A forward run (normal simulation) is a single run of ART3D using the values assigned to the parameters. A single grid dataset is written out for each specie. Any observation points are also solved at each grid timestep and at each time value assigned to any of the observation points.
Parameter Estimation Simulation
A parameter estimation simulation, or inverse run, consists of multiple runs of ART3D in an effort to optimize the parameters so that the calculated output best matches user-input field data. The user is required to enter starting values for each parameter and bounds on those parameters that are to be optimized. At the end of the optimization process, ART3D runs one last time with the optimized parameter values so that the user can view the optimized solution.
The optimization routine works by running ART3D without computing a grid solution. The values are calculated at the observation points and are compared to the user-input field values. The total error is calculated using the following equation:
where
n = number of observation points,
m = number of species,
wi,j = weight value for species j at observation point i,
Cc = the calculated concentration at observation point i, and
Co = the observed concentration at observation point i.
The weight value described above is calculated from the standard deviation entered in the observation coverage dialog as:
The total error along with the bounds on the parameters are then passed back to the optimization routine and each parameter is changed a small amount one at a time. Each time a parameter is changed, ART3D is run again and the error is re-calculated. In this way the gradient of the objective function with respect to each parameter can be estimated. Once all of the gradients are known, all the parameters are changed down gradient and the process begins again. This process continues until one of several stopping tolerances are met.
Because this type of optimization is very sensitive to the starting parameter values provided by the user, it is important to try the optimization simulation multiple times with different starting values. Other methods of improving the calibration include the changing of the parameter bounds, and stopping tolerances.
After running in inverse mode, the optimized solution can be read into the project where calibration targets and plot options can be used to assess the success of the calibration or to compare it with other calibrations.
In a stochastic simulation, ART3D will be run multiple times with randomized parameters. The random values are chosen to honor statistical information provided by the user. If the distribution data is accurate, each simulation can be assumed to represent an equally possible solution. If enough simulations are run, they can be used to determine the likelihood of the occurrence of a given scenario. In this way, the uncertainty in the input parameters can be reflected by the uncertainty in the output solutions. See the section on Risk Analysis for an explanation of threshold analyses.
Related Links:
Building an ART3D Simulation
General Options