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How Hydrodynamic Models Are Used

What is a hydrodynamic model?
Hydrodynamics is the study of motion of liquids, and in particular, water. A hydrodynamic model is a tool able to describe or represent in some way the motion of water. Before the advent of widely available computer systems, a hydrodynamic model could in fact be a physical model built to scale. However, virtually all hydrodynamic models in use today are computational numerical models.

With the technological development of numerical models along with advanced computational systems, hydrodynamic modeling has become part of the larger field of computational fluid dynamics (CFD). Therefore, hydrodynamic models used for coastal ocean applications are related to models developed for meteorology, aerospace and automotive design, ventilation systems, and so on. The common basis for these modeling activities is the numerical solution of the governing equations of conservation of momentum and mass in a fluid.

Hydrodynamic modeling differs from other CFD specializations is its focus on the movement of water. The National Ocean Service (NOS) is focused on water flow in the coastal ocean, and therefore works in the specific field of geophysical fluid dynamics, which focuses on fluid motion in earth systems. For NOS, this primarily means the ocean and estuaries but also includes the Great Lakes and coastal rivers. The hydrodynamic models developed and implemented by the Marine Modeling and Analysis Programs (MMAP) are used to simulate flow of water and its corresponding change in properties (temperature and salinity). These models represent the coastal environment by the laws of physics solved for by computational numerical techniques. They have been shown to be accurate for a wide range of coastal processes. Hydrodynamic modeling is accomplished through skillful development combined with understanding of the physical system. CFD models are limited to systems with the properties described by the governing equations, by the capability of the numerical algorithm solving the equations, and by the capacity of the computational system. These factors define the ability of the model to represent a physical system in its numerical framework and a require that a user understand the limitations of the modeling approach.

How do hydrodynamic models work?
The basis of computational hydrodynamic models is the set of equations that describe the motion of fluids: the Navier-Stokes equations. These equations are derived from Newton’s laws of motion and describe the action of force applied to the fluid; that is, the resulting changes in flow. This is the property of conservation of momentum and is simply Newton’s second law: acceleration is dependent upon the force exerted and proportional to its mass. Computational hydrodynamics also imposes the continuity principle: mass and energy are conserved unless they pass out of the domain. For hydrodynamic modeling, the Navier-Stokes equations are simplified by the specific properties of the coastal ocean. The resulting equations are the shallow water equations, so called since the scale of features in the horizontal is much greater than in the vertical. Oceans and estuaries are much larger in length and width than they are in depth. They are much more of a puddle than bucket, and motions in them are predominantly horizontal (e.g., tides and currents). The shallow water equations allow for more efficient numerical solution of flow in this environment.

The complexity of the system of interest (a river, estuary, or ocean) prevents solution of the governing equations analytically. Scientific computing has enabled researchers to address these complex problems through numerical methods. However, computers can only perform discrete calculations and therefore the continuous governing equations must be broken into small individual problems that can be quickly solved on a computer. This procedure is governed by the numerical method used for a particular model. Two classes are common in hydrodynamic models: structured grid approaches (primarily finite difference algorithms) and unstructured grid approaches (including finite element and finite volume methods). The numerical methods deal with the domain by separating it into numerous components through a discretization process that produces in a model grid. Structured grid models tend to use quadrilateral grid cells that limit the grid’s flexibility in resolving the complex shoreline but are characterized by their straightforward and efficient algorithms. Unstructured grid models have much more flexibility in their grid resolution by employing variable triangular elements, but tend to be more time consuming to run and more sensitive to numerical errors. Both types of numerical methods have been applied to high performance computing systems, enabling simulation of complex coastal regions at high resolution.

These coastal hydrodynamic models are applied to many different ecological problems by using a range of model configurations and forcing. For example, these models can be used in an efficient depth-averaged two-dimensional (2-D) application or in a full three-dimensional (3-D) form. For well-mixed systems, the effects of density variations due to temperature and salinity can be ignored and the model run in barotropic mode. The baroclinic (density) effects can also be included if necessary by solving for temperature and salinity forcing. Furthermore, equations describing the transport and fate of constituents in the water (e.g., contaminants such as oil or biota such as fish larvae) can be coupled to the hydrodynamic equations.

The accuracy of a coastal ocean model is closely related to the input provided to it, such as bathymetry and meteorological conditions. Coastal ocean models use a wide range of observational data and meteorological models to define the forcing for the model. Similarly, data such as river inflow and tidal signals are required at the boundaries of the model for driving the model. The model developer will apply the best data sources available to generate high quality output. However, the accuracy of the model is limited by the quality of data available.

How are hydrodynamic models used?

Hydrodynamic models are able to describe the motion of water in a range of coastal environments. Output can include a time history of water surface elevation, current velocity, temperature, and salinity, as well as transport and fate of constituents included in a coupled transport model. These results are useful to a wide range of users, providing that sufficient accuracy has been demonstrated from the model. This is generally done by comparing model results to observations. To demonstrate the accuracy (or skill) of a model application, MMAP has developed skill assessment software  to perform statistical analyses of the model-data comparison. In order for a model to be accepted into NOS’ suite of operational nowcast/forecast models, it is required to meet a suite of skill criteria. These criteria ensure that the model is providing accurate results that can be used for forecast guidance and additional applications.

Operational Modeling for Water Level and Current Forecast Guidance
One of the main uses of hydrodynamic models within NOS is to provide forecast guidance  for coastal ports, harbors, and estuaries. Forecast guidance means that predictions of oceanographic conditions over the near future (i.e., the next several days) are made available to weather forecasters and other users. Predictions of water levels and currents can be very important to the maritime community for planning safe navigation. Predictions of temperature and salinity fields are also generally produced.

The NOS nowcast/forecast systems are run routinely (daily or more frequently) by a short simulation of the recent past forced by observation data (the nowcast) followed by a forecast of the following several days. The nowcast is aimed to be an accurate representation of present conditions, and is generally used as the initial condition for both the next nowcast and forecast. The forecast is primarily driven by output from meteorological forecast models, and decreases in accuracy the further in time it extends. Hydrodynamic models used for forecast guidance are running operationally in a number of U.S. coastal systems  and continue to be developed.

Ecological Applications
The capability of hydrodynamic models to provide accurate predictions of oceanographic variables (water level, currents, temperature, and salinity) enables use of model output to drive ecological forecasts. The ecology of estuaries includes important species that impact the system and its users. Many of these species have behavior that is significantly affected by their environmental conditions, such as the surrounding water temperature, salinity, and current velocity. Therefore, forecasts of the behavior of many biota can be made based upon predictions of oceanographic variables from a hydrodynamic model.

One such application is the use of the Chesapeake Bay Operational Forecast System (CBOFS) to predict likely areas of sea nettle existence. The sea nettle (Chrysaora quinquecirrha) is a stinging jellyfish known to be largely present in waters of a certain temperature and salinity range. Therefore, predictions of temperature and salinity from CBOFS are used to predict the favorability of sea nettle distribution in Chesapeake Bay.

Another ecological application of hydrodynamic models is for providing forecasts of harmful algal blooms (HAB). HABs are a significant health risk to coastal ecology (and its users) because of their release of toxins that can harm shellfish, fish, and human populations. Operational hydrodynamic models are being utilized by NOAA to create regular HAB bulletins that describe the likelihood of HAB existence. These bulletins are based upon known linkages between oceanographic conditions and HAB activity. The bulletins are provided to coastal resource managers who can then take appropriate action to minimize their impact.

Geospatial Applications
All hydrodynamic models vary in both time and space, and the output results can be linked to numerous geospatial applications. Examples of variables that are output from the model include water levels, currents, salinity and temperature. The changes in these variables over time and space can be shown visually for users, an example of which is shown below for water levels and currents from two operational nowcast/forecast models:

Color coded map of Chesapeake Bay showing water levels relative to MLLW.      Color coded current variations based on operational nowcast/forcast models.

Model results can also be analyzed over time to reveal the average value of variables. For example, harmonic analysis of time series at each spatial location in a model can show the influence of specific tidal frequencies throughout a coastal region. Another example is examining water level time series to compute the average of the high and low water values, the results of which can be used to determine tidal datums such as mean higher high water (MHHW), mean high water (MHW), mean tide level (MTL), diurnal tidal level (DTL), mean lower water (MLW) and mean lower low water (MLLW).

These examples of geospatial information extracted from the models may then be integrated in software and GIS applications to serve specific user applications. The tidal datums, for example, are imported into the VDatum software for vertical datum transformations across a given geographic area. For more information on VDatum, visit the Coast Survey VDatum page
Model computed tidal amplitude of the M2 constituent in North Carolina     Model computer Mean HIgher High Water tidal datum in California.
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