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New approaches to modelling the gobal distribution of trace gases in the troposphere
Mathematics and Computers in Simulation North-Holland
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32 (1990) 59-64
NEW APPROACHES TO MODELLING THE GLOBAL DISTRIBUTION OF TRACE GASES IN THE TROPOSPHERE J .A . TAYLOR Centre for Resource and Environmental Studies, Australian National University, Canberra, ACT, Australia
1.
INTRODUCTION Currently a revolution in our understanding of the physics and chemistry of the global
atmosphere is occurring . Perhaps the most striking examples of this revolution are the improved understanding of the depletion of the ozone layer, the 'greenhouse' effect and their probable impact on global climate . The reasons for this revolution in our understanding are many, however a few stand out as most significant - in particular, the development of the earth observing satellites and in t uments to observe chemical species remotely from space and at the earth's surface . The most famous example of our ability to measure trace species from space is the observation of stratospheric ozone concentrations . While the development of the electron capture detector by Lovelock [11 has allowed the precise measurement of the ozone destroying chlorofluorocarbons (CFCs) with a precision of parts per trillion (ppt) . The measurement of other trace gases such as carbon dioxide (C02) in parts per million (ppm) amounts by Keeling et al [21 also dramatically changed our perception of the importance of trace chemical species in the atmosphere and their potential for altering global climate . While comprehensive and precise measurements for a few chemical species have been available for some time, detailed measurements, with global coverage, of the thousands of trace chemical species present in the troposphere remains beyond the reach of modern technology . Accordingly, theoretical studies requiring the development of high resolution global chemical transport models able represent the tropospheric chemistry and global atmospheric circulation have commenced . These models must also include a realistic treatment of small scale processes responsible for producing 10
significant perturbations at the larger scale if we are to develop an accurate understanding of global tropospheric chemistry and the cycles of chemical species which pass through the atmosphere . 2.
A GLOBAL ATMOSPHERIC TRACER TRANSPORT MODEL As a first step in the process of developing a global tropospheric chemistry and transport model
we must develop a, high resolution transport model . A stochastic global 3-dimensional l .agrangian tracer transport model has recently been developed for the purpose of studying the sources and sinks of trace gases important to climatic change [31 . Model advection terms are derived from the European Centre for Medium Range Weather Forecasting (ECMWF) analysed grids . Source and sink terms for 0378-4754/90/$3 .50 tt 1990.
IMACS/Elsevier Science Publishers
B .V.
(North-Holland)
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J.A . Taylor / Modelling the global distribution of trace gases
carbon dioxide, methane . and the chlorofluorocarbons CFC-11 and CFC-12, radon and methyl-chloroform have been incorporated within the model . Model predictions are usually compared with available atmospheric observations of the respective trace gases [3] . The Lagrangian equation for atmospheric dispersion of a chemical species is as follows [4] : c < c(r, t)
> = f J r ~ p(r, t/rt , t 1 ) s(rr , t ) drl dtl o
(1)
-~
where < c(r, 1) > represents the ensemble average concentration at r at time t; s(rl, ti) is the source of the chemical species (g m - 3 see- ') ; p(r, t/rt, 11) is the probability density function (m 3) that an air parcel moves from rl at ti to r at 1, where, for any given rt and t > tt the following must hold [4] :
f ~p(r' t/r1, t1) dr= 1
(2)
in order to satisfy the conservation of mass of the chemical species . If physical or chemical removal processes are included then the integral in equation (2) is set to a value less than one . The term s(rl, 11) > 0 only at the point of release and where chemical transformation of secondary species within the atmosphere occurs . As it is not always possible to evaluate the release of the pollutant for -w < tr < t equation (1) can be rewritten to [4] :
< c(r, 1) > = J~~p(r, t/r I , c0
+f t
t
, t0 )> drI
J r ~p(r, t/r , t) s 1, t 1 ) drl dtl
(3)
o
where only the trace gas emissions during is < ti < t are included as the first term represents the release of the trace gas prior to t° . The first integral term is approximated by the average concentration
J .A . Taylor / Modelling the global distribution
of trace gases
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u, c and to according to [3] : D = of (rn + a N[O, 1])
(4)
where D is the air parcel displacement, of is the time step, m is the appropriate bi-monthly mean wind speed and c7 the standard deviation of the wind velocity averaged over a bi-monthly time period, and N/O, l jrepresents a sample from the standard normal distribution . 3.
COMPARISON WITH EULERIAN APPROACHES
Previous attempts at modelling atmospheric tracer transport and the study of sources and sinks of trace gases were based on the Eulerian modelling approach incorporating eddy diffusion . The majority of these models are 2-dimensional 'tonally averaged with relatively low resolution . Eddy diffusion coefficients are themselves very uncertain and should strictly be evaluated separately for each chemical species under study . A further difficulty with Eulerian models is the introduction of artificial advection arising from the numerical solution of the finite difference form of the advection equations which leads to a failure to conserve trace mass . This problem is currently resolved through the introduction of numerical fixes . The Eulerian approach also requires that the transport of chemical species be independently evaluated for each chemical species included in a model simulation . Finally, the computational costs of Eulerian models applied at high resolution and for simulations over a number of years are so considerable that no such studies have been undertaken [5] . The Lagrangian model, described in detail by Taylor [3], offers a number of significant advantages over previous modelling approaches . Most importantly, the approach is flexible in that different transport fields, trace gas source functions and initial tracer concentration fields may be readily incorporated into the model . Multiple trace species may be advected simultaneously, numerical instabilities associated with Eulerian advection are avoided and conservation of tracer mass is ensured using the Lagrangian approach . The model is also sufficiently fast computationally that one year model simulations can be performed in -140-200 seconds of central processing time on a CRAY X-MP/18 . This low computational cost allows a range of possible source functions to be investigated and multi-year simulations to be performed for carbon dioxide, methane, the chlorofluorocarbons CVC-11 and CFC-12, radon and methyl chloroform . 4.
COMPUTATIONAL EFFICIENCY OF LAGRANGIAN APPROACHES As an example of the current limitations of the application of Eulerian based models Rood and
Kaye [5] estimate that for a one year model simulation a stratospheric general circulation model with chemistry using a 4' latitude by 5' longitude grid with 19 vertical levels would require approximately 7(i days on a dedicated CYBER 205 supercomputer, assuming that the model could be efficiently fit
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J.A . Taylor / Modelling the global dictribution of trace gases
J. A . Taylor / Modelling the global distribution of trace gases
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into memory . Clearly, even if such resources could be made available the results of such a model run would be of limited use due to the difficulties of performing sensitivity studies- Other Eulerian 3-dimensional tracer transport models have been developed where a general circulation model is run independently of the chemistry sub-model [6] . The model transport is stored as coefficients and used as a parameter to the chemistry model . Such model simulation runs are reported as requiring about 20 hours of CPU time to transport one chemical species for one model year . In comparison the Lagrangian approach is about 400 to 40,000 times faster than the comparable Eulerian models at lower resolutions for 3-dimensional transport of one chemical species . If we also take into account the fact that the Eulerian approach must advect each chemical species independently then the efficiency, e, defined as the ratio of computational times of the Eulerian methods to Lagrangian methods for n chemical species, nchem , will be
e "' 4, 000
achem
(5)
Further, in the event that Eulerian methods become as computationally fast as Lagrangian methods in advecting one chemical species then the Lagrangian approach would still remain nchem times more efficient . Future studies of atmospheric chemistry will see nchem increasing towards the many thousands of chemical species present within the atmosphere . 5 . LAGRANGIAN MODEL RESULTS As an example of the performance of the Lagrangian model [3] a simulation run with an inert pseudo-tracer was performed . The duration of the model simulation was five years . It was assumed that no loss of tracer by chemical reaction or by transport to the stratosphere was occurring . The spatial distribution of the release of tracer was assumed to be proportional to the release of CFC-11 rate was assumed to be 250 . x 10 9 g yr - 1 . The release of tracer occurs at a uniform rate throughout the model simulation . Figure Ia shows the model predicted surface concentration (ppt) of the inert tracer averaged over the month of June for the final year of the simulation run . Above the 2-dimensional contour plot is a 3-dimensional line graph of the same data . The line graph is at the same resolution as the model . Figure lb presents the zonally averaged concentration (ppt) of tracer corresponding to Figure la . Figure lc illustrates the increase in the globally averaged model surface layer (assumed to be the lowest height level of the model corresponding to the pressure range (1000-925 hPa) tracer concentration (ppt) for the final year of the model run . These model results are in excellent qualitative agreement with Eulerian model studies [6] and when account is taken of the different absolute magnitudes of the concentrations the results displayed in Figure 1 are in excellent quantitative agreement with Eulcrian model results [6] .
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J.A . Taylor / Modelling the global distribution of trace gases
6 . CONCLUSIONS The development of high resolution 3-dimensional global atmospheric transport and chemistry models has only recently begun . Such models are urgently required to address a range of global problems, most particularly the 'greenhouse' effect and the drop in stratospheric ozone concentrations . In this paper it has been shown that Lagrangian models are computationally more efficient than the equivalent Eulerian based approaches . As the Lagrangian approach can advect multiple chemical species simultaneously, the Lagrangian approach will always provide a more efficient solution for the simulation of atmospheric transport especially as the number of chemical species in the chemistry models increases . Finally, the Lagrangian approach ensures the conservation of tracer mass whereas computational fixes must be introduced into Eulerian models in order to conserve tracer mass . The effects of computational fixes included in Eulerian models will become more difficult to determine with the increasing number of chemical species and the inclusion of chemical reactions between these chemical species . Acknowledgements The model simulations were undertaken while a Visiting Scientist at the United States National Center for Atmospheric Research . The National Center for Atmospheric Research is sponsored by the National Science Foundation . The author would also like to thank Shelley Santoso for assistance with word processing . References [1 [2 [3] [4] [5] 6]
Lovelock, J .E ., Atmospheric halocarbons and stratospheric ozone, Nature, 252, 292-294,1974 . Keeling, C .D ., Bacowstow, R .B ., Bainhridge, A .E ., Ekdahl, C .A ., Guenther, P .R ., Waterman, L .S . and J .S . Chin, Carbon dioxide variations at Mauna Loa Observatory, Hawaii, Tellus, 28, 538-562,1976 . Taylor, J .A ., A stochastic Lagrangian atmospheric transport model to determine global C02 sources and sinks - a preliminary discussion, Tellus, 41B, 272-285, 1989 . Zannetti, P ., in Encyclopedia of Environmental Control Technology, Vol . 2, Air pollution control, Cheremisinoff, ed ., Gulf Publishing Company, 1989 . R.B . Rood and Kaye, J .A . , Chemistry and transport in a three-dimensional stratospheric model : Chlorine species during a simulated stratospheric warming, J . Geophys . Res . ; 94, 1057-1083, 1989 . Prather, M_ McElroy, M . . Wofs,y, S ., Russel, G . and D . Rind, Chemistry of the global troposphere : Fluorocarbons as tracers of air motion, J . Geophys . Res., 92, 6579-6613, 1987 .