Selecting Numerical Modeling Alternatives for Water Projects

A summary and guide for regulatory, development and environmental stakeholders.

Consulting engineers and environmental scientists are frequently asked what type of modeling is required to achieve a project’s goals from a regulatory, design or habitat standpoint. The answer is integrally tied to the project setting as well as the project’s objectives. This article explores some of the many modeling options available to solve the broad scope of problems encountered in engineering and environmental projects.

Water projects have a long history in both Oriental and Occidental civilizations. Many ancient water projects were so well conceived by their designers that they still exist today, with some still functioning in their original intent. In China, the Du Jiang Weir, Minjiang River (a tributary of the Yantze River), has been operating for over 2,200 years providing flood control and irrigation to approximately 1.7 million acres of farmland in Sichuan Province. Twelfth Dynasty (ca 2300 BCE) pharaohs dug the Bahr Yussef Canal, between the Nile River and Lake Moeris (Birket Qarun), 50 miles southwest of Cairo, Egypt, for flood control on the Nile and irrigation. Mohenjo-daru ruins (ca 2600 BCE) of Sindh Province, Pakistan, incorporated a complex system of water and wastewater for baths and religious practice (Krishnamurthy, 1996). Clay pipe water distribution, lined wells (ca 600 BCE), cisterns, wastewater drainage, a water clock and fountains (ca 400 BCE) have been discovered in the Agora of ancient Athens. Other ancient cultures with significant water projects include Mesopotamians, Romans and various cultures throughout the Americas (Mays 2009).

Today, water projects are more complex in their nature and scope, requiring a level of analysis unimaginable as recently as early last century. While the mathematical concepts that form the basis of water projects have changed only modestly since the time of the great projects of antiquity, our ability to analyze and investigate these concepts has both deepened and broadened with the aid of computer resources.

Essentially computers provide a method by which very large numbers of calculations can be made in a fraction of the time required to be completed by hand. While this fact may be obvious on its face, it is this ability that allows scientists and engineers to consider how project-related changes in hydraulics will impact habitat, where changes in land use will alter stream geomorphology, and what methods may be best employed to reduce anthropogenic chemicals in urban surface waters. While estimates concerning these and other types of environmental and engineering projects can be made without the use of computers and computer models, hand calculations may be less precise and accurate since their breadth may inhibit consideration of fine details, and because they are difficult to repeat.

Before we continue it is important to introduce the three main types of modeling available for environmental studies. Physical models are models where the system being analyzed is assembled to an exact scale of the system that exists or will be built. Physical models are best where the knowledge about parameters of the modeled system are not well recognized, but are significant to the outcome of the project. For example, in stream restoration projects plant communities often require more than one growing season to become fully established. For such restoration projects fabric mats are often placed on the stream banks to prevent erosion and allow for plants to root themselves enough not only inaugurate the plant community, but so that the plant roots will also help stabilize the stream banks and reduce bank erosion. Physical models, both and fractional and full scale, were created to examine the strength and effectiveness of the mats prior to their approval for use in restoration projects in general. (These studies vary from product to product.)

Where physical models examine a scaled system as a whole, mathematical models are representations of a specific behavior in a system on an analytical level and considering only known quantities or parameters. Mathematical models are successfully utilized where the phenomena being calculated is well understood and the parameters that control the outcome of the model are known or can be determined at least on average. The rate of ground water recharge from impounded surface water can be calculated from mathematical models that consider the volume of water and the physical characteristics of the soil through which the water percolates.

Finally, numerical models are computer programs where mathematical models are employed iteratively to examine complex systems, how parameters of systems change, or other computationaly intensive calculations concerning a system. Numerical models are best utilized for problems where the level of detail exceeds what can be rendered for a simple mathematical model, or where the number of calculations surpasses what is practical by an individual. The analysis of erosion around bridge piers in a stream resulting from changing water levels is one such example.

Numerical modeling for surface water studies fall into three categories and may be defined by the nature of the study. There are certainly other types of water studies, but the three kinds considered herein are broadly categorized as hydrology, hydraulics and transport (or water quality) models. Other types include ground water models and limnological models.

Modeling for hydrology studies deals with the way rainfall moves across the land on a scale from sub-watersheds to multiple watersheds. A watershed can be thought of as a sloping area of land that drains to a single, downslope location. Hydrology models will consider how the water distributes itself as runoff, and consider many factors affecting runoff such as the roughness of the ground surface, the rate of infiltration into the ground, the evapotranspiration of water by plants, ponding of water in low-lying depressions, and the time required for water to concentrate at the apex of a watershed. Hydrology models are commonly employed to determine the design discharge entering a stream section and quantifying the volume of water running off watershed for infiltration studies.

Hydraulic models are used to calculate parameters including velocity and depth in streams and culverts. Hydraulic models consider conduit roughness, shape and slope to determine the characteristics of the water flows. Interestingly, hydraulic models can be further subdivided based on the dimensionality of the problem. One-dimensional models are used to deal individual channels and channel networks where the flow of water moves primarily in the along-stream direction. Models that employ two-dimensional hydraulics are used for analysis that involves the flow of water both in the along-stream and cross-stream directions, such as flow across alluvial fans. Estuarine dynamics and other complex problems with fluids of different densities are modeled in three dimensions. Hydraulic models are typically used to calculate the jurisdictional limits of a channel, the base flood elevation in FEMA studies, habitat impacts in channel improvements studies, and the change in stream flow parameters resulting from the installation of bridges and other structures.

Transport models, finally, are typically hydrologic or hydraulic models that contain extra computational features that keep track of water quality constituent concentrations. Typical uses of transport models include contaminant runoff analysis for TMDL studies (hydrologic model) and sediment transport in bed erosion studies (hydraulic model).

The choice of a model is a function of the project need and, to a lesser extent, cost. A client should communicate clearly the nature and aims of the project to determine the kind of modeling most suited to achieve the project goals. As should be clear from the description above, different project types will require a wide range of analysis: land development will require different models than restoration projects, and large projects incorporating multiple watersheds will utilize dissimilar models than efforts examining stream systems. It is important to note that regulatory and permitting requirements may dictate the type, author and version of the model used. This is because different agencies have different modeling and permitting requirements. An unclear jurisdictional or permitting landscape may then lead to delays or revisions resulting from the variety of modeling requirements. Modeling cost is almost wholly a function of model complexity, and model complexity reflects the complexity of the project setting and design. In most circumstances the consultant will have only a limited ability to restrict the complexity of the modeling and, hence, the cost. A simple hydraulic model of a channel adjacent to new home development will require much less sophisticated modeling than the analysis of comingling of waters in a coastal lagoon with distinctly different water quality concerns. Clients, then, should contact modeling consultants early in the design process to ensure modeling efforts meet project goals, control costs, and achieve regulatory standards.