What This Solves
Routes an inflow hydrograph through a detention basin or reservoir using the Modified Puls method to determine peak attenuation, lag time, and maximum storage.
Best Used When
- You need to demonstrate that a detention pond reduces the post-development peak flow to pre-development levels
- You have an inflow hydrograph and stage-storage-discharge relationships and need the outflow hydrograph
- You are refining pond and outlet sizing after preliminary estimates from pond-sizing calculations
Do NOT Use When
- You need to route a hydrograph through a river or channel reach (not a reservoir) — Use Muskingum Routing Calculator
- You only need preliminary storage volume estimation without full routing — Use Storage Volume Calculator
Key Assumptions
- The water surface in the reservoir is level (no significant velocity head or wind effects)
- The stage-storage and stage-discharge relationships are single-valued (no hysteresis)
- Inflow and outflow vary linearly within each time step
- No significant seepage, evaporation, or direct rainfall on the pond during the event
- The outlet structure operates as designed (no clogging or debris blockage)
Input Quality Notes
Accurate stage-storage and stage-discharge curves are essential. Use surveyed contours for storage and calibrated outlet equations for discharge. Time step should be small enough to capture the inflow peak.
Route an inflow flood hydrograph through a detention basin, pond or reservoir using the Modified Puls (Storage-Indication) method to find the attenuated outflow hydrograph, peak reduction, lag time and maximum water surface elevation.
Route Hydrograph Through Storage
For educational purposes only. Not a substitute for professional engineering judgment.
Modified Puls Method Overview
The Modified Puls (Storage-Indication) method routes flood hydrographs through reservoirs and detention basins. It assumes a level pool where outflow is a function of storage only.
Key Equations
- Storage-Indication: SI = 2S/dt + O
- Routing equation: (2S2/dt + O2) = (2S1/dt - O1) + I1 + I2
Where:
- S = Storage volume (acre-ft)
- O = Outflow discharge (cfs)
- I = Inflow discharge (cfs)
- dt = Routing time step (minutes)
Common Applications
Detention Basin Design
Size storage to meet peak flow reduction targets
Reservoir Flood Routing
Determine outflow hydrograph and peak water level
Dam Safety Analysis
Evaluate spillway capacity during design floods
Stormwater Management
Demonstrate compliance with post-development limits
Design Tips
Time step selection: Use a time step no larger than Tp/5 where Tp is the time to peak. Smaller time steps provide better accuracy but increase computation.
Storage-discharge curve: Ensure your data covers the full range of expected water levels. The method will extrapolate if values exceed the provided range.
Volume balance: Check that total inflow volume equals total outflow volume. Errors greater than 1% may indicate numerical instability.
How level pool routing works
Level pool (reservoir) routing solves the continuity equation for a storage facility where the water surface is assumed horizontal and outflow depends only on the stored volume. The continuity equation, written in finite-difference form over a time step Δt, rearranges to the storage-indication recurrence used by the Modified Puls method:
- Storage-indication value: SI = 2S/Δt + O
- Routing equation: (2S2/Δt + O2) = (2S1/Δt − O1) + I1 + I2
Everything on the right side is known at the start of each step, so the new 2S2/Δt + O2 is computed directly and the matching outflow O2 (and storage and elevation) is interpolated from a storage-indication curve built once from the stage–storage–discharge data. The procedure marches through every ordinate of the inflow hydrograph to build the full outflow hydrograph.
Where:
- S = storage volume (acre-ft or m³)
- O = outflow discharge (cfs or m³/s)
- I = inflow discharge (cfs or m³/s)
- Δt = routing time step (minutes)
- subscripts 1 and 2 = start and end of the time step
When the outlet is a single orifice, the calculator generates the discharge side of the curve with the orifice equation Q = Cd · A · √(2gh), using g = 32.2 ft/s² (imperial) or 9.81 m/s² (metric). Internally, storage is converted to flow–time units (1 acre-ft = 726 cfs·min; 1 m³ = 1/60 cms·min) so the storage and discharge terms share consistent units. The peak attenuation is the difference between peak inflow and peak outflow, and the lag time is the shift between their peak arrival times.
Typical orifice discharge coefficients (Cd)
The outlet orifice equation Q = Cd · A · √(2gh) needs a discharge coefficient. The calculator defaults to 0.6 (sharp-edged orifice) and accepts values from 0.4 to 0.9. Use a value appropriate to the outlet geometry.
| Outlet / orifice type | Typical Cd | Notes |
|---|---|---|
| Sharp-edged (thin plate) orifice | 0.60 | Default; most common submerged outlet assumption |
| Square-edged entrance in thick wall | 0.60 – 0.62 | Riser or headwall orifice |
| Rounded / bell-mouth entrance | 0.90 – 0.98 | Streamlined inlet, minimal contraction |
| Short tube / ragged opening | 0.40 – 0.50 | Higher losses; use the lower end of the range |
Indicative values for preliminary sizing. Confirm against the outlet structure standard for your jurisdiction (e.g. state stormwater manual or USACE/NRCS guidance) and against manufacturer data for proprietary outlet controls.
Assumptions and when not to use it
Key assumptions
- The water surface stays horizontal (level pool).
- Outflow is a unique function of storage (no hysteresis).
- The stage–storage–discharge relationship is known and accurate.
- The time step is small enough to capture the hydrograph shape.
Not suited for
- Long, narrow reservoirs with significant velocity head or a tilted surface.
- Rivers or channels needing kinematic or dynamic (Muskingum / St. Venant) routing.
- Outlets with backwater effects or hysteresis in the rating curve.
- Very short floods relative to reservoir travel time.
Based on the methodology documented in USACE EM 1110-2-1417 and the NRCS National Engineering Handbook Part 630. Always verify detention designs against local stormwater criteria.
Frequently asked questions
What is the Modified Puls (level pool routing) method?
The Modified Puls method — also called the Storage-Indication method — routes an inflow flood hydrograph through a reservoir or detention basin to produce the outflow hydrograph. It assumes a level pool, meaning the water surface stays horizontal and outflow is a unique function of storage. It is one of the most widely used techniques for detention basin design and reservoir flood routing, and is documented in USACE EM 1110-2-1417, the NRCS National Engineering Handbook Part 630, McCuen (2005) and Maidment (1993).
What is the storage-indication routing equation?
The routing recurrence is (2S₂/Δt + O₂) = (2S₁/Δt − O₁) + I₁ + I₂, where S is storage, O is outflow, I is inflow, and Δt is the time step. The right-hand side is fully known at each step, so the new storage-indication value 2S₂/Δt + O₂ is found directly, and the corresponding outflow O₂ is read from a pre-computed storage-indication curve (2S/Δt + O plotted against O). No iteration is required.
How does an orifice outlet control the outflow?
For a submerged orifice the calculator uses Q = Cᵈ · A · √(2gh), where Cᵈ is the discharge coefficient (default 0.6, sharp-edged orifice), A is the orifice area, g is gravitational acceleration (32.2 ft/s² imperial, 9.81 m/s² metric) and h is the head above the orifice center. The discharge scales with the square root of head, which is what produces the characteristic flattening of the outflow hydrograph as the pond fills.
How small should the routing time step be?
A common guideline is Δt ≤ Tₚ/5, where Tₚ is the inflow time to peak. A step that is too large can miss the peak and introduce mass-balance error. The calculator flags a warning when Δt exceeds Tₚ/5, and it reports a volume balance check — total inflow volume should equal total outflow volume to within about 1% for a numerically stable run.
Why is the outflow peak lower and later than the inflow peak?
As inflow exceeds outflow the pond fills and water is held in storage, so the peak outflow is reduced (attenuated) relative to the peak inflow. The held volume is released gradually, so the outflow peak also occurs later — the lag time. The outflow peak always lies on the receding limb of the inflow hydrograph, intersecting it at the point of maximum storage. This attenuation is exactly the effect detention basins are designed to provide for stormwater compliance.
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Last verified: February 2026