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Atmospheric Tracer Transport in a Lagrangian Model T ellus (2002), 54B, 278–299 Copyright © Blackwell Munksgaard, 2002 Printed in UK. All rights reserved TELLUS ISSN 0280–6509 ATTILA: atmospheric tracer transport in a Lagrangian model By CHRISTIAN REITHMEIER* and ROBERT SAUSEN, Institut fu¨r Physik der Atmospha¨re, Deutsches Zentrum fu¨r L uft- und Raumfahrt (DL R) e.V., D-82234 Wessling, Germany (Manuscript received 1 August 2000; in final form 5 February 2002) ABSTRACT The model ATTILA has been developed to treat the global-scale transport of passive trace species in the atmosphere within the framework of a general circulation model (GCM). ATTILA runs online within the GCM ECHAM4 and advects the centroids of 80.000 to 190.000 constant mass air parcels. Each trace constituent is thereby represented by a mass mixing ratio in each parcel. ATTILA contains state-of-the-art parameterizations of convection, turbulent boundary layer mixing and inter-parcel transport, and provides an algorithm to map the tracer concentra- tions from the trajectories to the ECHAM model grid. The transport characteristics of ATTILA are evaluated against observations and the standard semi-Lagrangian transport scheme of ECHAM by two experiments. (1) We simulate the distribution of the short-lived tracer radon (222Rn) in order to examine fast vertical transport over continents, and long-range transport from the continents to remote areas. (2) We simulate the distribution of radiocarbon (14C) from nuclear weapon tests in order to examine upper tropospheric and stratospheric transport charac- teristics. Contrary to the semi-Lagrangian scheme, ATTILA shows a greatly reduced meridional transport in the upper troposphere and lower stratosphere, and a reduced downward flux from the stratosphere to the troposphere, especially in mid-latitudes. Since ATTILA is a numerically non-diffusive scheme, it is able to maintain steep gradients, which compare better to the observa- tions than the rather smooth gradients produced by the semi-Lagrangian scheme. 1. Introduction developed Lagrangian transport scheme ATTILA (Atmospheric Tracer Transport In a LAgrangian Modelling of transport, transformation and model) which has been implemented in the GCM removal processes of trace species in the atmo- ECHAM4. sphere is becoming more and more important for Traditional approaches to represent the evolu- studying Earth’s climate system. Numerous trace tion of trace species concentrations on global scale species dominate radiative and chemical processes have been Eulerian, using grids and finite differ- in the atmosphere, and primarily by emitting ences, or pseudospectral. While these methods several kinds of these species into the atmosphere, work quite well when applied to smoothly varying mankind influences the climate system. meteorological fields, they can lead to several This paper will show how a Lagrangian advec- problems when advecting highly inhomogeneous tion scheme for atmospheric tracers can be used tracer distributions. In the presence of sharp gradi- within the framework of a general circulation ents, many schemes tend to produce negative model (GCM). We will present the newly concentrations, or result in considerable numerical diffusion. In addition, many Eulerian schemes * Corresponding author. have to satisfy a stability criterion, like the e-mail: [email protected] Courant number restriction on the time step Tellus 54B (2002), 3 279 Dt∏Dx/u, where u is the velocity, and Dt and Dx centroids of the parcels, such a scheme is strictly are the intervals of time and space discretization. mass conserving and does not exhibit numerical Spectral techniques suffer from spectral trunca- diffusion; in fact, as we shall see later, diffusive tion errors and from the Gibbs phenomenon, mixing has to be introduced explicitly to make a which produces regions of over- and undershoots Lagrangian model work (Section 3). Moreover, when gradients are sharp. While undershooting all trace constituents are advected simultaneously, often results in negative concentrations and can and therefore the computational cost of the advec- therefore be corrected a posteriori, it is not so tion scheme is independent of the number of easy to detect regions of overshoots. In the case tracers transported. This is the reason why of water vapour, for example, overshooting can Lagrangian methods are preferred when a large lead to supersaturation and, consequently, to pro- number of trace species is involved. The duction of spurious precipitation (Williamson and Lagrangian chemistry-transport model (CTM) Rasch, 1989). STOCHEM, for example, uses up to 70 chemical Another (Eulerian) approach to treat the advec- trace constituents to simulate tropospheric chem- tion of trace species in a wind field is the so-called istry on a global scale (e.g., Johnson et al., 2001; semi-Lagrangian technique (Williamson and Collins et al., 1997). Rasch, 1994). It calculates for every grid point at There are also several potentially serious prob- every time step a ‘departure point’ which is the lems associated with the Lagrangian approach. point at which a trajectory has to start in order First, tracer concentrations are defined on the to arrive at the given grid point after one time centroids of the parcels, but they are needed on step. The new tracer concentration at a grid point the model grid for calculating feedbacks on, e.g., is taken to be the interpolated value of the concen- radiation or dynamics, or on at least some grid tration field of the previous time step at the for an easy post-processing. Depending on associated departure point. These schemes are in whether more than one or no parcel centroids are general unconditionally stable, which means that located near a grid point, the grid point concentra- they have no stability condition restriction on the tions can be over- or underdetermined. Having time step, and thus do not suffer from the usual on the average one parcel centroid located near pole problem associated with explicit grid schemes each grid point would require a grid with all grid using a regular latitude–longitude grid on a sphere. boxes containing the same mass of air, which is By choosing an adequate interpolation scheme, not the case with the vertical discretizations of semi-Lagrangian schemes can have desirable prop- most GCMs and certainly not the case with a erties like maintaining positive concentrations or regular longitude–latitude grid. Further, the con- being essentially non-oscillatory. However, they cept of coherent air parcels becomes invalid when still exhibit serious numerical diffusion, and it is integrating over a sufficient long period of time, difficult to construct semi-Lagrangian schemes because the parcel shapes are distorted rapidly that strictly conserve mass (Rasch and Williamson, due to shears in the wind distribution. This prob- 1990a). Furthermore, treating a large number of lem can be overcome by a continous redefinition tracers can become prohibitively expensive, of the parcel boundaries, which can be represented because the interpolation has to be performed for by partially mixing adjacent parcels after each every tracer separately, and an accurate (and hence advection step (Walton et al., 1988). Finally, one expensive) interpolation is required (Rasch and has to keep in mind that the spatial resolution Williamson, 1990a). can only be controlled indirectly, namely by the A Lagrangian approach, on the other hand, initial distribution of the air parcels. If the chosen does not suffer from these problems. By this distribution is unstable, i.e., the number density of method, the model atmosphere is divided into a the parcels in a certain region shows a non-zero large number of air parcels, the centroids of which trend, re-initialization steps will be necessary are advected. Each trace constituent is thereby which potentially introduce numerical errors represented by a mass mixing ratio in each parcel. (Section 2.2.2). Since the tracer concentrations themselves are not In this paper we will present the newly altered by the advection scheme, but the locations developed Lagrangian transport scheme ATTILA of the concentrations, i.e., the locations of the which runs on-line within the GCM ECHAM4. Tellus 54B (2002), 3 280 . . This approach combines the numerical advantages enon. The remaining prognostic variables are of a Lagrangian scheme with the advantages and advected by a spectral advection scheme. extended possibilities of on-line modelling. It is ECHAM4 contains state-of-the-art para- intended for studies involving a large number of meterizations of radiation, cloud formation and tracers, and is not necessarily restricted to model- precipitation, convection, horizontal diffusion, sur- ling chemistry. Modelling aerosols with many size face fluxes and vertical diffusion, gravity wave and type classes, for example, would be another drag, and land surface processes. We apply a potential application. The on-line approach slightly modified version of the operational enables a feedback of the transported species on ECHAM4 model in which the numerical formula- the dynamics via radiation. tion of the convection scheme has been altered in In a first step, the model has been developed to order to make it strictly positive (Brinkop and treat the transport of passive tracers only, thereby Sausen, 1997). adopting several algorithms and concepts from The model atmosphere is vertically partitioned the already established CTM STOCHEM (Collins into 19 non-equidistant layers using a hybrid s–p- et al., 1997). Parameterized processes include coordinate
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