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# RMA4

RMA4 is a finite element water quality transport numerical model in which the depth concentration distribution is assumed uniform. It computes concentrations for up to 6 constituents, either conservative or non-conservative, within the computational mesh domain.

# Background

RMA4 was originally developed by Norton, King, and Orlob of Water Resources Engineers in 1973 for the Walla Walla District Corps of Engineers. Subsequent enhancements have been made by King and Rachiele, of Resource Management Associates (RMA) and by the WES Hydraulics Laboratory, culminating in the current version of the code supported in SMS. Personnel in the Hydraulics Laboratory at WES developed the data input module and gradual boundary condition reinstatement after a flow reversal.

# RMA2 Applications

RMA4 Applications
The water quality model RMA4 is designed to simulate the depth-average advection-diffusion process in an aquatic environment. The model is used for investigating the physical processes of migration and mixing of a soluble substance in reservoirs, rivers, bays, estuaries and coastal zones. The model is useful for evaluation of the basic processes or for defining the effectiveness of remedial measures. For complex geometry, the model utilizes the depth-averaged hydrodynamics from RMA2.

The water quality model has been applied to define the horizontal salinity distribution to:

- Trace temperature effects from power plants
- Calculate residence times of harbors or basins
- Optimize the placement of outfalls
- Identify potential critical areas for oil spills or other pollutants spread
- Evaluate turbidity plume extent
- Monitor other water quality criterion within game and fish habitats

# RMA4 Capabilities

RMA4 is a general purpose model designed to investigate physical processes which are responsible for the distribution of pollutants in the environment, and for testing the effectiveness of remedial control measures at high speed and low cost. The methodology is restricted to one-dimensional and two-dimensional systems in which the concentration distribution in the third dimension is assumed uniform.

RMA4 has the capability to:

- Re-start (hotstart) the simulation from a prior RMA4 run and continue.
- Read one-dimensional and/or two-dimensional hydrodynamics from RMA2, or allow manual specification of the velocity field.
- Appropriately handle marsh porosity and wetting and drying from RMA2.
- Handle all one-dimensional flow control structures that are available in RMA2.
- Compute mass flux at continuity check line points.
- Accept boundary condition concentrations by node, line, or mass loading.
- Model up to 6 constituents as conservative or non-conservative using a first order decay.
- Permit temporary storage of re-solution files designed to speed up the solution calculations when the velocity file recycles, such as during a simulation of many repeated tidal cycles.
- Simulate advection-diffusion in the aquatic environment.

# RMA4 Limitations

RMA4 is limited to one-dimensional (cross-sectionally averaged) and two-dimensional (depth-averaged) situations in which the concentration is fairly well-mixed in the vertical direction. It will not provide accurate concentrations for stratified situations in which the constituent concentration influences the density of the fluid.

RMA4 (and the sediment model SED2D) are very sensitive to gain and loss of mass across excessively large boundary break angles (greater than 10 degrees). That is to say that the mesh must be designed to have a very smooth boundary for every scenario of wetted/dried edge throughout the simulation. The RMA2 Marsh Porosity option may help to alleviate edge problems.

# RMA4 Modeling Process

Like all of the TABS-MD models, RMA4 modeling process requires a basic set of input files and output files to conduct the simulation. The basic file essentials include: run control instructions including boundary conditions and pollutant loads, geometry, hydrodynamics, and concentration output.

RMA4 typically uses a hydrodynamic solution from RMA2 which has been obtained from the exact same geometry to be used for RMA4. An RMA4 simulation is always run in transient, i.e., dynamic mode, regardless of whether the RMA2 hydrodynamic results are steady state or transient. If the RMA2 hydrodynamics are steady state, these same results are reapplied at every time step of the RMA4 simulation. If the RMA2 hydrodynamics are transient (dynamic), you have control of the starting and stopping time of the RMA2 solution to be applied to the RMA4 simulation. Again, the hydrodynamics are rewound to the designated starting point if the RMA4 simulation is longer than the supplied hydrodynamics.

The following flow chart illustrates the RMA4 modeling process. Items with bold borders are required, others are optional.

# How RMA4 Works

RMA4 makes use of an advection-diffusion equation to obtain a solution, rather than an iterative process as in RMA2. From a set of initial conditions, RMA4 calculates concentrations for a specified number of constituents.

RMA4 has the capability for the simulation of the advection-diffusion process in the aquatic environment. The methodology is restricted to two dimensional systems in which the vertical concentration distribution (in the third dimension) is assumed uniform. Although this model is presented as an application to water quality problems, the technique is applicable to a large class of other environmental transport problems.

To use RMA4, the user must supply the basic physical description of the system (which is generated by SMS), the velocity fields (which is usually generated by RMA2), and the boundary conditions and pollutant loads. The output from the model consists of tabulated values (for viewing in a spreadsheet program) and binary solutions file (for viewing within SMS) of pollutant concentrations throughout the system for time steps during the simulation. The model will treat pollutants either as conservative or non-conservative using a first order decay.

The model is written in FORTRAN 77, is compatible with FORTRAN-90, and uses the finite element method of numerical solution. The program has a number of user options and can be operated with or without the time terms activated in the governing equations. Currently the model is most valuable for the investigation of physical processes which are responsible for the distribution of pollutants in the environment and for testing the effectiveness of remedial control measures at high speed and low cost.

# Specifying the Pollutant Data

The specification of the sources of pollutants requires a detailed description of the time history for each loading source. It is up to the user to determine these data, and typically they will come from a number of sources. For purposes of model validation or short term operational control, the data should be collected from field measurements and observations. For other studies, such as long term planning activities, typical operation schedules and average discharges conditions are appropriate.

# Specifying the Diffusion Coefficients

RMA4 requires two coefficients, one for the x-direction (DX card or DF card) and the other for the y-direction (DY card or DF card), which reflect the influence of turbulent behavior in the convective field. These coefficients are sometimes referred to as dispersion coefficient or diffusion coefficients. Although these coefficients have a somewhat artificial physical basis, they may be estimated from observed data.

If no data exists, then the user may find these guidelines helpful:

- Use the automatic diffusion capability, Peclet method, within RMA4
- Obtain guidelines from the pre-processor utility program MAKE_EV_DF.EXE (available in our SMS download area)
- Choose values known to be satisfactory in similar physical locations
- Choose values which are conservative in regard to the study’s objectives
- Choose larger values as the detail in the velocity diminishes

For water quality studies, convection is usually the dominant transport process and modeling results may be relatively insensitive to the mixing coefficients. Therefore, it is often beneficial to run the model with a range of possible coefficients to determine how sensitive the predicted levels of quality are to these values.

There are two methods of assigning the diffusion coefficients, the modeler may directly specify them or activate the automatic calculation method.

# Assigning Initial Conditions

In the time-dependent mode of operation, the RMA4 model moves forward in time from some beginning, or initial condition. The concentrations specified at the starting time are called the initial conditions. The calculated concentrations at the beginning of a simulation are highly influenced by the initial conditions, but to a lesser degree as time progresses.

You may have access to extensive field measurements, or output from another model, to permit a good estimate of concentrations contours in the study domain at a particular time. There are two techniques available to assign an initial estimate of concentrations for the domain.

- Creating Distinct Initial Concentration
- Creating Gradual Initial Concentration
- Using a Hotstart as the Initial Condition

# Creating Distinct Initial Concentrations

One practical straightforward approach for setting initial conditions is to start the simulation with an arbitrary global value for concentration and simply let the RMA4 model proceed with specified inputs until the state of the system is independent of the starting condition. For this technique, a rule of thumb for "how long is long enough" is to run the simulation for a period of approximately twice the time it takes for the velocity field to move across the area being simulated. After satisfying this criterion, the initial conditions should have little influence on the model’s results. However, if you can initialize the model with realistic concentration contours, the best solution will be obtained in the least amount of computational time.

The global assignment may be the simplest method to create initial contours of concentration, however it may be improved by making use of the material types, element numbers, or node numbers to assign an initial condition. This may be achieved quickly with the IC card with the T option using element material types, if the material types were assigned with the intent of using them to apply the initial concentration values.

# Creating Gradual Initial Concentrations

Another technique for obtaining initial contours of concentration is to let the RMA4 model calculate gradual concentrations starting from the contaminant source point.

The strategy is as follows:

- Initialize the entire model domain with the IC card to permit a representative starting concentration.
- Strategically assign continuity check lines throughout the model domain.
- On the TC card, set the delta time step to a value of zero and the steady state flag to a value of one.
- Define a boundary condition with a negative continuity check line number at pertinent locations using the BC card with the L option.
- Run the RMA4 model for one time step and save both the solution and the Hotstart file.
- Examine the concentration contours of the RMA4 solution to determine if the continuity check lines are assigned and located appropriately. Some experimentation may be necessary.
- Once you are satisfied with the initial condition concentration patterns, then Hotstart RMA4 and proceed with the simulation.

# Using a Hotstart as the Initial Condition

Any initial conditions supplied by the user on the IC card(s) are ignored when Hotstarting because they are superseded by the read from a Hotstart file. A hotstart is generated from a previous RMA4 simulation. Hotstarting is activated by specifying a positive number for the IHOTN and/or IHOTO variables on the $L card.

The Hotstart binary file is unique in that the hotstart output file for one simulation becomes the hotstart input file defining the initial conditions of the continuation run.

# Specifying Boundary Conditions

A concentration boundary condition should be applied at every potential inflow boundary location.

There are two main categories of boundary conditions for RMA4:

- Concentration Boundary Condition
- Mass Loading Boundary Condition

# Concentration Boundary Condition

Concentration may be specified by node, or across a check line, for each of the constituents (1-6). The assigned value is held to its specified value for all portions of the simulation when the flow direction is into the model. If the flow direction is out of the model, the default exit value is the calculated concentration at that location. The user may over ride the default, by forcing the exit concentration to be the specified value by flagging the continuity line as negative on the BC card.

Later, if the flow direction is once again directed into the model, the specified concentration is reactivated at the boundary. This strategy is not always satisfactory for a boundary flow reversal situation, because unrealistic sharp concentration gradients may result.

# Mass Loading Boundary Condition

The BL card is used to specify mass loading of a pollutant. Mass loading, for each of the constituents (1-6), may be specified globally, or by individual element, or material type on the BL card.

The advantage of specifying a mass loading is that the user has control over the total mass that is input to the model. If an internal point boundary condition were allowed the concentration is fixed at the specified value, but the effective total input to the model is impossible to calculate for all practical purposes.

# Long Term Simulations

There are several issues and obstacles to bear when a long term simulation is considered. Some of these issues are:

- Residence Time
- Computational Requirements

# Residence Time

One of the primary issues to be addressed when considering performing a long term simulation is "how long is long enough". In other words, you must know the residence time (Tresidence). Furthermore the residence time should be defined relative to the study objective. For example, typically a complex system would have a residence time of a month or more, but if the study objective was concerned about a local pier slip, then the residence time would be in units of days or weeks. Once the residence time has been estimated, it is advisable to run the RMA4 model for a multiple (N) of the residence time matching the study objective.

- RMA4 Simulation Time = N * Tresidence

We know that N should never be less than one, but the actual value is debatable. The appropriate value of 'N' probably lies between a 2 and 6. For instance, the residence time multiplier of N=3 for the Newark Bay, New Jersey, project was insufficient. One way to tell if N is sufficient is to plot the long term concentrations between the base condition and the channel deepening plan condition. It is particularly helpful to examine the differences to determine if they are still growing at the end of the simulation. This non stabilized difference suggests a larger residence time multiplier is necessary.

*This example plot illustrates two problems. First there is no sign of equilibrium. Secondly the differences between base and plan get larger
with time.*

# Computational Requirements

The obvious issues related to long-term simulations are computer related. Estimating the amount of memory, disk space, and archival space required not only to run the model long term, but also to process the data and analysis it satisfactorily is essential.

Ideally it is desirable for the problem to fit entirely in memory so that no auxiliary buffering to disk will cause excessive input/output (I/O) and slow the computational speed. For small to medium projects, the memory requirements to accomplish this are very affordable.