GMS:ART3D: Difference between revisions
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__NOINDEX__ | |||
{{Infobox Model | | {{Infobox Model | | ||
|name= ART3D | |name= ART3D | ||
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|tutorials= [[GMS:Tutorials#Models|ART3D Tutorials]] | |tutorials= [[GMS:Tutorials#Models|ART3D Tutorials]] | ||
}} | }} | ||
{{GMS Deprecated Feature}} | |||
ART3D is a three-dimensional analytic reactive transport model developed by Dr. T. Prabhakar Clement. As a screening model, it is fairly simple and requires homogeneity and constant transport properties. It allows for complex reaction sequences with first order decay as well as three dimensional dispersion. A single retardation coefficient must be applied to all species. The user can enter any number of observation points and ART3D will exactly calculate the concentration of each specie at these points and compare then to known values (if included). In addition to a simple forward run, ART3D can be run in inverse and stochastic mode. | ART3D is a three-dimensional analytic reactive transport model developed by Dr. T. Prabhakar Clement. As a screening model, it is fairly simple and requires homogeneity and constant transport properties. It allows for complex reaction sequences with first order decay as well as three dimensional dispersion. A single retardation coefficient must be applied to all species. The user can enter any number of observation points and ART3D will exactly calculate the concentration of each specie at these points and compare then to known values (if included). In addition to a simple forward run, ART3D can be run in inverse and stochastic mode. | ||
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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: | 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: | ||
[[Image:error.png]] | :<math>error = \sum_{j-1}^m\sum_{i-1}^n w_{ij}|(c_c-c_o)_i|</math> | ||
<!--[[Image:error.png]]--> | |||
where | where | ||
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The weight value described above is calculated from the standard deviation entered in the observation coverage dialog as: | The weight value described above is calculated from the standard deviation entered in the observation coverage dialog as: | ||
[[Image:weight. | :<math>weight = \frac{1}{stdev^2}</math> | ||
<!--[[Image:weight.png]]--> | |||
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. | 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. | ||
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{{Navbox GMS}} | {{Navbox GMS}} | ||
[[Category:ART3D]] | [[Category:ART3D]] | ||
[[Category:Archived]] | |||
[[Category:Equations]] | [[Category:Equations]] | ||
