JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. D5, PAGES 9023-9037, MAY 20, 1993 A Two-Dimensional Zonally Averaged Transport Model Including Convective Motions and a New Strategy for the Numerical Solution ASBJORNSTRAND AND OYSTEIN HOV Geophysical Institute, University of Bergen,Bergen,Norway A two-dimensional zonally averaged transport model of the atmosphere up to 10 mbar (--33 km) has been developed. Thetransport is described by aneffective stream function and a diffusion tensor derived from a three- dimensional general circulation model. The numerical solution of the transport equations has been givenspecial attention, anda positive definite mass conservative advection scheme which produces small numerical diffusion hasbeenmodifiedfor usein the model.In addition to the verticaltransport described by the transport equations, a parameterization of the verticalmixing due to convective clouds and frontal circulation is included in the model. The model has been tested with different tracers which indicated a realistic representation of the atmospheric transport. 1. INTRODUCTION toosphere. It is clear that we can expect most realistic results for The complexity of the atmosphere makes it difficult to predict compounds that are reasonably well mixed zonally, i.e., compounds with an average atmospheric residence time of at least 10 daysor with a source the impacts of man-made pollutants. Chemical species withdistribution which is smooth in the longitudinal direction. One important worldwide sources and/or long chemical lifetimes (weeks or argument in support of using a2-D pole-to-pole model is that man-made longer) canhave a global atmospheric influence. The global emissions have avery distinct latitudinal distribution, and provided that its distribution of theconstituents of interest canbe determined by a limitations are fully understood andthe model is applied correctly, a combination of methods where numericalmodels are an important two-dimensional model can bea useful tool to aidourunderstanding of the tool, often used in combination with observations.One- or two- atmosphere. dimensional models have been the most widely used so far. One-dimensional models, whereone column of air at a certain 2. METHODOLOGY latitude or location is considered, have among others been applied 2.1. The Transport Coefficients by Chameides and Cicerone [1978] andKasting and Singh [1986] for the study ofthe chemical processes which occur in the air Todescribe the transport of inert tracers, the present work column. Two-dimensional (2-D) tropospheric models have been makes use of the circulation derived byPlumb and Mahlman developed by Derwent and Curtis [1977], Logan etal. [1981], [1987]. They used the output of the Geophysical Fluid Dynamics Derwent [1982], Isaksen and coworkers [Isaksen and Rodhe, 1978; Laboratory (GFDL) general circulation/tracer model [Mahlman and Rodhe and Isaksen, 1980; Isaksen etal., 1985; Isaksen and Hov, Moxim, 1978] togenerate transport coefficients for use inzonally 1987], Hough [1989], Kanakidou etal. [1991] and others. The averaged transport models. They did this byassuming a flux models have been applied for the study of chemical processes in gradient relationship and then, given gradients and flux statistics the troposphere. During the last few years three-dimensional from two independent and contrived model tracer experiments, to models have been developed. Theapplication of a three- derive the coefficients byinversion of this relation. When the dimensional model to the transport of tracers has been described mean meridional circulation from theGCMis given, the by Jacob et al.[1987] and by Prather et al.[1987]. Work on a antisymmetric and symmetric parts ofthe transport coefficients separate modeling exercise has been reported by Zitnmermann tensor determine the advective and diffusive contributions to the net meridional transport in the model as illustrated by the authors. [1988]. Three-dimensional modelsare, however, expensive to run The effectivetransport circulation definedas a combination of this and requireextensive input data. It is therefore often required to run these models with avery simplified chemistry only. antisymmetric part (with 0 onthe diagonal) and the mean The purpose of the present work is to describe a new meridional circulation is different from the Lagrangian mean and the residual circulations and is in fact simplerthan either of these. two-dimensional zonally averaged transport model.In the present work the model has been applied to simulate different tracers in The validity of the flux gradient relation as aparameterization order to investigate the transport properties ofthe model. Theof eddy transport processes was tested by Plumb and Mahlman simulations of222Rn, •SKr and water vapor made it possible to compare the model results with measurements. structure ofthe general circulation model (GCM) was as far as The model isnow used to study the trend inthe atmospheric possible unchanged in this 2-D model. This involved nine vertical lifecycles of chemical constituents in the troposphere. Thelayers and 75 latitude points. They ran anumber of experiments emphasis is put on organic compounds with lifetimes up to several by the 2-D model using the derived transport coefficients and years and their interaction with constituents of short atmospheric compared the results to those obtained by the fully three- lifetime. dimensional GCM. It wasfound that the 2-D model could Since variations around latitude circles cannot be described in reproduce wellthe zonally averaged evolution of tracers in the GCM. The authors concluded that the quantitative errorsthat were a two-dimensional model,it givesan incomplete pictureof the at- found were due to finite model resolution rather than errors in the Copyright 1993 by the American Geophysical Union. formulation, and therefore although the flux gradient relation is formally justified only in the small-amplitude limit, it appears to Paper number 93JD00201. be a useful practical description of large-scale eddy transport by 0148-0227/93/93JD-00201 $05.00 finite amplitudeeddies. 9O23