Rafik Djouad

Numerical simulation of aqueous-phase atmospheric models: use of a non-autonomous Rosenbrock method

We present in this article an efficient numerical solver for the time integration of atmospheric multiphase chemical kinetics. This solver is based on a second-order Rosenbrock scheme, that has been proposed by Verwer et al. (SIAM J. Sci. Comput. 20 (4) (1999) 1456) for gas-phase chemical kinetics. We show that the stiff time dependence of cloudy events (through liquid water content) has to be solved by the numerical scheme and a non-autonomous version has to be used. We benchmark the non-autonomous ROS2 scheme with the classical LSODE solver for two kinetic schemes. For detailed schemes such as RADM2, the speed-up is of magnitude 5 for the same accuracy.

Reduction of Multiphase Atmospheric Chemistry

The aim of this article is to investigate the dynamical behaviour ofmultiphase atmospheric chemical mechanisms. Reducing procedures areapplied to a multiphase chemical box model including gas-phasereactions, aqueous-phase reactions and interfacial mass transfer. The lumping of species is computed in an automatic wayusing an efficient algorithm (apla). The computed lumped species arerelated to the fast behaviour of chemical and microphysical processessuch as Chapman cycle, ionic dissociations within the cloud drops andinterfacial Henrys equilibria. Depending on some parameters (liquidwater content, droplet radius) mixed lumped species (including both phases) may also becomputed. We show the existence of hierarchical reduced models due to the existence ofmultiple timescales. We use a special algorithm (dan2) in order tosolve the reduced models. Such models are accurate and the relative errorremains under the threshold of 1%. The speed-up is up to a factor 5comparedwith a fully implicit method (Gear) for the same accuracy. The key pointis that it provides a good qualitative understanding for the behaviourof the kinetic scheme.

Solving reduced chemical models in air pollution modelling

This article follows [R. Djouad, B. Sportisse, Appl. Numer. Math. 43 (2002) 383] in which we have proposed an automatic method in order to generate reduced atmospheric chemical mechanisms. On the basis of the slow/fast behaviour of chemical kinetics the exact model is replaced by a differential-algebraic system. We propose here an easy to perform algorithm in order to integrate such systems with a low CPU cost. Comparison is made with some classical solvers such as Euler Backward Implicit (EBI), QSSA and the second-order Rosenbrock method ROS2. This proves the efficiency and the accuracy of the proposed algorithm. We also show that the classical QSSA-like methods cannot be used apart from the framework of reduction procedures, which explains their rather poor accuracy.

Partitioning techniques and lumping computation for reducing chemical kinetics: APLA: an automatic partitioning and lumping algorithm

The time integration of Air Pollution Models is a difficult task due to numerical stiffness, nonlinearity and coupling between equations and implicit schemes are usually advocated. Based on the slow/fast behaviour of the chemical dynamics, reducing procedures are alternative efficient techniques leading to nonstiff systems. Reduced models are defined by a set of lumped species and algebraic constraints and their validity is related with the correct partitioning of dynamics (species and reactions). By using some axiomatic hypothesis and algebraic properties we propose in this paper an efficient partitioning technique and an algorithm in order to compute the lumping of species in an automatic way. This is applied to four atmospheric chemical mechanisms.

A sensitivity analysis study for radm2 mechanism using automatic differentiation

A sensitivity analysis of an atmospheric multiphase mechanism is performed using an automatic differentiation tool. The sensitivity of some key concentrations is computed with respect to some input parameters (kinetic rates, microphysical parameters). The package odyssee is used in order to obtain the so-called linear tangent model giving the derivatives of outputs with respect to inputs. The direct model takes into account gas-phase reactions, aqueous-phase reactions and interfacial mass transfer and is based on the radm2 mechanism. Local sensitivity coefficients are computed for two different scenarii, rural and sub-urban. We focus in this study on the sensitivity of the gas-phase O3–NOx–HOx system with respect to some aqueous phase reactions and we investigate the influence of the reduction in the photolysis rates in the area below the cloud region. This preliminary work illustrates how powerful automatic differentiation tools may be for the study of large chemical mechanisms. We show for instance that the oxidation of trace metals (FeII, FeIII, Cu+ and Cu2+) in the case of low S(IV) polluted area is not always in disfavor of HOx gaseous concentrations, as it is usually claimed.

Modeling of Atmospheric Multiphase Chemistry: Numerical Integration and Sensitivity Analysis

The presence of clouds in the atmosphere can substantially modify the chemical kinetics and thus the rates of destruction and production of chemical species. Multiphase models are suffer and rather more difficult to integrate than pure gas models. They contain moreover many physical and microphysical parametres whose values are often known with poor accuracy. In this paper we focus on two major points. The first one is time integration. We propose the nonautonomous second-order Rosenbrock method in order to solve such heterogenous models. In the second part we focus on the sensitivity analysis of the model outputs with respect to the input parameters using an automatic differentiation tool (ODYSSEE).

Some Reduction Techniques for Simplifying Atmospheric Chemical Kinetics

We review in this article some issues related to reduction techniques for atmospheric chemical kinetics. There is indeed a wide range of characteristic timescales for atmospheric chemistry and the time evolution is characterized by a slow-fast behaviour. We present here some related points: the existence of an underlying reduced model, the partitioning techniques to build reduced models, time integration of the reduced models and finally the application of Proper Orthogonal Decomposition (POD) method for reducing chemical systems.