1. airborne material released from a point source in an urban environment
Validation of an inverse method for the source determination of a hazardous
airborne material released from a point source in an urban environment
G. C. Efthimiou1, S. Andronopoulos1, I. V. Kovalets2, A. Venetsanos1, C. D. Argyropoulos3, K. Kakosimos3
1Environmental Research Laboratory, INRASTES, NCSR Demokritos, Patriarchou Grigoriou & Neapoleos Str., 15310, Aghia Paraskevi, Greece.
2Department of Environmental Modelling, Institute of Mathematical Machine and System Problems, National Academy of Sciences of Ukraine, Kiev, Ukraine.
3Department of Chemical Engineering & Mary Kay ‘O Connor Processes Safety Center, Texas A&M University at Qatar, Education City, Doha, Qatar, PO Box
Introduction
The computational simulations of MUST
The characterization of an unknown atmospheric pollutant’s source following a release is a special case of inverse atmospheric dispersion problem. Such kind of inverse problems are to be solved in a variety of application areas such as emergency response, pollution control decisions and indoor air quality.
In some cases of inverse modeling there are some limitations. There is a typical problem for non-linear least squares fitting due to the ill-posed minimization problem and the non-convex cost function. This problem is called ‘overfitting’ effect. According to this effect, the calculation errors which are introduced by the wrong source location and lead to significant underestimation of the concentration are compensated by the overestimated source rate. Thus, the resulting quadratic cost function reaches minimum for the wrong combined solution (source location and source rate). In context of data assimilation this problem is especially important when the number of measurements is insufficiently small.
Efthimiou et al. (2016) presented an integrated and innovative approach, to eliminate the ‘overfitting’ effect, based on two main improvements.
First, we propose a non-simultaneous determination of the source location and rate, based on a two-step segregated approach combining a correlation and cost functions.
Second, we suggest a correlation coefficient of measured and calculated concentrations, instead of a cost function (as in Kovalets et al 2011).
The wind flow and passive dispersion – forward problem – was solved for the 3D domain which is rectangular with the x- and y-axes as presented in the previous Figure and the z-axis in the vertical direction. The domain dimensions are 243 m along the x-axis, 268 m along the y-axis and 21 m in the vertical, while we discretized it using two selected grids resolutions. The coarsest grid was constructed such as to be close to the grid of Kovalets et al. (2011). The finer grid was constructed to examine its effect on the results of the forward and inverse problem.
Grid
Total number of cells
Minimum/maximum cell sizes X Y Z
58,500 45 50 26
4.93/9.9
4.95/6.2
0.2/2.06
209,950 85 95
2.5/7.5
2.5/4.36
Method of validation of the predicted source location and rate
In order to understand the order of magnitude of the error we have used
the horizontal
and vertical
distances of the estimated source location (xs, ys, zs) from the true source location where index “t” stays for the true source. We have assumed that the predicted source (xs, ys, zs) is located at the center of the cell.
Concerning the source rate we have calculated the relative source rate ratio
which is always greater than unity for both underestimated and overestimated source rates.
Methodology
The proposed correlation coefficient of measured and calculated concentrations is:
where denotes arithmetic averaging over all measurements while minimum is sought over all possible source locations, c is concentration, index “c” stays for calculated value and index “o” stays for observed value.
This equation is minimized with respect to source coordinates only, while arbitrary source rate, is used for the minimization procedure.
As a second step, the source rate can be identified by minimizing the quadratic cost function
with respect to :
Here n is the number of observation record and K – total number of observations. A Source Receptor Function (SRF) is applied as in Kovalets et al. (2011) for the node (being the solution found in Step 1).
Results
For the coarse grid, the horizontal distance (rH) between the real and the predicted source was found equal to m and the vertical distance (rV) equal to 0.54 m which are slightly better results than Kovalets et al. (2011) (rH=11 m and rV=0.8 m).
For the fine grid, the horizontal distance (rH) between the real and the predicted source was found equal to 3.54 m and the vertical distance (rV) equal to 0.1 m which are better results than the coarse grid and Kovalets et al. (2011).
For the coarse grid, the relative source rate ratio was found equal to 2.26 which is again better result than Kovalets et al. (2011) (δq=3.1).
For the fine grid, the relative source rate ratio was found equal to 1.59 which is again better result than the coarse grid and Kovalets et al. (2011).
Dependence of probability of achieving good solution of inverse problem on the number of sensors used in source estimation.
Conclusions
The MUST wind tunnel experiment
A major change in the data assimilation code of Kovalets et al. (2011) was performed in Efthimiou et al. (2016) and included the implementation of a two-step approach:
At first only the source coordinates were analyzed using a correlation function of measured and calculated concentrations.
In the second step, the source rate was identified by minimizing a quadratic cost function.
The validation of the new algorithm was performed for the source location and rate by simulating a wind tunnel experiment on atmospheric dispersion among buildings of a real urban environment. Good results of source location and rate estimation have been achieved when all available measurements (244) were used to solve the inverse problem.
In MUST experiment the obstacles were arranged in 12 rows consisting of 10 obstacles. The obstacles were nearly identical and had average length, width and height: 12.2 m × 2.42 m × 2.54 m. The contaminant’s concentration has been measured by an array consisting of 256 detectors arranged along obstacle rows in the part of the domain covered by plume. All detectors were arranged at the same height equal to 1.28 m. Therefore non-zero
concentrations have been measured by
nearly all (244 out of 256) detectors. Here
we should note that only those
measurement data are described that were
available to authors (through data base of
COST 732 project). The wind flow was
characterized by neutral stratification, wind
speed at the roof level: Uref = 8 m/s, and
wind direction: −45o in experimental
coordinate system.
References
Efthimiou G.C., Andronopoulos S., Venetsanos A., Kovalets I.V., Kakosimos K., Argyropoulos C.D., Modification and validation of a method for estimating the location of a point stationary source of passive non-reactive pollutant in an urban environment, 17th International Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes, 9-12 May, Budapest, Hungary.
Kovalets I.V., Andronopoulos S., Venetsanos A., Bartzis J.G., Identification of strength and location of stationary point source of atmospheric pollutant in urban conditions using computational fluid dynamics model. Mathematics and Computers in Simulation, 82,
Contact
Acknowledgements
Dr. George C. Efthimiou
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This publication was made possible by a NPRP award [NPRP ] from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.
35th International Technical Meeting
on Air Pollution Modelling and its Application, Chania, 3-7 October 2016