Modified Rational Method (MRM)

Overview

The Modified Rational Method extends the Rational Method to estimate the required detention storage volume for a site. While the Rational Method computes only a peak flow, the MRM creates a simplified trapezoidal hydrograph and uses volumetric analysis to determine how much storage is needed to reduce the post-development peak flow to the pre-development (allowable) release rate.

Important: The MRM is a required volume computation only. It determines the minimum detention storage volume needed, but does not perform hydrograph routing or model the actual pond outflow behavior. The outfall structure (outlet pipe, orifice, weir, etc.) should be designed such that the design flow through the structure is less than or equal to the allowable release rate for each design storm event. Care should be taken not to over-detain, as the MRM does not verify that the pond releases enough flow to prevent overtopping. The engineer is responsible for designing the outfall structure to control releases appropriately.

How MRM Works

The MRM computes the required detention storage volume by comparing the inflow volume (from rainfall runoff) against the allowable outflow volume across a range of storm durations. The critical duration — the duration that produces the maximum difference between inflow and outflow volume — determines the required storage. HydraLink supports two detention sizing approaches: the Standard Method and the Regional IDF Method.

Detention Method Options

Standard Method

The Standard Method is a general-purpose approach applicable to any region. It uses rainfall intensity-duration-frequency data (NOAA Atlas 14 or user-entered IDF data) and iterates through storm durations from Tc up to 1440 minutes in 1-minute steps. Iteration stops early if the required storage has been decreasing for 20 consecutive steps past the peak, since the critical duration has already been found.

For each duration:

  1. Computes the peak inflow and inflow volume:
    Q = C × i × A   (cfs)
    Vin = Q × td × 60   (ft³)

    Where C = runoff coefficient, i = rainfall intensity (in/hr) at duration td, A = drainage area (acres), and td = storm duration (minutes). The factor of 60 converts minutes to seconds.

    If the 1.008 conversion factor is enabled in Project Settings, the exact acre-inch-per-hour to cfs conversion (43,560 / (12 × 3,600) ≈ 1.00833) is applied to Q. When disabled (default), the standard approximation 1 acre-in/hr ≈ 1 cfs is used.

  2. Computes the outflow volume:
    Vout = 0.5 × (Td + Tc) × Qallow × 60   (ft³)

    Where Td = storm duration (min), Tc = time of concentration (min), Qallow = allowable release (cfs). The 0.5 factor assumes a triangular outflow hydrograph.

  3. Required storage = Vin − Vout
  4. The critical duration is the one that maximizes the required storage.

Regional IDF Method (iSWM / Atlanta Regional Commission)

HydraLink supports the regional IDF table-based detention method used by both the NCTCOG iSWM (Integrated Stormwater Management) program in the Dallas-Fort Worth metroplex and the Atlanta Regional Commission Georgia Stormwater Management Manual. Both programs use the same underlying equations (Debo & Reese, 1995/2003) with region-specific rainfall coefficients.

Equations

Qa = Ca × i × A   (Eq 1.26 — allowable release)
Td = √(2 × C × A × a × b / Qa) − b   (Eq 1.27 — critical duration)
Vreq = 60 × [C × A × a − √(2 × C × a × b × A × Qa) + (Qa/2) × (b − Tc)]   (Eq 1.28)

Where a and b are county/region-specific rainfall coefficients and Qa is the allowable pre-development release rate.

Supported Regions

ProgramRegions
NCTCOG iSWM (Texas) Collin, Dallas, Denton, Ellis, Erath, Grayson, Hood, Hunt, Johnson, Kaufman, Navarro, Palo Pinto, Parker, Rockwall, Somervell, Tarrant, Wise
Atlanta Regional Commission (Georgia) Albany, Atlanta, Athens, Augusta, Bainbridge, Brunswick, Columbus, Macon, Metro Chattanooga, Peachtree City, Rome, Roswell, Savannah, Toccoa, Valdosta, Vidalia

Supported return periods for the regional method: 1, 2, 5, 10, 25, 50, and 100 years. Each county/city has unique a and b coefficients for each return period.

MRM Basin Roles

When multiple basins drain to a pond, each basin is assigned a role:

Role Description Effect
Design Area Post-development area detained by the pond C and area included in composite inflow calculation
Target Pre-development reference Peak flow defines the allowable release rate for the pond
Bypass Site flow that does not enter the pond Reduces the allowable release from the pond, increasing required detention
Pass-Through Off-site flow that enters pond but is not detained Outfall structure must be sized larger to convey pass-through flow in addition to the allowable detained release

MRM Detention Sizing Results

Output Units Description
Required Storage Volume ft³ Maximum required storage across all durations
Critical Storm Duration minutes Duration producing the maximum storage requirement
Allowable Release Rate cfs Combined target flow defining max permitted outflow
Inflow Volume (at critical duration) ft³ Total inflow volume at the critical duration
Outflow Volume (at critical duration) ft³ Total outflow volume at the critical duration

Assumptions and Limitations

  • The MRM computes required storage volume only — it does not perform dynamic routing or model the actual pond behavior over time
  • Assumes the entire contributing area has uniform C and Tc
  • Trapezoidal hydrograph approximation may not capture complex runoff patterns
  • Does not account for downstream routing effects

Outfall Structure Design: The outfall structure (outlet pipe, orifice, weir, riser, etc.) must be designed so that the design flow through the structure is less than the allowable release rate for the design storm event. The MRM does not check that the pond releases enough flow to avoid overtopping — care should be taken not to over-detain. The engineer should verify that the outfall structure provides adequate release capacity through all stages of the storm event.

MRM vs. Full Hydrograph Routing

The choice between MRM detention sizing and full hydrograph routing depends on the project requirements, local jurisdiction criteria, and the engineer’s judgment:

  • MRM is a volumetric sizing tool appropriate for detention sizing in jurisdictions that accept the Rational Method approach. It determines the required storage volume but does not model the pond’s dynamic response.
  • Full Routing (Unit Hydrograph + Modified Puls) provides a more detailed analysis including stage-discharge behavior, multi-outlet evaluation, and dynamic inflow/outflow modeling. This approach may be required by some jurisdictions or for complex sites.

When using MRM for detention sizing, the engineer should independently design the outfall structure to meet the allowable release rate while also ensuring the pond can drain adequately between storm events. For complex sites with multiple outlets, full hydrograph routing provides a more complete picture of pond performance.

References

  • NRCS (1986). Urban Hydrology for Small Watersheds, TR-55.
  • iSWM Technical Manual, North Central Texas Council of Governments.
  • Malcom, H.R. (1989). "Elements of Urban Stormwater Design."