(456a) Estimating Uncertain Atmospheric Aerosol Dynamics with an Input Observer

Atmospheric models simulate mass balances of gaseous pollutants and particulate matter – or atmospheric aerosols – in the atmosphere. Typical methods to solve atmospheric inverse problems minimize the model error based on a simplified version of the model [1]. However, these methods may have issues estimating nonlinear aerosol dynamics. In this paper we propose a passivity-based input observer (PBIO) that estimates parameters based on nonlinear conservation laws that can be represented exactly. The method used here is similar to inventory control in which the model states and measurements are projected to a set of inventories. Inventories are positive, additive, and continuously-differentiable variables that follow general conservation laws (like mass or energy).

The PBIO estimates a set of parameters by forcing the model bias, in terms of the inventory variables, to zero. We formulate a quadratic storage function in terms of the model bias. Additionally, the storage function rate of change is constrained to a negative quadratic in terms of the model bias. The parameter update law is derived using these two constraints, leading to a proportional feedback and nonlinear feedforward decoupling on the model bias to update the parameters. This approach reduces the closed-loop system’s sensitivity to model mismatch, which can be tuned by adjusting the feedback gain.

Atmospheric models include significant model mismatch due to uncertainty in model inputs (emission fields, meteorology, land type, etc.), model parameters (reaction rate constants, empirical parameters, etc.), and sometimes unknown atmospheric physics and chemistry. The Intergovernmental Panel on Climate Change has characterized how this model mismatch propagates to uncertainty in aerosol’s radiative effects in the atmosphere and in clouds [2]. Predicted concentrations of cloud condensation nuclei (CCN), or particles that activate to form cloud droplets, is one of the significant drivers of uncertainty in recent climate change. The particle number size distribution and composition are necessary to predict CCN concentrations. Therefore, in this work, we focus on improving predictions of the number size distribution by estimating uncertain aerosol dynamics based on ground-site measurements.

We choose to estimate scaling factors for the rates of key uncertain processes in the model so that the system is input-affine and is easily inverted for the unknown scaling factors. Key uncertain aerosol processes that we consider are primary organic aerosol emissions, nucleation of new particles from condensable vapors, and condensation of volatile organic compounds (VOCs). Primary aerosol emissions are difficult to monitor and calculate due to the variability in emission fluxes and intensity levels within each type of source. The chemistry that drives nucleation of particles from molecular clusters of compounds possibly including sulfuric acid, water, amines, and organic compounds is still an active area of research. There are large uncertainties in the identity of VOCs and the yield of VOCs partitioning to the particle phase.

Here, we present the design of a PBIO to estimate aerosol dynamics and preliminary applications to a zero-dimensional or box model. We use a zero-dimensional version of the TwO-Moment Aerosol Sectional (TOMAS) microphysical code, which models size-resolved aerosols with the discretized general dynamic equation. We generate synthetic measurements by running TOMAS with a set of “true” rates for primary emissions, nucleation, and SOA production. Then, we start a TOMAS simulation with a set of process rates biased from their “true” value. We quantify the PBIO performance in terms of the bias in the estimated inventory variables, process rates, and the full number size distributions. The methodology developed here will facilitate future work that estimates primary aerosol emissions, nucleation, and VOC condensation rates in a global model based on a measurement network.

[1] Rao, K. S. (2007). Source estimation methods for atmospheric dispersion. Atmospheric Environment, 41, 6964–6973. https://doi.org/10.1016/j.atmosenv.2007.04.064

[2] U. D. Cubasch, D. Chen, M. Facchini, D. Frame, N. Mahowald, and J. G. Winther. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, 2013.