Simplified aerosol modeling for variational data assimilation

Simplified aerosol modeling for variational data assimilation N. Huneeus, O. Boucher, and F. Chevallier Laboratoire des Sciences du Climat et de l’Environnement, L’Orme de Merisier, Gif sur Yvette, France Met Office, Hadley Centre, Exeter, UK Received: 28 May 2009 – Accepted: 5 June 2009 – Published: 23 June 2009 Correspondence to: N. Huneeus (nicolas.huneeus@lsce.ipsl.fr) Published by Copernicus Publications on behalf of the European Geosciences Union.

remains large.
Traditionally, emissions have been estimated through bottom-up techniques which integrate source information across sectors. However, top-down techniques have been developed in recent years that exploit the combination of satellite data and numerical models through inverse techniques. An important technique for this purpose is varia-10 tional data assimilation. It allows obtaining an optimal initial state estimate by finding the best compromise between background information and observations. This technique is widely used in numerical weather prediction (NWP) centres (e.g. Rabier et al., 2000;Lorenc et al., 2000) and has been very successful in significantly improving the weather forecast performance (Rabier, 2005). It has already been applied to the model computationally efficient and conceptually easier to understand. Sandu et al. (2005) developed an aerosol model for inverse modeling of aerosol dynamics that focuses only on the physical particle dynamics excluding the chemical and thermodynamic transformations. Zhang et al. (2008) used an aerosol model with a simplified aerosol representation in the first attempt to operationally assimilate aerosols into nu-10 merical weather prediction (NWP). An aerosol model was developed and introduced into the Integrated Forecast System (IFS) of the European Centre of Medium Range Weather Forecast (ECMWF) to assimilate satellite aerosol products into a NWP model for reanalysis and forecast Benedetti et al., 2009).
We present in this paper a simplified aerosol model that computes AOD from emis- 15 sion fluxes of the main aerosol species and gaseous precursors. The model has been designed with the aim to estimate the intensity of the aerosol emissions through variational data assimilation of AOD. As a consequence the tangent linear and adjoint versions of the new model have also been developed. Applications of this aerosol model to variational data assimilation will be presented in a forthcoming article. We Introduction

Reference general circulation model
The general circulation model of the Laboratoire de Météorologie Dynamique (LMDz) in its version 3.3 simulates the global life cycle for the main aerosol species, namely sea salt (SS), desert dust (DD), organic matter (OM), black carbon (BC) and sulfate (SU). Its standard version has a resolution of 3.75 • in longitude, 2.5 • in latitude, and 5 19 levels in the vertical with a hybrid σ-pressure coordinate with five of its levels under 850 hPa and nine above 250 hPa. The model computes the atmospheric transport with an Eulerian finite volume transport scheme for large scale advection, a turbulent mixing scheme within the boundary layer and a mass flux scheme for convection. The time step for the dynamics equations is three minutes. The mass fluxes are accumulated 10 over 5 time steps in order to apply the large scale advection every 15 min. The physical and chemical parametrisation are applied every 30 min. An operator splitting technique is applied to the different processes that affect the prognostic variables (Boucher et al., 2002). The sulfur cycle includes six sulfur species: dimethylsulfide (DMS), sulfur dioxide 15 (SO 2 ), hydrogen sulfide (H 2 S), dimethylsulfoxide (DMSO), methanesulfonic acid (MSA) and sulfates (SU). These last two species are assumed to be in the particulate phase. The sulfur emissions from fossil fuel combustion and industrial processes are taken from the EDGAR version 3.0 database (Olivier and Berdowski, 2001), from which a fixed 5% from combustion sources is assumed to be emitted directly as sulfate. An ad-20 ditional source of sulfur is the antropogenic emission of H 2 S. For the natural emissions we take the same sulfur emissions as those described in Boucher et al. (2002) global mass. The model considers only two modes of dust aerosols: fine particles with radius between 0.03 and 0.5 µm and coarse particles with radius between 0.5 and 10 µm . 15 Organic matter is emitted as organic carbon (OC) with a conversion rate of 1.4 and 1.6 for fossil fuel and biomass combustion, respectively. The OC emissions from biomass burning are calculated considering an OC to BC ratio of 7. The emissions of BC due to biomass burning are taken from Cooke and Wilson (1996) The model considers the processes of dry and wet deposition as well as sedimentation. Dry deposition is calculated as a function of the concentration in the lowest level and a deposition velocity (Tables 1 and 2). This deposition velocity is taken constant for the different types of surface considered. The model does not differentiate between hydrophilic and hydrophobic particles of OM or BC when calculating dry deposition.

5
Wet deposition is split between in-cloud and below-cloud scavenging and hydrophobic and hydrophilic particles are treated differently in below-cloud processes. The sedimentation is calculated by LMDZ in terms of a sedimentation velocity. This velocity depends on the dry aerosol diameter, the atmospheric conditions of temperature and pressure for the desert dust, and the dependence of size to relative humidity for sea 10 salt aerosols.
For the optical properties the same configuration as in Reddy et al. (2005) is taken. Aerosols are described as an external mixture. Their optical properties such as single scattering albedo (ω, mass extinction coefficient (α e ) and the asymmetry factor are computed using the Mie theory and prescribing the refractive indexes.

Forward model
The forward model (H) computes the observations (y) from the input parameter (x). In this work y is taken to be the total and fine mode AOD fields whereas x is the emissions of the main aerosol species and the chemical lifetime of precursor gases, expressed The model H corresponds to a reduced aerosol model (hereafter referred to as SPLA) derived from the general circulation model LMDz described in the previous section. Modifications were introduced only in the aerosol module, the meteorology Introduction

Conclusions
References Tables  Figures   Back  Close Full Screen / Esc

Printer-friendly Version
Interactive Discussion and transport are the same than LMDz. The main simplification is the reduction of the scheme from 24 original species into 4 species. These are the gaseous aerosol precursors, the fine mode (or accumulation mode) aerosol, the coarse mode desert dust aerosols and the coarse mode sea salt aerosols. The gaseous aerosol precursor variable groups together DMS, SO 2 and H 2 S. The aerosol fine mode includes SU, BC, 5 OM, DD with radius between 0.03 and 0.5 µm and SS aerosols with radius smaller than 0.5 µm. The coarse DD mode corresponds to particles with radius between 0.5 and 10 µm whereas the SS coarse mode groups together particles with radius between 0.5 and 20 µm. The emissions from the original model are mapped onto the new set of variables with the total mass of aerosol precursor and aerosol emitted being the same.

10
The simplified model has the same meteorology and transport than LMDz. The original oxidation pathways in gaseous and aqueous phases for the sulfur chemistry are reduced into one oxidation mechanism. The gaseous precursors are oxidized as a function of a lifetime representative of the oxidation of DMS and SO 2 . The production of sulfate (P SU ) for each time step ∆t is: where [PG] is the concentration of precursor gases and τ chem [days] is the chemical lifetime of precursor gases estimated through: where θ is the latitude in radians. The lifetime τ chem varies from 3 days in the equator 20 to 8 days in the poles. This choice was taken in order to best reproduce the columns of precursors and fine mode aerosols in LMDZ. No seasonal or height dependence was introduced in the computation of this chemical lifetime. The parametrisation of dry deposition is the same as in the original model; changes were introduced in the deposition velocities in order to adapt them to the new set of 25 species. The new deposition velocities in SPLA for each one of the species are presented in Table 3. Over the ocean, the deposition velocities for the precursor gases GMDD Introduction

Conclusions
References Tables  Figures   Back  Close Full Screen / Esc

Printer-friendly Version
Interactive Discussion (species 1) were calculated as the average of the deposition velocities of DMS and SO 2 weighted by their surface concentration. However, over continental surfaces, SO 2 velocity was considered for species 1 since this gas predominates in terms of concentration over the other gases considered. In the same way, the deposition velocity over ocean for specie 2, i.e. fine mode aerosols, is calculated as the weighted average of 5 the velocities of each one of the species considered in specie 2 (i.e. SU, BC, POM, DD and SS aerosols with a radius smaller than 0.5 µm). The dry deposition over the continents is calculated considering the concentrations and the deposition velocities over land and applying the same procedure as over ocean. The deposition velocity over sea and land ice corresponds to an average of the velocity of sulfate and the remaining 10 components of species 2 over the same surfaces. Species 3 is the same as the one used in LMDz, therefore the deposition flux of specie 3 is equivalent to the second dust bin in LMDz. Finally, for species 4, we have considered a deposition velocity of 1.2 cm s −1 corresponding to a weighted average velocity for sea salt bins with radius between 0.5 and 20 µm. 15 In terms of wet deposition, the distinction between hydrophilic and hydrophobic aerosols was eliminated. The dissolution constant in in-cloud scavenging processes for fine mode aerosols (species 2) was set to the corresponding value of SO 4 used in LMDz, whereas for the coarse modes (both desert dust and sea salt) the same constant value of 0.7 is used as in the original model.

20
The sedimentation in SPLA is only applied to coarse desert dust (species 3) and sea salt aerosols (species 4). It is parametrized, as in LMDz, as a function of a mass median diameter. This parameter was adjusted in SPLA as to minimize the differences in burden of desert dust and sea salt between SPLA and LMDz. The mass median diameter of sea salt was taken as 90% of the value corresponding to a size distribution 25 between 0.5 and 20 µm and a RH of 80%, whereas for the desert dust, the mass median diameter used corresponds to one of a size distribution between 0.5 and 10 µm. Tables 4 and 5 give the values used in LMDz and SPLA, respectively. The total AOD and fine mode AOD are computed at three wavelengths within SPLA, namely 550, 670 and 865 nm. It is, as in LMDz, the vertical integral of the product of the mass extinction coefficient, calculated off-line, and the mass of the corresponding aerosols species. For our species 2 (fine mode aerosols) the mass extinction coefficient (α e<2> ) is calculated from the sulfate (α SO 4 ) one, which is a function of RH and 5 wavelength (λ), and scaled to the mass of ammonium sulfate as followed: where M SO 4 and M (NH 4 ) 2 SO 4 are the molecular masses of sulfate and ammonium sulfate, respectively. For the coarse mode desert dust (species 3), the unit mass extinction coefficient 10 considers a size distribution equivalent to the one used in the original model and is calculated as follows: where r min and r max are the lower and upper limits, respectively, of the desert dust size distribution (0.5 and 10 µm, respectively), n(r)dr is the number of particles with a 15 radius between r and r+dr, ρ the density of the particles and σ e is the mass extinction coefficient of desert dust. Finally, the coarse mode of sea salt (species 4) groups the original sea salt bins with radius between 0.5 and 20 µm. The mass extinction coefficient (α e<4> ) is calculated as GMDD 2, 2009 Simplified aerosol modeling for variational data assimilation Interactive Discussion the weighted average of the extinction coefficient for each bin in the original model: where j min and j max correspond to the range of bin indices in LMDz considered for our species 4, B j is the globally and annually-averaged burden of each bin j and α j e is the mass extinction coefficient of bin j .

Tangent linear model
The tangent linear model corresponds to the linearized equations at a given state of a non-linear model. It provides a first order approximation to the evolution of perturbations in the input parameters. For a given model H denoted by Eq. (1) the tangent linear model is then: with H the matrix of derivatives of H also known as the jacobian matrix. Each element of this Jacobian matrix is given by the partial derivatives of the output (fine mode and total AOD) with respect to the input (emission fluxes and the chemical lifetime of gaseous precursors): where i corresponds to all output parameters and j to all input parameters. Each computation with the tangent linear provides the sensitivities of all output parameters with respect to one input parameter, i.e. one column of the Jacobian matrix.

Tables Figures
Back Close

Full Screen / Esc
Printer-friendly Version

Interactive Discussion
The tangent linear of SPLA was derived using an automatic differentiation tool called TAPENADE (Hascoët and Pascual, 2004;Hascoët, 2004), while use is made here of the tangent linear code of the LMDz transport modules (Chevallier et al., 2005).
The forward model as observation operator computes the AOD fields comparable to satellite products such as those delivered by MODIS (Remer et al., 2005) and PARA-5 SOL (Deuzé et al., 2000(Deuzé et al., , 2001. For the analysis of linearity (Sect. 3.2.1) and sensitivity (Sect. 3.2.2) presented below, we choose to produce MODIS-like AOD fields and thus do not compute the AOD for regions where no satellite product is given. For the total AOD these regions correspond to the desert surfaces with high reflectivity, whereas for the fine mode AOD computations are only conducted over ocean since MODIS 10 retrievals for the fine mode AOD are not reliable over land.

Model linearity
A linear observation operator H implies a quadratic cost function which facilitates the minimization of the cost function. In order to deal with non-linear models, the minimizer in the variational data assimilation system needs to handle non-quadratic cost func- 15 tions. This can be obtained with an increase of the computational load compared to the linear case (e.g. Trémolet, 2004).
We first conduct two SPLA runs using in one case an unperturbed state and in the other case a perturbed one. We define as total initial perturbation the difference between these two states. We then apply the initial perturbation to the tangent linear 20 model and compare it with the difference between the two SPLA runs. The difference between the total initial perturbation and the tangent linear one provides the non-linear part of the perturbation that is not explained by the linearized model.
We apply a rather small perturbation (10%) to the aerosol emission fluxes and chemical lifetime of gaseous precursors. Both, the perturbed and unperturbed emis-25 sion fluxes are within the range of emissions of global models analyzed in Textor et al. (2006). We explore the linearity for the month of July 2002 and analyze the corresponding perturbations in total AOD at 550 nm. The tangent linear model (Fig. 1b) 650 Introduction

Tables Figures
Back Close

Full Screen / Esc
Printer-friendly Version Interactive Discussion shows similar perturbations than the difference between the perturbed and unperturbed simulations (Fig. 1a). Both present the same horizontal distributions, namely maximum sensitivity in AOD to perturbations in the emissions of desert dust particularly over Central Asia, large sensitivities to emissions of sea salt and of fine mode aerosols (species 2). The sensitivities to the emissions of fine mode aerosols occur 5 over regions with industrial and fossil fuel emissions. The part of the non-linear model not explained by the linearized model is presented in Fig. 1c in percentage. The largest differences are now observed north of New Guinea (Fig. 1c) in a region of important gaseous precursor burden (Fig. 4). The same result but smaller in magnitude is observed when analyzing the discrepancies between tangent linear model and the total 10 initial perturbation with respect to the fine mode AOD at 550 nm ( Fig. 1d). The pattern of discrepancies for both, fine and total AOD, corresponds to regions with large root mean square for daily and monthly averages (Fig. 8). Sensitivity tests (not shown) indicate that the chemical production of SU (Eq. 2) is mostly responsible for the nonlinearity of the model.

Model sensitivities
We focus our analysis in examining the perturbations in the total AOD and results corresponding to the month of July 2002 are shown. We apply the same relative perturbation to chemical lifetime of gaseous precursors and to the emission fluxes. We analyze simultaneously the perturbations on AOD at 550 nm due to perturbations 20 in the emissions of BB and FF ( Fig. 2a and b, respectively); both represent carbonaceous emission and thus will ease the comparison with the global cycle of carbonaceous aerosols in LMDz (original model) as presented in Reddy and Boucher (2004).
The total AOD at 550 nm presents positive sensitivities to the carbonaceous sources over Africa, Southeast Asia, Europe and South America coincident with the AOD dis-25 tribution presented in Reddy and Boucher (2004). This reflects that an increase in emissions translates into a regional increase of AOD consistent with what is expected. Largest sensitivities are seen over sub-Saharan Africa for BB (Fig. 2a) . 2b) with the sensitivity to BB emissions being almost a factor three larger than that for FF. Smaller sensitivities are observed in South America, Central and South Africa for BB and Southeast Asia, India, South Africa and North and South America for FF emissions. Some differences are appreciable over South America and Southeast Asia.

5
Fine mode and coarse mode desert dust present the same horizontal distribution of sensitivities associated to the main dust load contributors (Prospero, 1996;Tanaka and Chiba, 2006); maxima over Central Asia and smaller sensitivities associated to the sources in the Middle East and the Saharan desert ( Fig. 2c and d, respectively). However, differences in the intensity can be noted. The fine mode sensitivities are 10 almost twice those of the coarse mode. The previous is because in SPLA the fine mode has larger values of single scattering albedo than the coarse mode, i.e. the fine mode desert dust is more efficient in scattering light than the coarse mode. Thus for the same perturbation in emissions the fine mode will produce a larger perturbation in AOD than the coarse mode. No sensitivity maxima are appreciated over Sahara 15 or Middle East since the model does not conduct computations in regions where no MODIS AOD product is available. The sensitivity distribution presented agrees with the horizontal distribution of desert dust AOD presented in Reddy et al. (2005). The same feature is observed when comparing to the AOD from different models presented in Tegen (2003).

20
The total AOD presents sensitivity to emissions of fine mode ( in Ma et al. (2008). However differences are observed when comparing to the AOD distribution in Reddy et al. (2005), especially in the northern ocean where no important sensitivity regions are observed corresponding to the regional maxima of sea salt AOD.
For the analysis of the model sensitivities with respect to SU emissions and its Interactive Discussion gaseous precursors, we perturb on one hand the emissions of gaseous precursors simultaneously with the SU emissions and on the other hand we also perturb the SU production from its gaseous precursors (described in Sect. 3.1). A positive perturbation increases the lifetime of gaseous sulphur species and therefore reduces sulphate production for a same period of time. Consequently the AOD sensitivities to pertur-5 bations in the chemical lifetime present negative values; a positive perturbation in the chemical lifetime decreases sulphate production, its atmospheric load and the AOD (Fig. 2h). The AOD sensitivities to perturbation in gaseous precursors and SU emissions on the contrary present positives values coherent with the fact that a higher load of SU aerosols increases the AOD (Fig. 2g). Both sensitivities present similar horizontal distribution but with opposite sign and stronger sensitivity for SU emissions; the AOD at 550 nm is more sensitive to the emissions of gaseous precursors and SU than to chemical production of SU. The maxima (in absolute terms) are located over the continents in the Northern Hemisphere close to the emission sources. In both cases the largest maxima (in absolute terms) are located over eastern Asia, followed by Europe, 15 North America and Central Asia. A small region of sensitivity is observed in the Southern Hemisphere over western South America probably associated to copper smelters and over western Central Africa.

Adjoint model
The adjoint model provides the sensitivities of the input parameters to perturbation in 20 the output parameters. For a forward model H and its tangent linear model H, the adjoint model is where H T is the adjoint model and the transpose of the jacobian matrix H (Eq. 7), x * is the output sensitivities in the input space and y * the input sensitivities in the observation As for the tangent linear model, the adjoint model of SPLA was derived using the automatic differentiation tool called TAPENADE (Hascoët and Pascual, 2004;Hascoët, 2004) and the adjoint code of the LMDz transport modules (Chevallier et al., 2005) was used. The adjoint model was found accurate to within 130 times the zero of the computer. 5 We use the adjoint model to present the sensitivities of the AOD to aerosol emissions. In contrast to the tangent linear model that computes the sensitivity in the AOD for perturbations in the emission field, the adjoint model allows to compute the perturbation in the emission field needed to produce a given signal in the AOD. To illustrate the adjoint sensitivities we conceive an experiment where the y * vector in Eq. (9) consists of a point and instantaneous perturbation in the fine mode AOD at 550 nm. This point perturbation is defined off the coast of Central Africa for the last day of July 2002. All resulting sensitivities will relate to this particular observation.
We show the sensitivity in the emission field two and five days before the observation. Results corresponding to two days before indicate that the single observation is most 15 sensitive to emissions of fine mode sea salt originated to the south than to biomass burning emissions from Central Africa (Fig. 3a). The wind field for the simulated days presents predominant southerly winds in the lower layers of the atmosphere and easterly winds increasing in magnitude with increasing height (not shown). Five days prior the observation however the highest sensitivity is now observed over sub-Saharan 20 Africa and only weak sensitivities are observed in distant ocean regions (Fig. 3b). The maximum sensitivities over Africa coincide with the southeasterly winds whereas the long range transport from south of the Indian subcontinent is due to the large scale easterly winds at higher levels (not shown). Differences in magnitude between both analyzed cases illustrate that for a same source region and a given perturbation the

Validation of SPLA
We explore the performance and fidelity of SPLA by comparing it with AOD AERONET data and LMDz outputs. The analysis will be focused on the AOD at 550 nm. Furthermore, the fidelity of SPLA in reproducing the aerosol cycle of emission, transport, deposition and sedimentation will be indirectly evaluated by comparing the burden be-5 tween the two models.

Validation of SPLA with LMDz
We start by comparing SPLA against LMDz with respect to the burden for each one of the species defined in SPLA and we then extend the comparison to the AOD at 550 nm. The advantage of this approach is that it allows identifying possible errors in 10 the AOD as being due to errors in the aerosol cycle or in the computation of the AOD itself. Outputs of LMDz are grouped in the same way species are constructed in SPLA in order to make results comparable.

Aerosol burden
The simplified model simulates the main features of the horizontal distribution of the 15 burden of gaseous precursors (species 1) (Fig. 4). The model reproduces the maxima over the continents, underestimates the burden in the Southern Hemisphere and Equatorial Pacific and overestimates it over the Atlantic Ocean in the Northern Hemisphere. The main reason for these differences is the simplification of the sulfur chemistry. In the original model the sulfur chemistry is limited by the availability of oxidants as O 3 , 20 H 2 O 2 , OH and NO 3 radicals. In SPLA however, the chemistry of sulfur depends on a chemical lifetime that varies only with respect to latitude. The differences in Fig. 4 between both models coincide with the variability of these oxidants (not shown). The overestimation is produced in the regions where there is a larger oxidant concentration due to a larger influence of anthropogenic emissions whereas the underestimation

Printer-friendly Version
Interactive Discussion is produced in regions with cleaner air and thus with a smaller oxidant concentration. The parameterization of the chemical lifetime in the sulfur chemistry in SPLA does not differentiate between hemispheres according to the concentration of oxidants for two points at the same latitude. This can produce the overestimate of SO 2 , (species 1) in regions with a higher concentration of oxidants through a smaller conversion of SO 2 5 in sulfate and an underestimate of SO 2 in remote regions with cleaner air through a larger conversion. Another reason for the differences above the ocean of the Southern Hemisphere is the difference in deposition velocities between the two models. The regions with an underestimation of the burden correspond to regions where DMS dominates with respect 10 to other species considered in species 1. The deposition velocity for DMS increased from 0.0 cm s −1 in LMDz (Table 1) to 2.8 cm s −1 in SPLA (Table 3), hence the simplified model now presents dry deposition where before there was no dry deposition. However, this explanation is not valid in the Northern Hemisphere oceans where an overestimation is observed. In these regions the overestimation is more likely linked to 15 the SO 2 concentration than to DMS. The SO 2 presents a deposition velocity smaller in SPLA than in LMDZ (Tables 1 and 3, respectively) and produces therefore the opposite effect than observed over regions with an underestimate.
SPLA reproduces the horizontal distribution of species 2 with maxima over Africa, Middle East, Central Asia and Southeast Asia presenting only minor differences with 20 respect to LMDz (Fig. 5). However, it overestimates the burden over eastern Asia and eastern Europe. The maximum in burden over North and Central Africa is associated to desert dust and biomass burning and the corresponding differences between both models is due to the increase in the deposition velocity in SPLA (Table 3) increasing thus the deposition flux and decreasing the burden of species 2 with respect to LMDz.

25
Despite the important contribution of BC, POM and DD to species 2 over eastern Asia, the overestimation in burden is produced by the decrease of the sulfate deposition velocity in SPLA. This last also explains the overestimate observed over the oceans.
With respect to the coarse mode of DD (species 3) and SS (species 4), the difference GMDD Introduction

Tables Figures
Back Close

Full Screen / Esc
Printer-friendly Version Interactive Discussion between both models are the different mass median diameters used in computing the sedimentation (Figs. 6 and 7, respectively).

Aerosol optical depth at 550 nm
The AOD of both models is now compared at 550 nm in terms of the root mean square error (RMSE) of the simplified model with respect to LMDz. The RMSE of the daily and 5 monthly averages is presented in Fig. 8. A much higher difference is observed in the RMSE of the daily average than the monthly one. The differences in the daily variability can go up to 40%, whereas the difference in monthly variability does not exceed 7%, indicating a larger difficulty of SPLA to simulate the daily variability than the monthly one. The largest differences between both models are observed over Southeast Asia 10 and north of Australia. These differences are mainly due to the differences in the burden observed for species 1 and 2 and described in the previous section.

Comparison of SPLA against AERONET measurements
We compare the AOD at 550 nm from SPLA against AERONET measurements. This is a global network of photometers that delivers numerical data to monitor and char- 15 acterize the aerosols in a regional and/or global scale. The network has more than 300 stations distributed in the world measuring clean atmosphere in remote regions and polluted areas (Holben et al., 1998 The measurements in the first group of sites (Abracos Hill, Mongu and Skukuza), are mainly influenced by biomass burning and present an annual cycle with maximal values of AOD towards the end of the year (Fig. 9a-c). SPLA follows closely the monthly variability of LMDz and its AOD is fully determined by species 2. It slightly underestimates LMDz during the month of maximum AOD which can be attributed to the increase in deposition velocity of species 2 (Table 1 and 3). Both models reproduce the seasonal cycle of biomass burning with larger differences in the biomass burning season and a shift of 1 or 2 month in the peak of AOD. The difference between models and measurements is associated to a possible underestimation of emission sources .

10
The simplified model reproduces the seasonal variability of both LMDz and AERONET at stations dominated by desert dust (Sede Boker, Solar Village and Nes Ziona) (Fig. 9d-f). The model overestimates the AOD of LMDz throughout the year especially during the seasonal maxima of April in Sede Boker and Nes Ziona and April/August in Solar Village. This is caused by an underestimation of the sedimenta-15 tion, caused partly by the absence of sedimentation of the fine mode DD in SPLA. The overestimation of AOD by SPLA improves its performance with respect to AERONET at Solar Village. The simplified model stays within the range of the observations during most of the year at all stations. The total AOD of SPLA is attributed to species 2 and 3 (DU).

20
The sites mainly affected by industrial aerosols (GSFC, Stennis and Venice) present an annual cycle with maximal values of AOD during the summer month in the North American sites of GSFC and Stennis whereas Venice presents relatively constant measurement around 0.2 throughout the year (Fig. 9g-i). SPLA shows different performance for these two distinct types of sites. It underestimates the measurements in the 25 month of maximum AOD for the North American sites whereas it overestimates it at Venice in the second half of the year. For the former the underestimation is probably due to the simplification in conversion of SO 2 to sulfate which does not take into account the increase of oxidation rate in summer while in Venice the overestimation is GMDD Introduction

Tables Figures
Back Close

Full Screen / Esc
Printer-friendly Version Interactive Discussion due to episodic dust transport from Africa. Finally, the stations of Tahiti, Bermuda and Ascension Island, influenced by marine aerosols (i.e. sea salt and natural sulfur) and long range transport of continental aerosols , present relatively constant cycle throughout the year with small amplitude peaking in different times of the year according to the station (Fig. 9j-5 l). Both models predict the seasonal cycle in agreement with the measurement with magnitudes within the range of the AOD. The three stations are affected by different sources and aerosol types; Tahiti is dominated by sea salt and sulfate, Bermuda is by marine aerosols in addition to dust from Africa and sulfate from North America and finally Ascencion Island is influenced by sea salt in addition to carbonaceous aerosols 10 from Africa . Nevertheless SPLA follows closely and with negligible differences the AOD from LMDz throughout the year at all stations. The differences between models can be explained by changes in deposition velocities, sedimentation and the simplification of the sulfur chemistry as well as the modifications introduced in the computation of the AOD. 15 Similar performance was obtained when comparing the model AOD against LMDz & AERONET at 670 and 865 nm for the same sites (Figures not shown).

Conclusions
Uncertainties in aerosol emissions introduce uncertainties about their final impact on climate. Variational data assimilation techniques have been developed for individual 20 aerosol species that determine the emission field that represents the best compromise between a given set of observations and the a priori information. This work presents a first step towards estimating the intensity of the emissions of the main aerosol species through variational data assimilation. For this purpose the general circulation model LMDz in its version 3.3 has been simplified into the Simplified Aerosol Model (SPLA) 25 and its corresponding tangent linear and adjoint versions were derived.
The complexity of LMDz for the simulation of the global life cycle for the main aerosol Interactive Discussion species (SS, DU, OM, BC and SU) was reduced in SPLA. This model groups together the 24 aerosol species simulated in LMDz into 4 species, namely the gaseous precursors, the fine mode aerosols, the coarse mode of desert dust and the coarse mode of sea salt. As a consequence of this, several modifications had to be introduced; the deposition velocity of each new species was adapted according to the species it con-5 tained, the mass median diameter for the sedimentation of only coarse mode aerosol, both SS and DD, was also adapted to represent their new size distribution and the mass extinction efficiencies were recomputed according to the new species. Furthermore, the sulfur chemistry was reduced to an oxidation mechanism as a function of latitude and no distinction between hydrophilic and hydrophobic OM and BC was done.

10
The performance of SPLA was evaluated by comparing it against LMDz in terms of burden and AOD and against AERONET AOD. The simplified model successfully manages to reproduce the main features in LMDz of the horizontal distribution of the burden for each one of the species. The main differences between the models are on one hand due to differences in the deposition and sedimentation fluxes associated to 15 new deposition and sedimentation velocities, respectively and on the other hand to the simplification of the sulfur chemistry to a simple oxidation of sulfur to sulfate. Distinct behavior can be identified in the performance of the aerosol burden and the AOD. The largest differences with respect to the burden are observed in species 1 and 2 where most of the modifications were introduced, while species 3 and 4 keep more 20 similarities with their original counterpart and therefore do not differ greatly. The largest differences in AOD, with both LMDz and AERONET, are observed over sites with strong DD influence (species 4). However, simulated AOD remains within the variability of the observations for all species and all sites throughout most of the year. SPLA follows closely the seasonal cycle of LMDz and has therefore a similar performance to LMDz 25 in simulating total AOD. Finally, the model has a better performance in reproducing the monthly variability of LMDz than in reproducing the daily one.
The simplified model shows some differences in the sensitivities between the tangent linear model and the SPLA when increasing the emissions fluxes and chemical life-GMDD 2, 2009 Simplified aerosol modeling for variational data assimilation N. Huneeus et al. time rate by 10%. These differences illustrate the non-linearity of the simplified model, which is mostly due to the simplified sulfur chemistry. When examining in more detail the sensitivities of SPLA, the model shows positive sensitivities for perturbations in the emission flux but negative ones when perturbing the chemical lifetime of gaseous precursors. This is consistent with the fact that a higher aerosol load increases the AOD 5 whereas a positive perturbation in the chemical lifetime rate increases the duration of gaseous sulfur species and thus reduces sulfate production and AOD with it. Maximum sensitivities for each aerosol species coincide with regions of maximal AOD situated over and in the vicinity of emission regions coherent with the known regional impact of aerosols. The sensitivity analysis reveals differences with respect to the original model 10 in the location of BB sources over South America and on the magnitude of the DD burden.
The adjoint model of SPLA was successfully derived through automatic differentiation and was found accurate to within 130 times the zero of the computer. It was implemented together with the direct model described in this work in an already ex- 15 isting variational data assimilation scheme (Chevallier et al., 2005). Daily averages of total and fine mode AOD from MODIS at 550 nm will be assimilated and the estimation of the intensity of the emissions for the five main aerosol species (SU, BC, OM, DD and SS) in predefined regions will be derived. The results of this work will be presented in a forthcoming publication. GMDD 2, 639-680, 2009 Simplified aerosol modeling for variational data assimilation  Rabier, F., Järvinen, H., Klinker, E., Mahfouf, J.-F., and Simmons, A.: The ECMWF operational implementation of four-dimensional variational data assimilation. I: Experimental results with simplified physics, Q. J. Roy. Meteorol. Soc., 126, 1143-1170, 2000 Overview of global data assimilation developments in numerical weather-prediction centres, Q. J. Roy. Meteorol. Soc., 131, 3215-3233, 2005. GMDD 2, 2009 Simplified aerosol modeling for variational data assimilation Takemura, T., and Tie, X.: Analysis and quantification of the diversities of aerosol life cycles within AeroCom, Atmos. Chem. Phys., 6, 1777-1813, http://www.atmos-chem-phys.net/6/1777: Diagnostics of linear and incremental approximation in 4D-Var, Q. J. Roy. Meteorol. Soc., 130, 2233-2251, 2004.   ) and for all surfaces considered in LMDz. The corresponding particle radii are from 0.03 to 0.06, 0.06 to 0.13, 0.13 to 0.25, 0.25 to 0.5, 0.5 to 1.0, 1.0 to 2.0, 2 to 5, 5 to 10, 10 to 15 and 15 to 20 µm (sizes are for 80% RH).