Estimation of surface O Vertical correlations and covariances ......Estimation of surface O3 from lower-troposphere partial-column information: Vertical correlations and covariances

Estimation of surface O3 from lower-troposphere partial-column information:Vertical correlations and covariances in ozonesonde profiles

Q5 Robert B. Chatfield a,*, Robert F. Esswein a,b

aNASA Ames Research Center, Moffett Field, CA 94035, USAbBay Area Environmental Research, 560 Third Street West, Sonoma, CA 95476, USA

h i g h l i g h t s

< We parametrize vertical autocorrelations and covariances structure of N American O3.< Covariances define a mapping from the remotely retrievable to the pollution-relevant.< Sources and mixing processes explain lower-troposphere O3 variability.< Near-surface ozone mapscan be inferred from 0 to 3 km averages.< New satellite remote-retrieval instruments can map near-surface ozone.

a r t i c l e i n f o

Article history:Received 8 November 2011Received in revised form2 June 2012Accepted 11 June 2012

Keywords:Remote retrievalSmog ozoneSurface ozoneStatistical structure of atmosphereOzonesondeBoundary layer structurePollution layering

a b s t r a c t

Analysis of the spatial correlation of ozone mixing ratio in the vertical provides information useful forseveral purposes: (a) it aids description of the degree of regionality of the ozone transport-transformation processes, (b) the information provided in the form of a priori covariance matrices forremote retrieval algorithms can simplify and sharpen accuracy of the resulting estimates, and mostimportantly, (c) it allows a first evaluation of the improvement that remote retrievals can give overboundary-layer climatology. Vertical profiles of mean, variance, and vertical autocovariance, and verticalautocorrelation of ozone mixing ratios were estimated and given parameterizations. The WOUDC ozo-nesonde network database was used. During the years 2004e2006, these were considerably augmentedby sondes taken by NASA, NOAA, and Canadian agencies during recent summertime intensive periods inNorth America. There are large differences across the North American continent in the patterns andmagnitudes of correlation, especially in the lowest 2e3 km of the troposphere. This is especiallysignificant for the near-surface layers (100’s of meters deep) which determine actual surface O3 smogexposure and phytotoxicity, since satellite retrievals typically characterize at best a thick layer extending3 km or more from the surface. The relative variation of O3 decreases in the vertical, particularly for thesomewhat polluted launch stations, and this affects inference of surface O3 significantly. We outlinea simple synthesis of mixed-layer and ozone-chemistry behavior to aid discussion of this and similarphenomena. Regional differences suggest broad if qualitative explanations in terms of larger-scale(interstate-transport) and local-scale phenomena (lake and sea breezes, degree/frequency of subsi-dence), inviting future study. The character of near-surface-to-full-layer covariance suggests that remoteretrieval can describe surface ozone surprisingly well using 0e3 km partial-column ozone. for manysituations. This indicates that there is substantial utility for new remote-retrieval methods that exploitozone absorption in multiple wavelength regions, e.g., UV þ Vis, UV þ IR, or UV þ Vis þ IR. In summary,we find considerable value in interpreting retrievable O3 columns to estimate O3 quantities that areclosely relevant to air pollution mitigation.

Published by Elsevier Ltd.

1. Introduction

The measurement of atmospheric ozone from space has a longhistory and retrievals of the total column have become so precise(Liu et al., 2010) that it is natural to use retrievals to map pollutant

* Corresponding author. Tel.: þ1 650 604 5490; fax: þ1 650 604 3625.E-mail address: [email protected] (R.B. Chatfield).

Contents lists available at SciVerse ScienceDirect

Atmospheric Environment

journal homepage: www.elsevier .com/locate/atmosenv

1352-2310/$ e see front matter Published by Elsevier Ltd.http://dx.doi.org/10.1016/j.atmosenv.2012.06.033

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Please cite this article in press as: Chatfield, R.B., Esswein, R.F., Estimation of surface O3 from lower-troposphere partial-column information:Vertical correlations and covariances in ozonesonde profiles, Atmospheric Environment (2012), http://dx.doi.org/10.1016/j.atmosenv.2012.06.033

ozone near the surface.Q1 The characterization of near-surfaceozone is important for human health and plant growth (US EPAOzone (O3) Standards: http://www.epa.gov/ttn/naaqs/standards/ozone/s_o3_cr.html). Promising newly refined methods forremote retrieval of tropospheric ozone (Worden et al., 2007;Landgraf and Hasekamp, 2007; Natraj et al., 2011) allow samples formore appropriate regions, i.e., partial column estimates with 2e3pieces of information for the whole troposphere. The lowest layercan be about 3 km deep. Description of the vertical profile in higherlayers of the troposphere is also relevant. Middle and uppertropospheric ozone need to be mapped for the interest of severalagencies (e.g., in the USA, EPA, NOAA, and NASA) in understandinghemispheric and global pollution, particularly as it progressivelyhas increasing effects on the radiation budget and global climatechanges. For these reasons, it is important to quantify ozone byaltitude and by concentration as accurately as possible, and tounderstand how relevant partial-column estimates are to thedetermination of vertical profiles.

One goal of this report is to aid retrieval of the whole profile oftropospheric ozone by describing the sounding-to-soundingmeansand variances of ozone at a level as they varydsignificantlydbygeographical location and in the vertical. These aid ozone retrievals.It is easy for the convergence search of estimation procedures tostray to clearly unreasonable solutions since the retrieval problemis poorly posed and susceptible to solutions far from the norm(solutions that are mathematically allowable but not likely in termsof our prior experience) (Backus and Gilbert, 1970). The range ofreasonable estimates e.g., mean, standard deviations, and thelikelihood that these change rapidly in the vertical, also aids thealgorithm by suggesting soft limits for parameter estimates as wellas first-guess values. The expected covarying structure of estimatedparameters like cO3

between differing levels is also useful in esti-mation algorithms (Rodgers, 2000; Maddy and Barnet, 2008).Understanding the vertical covariance structure of ozone mixingratio, cO3

, level to level, helps to prescribe the smoothness ofsolutions.

A more immediate use of a better description of verticalcovariances is to assess the correspondence of the retrievable(a layer average of tropospheric ozone) to the relevant (maps ofozone as it determines daily human exposure). Satellite mappingcan serve several purposes to the extent that a retrieval of a partialcolumn can relate strongly to what we will describe as “near-surface ozone,” nsO3. Wewish nsO3 to have dimensions of a mixingratio, ppb, and to be a useful description for the ozone budget overmany hours of the day, not necessarily a mixing ratio measured ata single site, e.g., a particular existing measurement station. Morediscussion of the averaging implied by this desire appears below.We used a pressure coordinate system for the vertical, whichsimplifies averaging; however, the near-surface layer had to respectsurface pressure variation. We chose the bottom of the layer to bethe 80th percentile surface pressure level pSfc;80, and the top of thelayer to be pSfc;80 " 50, i.e., 50 hPa lower pressure, ca. 500 m higheraltitude. The pSfc;80 varies from 0 to ca. 125 m off the surface. Thisallows a pressure coordinate but also describes a region ca. 500 mdeep, sometimes slightly less deep. The reasons for this choice willbecome more evident in a later section on origins of vertical vari-ation of ozone.

2. Background

From early in the era of ozone-remote-sensing instruments, theadvent of TOMS (Total Ozone Mapping Spectrometer, launched1978), there have been repeated observations of features identifi-able as regional smog in total ozone imagery (Fishman et al., 1987).Early methods concentrated on removing the large partial column

of stratospheric ozone from the TOMS signal, leaving a muchsmaller partial column of ozone, a Tropospheric Ozone Residual or“TOR,” (Fishman et al., 1990). The noisy difference, the TOR,represents at best ozone in the whole the troposphere; correlationsbetween total tropospheric ozone and surface ozone may thereforebe sporadic, depending on the variance in ozone above the pollutedboundary layer. Nevertheless, statistical relationships of TOR andgeographical patterns of surface ozone and surface effectshave been noted repeatedly, although surface concentrations arenot typically estimated (Hudson et al., 1995; Fishman et al., 2010;Wang et al., 2011). Accuracy of algorithms has improved, and thesuccessor to TOMS, the OMI (Ozone Monitoring Instrument),provides retrievals of total ozone column to a very few percent. Amore recent TES (Tropospheric Emission Spectrometer) techniqueusing thermal IR appears to give good resolution of two layers(partial column estimates) of ozone 2e5 km, and 5e12 km (Nassaret al., 2008). As a conspicuous example, as Nassar’s Section 6indicates, in the first release of TES estimates, a large number ofretrievals which minimized error also differed greatly in shape and0e1 km magnitude from results that conform to prior experienceand also the initial guess. A common feature of retrieval sets tocontain somewidely unrealistic appearing profiles. This is probablydue to a minimization finding a physically unrealistic minimum(Rodgers, 2000), can be ameliorated when there is better knowl-edge of a mean expectable profile and the typical (We will addressthis feature of retrievals again in the latter portion of our report.).IASI or future instrumentation may do slightly better than TES(Natraj et al., 2011).

Thermal techniques have nearly zero information at the surface(see Fig. 1), where air and surface temperatures are nearly equal,denying any distinction of a vertical scale. Techniques based on UValone also havemarkedly decreased sensitivity near sea level due torapidly increasing competition of Rayleigh scattering with O3absorption (Natraj et al., 2011). However, several retrieval situations,e.g., with low clouds or scattering aerosol can improve thediscrimination of near-surface ozone. Ziemke et al. (2001, 2009)have shown how cloud-slicing can enhance retrievals of boundary

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Fig. 1. Ability of several instrumental combinations to resolve lower troposphericozone, using data from Natraj et al. (2011). In this presentation, the degrees of freedomfor signal are integrated from the surface upwards. Green: IR only, Orange: UV þ Vis,Red: UV þ IR, black dots: UV þ Vis þ IR. (For interpretation of the references to color inthis figure legend, the reader is referred to the web version of this article.)

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layer ozonewhen there ismoderate cover by lowclouds. Joiner et al.(2009) extend this methodology while emphasizing the need tounderstand the scattering and absorbing properties of the cloudlayer on retrievals. When there are appropriately distributed low-level clouds one may estimate a layer height above the surface andthe ozone within that layer. A very different approach uses neuralnetwork techniques developed in land-surface sensing to estimatenear-surface ozone directly, but the geographical regions andconditions in which this will give reproducible results are not yetclear (Sellitto et al., 2011). The network selectedwithout guidance toemploy wavelength regions thought to be uninformative, theChappuis bands near 600 nm. While such methods provide littlephysical insight, the result promises that detailed attention to thephysics of retrieval will be rewarding.

Data assimilation of ozone is an extremely promising approachto the characterization of near-surface ozone. The technique’ssuccess in the stratosphere the uppermost troposphere andtropospheric column (Stajner et al., 2008; and references) hasworked its way down in the troposphere (Doughty et al., 2011) andto the boundary layer (Zoogman et al., 2012). Three aspects ofassimilation are worth noting; these suggest that it can beaugmented by non-assimilation methods. First, the techniquecombines observations and modeling (simulations based on“bottom-up” or physical and chemical theory) in ways that can bedifficult to disentangle. It adds in information from other times, butthese additions necessarily require theoretical understandings ofreaction, conservation, transport, and sources (a model, or thesynthesis of several models) that may not always apply. Dataassimilation faces a persistent criticism that it is just simulationthat has been perversely edited so as only not to be contradicted bydata, and only when there is data (The authors’ outlook is that thisview is oversimplified, but contains some truth which could beemphasized in legal or political discourse.). Secondly, in the case ofozone, assimilation does well on the upper troposphere wherechemical timescales are long and flow is predominantly isentropic,broad-scale, and accurate. The lowermost troposphere is morestrongly and locally affected by isolated but widely distributedsources of ozone precursors and destroyers. Thirdly, evaluation ofassimilation’s success rests on statistical theory that is broadlysimilar to kinds of inference that we use below. Amain difference isthat with assimilation, physical theory and statistics are complexlyintermixed. Nevertheless, assimilation will play a role in thedescription of air pollution; we guess that it will work especiallywell when subsidence (responding to data) and local influences(responding to strong local sources and sinks of ozone) play similarroles. This publication will suggest that more clearly definedmodeling, e.g., statistical models of geophysical correlation bothhave their independent role and also cannot be ignored in under-standing the origins of the success of assimilation.

Following this background, our work begins with a descriptionof methods and the quantification of level-to-level means, variance,and vertical-coordinate covariances. In practical terms, this isa portrayal of correlations between pairs of 50-hPa thick layers allthroughout the troposphere. This description moves to the math-ematical descriptions of the variance-covariance matrices them-selves. We publish spline-function descriptions in an attempt toreport them systematically for use in retrieval calculations. Thismethod is relatively free of dependence on our sampling grid, andso should be easy to apply on other vertical grids.

Details of the variation seen at more polluted stations differfrom the others and have implications for the practical usefulnessof retrievable ozone data. Consequently, we outline a review/synthesis of current knowledge about sources, meteorology andchemistry of the lowest kilometers of the troposphere that maysimplify the reader’s interpretation of the different stations.

Finally, we examine our central question, the relationship ofnear-surface ozone to layer-average ozone in the lower tropo-sphere, lower-tropospheric partial column O3, or ltpcO3. Followingrecent results on retrievability (Natraj et al., 2011), we take ltpcO3 tomeasure mean O3 for the region 0e3 km, expressed as an equiva-lent mean mixing ratio. These lower-tropospheric correlationsappear to exhibit broad regional patterns; we speculate on effectsthat forthcoming local studies may confirm.

3. Variance and vertical autocorrelation in the troposphereand stratosphere

In our analysis, ozonesondes were used to describe the structureof the atmosphere for the troposphere and up to approximately25 km in the stratosphere. The ozonesondes launches chosen foranalysis were sponsored or coordinated by three main groups, theNOAA CMD (Global Monitoring Division, Samuel Oltmans), theCanadian Atmospheric Environment Service (David Tarasick,Environment Canada, Air Quality Research Division), or NASA’scontinuing IONS project (Thompson et al., 2010). Most of thestations are in remote or lightly populated sites. Exceptionalstations, in polluted areas, were in Houston, TX, Beltsville, MD, andBoulder, CO. These stations were in the center of a large highlyindustrialized city, in a suburb of Washington DC, and in a smallercity near a larger metropolis, Denver, CO. A summary of themeasurement program through 2008 may be found in Tarasicket al. (2010) and Thompson et al. (2010). A broader summary ofozonesonde statistics may be found in Tilmes et al. (2011). Datawasassembled from the World Ozone and Ultraviolet Radiation DataCenter (WOUDC) and the NASA Goddard sites for the IONS projects.

Examinationof thevariationsof sondeprofiles in the stratospheresuggests that the statistics on the important amount of ozone above22e26 km is now better described by satellite retrievals exploitinglimb scanning such as the Microwave Limb Sounder than by sondesin the region w22e30 km, where demands on pumps in the ozo-nesonde instrument become extreme. The statistical description ofozone’s probability distribution of values has two aspects which weattempt to harmonize. From the viewpoint of retrieval, the Rodgersoutlook stresses an understanding of a priori (current knowledge)mean, variance, and vertical covariance. The former is a vector ofmeans, the latter two are combined into a covariance matrix (or therelated error-covariance matrix). More detailed information on thedistribution is desirable but not often available (Rodgers, 2000,chapter 4). The natural measures are related directly to the effects ofO3 on radiances, i.e., partial columns measured in mole cm"2 or inDobson units (2.69 # 1016 mole cm"2). These are also additive toa total O3 column. However, for human comprehension, it makessense to use O3 mixing ratios in ppb (c as indexed by vertical levelabove the surface,ci; the specifierO3 used above,cO3

,will be omittedfrom here on). These work more intuitively in consideringtransport processes and chemical transformation. We will harmo-nize these views by describing the mass-averaged mixing ratiowithin a characterized level ci, where the averaging relationship forlayer i bounded by pressure levels pb and pt (in hPa) is

ci ¼ ðpb " ptÞ"1Zpt

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The use of mixing ratios also facilitates the adaptation to onesown most suitable set of levels. Logarithms of ozone are also used

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for iterative retrieval calculations; for these additivity does not holdand near-conservation of column estimates might be considered asone test of accuracy.

Means and standard deviation estimates over many samples forMeanðciÞ ¼ c and

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarðciÞ

pof a selection of the sondes that we

analyzed are graphed in Fig. 2. These describe the atmosphere up toapproximately 55 hPa. Themean and variances were derived and fitwith spline curves to this level, as shown. These statistics are usefulin remote sensing studies, as they can define a priori values for theretrieval. The variance estimates associated with the standarddeviations shown are also useful in defining the strictness or laxitythat should be accorded to estimation at each level. For example,wide variations allow the algorithm to define a high-tropopausesituation (low ozone mixing ratio) or a low-tropopause situation(high mixing ratio).

These regions of high variance are functions of both latitude andlongitude, as the Fig. 2 shows. Stations to the west of Valparaiso inthe Midwest and north of 35 N show a region with wide variationand a defined “knee,” or bend, at 175e250 hPa, that is transitionalto the stratosphere.

Fig. 3 describes the spatial ozone autocorrelation structure inthe troposphere. While autocovariances determine the mathe-matics of retrieval, autocorrelations are more easily understood bythe human eye. The autocovariance matrix is easily regained by

multiplying the autocorrelation matrix by a diagonal matrix con-sisting of the variances at each level (Incidentally, all calculationsdescribing autocorrelations were derived by reversing this process.All operations used the statistics of the autocovariances of layerpartial-column ozone, since variances add but correlations do not.)The variation above and below the reference level is not symmetricin Fig. 3, since these portrayals of the autocorrelation describe thecolumns of the autocorrelation matrix, not the cross-diagonals(Symmetrical graphsmay be obtained by ameasure of “off diagonaldistance” between pressure levels. This portrayal is the basis of thenumerical fits we describe below in the Supplementary Material.No graphs of these are shown.). The figures show the relationshipscentered on a single level and the autocorrelationwith levels aboveor below. For several of the stations and reference altitudes, thecorrelation dies off rapidly with altitude, for others not.

Glancing across the first row of local autocorrelation plots inFig. 3, one can see that the breadth (vertical separation) of theautocorrelation traces tend to become broader as the stationsprogress from west to east. This is most obvious for the tracesdescribing the near-surface reference levels (long trace line above,short one below the reference point), by 500 hPa, mid-troposphere,the broadening is much less. Indeed, the jaggedness of the auto-correlation estimates down near 0.3 or less suggests that samplingerror is becoming important.

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Fig. 2. Profiles of mean ozone mixing ratio (ppmv) with standard deviation indicated to the left and right of means, summertime six months 2004e2006. The solid lines indicatespline fits made for the mean and variance in ppmv terms. Tarasick et al. (2010) and Thompson et al. (2010) for description of stations and dates of soundings.


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4. Parameterized covariance estimates for remote sensing

The Supplementary Material gives spline fit coefficients for theprofiles of mean and (square root of) variance for the NorthAmerican sonde set some of which are shown in the graphs ofFig. 2. Variance estimates were obtained from layer partial-columnozone and normalized by layer depth to form an equivalent mixingratio. Then log10(Ci,i) the variance diagonal of the autocovariancematrix was spline fit in terms of p¼ log10(Pressure): a sample fittedfunction according to this formula is shown in Fig. 4 in terms of thestandard deviation. Fig. 4 illustrates the judgments we maderegarding the need to spline-fit sampling variability and structureevident from several sounding sites. The spline fit parameters arelisted in the Supplementary Material.

We took care to provide estimates that could be easy to move toanother grid. For example, separation between levels can bedescribed in differences between the center pressures of the layersthat we chose, layers that fit our dataset. Variance and autocorre-lation expressed this way can be adapted to other grids. One note:although we find it easy to graph and describe correlations and plot

standard deviations, all formal estimation is based on estimates ofmeans, variances, and autocovariances. The statistics of means andvariances add, and therefore they average correctly (Graphsshowing a satisfying symmetry of autocorrelations and autoco-variances around a center diagonal are obtainable using the user’smeasure of “off diagonal distance” measured by difference ofpressure levels. This portrayal is the basis of the numerical fits wedescribe below in the Supplementary Material).

It is a frequent practice to use logðcÞ rather than c in retrievalpractice (Natraj et al., 2011). More properly, the log of partial opticalpath (e.g., Dobson units) is the fundamental quantity, but this canbe related to the appropriately pressure-averaged mixing ratiounits. One good feature of logs is that the distribution of ozoneamounts in the region of high variability at and above the tropo-pause is better described: high standard deviation in c iscompensated by high mean. Some stations shown in Fig. 2 haveextreme standard deviations that do not describe the distributionwell, implying at worst negative concentrations. However, wefound that use of logarithms required us to loosen the strict addi-tivity used for non-log estimates. Still, all this estimation was

Fig. 3. Vertical autocorrelation scales in the troposphere. These describe the columns of the autocorrelation matrix ri,j. Legends indicate the “reference level” for each column of thecorrelation matrix (see text). Similarities between plots help suggest statistical variation; variations in the progression to lower values also indicate sampling variance of theestimates. Error bars are somewhat elusive: neighboring estimates have more combined certainty than individual estimates.


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carried out using the basic rules that pressure-layer depths, andmeans and variances have simple summation rules, and so produceappropriate averages. Since the estimation procedure converges ona state vector described by logðcÞ, these are taken as additive oncethe narrow-layer averages are established. These estimates areavailable from the authors.

5. Origins of the vertical variations of lower tropospheric O3

Our focus now turns from broad perspectives of process ofestimation of atmospheric ozone with maximum accuracy to thetopic of how well retrievals can characterize smog ozone forexposure and regulation. In the following sections, we will discusssome recurrent but perhaps unexpected trends in mean, variance,and covariance in the first few thousand meters above the surface.To avoid repetition in discussing several stations and features, is

useful to provide a review synthesizing aspects of lower-tropospheric boundary layer meteorology, reaction, and sourcesthat have proven useful in our current analysis. It is particularlyappropriate to an analysis of urbanized regions like Baltimore-Washington region (the Beltsville, MD, sondes, also, Chatfieldet al., manuscript in preparation, 2012). Fig. 5 shows mixing in thelowest kilometers of the atmosphere over a land surface and overa period of three days of fair weather without frontal passages orthunderstorm activity. These conditions appear to be useful in ouranalysis of several features of the ozone mean and variancestatistics. We will suggest that stations with other behavior haveplausible differences usefully describable as contrasts or additionsto the picture.

During each of the three days shown, starting soon after dawn,air from the surface to the mixing layer top is carried by thermalsand other eddies that also generate smaller eddies which complete

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Fig. 4. Sample plots of spline fits to autocorrelation data for Beltsville. (a) Autocorrelation in the lower troposphere (centered on 780 hPa) is maintained for several hundred hPa andthen drops precipitously. (b) Autocorrelation near the mean tropopause (238 hPa) has very short length scales. Green dots shown the spline fits described in the SupplementaryMaterial. Red dots show the individual autocorrelation estimates. Three adjacent pressure levels served as the basis for each spline fit; hence the large number and scatter of thedots. The central pressure level (e.g., 350 and 238 hPa) had significantly stronger weight. (For interpretation of the references to color in this figure legend, the reader is referred tothe web version of this article.)

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Fig. 5. “Retrievable” and “relevant”. A cartoon depiction of the daily cycles (slightly variable) of PBL-inversion height, convective eddies and appearance of full mixing vs layering ofair pollutants. Vertical axis is distance from the surface, while horizontal axis shows time progressing through three days and also some horizontal features such as eddy-turnover.The region marked with yellow shows a ca. 3-km region that can be reliably characterized from space, while the regions highlighted in green shows a region strongly useful thecharacterization of air pollution on scales of several kilometers wide, i.e., the retrievable and the relevant. The afternoon mixed layer reaches various heights on the different days, asthe planetary boundary layer height responds to surface heating and also to possible large-scale air subsidence. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)


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the diffusive mixing. Mixing progresses over 0.4 h (initial plumetransit bottom to top) to '2 h (substantial homogenization ifchemical reaction does not interfere). Several factors make thebehavior similar and generalizable among days with more or lesssurface heating and subsidence at the mixing layer top. 20e45% ofmixing-layer air is in the updraft, as the thermals expand and diluteduring their rise (Stull, 1987; Chatfield and Brost, 1987, andreferences). Typical dimensions of whole thermal regions arew1.5# broader than their height (Stull, 1987; Lothon et al., 2006);the general size is therefore determined by the boundary layer top.As thermals penetrate slightly into the inversion at the planetaryboundary layer top, they gradually raise the boundary layer depthover hours, as shown. The boundary layer top in Fig. 4 is portrayedas a single thin line, but occasional small pockets of previouslylofted air are trapped in a region of stable air just above the line inthe boundary layer inversion: these quiet regions preserveconcentrations of air mixed at a previous time or, occasionally, bitsof relatively unmixed near-surface air. Often the inversioncontinues to rise with further thermals, and these regions areentrained into the underlying mixed layer. Transport above themixing layer top is indicated very simply in the figure. Fourimportant processes require mention: (i) oftentimes the stability tooverturning at the mixed layer top allows differential advection, sothat, e.g., high concentrations of pollutant ozone are replaced bylow concentrations from regions exposed to a cleaner boundarylayer; (ii) small fair-weather clouds can mix pollution upward fromthe top, forming a semi-mixed region with some character of themixed layer; and (iii) synoptic weather patterns can either act to liftthe air pollution to 2 or 3 km, typically involving clouds of onlyhundreds of meters deep, or (iv) compensating subsidence regionsproduced by synoptic weather can push down the mixed layer top,as shown in the second day of Fig. 4.

How do ozone variations relate to all this? Ozone is a secondarypollutant species, so its production occurs very broadly throughoutthe mixed layer and above. Production is due to chemistry thatvaries in timescale from w6 h with particularly concentratedemissions of VOC and NOx pollutant in optimal proportions tow10days with little pollution; Ozone-determining pollution enters theboundary layer at very low levels, 0e3 m for nitrogen oxides andVOC’s associated with traffic, and a few hundred meters forindustrial power plants (which are widely scattered but significantsources). Both industrial and traffic emissions of NO act to destroyO3 very locally, via the reaction NOþ O3/NO2 þ O2, diminishing itfrom a small percentage all the way to 0 ppb (complete titration ofozone). Regions of significant titration are limited both horizontallyand vertically during the day. Unfortunately, most O3 monitors areplaced at a few meters altitude, and a significant fraction can beunder the strong influence of one or several nearby NO sources.Some monitors are more free of these effects, but we know of nosystematic discussion or characterization of monitors. All arelocated at the bottom of the mixed layer, an ozone destructionregion which responds to the full mixed layer ozone budget.Thermals and other eddies carry NO aloft and its effects in titratingO3 decrease as the thermals expand and dilute.

Above this region, variations in tropospheric ozone derive froma mixture of effects: older smoggy or clean areas lofted by mid-latitude storms in warm fronts, wisps and airmasses of clean anddirty air from far upwind (Europe, Asia, the Gulf of Mexico,.), andstreamers of O3 from the stratosphere that have had variableamounts of dilution (Newchurch et al., 2003; Li et al., 2005;Doughty et al., 2006).

Some implications of this discussion are that (i) the verticalregion that determines ozone levels upon which daily and hourlyeffects build is conveniently approximated as at least the depth ofthe highest afternoon mixed layer, w1ew2 km, the region that is

fully mixed in a day’s time and (ii) variability in ozone shouldcommonly decrease in the vertical from the surface to several km,as the destruction and production effects of precursor emissionsdie away; (iii) since the regions in the first km of the Earth’ssurface tend to influence regions above with diminishing effect,satellite resolution of concentrations characterizing a several-kmdeep region may be quite informative about the first kilometers,where the budget of ozone affecting surface conditions is deter-mined. All of these generalities deserve detailed analysis forparticular sites; in the following sections they help to form animpression on the extent to which such a narrative may be useful.

6. Correlation near surface and individual levels aloft

How well might we characterize the lower troposphere?Evidence from simulation studies regarding methods to estimatelower tropospheric column ozone using the different informationavailable from several wavelength regions gives us reason to expectthat remote retrieval of ozone can be relevant to smog pollution,but also sets limits on how well we can estimate surface ozone.Fig. 1 represents from a new perspective the information on someestimated capabilities of remote sensing of (Natraj et al., 2011) toframe the question. It portrays a current understanding of ourability to resolve ozone mixing ratio in layers of the atmosphereextending from the surface up, under the conditions of clear skiesand low aerosol loading (Cloud and aerosol effects can help as wellas hinder retrievals of lowermost-troposphere ozone, as currentwork by Natraj and the GEO-CAPE remote-sensing sensitivity teamwill show.). A common situation of stronger aerosol influence,where there is a scattering, not too absorbing, layer near thesurface, can significantly enhance resolution near the surface.Photons returning to the satellite sensor, have a longer path lengthin the layer (V. Natraj, X. Liu, personal communications, 2011,manuscripts in progress).

The vertical lines of Fig. 1 are of particular significance. The lineshowing “Degrees of Freedom for Signal” (DoFS) ¼ 1 roughly indi-cates a region that is fully resolved. For the most informativecombinations of wavelengths and instruments this occurs withlayers extending from the surface to 650e690 hPa, or about 3 km.This is a characterization of the radiation physics and retrievalmethodology examined, and is a quantification of a transitionbehavior; i.e., retrievals can still have some sensitivity to large ozonechanges somewhat above the layer, and retrievals with onlyDoFS¼0.8 can still be primarily sensitive to ozone below3km. SinceDoFS depends on radiational physics, instrumental noise, andretrieval numerics, it is not sensitive to the actual variability of ozonein the vertical due to geophysical processes. Variation in a retrievedlayer can be predominantly due to the most variable sub-regions;we shall see that these regions are often near the surface.

Consider now the correlation of surface ozone with ozone atvarious levels aloft. The red lines of Fig. 6 show the correlationcoefficient rðc0;ciÞ of near-surface ozone mixing ratio (nsO3), c0,with ozone aloft, ci, at various 50-hPa layers for three ozonesondestations. Note the large variation in the plots. The vertical spatialautocorrelation is quite small at the westernmost region, TrinidadHead, CA. Inmid-country, the correlation remains highuntil 850hPaor so, and in the Atlantic seaboard, the correlation drops somewhatto 850e900 hPa, but then remainsmodestly high, rðc0;ciÞ ( 0:45, upto about 650 hPa. These patterns appear to be quite reasonable interms of basic large-scale regional meteorology (Barry (Barry andChorley, 2009) (“Large scale”: ca. 10) NeS by 20) WeE.)). We willdiscuss the patterns further in the next section, where a largernumber of stations across North America are considered.

The black lines in Fig. 6 describe a linear “transfer function” b ¼Covðc0;ciÞ=VarðciÞwhich can be used to estimate variations aloft in


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ppb aloft down to estimated ppbs of surface ozone. These arisedirectly from estimates of variances and correlation coefficients or,equivalently, by simple linear regression ðc0 ¼ aþ bciÞ. Thesymbols Mean; Var; Cov; a; b refer to estimates with vertical andstation dependence and using appropriate layer averages of thesampling of ozonesondes available. All calculations are carried outusing additive quantities, i.e., pressure-weighted averages madeover pressure layers, and averages based on the addition rules ofmeans and variances of quantities. In the case of Trinidad Head, thenarrative on correlations suggests that lamina have very littlecorrelation, and the transfer function drops rapidly to zero. (Thismeans that the mean measurement for nsO3 has less error thaninference from layers above.) The transfer function for Beltsville isinitially more puzzling. Again, the Huntsville behavior is interme-diate. However, if it is posited that air at levels aloft has beeninfluenced by air from below, air with generally similar trajectoriesand ozone production/loss processes, but has other influences also,then the surface-related variation will have been diluted. Thetransfer function must be greater than 1 to compensate for thisdiluted effect. In fact, this behavior is fairly common. Since

r"c0;ci

#¼ Covðc0;ciÞ=

$ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarðc0Þ

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarðciÞ

p %

Dc0 ¼ Covðc0;ciÞ=VarðciÞDci¼ r

"c0;ci

# ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarðc0Þ

p=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarðciÞ

pDci ¼ bDci

defines the transfer function, so

Dc0>Dci wheneverffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarðc0Þ

p>r

"c0;ci

#& ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarðciÞ

p

We shall see that variability and variance do decrease withaltitude for several km at many stations, presumably because thedriving forces of variation of smog chemistry and deposition nearthe surface produce large variations. An unexpected consequence isthat an onlymoderately high correlation coefficient rðc0;ciÞ can stillimply a considerable effect on the number of ppb change, Dc0, to beexpected near the surface. These effects can be seen in Fig. 6. Notethat the green dots marking the standard-deviation of mixing ratioare consistent with the both r and Cov among the three stations.Furthermore, there is general continuity of these behaviors for the

many ozonesonde locations across the continent, as will be seen inthe next section, where we consider averages over thicker layers.

7. Inference of nsO3 from retrievable average lowertropospheric ozone

While level-to-level correlations describe the climatology ofozone correlations in some detail, we can examine a more basicquestion on the relevance of remotely sensed ozone to the analysisof smog. Satellite retrievals, especially from nadir-facing instru-ments, retrieve layer averages with sensitivity functions weightingsome individual levels more heavily. These sensitivity functions (orlayer-oriented averaging kernels) may vary with atmosphericconditions such as aerosol scattering or temperature lapse rate.Consequently we will describe a simple general relationship ofnsO3 with these layers as if the weighting were uniform with thenumber of molecules sampled throughout a layer. We will simplifythe view presented by Fig. 1 by assuming sensitivities can be rep-resented by straight lines approximating the curves over theappropriate interval. This approximation is reasonable for thecurves marked in orange, red, and black, as they vary between DoFSfrom 0 to 1. For the green curve, describing the use of thermalradiation only (instruments such as TES or IASI), the linear 0-to-1DoFS approximation might be better taken as extending betweenca. 900 hPa and 450 hPa.

Fig. 7 shows the correlation of near-surface (thin-layer) to lowertropospheric partial-column ozone directly for twelve NorthAmerican stations. Our goal is to predict c0, near-surface ozonemixing ratio (nsO3), using quantities that can be retrieved usingsatellite radiances. We want to understand the best linear-regression predictor of c0, and the confidence we have in therelationship. The annotation “Predict this layer” thick short reddouble-headed arrow describes c0, and all the graphed quantitiesrefer to aspects of its prediction.

We expect to use various remote retrievals of partial columnozone lower tropospheric average mixing ratio ci or pcltO3. Theoverbar in ci emphasizes the thickness of the averaging layer.“Optimistic” estimates: the long red arrows describe a region withDoFS ¼ 1 using the best estimators, i.e., the multi-instrumentretrievals (red and orange lines and dotted black line in Fig. 1).

trinidad 130 sondes

linear response and correlation

prs

(hPa

)

0.0 0.5 1.0 1.5

1000

900

800

700

600

b(layer,980 hPa)r(layer,980 hPa)10 x std deviation

huntsville 61 sondes


prs

(hPa

)0.0 0.5 1.0 1.5

1000

900

800

700

600


beltsville 20 sondes


prs

(hPa

)

0.0 0.5 1.0 1.5

1000

900

800

700

600


a b c

Fig. 6. (Red lines) Correlations of surface ozone, r, (nsO3) with ozone at the indicated levels in the lower atmosphere. (Black lines) “Amplification factors,” or transfer functioncoefficients, b, by which nsO3 concentrations are to be multiplied so as to estimate ozone at higher altitudes. Green dots: Standard deviation of ozone at the indicated levels, ppb,with a scale factor of 0.1. Notice the strong differences between the extreme West Coast station, Trinidad Head, CA (a), affected by frequent subsidence and strongly laminatedcomposition, as compared to the stronger correlation with the East Coast site at Beltsville, MD (c), which experience frequent episodes of airmasses with similar ozone chemistry upto w3 km (700 hPa). The Huntsville, AL (b), trends are intermediate, possibly indicating an alternating influence of recirculating East Coast and Southeast Central air pollution withan influence of cleaner Gulf Coast air, particularly above w2 km, 800 hPa. Values of b greater than 1 may be attributed to the greater productivity on O3 with rising and dilution ofprecursors (Chatfield and Delany, 1990) as well as more local production/loss processes near the ground. The latter could moderate and dilute larger scale regional variations. (Forinterpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)


891892893894895896897898899900901902903904905906907908909910911912913914915916917918919920921922923924925926927928929930931932933934935936937938939940941942943944945946947948949950951952953954955

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Another region above, not marked by an arrow, can also be esti-mated with DoFS ¼ 1 (These regions are also marked in Fig. 1.).“Conservative” estimates: the region marked by the green arrow isan approximation to a region using very low noise thermal sensing,slightly better than are available from TES or IASI today (Natrajet al., 2011). Conservative estimates are available with currenttechnique. Early versions of the Optimistic estimates have been

outlined in theory (Worden et al., 2007) and satellite retrievals arenow being improved (Xiong Liu, Kelly Chance, personal commu-nication, 2011).

Using terminology similar to the previous section, we graph theseveral quantities. The correlation coefficients rðc0;ciÞ shown by thethick angled red and green lines deserve first attention. If they arehigh enough, use of satellite data deserves our attention. The actual

trinidad 107 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.41

predict this layer

r Optimisticr Conservative0.1 s

(ppb)b Optimistic

0.16

richland 24 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.76

predict this layer


(ppb)b Optimistic

0.43

valparaiso 20 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.85

predict this layer


(ppb)b Optimistic

0.41

beltsville 20 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.92

predict this layer


(ppb)b Optimistic

0.55

wallops 36 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.87

predict this layer


(ppb)b Optimistic

0.53

narragansett 81 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.79

predict this layer


(ppb)b Optimistic

0.47

valparaiso 20 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.85

predict this layer


(ppb)b Optimistic

0.41

walsingham 43 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.75

predict this layer


(ppb)b Optimistic

0.34

sable 61 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.87

predict this layer


(ppb)b Optimistic

0.71

holtville 13 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.94

predict this layer


(ppb)b Optimistic

0.35

houston 50 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.84

predict this layer


(ppb)b Optimistic

0.58

huntsville 50 sondesprs (hPa)

0.5 0.0 0.5 1.0 1.5 2.01000

800

600

400

0.85

predict this layer


(ppb)b Optimistic

0.59

Fig. 7. Correlation of surface ozone with partial-column ozone in the lower troposphere for the levels indicated by the arrows, by region, as diagnosed from ozonesonde sites listed.Horizontal lines indicate approximate layers where DoFS reach values of 1 and 2 as integrated from the surface upward. Vertical double arrows at left indicated “optimistic” and“conservative” regions resolvable at ca. 1 DoFS, thick short arrow the region whose O3 is to be estimated (See text for detailed definition of regions.). Correlation coefficients,standard deviation, and “transfer function” b are shown.


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estimates of nsO3 variation are given by c0 ¼ aþ bci, whereb ¼ Covðc0;ciÞ=VarðciÞ. The intercept can be estimated bylinear regression over the sonde samples or equivalently asa ¼ Meanðc0 " bciÞ: The first six diagrams describe correlationsranging across the middle of the continent from Pacific to Atlantic.The next three sondes diagrams include examples extending to thenortheast from the US Midwest, by Walsingham southeast of Tor-onto, up to Sable Island in the Maritimes, a station commonly understrong influence of outflow of North American pollution in thesummertime. The last three sondes describe the southern UnitedStates. Holtville, CA had sondes in only one month, August, 2006,although Houston, TX, and Huntsville, AL, had repeated measure-ment campaigns. We do not venture into mathematical statisticsdescribing confidence intervals in this work, since the underlyingsource of “error” variation has temporal autocorrelation mostlydescribed by weather, which has autocorrelation structure overhours, days,months, and year-to-year (Sample calculationswemadewhich added 5% or 10% sample-to-sample completely random error,s=mz0:05 to 0:10, suggested onlyminor changes in the estimates.).

A broader view of these correlations is mapped out overtemperate North America in Fig. 8, using the complete set of sondesover mid-latitude North America, and using a “sensed” layer thatextends from 0.5 to 4 km. Fig. 8 shows broad similarities amongsites geographically near to each other with the most generalvariation extending from northwest to southeast across NorthAmerica. However, regions near bays, oceans or lake shores,particularly in the Great Lakes region, show smaller correlationthan other regions.

The patterns we see in Fig. 8 suggest a narrative of regionalmeteorology on ozone correlations involving near surface layers.We expect that this description can be tested and expanded by casestudies and further statistics. Jensen et al. (2012) provide anexample of such a statistical approach. Rather than establishparticular descriptions of correlations at individual stations, we

wish to motivate a sense of weight of evidence: correlations appearto vary geographically with reasonable patterns. If this is so,neighboring estimates tend to provide mutual reinforcement of ourconfidence. For example, Trinidad Head is frequently under theinfluence of the eastern, subsiding side of the permanent PacificAnticyclone. The effect of the subsidence is to produce a stableatmosphere in which lamina remain unmixed but spread out hor-izontally (thus becoming thinner) as they descend. Very littlevertical correlation of ozone producing or destroying regionsremains. The Eastern Seaboard from theMid-Atlantic northwards ischaracterized by migratory anticyclones and cyclones. Air from theregion and points to the west can form ozone in regions 1e3 kmthick (adding to a 1e1.5-km boundary layer produced by dryconvection is commonmixing upwards by hundreds of meters) dueto fair-weather cumulus clouds. The anticyclone may remain andrecirculate in some circumstances. When themigratory anticycloneis displaced by a warm frontal region, polluted air will movegenerally toward the northeast on the western side of the high andrise, often toward a cyclonic system. Fair-weather clouds can addadditional lofting. These motions produce a vertical structure inwhich different altitudes have ozone concentrations producedunder broadly similar conditions. The interplay of ozone produc-tion and mixing produces variations within a larger scale generalrise of ozone levels. When cool air-masses move in, concentrationscan initially lower as relatively unpolluted air from the Great Plainsand the Central and Prairie Provinces moves in. Alternatively, lesspolluted air can move in from the Atlantic or the Gulf of Mexico,with the greatest effect near the coasts (Such maritime air may alsobe polluted in recirculation that extends offshore.). Similar versionsof this explanation obtain across continental North America. Thereare stations that exhibit lower correlations, 0.77e0.79. Commonly,these are regions in which lower tropospheric winds are likely totake air over land-sea or land-Great Lake trajectories within thepast few hours, presumably creating internal boundary layers andstructures. When it is likely that near-surface air is exposed tomultiple landewater transitions (e.g., Walsingham, ON, Egbert, ON,Pellston, MI, the ship RMV Ron H. Brown, when stationed near NewHampshire in the Gulf of Maine, Sable Island, NS, Narragansett, RI)correlations seem particularly low, 0.7e0.77. On the other hand,Boulder, CO, is well known to exhibit frequent sharp transitions inat layers wherewesterlies flowunimpeded past the high wall of theFront Range. Downtown Houston, TX, and Valparaiso, IN, nearChicago exhibit somewhat lower correlations, 0.84e0.85. Althoughthe statistics of the sampling variance of the correlation coefficientcan be complex, the geographical patterns generally suggest thatcorrelation patterns will reproduce no worse than *0.03.

8. Conclusions

We presented a first attempt to relate satellite “retrievable”quantities to measures of O3 that are “relevant” to air pollutionassessment, mitigation measures, and forecasting. Our statistics(Figs. 6 and 7) reinforce the conclusion that full-troposphere-residual (TOR) estimates rarely are quantitatively useful indescribing near-surface ozone measures that are useful for airpollution surveys; when middle and upper troposphere variationsare minimal or averaged away, they can be useful (Fishman et al.,1990). The evidence of the ozonesondes we have analyzed showsthat ozone mixing ratios in our analysis exhibited considerablecorrelation in the vertical, especially in the lowest kilometers of theatmosphere. Since it appears possible to retrieve partial columnlower tropospheric ozone (pcltO3) in regions approximately 3 kmabove the Earth’s surface in clear skies, this analysis suggests verysubstantial skill in describing near-surface ozone nsO3, defined asthe layer average approximately 500 m above the surface. This skill

0.920.77

0.82

0.76

0.90

0.77

0.77

0.94

0.84

0.85

0.86

0.790.820.82 0.70

0.94

0.76 0.87

0.90

0.41

0.850.87

0.75

0.79

0.2 0.4 0.6 0.8 1.0

Correlation of BL ozone to ozone in ~0-3 km above surface

Fig. 8. Map of the correlation of nsO3 with 0e3 km partial-column ozone pcltO3 forNorth America. See text for discussion.


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is sometimes better than simple vertical autocorrelation functiongraphs seem to suggest (see Fig. 4), due to the interaction of sour-ces, chemistry, and meteorology which we cartooned in Fig. 5. Thisapproximate description merits additional study concentrating onindividual stations and their weather. There are two contributingreasons (a) the layer averaging tends to smooth variations inautocorrelation seen at finer scales, and (b) the frequent decrease invariance with distance from the surface (Fig. 2, notably the stationswith stronger precursor emissions) tends to emphasize thecontribution of the nsO3 layer and other layers relatively near thesurface. Locations with high variance near the surface provideconsiderable information for covariance analyses, and this bodeswell for good statistics in regions with strong precursor emissions.

The geographic pattern of correlation of pcltO3 to nsO3 seemsgenerally reasonable and will reward more detailed analyses of theeffects of general lower tropospheric subsidence, frequency oflifting of surface ozone and precursors by clouds, and de-correlation when frequent landewater transitions produceinternal boundary layers, etc.

Besides emphasizing the usefulness of remote retrieval of pcltO3by methods now being evaluated (Natraj et al., 2011) and imple-mented (Worden et al., 2007), the analysis may be useful in con-straining remote retrievals, providing estimates of a priori mean ciand cross-covariance Covðci;cjÞ. We present in the figures and inthe Supplementary Material details which allow a relatively simpleadaptation to any user’s own vertical grid.

Uncited reference

Barry and Chorley, 1998; Fishman et al., 2008; Lothon et al.,2009; Schnell et al., 2009; Szykman et al., 2011Q4 .

Acknowledgments

We particularly appreciate the contributions of the many ozo-nesonde operators and the industry of the organizers (especiallyD.W. Tarasick, S.J. Oltmans, and A.M. Thompson) of the sondenetworks, funded by Environment Canada and allied organizations,NOAA, and NASA. Funding for this effort was provided by the EarthScience Division of the NASA ScienceMission Directorate. Thanks toLaura Iraci and Michael Newchurch who reviewed an earlier draft.

Appendix A. Supplementary material

Supplementary material related to this article can be foundonline at http://dx.doi.org/10.1016/j.atmosenv.2012.06.033.

References

Backus, G.E., Gilbert, J.F., 1970. Uniqueness in the inversion of inaccurate gross earthdata. Roy. Soc. Lond. Phil. Trans. A 266, 123e192.

Barry, R.C., Chorley, R.J., 1998. Atmosphere, Weather and Climate. Routledge,London.

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