Storm Water Management Model
The Storm Water Management Model (SWMM) is a public-domain hydrology-hydraulic-water quality simulation model developed by the United States Environmental Protection Agency (EPA) for analyzing stormwater runoff in urban and suburban watersheds.[1][2] Originally created between 1969 and 1971 to evaluate combined sewer overflow problems, SWMM has evolved through multiple upgrades to address broader stormwater management needs, including infiltration, retention, and low-impact development practices.[3][1] It supports both single-event and long-term continuous simulations of runoff quantity and quality, routing flows through conveyance networks, and evaluating control measures such as detention basins and water quality units.[4][5] Widely used globally by engineers and planners, SWMM facilitates applications like drainage system design for flood control, pollution source assessment, and compliance with regulatory objectives for reducing urban runoff impacts.[1][4] The model's open-source availability and integration with geographic information systems have enhanced its adoption for real-time forecasting and scenario analysis in municipal stormwater programs.[2][1]Introduction
Program Description
The Storm Water Management Model (SWMM) is a dynamic simulation program developed by the United States Environmental Protection Agency (EPA) to model the quantity and quality of stormwater runoff in primarily urban and suburban catchments.[1] It supports both single-event and long-term (continuous) simulations, enabling users to predict hydrologic, hydraulic, and pollutant transport processes over time.[4] Originating in 1971 with subsequent upgrades, SWMM operates in the public domain and is available for free download, facilitating widespread use by engineers, planners, and researchers globally for stormwater system analysis and design.[1][3] SWMM's core capabilities encompass surface runoff generation, which accounts for factors such as time-varying rainfall, evaporation, snow accumulation and melt, and depression storage; conveyance routing through networks of pipes, channels, and storage units; and water quality modeling via buildup and washoff of pollutants from surfaces, along with their transport and decay in receiving waters.[4] Hydraulic routing options include dynamic wave, kinematic wave, and steady flow methods, while infiltration is simulated using methods like Horton, Green-Ampt, or curve number procedures.[6] The model also integrates low impact development (LID) and best management practices (BMPs), such as rain barrels, permeable pavements, bioretention cells, infiltration trenches, vegetative swales, and green roofs, to evaluate runoff reduction through infiltration, storage, and evaporation.[4] Applications of SWMM include designing flood control measures, sizing detention facilities, developing combined sewer overflow (CSO) control plans, performing waste load allocation for pollutants, and assessing the effectiveness of green infrastructure in mitigating runoff impacts.[4] It supports floodplain mapping approved by the Federal Emergency Management Agency (FEMA) and aids in evaluating strategies under regulatory frameworks like the National Pollutant Discharge Elimination System (NPDES).[4][7] The program's flexibility allows customization for specific drainage systems, including backwater effects and interflow between groundwater and drainage networks, making it a foundational tool for urban water management.[8][4]Applications and Scope
The Storm Water Management Model (SWMM) is applied worldwide for planning, analysis, and design of stormwater runoff, combined and sanitary sewers, and other drainage systems, primarily in urban and suburban areas.[1] It has been employed in thousands of studies since its development, supporting tasks such as flood control infrastructure design, detention basin sizing, and evaluation of strategies to mitigate combined sewer overflows.[9][4] Key applications include simulating the performance of green infrastructure and low-impact development techniques, such as rain gardens, infiltration trenches, and porous pavements, to reduce runoff volumes, peak flows, and pollutant transport.[1] SWMM also facilitates assessment of water quality impacts from urban pollutants, aiding compliance with regulatory standards like those under the Clean Water Act.[1] These uses extend to non-urban settings for broader drainage system evaluations, though its core strengths lie in detailed urban hydrology and hydraulics.[10] In scope, SWMM functions as a dynamic rainfall-runoff simulation tool for both single-event and long-term continuous modeling of runoff quantity and quality.[1] It encompasses hydrologic processes like infiltration and surface runoff generation, hydraulic routing through pipes, channels, and overland flow paths, and pollutant buildup, washoff, and transport.[9] The model supports representation of control structures, storage units, and land use practices but does not simulate groundwater interactions or detailed subsurface flows.[1] Its flexibility allows customization for specific scenarios, including climate change impact assessments via adjusted rainfall inputs.[10]Historical Development
Origins (1969–1975)
The Storm Water Management Model (SWMM) was initiated by the United States Environmental Protection Agency (EPA) in 1969 to provide a comprehensive tool for simulating urban stormwater runoff quantity and quality, amid rising concerns over pollution from combined sewer overflows and urban drainage systems prior to the Clean Water Act of 1972.[7] The project received approximately $350,000 in EPA funding during its initial phase, reflecting significant investment in computational modeling for environmental engineering at the time.[7] Development involved collaboration among EPA staff and contractors, including Metcalf & Eddy, Inc., Water Resources Engineers, Inc., and the University of Florida under Professor Wayne Huber, who contributed to hydrologic components.[3] [7] The first version, SWMM I, was completed and documented in a final report by July 1971, coded primarily in Fortran IV to leverage available computing resources for scientific simulations.[3] [11] This release introduced a dynamic, distributed-parameter framework capable of handling single-event or continuous rainfall-runoff processes, including subcatchment discretization, infiltration via methods like Horton's equation, surface runoff generation, and basic flow routing through channels and pipes using techniques such as the kinematic wave approximation.[11] It also incorporated initial pollutant buildup and washoff modules to track water quality, marking SWMM as one of the earliest models to integrate hydrologic, hydraulic, and quality aspects for primarily urban and suburban watersheds.[7] Validation drew from real-world data in test catchments, emphasizing empirical calibration against observed hydrographs and pollutographs. By 1975, SWMM underwent its first major upgrade to Version 2, which enhanced storage-based routing options, improved numerical stability for longer simulations, and integrated the EXTRAN block—developed circa 1973 by Water Resources Engineers—for more detailed dynamic wave routing in conveyance networks, addressing limitations in overland and sewer hydraulics from the original version.[7] These refinements, informed by early user feedback and expanded EPA testing, solidified SWMM's role in regulatory planning for stormwater control, though computational demands restricted applications to mainframe systems.[3] Water Resources Engineers, later acquired by Camp Dresser & McKee (now CDM Smith), played a key role in these hydraulic advancements.[12]Major Version Evolutions (1975–2005)
Version 2 of the Storm Water Management Model (SWMM), released in 1975 by developers at Water Resources Engineers (later acquired by CDM Smith), introduced the EXTRAN block, enabling fully dynamic simulation of unsteady flow in open channels and closed conduits using the Saint-Venant equations.[3] This upgrade expanded beyond the original Version 1's steady-state kinematic wave routing to handle complex hydraulic interactions, including backwater effects and surcharging, which were critical for modeling combined sewer overflows (CSOs) in urban systems.[3] Continuous simulation capabilities were added, allowing long-term analysis of runoff processes with hourly time steps, alongside initial support for snowmelt and pollutant transport, though computations often required mainframe resources like NASA systems.[3] SWMM Version 3, developed collaboratively by the University of Florida and CDM Smith and released in 1981, enhanced water quality modeling through explicit soil infiltration methods and buildup/washoff algorithms for pollutants, enabling more accurate prediction of nonpoint source contributions during extended simulations.[3] Hydraulic routing was refined with improved EXTRAN implementations for modeling ponds, lakes, rivers, and underground storage facilities, supporting both steady and unsteady flows in branched networks.[3] A dedicated Statistics block was incorporated to facilitate planning and design applications, processing rainfall and temperature data for frequency analysis, while an interactive version emerged around 1982 from the University of Guelph, marking early steps toward user-friendly interfaces.[7] These changes addressed limitations in prior versions' event-based focus, broadening applicability to regulatory assessments of urban stormwater impacts.[6] By 1988, SWMM Version 4 introduced groundwater simulation, including aquifer levels and their interactions with sewer systems, allowing coupled analysis of subsurface and surface flows for more realistic depictions of infiltration excess and baseflow contributions.[3] Optimized for personal computers, it featured free-format data input, inline comments, and the RTK (Road Research Laboratory-Transport) unit hydrograph method for infiltration, improving computational efficiency over Fortran-based predecessors.[3] Hydrologic and transport blocks were refined for better handling of land-use variability and pollutant dynamics, with subsequent enhancements (1989–1994) integrating geographic information systems (GIS) for spatial data import and multiple graphical user interfaces (e.g., XP-SWMM) emerging in the 1990s to streamline preprocessing and postprocessing.[7] The evolution culminated in the development of SWMM Version 5, initiated around 2001 by the U.S. Environmental Protection Agency (EPA) in partnership with CDM Smith (key contributors Lew Rossman and Bob Dickinson), addressing legacy Fortran code maintenance challenges through a complete rewrite in C language.[7] This version unified the modular blocks (RUNOFF, TRANSPORT, EXTRAN, etc.) into a single executable, incorporating a public-domain graphical user interface and initial real-time control features for adaptive operations like pump scheduling.[3] Released in 2005, it enhanced numerical stability for large networks and prepared the model for future extensions in low-impact development, reflecting accumulated empirical refinements from decades of CSO and stormwater validation studies.[7]Recent Updates and Maintenance (2005–Present)
The U.S. Environmental Protection Agency (EPA) released version 5.0 of the Storm Water Management Model (SWMM) in March 2005, marking a complete rewrite of the software with a unified dynamic simulation engine for hydrology, hydraulics, and water quality processes.[13] This version introduced improved numerical solvers, such as the modified Picard iteration for dynamic wave routing, and expanded options for runoff quality modeling, including build-up/wash-off processes and treatment in storage units.[14] Subsequent builds in the 5.0 series, through 2008, addressed bugs in infiltration calculations (e.g., Horton method conversions), added elements like ideal pumps and custom conduit shapes, and refined reporting tables for storage units and system status.[14] Version 5.1, with builds commencing around 2014 and culminating in releases like 5.1.015 by May 2020, focused on enhancing simulation of green infrastructure and low-impact development (LID) controls to support sustainable stormwater management.[14] Key additions included detailed modeling of LID units such as rain gardens, green roofs, vegetated swales, and permeable pavement, with parameters for soil moisture, drainage, and evapotranspiration; modified Horton infiltration; and options for monthly climate adjustment factors to assess future scenarios.[14] These updates also incorporated mixed infiltration methods across subcatchments, variable routing time steps, and improved surcharge handling with EXTRAN/SLOT methods, alongside fixes for execution times and RDII (rainfall-derived infiltration/inflow) file handling.[14] Version 5.2, first released in November 2021 with builds up to 5.2.4 by July 2023, introduced advanced hydraulic features such as explicit street surface modeling for ponding and inlet capture, type 5 pumps defined by power curves, pre-defined storage shapes (e.g., paraboloid), and expanded control rules for conditional logic.[15] Engine enhancements included optional normal flow limits in dynamic wave routing, parallel processing for routing steps, and refined LID underdrain and pollutant tracking to resolve mass balance issues.[14] Maintenance has emphasized code refactoring for stability, GUI improvements like enhanced reporting options, and integration with ancillary tools such as SWMM-CAT for climate-adjusted simulations.[1] The EPA has maintained SWMM as open-source software via GitHub since at least 2021, enabling community-vetted contributions while ensuring core development remains under the Office of Research and Development.[2] Ongoing updates prioritize empirical validation against field data, with peer-reviewed documentation in reference manuals verifying model accuracy for urban runoff prediction.[13]Model Architecture
Conceptual Framework
The Storm Water Management Model (SWMM) employs a compartmentalized conceptual framework to simulate hydrologic and hydraulic processes in urban and suburban drainage systems, representing water and pollutant flows across four primary compartments: the atmosphere (providing precipitation and evaporation), the land surface (where infiltration, runoff, and depression storage occur), groundwater (interacting via seepage and baseflow), and the transport network (conduits and storage units for routing flows).[9] This structure enables dynamic simulation of single-event or continuous rainfall-runoff scenarios, tracking quantities such as flow rates, depths, and pollutant concentrations over specified time periods.[1] The model discretizes the watershed into interconnected elements—subcatchments for surface processes, nodes for storage and junctions, and links for conveyance—allowing for detailed representation of spatial variability in land use, soil properties, and infrastructure.[9] At the core of SWMM's framework are subcatchments, defined as hydrologic units that generate runoff from precipitation inputs, accounting for impervious and pervious fractions with parameters like area, slope, Manning's roughness, and infiltration capacity.[9] Runoff from each subcatchment outlets to a downstream node or another subcatchment, incorporating losses such as initial abstraction, evaporation, and snowmelt where applicable. Nodes serve as endpoints for inflows and decision points for routing, categorized as junctions (for link confluences with defined invert elevations and maximum depths), outfalls (fixed downstream boundaries), dividers (for splitting flows based on criteria like depth or velocity), and storage units (offering volume via functional surface area-depth relationships).[9] Links connect nodes to model conveyance, including conduits (rectangular, circular, or irregular shapes governed by Manning's equation), pumps (following predefined curves), and regulators (orifices, weirs, or outlets with discharge coefficients).[9] The simulation proceeds sequentially through runoff generation, transport routing, and exfiltration processes, with time steps adjustable for wet and dry periods to balance computational efficiency and accuracy.[9] Runoff employs a nonlinear reservoir method to compute surface flows, while routing options include steady flow, kinematic wave (approximating wave propagation without backwater effects), or full dynamic wave (solving Saint-Venant equations for unsteady flow with inertia, pressure, friction, and continuity).[9] Groundwater components link subcatchments to aquifers, simulating vertical infiltration and lateral baseflow to nodes using Darcy's law and storage coefficients.[9] Low impact development (LID) controls integrate into subcatchments as layered systems (e.g., vegetation, soil, drainage) to mimic retention practices like rain gardens or permeable pavements, reducing peak flows through infiltration and evapotranspiration.[9]| Component | Role in Framework | Key Parameters |
|---|---|---|
| Subcatchments | Runoff generation and losses | Area, % impervious, slope, Manning's n, infiltration method (e.g., Horton, Green-Ampt)[9] |
| Nodes | Storage and flow division | Elevation, max depth, surcharge allowance[9] |
| Links | Flow conveyance | Length, cross-section shape, roughness, slope (minimum 0.001 ft/ft)[9] |
| Aquifers | Subsurface interaction | Hydraulic conductivity, porosity, water table depth[9] |
Core Components and Parameters
The Storm Water Management Model (SWMM) employs a network of interconnected elements to simulate urban drainage systems, comprising subcatchments for runoff generation, nodes (primarily junctions and outfalls) as connection points, and links (such as conduits) for flow conveyance. These core components enable representation of hydrologic, hydraulic, and water quality processes through user-defined parameters that reflect physical properties and simulation choices. Subcatchments model impervious and pervious land surfaces contributing inflow to downstream nodes, while nodes aggregate flows and links route them under specified hydraulic conditions.[9] Subcatchments are the primary units for discretizing the watershed into areas of uniform hydrologic characteristics, each routing generated runoff to a single outlet node or another subcatchment. Essential parameters include total area (in acres or hectares), percentage of impervious cover, characteristic width of the overland flow path (feet or meters), average slope (as a percentage), Manning's roughness coefficients for impervious (typically 0.01–0.02) and pervious (0.05–0.15) surfaces, and depression storage depths (e.g., 0.05 inches for impervious, 0.1 inches for pervious). Infiltration is parameterized via selectable methods—Horton (with maximum rate, minimum rate, decay constant), Modified Green-Ampt (suction head, conductivity, initial deficit), or Curve Number (CN value, dryness factor)—along with options for groundwater interaction, snowmelt, and low-impact development controls. Runoff routing within the subcatchment can be intermitted (treating impervious and pervious areas separately) or broad-crested weir, with adjustable percentages of generated flow routed to the outlet.[9] Junctions serve as nodes where multiple links converge, simulating manholes, inlets, or channel confluences with potential for ponding and surcharge. Key parameters encompass invert elevation (feet or meters), maximum depth (e.g., 4–8 feet for typical manholes), initial depth, surcharge head allowance, and ponding surface area (square feet or meters, default 0 if disabled). External inflows—dry weather, rainfall-dependent, or time-series—can be specified, alongside water quality treatment functions. Coordinates for spatial mapping and optional tags aid visualization and querying.[9] Conduits model open channels or closed pipes linking nodes, supporting various cross-sections (circular, rectangular, irregular via tables). Critical parameters include length (feet or meters), Manning's roughness (0.01–0.013 for concrete pipes), shape and size (e.g., diameter for circular), inlet/outlet elevations or offsets, initial flow, and maximum flow limits. Hydraulic losses are captured via entry/exit/average coefficients, with options for flap gates to prevent backflow, culvert equations (e.g., FHWA codes), and seepage rates (inches per hour). Conduit slope is computed from node elevations unless overridden.[9] Outfalls terminate the network at receiving waters, with parameters defining boundary conditions: invert elevation, type (free discharge, normal depth, fixed/tidal/time-series stage), and associated curves or series for varying heads. Storage units supplement nodes for detention basins, parameterized by elevation-area-depth curves, initial depth, evaporation factors, and treatment options. Global simulation parameters, such as routing step (e.g., 1–5 minutes for dynamic wave) and flow units (CFS, MGD), govern time-stepping and units consistency across components. Pumps and flow dividers extend links for active control, with pump curves (head vs. flow) and divider ratios or conditions.[9]Hydrologic Processes
Infiltration Methods
SWMM simulates infiltration from pervious subcatchment surfaces using five distinct methods, each representing different empirical or physically based approaches to estimating the rate of water entry into soil. These methods compute the infiltration rate as a function of time, soil properties, and antecedent conditions, subtracting infiltrated volumes from total precipitation to determine excess rainfall available for runoff. Selection of a method is specified globally for the simulation or per subcatchment, with parameters calibrated to local soil data; switching methods requires redefining parameters except between paired variants like Horton and modified Horton.[9] The Horton method employs an empirical exponential decay function derived from field observations of decreasing infiltration capacity during rainfall events. The infiltration rate f(t) starts at a high initial value and declines to a minimum rate approximating saturated hydraulic conductivity, modeled as f(t) = f_c + (f_0 - f_c) e^{-kt}, where f_0 is the maximum rate, f_c the minimum rate, k the decay constant (typically 2–7 per hour), and t the elapsed time since ponding began. Key parameters include maximum rate (in/hr or mm/hr), minimum rate (in/hr or mm/hr), decay (1/hr), and drying time (days, often 2–14 for soil recovery between events); an optional maximum infiltration volume limits total infiltration based on soil porosity minus residual moisture times depth. This method suits scenarios where direct measurement of soil hydraulic properties is unavailable but empirical calibration data exist.[9] The modified Horton method refines the standard Horton approach by tracking cumulative infiltration and soil moisture as state variables, enabling better recovery of infiltration capacity during inter-event dry periods and improved performance under low-intensity rainfall. It retains the same exponential equation as Horton but adjusts the effective moisture deficit dynamically, reducing errors in partially saturated conditions compared to the base method. Parameters mirror those of Horton, with added implicit handling of initial soil moisture; drying time governs the rate at which capacity regenerates, typically assuming full recovery after 7–14 days. This variant enhances accuracy for continuous simulations spanning multiple events.[9] The Green-Ampt method is a physically based model assuming a sharp wetting front advancing through homogeneous soil, where infiltration is driven by the matric suction head at the front and gravity. The rate f(t) is given by f(t) = K \left[1 + \frac{\psi \Delta \theta}{F}\right], with K as saturated hydraulic conductivity (in/hr or mm/hr), \psi the suction head (typically 0.1–0.5 ft or 30–150 mm for loams), \Delta \theta the initial moisture deficit (fraction, often 0.2–0.4), and F cumulative infiltration depth; at equilibrium, f(t) approaches K. Parameters include suction head, conductivity, and initial deficit, derived from soil texture data such as those in USDA classifications (e.g., K = 0.3 in/hr for sandy loam). It excels in event-based simulations with measured soil properties but assumes uniform soil and instantaneous ponding.[9] The modified Green-Ampt method extends the standard Green-Ampt to heterogeneous, layered soils by parameterizing multiple horizons with varying conductivity, suction, and deficit per layer, computing effective rates through sequential wetting front propagation. It uses the same core equation but iterates across layers, halting if an impermeable layer is reached; total infiltration is capped by the summed deficits of accessible layers. Parameters expand to include number of layers (up to 10), each with its conductivity, suction, and deficit, plus field capacity for upper layers; this allows representation of crusting or compaction effects. Applicable to urban sites with profiled soils, it provides greater realism than single-layer models for depth-varying permeability.[9] The curve number (CN) method, introduced in SWMM 5, adapts the U.S. Natural Resources Conservation Service (NRCS, formerly SCS) empirical procedure for estimating abstractions from rainfall based on hydrologic soil groups, land cover, and antecedent wetness. Infiltration capacity diminishes as cumulative rainfall increases, with potential abstraction S (in inches or mm) computed as S = \frac{1000}{CN} - 10 for average conditions, and excess rainfall as Q = \frac{(P - 0.2S)^2}{P + 0.8S} where P is total precipitation; initial abstraction is 0.2S, and infiltration derives from the difference. Parameters are CN (30–98, from NRCS TR-55 tables), drying time (days), and optionally hydraulic conductivity (deprecated in later versions); antecedent moisture is adjusted via CN classes (I–III). This index-based approach simplifies calibration using land use maps but lacks explicit time-dependency, making it less suitable for highly transient events.[9]Runoff Generation and Losses
In the Storm Water Management Model (SWMM), runoff generation occurs within subcatchments modeled as nonlinear reservoirs that receive precipitation inputs and accumulate excess water as ponded depth after accounting for losses.[13] Subcatchments are divided into pervious and impervious portions, with the impervious fraction typically ranging from 0% to 100% based on land use characteristics such as urban density.[13] Impervious areas may further be split, with a user-specified percentage (e.g., 25%) assumed to lack depression storage and contribute direct runoff immediately upon rainfall.[13] The governing mass balance equation for surface water depth d is \frac{\partial d}{\partial t} = i - e - f - q, where i is rainfall intensity, e is evaporation rate, f is infiltration rate (handled via separate methods), and q is runoff rate; this is solved numerically using Runge-Kutta integration at user-defined time steps, typically 5 minutes for wet periods.[11] Evaporation losses are applied uniformly across pervious and impervious surfaces, limited by the available ponded depth, and computed from constant values, monthly averages (e.g., via time patterns), time series, or climate files incorporating methods like Hargreaves based on temperature and solar radiation.[13] [11] These losses are generally minor compared to other processes but reduce the effective rainfall available for ponding, with total evaporation depth reported per subcatchment in simulation outputs.[13] Depression storage captures initial abstractions by filling surface irregularities such as puddles and micro-depressions before overflow generates runoff.[11] Maximum storage depths are specified separately: 0.05–0.10 inches for impervious areas and 0.10–0.30 inches for pervious areas, adjustable monthly via multipliers.[13] Runoff initiates only when ponded depth exceeds these capacities, with losses reported as total depth in subcatchment summaries.[13] Surface runoff rate q (in cfs/ft of width) is computed using a kinematic wave approximation of Manning's equation for overland sheet flow once effective depth d - d_s (where d_s is depression storage depth) is positive: q = \frac{1.49}{n} W (d - d_s)^{5/3} S^{1/2}, with n as Manning's roughness coefficient (0.01 typical for impervious, 0.10 for pervious), W as characteristic overland flow width (derived from subcatchment area and flow path length), and S as average slope in ft/ft.[11] [13] Total subcatchment runoff combines separate hydrographs from pervious and impervious contributions, which may be routed directly to the outlet node or interchanged (e.g., impervious runoff to pervious for additional losses), with volume equaling integrated q times area.[13] Peak rates and coefficients emerge from rainfall intensity, surface properties, and losses, enabling simulation of both single events and continuous periods.[11]Hydraulic Processes
Flow Routing Options
The Storm Water Management Model (SWMM) provides three primary options for routing flows through conveyance system elements such as pipes, channels, and storage units: Steady Flow, Kinematic Wave, and Dynamic Wave.[13] These methods differ in their treatment of flow dynamics, computational demands, and applicability to various hydraulic conditions, with Dynamic Wave offering the highest fidelity to physical processes at the cost of increased simulation time.[13] Selection depends on factors like network complexity, desired accuracy for phenomena such as backwater effects or surcharging, and available computational resources; for instance, simpler methods suffice for preliminary screening of large systems where full unsteady hydraulics are unnecessary.[13] Steady Flow routing, the simplest option, computes a steady-state flow for each conduit at every time step by assuming constant inflow rates without temporal variation in depth or velocity.[13] It applies the Manning equation to determine uniform flow conditions, ignoring momentum and pressure forces, which makes it computationally efficient but unsuitable for capturing transient effects like wave propagation or storage interactions.[13] This method, previously termed "Runoff" routing in earlier SWMM versions, is appropriate only for systems where inflows are relatively constant or for quick approximations in oversized conduits dominated by gravity flow.[16] Kinematic Wave routing approximates unsteady flow by allowing depth and flow to vary both spatially and temporally within conduits, but it neglects pressure gradients, backwater curves, and inertial terms in the momentum equation.[13] It solves a simplified continuity equation combined with Manning's equation for normal depth, assuming flow is always at kinematic equilibrium without downstream influences propagating upstream.[17] Formerly known as "Transport" routing, this method is faster than Dynamic Wave and adequate for mildly sloped channels or steep pipes where attenuation is minimal, but it overpredicts peak flows and fails to model surcharging or reverse flows.[13] Computational stability requires routing time steps on the order of the time of concentration divided by 5 to 10.[13] Dynamic Wave routing employs the full one-dimensional Saint-Vénaut equations—comprising continuity and momentum conservation—to simulate unsteady, gradually varied flow, including backwater effects, surcharge, tidal influences, and pressurized flow in closed conduits.[18] This method discretizes the conveyance network into links and nodes, solving nonlinear partial differential equations via an adaptive time-stepping implicit finite difference scheme that handles wetting/drying and hydraulic discontinuities like pumps or regulators.[13] Previously called "Extran" routing, it is the default and most versatile option, essential for urban drainage systems prone to flooding or ponding, though it demands smaller time steps (typically 1-5 seconds for stability in looped networks) and can exhibit numerical instabilities if slopes approach critical limits.[13] Parameters such as the routing time step, minimum/maximum depths, and inertia terms (which can be neglected for further simplification in shallow flows) are adjustable to balance accuracy and efficiency.[19]Conduit and Network Hydraulics
Conduits in the Storm Water Management Model (SWMM) represent pipes, open channels, and natural streams that convey stormwater through the drainage system. These elements support a variety of standard closed conduit shapes, such as circular and egg-shaped, as well as open channel geometries including rectangular, trapezoidal, and parabolic forms, with custom cross-sections also permitted.[1] Flow within conduits under dynamic wave routing is governed by the conservation of mass and momentum equations, approximating the one-dimensional Saint-Venant equations for gradually varied, unsteady flow.[9] For non-pressurized conditions, the Manning equation determines flow: Q = \frac{1.49}{n} A R^{2/3} S^{1/2} in US customary units, where Q is discharge, n is Manning's roughness coefficient (typically 0.011–0.026 for pipes), A is wetted area, R is hydraulic radius, and S is the slope of the energy grade line.[9] Pressurized flow in force mains employs either the Hazen-Williams equation, Q = 1.318 C A R^{0.63} S^{0.54} with Hazen-Williams coefficient C, or the Darcy-Weisbach equation based on friction factor and velocity head loss.[9] Network hydraulics in SWMM simulate the conveyance of runoff and external inflows through interconnected nodes and links, enabling representation of arbitrarily sized drainage systems with dendritic or looped topologies. Nodes include junctions for connecting conduits, outfalls defining system boundaries (e.g., free discharge or fixed head), and storage units for detention basins.[1] Junctions enforce mass continuity by balancing inflows and outflows, with optional ponding of excess water if a non-zero ponded area is specified, allowing simulation of surface flooding.[9] Conduits link nodes, incorporating parameters such as length, inlet/outlet offsets, seepage rates, and minor losses via entry/exit coefficients (e.g., 0.5 for entry, 0.25 average).[9] The dynamic wave method, recommended for detailed hydraulic analysis, solves the coupled system iteratively using an explicit finite difference scheme on a fixed time grid, typically with steps of 5–30 seconds during wet periods to satisfy the Courant stability criterion with a 75% safety factor.[9] Momentum equations account for inertial terms, adjustable via damping options (none, partial, or full) to enhance numerical stability in looped networks or under surcharging conditions, where water depth exceeds the highest connected conduit crown.[9] Backwater effects, flow reversal, and pressurized flow are captured through iterative head adjustments at nodes with convergence tolerances of 0.005 ft and up to 8 trials per step.[9] Surcharging is modeled by extending junction depths beyond maximum values, delaying overflow until surcharge limits are reached, with continuity errors maintained below 10% for accuracy.[9] This approach contrasts with simpler kinematic or steady flow routing, which neglect inertial and pressure forces, limiting their use to steep, non-interacting conduits.[1]Water Quality Simulation
Pollutant Accumulation and Transport
In the Storm Water Management Model (SWMM), pollutant accumulation, or buildup, on subcatchment surfaces is simulated during dry antecedent periods using one of several empirical functions tied to land use categories. The power function, commonly applied, computes buildup as B = \min(C_1, C_2 \times t^{C_3}), where B is the accumulated mass per unit area or curb length, C_1 is the maximum buildup mass, C_2 is the rate constant, C_3 is the power exponent (typically ≤1), and t is the number of antecedent dry days.[9] Alternative functions include exponential buildup B = C_1 (1 - e^{-C_2 t}), approaching an asymptote C_1, and saturation buildup B = C_1 t / (C_3 + t), where C_3 is a saturation constant; external time series can also drive buildup.[9] Parameters are user-specified per pollutant and land use, with initial buildup calculated from simulation start conditions, and reductions possible from street sweeping (modeled as fractional removal efficiency applied periodically).[9] Pollutant transport begins with washoff from subcatchments during wet-weather runoff, depleting the accumulated buildup. The exponential washoff method, widely used, calculates the washoff rate as W = C_1 q^{C_2} B, where W is mass per unit time, q is the runoff rate, C_1 is the washoff coefficient, C_2 is the exponent (often around 1.5), and B is the current buildup.[9] Other options include rating curve washoff W = C_1 Q^{C_2} (independent of buildup, with Q as runoff flow rate) and event mean concentration (EMC), applying a fixed concentration C_1 to total event runoff.[9] Washoff concentrations are computed dynamically at each time step and routed as inflow to the drainage network, with user-defined pollutants (e.g., total suspended solids in mg/L) tracked alongside dry-weather or groundwater contributions.[9] Once in the conveyance system, pollutants are transported via advection with flow routing methods (e.g., dynamic wave or kinematic wave), modeled as concentrations in conduits and nodes assuming complete mixing.[9] At nodes, inflow concentrations are flow-weighted, and first-order decay can be applied using a user-specified coefficient K_d (1/day), reducing mass as C = C_0 e^{-K_d \Delta t}.[9] Conduit transport simplifies the advection-dispersion equation via tanks-in-series approximation, with no explicit erosion or settling in standard SWMM unless extended; treatment at nodes (e.g., via BMP removal percentages) further modifies loads before outfall discharge.[9] Output includes time-series concentrations and total event loads, enabling assessment of nonpoint source pollution dynamics.[9]| Buildup/Washoff Function | Key Equation | Primary Parameters |
|---|---|---|
| Power Buildup | B = \min(C_1, C_2 t^{C_3}) | C_1: max mass; C_2: rate; C_3: exponent |
| Exponential Buildup | B = C_1 (1 - e^{-C_2 t}) | C_1: max mass; C_2: rate constant |
| Exponential Washoff | W = C_1 q^{C_2} B | C_1: coefficient; C_2: exponent; B: buildup |
| Rating Curve Washoff | W = C_1 Q^{C_2} | C_1: coefficient; C_2: exponent |