Abstract. Atmospheric chemical transport models (CTMs) are essential tools for the study of air pollution, for environmental policy decisions, for the interpretation of observational data, and for producing air quality forecasts. Many air quality studies require sensitivity analyses, i.e., the computation of derivatives of the model output with respect to model parameters. The derivatives of a cost functional (defined on the model output) with respect to a large number of model parameters can be calculated efficiently through adjoint sensitivity analysis. While the traditional (first order) adjoint models give the gradient of the cost functional with respect to parameters, second order adjoint models give second derivative information in the form of products between the Hessian of the cost functional and a user defined vector.In this paper we discuss the mathematical foundations of the discrete second order adjoint sensitivity method and present a complete set of computational tools for performing second order sensitivity studies in three-dimensional atmospheric CTMs. The tools include discrete second order adjoints of Runge Kutta and of Rosenbrock time stepping methods for stiff equations together with efficient implementation strategies. Numerical examples illustrate the use of these computational tools in important applications like sensitivity analysis, optimization, uncertainty quantification, and the calculation of directions of maximal error growth in three-dimensional atmospheric CTMs.

This study investigates the impacts of the 2011 severe drought in the southern United States on ground-level fine aerosol (PM 2.5 ) concentrations in the summer. The changes in surface concentrations and planetary boundary layer (PBL) budget of PM 2.5 between June 2010 (near-normal rainfall) and June 2011 (severe drought) are quantified using surface observations and the GEOS-Chem model. Observations show an average enhancement of 26% (p , 10 24 ) in total PM 2.5 over the southern U.S. (SUS) region during the drought, which is largely attributed to a ;120% increase in organic carbon (OC). Over Texas (TX) under extreme drought conditions, surface PM 2.5 shows a mean decrease of 10.7% (p , 0.15), which is mainly driven by a decrease of 26% (p , 0.03) in sulfate. Model simulations reproduce the observed relative changes in total PM 2.5 , OC, and sulfate during the drought. The model correctly identifies OC as the major contributor to the overall PM 2.5 increase over SUS and sulfate as the key driver of the PM 2.5 decrease over TX. Budget analysis suggests that increased OC emissions from wildfires (158 kt C month 21 ), enhanced SOA production (11.1 kt C month 21 ), and transboundary inflow from Mexico (18.6 kt C month 21 ) are major contributors to the increase in atmospheric OC contents over SUS. Over TX, a 70% decrease of aqueous-phase oxidation of sulfate, driven by decreasing low clouds, outweighs the combined effects of reduced wet deposition and decreased outflow as the key driver of sulfate decrease both at the surface and within the PBL.

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Moving neutralization boundary (MNB) is an important foundation to understand and improve IEF. However, there are obstacles in theoretical predictions of MNB on IPG strips due to the unknown local concentrations of carrier ampholytes on commercial IPG strips and the time-varying boundary velocities. We introduce a recursion approach to extend the current MNB theories into the space-time varying MNB system. The recursion approach emphasizes the localizability of physicochemical parameters in the discrete time intervals and local positions in Lagrangian coordinates, such as local concentrations of carrier ampholytes, local OH concentrations, local boundary velocities, local judgments, etc. The boundary-position recursion equation in a complete time sequence was presented to quantitatively predict the MNB position-time curves by distinguishing three kinds of titration cases according to NaOH concentrations in rehydration buffers. The theoretical position-time curves and local relative judgments of boundaries were satisfactorily validated by corresponding images of boundary migrations achieved from the IPG-MNB experiments with the some typical NaOH concentrations-bromophenol blue-rehydration buffers on pH 4-7 IPG strips. The results achieved herein have evident significances to the development of moving reaction boundary and IEF.

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