SWMM5 Complete Runoff Engine — Three Surfaces · Cash-Karp RK5

🇺🇸 US Customary (ft, in, ac, cfs)

🌍 SI Metric (m, mm, ha, m³/s)

Hydrology/Runoff

Infiltration

ODE Solver

Routing

Core Engine

SWMM5 Runoff Computation Call Graph

The Nonlinear Reservoir — Three Surfaces (subcatch.c) SWMM5 splits each subcatchment into A1, A2, A3: A1 Imperv (no DS): dd₁/dt = i(t) − q₁(d₁) d_s = 0 A2 Imperv (w/ DS): dd₂/dt = i(t) − e(t) − q₂(d₂) d_s > 0 A3 Pervious: dd₃/dt = i(t) − e(t) − f(t) − q₃(d₃) d_s > 0, infiltration Outflow: qⱼ = Wⱼ · (1.49/nⱼ) · (dⱼ − d_sⱼ)^(5/3) · S^(1/2) [Manning's overland flow] Total Q = q₁ + q₂ + q₃ ODE Solution (odesolve.c): Each surface depth solved independently via Cash-Karp RK5. 6 function evaluations per step, embedded 4th/5th order error estimate, adaptive step-size.

Cash-Karp RK5 Adaptive Solver — odesolve.c

SWMM5 solves each surface's depth ODE with a 5th-order Runge-Kutta (Cash-Karp variant). Six stages k₁…k₆ are evaluated per step. The difference between 5th and 4th order solutions gives a truncation error estimate for adaptive step-size control.

k₁

—

k₂

—

k₃

—

k₄

—

k₅

—

k₆

—

Cash-Karp Butcher Tableau (odesolve.c) 0 | 1/5 | 1/5 3/10 | 3/40 9/40 3/5 | 3/10 −9/10 6/5 1 |−11/54 5/2 −70/27 35/27 7/8 | 1631/55296 175/512 575/13824 44275/110592 253/4096 ──────────────────────────────────────────────────────────── 5th: 37/378 0 250/621 125/594 0 512/1771 4th: 2825/27648 0 18575/48384 13525/55296 277/14336 1/4

Step-Size Control (odesolve.c) // Truncation error estimate err = max |y₅[i] − y₄[i]| / (|y₅[i]| + TINY) if (err > TOL) { h_new = SAFETY · h · err^(−0.25) // shrink h_new = max(h_new, 0.1·h) // floor } else { h_new = SAFETY · h · err^(−0.2) // grow h_new = min(h_new, 5.0·h) // ceiling } SAFETY = 0.9, TINY = 1.0e-30, TOL = 1.0e-5

Interactive RK5 Single-Step Explorer

Surface A3 Pervious

Depth d₀ (ft) 0.010

Rain (in/hr) 2.0

Δt (sec) 30

Manning n 0.015

Dep. Storage (in) 0.05

🌧️ Design Storm

Pattern

Total Depth 4.0 in

Duration 24 hr

Wet Time Step 2 min

Subcatchment

Area 121 ac

Slope 0.4%

Evaporation 0.00 in/hr

Internal Routing

Three Surfaces

A1 Imperv no DS

A2 Imperv w/ DS

A3 Pervious

% Impervious 50%

% Imperv w/o DS 25%

A1: Imperv (no DS)

Surface type

n₁ 0.012

Width₁ 500 ft

💡 Width ≈ Area / longest overland flow path

A2: Imperv (w/ DS)

Surface type

n₂ 0.012

d_s₂ 0.05 in

Width₂ 500 ft

A3: Pervious

Surface type

n₃ 0.150

d_s₃ 0.20 in

Width₃ 500 ft

Infiltration (A3 — Pervious)

Model

f₀ max rate 3.0 in/hr

f∞ min rate 0.50 in/hr

k decay 4.0 /hr

Advanced

Mode

t = 0.0 hr

Speed: 1×

t = 0.0 hr

🧮 Live RK5 Stages — Current Time Step (all 3 surfaces)

A1 Imperv (no DS)

A2 Imperv (w/ DS)

A3 Pervious

Hyetograph & Total Hydrograph

Three-Surface Outflow Breakdown

Surface Water Depths (d₁, d₂, d₃)

Infiltration & RK5 Sub-Steps

🔬 RK5 4th vs 5th Order Solutions & Error (A3 Pervious)

Shows where the embedded 4th and 5th order solutions diverge — error spikes indicate the ODE is stiffest and the solver works hardest.

💧 Water Balance Summary

📋 Subcatchment Runoff Summary (SWMM5 RPT Format)

📂 Compare with SWMM5 RPT File

Export the .INP above, run it in EPA SWMM5, then drop the .RPT file here to compare results side-by-side.

📄

Drop SWMM5 .RPT file here or click to browse

Parses Subcatchment Runoff Summary + Flow Routing Continuity

📊 Drop SWMM5 .OUT File — Real Time Series Overlay

The .OUT binary contains every reported time step from your SWMM5 run — node depths, link flows, subcatchment runoff. Drop the file and the app overlays the real engine's hydrograph on the in-browser RK5 simulation.

💾

Drop SWMM5 .OUT binary here or click to browse

Parses header + per-period time series for subcatchments, nodes, and links

🔗 Running SWMM Hydrology in ICM InfoWorks

InfoWorks ICM can run EPA SWMM runoff natively within an InfoWorks network. The same three-surface nonlinear reservoir model — impervious without depression storage, impervious with depression storage, and pervious with infiltration — is available as a routing model type called "SWMM" in the ICM Runoff Surface editor. This page maps every SWMM5 parameter to its ICM InfoWorks equivalent.

Step-by-Step: Setting Up SWMM Runoff in ICM InfoWorks

Create 3 Runoff Surfaces

In the Runoff Surface editor, create three surfaces:
• Imperv_noDS — Fixed runoff (coeff=1.0), Routing=SWMM
• Imperv_wDS — Fixed runoff (coeff=1.0), Routing=SWMM
• Pervious — Horton or Green-Ampt volume model, Routing=SWMM
Set Manning's n in the Runoff routing value field for each.

Create a Land Use

In the Land Use editor, create a land use that references all three runoff surfaces. Set the area percentages for each surface to match your SWMM5 subcatchment's %Imperv and %Zero-Imperv splits.

Assign to Subcatchments

In the Subcatchment editor, assign the Land Use to each subcatchment. Set the total area, slope, and subcatchment width. The width applies to all three surfaces in ICM (same as SWMM5).

Set Infiltration

On the pervious Runoff Surface, set the infiltration parameters:
• Horton: f₀ (max rate), f∞ (min rate), k (decay)
• Green-Ampt: Ψ (suction head), Ks (conductivity), Δθ (deficit)
Set initial conditions in the Rainfall Event editor.

Configure Rainfall Event

Add a Rainfall Event with the appropriate profile. Set initial conditions for Horton moisture store or Green-Ampt moisture deficit. Match the subcatchment Rainfall Profile name to the event profile name.

Run Simulation

Create a Run with the rainfall event. ICM will use the SWMM nonlinear reservoir + Manning's overland flow equation (the same RK5 ODE solver) for each of the three surfaces on every subcatchment.

📋 Complete Parameter Mapping: SWMM5 ↔ ICM InfoWorks

EPA SWMM5 (subcatch.c)

↔

ICM InfoWorks

Subcatchment-Level Parameters

Parameter	SWMM5 INP Field	ICM InfoWorks Field	Editor Location
Total Area	[SUBCATCHMENTS] → Area	total_area	Subcatchment
Outlet Node	[SUBCATCHMENTS] → OutID	node_id	Subcatchment
% Impervious	[SUBCATCHMENTS] → %Imperv	Runoff Surface area %	Land Use → surfaces
Characteristic Width	[SUBCATCHMENTS] → Width	width (on subcatchment)	Subcatchment
Slope	[SUBCATCHMENTS] → %Slope	slope	Subcatchment
Rain Gage	[SUBCATCHMENTS] → Rain Gage	rainfall_profile	Subcatchment

Surface A1: Impervious WITHOUT Depression Storage

Parameter	SWMM5 INP Field	ICM InfoWorks Field	Editor Location
Manning's n	[SUBAREAS] → N-Imperv	runoff_routing_value	Runoff Surface
Depression Storage	— (d_s = 0 always)	initial_loss_value = 0	Runoff Surface
% of Impervious	[SUBAREAS] → %Zero-Imperv	area % in Land Use	Land Use
Volume Model	Fixed 100% runoff	runoff_volume_type = Fixed, coeff = 1.0	Runoff Surface
Routing Model	Nonlinear reservoir	routing_model = SWMM	Runoff Surface

Surface A2: Impervious WITH Depression Storage

Parameter	SWMM5 INP Field	ICM InfoWorks Field	Editor Location
Manning's n	[SUBAREAS] → N-Imperv	runoff_routing_value	Runoff Surface
Depression Storage	[SUBAREAS] → S-Imperv	initial_loss_value	Runoff Surface
Initial Loss Type	Depth-based	initial_loss_type = Absolute	Runoff Surface
Volume Model	Fixed 100% runoff	runoff_volume_type = Fixed, coeff = 1.0	Runoff Surface
Routing Model	Nonlinear reservoir	routing_model = SWMM	Runoff Surface

Surface A3: Pervious

Parameter	SWMM5 INP Field	ICM InfoWorks Field	Editor Location
Manning's n	[SUBAREAS] → N-Perv	runoff_routing_value	Runoff Surface
Depression Storage	[SUBAREAS] → S-Perv	initial_loss_value	Runoff Surface
Volume Model	Horton / Green-Ampt	runoff_volume_type = Horton / Green-Ampt	Runoff Surface
Routing Model	Nonlinear reservoir	routing_model = SWMM	Runoff Surface

Horton Infiltration Parameters (Pervious Surface Only)

Parameter	SWMM5 INP Field	ICM InfoWorks Field	Editor Location
Max Infil Rate (f₀)	[INFILTRATION] → MaxRate	horton_max_rate	Runoff Surface
Min Infil Rate (f∞)	[INFILTRATION] → MinRate	horton_min_rate	Runoff Surface
Decay Constant (k)	[INFILTRATION] → Decay	horton_decay	Runoff Surface
Drying Time	[INFILTRATION] → DryTime	horton_drying_time	Runoff Surface
Initial Moisture Store	[INFILTRATION] → MaxInfil	Set in Rainfall Event → Initial Conditions	Rainfall Event

Green-Ampt Infiltration Parameters (Pervious Surface Only)

Parameter	SWMM5 INP Field	ICM InfoWorks Field	Editor Location
Suction Head (Ψ)	[INFILTRATION] → Suction	green_ampt_suction	Runoff Surface
Conductivity (Ks)	[INFILTRATION] → Ksat	green_ampt_conductivity	Runoff Surface
Initial Deficit (Δθ)	[INFILTRATION] → IMD	Set in Rainfall Event → Initial Conditions	Rainfall Event

⚠️ Key Differences & Notes

Three-Level Hierarchy: In SWMM5, surface parameters live directly on the subcatchment ([SUBAREAS] + [INFILTRATION] sections). In ICM InfoWorks, there's a three-level hierarchy: Subcatchment → Land Use → Runoff Surface. Multiple subcatchments can share the same Land Use, and multiple Land Uses can share the same Runoff Surface definitions.

Width Field: In SWMM5, the width is set once on the subcatchment and applies to all three surfaces. In ICM InfoWorks, the width is also on the subcatchment, and the SWMM routing model uses it for all surfaces. The Manning's n is always the Runoff routing value field regardless of what routing type is displayed in the UI.

Slope-Related vs Absolute Initial Loss: ICM allows both slope-related initial loss (recommended value 0.000071 m for impervious, matching Wallingford model) and absolute depth. SWMM5 always uses absolute depth for depression storage. Use Absolute type in ICM to match SWMM5 behavior exactly.

Infiltration Initial Conditions: SWMM5 puts initial moisture/deficit in the [INFILTRATION] section. ICM requires these in the Rainfall Event editor → Initial Conditions tab. This is a common gotcha during conversion — if you miss it, Horton starts fully recovered and Green-Ampt starts fully saturated.

Groundwater: ICM supports groundwater modeling but uses its own InfoWorks method rather than the SWMM5 two-zone groundwater equations. If your SWMM5 model has [GWF] sections, these need manual re-calibration in ICM.

SWMM5 Import: ICM can directly import SWMM5 .INP files. The importer automatically creates the Runoff Surfaces, Land Uses, and Subcatchment assignments. It creates one Runoff Surface per unique parameter set and shares them across subcatchments.

💎 Ruby Script: Auto-Configure SWMM Runoff Surfaces in ICM

# Ruby script to set up SWMM hydrology in ICM InfoWorks # Run from ICM UI Script → applies to current network net = WSApplication.current_network # --- Step 1: Define three SWMM Runoff Surfaces --- net.transaction_begin # Surface A1: Impervious, no depression storage s1 = net.new_row_object('hw_runoff_surface') s1['surface_id'] = 'SWMM_Imperv_noDS' s1['routing_model'] = 'SWMM' s1['runoff_volume_type'] = 'Fixed' s1['fixed_runoff_coefficient'] = 1.0 s1['runoff_routing_value'] = 0.012 # Manning's n s1['initial_loss_type'] = 'Absolute' s1['initial_loss_value'] = 0.0 # No depression storage s1.write # Surface A2: Impervious, with depression storage s2 = net.new_row_object('hw_runoff_surface') s2['surface_id'] = 'SWMM_Imperv_wDS' s2['routing_model'] = 'SWMM' s2['runoff_volume_type'] = 'Fixed' s2['fixed_runoff_coefficient'] = 1.0 s2['runoff_routing_value'] = 0.012 # Manning's n s2['initial_loss_type'] = 'Absolute' s2['initial_loss_value'] = 0.05 # 0.05 in depression storage s2.write # Surface A3: Pervious, Horton infiltration s3 = net.new_row_object('hw_runoff_surface') s3['surface_id'] = 'SWMM_Pervious' s3['routing_model'] = 'SWMM' s3['runoff_volume_type'] = 'Horton' s3['runoff_routing_value'] = 0.15 # Manning's n for overland s3['initial_loss_type'] = 'Absolute' s3['initial_loss_value'] = 0.20 # 0.20 in depression storage s3['horton_max_rate'] = 3.0 # f0 (in/hr) s3['horton_min_rate'] = 0.5 # fc (in/hr) s3['horton_decay'] = 4.0 # k (1/hr) s3.write net.transaction_commit puts "Created 3 SWMM runoff surfaces" # --- Step 2: Create Land Use referencing all 3 surfaces --- net.transaction_begin lu = net.new_row_object('hw_land_use') lu['land_use_id'] = 'SWMM_Mixed' # Set surface areas (example: 50% imperv, 25% of that has no DS) # A1 = 50% × 25% = 12.5%, A2 = 50% × 75% = 37.5%, A3 = 50% lu.write net.transaction_commit # --- Step 3: Assign to subcatchments --- net.transaction_begin net.row_objects('hw_subcatchment').each do |sc| sc['land_use_id'] = 'SWMM_Mixed' # Width comes from SWMM5 subcatchment width # sc['width'] = 500 # ft — set per subcatchment sc.write end net.transaction_commit puts "Assigned SWMM land use to all subcatchments"

🏛️ Architecture Comparison: Data Flow

EPA SWMM5 Data Structure [SUBCATCHMENTS] Name RainGage Outlet Area %Imperv Width Slope S1 RG1 J1 10 50 500 2.0 [SUBAREAS] Subcat N-Imperv N-Perv S-Imperv S-Perv %Zero Route S1 0.012 0.15 0.05 0.20 25 OUTLET [INFILTRATION] Subcat MaxRate MinRate Decay DryTime MaxInfil S1 3.0 0.5 4.0 7 0 → All 3 surfaces defined FLAT on the subcatchment → One-level structure: Subcatchment has everything

ICM InfoWorks Data Structure Runoff Surface (hw_runoff_surface) SWMM_Imperv_noDS → routing=SWMM, n=0.012, ds=0 SWMM_Imperv_wDS → routing=SWMM, n=0.012, ds=0.05 SWMM_Pervious → routing=SWMM, n=0.15, Horton Land Use (hw_land_use) SWMM_Mixed → 12.5% Imperv_noDS → 37.5% Imperv_wDS → 50.0% Pervious Subcatchment (hw_subcatchment) S1 → land_use=SWMM_Mixed, area=10ac, width=500 → Three-level hierarchy: Subcatch → LandUse → Surface → Surfaces are SHARED across subcatchments

SWMM5 Runoff Engine — Complete Explorer

SWMM5 Runoff Computation Call Graph

Cash-Karp RK5 Adaptive Solver — odesolve.c

Interactive RK5 Single-Step Explorer

🌧️ Design Storm

🧮 Live RK5 Stages — Current Time Step (all 3 surfaces)

Hyetograph & Total Hydrograph

Three-Surface Outflow Breakdown

Surface Water Depths (d₁, d₂, d₃)

Infiltration & RK5 Sub-Steps

🔬 RK5 4th vs 5th Order Solutions & Error (A3 Pervious)

💧 Water Balance Summary

📋 Subcatchment Runoff Summary (SWMM5 RPT Format)

📂 Compare with SWMM5 RPT File

Hydrograph Overlay: RK5 Explorer vs EPA SWMM5

📊 Drop SWMM5 .OUT File — Real Time Series Overlay

Time Series Overlay: RK5 Explorer vs Real SWMM5 .OUT

🔗 Running SWMM Hydrology in ICM InfoWorks

Step-by-Step: Setting Up SWMM Runoff in ICM InfoWorks

Create 3 Runoff Surfaces

Create a Land Use

Assign to Subcatchments

Set Infiltration

Configure Rainfall Event

Run Simulation

📋 Complete Parameter Mapping: SWMM5 ↔ ICM InfoWorks

EPA SWMM5 (subcatch.c)

ICM InfoWorks

Subcatchment-Level Parameters

Surface A1: Impervious WITHOUT Depression Storage

Surface A2: Impervious WITH Depression Storage

Surface A3: Pervious

Horton Infiltration Parameters (Pervious Surface Only)

Green-Ampt Infiltration Parameters (Pervious Surface Only)

⚠️ Key Differences & Notes

💎 Ruby Script: Auto-Configure SWMM Runoff Surfaces in ICM

🏛️ Architecture Comparison: Data Flow