Atmospheric Tracer Transport in a Lagrangian Model

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 concentrations 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 characteristics. 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 observations 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

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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.

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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 system (Roeckner et al., 1992). The convective mixing, mixing due to inter-parcel uppermost model layer is centred at 10 hPa, the exchange, and boundary layer turbulence. lowermost layer approximately at 30 m above the The intention of this paper is to introduce the surface. The boundary layer is resolved by model ECHAM4/ATTILA and to evaluate the approximately 4–5 model layers. In the tropo- transport characteristics of the Lagrangian advec- pause region the vertical resolution is about 2 km. tion scheme ATTILA. In the following section a A spectral horizontal resolution of T30 was chosen brief review of the main characteristics of for the current study, corresponding to an iso- ECHAM4 and a detailed description of ATTILA tropic resolution of 6° on a great circle (#670 km) will be given. Problems associated with the for dynamic processes. The associated Gaussian Lagrangian approach will be addressed and pos- transform grid, which is used for calculating the sible solutions will be presented and discussed. In non-linear terms, diabatic processes, and the semi- Section 3 the performed model experiments are Lagrangian transport, has a resolution of approxi- described, and the results are discussed in mately 3.75°×3.75°. The time step is 30 min. Section 4. A summary and concluding remarks are given in Section 5. 2.2. T he L agrangian transport scheme AT T IL A ATTILA (Atmospheric Tracer Transport In a 2. Model description LAgrangian model) is a transport scheme which runs on-line within ECHAM4. It can be used as 2.1. T he general circulation model ECHAM4 an alternative to the operational semi-Lagrangian The spectral atmospheric general circulation scheme to transport passive tracers. model ECHAM4 is the fourth generation of the Hamburg climate model (Roeckner et al., 1996). 2.2.1. General features. Depending on the It integrates the primitive equations. Prognostic chosen horizontal resolution of ECHAM the variables are vorticity, divergence, temperature, model atmosphere is divided into about 83 000 (at (logarithm of ) surface pressure, humidity, cloud T21 resolution) or 187 000 (at T30 resolution) air water content (ice and water phase), and, option- parcels of constant mass. This gives an average of ally, up to 21 passive tracers. about 2 air parcels per grid box. However, Humidity, cloud water and the tracers are depending on the mass of air in a grid box, the advected by a semi-Lagrangian transport (SLT) number of air parcels in a grid box can be as high scheme employed in the grid point domain as 6 (at the equator in the model layer centred at (Williamson and Rasch, 1994). Since this scheme about 600 hPa) or as low as 0.06 (top layer in is not mass conserving, a mass fixer is used (Rasch polar regions). In mid-latitudes the average cell and Williamson, 1990b). The SLT scheme is used occupancy is 2–4 throughout the free tropo- in order to avoid negative concentrations resulting sphere (Fig. 1). from sharp gradients due to the Gibbs phenom- At every ECHAM time step the centroid of

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if regions were becoming devoid of trajectories, a reinitialization step would be necessary in which the trajectories are newly distributed. However, such steps should be avoided, because they introduce essentially the same errors which are inherent with semi-Lagrangian schemes (Rood, 1987). In fact, a semi-Lagrangian scheme can be looked at as a purely Lagrangian scheme in which a reinitialization step is performed after every time step. Fortunately, a control run of ATTILA over 30 yr indicated that the trajectories remain well distributed throughout the whole time of integration Fig. 1. Initial distribution of air parcels. Shown is the (Fig. 2). Therefore no reinitialization procedure zonally averaged number of air parcels per ECHAM was included in the model. grid box. The ticks at the vertical axis indicate the ECHAM model levels, labelled with the approximate pressure (hPa), if the height of the orography is zero. 2.2.3. Inter-parcel mixing. During advection the Contour values are 0.25, 0.5, 1, 2, 3, 4, 5, 6 (parcels per Lagrangian cells are considered to be isolated grid box). parcels of air. However, in reality the air is mixed with other parcels by diffusion characteristic of the size of a parcel. Furthermore, as the parcels each parcel is advected using the GCM produced are moved, their shapes get distorted due to shears wind field (Section 2.2.2). The mass mixing ratios in the wind field, and the masses of air associated of the tracers are defined on the centroids and with them become intermingled and mixed. In thought to be representative for the whole air order to keep the mass of air associated with a parcel. For grid point calculations (Section 2.2.4) parcel as a compact volume around the parcel and easy post-processing, the tracer concentra- centroid, a continous redefinition of the parcel tions are mapped from the parcel centroids to the boundaries is necessary, which in turn can be GCM model grid at every time step (Section 2.2.7). represented by mixing adjacent parcels to a certain degree. 2.2.2. Advection. At every time step the parcel In ATTILA these mixing processes are repres- centroids are advected using the fourth order ented by bringing the mass mixing ratio c of a Runge–Kutta method (Press et al., 1990, p. 550). species in a parcel closer to an average background Trajectories are calculated three-dimensionally, mixing ratio c: at every time step by adding the i.e., the model 3-D wind is used at parcel locations term (c: −c)d, where d is a dimensionless parameter instead of making isentropic or other assumptions. controlling the degree of exchange. The back- Winds are calculated by linear interpolation hori- ground mixing ratio c: is calculated as the average zontally and by cubic Hermite interpolation verti- mixing ratio of all the parcels within a grid box. cally from the wind field on the ECHAM grid. Thus, at a subsequent time step, the tracer mixing After each advection step, every parcel located in ratios ci in the individual parcels within a grid the boundary layer is randomly reallocated in the box amount to vertical within the boundary layer (see Section c (t+Dt)=c (t)+[c: −c (t)]d, 2.2.5 on calculating the boundary layer height). i i i As in the UK nuclear accident model NAME whereby the tracer mass is conserved in each grid =Wn (Maryon et al., 1991), the underlying assumption box [because c: i=1 ci(t)/n]. is that, after one time step, a parcel in the boundary In the experiments conducted during the devel- layer will have lost its identity due to rapid mixing, opment of ATTILA a choice of d=10−3 turned and thus, will have ‘forgotten’ its vertical position. out to be reasonable, as in the STOCHEM model When integrating over long periods of time (Collins et al., 1997). This value seems to be chosen (tens of years) one has to monitor the distribution somewhat arbitrarily; however, we found that of the air parcels in the model atmosphere. If tracer transport, and especially the transport of trajectories were accumulating at certain places or the short-lived tracer 222Rn, is not very sensitive

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the two being arbitrarily made at approximately 160 hPa (cf. Collins et al., 1997).

2.2.4. Convection. Convective mixing plays an important role in tracer transport by lifting them out of the boundary layer or by bringing them down from the top of the troposphere, (e.g., Stevenson, 1998). Since ATTILA runs on-line in ECHAM, the full diagnostic information provided by a GCM is easily accessible. In fact, in ATTILA the vertical transport due to subgrid-scale convection is identical to that of the ECHAM tracers. This is accomplished in three steps (Fig. 3). (1) The concentrations of the ATTILA tracers are mapped from the parcels to the ECHAM grid. This is done by calculating the total tracer mass m(t) contained in all parcels located in a given grid volume and dividing it by the mass of air in that grid volume. The previously calculated background concentration c: from Section 2.2.3 can be (t)= used in this calculation, because m nc:mcell and = (t) cbox m /mbox, where cbox is the wanted mass mixing ratio in the grid box, n is the number of cells in the grid box, mcell is the mass of air in a cell, and mbox is the mass of air in the grid box. (2) The concentrations on the grid now serve as input to the ECHAM convection scheme. This means that the transport due to subscale convection is calculated in exactly the same way as for a standard ECHAM tracer. The output of this Fig. 2. Evolution of the cell distribution during the first scheme are convective mass fluxes from which the (t) 35 model years. Shown is the horizontally averaged change of mass Dmijk of a tracer in a grid volume number of air parcels in each ECHAM model level. The can be derived (i, j, k denote the grid indices in number of parcels decreases in the three uppermost zonal, meridional and vertical direction, respect- model levels and increases in the mid-tropospheric levels during the first 5 yr. However, afterwards no trend is ively). Note that the convection scheme is mass W (t) = visible. conserving in each grid column ( k Dmijk 0) which in turn ensures conservation of mass in ATTILA. to changes in d (by, say, a factor of 10), which is in agreement with the results of Stevenson et al. (1998). A long-lived tracer with sharp gradients, such as radiocarbon, is more sensitive to changes in d. However, sensitivity studies showed that the calculated distributions change only slightly for values of d<10−3, which yield the best results. As in the GRANTOUR model (Walton et al., 1988) we reduce d by a factor of 2 in the upper model levels to account for reduced mixing, so that in the present version of ATTILA, the parameter d is taken to be 10−3 in the troposphere and Fig. 3. Schematic illustration of the convection scheme, 5×10−4 in the stratosphere, the division between see text for details.

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(t) (3) The calculated tendencies Dmijk are mapped the stability situation was considered more appro- back to the air parcels. This means that the parcel priate than the model diagnosed surface temper- mixing ratios are unchanged in the limit of zero ature) until it intersects the environmental (t) = change on the grid (Dmijk 0), i.e., when there is temperature profile. (2) In a Richardson number no convection. If a grid volume gains tracer mass approach, the boundary layer height is taken to (t) > (Dmijk 0), the additional mass is distributed be the first model layer at which the bulk evenly among the cells in the grid volume; if a Richardson number exceeds the critical value of (t) < grid volume loses tracer mass (Dmijk 0), all cells 1.3. The higher of the values obtained by methods in the grid volume lose tracer mass according 1 and 2 is then used as boundary layer height. (t) to the mass available, that is, if mold and (t) = (t) + (t) < (t) mnew mold mijk ( mold) are the tracer masses in 2.2.6. Sources and sinks. Sources can be pre- the grid volume before and after convection, the scribed in form of emissions. Surface emissions (in mass mixing ratios of the cells in the given grid terms of mass per time step) are distributed evenly (t) (t) volume are multiplied with the factor mnew/mold among all cells in the boundary layer over a given (<1). grid square; 3D emissions are distributed evenly However, there is the problem of ‘empty grid among all cells in a given grid volume. If no cells boxes’, i.e., grid boxes with no air parcels in them, are present, the emissions are stored until a cell because tracer concentrations are not defined in passes by. Since the only sink in our study is such grid boxes and it is not obvious how to deal radioactive decay, sinks are prescribed in form of with non-zero tendencies. In such a case, we half-lifetimes. proceed as follows. In step (1), the convection scheme assumes a zero concentration in an empty 2.2.7. Model output. Although the model itself grid box, and carries out the usual calculations. is Lagrangian, the most useful way to visualize In step (2), before updating the tendencies in the the output is as concentrations on a regular grid. grid boxes, the calculated convective tracer mass The chosen grid is the ECHAM model grid, and up down fluxes (Fk±1/2 and Fk±1/2 in Fig. 3) to and from the concentration in a grid box is taken to be the empty grid boxes are set to zero, which ensures a average of all cells in that grid box (the previously zero tendency in that box and mass conservation. calculated concentrations c: from Section 2.2.3 are Although this formulation means an artificial used). In order to fill in holes where no cells are reduction of convective transport, the effect is in a grid box and to smooth the distributions in expected to be small, because convection is not regions with a low cell density, the concentration very likely to occur in regions with a low cell field is horizontally smoothed by calculating for a density, which are primarily the pole regions and given grid point a distance weighted average of the uppermost and lowermost model layers. For all grid point concentrations in the same model ° example, equatorward of 40 , where about 60% layer within a great circle distance of Rmax (Collins of all convection events take place, in less than et al., 1997). The weights are calculated as w= 2% of all events a flux reduction had to be applied; exp(−r2/R2), where r is the great circle distance at mid-latitudes (40–65°, 30% of all convection and R is a disposable parameter controlling the events) it was in about 8% of all events. degree of smoothing. Empty grid boxes are weighted zero. The concentration fields were found 2.2.5. Boundary layer height. Maryon and Best to be not very sensitive to the choice of R and ff = ° (1992) tested six di erent methods to diagnose the Rmax, so that a practical choice of Rmax 10 at = ° boundary layer height from wind and temperature T21 resolution, and Rmax 6.5 at T30 resolution profiles of numerical weather prediction models was made. R was chosen such that for a grid point and compared them against actual radio-sonde at the equator the nearest neighbouring grid points ascents. The recommended scheme which is also have a weight of 0.05 (i.e., R#3.25° at T21 employed in this model involves two different resolution, R#2.17° at T30 resolution). Thus, the methods. (1) In a dry adiabatic method, the dry concentrations in grid boxes where cells are pre- adiabatic lapse rate is followed up from a near sent remain virtually unchanged, whereas empty surface temperature (the lowermost model layer grid boxes roughly get the same concentration as temperature plus an added value depending on the nearest non-empty grid box. The underlying

Tellus 54B (2002), 3 284 .   .  assumption is that, for example, in a region with transport models. In this study, we will use a grid boxes containing half the mass of air of a radon simulation to compare the advection Lagrangian cell, every second grid box remains scheme ATTILA against the semi-Lagrangian empty at every time step, and that the concentra- scheme in ECHAM and against available observations of each Lagrangian cell should be copied to tional data in order to evaluate vertical mixing two grid boxes in order to obtain the same global due to convection and boundary layer turbulence, mass of the trace species. Although the smoothing and to investigate general transport characteristics algorithm cannot be expected to produce exactly of the newly developed scheme. the same global mass of the trace species as is contained in the Lagrangian cells, it works sur- 3.1.2. Experimental set-up. In order to facilitate prisingly well; in all our experiments the relative comparison with other models we use the same error in the global tracer mass was below 1%. emissions as specified for the model intercompar- Nevertheless, in a completing step the global ison study organized by the World Climate concentration field is rescaled in order to produce Research Programme (WCRP) in 1993 (Jacob the correct global mass. Note that this algorithm et al., 1997). From 70 to 90° geographical latitude is just a diagnostic tool, so that errors do not emissions are zero; from 60 to 70° a flux of influence the transport at subsequent timesteps 0.005 atom cm−2 s−1 is specified. Between 60°S nor do they propagate or accumulate. and 60°N the emission flux from oceanic surfaces amounts to 0.005 atom cm−2 s−1, which can be considered an upper limit (Wilkening and 3. Design of model experiments Clements, 1975), and the emission flux from continental surfaces in this latitude band is specified 3.1. Radon as 1.2 atom cm−2 s−1 in order to yield a global 3.1.1. Background. The natural radioisotope radon source of 72 mol yr−1. radon (222Rn) is a noble gas which is produced by The only operating sink is radioactive decay the radioactive decay of radium (226Ra) ubiquit- with a half-life of 3.8 d (e-folding lifetime of 5.5 d). ously existent in crustal material (Nazaroff, 1992). The model is run for 11 yr with the first year as Radon itself decays with a half-life of 3.8 d, which spin-up period (an equilibrium state is already is the only sink of radon in the atmosphere. Radon reached within a few weeks). Thus, all sub- enters the atmosphere primarily at continental sequently presented monthly or seasonal means surfaces by exchange between the soil pores and are averages over ten different model years and the surface atmosphere. Estimates of the global should therefore represent the variability of the mean flux range from 0.75 atom cm−2 s−1 model. (Wilkening et al., 1975; Lambert et al., 1982) to 1.2 atom cm−2 s−1 (Turekian et al., 1977). A 3.2. Radiocarbon source strength of 1 atom cm−2 s−1 is considered 3.2.1. Background. Radiocarbon (14C) is a radio- to be accurate to within 25% globally (Turekian active substance with a natural cosmogenic source et al., 1977; Balkanski et al., 1993) and to within in the upper atmosphere, which leads to both 14 14 a factor of 2 regionally (Wilkening et al., 1975; CO2 and CO (Lal and Peters, 1962). We will, Schery et al., 1989; Graustein and Turekian, 1990; however, not simulate the naturally produced Nazaroff, 1992). The radon emission flux from the radiocarbon, but the excess 14C which was anthro- ocean surface is about 2 orders of magnitude pogenically produced during the nuclear bomb lower (Wilkening and Clements, 1975), and can tests in the early 1960s (referred to hereafter as 14 14 be neglected except for defining background con- CO2). During these tests CO2 was primarily centrations in the purely marine boundary layer. injected into the northern hemispheric lower stra- Surfaces covered by permanent ice do not exhale tosphere, which led to a much stronger signal than radon. the natural production. Despite of these uncertainties, radon is consid- Radiocarbon decays with a half-life of 5730 yr, ered as a useful tracer with a well defined source so that this sink can be neglected on the timescales and sink on global scale, and has been widely considered here. The far more important sink is 14 used for validation of global and regional scale due to partaking of CO2 in the global carbon

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14 1 cycle, i.e., uptake of CO2 at the surface, in into the ocean . Over land the terrestrial biosphere vegetation and sea surface waters. is divided into three reservoirs. The first represents 14 Since CO2 is otherwise inert, it is an attractive fine roots, twigs and leaves [with a total content tracer to gain information on stratospheric trans- of 105 Pg(C)], the second big roots, stems and port and stratosphere–troposphere exchange branches [675 Pg(C)], and the third slowly (STE). The exchange processes at the tropopause decomposing material from the other two reser- are different for upward and downward transport voirs [1420 Pg(C)]. A global flux of 60 Pg(C) yr−1 14 (Holton et al., 1995), and we will use CO2 in from the atmosphere into the first two boxes is particular to study the downward transport in assumed, with a flow of 35 Pg(C) yr−1 into the ATTILA. first box and a flow of 25 Pg(C) yr−1 into the second box. The flows in the opposite direction are assumed to be 33.1 and 23.1 Pg(C) yr−1, 3.2.2. Experimental set-up. On the basis of meas- respectively. The remaining flows of urements done by the US Atomic Energy 1.9 Pg(C) yr−1 from box one and two go into the Commission, Johnston (1989) established a 14CO 2 third box, representing the process of decomposi- data set particularly adopted as initial condition tion of organic material. Hence, a flow of in atmospheric transport models. The data set 3.8 Pg(C) yr−1 from the third box into the atmo- describes the 14CO distribution in October 1963 2 sphere is assumed. This means that the turnover well after the Test Ban Treaty, and has a horizontal times in the three reservoirs are 3, 27 and 375 yr, resolution of 10° and a vertical resolution of 1 km respectively. The actual 14CO flux between the between the surface and 50 km height. It is zonally 2 different reservoirs is calculated as the 12C flux as uniform, but since at the end of 1963 the original given above times the ratio between 14C and 12C signal from the nuclear weapon tests was already in the different reservoirs2. For a schematic illus- zonally well mixed, this is not a critical assump- tration of these fluxes see Land (1999). tion. The initial data were interpolated to the ECHAM model grid (Kjellstro¨m et al., 2000), and are plotted in Fig. 4. 14 4. Results and discussion In order to account for the sink of CO2 at the surface we follow the approach of Hesshaimer et al. (1994) and simulate the global carbon cycle 4.1. Radon (see also Kjellstro¨m et al., 2000; Land, 1999). Over 4.1.1. Model intercomparison by global distribu- the oceans a constant sink is assumed with a tions. Figure 5 shows the zonally and seasonally global flux of 60 Pg(C) yr−1 from the atmosphere averaged radon concentrations3 for the northern hemispheric summer obtained with the Lagrangian and semi-Lagrangian transport scheme, respectively. Both schemes produce quite similar distributions, with largest concentrations in the northern mid-latitude boundary layer and lowest concentrations in polar regions and in the stratosphere. Upward transport due to convection is clearly visible in the northern hemisphere as

1 1Pg=1012 kg. 2 12 In the atmosphere a CO2 concentration of 310 ppmv is assumed for 1963. In the three boxes the initial ratio of 14C and 12C is zero. 3 In Figs. 5 and 6 radon concentrations are given in 10−21 mol/mol. Other commonly used units are mBq/SCM or pCi/SCM, where SCM refers to one cubic 14 Fig. 4. Initial distribution of CO2 in October 1963. The metre of air under standard conditions, which are deﬁned ticks at the vertical axis indicate the ECHAM model by a pressure of 1023.25 hPa and a temperature of levels, labelled with the approximate height in hPa. 273.15 K. Conversion is calculated by 10−21 mol/mol= Units: 10−15 mol/mol. 56 mBq/SCM=1.52 pCi/SCM.

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empty boxes occur more often in the lower model layers, where the boxes contain relatively few mass (Fig. 1), this effect might contribute to the differences in the lower troposphere. However, convective transport to the middle and upper troposphere does not seem to be affected by this effect. Large differences can be seen in the stratosphere and in the tropopause region, where horizontal and vertical gradients are sharp. This fact is more clearly discernible in Fig. 6, which shows global distributions at the 100 hPa surface in July. Maximal concentrations are attained in the tropics, where radon-rich air is lifted up from the surface by convection. Both schemes agree well in this region, which confirms our assumption that the effect of the ‘empty grid box problem’ in the convection scheme of ATTILA (Section 2.2.4) is small. However, meridional poleward transport, especially to the winter hemisphere, is considerably pronounced in the semi-Lagrangian scheme, producing concentrations of an order of magnitude higher in the southern extratropics than ATTILA.

Fig. 5. Zonally and seasonally averaged radon concentrations (10−21 mol/mol) for summer (JJA) as simulated with ATTILA (top) and relative difference (%) between the semi-Lagrangian scheme and ATTILA (bottom). well as transport of radon-poor air from the upper troposphere in the downward branch of the Hadley cell. However, in the troposphere, there are some differences in the detail. The semi- Lagrangian scheme produces higher concentrations in the boundary layer, especially in the northern extratropics, and in the lower and middle troposphere in the region between 30 and 40°N. Mainly two reasons come into question for these differences. First, boundary layer turbulence is parameterized differently in the two schemes. In ATTILA, the whole boundary layer is completely mixed every time step without consideration of its vertical structure (Section 2.2.2), which may lead to a more intense mixing and, thus, to lower concentrations near the surface. Second, convect- Fig. 6. Radon concentrations at 100 hPa in July as ive transport is inhibited in ‘empty’ grid boxes simulated with the Lagrangian and semi-Lagrangian where no parcels are present (Section 2.2.4). Since transport scheme, respectively. Units: 10−21 mol/mol.

Tellus 54B (2002), 3  287

Since both schemes see the same meteorology, ing the range calculated from the standard devi- numerical diffusion surely plays a significant role ation (±1s). The model average over the ice-free here and is responsible for smoothing out the continents comprises all land surfaces between sharp gradients in the semi-Lagrangian scheme. 60°S and 60°N, which is the same region used for To investigate whether horizontal or vertical defining the land surface emissions. In the average diffusion is the dominant process, we conducted over the oceanic regions we excluded all ‘coastal’ another experiment with a short-lived tracer emit- grid squares and all ocean squares adjacent to ted in the upper tropical troposphere (the case C, these coastal squares. This method reduced the tropical lightning tracer experiment in Jacob et al., mean values by a factor of 2, and is thought to be 1997). In this experiment both schemes produced more representative for the larger part of these quite similar vertical gradients, whereas the hori- regions. zontal gradient in the upper troposphere was Except for the ice-free continents both schemes much larger in ATTILA. Since the tracer was agree fairly well, but they still produce values in emitted in the tropics only, meridional transport the oceanic regions that are too high. This may is the dominant process here. Hence, horizontal be caused partly by an emission rate over the diffusion is the best candidate to explain these oceans that is too high and partly by high concen- differences. tration values in grid squares near the continents. Excluding more squares near the coast should 4.1.2. Area averaged surface concentrations. reduce these values further. In the Antarctic region Lambert et al. (1982) reviewed a variety of meas- the mean values agree, but neither model captures urements of surface radon concentrations per- the observed high variability. formed throughout the year. They divided the There are considerable differences over the ice- globe into four regions and derived from measure- free continents. Both models calculate values that ments in these regions characteristic values of are too high, but whereas the Lagrangian model surface concentrations. The regions were defined is about a factor of 1.3 too high, the semi- as follows: (1) ice-free continents, (2) the Atlantic Lagrangian model produces values almost a factor and Indian oceans north of 20°S and the Pacific of 2 too high. These discrepancies might be due ocean north of the equator (‘Northern oceans’), to the different parameterizations of turbulent (3) the Atlantic and Indian oceans south of 20°S boundary layer mixing. Furthermore, the chosen and the Pacific ocean south of the equator emission flux over land is an upper limit in the (‘Southern oceans’), and (4) the Antarctic contin- range given in the literature (Section 3.1). When ent. Table 1 shows for each region the observed reducing the values by a factor of 2/3, correspond- mean value including a range of the observed ing to the lower limit in the range, the Lagrangian values as given in (Lambert et al, 1982), and the model would give values that are slightly too low, model values averaged over the whole year includ- and the semi-Lagrangian model would be a factor

Table 1. Surface concentrations of radon averaged over four diVerent regions as observed and as calculated by the L agrangian and semi-L agrangian transport scheme, respectivelya)

Ice-free Northern Southern Antarctica continents oceans oceans

Observation 4600 180 37 18 (2600–6300) (110–370) (18–66) (3.7–150) Lagrangian scheme 5800 330 100 23 (4800–6800) (210–450) (76–124) (8–38) Semi-Lagrangian scheme 8600 340 120 27 (7400–9800) (230–450) (100–140) (12–42) a) The values given in parentheses indicate the range of the measured values as given in Lambert et al. (1982) for the observations and the mean value plus and minus the standard deviation (of the area and 12 h averaged values) for the model calculations, respectively. The exact deﬁnition of the four regions is given in the text. Units: mBq/SCM.

Tellus 54B (2002), 3 288 .   .  of 1.3 too high. Surface concentrations are now concentrations and higher, and are strongest examined more closely in the next section. during austral winter (Polian et al., 1986). When comparing the observations to the model 4.1.3. T ime series at various stations. In Fig. 7 results, one notices a systematic overestimation by the monthly mean concentrations of radon at both models at all three stations. The overesti- eight different stations are displayed. The four mation is severest at the sub-Antarctic island remote stations Crozet (46°S, 52°E, 150 m asl4), Kerguelen, where calculated values are about a Kerguelen (49°S, 70°E, 30 m asl), Amsterdam factor of 2 too high. One reason for this may be Island5 (38°S, 78°E, 50 m asl), and Mauna Loa a too high emission rate over the oceans. Dentener (Hawaii, 20°N, 156°W, 3400 m asl) are far away et al. (1999) set the oceanic emission to zero in from the continents and will be used to evaluate their experiments, and they found a far better the long-range transport, whereas the stations agreement of the background concentrations. Cincinnati (Ohio, USA, 39°N, 84°W) and Socorro However, they still report values a factor of 2 too (New Mexico, USA, 34°N, 107°W) are purely high from April to September, resulting from a continental sites, which will be used to evaluate general overestimation of the concentrations in the models’ fast vertical transport due to convec- high radon events. This fact is confirmed in our tion and turbulent boundary layer mixing. time series where radonic storms at Kerguelen Bombay (19°N, 73°E) is located on the west coast carry concentrations of 200–500 mBq/SCM, com- of India and is influenced largely by the monsoon pared to 100–200 mBq/SCM in the observational regime. Bermuda (33°N, 65°W, 51 m asl) can be data. However, Dentener et al. (1999) conclude considered a marine site under continental from a high correlation of modelled and observed influence. time series that the radon emission strength or the For Bermuda and the four remote stations we description of vertical mixing may be inaccurate use the same observational data as Dentener et al. rather than the model transport. (1999), who also give a detailed description of the At Crozet, which is more influenced by emis- measurements, the main points of which will be sions from Africa, and at Amsterdam Island, which repeated here. is located nearer to the tropics, a better agreement of modelled and observed values is found, especi- Remote sites: Radon concentrations at Crozet, ally from April to September, when surface con- Kerguelen, and Amsterdam Island were measured centrations are less dominated by the background by the French Centre de Faibles Radioactivite´s concentrations. The seasonal cycle is well repres- and the Laboratoire de Modelisation du Climat ented by both models, and the intraseasonal vari- et de l’Environnement with a time resolution of ability, too, which is indicated here by the 1–2 h (Lambert et al., 1970, 1982), and have been calculated first and third quartiles, agrees well processed to eliminate periods of local radon with the observations. emissions (Dentener et al., 1999). The time series Jacob et al. (1997) report an occurence of are characterized by low background con- approximately 3 storms per season at Crozet and centrations (20–60 mBq/SCM at Amsterdam seasonal maximal concentrations ranging from Island, 10–40 mBq/SCM at Kerguelen, about 730 to 2000 mBq/SCM, with a median value of 60 mBq/SCM at Crozet) interrupted by periods 1300 mBq/SCM. This agrees well with both of high radon concentrations, so-called ‘radonic models which produce 2–5 storms per season and storms’, which are associated with fast boundary maximal concentrations ranging from 800 to layer transport from southern Africa (Lambert 2000 mBq/SCM, with a median value of et al., 1970). They can lead to concentrations an 1500 mBq/SCM (Lagrangian scheme), and 710 order of magnitude higher than the background to 1700 mBq/SCM, with a median value of 1100 mBq/SCM (semi-Lagrangian scheme), respectively. However, there is a systematic difference 4 Above sea level. 5 The islands Crozet, Kerguelen and Amsterdam between the two models, namely the production Island are located in the Indian Ocean, south-east of of lower surface concentration in the Lagrangian South Africa. model. This is most probably due to the different

Tellus 54B (2002), 3  289

Fig. 7. Monthly averaged radon concentrations at various stations from observations (OBS) and as calculated by the Lagrangian (LT) and semi-Lagrangian (SLT) model. At Crozet, Kerguelen and Amsterdam Islands the medians are shown for the models, and the error bars denote the first and third quartiles. At all other stations the mean values and standard deviations are shown (except at Cincinnati where the error bars indicate the range of the monthly mean values for the individual years). Model values are taken from the lowest model level, except for Mauna Loa, where the values at 3400 m above sea level were used. 290 .   .  description of boundary layer mixing. The ally high concentrations in the upper troposphere Lagrangian scheme mixes the boundary layer over Hawaii, although the agreement at MLO completely and does not take into account details improves. Furthermore, the concentrations at of the vertical structure, which may lead to a less MLO respond only very weakly to an enhance- vigorous mixing in the semi-Lagrangian scheme. ment of boundary layer mixing in Asia (Dentener In this special case the Lagrangian model seems et al., 1999; Stockwell et al., 1998). This fact is to give the better results, but the picture could confirmed in our study, because the Lagrangian change; however, when the surface emission fluxes scheme tends to mix the boundary layer more are set to lower and perhaps more realistic values. thoroughly (especially over the continents, see Radon at the Mauna Loa Observatory (MLO), below) but produces the same concentrations at Hawaii (20°N, 156°W, 3400 m asl) was measured MLO as the semi-Lagrangian scheme. At the by the DOE/EML (USA Department of Energy, WCRP ‘Workshop on Global Tracer Transport Environmental Measurements Laboratory), is Models’ held in August 1995, it was suggested electronically available6 and is described in Hutter that the underestimation at MLO could arise from et al. (1995). Measured concentrations range incorrect model meteorology. It was reported that between 50 and 1000 mBq/SCM, and the variabil- the UKMO model, for example, which had rela- ity is quite large. The concentrations are influenced tively strong convection over Asia and a jet stream both by local emissions from the island itself, and located further to the south than most other by long-range transport. To eliminate local effects, models, showed a substantially better summer only measurements obtained during the night from simulation than most other models (WCRP, 1999). 12 p.m. to 7 a.m. have been used, when MLO is mostly located above the average trade-wind Marine sites under continental influence:Asat inversion height. The synoptic meteorology is also MLO, radon measurements at Tudor Hill, quite variable and is influenced by trade winds as Bermuda (33°N, 65°W, 28 m asl) were performed well as strong westerly winds which transport by the EML and are electronically available (see radon from the Asian continent (Merrill et al., MLO above). Concentrations vary strongly, with 1989; Kritz et al., 1990; Whittlestone et al., 1992). lowest values of around 100 mBq/SCM and We compare this data set to the model calcu- extended periods with high concentrations of lated values at 3400 m above sea level at Hawaii. around 2000 mBq/SCM. During winter the Both the Lagrangian and the semi-Lagrangian weather at Bermuda is dominated by westerly model produce almost identical results, but they winds which advect continental air from North underestimate the observed values by a factor of America, whereas during summer Bermuda is 1.5–3. However, the seasonal variability is well influenced by the Azores high and air masses are represented, with a maximum in spring, when more of a marine origin. To exclude local influ- westerly winds prevail. Since many other models ences by island emissions, measured wind data have problems in reproducing middle and upper were used to reject radon measurements obtained tropospheric radon concentrations near Hawaii during periods with seaward wind directions and (Dentener et al., 1999; Stockwell et al., 1998; Jacob wind speeds less than 2.5 m s−1 (Dentener et al., et al., 1997), various reasons for this underestima- 1999). tion have been discussed in the literature. The Again, both the Lagrangian and the semi- main sources of radon at Hawaii are the Island of Lagrangian scheme produce nearly the same Hawaii itself and Asia (Whittlestone et al., 1992), results, except maybe in winter, where the so that possible reasons connected with the distant Lagrangian schemes produce somewhat higher sources are an underestimated emission rate over values. Compared to the observations, the models Asia, convective activity over Asia that is too overestimate the radon concentrations, but the weak, and the missing of a fast upper tropospheric calculated and observed standard deviations agree transport layer in the model. However, Dentener reasonably well. It is worth noting that the mod- et al. (1999) showed that increasing the emission elled values in this experiment, which should rep- rate over Asia (by a factor of 3) leads to unrealistic- resent climatological values, agree better with the observations, especially in summer, than the calcu- 6 http://www.eml.doe.gov/databases/radon/ lated values of Dentener et al. (1999), who used

Tellus 54B (2002), 3  291 the semi-Lagrangian scheme of ECHAM in a finer ences in the seasonal variation. The modelled horizontal resolution (T42) and constrained the values clearly follow the seasonal variation of the GCM to the observed meteorology of one year vertical mixing intensity with minimal concentra- by the so-called ‘nudging’ method, see Jeuken tions in summer and maximal concentrations in et al., 1996). This indicates that the meteorology winter, while the curve for the observed values is as well as the relevant transport processes in the somewhat shifted, exhibiting minimal concentra- North America region are well described in tions in spring and maximal concentrations in fall. ECHAM4. Since Cincinnati is a purely continental site, this Gesell (1983) gives a review of radon measure- seasonal behaviour is most likely due to regional ments at various sites throughout the world, which changes in the emission flux which are not repres- were performed for at least one year to obtain ented in the model. In winter, frost and snow information about the seasonal and daily variation cover can prevent radon from being exhaled from of radon concentrations at the surface. The the surface, thereby reducing the emission flux reported data at Bombay, India (19°N, 73°E), (George, 1981). In spring, the minimal concentra- were taken twice a day (morning and afternoon) tions could be explained by an increased soil over a period of 10 yr (Mishra et al., 1980). The moisture which may also reduce the radon emis- monsoon regime is clearly visible at Bombay by sion flux. However, the effect of soil moisture is the rapid decrease of radon concentrations with poorly understood, and conflicting results are the onset of the SW monsoon in April, bringing reported in the literature (Jacob and Prather, radon-poor air from the Indian ocean, and the as 1990). Another uncertainty, generally for contin- rapid increase in October. Concentrations are ental sites, arises from regional variations in the maximal in winter during the NE monsoon, which emission flux, which also depend on geophysical advects air masses of continental origin. properties of the soil and the 226Ra concentration Although both models overestimate the radon in the soil. In the model experiments, on the other concentrations, they capture the seasonal variation hand, we assumed a constant emission flux over due to the monsoon regime reasonably well, land. especially the swift increase in fall. This indicates Therefore we turn to another continental site that the overall transport characteristics in this which is not or to a lesser extent influenced by region are well described in the models, the over- the meteorological effects on the emission flux as estimation being more likely due to emission rates discussed above, namely Socorro, New Mexico over land that are too high. (34°N, 107°W). Measurements were performed by Wilkening (1959) for a period of 6 yr, and again, Purely continental sites: Gold et al. (1964) we use only the values taken at 15:00 local time, report average monthly morning and afternoon as reported by Jacob and Prather (1990). Both concentrations at Cincinnati, Ohio (39°N, 84°W), modelled and observed values show a seasonal measured during the years 1959–1963. Since the variation which is primarily regulated by dry morning concentrations are considerably higher convection, resulting in minimal concentrations in than the afternoon concentrations (see also Cox summer and maximal concentrations in winter. et al., 1970), especially in late summer, and since Whereas the Lagrangian scheme captures the we do not expect the models to resolve the sharp absolute values quite well, the semi-Lagrangian concentration gradients developing in a shallow scheme overestimates the concentrations by boundary layer, we compare the afternoon values, almost a factor of 2. Again, we think that this is which were taken at 15:00 local time, to the model due to the different parameterization of vertical values at 19:007. The error bars indicate the range mixing in both models. Although it is difficult to of the monthly mean values for the individual separate the influence of the boundary layer para- years. Whereas both models represent the absolute meterization on the surface concentrations from values and the variation of the observed monthly other transport mechanisms, there are two facts mean concentrations quite well, there are differ- which corroborate our conjecture: (1) ATTILA and SLT produce quite similar results (difference 7 Data were archived at 0:00 and 12:00 UT, corre- less than 5%) throughout the free troposphere sponding to a local time of 19:00 and 7:00 at Cincinnati. where the vertical mixing intensity is low (e.g.,

Tellus 54B (2002), 3 292 .   .  winter hemisphere, Fig. 5). (2) The surface concen- Nevertheless, in Fig. 8 we compare this profile trations averaged over the continents show the with the model calculated profiles. The latter are same feature (Table 1), so that differences in lateral means over the summer season and averaged over transport seem to play a minor role. However, we the seven locations where the observed profiles cannot rule out the possibility that some other were measured. The individual locations are numerical effect is responsible for the differences weighted according to how many profiles were in the surface concentrations. Therefore, we turn measured there. now to vertical profiles to gain further insight into Above 9 km both models produce the same vertical mixing processes. concentrations and they agree well with the observed values. This indicates that the upward 4.1.4. Vertical profiles. When studying fast ver- transport due to deep convection is well described. tical transport processes over land surfaces by In the middle troposphere (3–8 km) both models simulating the radon distribution, it is desirable underestimate the observed concentrations, below to consider not only surface concentrations as in 6 km the Lagrangian scheme even more than the the previous section, but also to examine the semi-Lagrangian scheme. However, both models distribution of radon throughout the troposphere. are within the range given by Liu et al. (1984). However, measured vertical profiles of radon Below 3 km the agreements are better, with the extending the boundary layer are scarce. Liu et al. Lagrangian scheme exhibiting a more intense ver- (1984) reviewed a number of measurements and tical mixing of the lower troposphere. The compiled a vertical profile which comes nearest to resulting lower surface concentrations seem to be what can be called a climatological representative more realistic, as already mentioned in the previ- profile for continental sites in summer. However, ous section, but neither model captures the sharp one has to keep in mind that this profile comprises gradient in the boundary layer. as few as 23 measured profiles from seven different locations in North America and Eastern Europe. 4.2. Radiocarbon Regarding the large variability of the profiles 4.2.1. L ong-term trends. The global 14CO con- (indicated by the error bars in Fig. 8) and taking 2 tent in the model domain decreases exponentially into account that one measured profile is strongly with time with an e-folding time of 8.2 yr, seen influenced by the current local thermodynamic over the period from October 1963 until December state of the tropospheric column in consideration, 1972 (Fig. 9). The calculated e-folding time lies it is difficult to judge whether the profile presented between the value of 7 yr calculated by Kjellstro¨m here is really representative. et al. (2000), who transported with the semi- Lagrangian scheme in ECHAM, and the value of 9.4yr calculated by Land (1999), who also used the semi-Lagrangian scheme in ECHAM, but in a model configuration with increased vertical resolution [ECHAM4.L39(DLR), with 39 vertical

Fig. 8. Vertical profiles of radon averaged for summer and for seven different continental locations. Error bars Fig. 9. Temporal evolution of global, tropospheric, and 14 indicate the standard deviation of the 23 measured pro- stratospheric contents of bomb CO2 as simulated by files from the mean, see Liu et al. (1984) for details. ATTILA.

Tellus 54B (2002), 3  293 layers between the surface and 10 hPa, see Land et al., 1999]. 14 The tropospheric CO2 content increases at the beginning of the integration due to input of 14 stratospheric CO2-rich air, but already after one year of integration the surface sink of becomes stronger than the stratospheric input, and the 14 tropospheric CO2 content decreases. 14 The stratospheric CO2 content is characterized by a strong exponential decrease in the first year of the simulation, when the main part of the 14 stratospheric CO2, which is located in the northern lower stratosphere, is removed to the troposphere. The decrease is weaker later on. This behaviour is also apparent in observational data, from which Johnston (1989) estimated the 14 e-folding time of stratospheric CO2 to be 2.3 yr from January 1963 until October 1964, and 5.7 yr from January 1965 until July 1966. We calculate corresponding lifetimes of 1.5 yr for the period between October 1963 and October 1964, and 4 yr for the latter period. The rapid decrease at the beginning of the simulation is even more pronounced in the semi-Lagrangian scheme of ECHAM; Kjellstro¨m et al. (2000) calculated a corresponding lifetime of 1.3 yr, and Land (1999) came to the same value with the L39 version of ECHAM [ECHAM4.L39(DLR)]. The difference between ATTILA and the semi-scheme becomes more distinctive when looking at the first 3 months of the simulation, where sharp vertical gradients 14 in CO2 concentration are present in the stratosphere. For the period between October 1963 and December 1963 we calculate an e-folding time of 2.5 yr, whereas ECHAM4.L39(DLR) produces a value of 1.6 yr (Land, 1999). This indicates that the downward flux from the stratosphere to the troposphere is reduced in ATTILA. On the other hand, when looking at the period 14 ° between January 1965 and July 1966, the rather Fig. 10. Vertical profiles of CO2 at 70 N from January low lifetime of 4 yr in ATTILA compared to the 1964 to January 1966 as observed by Johnston (1989) (labelled as OBS), and as simulated by the semi- corresponding value of 5.2 yr in ECHAM Lagrangian (SLT) and Lagrangian (LT) scheme. The (Kjellstro¨m et al., 2000) suggests that the vertical profiles of the Lagrangian scheme were derived both by transport in the uppermost model domain is faster evaluating the output on the ECHAM model grid in ATTILA than in ECHAM. For a more detailed (LT-G) and by directly evaluating the trajectory posi- investigation of these features, we turn our look tions on a 10 hPa grid (LT-T, see text for further details). 14 All modelled values are zonally averaged profiles. now to vertical profiles of CO2.

4.2.2. Vertical profiles. In Figs. 10–12, observed vertical profiles by Johnston (1989) are compared with simulated zonal mean profiles at 70°N, 31°N

Tellus 54B (2002), 3 294 .   . 

Fig. 11. As Fig. 10, but at 31°N. Fig. 12. As Fig. 10, but at 9°N.

Tellus 54B (2002), 3  295 and 9°N. We included two vertical profiles for low density of trajectories, i.e., the low number of ATTILA. The first one (LT-G) was derived using trajectories per latitude band, especially in polar the standard output data of ATTILA, which is regions and in the uppermost and lowermost available on the ECHAM model grid just like the model layers. However, an additional model run output of the ECHAM model itself. However, in with a three-fold number of trajectories produced a model one is not constrained to use a certain almost identical vertical profiles, so that the low grid, and since the vertical resolution of ECHAM density of trajectories does not seem to be a in the stratosphere is quite coarse compared to problem here. Furthermore, the maximum of the the variability of the observed profiles (e.g., the vertical profile lies in a region which is influenced stratospheric peak in the initial distribution at by polar vortex dynamics. Since the polar vortex 31°N is vertically resolved by only 5 grid points), is quite variable on the Northern hemisphere (cf. we calculated a second profile directly from the Grewe et al., 1998) and the model was not con- trajectory data by mapping the data to a vertical strained to reproduce the observed dynamics, grid with a resolution of 10 hPa (LT-T). In most another possible reason could be an unrealistically cases these two profiles agree fairly well, but when strong downward movement in the winter consid- different, the second one compares better to the ered here (which may not be seen in a smoothed observations (except at 70°N, see below). This can out profile like the one produced by the semi- especially be seen at 31°N, where the sharp peak Lagrangian scheme). Additional simulations with in the stratosphere at the beginning of the simula- different initial meteorological conditions could tion is best reproduced by the second profile. perhaps help to clarify the situation. It is a general feature of all plots that ATTILA Another interesting difference concerns the better reproduces the amplitude of the peak in the transport characteristics in the uppermost model first months, and maintains a sharper gradient domain. In most cases both schemes underestimate throughout the simulation. This is what we had the mixing ratios above 15 km, with the expected from the numerical properties of a Lagrangian scheme producing higher values closer Lagrangian scheme, i.e., the non-diffusivity. The to the observations. During the course of the less steep gradients in the semi-Lagrangian scheme integration, however, the mixing ratios produced produce higher mixing ratios in the troposphere by ATTILA in this altitude region decrease faster and lower stratosphere at all latitudes except 70°N, than the ones produced by the semi-Lagrangian and suggest an overestimation of the downward scheme, resulting in even lower mixing ratios than fluxes from the stratosphere to the troposphere in the semi-Lagrangian scheme in 1966. Hence, (cf. Kjellstro¨m et al., 2000). Since the scheme while the semi-Lagrangian scheme exhibits a ver- agrees very well with the observations in this tical transport in the uppermost model domain altitude region (at 31°N) or at least exhibits a less that is too slow (Kjellstro¨m et al., 2000), the pronounced overestimation (at 9°N), we conclude transport in ATTILA might be too fast. that one reason for this overestimation of the Summarizing, we can say that ATTILA repro- downward fluxes is to be found in the numerical duces well the main transport characteristics of 14 properties of the semi-Lagrangian transport CO2 as they were observed. The advantage of scheme. being non-diffusive comes into effect especially in At 70°N, however, the situation is different. this experiment, because the initial distribution of 14 Whereas ATTILA reproduces the amplitude of CO2, from which the experiment was started, the stratospheric peak at the beginning of the shows a strong peak in the stratosphere of the simulation very well, it underestimates the altitude northern high and mid-latitudes. Consequently, of the peak by at least 3 km. This leads to an ATTILA is able to maintain higher amplitudes of overestimation of the mixing ratios in the tropo- the peak and steeper gradients, which are closer sphere and lower stratosphere, which is even more to the observations than in the semi-Lagrangian pronounced in the second (LT-T) profile, but after scheme. Furthermore, since a Lagrangian scheme 15 months of integration the calculated profiles works without a grid, one is free to choose different again agree with the observations below 15 km. appropriate diagnostic methods as long as the One possible explanation is that this might be a tracer concentrations are not required to feed back single event which has something to do with the to the model and are therefore needed on the

Tellus 54B (2002), 3 296 .   .  model grid. Evaluating the output of ATTILA ATTILA might actually underestimate the surface directly from the trajectory positions and the concentrations. Secondly, the meridional transport mixing ratios at these positions by mapping them at 100 hPa is greatly reduced in ATTILA, especi- to a vertically higher resolved grid results in ally in the winter hemisphere, where ATTILA further improvement, especially at 31°N in the maintains a horizontal gradient from the equator first months of the integration. to the pole which is a factor of 10 higher than in the semi-Lagrangian scheme. In several model intercomparison studies it was noted that the 5. Summary and conclusions meridional transport of ECHAM in the upper troposphere and lower stratosphere is stronger We developed a purely Lagrangian transport than in most other models (Danilin et al., 1998; scheme (ATTILA) to treat the transport of passive van Velthoven et al., 1997; Jacob et al., 1997)8. tracers in the general circulation model ECHAM4. Thus, in this regard ATTILA compares better to The main motivation for this work lies in the many other models than the semi-Lagrangian numerical properties of a Lagrangian scheme: scheme. However, unless observations of radon in ATTILA is strictly mass conserving and does not this region are available, we cannot judge which suffer from numerical diffusion, which is especially transport scheme is better. Nevertheless, since a problem in the standard semi-Lagrangian both schemes use the same meteorology, the scheme of ECHAM. With respect to future devel- differences between them must be due to numerical opments, e.g., of fully coupled chemistry climate reasons. This indicates that the semi-Lagrangian models (Hein et al., 2001), or the transport of scheme might indeed suffer from exceptional high many classes of aerosols, ATTILA has the addi- numerical diffusion. 14 tional advantage that it allows the transport of a In the CO2 experiment ATTILA also produces large number of tracers without being prohibit- quite satisfactory results. As one would expect ively expensive. As is the case with few other from a Lagrangian scheme, ATTILA is able to Lagrangian models (e.g., Chuang et al., 1997), maintain steeper gradients and higher peaks than ATTILA runs on-line in a GCM (ECHAM4). In the semi-Lagrangian scheme does. The steeper our case, this means that ATTILA is driven by gradients are in better agreement with the observa- temporal highly resolved data (Dt=30 min) and tions. Diagnosing the vertical profiles directly from by a comprehensive set of diagnostic data, which the trajectories instead of using the ECHAM grid is provided by ECHAM and is used, e.g., to treat yields even better results. We conclude that the subscale convection in ATTILA. Furthermore, the overestimation of the downward flux from the feedback of species on the dynamics may be stratosphere to the troposphere in ECHAM is considered in a later phase of the model rather due to the numerical properties of the semi- development. Lagrangian scheme than due to an incorrect model In order to evaluate the transport characteristics meteorology. of ATTILA, we conducted two experiments. Altogether, they show that ATTILA is able to 222 14 simulate the transport of Rn and CO2 quite 6. Acknowledgements realistically. The main features of the observed radon distribution, such as the variability at vari- We thank Colin Johnson (UK Meteorological ous surface stations and the vertical distribution Office) for providing the STOCHEM code and in the continental troposphere, are reproduced for many fruitful discussions about Lagrangian satisfactorily. Compared to the semi-Lagrangian methods, which facilitated the development of scheme ATTILA produces in most cases similar ATTILA considerably. We are also grateful to results, with two noteworthy exceptions. First, ATTILA tends to produce lower surface concen- 8 In the three studies mentioned, ECHAM3 SLT was trations which seem to be in better agreement / used which differs in many aspects from ECHAM4. with the observations. However, considering the However, with respect to the horizontal transport of rather high emission flux of radon in the simula- radon in the tropopause region, both models produce tion, this agreement might be fortuitous and comparable results.

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Erik Kjellstro¨m, who provided a preliminary ver- measurements. We would like to thank Sabine sion of the paper (Kjellstro¨m et al., 2000), and all Brinkop, Michael Ponater, Christine Land and 14 data needed to run and evaluate the CO2 experi- Johann Feichter for helpful discussions concern- 14 ment (intitial distribution of CO2, code of the ing the ECHAM model and the experimental carbon cycle, observed vertical proﬁles). We also set-ups. This study was sponsored by thank Johann Feichter and Frank Dentener for Aerosolforschungsschwerpunkt (AFS) of the providing a preliminary version of the paper German Bundesministerium fu¨r Bildung und (Dentener et al., 1999) and numerous radon Forschung (project 07 AF 311/3).

REFERENCES

Balkanski, Y. J., Jacob, D. J., Gardner, G. M., Graustein, air. In: T he natural radiation environment (eds. J. A. S. W. M. and Turekian, K. K. 1993. Transport and resi- Adams and W. M. Lowder). University of Chicago dence times of continental aerosols inferred from a Press, Chicago, 369–382. global three-eimensional simulation of 210Pb. J. Geo- Graustein, W. C. and Turekian, K. K. 1990. Radon fluxes phys. Res. 98, 20,573–20,586. from soils to the atmosphere measured by 210Pb-226Ra Brinkop, S. and Sausen, R. 1997. A finite difference disequilibrium in soils. Geophys. Res. L ett. 17, approximation for convective transports which main- 841–844. tains positive tracer concentrations. Beitr. Phys. Grewe, V., Dameris, M., Sausen, R. and Steil, B. 1998. Atmosph. 70, 245–248. Impact of stratospheric dynamics and chemistry on Chuang, C. C., Penner, J. R., Taylor, K. R., Grossmann, northern hemisphere midlatitude ozone loss. J. Geo- A. S. and Walton, J. J. 1997. An assessment of the phys. Res. 103, D19, 25,417–25,433. radiative effects of anthropogenic sulfate. J. Geophys. Hein, R., Dameris, M., Schnadt, C., Land, C., Grewe, V., Res. 102, 3761–3778. Ko¨hler, I., Ponater, M., Sausen, R., Steil, B., Land- Collins, W.J., Stevenson, D. S., Johnson, C. E. and graf, J. and Bru¨hl, C. 2001. Results of an interactively Derwent, R. G. 1997. Tropospheric ozone in a global- coupled atmospheric chemistry — general circulation scale three-dimensional Lagrangian model and its model: comparison with observations. Ann. Geophys. response to NOX emission controls. J. Atmos. Chem. 19, 435–457. 26, 223–274. Hesshaimer, V., Heimann, M. and Levin, I. 1994. Cox, W. M., Blanchard, R. L. and Kahn, B. 1970. Rela- Radiocarbon evidence for a smaller oceanic carbon tion of radon concentration in the atmosphere to total dioxide sink than previously believed. Nature 370, moisture retention in soil and atmospheric thermal 201–203. stability. In: Radionuclides in the environment. Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglas, Advances in Chemistry Series 93, American Chemical A. R., Rood, R. B. and Pfister, L. 1995. Stratosphere– Society, Washington, DC, 436–446. troposphere exchange. Rev. Geophys. 33, 403–439. Danilin, M. Y., Fahey, D. W., Schumann, U., Prather, Hutter, A. R., Larsen, R. J., Maring, H. and Merrill, J. T. M. J., Penner, J. E., Ko, M. K. W., Weisenstein, D. K., 1995. 222Rn at Bermuda and Mauna Loa: local and Jackman, C. H., Pitari, G., Ko¨hler, I., Sausen, R., distant sources. J. Radioanal. Nucl. Chem. 193, Weaver, C. J., Douglass, A. R., Connell, P. S., Kinnison, 309–318. D. E., Dentener, F. J., Fleming, E. L., Berntsen, T. K., Jacob, D. J. and Prather, M. J. 1990. Radon-222 as a Isaksen, I. S. A., Haywood, J. M. and Ka¨rcher, B. test of convective transport in a general circulation 1998. Aviation fuel tracer simulation: model inter- model. T ellus 42B, 118–134. comparison and implications. Geophys. Res. L ett. 25, Jacob, D. J., Prather, M. J., Rasch, P. H., Shia, R.-L., 3947–3950. Balkanski, Y. J., Beagley, S. R., Bergmann, D. J., Black- Dentener, F., Feichter, J. and Jeuken, A. 1999. Simulation shear, W. T., Brown, M., Chiba, M., Chipperfield, of the transport of radon-222 using on-line and off- M. P., de Grandpre´, J., Dignon, J. E., Feichter, J., line global models at different horizontal resolutions: Genthon, C., Grose, W. L., Kasibhatla, P. S., a detailed comparison with measurements. T ellus Ko¨hler, I., Kritz, M. A., Law, K., Penner, J. E., 51B, 573–602. Ramonet, M., Reeves, C. E., Rotman, D. A., Stockwell, George, A. C. 1981. Radon flux measurements. In: D. Z., van Velthoven, P. F. J., Verver, G., Wild, O., USDOE rpt. EML -399. Environmental Measurements Yang. H. and Zimmermann, P. 1997. Evaluation and Laboratory, US Dept. of Energy, New York, 207–212. intercomparison of global atmospheric transport Gesell, T. F. 1983. Background atmospheric 222Rn con- models using 222Rn and other short-lived tracers. centrations outdoors and indoors: a review. Health J. Geophys. Res. 102, D5, 5953–5970. Phys. 45, 289–302. Jeuken, A., Siegmund, P., Heijboer, L., Feichter, J. and Gold, S., Barkhau, H. W., Shleien, B. and Kahn, B. 1964. Bengtsson, L. 1996. On the potential of assimilated Measurement of naturally occurring radionuclides in meteorological analysis in a global climate model for

Tellus 54B (2002), 3 298 .   . 

the purpose of model validation. J. Geophys. Res. 101, Indian land mass, inside deep mines and over 16,939–16,950. adjoining oceans. In: Natural radiation environment III Johnson, C. E., Stevenson, D. S., Collins, W. J. and (eds. T. F. Gesell and W. M. Lowder). US Department Derwent, R. G. 2001. Role of climate feedback on of Energy, Special Symposium Series 51, CONF methane and ozone studied with a coupled ocean– 780422, 327–346. atmosphere chemistry model. Geophys. Res. L ett. 28, Nazaroff, W. W. 1992. Radon transport from soil to air. 1723–1726. Rev. Geophys. 30, 137–160. Johnston, H. 1989. Evaluation of excess carbon-14 and Polian, G., Lambert, G., Ardouin, B. and Jegou, A. 1986. strontium-90 data for suitability to test two-dimen- Long-range transport of continental radon in Sub- sional stratospheric models. J. Geophys. Res. 94, D15, antarctic and Antarctic areas. T ellus 38B, 178–189. 18,485–18,493. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Kjellstro¨m, E., Feichter, J. and Hoffmann, G. 2000. Vetterling, W. T. 1990. Numerical recipes — the art of 14 Transport of SF6 and CO2 in the atmospheric general scientific computing (FORT RAN version), Cambridge circulation model ECHAM4. T ellus 52B, 1–18. University Press, Cambridge, UK. Kritz, M.A., Le Roulley, J. C. and Danielsen, E. F. 1990. Rasch, P. J. and Williamson, D. L. 1990a. On shape- The China Clipper — fast advective transport of preserving interpolation and semi-Lagrangian trans- radon-rich air from the Asian boundary layer to the port. SIAM J. Sci. Comput. 11, 656–687. upper troposphere near California. T ellus 42B, 46–61. Rasch, P.J. and Williamson, D. L. 1990b. Computational Lal, D. and Peters, B. 1962. Cosmic ray produced iso- aspects of moisture transport in global models of the topes and their application to problems in geophysics. atmosphere. Q. J. R. Meteorol. Soc. 116, 1071–1090. Progr. Elementary Particle Cosmic Ray Phys. 6, 1–74. Roeckner E., Arpe, K., Bengtsson, L., Brinkop, S., Lambert, G., Polian, G. and Taupin, D. 1970. Existence Du¨menil, L., Esch, M., Kirk, E., Lunkeit, F., of periodicity in radon concentrations and in the large- Ponater, M., Rockel, B., Sausen, R., Schlese, U., scale circulation at lower altitudes between 40° and Schubert, S. and Windelband, M. 1992. Simulation 70° South. J. Geophys. Res. 75, 2341–2345. of the present-day climate with the ECHAM model: Lambert, G., Polian, G., Sanak, J., Ardouin, B., Bouis- impact of model physics and resolution. Report No. 93, son, A., Jegou, A. and Le Roulley, J. C. 1982. Cycle ISSN 0937-1060, Max-Planck-Institut fu¨r Meteor- du radon et de ses descendants: application a` l’e´tude ologie, Hamburg, Germany. des ećhanges troposphe`re–stratosphe`re. Ann. Geóphys. Roeckner, E., Arpe, K., Bengtsson, L., Christoph, M., 38, 497–531. Claussen, M., Du¨menil, L., Esch, M., Giorgetta, M., Land, C. 1999. Untersuchungen zum globalen Spuren- Schlese, U. and Schulzweida, U. 1996. The atmo- stofftransport mit dem Atmospha¨renmodell ECH- spheric general circulation model ECHAM-4: model AM4.L39(DLR). Ph.D. T hesis, February 1999, description and simulation of present-day climate. Ludwig-Maximilians-Universita¨t, Mu¨nchen, Ger- Report No. 218, ISSN 0937-1060, Max-Planck-Institut many, available as: Forschungsbericht 1999-32, ISSN fu¨r Meteorologie, Hamburg, Germany. 1434-8454, Deutsches Zentrum fu¨r Luft- und Raum- Rood, R. B. 1987. Numerical advection algorithms and fahrt e.V., Ko¨ln, Germany. their role in atmospheric transport and chemistry Land, C., Ponater, M., Sausen, R. and Roeckner, E. 1999. models. Rev. Geophys. 25, 71–100. The ECHAM4.L39(DLR) atmosphere GCM, Tech- Schery, S. D., Whittlestone, S., Hart, K. P. and Hill, S. E. nical Description and Model Climatology. For- 1989. The flux of radon and thoron from Australian schungsbericht 1999-31, ISSN 1434-8454, Deutsches soils. J. Geophys. Res. 94, 8567–8576. Zentrum fu¨r Luft- und Raumfahrt e.V., Ko¨ln, Stevenson, D. S., Collins, W. J., Johnson, C. E. and Germany. Derwent, R. G. 1998. Intercomparison and evaluation Liu, S. C., McAfee, J. R. and Cicerone, R. J. 1984. of atmospheric transport in a Lagrangian model Radon-222 and tropospheric vertical transport. J. Geo- (STOCHEM), and an Eulerian model (UM), using phys. Res. 89, D5, 7291–7297. 222Rn as a short-lived tracer. Q. J. R. Meteorol. Soc. Maryon, R. H. and Best, M. J. 1992. ‘NAME’, ‘ATMES’ 124, 2477–2491. and the boundary layer problem. Met O (PR) T urbu- Stockwell, D. Z., Kritz, M. A., Chipperfield, M. P. and lence and DiVusion Note No. 204, Met. Office, Brack- Pyle, J. A. 1998. Validation of an off-line three-dimen- nell, UK. sional chemical transport model using observed radon Maryon, R. H., Smith, F. B., Conway, B. J. and Goddard, profiles, 2. Model results. J. Geophys. Res. 103,D7, D. M. 1991. The UK Nuclear Accident Model. Progr. 8433–8445. Nucl. Energy 26, 85–104. Turekian, K. K., Nozaki, Y. and Benninger, L. K. 1977. Merrill, J. T., Uetmatsu, M. and Bleck, R. 1989. Meteoro- Geochemistry of atmospheric radon and radon prod- logical analysis of long range transport of mineral ucts. Ann. Rev. Earth Planet. Sci. 5, 227–255. aerosols over the North Pacific. J. Geophys. Res. 94, van Velthoven, P. F. J., Sausen, R., Johnson, C. E., 8584–8598. Kelder, H., Ko¨hler, I., Kraus, A. B., Ramaroson, R., Mishra, V. C., Rangarajan, C. and Eapen, C. D. 1980. Rohrer, F., Stevenson, D., Strand, A. and Wauben, National radioactivity of the atmosphere over the W. M. F. 1997. The passive transport of NOx emissions

Tellus 54B (2002), 3  299

from aircraft studied with a hierarchy of models. Wilkening, M. H. 1959. Daily and annual courses of Atmos. Environ. 31, 1783–1799. natural atmospheric radioactivity. J. Geophys. Res. Walton, J. J., MacCracken, M. C. and Ghan, S. J. 1988. 64, 521–526. A global-scale Lagrangian trace species model of Wilkening, M. H. and Clements, W. E. 1975. Radon-222 transport, transformation, and removal processes. from the ocean surface. J. Geophys. Res. 80, 3828–3830. J. Geophys. Res. 93, D7, 8339–8354. Wilkening, M. H., Clements, W. E. and Stanley, D. 1975. WCRP (WMO/ICSU/IOC World Climate Research Radon-222 ﬂux measurements in widely separated Programme), 1999. CAS/ JSC Working Group on regions. In: T he natural radiation environment II (eds. Numerical Experimentation: Global tracer transport J. A. S. Adams et al.). USERDA CONF-720805, US models — proceedings of a WCRP workshop on mod- Energy and Res. Dev. Admin., Oak Ridge, Tenn., elling the transport and scavenging of trace constitu- 717–730. ents by clouds in global atmospheric models Williamson, D. L. and Rasch, P. J. 1989. Two- (Cambridge, UK, 1–4 August 1995). WMO Weather dimensional semi-Lagrangian transport with shape- Prediction Research Programmes Report No. 29, edited preserving interpolation. Mon. Wea. Rev. 117, 102–129. by P. Rasch, May 1999, WMO/TD-No. 950. Whittlestone, S., Robinson, E. and Ryan, S. 1992. Radon Williamson, D. L. and Rasch, P. J. 1994. Water vapor at the Mauna Loa Observatory: transport from distant transport in the NCAR CCM2. T ellus 46A, 34–51. continents. Atmos. Environ. 26A, 251–260.

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