Modeling of atmospheric transport of chemical species in the polar regions

Abstract

This work is concerned with the reconstruction of unknown atmospheric distributions of species' concentrations and the simultaneous identification of unknown physical parameters. The physical and chemical processes are represented by a simplified chemical transport model. The second focus of the contribution lies on the development and the application of the adaptive techniques to the resulting inverse problem. The underlying theoretical framework is the Dual Weighted Residual (DWR) method for goal-oriented mesh optimization.Index Terms-Atmospheric modeling, inverse problems, goal-oriented adaptivity, mesh optimization. IntroductionIn this contribution, we showcase the methods stemming from optimal control theory for modeling the transport of chemical species in the Earth's atmosphere by remote sensing techniques such as satellite imaging. The goal of the presented work is the reconstruction of three-dimensional time-dependent concentration fields of chemical constituents in the Earth's atmosphere using indirect measurements such as satellite-based observations. For the latter case, the observations are generally given in form of vertical column densities (VCD).In the last years, significant effort has been spent on refining models to appropriately describe processes affecting the atmospheric constituent transport. The "general" chemical transport model is given by a system of weakly coupled parabolic equations. The coupling between the equations usually occur due to the chemical transformations, affecting the species' concentrations. The use of such models implies that the chemical mechanisms are precisely known. However, there are many situations in which these transformations cannot be modeled properly since the chemical mechanism is only poorly understood. Furthermore, depending on the form of the given measurements and the unknown parameters, the use of such a general model could be not appropriate. To address this issue, we propose a simplified model which allows to reconstruct the constituent concentrations together with unknown sources and sinks, including chemical transformations. However, other parameters can also be the goal of the computations. E.g. in the event that there are many candidates for modeling the chemical processes of a species, the reconstructed source/sink terms could also serve as a guideline for choosing the "right" mechanism.The resulting problems are solved using the Galerkin finite element method. On uniformly refined meshes this method leads to the same algebraic systems as the discretization using finite differences. However, the Galerkin discretization offers the possibility for the systematic a priori and a posteriori error analysis. Moreover, the a posteriori error analysis gives the opportunity to optimize the meshes used in the solution process and in the error control.To this end, we shortly describe the Dual Weighted Residual Method originally proposed in [1] and [2]. The method provides reliable a posteriori error estimators based on local residuals weighted by s...

Climatically-active gases in the Eastern Boundary Upwelling and Oxygen Minimum Zone (OMZ) systems

“…Using optimal control and inverse problem modeling, in this contribution we will derive the mapping of F using Earth Observation and satellite data [6,7]. It will estimate sources and sinks of gases, based on vertical column densities (VCD), at the spatial resolution of VCD data.…”

“…GHG air-sea fluxes determination can be inferred from inverse modeling applied to VCDs, using state of the art modeling, at low spatial resolution [6,7]. Due to the long life-time of GHGs in the atmosphere, significant contributions of the VCDs may have been transported from far afield.…”

Reconstruction of super-resolution ocean <i>p</i>CO<sub>2</sub> and air–sea fluxes of CO<sub>2</sub> from satellite imagery in the southeastern Atlantic

“…Another new avenue for inferring air-sea GHG fluxes is through inverse modeling applied to vertical column densities (VCDs) extracted from satellite spectrometers, i.e., Greenhouse gases Observing SATellite (GOSAT) and SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY), at low spatial resolution (Garbe and Vihharev, 2012). A global estimation of CO 2 fluxes in the ocean has been derived at 1 • × 1 • spatial resolution from global atmosphere observations used in a data assimilation system for CO 2 called CarbonTracker (Peters et al, 2007).…”

“…This turns out to be suboptimal for our super-resolution approach. Garbe and Vihharev (2012) developed an optimal control approach to invert interfacial fluxes using a simplified inverse problem of atmospheric transport. The inverse problem is solved using the Galerkin finite element method and the dual weighted residual (DWR) method for goal-oriented mesh optimization.…”

“…Using optimal control and inverse problem modeling, a map of F can be derived using Earth observation data (Garbe and Vihharev, 2012 (Peters et al, 2007). CarbonTracker system assimilates and integrates a diversity of atmospheric CO 2 data into a computation of surface CO 2 fluxes, using a state-of-the-art atmospheric transport model and an ensemble Kalman filter.…”