Reconstructing height of an unknown point release using least‐squares data assimilation

Abstract

Reckoning the height of a release in the source term estimation is important since a ground‐level approximation of the release leads to errors in capturing the actual extent of a plume. A least‐squares inversion technique, free from initial guess, is adapted here for the reconstruction of an elevated point release in a discretized space. Primarily, this involves estimation of the effective height of the release above the ground along with its location and strength from a limited set of noisy concentration measurements. The methodology is evaluated here with the nine runs from the Idaho diffusion experiment (1974) corresponding to low wind, stable conditions. Both real and model‐generated synthetic data are used to test the method. With synthetic data, the methodology can exactly reproduce the input source terms. With real data, the average release height is estimated as 3.1 m, which is very close to the effective release height (3 m) reported in the Idaho data. The release location is retrieved with an average error of 30 m, whereas the minimum distance between source and detectors is 100 m; strength is retrieved within a factor of two in all the runs. The deviations in the source parameters from their prescribed values are explained in the context of model representativeness, wind variability and available monitoring network. The sensitivity of the source term estimation is evaluated against several parameters: (i) receptors' height either neglected or duly taken as 0.76 m, (ii) measurement noises and (iii) number of receptors utilized in the inversion. In addition, the limitations and meteorological issues related to the inversion of an elevated release are highlighted.

An Optimization‐Based Approach for Source Term Estimations of Atmospheric Releases

“…In order to minimize such a cost function, a variety of methods has been proposed (see Hutchinson et al, 2017;Zheng & Chen, 2011). The next section focuses, and generalizes, the one used by Issartel et al (2011), Sharan et al (2011Sharan et al ( , 2012, or Singh and Rani (2014).…”

“…Note that different selections of W m will produce different solutions. A least squares solution is obtained by choosing W m as the Identity matrix Singh & Rani, 2014). If W m is taken as the inverse of the Gram matrix AW À1 n A T (where W n ∈ ℝ n × n is a diagonal matrix whose components satisfy the so-called renormalizing conditions) the renormalized solution is obtained Sharan et al, 2012).…”

“…As recalled in section 3.1, there are different possible choices for W m (identity matrix, renormalized Gram matrix, covariance matrix of the noise, …). Here for a matter of simplicity and following Singh and Rani (2014), the matrix W m is chosen as the identity matrix. Finally, x 0 is determined by searching the maximum or minimum values on the 2-D cost surface, while the intensity is estimated by using the expression in (8).…”

“…Most of them are efficient for finding, iteratively, a global optimum, but they often take excessive time to converge (Hutchinson et al, 2017). To shorten the duration of the optimization process, some authors, such as Issartel et al (2011), Sharan et al (2011Sharan et al ( , 2012, or Singh and Rani (2014), used a strategy that consists in reducing the TURBELIN ET AL. 950…”