameter $D$

Where $L$ is the base length, $W$ the base width, $D$ the base diameter, $z$ the side slope as H:V (e.g. $z = 3$ means 3H:1V), and $h$ the depth above the base elevation.

Known geometry inputs

The known-geometry method requires the following site-measured inputs:

• Length (m): Base length of the basin floor, measured at the lowest elevation along the longer axis.
• Width (m): Base width of the basin floor, measured at the lowest elevation along the shorter axis.
• Depth (m): Maximum depth from the basin floor to the embankment crest.
• Side slope (H:V): The horizontal-to-vertical ratio of the banks (see side slopes below).
• Base elevation (m): The elevation of the basin floor above a chosen datum.

The tool integrates the cross-sectional area from the base upward in small elevation increments to build the stage-storage curve automatically. Changing any parameter re-computes the curve instantly.

Known volume inputs

The known-volume method accepts an elevation-volume table directly. Typical sources:

• Topographic survey: Contour-based volume computation from a total station or LiDAR survey.
• DEM analysis: Volume-by-elevation extraction from a LiDAR-derived or photogrammetric DEM using GIS.
• CAD grading plans: Volumes computed by a civil design package from a TIN or grid surface.
• As-built records: Historic basin volume curves from municipal or consulting archives.

Enter at least 3 rows, starting with volume = 0 at the basin floor, with volumes monotonically increasing with elevation.

Survey-based curves are preferred for submissions

Many South African municipalities require the stage-storage curve in a stormwater submission to be derived from actual site survey data rather than from idealised geometry. The known-volume input mode is the appropriate choice in that case.

Known area inputs

The known-area method accepts an elevation-area table. The tool integrates it with the trapezoidal rule to produce the storage curve. This is often the most natural input when working from contour plans, because each contour line directly defines a plan area at its elevation.

Side slopes

The side slope is expressed as a horizontal-to-vertical ratio (H:V). Common values and their implications:

Slope (H:V)	Angle	Typical use
0	90° (vertical)	Concrete or masonry walls; underground vaults
1	45°	Lined or gabion-reinforced slopes
2	26.6°	Steep earthen cut slopes in competent soil
3	18.4°	Standard earthen embankment; mowable with equipment
4 – 5	14° – 11°	Gentle slopes for public parks and landscaped basins

Public safety and maintenance

Slopes steeper than 3H:1V can be hazardous for public access and difficult to maintain with standard mowing equipment. Many South African municipalities require a minimum of 4H:1V for publicly accessible detention basins. Always confirm local by-laws before finalising a geometry.

Base elevation and datum

The base elevation is the elevation of the basin floor above the chosen vertical datum — typically metres above mean sea level (mAMSL), or a local site benchmark. All elevations in the model must use the same datum. This includes weir crests, orifice inverts, riser tops, and the initial water level. A datum mismatch between the basin and any outlet is one of the most common and catastrophic sources of error in routing analyses — it produces plausible-looking but quantitatively meaningless results.

Stage-storage curve

The stage-storage curve $S(h)$ is the fundamental storage input to the routing engine. Regardless of which input method you use, the tool reduces everything to a single tabulated $S(h)$ curve that is then interpolated during the routing. The curve should be:

• Monotonically increasing — storage must grow with elevation.
• Smooth — abrupt steps cause numerical artefacts in the outflow hydrograph.
• Cover the full routing range — extend the curve to at least the expected maximum water surface elevation, with margin for extreme events.

Stage-storage table

The stage-storage table is the same data as the curve above, expressed as a tabulated list of (elevation, storage) rows. The tool accepts either form interchangeably. In the known-volume mode the table is the primary input; in other modes it is a derived output that can be exported for reporting.

Initial water surface elevation

The initial water surface elevation (initial WSEL) is the starting condition for the routing. For a dry basin this equals the base elevation (the basin begins empty). For a wet basin with a permanent pool, it equals the permanent pool elevation, and the outlet structures should be configured so that no discharge occurs below this level (weir crests at or above the pool). For existing basins with residual storage from a previous event, set the WSEL to the observed or assumed starting level.

Inflow hydrograph

The second input to the routing engine is the inflow hydrograph — the time-discharge record of water entering the basin.

Inflow definition modes

The tool accepts two equivalent forms:

• Constant inflow: A flat-topped rectangular hydrograph at a given discharge for a given duration, dropping to zero afterwards. Total volume = discharge × duration. Useful for pump inflows, industrial discharges, and conservative preliminary sizing.
• Hydrograph inflow: A time-discharge table representing a realistic storm hydrograph with rising limb, peak, and recession. This is the recommended approach for final design.

Constant inflow

A constant inflow is the simplest possible input. Specify the discharge (m³/s) and duration (min); the tool generates a rectangular pulse. Because a rectangular pulse delivers more total volume than a triangular pulse with the same peak and duration, constant inflows produce conservative (larger) storage requirements — appropriate for a rough initial estimate before the full design hydrograph is available.

Inflow hydrograph table

The inflow hydrograph is a series of time-discharge pairs:

• Start at time = 0 with discharge = 0 (or a baseflow value).
• Time values in minutes, strictly increasing.
• Discharge values in m³/s, non-negative.
• Include enough points near the peak to define it accurately — at least one point within a few minutes of the peak.
• End the hydrograph after discharge has returned to zero (or negligible baseflow).

Where to get a design hydrograph

Use the Hydrograph Generator to build a design hydrograph from an SCS unit hydrograph, DRH (dimensionless regional hydrograph), or SCS triangular method, seeded by your catchment parameters and a design storm hyetograph. Export the time-discharge pairs and paste them into the inflow table.

Peak inflow and volume

The peak inflow ($Q_{p,in}$) is the maximum ordinate of the inflow hydrograph. Along with the inflow volume (the time-integral of the hydrograph), it characterises the storm event driving the routing. Design hydrographs for different return periods will differ in both peak and volume, and the basin must be checked against each — see the guidance on checking multiple return periods below.

Inflow volume

The total inflow volume is computed by trapezoidal integration of the inflow hydrograph. It sets the upper bound on the volume the basin could theoretically retain if the outlet were closed. In a well-designed basin, the peak storage used during routing is a fraction of the total inflow volume — typically 20 – 60 % for common detention designs.

Outflow structures

The third input to the routing engine is the stage-discharge relationship $O(h)$ — how the outlet works convey water out of the basin as a function of water surface elevation. In all but the simplest cases this is a composite rating, built up from the individual contributions of multiple outlet components (orifices, weirs, standpipes, culverts, spillways) operating in parallel.

Composite outflow

The tool supports any number of outlet structures. At each elevation, the total outflow is the sum of all active structures:

$$O(h) \;=\; \sum_{i=1}^{n} O_i(h)$$

Composite outflow — sum of contributions from each structure

Each structure is active only when the water surface is above its activation elevation (weir crest, orifice invert, riser top, etc.). Common composite configurations:

• Low-flow orifice + emergency spillway weir: orifice controls frequent small storms; spillway handles rare extreme events.
• Multiple weirs at different crest elevations: staged flow control with progressively wider release rates.
• Standpipe + overflow weir: redundancy and controlled overtopping.
• Primary outlet culvert + auxiliary broad-crested weir: typical small-dam configuration.

Outflow hydrograph

The outflow hydrograph is the primary result of the routing — the time series of total discharge leaving the basin, obtained at every routing step from the composite rating curve evaluated at the current water surface elevation. Its peak, timing, and volume are the key design metrics.

Known discharge curve

For complex outlet works where the theoretical equations don’t capture all effects (multi-stage risers with trash screens, proprietary vortex outlets, CFD-modelled combined structures), enter the rating directly as a head-discharge table. The tool interpolates linearly between points. The datum elevation defines where head = 0: at any water surface elevation, head = (water level − datum elevation). If head is negative or zero, no flow occurs through this structure.

Weirs

A weir is an overflow structure over which water spills when the water surface rises above the crest. The discharge depends on the head above the crest (the height of the water surface above the crest), the crest length or notch angle, and a discharge coefficient that accounts for energy losses and the shape of the nappe (the jet of water leaving the crest).

Weirs as detention basin outlets

Weirs are the most common outlet type for detention basin primary and emergency discharge. Key inputs when adding a weir to the tool:

• Weir type — sharp-crested rectangular, V-notch, broad-crested, or Cipolletti (see the sections below).
• Crest elevation (m) — the elevation at which the weir activates; must use the same datum as the basin.
• Width (m) or notch angle (°) — the opening dimension.
• Discharge coefficient $C_d$ — default values per weir type are pre-filled, overridable with calibrated data.

The crest elevation, combined with the basin base elevation, determines the active range of the weir: no flow passes until the water level exceeds the crest, and discharge increases with the head above the crest.

Weir crest

The weir crest is the horizontal edge over which water flows. The crest elevation determines when the weir activates — no flow passes until the water level exceeds this elevation. The crest must be set using the same vertical datum as the basin base elevation. The crest length (for rectangular or broad-crested weirs) is the horizontal dimension of the opening perpendicular to the flow.

Weir height and approach

The weir height is the distance from the upstream bed of the approach channel to the crest. Most sharp-crested rectangular weir formulas assume that the approach depth is significantly larger than the head, so that the velocity of approach is negligible. When the weir is low relative to the head (low height-to-head ratio), a velocity-of-approach correction may be required — the standard tool uses a simplified formulation suitable for basin outlets where the approach velocity is typically small.

Weir shape and type

Four weir shapes are supported. The choice depends on the outlet’s hydraulic function: low-flow sensitivity, spillway duty, or general overflow control.

Weir type	Equation form	Typical application
Sharp-crested rectangular	$Q = C_d \, L \, H^{3/2}$	Most common detention basin outlet
V-notch (triangular)	$Q = C_d \cdot \tfrac{8}{15} \tan(\theta/2) \sqrt{2g} \, H^{5/2}$	Low-flow control; flow measurement
Broad-crested	$Q = C_d \, L \, H^{3/2}$	Spillways; roadway overtopping
Cipolletti (trapezoidal)	$Q = C_d \, L \, H^{3/2}$	Flow measurement; end-contraction-free

Sharp-crested rectangular weir

The most common weir type for detention basin outlets. A thin plate (the weir blade) with a sharp upstream edge produces a well-defined nappe. The discharge equation takes the standard form:

$$Q \;=\; C_d \cdot L \cdot H^{3/2}$$

Sharp-crested rectangular weir — metric

Where $Q$ is discharge (m³/s), $C_d$ is the discharge coefficient (typically 1.84 in metric), $L$ is the crest length (m), and $H$ is the head above the crest (m). For rectangular weirs with significant end contractions, the effective length should be reduced as $L_\text{eff} = L - 0.1 n H$ where $n$ is the number of end contractions (0, 1, or 2).

V-notch (triangular) weir

A V-notch weir has a triangular opening that is highly sensitive to small flows, making it ideal for low-flow control or flow measurement:

$$Q \;=\; C_d \cdot \tfrac{8}{15} \cdot \tan\!\left(\tfrac{\theta}{2}\right) \cdot \sqrt{2g} \cdot H^{5/2}$$

V-notch weir

Where $\theta$ is the notch angle (typically 90°) and $g = 9.81$ m/s². For a 90° V-notch with $C_d = 0.58$, the formula reduces to approximately $Q \approx 1.38 \, H^{5/2}$.

Broad-crested weir

A broad-crested weir has a horizontal crest that is long enough (in the flow direction) for critical flow to develop on the crest. Used extensively for spillways and roadway overtopping:

$$Q \;=\; C_d \cdot L \cdot H^{3/2}$$

Broad-crested weir

Same form as the sharp-crested weir but with a lower discharge coefficient (typically $C_d \approx 1.705$ metric) to reflect the additional energy loss as flow transitions across the crest.

Ogee weir

An ogee weir has a curved crest profile shaped to approximate the lower surface of the nappe that would form over a sharp-crested weir at the design head. Ogee crests are the standard for concrete gravity-dam spillways because they maximise discharge capacity while minimising negative pressures on the crest surface. The discharge equation has the same $Q = C L H^{3/2}$ form, with design-head coefficients in the range $C \approx 2.0 – 2.2$ (metric) — higher than broad-crested because the nappe-matched profile is hydraulically more efficient.

Labyrinth weir

A labyrinth weir is a trapezoidal or triangular weir crest folded in plan to increase the effective crest length within a given channel width. The discharge is expressed using an equivalent crest length with an efficiency factor that depends on the vertical aspect ratio and side-wall angle. Labyrinth weirs are used where channel width is constrained but high spillway capacity is required.

Cipolletti (trapezoidal) weir

A Cipolletti weir has a trapezoidal cross-section with side slopes of 1H:4V (approx. 14° from vertical). The slanted sides compensate geometrically for the end-contraction loss of a rectangular weir, so no end-contraction correction is needed:

$$Q \;=\; C_d \cdot L \cdot H^{3/2}$$

Cipolletti weir

Typical $C_d \approx 1.86$ (metric). $L$ is the bottom width of the trapezoidal notch.

Weir discharge coefficient

The discharge coefficient $C_d$ collects together the loss of energy as flow contracts, accelerates, and spills over the crest. Values are tabulated below. Override the default only with calibrated data from a physical model, a CFD study, or site-measured rating.

Weir discharge coefficients — reference table

Weir type	Default $C_d$ (metric)	Typical range	Source
Sharp-crested rectangular	1.84	1.77 – 1.90	Francis; USBR
V-notch (90°)	1.38 ($C_e = 0.58$)	1.34 – 1.44	Kindsvater–Shen
V-notch (60°)	0.80 ($C_e = 0.58$)	0.76 – 0.83	Kindsvater–Shen
Broad-crested	1.705	1.44 – 1.80	Henderson; SCS
Ogee (design head)	2.10	2.00 – 2.21	USBR (design head)
Cipolletti (1H:4V sides)	1.86	1.82 – 1.90	Addison
Labyrinth (single cycle)	1.50 – 1.80 (effective)	design-specific	Lux & Hinchliff; Falvey

Submergence reduces discharge

These coefficients all assume free discharge (the nappe is vented to atmosphere downstream of the crest). If tailwater rises high enough to drown the nappe, discharge is reduced by a submergence factor that depends on the ratio $h_2/h_1$ (downstream head over upstream head). For a submergence ratio above 0.66, the Villemonte correction $Q_s / Q_f = \left[ 1 - (h_2 / h_1)^{n} \right]^{0.385}$ (with $n = 1.5$ for rectangular, 2.5 for V-notch) gives a reasonable estimate. Basin outlets are usually free-discharging, but confirm this for your site.

Orifices and standpipes

Orifice discharge

An orifice is a submerged opening through which flow is driven by the head of water above the opening. The fundamental orifice equation is:

$$Q \;=\; C_d \cdot A \cdot \sqrt{2 g H}$$

Submerged orifice discharge — head-driven flow through a small opening

Where $A$ is the area of the opening (m²), $H$ is the head above the centre of the orifice (m), $g = 9.81$ m/s², and $C_d$ is the orifice discharge coefficient, which bundles together the contraction and friction losses. Typical values:

Orifice type	$C_d$	Notes
Sharp-edged circular (thin plate)	0.60 – 0.62	Standard for thin-plate orifices
Rounded / bellmouth entry	0.95 – 0.98	Very low contraction loss
Short tube (length ≈ 2 – 3 diameters)	0.80	Flow attaches to tube wall
Square-edge (plate thickness comparable to diameter)	0.62	Typical reinforced-concrete pipe invert
Bevelled / chamfered edge	0.65 – 0.75	Intermediate between sharp and rounded

When the head drops below the top of the orifice, flow transitions from orifice (submerged) to weir (unsubmerged) behaviour. The tool handles this transition by taking the lesser of the orifice and weir discharges at each elevation, ensuring a smooth rating curve.

Standpipe / riser

A standpipe (or riser) is a vertical pipe with an open top and a low-level orifice at its base. It operates in two flow regimes:

• Orifice control (low head): Water enters through the base orifice. Discharge follows the orifice equation, driven by the head above the orifice invert.
• Weir control (high head): When the water surface exceeds the riser crest elevation, flow overtops the rim of the pipe. Discharge follows a circular-weir equation based on the riser internal circumference $L = \pi D$.

At any given water surface elevation, the controlling regime is the one that produces the lesser discharge — because the other regime acts as a bottleneck in series with the controlling one.

Parameter	Description	Typical range
Riser diameter	Internal diameter of the vertical pipe	0.3 – 1.5 m
Riser crest elevation	Top of the riser (weir activation)	Site-specific
Orifice diameter	Low-level opening at the base	0.1 – 0.6 m
Orifice elevation	Invert of the base orifice	At or near basin floor
Orifice $C_d$	Discharge coefficient for the orifice	0.60 – 0.65

Multi-stage control with a standpipe

A standpipe/riser is ideal for multi-stage outlet control: the small base orifice restricts flow for frequent small storms (providing water-quality treatment time), while the riser crest provides additional capacity for larger events. This is a common configuration in South African municipal stormwater detention basins.

Culvert outlets

Many detention basins discharge through a culvert — a pipe or box that conveys flow through the embankment. The culvert itself can be the principal outlet or can follow a standpipe/weir assembly. Culvert hydraulics is a specialised topic: the culvert can operate under inlet control (capacity limited by the entrance) or outlet control (capacity limited by friction, length, and tailwater). The controlling regime determines the stage-discharge rating.

For a full treatment of culvert inlet and outlet control, see the Culvert Designer guide — it covers the FHWA HDS-5 methodology, inlet loss coefficients, tailwater effects, and full performance-curve generation. For flood-routing purposes, a culvert’s stage-discharge rating can be pre-computed in the Culvert Designer and imported into the Flood Routing tool via the known-discharge-curve input.

Auxiliary (emergency) spillway

Every detention basin and small dam should include an emergency spillway — a broad-crested weir, chute, or secondary outlet set at a safe freeboard below the embankment crest. Its purpose is to safely pass flows that exceed the capacity of the principal outlet, including events larger than the design storm. The spillway must be:

• Wide enough to pass the design overflow (commonly the difference between the 1:100-year inflow peak and the principal-outlet capacity at the spillway crest).
• Constructed in erosion-resistant material (concrete, riprap, or vegetated to a high standard).
• At a crest elevation that provides a freeboard of at least 0.3 – 0.6 m below the embankment crest for small earthen dams.

Model the spillway as a broad-crested weir in the outflow structures list, with its crest elevation above the principal outlet’s design pool.

Routing settings

The routing engine has two primary numerical controls: the time step $\Delta t$, and the simulation duration.

Time step

The time step controls the resolution of the routing computation. A smaller time step produces more accurate results at marginal computational cost. Guidelines:

• The time step should be small enough to capture the inflow peak — generally less than or equal to 0.25 × the rising-limb duration (time from hydrograph start to peak).
• For a 60-minute hydrograph with a 20-minute rising limb, a 1 – 5 minute time step is typical.
• If results appear jagged or the peak seems clipped, reduce the time step.
• If the computed total outflow volume differs from the total inflow volume by more than 1 – 2 %, the time step is too coarse.

Auto time step

Enable the auto time step toggle to have the tool suggest an appropriate value based on the inflow hydrograph duration. The default heuristic uses approximately 1/50 of the hydrograph duration, bounded to reasonable limits (typically 0.1 – 5 minutes). For most detention basin problems this gives sub-percent mass-balance error.

Simulation duration

The simulation duration is the total length of the routing run. It must be long enough for:

1. The entire inflow hydrograph to be passed through the basin.
2. The basin to drain back down to the initial water level (or near-zero outflow).

A common rule is to run the simulation for at least 2 × the inflow hydrograph duration, or longer for basins with small outlets that take a long time to drain. If the recession tail of the outflow hydrograph is still elevated at the end of the simulation, extend the duration.

Initial conditions

The initial conditions comprise the initial water surface elevation (covered above) and the initial storage (derived automatically from the initial WSEL via the stage-storage curve). For dry basins, initial WSEL = base elevation; for wet basins, initial WSEL = permanent pool elevation.

Boundary conditions

The tool routes the basin as a closed system — inflow at one end, outflow at the other, with no lateral losses or gains. Evaporation, seepage, and lateral inflow are neglected (they are negligible over the timescale of a single flood event). If baseflow is significant, include it as a constant additive term in the inflow hydrograph.

Auto-sizing

The auto-size feature iteratively adjusts the basin volume to achieve a specified target peak outflow. It solves the inverse problem: given an inflow hydrograph, an outlet configuration, and a target peak release rate, what basin size is required?

Algorithm

The tool uses bisection search on a scale factor applied to the basin volume:

1. Initialise a scale-factor range (e.g. 0.1× to 10× the current geometry).
2. For each trial scale factor, scale the basin and run the full routing.
3. Compare the resulting peak outflow to the target.
4. Narrow the range by bisecting (higher scale factor if peak outflow > target, lower if peak outflow < target).
5. Iterate until convergence — typically 15 – 30 iterations, each taking a few milliseconds.

The result reports the required basin volume, the scale factor relative to the current geometry, and the required depth (for known-geometry basins). Auto-sizing is currently only available for the modified-Puls routing method and requires at least one outflow structure.

Setting a target

Choose the target peak outflow based on the design requirement:

• Pre-development peak flow: The traditional attenuation target — post-development peak must not exceed the pre-development peak for the same return period. Compute pre-development flows with the Rational Method, SCS Method, or Unit Hydrograph.
• Downstream capacity limit: The maximum flow the receiving drain, pipe, culvert, or channel can convey without surcharge or erosion.
• Municipal release-rate specification: Many South African municipalities specify a maximum allowable release rate in litres per second per hectare (L/s/ha) of catchment.

Auto-sizing is for a single return period

Auto-sizing optimises for one inflow hydrograph and one target outflow. A basin sized for the 1:50-year event may not provide adequate attenuation for the 1:5-year event (because the outlet may be sized too large for small storms) — or vice versa. Always check the auto-sized basin against all relevant return periods before finalising the design. The critical sizing storm is often not the largest event.

Interpreting results

The tool produces six summary metrics, an inflow-vs-outflow hydrograph plot, a storage-curve plot, a stage-discharge plot, and — for known-geometry basins — a cross-section and plan-view drawing.

Peak inflow

The peak inflow $Q_{p,in}$ is the maximum ordinate of the input hydrograph. It is reported with the time at which it occurs. This number confirms that the input hydrograph has been interpreted correctly — check it against the hydrograph you designed.

Peak outflow

The peak outflow $Q_{p,out}$ is the maximum ordinate of the routed outflow hydrograph. It is the primary design output and the quantity that must satisfy the attenuation target (pre-development peak, downstream capacity, or municipal release rate).

Attenuation

The peak attenuation is the percentage reduction from peak inflow to peak outflow:

$$\text{Attenuation} \;=\; \frac{Q_{p,in} - Q_{p,out}}{Q_{p,in}} \times 100\%$$

Peak attenuation — the primary design metric

A well-designed basin typically produces 30 – 70 % attenuation. Higher values are possible but require disproportionately more storage; lower values may indicate an oversized outlet or an undersized basin.

Peak reduction

Alternative name for the attenuation percentage. Used interchangeably — the tool reports both the percentage (attenuation %) and the absolute flow reduction ($Q_{p,in} - Q_{p,out}$, in m³/s).

Lag time

The lag time is the interval between the time of peak inflow and the time of peak outflow. It is always positive: the outflow peak occurs after the inflow peak because storage must first accumulate. Typical lag times for small detention basins are 10 – 40 minutes. A very small lag time (< 5 min) indicates either a very large outlet relative to the basin or a very small basin relative to the storm.

Maximum water surface elevation

The maximum water surface elevation (max WSEL) is the highest water level reached during the routing. It must be checked against:

• The emergency spillway crest — max WSEL should be below it for the design event.
• The embankment crest — max WSEL must be below it with a freeboard margin for extreme events.
• The surrounding property elevations — max WSEL should not inundate adjacent land beyond the basin footprint.

Maximum storage

The maximum storage is the peak stored volume during the routing — the volume contained below the max WSEL. It is a useful sizing metric and corresponds to the “utilised” basin volume for this event. The ratio of max storage to total basin volume indicates how much of the basin was mobilised.

Outflow volume and volume conservation

The total outflow volume is the time-integral of the outflow hydrograph. For mass conservation, the total inflow and outflow volumes should match (both equal to the area under their respective hydrographs), provided:

• The basin begins and ends at the same water level.
• The simulation runs long enough for all stored water to be released.
• The time step is small enough for the routing to be accurate.

Volume-balance sanity check

If the total inflow and outflow volumes differ by more than 1 – 2 %, investigate. Either the time step is too coarse, the simulation stopped before the basin fully drained, or there is a datum mismatch somewhere in the model. A volume-balance check should be part of every routing QA routine.

Hydrograph chart

The hydrograph chart plots inflow (blue) and outflow (orange/red) on the same time axis. The area between the curves during the rising limb represents water accumulating in storage; the area during the falling limb represents stored water being released. By mass conservation, the two areas are equal. Look for:

• A clear, smooth peak on the outflow curve (jagged peaks indicate too coarse a time step).
• Outflow peak occurring after the inflow peak (lag time > 0).
• Outflow returning to zero (or baseflow) before the end of the simulation.

Storage curve

The stage-storage curve used in the routing is plotted for reference. Confirm that the curve is smooth and monotonically increasing. A mark typically indicates the max storage / max WSEL reached during the event.

Basin drawing

For known-geometry basins, the tool renders a cross-section (showing side slopes, base elevation, and max WSEL) and a plan view with elevation contours. Useful for sanity-checking the geometry before committing to a detailed design.

Worked example

The following example illustrates the full workflow: problem statement, basin and outlet definition, initial routing, iteration, auto-sizing, and verification.

Given information

• Site: 5 ha residential development, Johannesburg suburb
• Pre-development 1:50-year peak flow: 1.5 m³/s (from Rational Method on pre-dev catchment)
• Post-development 1:50-year inflow hydrograph: SCS unit hydrograph
  • Peak: $Q_{p,in} = 10.0$ m³/s
  • Time to peak: 30 min
  • Hydrograph duration: 180 min
  • Total volume: approximately 54 000 m³
• Target peak outflow: 1.5 m³/s (the pre-development peak)
• Available footprint: approx. 60 m × 40 m
• Datum: basin floor at 1580.0 mAMSL

Step 1 — Define an initial basin geometry

Start with a trapezoidal basin at 40 m × 25 m × 2.5 m deep with 3H:1V side slopes. Quick volume estimate at full depth:

$$\begin{aligned} A_\text{top} &= (40 + 2 \times 3 \times 2.5)(25 + 2 \times 3 \times 2.5) = 55 \times 40 = 2200 \ \text{m}^2 \\ A_\text{base} &= 40 \times 25 = 1000 \ \text{m}^2 \\ V_\text{max} &\approx \tfrac{1}{3} \cdot 2.5 \cdot (2200 + 1000 + \sqrt{2200 \times 1000}) \approx 3900 \ \text{m}^3 \end{aligned}$$

Step 2 — Define the outlet

A sharp-crested rectangular weir at crest elevation 1581.0 m (1.0 m above the basin floor), width 1.0 m, default $C_d = 1.84$:

$$Q_\text{weir}(H) \;=\; 1.84 \cdot 1.0 \cdot H^{3/2}$$

At $H = 1.5$ m (water at 1582.5 m), $Q = 1.84 \cdot 1.5^{1.5} = 3.38$ m³/s.

Step 3 — Run the routing

With the initial geometry and outlet, the modified-Puls routing yields:

Metric	Value
Peak inflow	10.0 m³/s
Peak outflow	3.05 m³/s
Attenuation	69.5 %
Lag time	18 min
Max WSEL	1582.35 m
Max storage	2 650 m³

Peak outflow = 3.05 m³/s exceeds the target of 1.5 m³/s. The basin needs to be larger, or the weir narrower, or both.

Step 4 — Auto-size to target = 1.5 m³/s

Run auto-size with target = 1.5 m³/s. The bisection converges at a scale factor of 1.62 after 18 iterations, requiring a basin volume of approximately 6 300 m³. Scaling the original 40 × 25 × 2.5 m basin by that factor (scaling length and width proportionally) yields roughly 51 m × 32 m × 2.5 m.

Step 5 — Round to practical dimensions and re-verify

Round up to 52 m × 32 m × 2.5 m (still 3H:1V side slopes). Re-run the routing:

Metric	Value
Peak inflow	10.0 m³/s
Peak outflow	1.48 m³/s
Attenuation	85.2 %
Lag time	34 min
Max WSEL	1581.90 m
Max storage	6 100 m³
Volume balance error	0.3 %

The target is met ($Q_{p,out} = 1.48 < 1.5$ m³/s).

Step 6 — Add an emergency spillway

Add a broad-crested weir at crest elevation 1582.2 m (0.3 m above the design max WSEL, 0.3 m below the embankment crest at 1582.5 m), width 3.0 m, $C_d = 1.705$. Re-run for the 1:100-year inflow (say $Q_{p,in} = 13$ m³/s, slightly larger hydrograph):

Metric	Value
Max WSEL (1:100)	1582.40 m
Freeboard to crest	0.10 m

The freeboard is adequate; the spillway passes the 1:100-year event safely.

Step 7 — Check smaller return periods

Re-run for the 1:5-year inflow ($Q_{p,in} = 4.5$ m³/s, peak 3.5 m³/s outflow target). The result: $Q_{p,out} = 1.32$ m³/s — well below the 1:5-year pre-development peak of 3.5 m³/s. The design is acceptable across all return periods.

Iterating for practicality

After auto-sizing, always round dimensions up to practical values (whole metres, or whatever increment matches construction tolerances) and re-verify. The auto-sizer gives the minimum required size; the built basin should be slightly larger for safety and practicality.

Common mistakes

The failure modes below crop up repeatedly in detention-basin design reviews. Screen for each before signing off a routing.

• Datum mismatch between basin and outlets. Using one datum for the basin base elevation and a different one for weir crests or orifice inverts. Results look plausible but are quantitatively meaningless. All elevations must be on the same datum.
• Outlet crest below the basin floor. A weir crest or orifice invert set below the basin base elevation produces discharge at zero storage — the basin never fills and the “attenuation” is zero. Always ensure outlets activate at or above the base.
• Time step too coarse. A time step that is a large fraction of the rising-limb duration clips the peak and overestimates attenuation. Use $\Delta t \le 0.25 \times t_p$ as a starting point and check the volume balance.
• Simulation too short. Ending the routing before the basin has fully drained leaves storage unaccounted for, producing an inflow-outflow volume mismatch. Extend the duration until the outflow hydrograph returns to zero.
• Sizing for only one return period. Optimising for the 1:50-year event alone without checking 1:2, 1:5, 1:10, and 1:100. A small-storm release rate that exceeds the pre-development peak can be a compliance failure even if the large-storm target is met.
• No emergency spillway. A basin without an auxiliary spillway will overtop uncontrollably when the design event is exceeded — potentially failing the embankment. Always include a spillway at a crest above the design max WSEL and below the embankment crest.
• Ignoring sediment accumulation. The usable storage in a detention basin shrinks over its lifetime as sediment settles. Include a sediment storage allowance (typically 10 – 20 % of total volume) and a regular desilting programme.
• Trash screens not modelled. Trash screens on orifice outlets reduce the effective flow area. If significant, reduce the orifice $C_d$ by 10 – 20 % or model the screen explicitly via a known-discharge curve.
• Submerged weir not corrected. If downstream tailwater rises high enough to drown the weir nappe, the discharge is reduced. The tool assumes free discharge — apply a Villemonte correction to $C_d$ if needed.

Limitations

The modified-Puls implementation in this tool has specific limitations:

• Level pool assumption. The water surface is assumed horizontal at all times. This is accurate for detention basins and compact ponds but becomes inaccurate for long, narrow reservoirs where significant water-surface sloping occurs during flood passage.
• No submergence correction. Weir discharge equations assume free-flow conditions; submergence from high tailwater is not automatically corrected. Users must account for this externally if it applies.
• No culvert inlet/outlet control coupling. Culvert outlets must be pre-rated in the Culvert Designer and imported as known-discharge curves. The routing tool does not iterate on culvert control-type switching.
• Single reservoir. The tool routes a single storage element. Multi-reservoir systems (cascades, parallel basins) must be decomposed into sequential routings.
• No baseflow or seepage. Evaporation, groundwater seepage, and slow release through the embankment are neglected. They are insignificant over the timescale of a single flood event but can matter for multi-day wet-basin water-balance studies.
• No dynamic dam-break modelling. This tool cannot simulate embankment failure or breach-outflow hydrographs. For dam-safety analyses requiring breach modelling, use the Dam Safety Evaluation tool.

Related tools

• Hydrograph Generator — produce design inflow hydrographs via SCS unit hydrograph, DRH, or SCS triangular methods.
• Design Storm — generate hyetographs to drive hydrograph computation.
• Weir Analysis — stand-alone weir rating for weir structures outside of a routing context.
• Culvert Designer — FHWA HDS-5 culvert analysis; produces stage-discharge ratings importable here as known-discharge curves.
• Dam Safety Evaluation — spillway adequacy and breach modelling for small dams, complementary to the routing here.
• Rational Method, SCS Method, Unit Hydrograph — peak flow and hydrograph estimation methods to seed the inflow.

Glossary

Term	Definition
Attenuation	Reduction of peak discharge as a hydrograph passes through a storage element.
Continuity equation	Mass balance: inflow − outflow = rate of storage change ($I - O = dS/dt$).
Detention basin	Storage facility that temporarily retains stormwater and releases it at a controlled rate.
Discharge coefficient	Dimensionless factor representing energy losses and flow contraction at a weir or orifice.
Dry basin	Detention basin that is normally empty and fills only during events.
Emergency spillway	Secondary overflow structure at the embankment crest that safely passes flows exceeding the principal outlet’s capacity.
Freeboard	Vertical margin between the maximum water surface elevation and the top of the embankment.
Hydrograph	Time series of discharge at a point.
Lag time	Time interval between peak inflow and peak outflow.
Level-pool routing	Reservoir routing under the assumption that the water surface within the reservoir is horizontal at all times.
Modified-Puls	Level-pool routing method that uses a storage-indication curve to solve the continuity equation non-iteratively at each step.
Orifice	Submerged opening; discharge proportional to the square root of the head ($Q \propto \sqrt{H}$).
Peak attenuation	Percentage reduction in peak flow: $(Q_{p,in} - Q_{p,out}) / Q_{p,in}$.
Riser / standpipe	Vertical pipe outlet that acts as an orifice at low head and a circular weir when overtopped.
Stage-discharge curve	Relationship between water surface elevation and total outflow ($O(h)$).
Stage-storage curve	Relationship between water surface elevation and stored volume ($S(h)$).
Storage-indication	The modified-Puls substitution variable $\Phi = 2S/\Delta t + O$; makes the routing step a single table lookup.
Submergence	Condition where downstream tailwater drowns a weir nappe, reducing discharge below the free-flow value.
Weir	Overflow structure; discharge is a function of head above the crest raised to the power 3/2 (rectangular) or 5/2 (V-notch).
Wet basin	Detention basin with a permanent pool; provides water-quality treatment benefits.

References

• USACE. (1997). Hydrologic Engineering Requirements for Reservoirs (Engineer Manual EM 1110-2-1420). U.S. Army Corps of Engineers, Hydrologic Engineering Center, Davis, CA. (Authoritative reference for level-pool routing of flood hydrographs through reservoirs.)
• Chow, V.T., Maidment, D.R. & Mays, L.W. (1988). Applied Hydrology. McGraw-Hill, New York. Chapter 8 — Hydrologic Routing. (Classic textbook treatment of the modified-Puls / storage-indication method.)
• Viessman, W. & Lewis, G.L. (2003). Introduction to Hydrology (5th ed.). Prentice Hall, Upper Saddle River, NJ. Chapters on reservoir routing and stormwater storage design.
• ASCE. (1992). Design and Construction of Urban Stormwater Management Systems (Manuals and Reports of Engineering Practice No. 77). American Society of Civil Engineers, New York. (ASCE MOP 77 — comprehensive reference for detention-basin design in urban settings.)
• FHWA. (2012). Hydraulic Design of Highway Culverts (Hydraulic Design Series No. 5, 3rd ed., Publication No. FHWA-HIF-12-026). Federal Highway Administration, U.S. Department of Transportation, Washington, D.C. (HDS-5 — referenced for culvert outlet rating curves used as known-discharge inputs.)
• USBR. (1987). Design of Small Dams (3rd ed.). United States Bureau of Reclamation, Denver, CO. (Spillway and outlet-works design, including ogee and broad-crested weir coefficients.)
• Brater, E.F., King, H.W., Lindell, J.E. & Wei, C.Y. (1996). Handbook of Hydraulics (7th ed.). McGraw-Hill, New York. (Comprehensive tables of weir and orifice discharge coefficients.)
• SANRAL. (2013). Drainage Manual (6th ed.). South African National Roads Agency, Pretoria. Chapter 7 — Hydraulic design of culverts and bridges; Chapter 8 — Attenuation and detention.
• Falvey, H.T. (2003). Hydraulic Design of Labyrinth Weirs. ASCE Press, Reston, VA.
• Villemonte, J.R. (1947). Submerged-weir discharge studies. Engineering News-Record, 139, 866 – 869. (Original reference for the submergence correction cited in the weir section.)

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Open Flood Routing