Improving aerosol distributions below clouds byassimilating satellite-retrieved cloud droplet numberPablo E. Saidea,1, Gregory R. Carmichaela, Scott N. Spaka, Patrick Minnisb, and J. Kirk Ayersc

aCenter for Global and Regional Environmental Research, University of Iowa, Iowa City, IA 52242; bNASA Langley Research Center, Hampton, VA 23681-0001; and cScience Systems and Applications, Inc., Hampton, VA 23666

Edited by Mark H. Thiemens, University of California San Diego, La Jolla, CA, and approved June 12, 2012 (received for review April 6, 2012)

Limitations in current capabilities to constrain aerosols adverselyimpact atmospheric simulations. Typically, aerosol burdens withinmodels are constrained employing satellite aerosol optical proper-ties, which are not available under cloudy conditions. Here we setthe first steps to overcome the long-standing limitation that aero-sols cannot be constrained using satellite remote sensing undercloudy conditions.We introduce a unique data assimilationmethodthat uses cloud droplet number (Nd ) retrievals to improve predictedbelow-cloud aerosol mass and number concentrations. The assim-ilation, which uses an adjoint aerosol activation parameterization,improves agreement with independent Nd observations and within situ aerosol measurements below shallow cumulus clouds. Theimpacts of a single assimilation on aerosol and cloud forecastsextend beyond 24 h. Unlike previous methods, this technique candirectly improve predictions of near-surface fine mode aerosols re-sponsible for human health impacts and low-cloud radiative for-cing. Better constrained aerosol distributions will help improvehealth effects studies, atmospheric emissions estimates, and air-quality, weather, and climate predictions.

air quality ∣ indirect effect ∣ weather prediction ∣ stratiform cloud ∣microphysics

Ambient aerosols are important air pollutants with direct im-pacts on human health (1). They also play important roles in

Earth’s weather and climate systems through their direct (2),semi-direct (3), and indirect effects (4) on radiative transfer andclouds. Their role is dependent on their size, number, phase, andcomposition distributions, which vary significantly in space andtime. There remain large uncertainties in predictions of aerosoldistributions due to uncertainties in emission estimates and inchemical and physical processes associated with their formationand removal (5–9). These uncertainties in aerosol distributionslead to large uncertainties in weather and air-quality predictionsand in estimates of health and climate-change impacts (10).

Constraining ambient aerosol distributions with current Earth-observing systems is a difficult task. The most common approachis to assimilate satellite retrievals of aerosol optical depth (AOD)(11, 12), a quantity that represents total aerosol mass and com-position in the atmospheric column. The requirement of cloud-free conditions for a successful retrieval and the remaining chal-lenges of relating AOD to aerosol mass, size, and compositionlimit the utility of AOD retrievals (by themselves) in constrainingaerosol mass and composition (13, 14). These shortcomings areparticularly true in regions of persistent marine stratocumulus,such as the southeast Pacific off the coast of Chile and Peru,where aerosol–cloud interactions are important to the energybalance (15), and limitations in current observing and modelingcapabilities adversely impact regional and global weather and cli-mate predictions (16). A typical MODIS AOD scene in this re-gion (Fig. 1, Upper Left) shows that AOD provides essentially nouseful information to constrain aerosol distributions when lowclouds are present (Fig. S1).

Aerosols play an important role in cloud formation, acting ascloud condensation nuclei (CCN), and further affect cloudmacro-and micro-physical properties such as albedo (17), driz-

zling capacity and lifetime (18), and cloud base and top heights(19), among others. Despite uncertainties (10) and challenges(20) in modeling aerosol–cloud interactions, recent studies haveshown significant capabilities in predicting and explaining aerosolindirect effects in low cloud regimes (6, 7, 21). By building on thismechanistic understanding, observations of clouds may be used toinfer aerosol physicochemical properties. This is done by using aunique data assimilation technique presented in Methods anddescribed in depth in SI Text.

ResultsThe assimilation procedure is demonstrated for the case of thesoutheast Pacific’s persistent stratocumulus deck, where in situaircraft observations during the VOCALS-REx field experiment(22) provide independent accumulation mode aerosol mass andnumber concentrations (23) for verification. We predict meteor-ology and aerosol mass (M) and number (N) distributions atthe regional scale with theWRF-Chemmodel (24, 25) configuredfor this area (6). Cloud optical depth and effective droplet radiiretrieved from Terra MODerate-resolution Imaging Spectroradi-ometer (MODIS) and Geostationary Operational EnvironmentalSatellite (GOES) imager data (26, 27) are used to computeobserved Nd (28). We perform experiments utilizing these retrie-vals (see SI Text, Assimilation experiments). The impacts of as-similation of MODIS Nd on optimized modeled Nd, N, andaerosol sulfate mass concentration are shown in Fig. 1 for a daywith an extensive and thick stratocumulus deck (Fig. 1, UpperRight, and Fig. S1), which is a typical condition in the region[e.g., daytime cloud fraction was between 70–90% during theVOCALS-REx period (7)]. The background modeled Nd (prior)resolves the longitudinal gradient in the observations defined bythe indirect effects due to anthropogenic pollution (6) but gen-erally overestimates coastal amounts and underestimates remoteconcentrations. The assimilation produces an improved a poster-iori modeled Nd, as shown by a 30% fractional error reduction(*) and by the better resemblance of Nd assimilated fields com-pared to the observations (Fig. 1, first and second row). Assim-ilation increases (decreases) N and M in places where Nd isunder (over) predicted (Fig. 1, third and fourth row), activatingmore (less) particles, thus reducing the error.

As the observation operator for this assimilation technique is amixing-activation parameterization, the aerosols modified arethose most active in the activation process; i.e., below cloudand accumulation mode aerosols. Coarse aerosols do participatein activation, but their sensitivities are low because their number

Author contributions: P.E.S., G.R.C., and S.N.S. designed research; P.E.S. performedresearch; P.E.S., G.R.C., S.N.S., P.M., and J.K.A. analyzed data; and P.E.S., G.R.C., S.N.S.,P.M., and J.K.A. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

*Fractional error of 72% and 42% are obtained between GOES-10 retrieval and prior andassimilated fields respectively at one hour after assimilation (16Z).

1To whom correspondence should be addressed. E-mail: pablo-saide@uiowa.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1205877109/-/DCSupplemental.

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concentrations are small. As vertical mixing is also considered,the aerosols modified are not only those in the layer immediatelybelow clouds but also from lower near-surface layers. The verticalextent of the impact depends on the mixing state of the atmo-sphere below clouds. For cloud-capped marine boundary layers(as in the stratocumulus deck studied here), depending on thedecoupling state (29) the aerosol constraint can extend to thesea surface. Thus, this technique can directly improve estimatesof fine mode near-surface aerosol number, composition, and size.For instance, sulfate dominates the hygroscopic fine aerosol massin the marine boundary layer (MBL) in this region throughoutthis study period (7) and therefore receives the most constraintfrom assimilation (Fig. 1, fourth row). Species during this periodfound mainly in the coarser size bins like nitrate and sea salt (7)are not impacted as much, and those found in the free tropo-

sphere above the cloud layer, such as biomass burning organicaerosol (23), are not affected by the assimilation.

The impact of assimilation on constraining aerosol distribu-tions is evaluated in an experiment (see SI Text, Assimilationexperiments, for further details) where GOES-10 Nd was assimi-lated at the time when a research flight was conducted that did alongitudinal in situ sampling of the cloud deck (Fig. 2, Top). Themodel prior underestimates offshore aerosol mass and number,which the assimilation corrects, reducing fractional biases by25% and 33%, respectively. Similar assimilation experimentsfor two coastal pollution survey flights (Fig. 2, Bottom) improvedstatistical performance for below cloud aerosol mass and number,reducing fractional bias and error (30) and increasing spatiotem-poral correlation in each case. The use of retrievals from geosta-tionary satellites to constrain aerosols is an important advance-

Fig. 1. Observed and model maps for the southeast Pacific and coastal Chile and Peru. (Top Row) MODIS AOD (Left) and Nd (Right, in #∕cm3) at October 16,2008, at 15Z overpass. Second to fourth rows show prior (Left) and assimilated (Right) results for Nd, accumulation mode N (#∕cm3) and sub-micron sulfateconcentrations (μg∕m3) one hour after assimilating MODIS Nd . See SI Text, Assimilation experiments, for further details.

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ment because it provides a significant improvement in temporalresolution (approximately 16 retrievals per day) compared to po-lar orbiting satellites that produce one retrieval per day.

An important feature of the cloud droplet number assimilationis that it results in a change in aerosol distribution, which can im-pact cloud predictions forward in time over the lifetime of theaerosols throughout the region of analysis (approximately 2 daysin theMBL). To demonstrate this persistent effect of the constraintwe assimilate a single retrieval of MODIS Nd and evaluate theforecast of Nd by comparing to independent hourly resolvedGOES10Nd retrievals (Fig. 3). One to five hour after assimilation(Fig. 3, first day) the magnitude and variability of forecastNd overpolluted and clean geographical regions are improved as seen bythe enhancement in number and variability in the clean region anda decrease in mean and variability in the polluted zone, achieving aglobal 20–30% fractional error reduction. For the second day,model errors (6) and the transport of the aerosols out of thedomain reduce the impact of the assimilated fields. However,

the assimilation still has a positive impact on the forecasts thatextends beyond 24 h. A snapshot 22 h after assimilation (Fig. 3,Bottom) shows features in the assimilation-predicted fields thatresemble the observations and are not found in the prior: Nd en-hancement over 100 #∕cm3 (near 20 °S, 85 °W) that can be tracedto a plume present in the retrieval near 27 °S, 79 °W (Fig. 1); andan increase in cloud cover in the northwest of the domain that wasmissed in the background simulation. After 48 h, the assimilatedaerosol has exited the regional model domain, and only smalldifferences between background and assimilated fields remain.This lasting influence on cloud and aerosol properties could helpovercome one of the main issues in contemporary cloud assimila-tion methods, where information gained in the analysis is attenu-ated within hours after initialization (31, 32).

DiscussionThe technique presented here is designed for use with single-layer warm liquid cloud systems with vertically homogeneousNd. These conditions represent low stratiform clouds, which per-sistently cover large regions around the world (e.g., stratocumulusdecks off the west coasts of Africa and South and North America)and are pointed out as the main players in aerosol indirect forcing(33). While this first approach toNd assimilation does not resolvethe vertical Nd gradients and ice and graupel phases that arisefrom convection, convective clouds are often accompanied byor form from low clouds where this technique can be applied.Beyond regions of persistent low stratocumulus, single-layer li-quid cloud conditions can also be identified in model calculationsand matched with instantaneous cloud retrievals on a pixel-by-pixel basis and assimilated opportunistically throughout theworld, whenever and wherever they occur. The application of thistechnique to other regions requires further evaluation of the Ndsatellite retrieval calculation. Even though global estimates ofNdcan be made (34), region-specific expressions evaluated using insitu measurements can help reduce uncertainty in the retrievals(28). In this sense, it is encouraging that for a given region, a sin-gle formula can be used across satellites and instruments (GOESimager, MODIS Aqua, and Terra) with excellent performanceagainstNd in situ data, remarkably better than for other retrievedcloud properties (28, 35). The activation parameterization and itsassumptions represent another source of uncertainty (20), butagain, comparisons with in situ and satellite measurements helpbetter understand these limitations and their extent (6, 7). Ex-panded applications of this approach (e.g., aerosol retrieval andassimilation under multilayer, convective, and ice clouds) may bepossible, but additional research and testing is required on bothretrieval and modeling sides.

Potential applications for this technique are found throughoutthe atmospheric sciences and beyond. When incorporating aero-sol indirect feedbacks on clouds in numerical weather prediction,better aerosol predictions can further improve MBL height andcloud heights, liquid and precipitable water, precipitation rates,cloud optical properties, and cloud lifetime (6). As aerosol influ-ences on clouds have been shown to affect convective systems(36), lighting (37), tropical cyclones (38), and tornados (39), moreaccurate aerosol representation could also lead to better predic-tions for severe storms and hazards. In addition, better con-strained fine and below-cloud aerosol distributions will helpimprove air quality predictions (12) and reduce uncertaintiesin assessments of health and climate impacts due to aerosols(11). The use of this technique is not limited to 3DVAR andmay be used for sensitivity analysis (40) as well as being coupledto an adjoint of all model components for 4DVAR assimilation ofaerosol state and evolution (12) or used in inverse modeling tobetter estimate emission sources. In this sense, important appli-cations include improving highly uncertain estimates of oceanicorganic emissions (8, 9) and constraining anthropogenic emis-sions such as those occurring upwind of persistent cloud regimes

Fig. 2. Statistical comparison between modeled and in situ C-130 observa-tions (23) of accumulation mode aerosol number concentration and fine sul-fate mass. (Top) Longitudinal statistics as box and whisker plots for flight RF13(November 13, 2008). Center solid lines indicate the median, circles representthe mean, boxes indicate upper and lower quartiles, and whiskers show theupper and lower deciles. Number of 1-min samples contributing to each long-itudinal bin is indicated at the top. (Bottom) “Soccer goal” plot (30) showingbias and error improvements for flights RF11 (November 9, 2008), RF12 (No-vember 11, 2008), and RF13. Each arrow represents N (red) and SO4 (blue) foreach flight, where the arrow tail and tip represent the base and assimilatedmodel statistics, respectively. Arrows pointing toward ð0; 0Þ indicate thatassimilation improves both bias and error. The embedded table shows correla-tion (R) between models and observations. Model and measurements are be-low cloud. See SI Text, Assimilation experiments, for further details.

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(e.g., central Chile and northern California) (6) and thoseemitted below clouds (e.g., ship emissions). These applicationsare not limited to persistent stratocumulus decks; similar aerosolfeedbacks have been shown for other marine (41) and continental(42) shallow cumulus. Also, there is no limitation on aerosol com-position distribution (sulfate dominates the case studied) as longas the aerosol properties participating in the activation process(e.g., hygroscopicity, solubility) are specified correctly. These ap-plications are currently feasible given the availability of near real-time cloud retrievals (26).

The technique can be combined with AOD assimilation to con-strain aerosol distributions for mass, number, composition, andoptical properties over a broader range of conditions, as AODand Nd assimilation are complementary, employing observationsthat do not coexist (e.g., there is no AOD retrieval when there areclouds and vice-versa). Using these retrievals together enablesthe observing system (satellites retrievalsþmodel simulations)to “see aerosols” for a larger number of pixels in a scene, evenunder cloudy conditions.

MethodsWe propose a unique data assimilation technique (Fig. S2) to improve aerosolmass (M) and number (N) distributions from satellite retrievals of cloud dro-plet number (Nd ) and demonstrate it for a stratocumulus application, wherethese remote sensing products have been shown to accurately represent insitu Nd observations (28, 35, 43). The forward model includes a vertical mix-ing-activation parameterization used to predict Nd from meteorological

conditions and initial M (composition/size/phase resolved), N (size/phaseresolved), and Nd distributions. Sensitivities of predicted Nd derived with re-spect to these input variables are computed efficiently using the adjoint ofthe mixing-activation parameterization. These sensitivities are then utilizedin a formal data assimilation framework to find the optimal model state thatbest fits the Nd observations considering confidence in both the observationsand the initial conditions. We chose to optimize for initial N only because ithas been shown to be the most important contributor to Nd sensitivities overother variables such as vertical velocity and aerosol composition for most con-ditions (20, 44), especially over oceans (40, 45, 46). This is accomplishedthrough three-dimensional variational (3DVAR) data assimilation with alog-normal cost function and five-dimensional (3D in spaceþ sizeþ phase)N covariances. Assimilation yields size-, phase-, and space-resolved correctionfactors for N, which are further applied to eachM composition bin (assumingthe internal composition of each size/phase bin remains the same), resultingin an updated aerosol mass for each compound as well. Further details on thetechnique can be found in SI Text, Observations, Observation operator(Forward and Adjoint Models), and Assimilation method.

ACKNOWLEDGMENTS. We would like to acknowledge insightful commentsof Marc Bocquet, Elliott Campbell, and two anonymous reviewers. We alsothank all VOCALS-REx participants, specially Antony Clarke, Steve Howell andLindsey Shank for AMS and PCASP data. This work was carried out with theaid of National Science Foundation (NSF) Grant 0748012, Fulbright-CONICYT(Comisión Nacional de Investigación Científica y Tecnológica de Chile) scho-larship number 15093810, NASA grants NNX08AL05G and NNX11AI52G,the NASAModeling, Analysis and Prediction (MAP) Program, and the Depart-ment of Energy (DoE) Atmospheric System Research (ASR) Program. Thisresearch was supported in part through computational resources providedby The University of Iowa, Iowa City, Iowa.

Fig. 3. (Top) Box and whisker plots as in Fig. 2 for time series of GOES10 and modeled Nd statistics on 5° × 5° areas centered at 20 °S,85 °W (Top) and20 °S,75 °W (Bottom). In the assimilation, a single assimilation using MODIS Nd (Fig. 1, first row) is performed at 15 UTC on October 16 (first day), and thenthe model is run as a forecast for 72 h. Thick black vertical lines separate different consecutive days. (Bottom) Composite maps for GOES10 observations, modelprior, and assimilated model Nd for October 16 at 20Z (southeast box, 5 h after assimilation) and October 17 at 13Z (remainder of the map to the westand north, 22 h after assimilation). See SI Text, Assimilation experiments, for further details.

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Supporting informationSaide et al. 10.1073/pnas.1205877109SI TextS1 SI Methods. This section describes the observations, forwardand adjoint models, assimilation technique, forecast model, andexperiments. Fig. S2 presents a flow diagram describing the mainvariables and code used in the assimilation process and should beused as a guide when reading this section.

Observations. We use cloud optical depth (τ) and drop effectiveradius (re) observations (see examples in Fig. S1) to computecloud number droplet (Nd) assuming liquid water content in-creases linearly with height in the cloud layer (1):

Nd ¼ Kτ1∕2r−5∕2e

with K ¼ 1.4067 × 10−6 ½cm1∕2�, which generates good agree-ment with in situ observations for the domain analyzed (2, 3).This equation makes the assumption that cloud profiles are adia-batic, which is a good approximation for this region. In otherregions where this assumption might not be valid, other estimatesthat account for the subadiabaticity of the cloud can be used (4).Cases where τ and re retrievals might not be accurate should bescreened out beforeNd computation. An example is when a thickaerosol plume overlies the cloud. In the case of an absorbingsmoke plume, re computed from different channels (e.g., 1.6-and 3.9-μm for GOES or METEOSAT) will start showing discre-pancies, which can be used to screen them out. If a thick dustplume overlies the clouds, scattering will dominate and τ willbe affected. For these cases, even an AOD of 2–3 is at the lowerend of the cloud optical depth distributions (Fig. S1), thus thecloud signal will dominate and only optically thin clouds shouldbe screened out. Once Nd is computed, we use nearest neighborinterpolation to place observations onto the model grid, whereassimilation is performed.

Observation operator (Forward andAdjointModels).The observationoperator, which transforms model parameters being optimizedinto the observation space, is in this case the vertical mixingand activation parameterization (5) from the WRF-Chem v3.3model (6, 7). The parameterization is based on a maximum super-saturation determined from a Gaussian spectrum of updraftvelocities and the internally mixed aerosol properties within eachaerosol size bin (8) and has been shown to accurately representmarine stratocumulus dynamics (9, 10). Two phases are traced:dry (interstitial aerosol) and wet (activated aerosol). Startingfrom aerosol mass (M) and number (N) distributions and inputmeteorological variables, this forward model computes Nd foreach model vertical layer. In order to yield a column Nd directlycomparable to satellite observations, the model column value isaveraged over cloud-containing grid cells, because droplet con-centration tends to be relatively constant with height in theseclouds (4, 11). In order to compute sensitivities, the adjoint ofthe mix-activation and vertical averaging routines were obtainedusing the automatic differentiation tool TAPENADE v3.5 (12),which successfully passed tangent linear and adjoint tests with 4and 8 significant digits of accuracy, respectively. The adjoint pro-vides an efficient way to compute derivatives, because sensitivitiesof one Nd observational pixel with respect to all parameters (Nresolved in the vertical, in size, and in phase) can be computedwith a single run of the adjoint. Also, as the forward mix-activa-tion parameterization is vectorized in theX and Y spatial dimen-sion (because it is part of the WRF-Chem framework), then the

adjoint inherits this characteristic so sensitivities for several col-umns can be computed efficiently at the same time.

Assimilation method. We choose to implement a 3DVAR method(13) modified using a Gaussian anamorphosis (14), introducinglog-normal statistics in both state (15) and observation space.The use of log-normal statistics assumes errors to be of multipli-cative nature, which is convenient in this case because N (para-meters being improved) and Nd (observations assimilated) arealways positive, and they range over several orders of magnitude(10–104 and 10–103 for the study case, respectively). Thus, thefunctional J being minimized is

JðNÞ ¼ 1

2

�ln�H � ðN −NuÞ þCðNuÞ

Cobs

��tR−1

×�ln�H � ðN −NuÞ þCðNuÞ

Cobs

��…

þE2

�ln�NNb

��tB−1

�ln�NNb

��[S1]

where N is the aerosol number field, with sub-index b and u usedfor background (prior) and base state for the adjoint sensitivities(H) computation, respectively. Cð·Þ is Nd concentrations fromthe forward operator, Cobs is the Nd satellite observation, E aregularization parameter (15), and R and B the error covariancematrices for the observations and state. The minimum of J isfound numerically using the L-BFGS-B algorithm (16). Optimi-zation is performed using lower and upper bounds so the scalingfactor applied to the background is over 0.1 and less than 10. Be-cause the aerosol activation process is highly nonlinear, we im-plement an outer/inner loop strategy (17) that recomputessensitivities starting from the previous inner loop results.B is con-sidered nondiagonal with five dimensional correlations: threespatial, on aerosol bins (8 sections) and on phase (dry/wet), whichprovides stability in the solution. Covariances between any two i, jgridcells are computed using an exponential decay law (18)

Bij ¼ Iij � e−DxyijLxy � e−

DzijLz � e−

DbijLb � e−

DpijLp [S2]

Iij ¼� zi > CIHij or zj > CIHij 0

else 1[S3]

where Dqij represents distance between i and j on the horizontal(q ¼ xy), vertical (q ¼ z), size bins (q ¼ b), and phase (q ¼ p),with correlations lengths of Lb ¼ 0.5 on size bins, Lp ¼ 0.5 onphase, and Lxy ¼ 2 grid-cells (approximately 25 km) on the hor-izontal. We use a large vertical correlation length (Lz ¼ 100 le-vels, approximately 5 km) to simulate good mixing in the MBL,but we truncate correlations to 0 with grid-cells over the cloudlayer (Iij function), simulating the capping inversion height(CIHij) characteristic of this region (19). R is considered diag-onal and equal to the identity matrix, meaning that the errors onthe logarithmic factors of model vs. observation are the same forall observation pixels and are not correlated with each other. Thisis assumed for simplicity because this is the first application usingthis technique and can be modified for future applications pro-pagating the uncertainties contained in the cloud optical depthand drop effective radius retrievals to Nd. E is used to weighteach member of the right hand side of Eq. S1 and is chosen equal

Saide et al. www.pnas.org/cgi/doi/10.1073/pnas.1205877109 1 of 3

to 1, such that after assimilation similar net correction factors arefound for the analysis vs. prior N and modeled vs. observed Nd.This combination of assumptions generates a resultant modeledNd value in observation space directly comparable to contempor-ary satellite retrievals (see Fig. 1).

The assimilation produces an optimized N field, which is usedto modify the mass and composition distributions. Comparingassimilated and prior N, multiplicative correction factors are ob-tained, which have the same dimension as N (number of 3D spa-tial grids, size bins, and phases). Making the assumption that theassimilation does not change the aerosol composition within eachsize and phase bin, these factors are applied to each of the cor-responding mass distributions (M). Then the assimilated N andthe updated M are used as initial conditions in forecast model.

Forecast model. Forecasts were performed using the WRF-Chemv3.3 model (6, 7) configured specifically for this region (9). Thechemical and aerosol mechanism used is the CBMZ gas-phasechemical mechanism (20, 21) coupled to the 8-bin sectional MO-SAIC (22) aerosol module. In this implementation the aerosollower, upper, and center diameters for each size bin have fixedvalues (10). The WRF-Chem and MOSAIC version used keepstrack of nine aerosol mass composition (sulfate, nitrate, chloride,sodium, ammonium, organic and black carbon, other inorganics,and aerosol water) and total number distributions. WRF-Chem isconfigured to include aerosol direct (21) and indirect effects (5).The inclusion of indirect effects makes necessary the addition ofthe phase bin (wet and dry) to each of the composition and sizebins. Thus, the model advects a total of ð9þ 1Þ × 8 × 2 ¼ 160aerosol variables, where only aerosol number distribution (16variables) participates in the assimilation process and the rest(mass variables) are scaled as explained in Methods of the maintext and in Assimilation experiments.

Assimilation experiments.Two types of experiments are performed:Those that assimilate MODIS Nd (Figs. 1 and 3) and those thatassimilate GOES10Nd (Fig. 2). The MODIS experiment consistsof performing a single assimilation using data from the overpasson October 16, 2008, at 15Z (Fig. 1, Top Right). This date is cho-sen because it is a day with an extensive and thick stratocumulusdeck and also the MODIS overpass goes right over the region ofinterest. The assimilation is performed in the region over 18°–34 °S and 70°–90 °W, over the persistent stratocumulus deck. Then,WRF-Chem forecasts are performed using prior and posterioras initial conditions. GOES10 retrievals are considered as inde-pendent data in this experiment and used for evaluation.Although highly correlated with each other, the Nd values

estimated from GOES-10 are, on average, approximately 20%less than their MODIS counterparts because of differences in re-solution and retrieval methods (3). This difference has negligibleimpact on the implications of the comparisons because it does notsignificantly change the differences between the background andassimilation runs relative to the observations. We chose to assim-ilate MODIS and compare against GOES10 to use the detailedtime resolution provided by GOES10 to evaluate the assimilationperformance. Comparison is done by computing statistical differ-ences between GOES10 Nd and both models (prior and poster-ior). Fractional error and fractional bias (23) are computed over aregion for each GOES10 retrieval. The regions considered arethose over 18 °S–30 °S and 70 °W–90 °W during the first day(October 16, 2008) and over 15 °S–25 °S and 70 °W–90 °W regionduring the second day (October 17, 2008). Different regions arechosen for different days to account for aerosol advection. Fig. 3statistics are computed for 5° × 5° regions for each hour, includ-ing each satellite retrieval in the closest hour (usually two perhourr).

For the second type of experiment (Fig. 2), we assimilateGOES10 Nd and use VOCALS-REx NCAR C-130 aerosol mea-surements as independent observations to evaluate the assimila-tion performance. In this case, GOES10 is assimilated instead ofMODIS, because GOES10 enables us to choose a retrieval forassimilation that is close to the start time of each flight, so thatthe assimilation results can be compared to the in situ observa-tions. This second experiment also demonstrates that assimilationcan be done using either MODIS or GOES10 data. Assimilationis performed over 18 °S–30 °S and 70 °W–90 °Wand not through-out 34 °S as in the MODIS assimilation because the GOES10retrievals were only available up to 30 °S. We chose three flights,RF11, RF12, and RF13 (24), that measured the MBL duringdaytime because the GOES10 retrieval has limited skill at night.RF11 (November 9, 2008) and RF12 (November 11, 2008)conducted coastal pollution surveys between 20 °S–30 °S and72 °W–75 °W, while RF13 (November 13, 2008) sampled 20 °Sfrom 70 °W to 80 °W. We evaluate both forecasts (prior andposterior) against Particle Measuring Systems (PMS) PassiveCavity Aerosol Spectrometer Probe (PCASP) accumulationmode aerosol number concentration (19, 25) and Aerosol MassSpectrometer (AMS) submicrometer sulfate concentrations (26).Sulfate mass was considered as a proxy for submicrometer aero-sol mass because it dominated the hygroscopic fine aerosol massin the MBL in this region throughout the study period (10).Statistics (Fig. 2) are computed using flight legs within the MBL(below clouds).

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Fig. S1. GOES10 imagery for October 16, 2008, at 15UTC. Clockwise from top left corner: multichannel RGB, cloud phase, cloud effective radius (μm), cloudoptical depth. See http://www-angler.larc.nasa.gov.

Fig. S2. Flow diagram for droplet number concentration (Nd ) data assimilation. Numerical variables are found in open boxes and code or programs are foundin yellow boxes. re: droplet effective radius; τ: cloud optical depth; N: aerosol number concentration; M: aerosol mass concentration per specie.

Saide et al. www.pnas.org/cgi/doi/10.1073/pnas.1205877109 3 of 3