The chemistry of the atmosphere is controlled by a large number of complex chemical and physical processes. The study of such a complex system requires the use of numerical models which have increasingly developed over the past 10 years. These models are mathematical representations of the main physical and chemical processes controlling the spatial and temporal distribution of trace gases. The models have been developed in order to test our understanding of the atmospheric processes, to identify key variables and important interactions, and to interpret local, regional and global observations. Additionally, they can be used to predict the evolution of the chemical state of the atmosphere in response to natural or anthropogenic perturbations, and to help policymakers define emission reduction policies.
Over the last decade, efforts to improve our understanding of atmospheric processes have pushed the development of a hierarchy of models. Box models continue to be excellent tools to illuminate our understanding of chemical processes. They can now take into account several hundreds of chemical species linked by a few thousands chemical reactions. As many tropospheric chemical species are short-lived and exhibit large spatial and temporal heterogeneities, the use of regional and global three-dimensional chemistry- transport models has become more common. Considerable progress has been made over the last 10 years on the development and application of these sophisticated global three-dimensional models. The salient features of several of these models are listed in Table xx.1. As shown in this table, present day global tropospheric chemical transport models typically have horizontal resolutions of 250-500 km, and include a reasonably complex representation of chemistry, taking into account in many instances non-methane hydrocarbons chemical schemes of varying levels of complexity.
Table 1: Salient features of several recent global chemical transport models for oxidant chemistry
| Model | Focus | Horizontal Resolution |
Chemistry | References |
| MOGUNTIA LLNL CTM GFDL/GCTM GFDL/GCTM ECHAM IMAGES U. Oslo CTM TM3 Harvard/GISS CTM MOZART MATCH-MPIC |
O3 NOx/NOy NOx/NOy O3 O3 O3 + related species O3 O3 + related species O3 + related species O3 + related species O3 + related species |
4 x 5 (?) Lagrangian 265 km 265 km 3.75 x 3.75 5 x 5 8 x 10 5 x 3.8 4 x 5 2.8 x 2.8 1.9 x 1.9 |
O3-CH4-CO-NOx-HOx NOx/HNO3 Prescribed OH; parameterized NOy chemistry Prescribed NOx; parameterized O3 chemistry Online; O3-CH4-CO-NOx-HOx O3-CH4-CO-NMHC-NOx-HOx O3-CH4-CO-NMHC-NOx-HOx O3-CH4-CO-NMHC-NOx-HOx O3-CH4-CO-NMHC-NOx-HOx O3-CH4-CO-NMHC-NOx-HOx O3-CH4-CO-NOx-HOx |
Crutzen and Zimmermann (1991) Penner et al. (1991) Kasibhatla et al. (1991, 1993); Levy et al. (1999) Levy et al. (1997) Roelofs et al. (1995; 1997) Muller and Brasseur (1995) Berntsen et al. (1997a) Houweling et al. (1998) Wang et al. (1998a; b; c); Wang and Jacob (1998) Brasseur et al. (1998a); Hauglustaine et al. (1998) Crutzen et al. (1999); Lawrence et al. (1999) |
2.1 Box / Lagrangian models
Major advances in understanding atmospheric chemistry have resulted from the detailed analysis of individual processes. For this purpose, zero- dimensional or box models, which consider a box in which the air mass is well mixed, are commonly used. Box models are used to analyze observations of selected species, to study tropospheric chemistry under specific conditions and to simplify complex chemistry schemes. These models are also used to evaluate and parameterize subgrid processes such as the fast chemistry occurring near source areas with time scales shorter than the characteristic transport times in large scale models, resulting in an effective" source, for instance in the boundary layer, with significantly different chemical composition from the initial emissions. 2.2 Parameterization of the transport of chemical compounds
2.2.1 Advection schemes
2.2.2 Subgrid processes: convection scheme
Mixing processes, especially vertical mixing, often occur at scales smaller than those resolved by chemical transport or general circulation models. These models generally distinguish between mixing in the presence or absence of moisture. In the former case they are referred to as moist cumulus convection or simply convection and in the later case they are often referred to as boundary layer mixing or turbulent diffusion. Moist convective mixing processes have the capability of moving a boundary layer parcel to the tropopause during an intense event, such as a thunderstorm, and the inclusion of this process in models appears to significantly contribute to the simulated vertical transport (e.g. Mahowald, et al., 1997). Currently, there appears to be no best way to include cumulus convection in either chemical transport or general circulation models. Moist convective mixing parameterizations vary from simple increased diffusion in areas of moist convective instability (Levy et al., 1982) to complicated physically based schemes based on convective available potential energy (Pan and Wu, 1995). Currently available observational data are insufficient to judge which of the very different vertical profiles resulting from the different schemes is more realistic (e.g. Jacob, et al., 1997). 2.2.3 Transport of chemical species from the stratosphere to the troposphere
Eulerian models which have fixed spatial grids differ from lagrangian or trajectory models in which chemistry is calculated along the air parcel trajectory. In these models, source and sink terms vary as the air parcel moves into different spatial regions. Lagrangian and trajectory models, which allow a detailed consideration of chemistry, are often used for local or regional scale studies. Both types of models have the intrinsic difficulty that they do not include mixing processes, which makes the validity of these models on longer time scales questionable.
Tropospheric models also must take into account a significant number of chemical reactions to simulate accurately tropospheric chemistry. The parameterization of chemical processes in models is discussed in section 2.3.
The implementation of transport in chemical transport models is normally separated into resolved or large scale advection and subgrid-scale processes, usually subdivided into moist and dry mixing. In the real atmosphere, of course, this separation of scales does not play a role and the different parameterized processes occur simultaneously.
Advection by the resolved scale winds is theoretically a straight-forward process, but deciding how to numerically implement this process in a transport model requires compromise. The qualities desirable in an advection scheme include: computational efficiency, accurate solutions, movement of tracer should occur locally and in the downwind direction, solutions should be monotonic (i.e., no new extrema should be introduced without divergence in the flow), and mass conservative'. So far numerical solutions to the advective transport have had to compromise on one or more of these traits. For example, the semi-lagrangian transport schemes were not by nature conservative, so that a mass fixer had to be introduced, which caused the transport to be slightly non-local (Rasch and Williamson, 1990). The second order advection schemes use a slightly higher memory and computational cost to obtain accurate, mass conserving solutions (e.g., Russel and Lerner, 1981). New formulations of mass flux schemes (Lin and Rood, 1996; Rasch and Lawrence, 1998) appear to have improved stability and accuracy while being computational efficient and mass conserving. They have been implemented in various forms in chemical transport models and general circulation models. A very accurate algorithm, recommended for coarse resolution grids, has been proposed by Prather (1986): in this formulation, the tracer concentration inside a grid box is represented by second-order polynomials and its spatial distribution by second-order moments. This method, characterized by small numerical diffusion, requires a large computation time. Reviews of the different advection schemes used in chemistry-transport models are given for example in Rood (1987), Hov et al. (1989), Chock (1991), and Brasseur et al. (1999).
Dry convective mixing occurs when the boundary layer or other layers are statically unstable and is often parameterized using a simple diffusive approach based on local instability such as Louis (1979). This approach may simulate somewhat too little mixing in the boundary layer under highly unstable (daytime) regimes, which led to the development of non-local schemes such as Holtslag and Boville (1993). Comparisons of models such as Jacob et al. (1997) or Rasch, et al. (in press) suggest that the local Louis schemes may produce too little mixing but the non-local schemes may mix slightly too much. Since many species have surface sources, and many observations occur at the surface, improvements of parameterizations for the boundary layer have a high. Unfortunately, observations that can be used to unambiguously evaluate these parameterizations are scarce.
Many chemical transport models are off-line models, in which the winds and temperature are input to the model, and have been derived from another model, either a general circulation or a forecast center model. Recently, chemical transport models have added the ability to explicitly treat moisture in order to better capture the moist convective mixing and precipitation events which control especially soluble species in the atmosphere (e.g. Rasch et al., 1997). In this case, the temperature and humidity are predicted (using surface flux and radiative flux fields from the driving model) including the effects of moist convection and stratiform precipitation. These offline models are thus capable of simulating specific events using forecast center winds such as the NCEP or ECMWF winds and capturing the hydrological cycle (Lawrence, et al., 1999a + other references). Another approach which allows the simulation of specific events is to use an online model which is 'nudged' to the "observed" meteorology from forecast center analyses (Jeuken et al., 1996).
An important process that must be represented in studies of tropospheric oxidant chemistry is the downward transport of ozone (and to a lesser extent of NOx ) from the stratosphere. To do this accurately, one must realistically simulate stratospheric chemistry, downward transport in the stratosphere, and the space-time distribution of stratosphere-troposphere exchange events. The current generation of tropospheric chemistry models does not include a explicit an rigorous treatment of stratospheric chemistry. In the recent IPCC (1999) report on the impact of aircraft on the atmosphere, 2-D models were used to simulate stratospheric processes, while 3-D models were used for the troposphere, and the results were combined to obtain a global picture. This was recognized as a major weakness in the analysis of model results. It should be noted however that though models simulating both tropospheric and stratospheric chemistry are currently under development within a few modeling groups.
In almost all current models, the concentrations of O3 and related species are prescribed at some level in the stratosphere, usually at or below 10 hPa. Exceptions are the Harvard-GISS and MOGUNTIA (table xx.1) models which use an alternative parameterization by prescribing flux boundary conditions at the tropopause. An additional consideration is that the vertical (and in some cases horizontal) model resolution is often rather coarse and calculation of the relevant transport processes in the middle atmosphere is missing in most models, so that there are significant uncertainties in model-calculated stratospheric dynamics as well as in the dynamics of stratosphere-troposphere exchanges. While the global cross-troposphere flux of O3 is constrained to some extent by budget considerations, there is a considerable range in the "simulated" cross-tropopause O3 flux in various models. Furthermore, the differences in the models can lead to large differences in the context of the stratospheric contribution to tropospheric O3 at particular locations and time- periods.
| Species | Yearly (Y) or Seasonal (S) | Reference |
| NOx from soils Anthropogenic NOx Anthropogenic NOx Anthropogenic SO2 Anthropogenic SO2 Volcanic sulfur Nitrous oxide Volatile organic compounds Reactive chlorine Black carbon from fossil fuel Black carbon from biomass burning |
S Y S Y S Y Y S Y Y Y /TD> | Yienger and Levy, 1995 Benkovitz et al., 1996 Voldner et al. Benkovitz et al., 1996 Voldner et al. Andres and Kasgnoc, 1998 Bouwman et al., 1995 Guenther et al., 1995 8 papers -> ?? Dignon et al. Cooke and Wilson |
| Species | Global amount emitted (Tg) |
| CH4 Fossil fuel : combustion Fossil fuel : production Biofuel Industrial processes Land use/waste treatment CO Fossil fuel Biofuel Industrial processes Land use/waste treatment NOx Fossil fuel Biofuel Industrial processes Land use/waste treatment NM-VOC Fossil fuel:combustion Fossil fuel: non combustion Biofuel Industrial processes Land use/waste treatment |
4.8 89.3 14.1 0.8 211.4 262.6 181.0 34.8 495.9 21.9 1.3 1.5 6.2 41.6 27.3 30.7 33.5 44.4 |
2.5 Advances in computing technology
3.1 Model validation and intercomparisons
The accuracy and consistency of models used to simulate tropospheric chemistry and perform future predictions has been tested over the past five years through inter-comparison exercises. 3.2 Use of photochemical models for supporting field campaigns
Photochemical models can play an important role in field campaigns, both in helping to evaluate the observations, as well as in the planning and execution stages. Constrained box models have been particularly useful in helping to point out possible problems with the measurement techniques (Crawford et al., 1996), as well as to point towards possible missing knowledge of photochemical processes, e.g. a missing sink for OH in the marine boundary layer (Eisele et al., 1996). Recently, more complex chemistry-transport models have also come into the picture. For instance, MOZART (table xx.1) was used to examine the O3 photochemical budget of the Pacific Ocean based on data from MLOPEX (Brasseur et al., 1996). The O3 budget was further analyzed by Lawrence (1996) using a box model constrained by the MLOPEX observations (Ridley et al., 1992) and concentrations calculated using the MATCH model. The differences were found to be largely due to the NOx levels, which points out the importance of high quality NOx measurements (Crawford et al., 1996). Other examples of the use of 3-D CTMs for interpreting campaign data are the study of Singh et al. (1996), which concluded that transport of Asian NOy into the PEM-West A region served as a major source of NOy during the campaign, and Lawrence et al. (1999), who concluded that while convective pumping of low-ozone marine boundary layer air is the main process responsible for producing O3 minima in the upper troposphere, their severity may be influenced by a missing O3 sink, e.g. halogens. Finally, models have been employed to evaluate the sampling done during a campaign: Ehhalt et al. (1997) used a CTM with surrogate tracers to demonstrate that the sampling during PEM- West A and B was likely sufficient to capture the mean in the region sampled, while Lawrence et al. (1999a) used O3 simulations to conclude that the single cruise through the CEPEX region was likely insufficient to capture the mean, although it did point out that extremely low levels of ozone occur which had not been previously observed. 3.3 CTM results and climate forcing
Calculations of the radiative forcing due to changes in the distribution of well-mixed gases such as CO2 , CH4 , N2O and the CFCs have been performed over the last decades using radiative models. As seen in the previous chapters, ozone is more and more recognized as a greenhouse gas with an estimated contribution to the enhanced greenhouse effect since the preindustrial period of about 20%. Accurate calculations of the radiative forcing of ozone requires the knowledge of the spatial and temporal changes of the ozone distribution in the troposphere. The development of the CTMs has allowed the calculation of the three-dimensional evolution of ozone over the last century (Berntsen et al., 1997; Roelofs et al., 1997; Brasseur et al., 1998b and other references). However, previous studies have shown that changes in ozone in the vicinity of the tropopause might be the most important in terms of radiative forcing (Refs). No data are currently available concerning the long-term evolution of ozone in this altitude region, which is also a region where most models have a rather low vertical resolution, and calculated concentrations are affected by errors in the parameterization of exchanges between the stratosphere and the troposphere.
4.1 Nesting/variable resolution
With the current computer power available global chemistry-transport models (CTMs) with extensive chemistry can have horizontal grids of ~ 250 km or even ~100 km. It can be important to increase the resolution of a model over a region of interest, since transport and chemistry (including sources and sinks) are expected to be simulated more accurately with increasing resolution. Furthermore, comparisons of measurements and model results are more straightforward and significant in a high-resolution model. Two different approaches can achieve the increase in resolution, (1) place a high-resolution grid inside a coarse resolution grid where greater resolution or accuracy is desired (over a fixed region or following the path of a particular phenomenon) and (2) create a model with variable resolution. 4.1.1 Nesting approach
4.1.2 Variable resolution approach
4.2 Data assimilation and inverse modeling
A large amount of observation of meteorological parameters, distributions of atmospheric chemical species, ecosystems etc. has been collected over the last 2 decades, and the new generation of earth satellite observations will provide even much larger datasets. However, it is not possible to measure all the atmospheric quantities simultaneously in time and space, and the retrieval of satellite data will generally give access to sparse, heterogeneous and irregular distributions of atmospheric quantities. Objective approaches to combine our a priori knowledge about the physical system under consideration with these usually sparse and irregular observations are often referred to as data assimilation. Up to now, data assimilation techniques have mostly been used in numerical weather prediction, data retrievals from remote sensing experiments, and inverse modeling. Some interesting pioneering work on assimilating observations of chemical species in the atmosphere using photochemical models has been done recently and results of these recent research efforts demonstrated the feasibility of the approach and promised important benefits. 4.3 Aerosols and climate
The representation of the climatic effect of aerosols in global models has first used static simplified distributions derived from observations and Mie- calculations to assign optical parameters. Most of the model studies investigating the direct and indirect effect of aerosols and climate used these static climatologies. Since the pioneering study by Langner and Rodhe (1991), who used a coarse resolution chemical-transport model based on climatological meteorology, the complexity of the aerosol precursor chemistry, of particles dry deposition and wet removal included in the models has increased dramatically. Several models treat the aerosol precursor chemistry and the evolution of the particle mass interactively with the meteorology, taking into account the complex interactions between cloud processes, heterogeneous chemistry and wet removal (Benkovitz et al., 1997; Feichter et al., 1997, Roelofs et al., 1998; Rasch et al., 1999; Koch et al., 1999). However, the physical and optical properties of the aerosol components are prescribed. Such an approach allows the representation of the high variability of the mass distributions of the particles and is used more particularly when aerosol-cloud interactions are studied. 4.4 Coupled earth system models
As processes occurring in the oceans, atmosphere and continental areas determine the distribution of chemical species in the atmosphere are linked, coupled models are required to study the feedbacks between these different components of the Earth system. A few groups have started to work on integrated models, or Earth-system models, in which global dynamics, chemistry, biology and oceans are interactively coupled. Such models should help to understand how changes in climatic conditions affect the distribution of species such as greenhouse gases, as well as how changes in greenhouse gases affect climatic conditions. It should be noted however that the validation of such coupled models will represent a great challenge in the future.
The development of global atmospheric and "earth" system models over the past decade would not have been possible without the remarkable advances in computational capacity. There have been algorithm improvements ranging from highly automated solvers such as SMVGear to improved sparse matrix techniques (Ref). New versions of scientific languages such as Fortran 90 and modern utilities such as source control software have improved the development process and at the end model reliability, though rounding errors and computer artifacts have been reported (Rosinski and Williamson, 1997; Lawrence et al., 1999b). But it is the improvement in "raw" computer power from the gigaflop range a decade ago toward the teraflop mark today that has enabled our greatly improved simulations, together with large increases in storing capacities. Not only can we regularly perform higher resolution studies on a global basis but many complex elements such as clouds and subgrid processes can be simulated with enhanced fidelity at the global scale due to improved process detailed studies.
Today, with computer systems capable of sustaining hundreds of gigaflops, global simulations with regional spatial resolutions are practical. And models coupling realistic oceans, sea ice, biogeochemistry, and a chemically active atmosphere are on the horizon.
3 Applications of the models
Parameterization of convection in the models has been tested through simulations of the distribution of Radon-222, by comparing model results and observations. Twenty global 2-D and 3-D models participated in that exercise, which demonstrated that deep convection is not well represented by most models. Upper troposphere simulations appear to be very sensitive to the treatment of moist convection and to the scale of deep convection (Jacob et al., 1997).
24 photochemical codes used in CTMs of various scales have been isolated from the transport parameterizations, and have been compared within the IPCC'94 "Photocomp" intercomparison exercise (Olson et al., 1997; WMO, 1995). Their results show that model to model differences of 30% or more exist in the calculation of ozone and OH concentrations. These differences result from differences in the calculated photolysis rates, kinetic data, numerical methods used to solve the equations, and the set of photochemical reactions adopted to represent tropospheric photochemistry. In particular, the ozone photo-dissociation rates differ by ±20%, whereas the best agreement of ±5% was obtained for the NO2 photolysis rates, the other rates agreeing within ±15%. The largest deviations between models were calculated when non-methane hydrocarbons chemistry was included. The large dispersion of the results from calculations by several 2-D and 3- D models of ozone changes resulting from a 20% increase in CH4 concentrations showed that the ability of the models to predict tropospheric ozone changes induced by methane perturbations was not satisfactory (WMO, 1994).
A more recent intercomparison by Kuhn et al. (1998) of tropospheric chemical models for atmospheric conditions over Europe showed differences in oxidants levels up to 40% due to gas phase chemistry.
Following the recent fast development of global 3-D CTMs, an intercomparison exercise of these new generation of models has been performed in 1997-1998, under the initiative of GIM/IGAC. The objective of the Tropospheric Ozone Global Model Intercomparison Exercise was to systematically evaluate the capabilities of the current generation of 3-D global models to simulate tropospheric ozone and their precursor gases, and to identify key areas of uncertainty in our understanding of the tropospheric ozone budget (Kanakidou et al., 1999a; 1999b). Thirteen global CTMs participated in this exercise. Significant differences have been detected between the models although all of them capture the general patterns in the global distribution of carbon monoxide, nitrogen oxides and ozone. The comparison between model results, which used different surface emissions, and observations at selected stations indicates the models deviate from the observed annual mean CO concentrations by about ±50%. The main features of the ozone distribution were captured by all models although differences at some locations up to a factor of 3 have been detected between models.
Maximum deviations of models from surface ozone observations are of the order of 50% whereas models deviate much more from observations in the free troposphere and particularly close to the tropopause level where the ozone concentrations are sensitive to the parameterization of cross-tropopause transport. Interestingly, the photochemical lifetime of methane in the troposphere up to 300 hPa (or to the closest model level) was calculated to be 7.5 years globally and 8.6 years in the southern hemisphere against 6.8 years in the northern hemisphere (as the medians of model results). Model results vary within 30% of these values. This north-south asymmetry in the computed OH distribution requires further investigation.
Figures of CO and ozone intercomparison will be added
Models are often used in planning campaigns by providing estimates of what one might expect in terms of concentrations and gradients of various species. CTMs can also provide estimates of the amount of sampling which is needed to obtain a certain desired degree of representativeness in a future campaign (Lawrence, 2000), similar to the analysis which can be done with previous observations (Logan, 1999). Finally, during the last few years, photochemical models have seen increasing use in forecasting during the intensive field phases of campaigns. One of the first examples were described by Lee et al. (1997), who forecasted stratospheric constituents in the polar vortex for the ASHOE/MESA and SESAME campaigns, and by Flatoy et al. (1999) who provided tropospheric chemistry forecasts for the POLINAT campaign. Both of these studies used regional models. Global tropospheric chemsitry forecasts were done by Lawrence et al. (2000), Rasch et al. (2000), and Collins et al. (2000) for the INDOEX campaign. In all cases, the forecasts were received by the field investigators. Despite innacuracies in the model predictions, on several occasions, the forecasts were able to help point towards events which were of interest to observe.
4 New developments
Both approaches have pros and cons and have been used extensively in meteorological forecasting and to a lesser extent in studies involving chemistry. This section will briefly describe both techniques. It is important to remember that CTMs require the knowledge of meteorological fields (including cloud properties) to calculate the transport and transformation of chemical species. A meteorological model simulation over the area of interest provides this information (Brasseur et al, 1999 and references therein) which is then used offline.
The nesting approach consists of inserting a finer resolution model inside a coarse resolution model. There are basically two approaches to limited-area modeling, which can be characterized as one- and two-way interacting (Phillips and Shukla, 1973). In the one-way approach, time-dependent conditions are specified at the boundaries of a limited area, and the model is then integrated at high resolution over this area. In this setup, the larger scales of the flow that cannot be simulated on the fine grid are allowed to affect the fine grid solution. Discontinuities and distortions can develop at the interface in absence of feedbacks from the fine to the coarse grid. Also, because of the variation in resolution, reflection and refraction of waves occur (Courtier and Geleyn, 1988), particularly if the resolution varies abruptly (Gravel and Staniforth, 1992). Finally, one-way nesting implicitly assumes that small-scale phenomena have no major influence on the larger scale treated on the coarse grid (Skamarock et al., 1989). This is usually not the case for the physical and chemical processes in the atmosphere or the ocean. The two-way interactive nested grid approach addresses this problem. The procedure consists of integrating the fine grid along with the coarse grid. The lateral boundary conditions for the fine grid are taken from the coarse grid solution. The solution on the coarse grid is then updated with the fine grid solution at any coarse grid location where the two grids overlap (Skamarock et al., 1989). Nevertheless, numerical dispersion problems may still occur at resolution interfaces, particularly if the resolution varies too rapidly.
In a meteorological forecast model, the boundary conditions are set on all the prognostic variables (wind, temperature, humidity, cloud properties). In a CTM, the boundary conditions pertain to the chemical species distribution. Lateral boundary conditions (values or fluxes) are calculated by interpolating the necessary fields from the coarse grid solution. This interpolation introduces errors and noise. Because short-lived species adjust quickly to the ambient levels of long-lived species, only the latter need to be calculated at the boundary. Also, long-lived species usually exhibit a smoother distribution that tends to decrease the interpolation errors. The short-lived species are then calculated explicitly for the conditions defined by the long-lived ones. This ensures that the chemical system is balanced with the set of equations defining the chemical mechanism, both on the coarse and the fine grids. As far as we know only the one-way nesting approach has been used in CTMs (Chang et al., 1987; Ebel et al., 1991; Hess et al., 1999). Nevertheless, in going from fine to coarse grid only the long-lived need to be considered for the reason described above.
Even in an ideal situation where all the problems related to the specification of boundary conditions are solved, there is still the practical difficulty of having two systems (global and nested) to maintain (Côté et al., 1993). It would therefore be interesting to have a single model in which the resolution could be varied such that high resolution is focused over an area of interest, and therefore provides both global and regional simulations.
Courtier and Geleyn (1988) have described the first application of a conformal transformation that creates a region of high resolution with a continuous transition from coarse to high. This variable resolution model, with the pole rotated over the area of interest, leaves the governing equations almost unchanged (except for the multiplication of a few terms by a local map factor). Because there is a variation in model resolution, problems similar to loss of information and wave reflection at the boundaries in the nesting approach will have counterparts in this method but with a less damaging intensity (Courtier and Geleyn, 1988). There are nevertheless severe limitations, mostly associated with the use of a spectral model (Côté et al., 1993). Côté et al. have therefore applied the same map transformation but with a finite-element discretisation (and other numerical specificities), with considerable success (Côté et al., 1993).
In the case of CTMs, this approach might not be as feasible since there is no model available at this point that could provide the necessary meteorological fields on a variable resolution grid. It is therefore required to create such data sets by interpolating results from regular grid meteorological models. This can be first a cumbersome task and second, introduce noise in the dynamical fields, which might translate into spurious vertical velocities. Such approach has nevertheless been applied to the case study of the MLOPEX data (Ginoux, 1998). In that case, a triangular grid was used, with the equations of transport solved by the finite element method. Although the variable resolution approach is conceptually appealing, the limited number of models that could create the necessary fields for driving the CTM has hampered its use. The future might reside in the online simulation of chemistry within a variable resolution model.
The mathematical basis of data assimilation is estimation theory or inverse problem theory. In a conventional "forward" problem, one uses a set of a priori parameters to predict the state of the physical system. In the "inverse" or estimation problem, one attempts to use available observations of the state of the system to estimate poorly known model parameters and/or the state itself. Very broadly, commonly used data assimilation methods can be divided into variational and sequential techniques.
In variational data assimilation, one attempts to find optimal parameters (e.g. optimal initial conditions) that minimize a discrepancy between model results and measurements for a chosen analysis period. The variational data assimilation technique can be thought of as a constrained least-squares fit to a set of observations distributed over some period of time. The constraints are given by the model equations. In the sequential method, observations are "blended" with model simulations with certain weights as they become available to form new initial conditions for the model for the next time step.
The optimal weights are obtained from estimates of the model errors, errors of the current observations and errors of observations incorporated into the model previously.
Lyster et al. (1997) for the first time have used a two-dimensional transport model on isentropic surfaces and the Kalman filter technique to assimilate CLAES- and HALOE-measured methane from the UARS satellite.
Although very computationally expensive, their pioneering approach allows production of synoptic maps from irregularly distributed satellite measurements. Fisher and Lary (1996) have used variational data assimilation for assimilating and mapping the UARS/CLAES observations of O3 , NO2 , and HNO3 using a fairly simple 6 species/19 reactions photochemical box model in conjunction with a trajectory model. This was the first application of data assimilation techniques for analysis of photochemically active species in the stratosphere. Elbern et al. (1997) extended this variational to assimilation of various tropospheric gases. Khattatov et al. (1999) have applied the variational approach as well as the extended Kalman filter for assimilation of satellite stratospheric measured species using a relatively sophisticated box model and a trajectory model. It was also shown that concentrations of a number of non- observed species can be successfully derived from available data. Lamarque et al. (1999) have applied a similar method to assimilate with a 3-D CTM CO observed from space.
The emissions of chemical trace gases specified at the surface are generally poorly quantified, as they depend on complex processes related to meteorological conditions and human factors. As more and more observations of chemical species become available, it is in principle possible, using inverse modeling techniques, to optimize surface emissions, which also improves the agreement between observed and calculated distributions. Different methods have been developed over the past few years, and they have been first used to optimize surface emissions of CO2 (Enting and Mansbridge, 1991; Bousquet et al., 1999), CH4 (Hein et al., 1997; Houweling et al., 1999) and CFCs (Hartley and Prinn, 1993; Mahowald et al., 1997), and more recently of CO (Bergamaschi et al., 2000). The use of such methods is currently limited, as the number of observations sites is relatively small. Furthermore, optimization of surface emissions using inverse modeling requires an accurate treatment of the mixing between the boundary layer and the free troposphere. In the near future, more and more observations of tropospheric species will become available from satellite observations, which may considerably improve the results possibly leading to new insights into the distribution of surface emissions of chemical species and on their spatial and temporal variability.
Recent attempts have been undertaken in order to calculate also the particle number concentration using parameterizations of aerosol formation and dynamical processes. Two kinds of such models were developed, using spectral or bin schemes. In the spectral scheme, one or more aerosol modes of the particle distribution are described by lognormal distributions (Schultz et al., 1998; Wilson et al., 1999). In bin schemes, the particle mass is distributed over different size classes, each bin being characterized by its geometric mean diameter. Such schemes, which allow to reproduce changes in size distribution when a large number of size classes are taken into account, have been applied for example for sulfuric acid in the stratosphere (Timreck, 1999) and sea-salt aerosols (Gong et al., 1997).
Most of global climate and chemistry transport models have so far only considered the bulk aerosol mass of some specific components rather than the size spectra of externally and internally mixed aerosols and their size- dependent chemical composition. However, the size distribution and the chemical composition of the particles control the optical and deliquescence properties, the activation of particles to cloud condensation nuclei and their subsequent formation to cloud droplets. Currently, work is under way to improve the understanding of the presence of nitrate and organic aerosols, using thermodynamic equilibrium models. In particular, the description of the state of mixture is a challenging task for future research.
Even with all our present computational power, the development of highly coupled models is a daunting task that requires compromises to achieve century scale simulations. The spatial resolution of the experiments is often coarse, and therefore even parameterizations of important processes have to be greatly simplified. We can expect that future advances in computing will allow us to build interactive more accurate coupled models capable of century scale simulations.
References
Last modified: Thu Apr 27 16:36:56 CEST 2000