Principles of numerical models in stormwater management

October 2009 » Web Exclusive
Thomas E. Barnard, Ph.D., P.E.

Engineers, utility managers, permit reviewers, and regulators are faced with increasingly complex issues regarding the design, construction, and maintenance of stormwater management facilities. Historically, the principal (if not only) objective was to remove stormwater from the site as quickly as possible. While protection of property from flooding remains the primary objective, environmental concerns require that groundwater recharge, maintenance of the flow regime, downstream impacts, and water quality also be addressed in the planning of new facilities and operation of existing ones.

Stormwater professionals frequently turn to numerical models to simulate the hydrologic and hydraulic processes that move stormwater through their collection and conveyance systems. These models are used to measure the system's performance under a variety of conditions, resulting in innovative systems that meet a complex set of objectives.

This article introduces the basic principles in stormwater modeling and provides guidance in selecting the best software modeling package for collection system and planning needs.

Definitions
The term model has several meanings, frequently resulting in confusion among those who base decisions on model results. For this article three levels of models are defined.

The graphical user interface displays a representation of the stormwater model.

1) A numerical model is a set of equations that describe the hydrologic and hydraulic processes that transform rainfall to runoff and move the runoff through the collection/conveyance network. An example is the Green-Ampt equation for infiltration through unsaturated soil.

A typical data dialog in XPSWMM organizes the data in a graphical setting that allows the modeler to edit and review the data quickly.

2) A modeling software package is an integrated collection of programs that allow users to organize the input data, define the boundary conditions, solve the numerical model, and present the results. Some packages are based on a defined set of numerical models while others allow users choices in selecting the most appropriate equations for their systems.

XPSWMM's Hydraulics Job Control dialog is used to define numerous run-time parameters for fine tuning the solution.

3) A site-specific model is a set of input data, boundary conditions, and run-time parameters that are applied to a specific watershed and collection system. Site-specific models are based on a collection of numerical models and are usually developed within a single modeling software package.

Dynamic section animation presents results in three synchronized panels, allowing modelers to understand their network's performance.

Numerical models
The equations used in models are generally differential equations. They describe rates of change of various parameters with respect to time and space. To solve the equations, boundary conditions must be defined. Examples include initial soil moisture levels and the elevation of tailwater at the outfall of the collection system. Obviously, model results are dependent on the boundary conditions used in a simulation.

An analytical solution is a single answer to a defined set of conditions (equations). Analytical solutions are not generally useful for stormwater networks because a single set of conditions does not exist. Instead, we turn to models to perform simulations. The results of these simulations are a collection of time series that present responses over the simulation period. Examples include graphs of depth or flow at specific locations in the network.

Stormwater studies need to evaluate the response of a collection system over a range of boundary conditions and inputs. This may drive the number of simulations required to several dozen or perhaps even a hundred. These simulations may produce a thousand or more graphs. A skilled model is required to reduce this output to a succinct set of inputs-responses and trends. This information must then be synthesized for presentation to decision makers.

Developing a site-specific model
The task of building a site-specific model of a large collection system may be overwhelming. Consult the modeling software's documentation for a list of required data. The planning of the model-building task should focus on three issues:

Data sources — Model data is typically developed from a variety of data sources. These should be identified early in the project, as well as available formats and the procedures to be used for entering the data into the model.

Boundary conditions — Antecedent soil moisture conditions, initial levels in detention ponds, and tailwater elevations are examples of boundary conditions that impact model results. A succinct set of boundary conditions and the combination in which they will be applied should be developed.

Design events — The primary input to a site-specific stormwater model is the rainfall. Two types of rainfalls are used: design and historical. Commonly used design rainfalls include the SCS and Huff time series. Historical rainfall, especially when combined with observations of peak flow and high water marks, is extremely useful in calibrating models.

Choosing a software modeling package
Acquiring a modeling software package represents a major investment in time and money for stormwater professionals. In addition to the cost of the software package, also consider the cost to acquire and load data, run the simulations, analyze results, publicize the output, and train the modelers. Suggested criteria for software selection include:

  • Technical capabilities — The software package must have the capabilities to accurately model all of the processes occurring in a network.
  • Data interface — the software should have the ability to interface with all the software being used for input or output and provide for smooth data transfer.
  • Solution engine — Does the package include a reliable engine that will efficiently produce stable solutions to multiple configurations with a single command? Can the modeler adjust runtime parameters to ensure a stable solution under all conditions?
  • Documentation and training — The software should have extensive documentation including a hyperlinked help file, sample files, tutorials, and training program.
  • Model output presentations — Model results will be presented in tabular, graphical, and animation formats. The software must produce professional quality output for public presentations as well as technical reports.
  • Advanced features — Does the software support advanced features that are moving into the mainstream such as assessment of Best Management Practices and analysis of receiving water quality and 2D flow?
  • Support — Does the vendor provide personal technical assistance for issues ranging from installation, model building, and running the software?

Summary
Numerical models are an essential tool in stormwater management practice. A variety of commercial and public domain software packages are available for building models and running simulations. Choosing the least expensive software may result in increased costs to build and run a model and ultimately lead to a less than optimal stormwater management solution.

In selecting a stormwater modeling package, stormwater professionals should ensure that the product meets all of their needs. XPSWMM is an economical hydrodynamic model and analysis software package that provides all the major hydrology methods. It provides the modeler with an ideal environment for building and running models and publicizing results.

Thomas E. Barnard, Ph.D., P.E. , is a consulting water resources engineer in northeast Pennsylvania. His specialty is the use of numerical models to analyze and design infrastructure for water distribution, collection, and conveyance of wastewater and stormwater and floodways.


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