The stack plume contains coal combustion products that include compounds such as SO2, etc., whose typical signatures in the range that corresponds to the data above, is shown in the next figure.
The AES signature in the thermal IR portion of the spectrum, however, is dominated by the atmospheric interference , and the terrain background. In order to completely remove the atmospheric effects, detect the plume, and identify and quantify its contents, one has to have a decent knowledge of the environmental parameters that describes the radiative exchange. These parameters include, terrain temperature and spectral emissivity, atmospheric profiles of temperature, pressure, humidity, and other non-fixed components of the atmosphere. In addition, plume parameters such as temperature, composition, dimensions, are also required for a complete description. These parameters can be entered into an atmospheric propagation model (such as MODTRAN) and finally plume parameters extracted.
Since these environmental parameters are unknown, the approach constitutes and inverse problem , i.e., given the sensor measurements, the objective is to find out the environmental parameters that contribute to these measurements.
Inverse problems are ill-posed mathematical problems and are difficult to solve. Most common approach is based on many simplifications of the atmospheric parameters and the radiative exchange model as depicted below.
The approach for solving the inverse problem casts the problem as an optimization problem, minimizing an error function between model predictions and sensor observations. The optimization problem is then addressed using either a stochastic search process or a deterministic global optimization approach. In a typical problem such as atmospheric retrieval, the solution space resides in N-Dimensional space where N is typically a very large number (20 to 100).
One solution derived using genetic algorithms is depicted below. It shows the sensor data and the model predictions based on the parameter vector that was obtained from the optimization solution.
This solution does not take into account sensor errors, SNR, considerations, or uncertainty propagation. A deterministic global optimization based on the TRUST algorithms, with gradient enhancement of the Atmospheric propagation model, however, can address such issues as well.
Given that (i) this solution was derived with no supplied information regarding the environmental parameters, (ii) the error function, or difference between sensor measurments and model predictions is very small, and (iii) a full physics based model is used with no simplifications or approximations to the full radiative exchange, this is a pretty good result.
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