some unsolved problems in atmospheric radiative...

Some Unsolved Problems in Atmospheric Radiative Transfer:Implication for Climate Research in the Asia–Pacific Region

K. N. Liou, Y. Gu and W. L. Lee

Department of Atmospheric and Oceanic Sciences and Joint Institute forRegional Earth System Science and Engineering, University of

California, Los Angeles, California, [email protected]

Y. Chen

Center for Satellite Applications and Research, NESDIS,NOAA, Camp Springs, Maryland, USA

P. Yang

Department of Atmospheric Sciences, Texas A&M University,College Station, Texas, USA

A number of unsolved problems in atmospheric radiative transfer are presented, including the lightscattering and absorption by aerosols, the effect of mountains on radiation fields, and radiativetransfer in the atmosphere–ocean system, with a specific application to the Asia–Pacific region. Wediscuss the issues of two nonspherical and inhomogeneous aerosol types, dust and black carbon,regarding climate radiative forcings. Reduction in uncertainties of their radiative forcings mustbegin with improvement of the knowledge and understanding of the fundamental scattering andabsorption properties associated with their composition and size/shape. The effects of intensivetopography, such as that in the Tibetan Plateau, on surface radiation and the radiation field above,are significant and the solution requires a three-dimensional radiative transfer program. We showthat in a clear atmosphere, surface net solar flux averaged over a mesoscale domain can differby 5–20 W/m2 between a slope and a flat surface. Accurate calculations and parametrizations ofboth solar and thermal infrared radiative transfer in mountains must be developed for effectiveincorporation in regional and global models. The wind-driven air–sea interface is complex and affectsthe transfer of solar flux from the atmosphere into the ocean and the heating in the ocean mixedlayer. We point out the requirement of reliable and efficient parametrizations of the ocean surfaceroughness associated with surface winds. The scattering and absorption properties of irregularphytoplankton and other species in the ocean must also be determined on the basis of the rigoroustheoretical and experimental approaches for application to remote sensing and climate research.

1. Introduction

Radiative transfer is a subject of study in avariety of fields, including astrophysics, appliedphysics, optics, planetary sciences, atmosphericsciences, meteorology, and various engineering

disciplines. Prior to 1950, radiative transferwas studied principally by astrophysicists, alt-hough it was also an important research areain nuclear engineering and applied physics asso-ciated with neutron transport. In his ground-breaking book, Chandrasekhar (1950) presented

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the subject of radiative transfer in plane-parallel(one-dimensional) atmospheres as a branch ofmathematical physics and developed numeroussolution methods and techniques. The field ofatmospheric radiation, which evolved from thestudy of radiative transfer, is now concernedwith the study, understanding, and quantitativeanalysis of the interactions of solar and ter-restrial radiation with molecules, aerosols, andcloud particles in planetary atmospheres as wellas the surface on the basis of the theories ofradiative transfer and radiometric observationsmade from the ground, the air, and space (Liou,1980, 2002). A fundamental understanding ofradiative transfer processes is the key to under-standing the atmospheric greenhouse effects andglobal warming which results from externalradiative perturbations of the greenhouse gasesand air pollution, and to the development ofmethods to infer atmospheric and surface para-meters through remote sensing. In this article,we present three basic and largely unsolvedradiative transfer problems in the climate andweather research with an orientation toward theAsia–Pacific region.

The contemporary scientific issues asso-ciated with anthopogenic aerosols in climatechange and global warming are profound andtheir impacts on the environment and humanhealth are of great concern to scientists andthe lay public alike. Aerosols are globally dis-tributed in time and space, and affect theEarth’s radiation budget by the scattering andabsorption of the incoming solar radiation andthe emitted thermal infrared radiation in theatmosphere, referred to as the aerosol directeffect, and by modifying the microphysicaland radiative properties and lifetime of clouds,referred to as the aerosol indirect effect. Theradiative forcings of aerosols both direct andindirect remain the most uncertain elements inthe assessment of climate and climate change(IPCC, 2001), owing to our limited knowledgeof their chemical and microphysical propertiesthat directly affect the absorption and scattering

of radiation, as well as their intricate indirecteffects on cloud formation and the consequenceof radiation perturbation. We have provided thisreview of two key aerosol types, dust and blackcarbon, in terms of their impact on radiativetransfer in order to expand our knowledgeand understanding of their fundamental scat-tering and absorption properties in associationwith satellite remote sensing and application toclimate modeling and research.

In addition to aerosols, the transfer ofboth solar and thermal infrared radiation overmountainous regions complicates the studyof radiative transfer. In particular, the tem-poral and spatial distribution of surface solarradiation over intensive topography resultsfrom complex interactions among the incomingdirect solar beam, the atmosphere, and thesurface. This distribution in turn determinesthe dynamics of many landscape processes, suchas surface heating and moistening, evapotran-spiration, photosynthesis, and snow melting.Accurate calculation of radiative transfer iscrucial for many fields, including climatology,ecology, and hydrology. Significant progresshas been made on land–atmosphere interac-tions involving vegetation; however, the effect ofterrain inhomogeneity on the radiation fields ofthe surface and the atmosphere above has beenlargely neglected in weather and climate models.Many landscapes exhibit significant terrain fea-tures; for example, the Tibetan Plateau pro-foundly influences the general circulation of theatmosphere owing to its uplift of large scale flowpatterns and its insertion of heating with a con-fining lower boundary at high levels.

The final issue is one of quantifying theenergy transfer across the sea surface, whichis essential to understanding the general cir-culation of the ocean. Solar radiation fromthe sun contributes most of the heat fluxesthat penetrate the air–sea interface and aresubsequently absorbed throughout the oceanmixed layer. Thus, solar radiative transfer differsfrom other air–sea interaction processes, such

Some Unsolved Problems in Atmospheric Radiative Transfer 309

as wind stress, evaporation, precipitation, andsensible cooling, which occur only at the seasurface. Radiative transfer in the atmosphereand the ocean requires a specific treatment ofthe interface between air and water at whichthe state of the sea surface is largely controlledby surface winds. The scattering and absorptionof particulates in the ocean associated with thetransfer of solar radiation and the heating inthe ocean mixed layer require further researchfrom the perspectives of rigorous electroma-gnetic scattering theory as well as controlledlaboratory experiments.

This paper is organized following the pre-ceding three challenges of radiative transfer andwe have made a specific effort to apply theseradiation problems as they relate to East Asia.A summary is given in the last section.

2. Light Scattering and Absorptionby Aerosols

The importance of the scattering and absorptionproperties of aerosols for the radiation field andthe consequence of their climate impact havebeen briefly introduced. In this section we firstillustrate the climatic radiation effect of aerosolsover the East Asia region by employing a generalcirculation model (GCM) experiment. This isfollowed by a review of the composition, particleshape, and size of two types of aerosols, dustand black carbon (BC), which are particularlyimportant in climate radiative forcing analysis.

In what follows, we present results of aclimate numerical experiment using the UCLAGCM developed by Gu et al. (2003, 2006)to illustrate the importance of aerosol opticaldepth for precipitation simulation in the EastAsia region. The yearly and monthly meanaerosol optical depths at the wavelength of0.75µm over China, determined from thedata involving the daily direct solar radiation,sunshine duration, surface pressure, and vaporpressure from 1961 to 1990 (Luo et al., 2001),were used to investigate the effects of the

observed aerosols in China on climatic tem-perature and precipitation distributions. Thelarger aerosol optical depths are found insouthern China, with a maximum value of about0.7. In light of the available satellite data foraerosol-optical-depth climatology and for thereto be compatibility and consistency with thelong-term surface observations in China, weemployed a background aerosol optical depth of0.2 for the areas outside of China in the GCMsimulations to focus our analysis on the effect oflocalized aerosols on regional climate patterns.

The effect of the aerosol optical depth inChina on surface temperature and precipitationpatterns was examined by comparing the twoGCM experiments — the only difference isthat the observed aerosol optical depths inChina were used in one experiment and notthe other. Since the differences between thetwo experiments are mainly located in thesummer hemisphere associated with the positionof the sun, results are presented in termsof the July means for precipitation and out-going long-wave radiation (OLR) patterns, asshown in Fig. 1. Cooling in the mid-latitudesstrengthens the meridional circulation, resultingin increased precipitation in southern China,the Arabian Sea, and the Bay of Bengal, aswell as India and Myanmar. To compensatefor these increases, a broad band of decreasedprecipitation is located to the south of theincreased precipitation region, with a smalldecrease to the north. Increase in regional pre-cipitation, especially in the southern part ofChina and over areas of Indian where abundantmoisture is available in summer, appears tobe related to the increased aerosol opticaldepth that occurred in China. Positive diffe-rences in OLR are located at higher latitudes,while decreases are found to extend from NorthAfrica to southern China, where precipitationis enhanced, revealing increased convection inthis region. In a previous study, Menon et al.(2002) suggested that increase in the precipi-tation in southern China could be related to


(a) July Mean Precipitation Differences (mm/day)

(b) July Mean OLR Differences (W/m2)

Figure 1. Effect of the aerosol optical depth in China on simulations of the July OLR and precipitation differencepatterns determined from the two GCM experiments (denoted as CHIN and AERO in the figure) in which theonly difference is that the observed aerosol optical depths in China were used in CHIN (after Gu et al., 2006, withmodification).

increase in the absorbing aerosols, a hypothesiswhich differs from our current finding. This dif-ference illustrates the significance of using theaerosol optical depth (extinction) and single-scattering albedo (absorption) in GCM climatesimulations.

Understanding the direct radiative forcingof aerosols requires fundamental knowledge andreliable data on their scattering and absorptionproperties. The single-scattering properties ofaerosols are determined by their dielectric cha-racteristics (refractive index) associated withchemical composition and morphologies in termsof external geometric shape and composition.Aerosol shapes are diverse and span fromquasisphere to highly irregular geometry. In

addition to complex particle geometry, the inho-mogeneous composition of aerosols has beencommonly observed. Dust and carbonaceous(particularly BC) particles are two major typesof aerosols that profoundly affect climate.

(a) Dust particles. Dust can scatter andabsorb solar and terrestrial radiation, leadingto the positive and negative effects of aerosoldirect forcing. Moreover, the solar and infraredradiative forcings of dust may be of differentsigns, thus further complicating the total forcingassessment. Determination of the sign andmagnitude of direct radiative forcing by duston regional and global scales remains a keyunsolved problem (e.g. Sokolik et al., 2001).


With respect to the chemistry and compo-sition of dust particles, Falkovich et al. (2001)conducted chemical and mineralogical analysisof dust particles collected in a dust storm overIsrael and found that dust particles typicallyoccur in aggregated form with varying mineralo-gical composition, consisting mostly of Ca, Mg,Al, and Si. Analysis also showed that sulfur (S)and iron (Fe) adhered to the particle’s surface,which was suggested to have occurred from pro-cesses within the source region. Gao et al. (2001)studied the characteristics of soil-based aerosolsoriginating in China and the effects of globaltransport on the composition and reported thatthe mineralogy of the loess soil primarily con-sists of quartz (SiO2), feldspars, micas, claysas well as carbonates (CaCO3 in particular)and other trace minerals. Mineralogy of dustparticles is a function of geographical location.Near the source region, dust assumes the com-position of its parent soil; however, when dustis transported over large distances, the compo-sition will change depending on the directionof the dust plume. For example, airborne dustpassing through an urbanized region may mixwith local pollutants such as black carbon orit may mix with sodium chloride crystals asit gets transported over the oceans inside themarine boundary layer. Mineral dust rarelyexists as a pure mineral, but rather, owingto internal and external mixing, as a complexaggregate of several minerals. Sokolik et al.(1998) extensively studied the optical propertiesof a wide range of dust mixtures. Major mineralsinvestigated thus far include quartz, commonclays, (montmorillinite, illite, and kaolinite, toname a few), and the carbonates dolomiteand hematite, the latter is responsible for theredness sometimes seen in visible observations.Large uncertainties exist as to how to bestrepresent these minerals in an optical model forradiative flux calculations and remote sensingapplications.

Characterizing the shape of a dust particleis a difficult and challenging process. Through

laboratory analysis and in situ measurementsusing the scanning electron microscope, 2D par-ticle shape can be inferred by using one ofseveral shape parameters. One commonly usedparameter is circularity, which is defined asC = L2/4πA, where L is the particle’s peri-meter (µm) and A is the 2D projection area ofthe particle (µm2). C = 1 refers to a circularparticle, and a square has a C equal to 1.27.Dust partcles typically have C values rangingfrom 1 to as high as 4 or 5. Based on histo-grams from the dust samples collected in China,the bulk of C values range from 1 to 2 (Gaoet al., 2001). Recent individual analysis dataon Saharan dust particles show that as par-ticle size increases, as is the case during heavydust outbreaks, so too does its circularity, indi-cating that dust is rarely spherical. Most dustparticles are highly irregular and angular, pos-sessing sharp corners (Koren et al., 2001; Gaoet al., 2001). They also tend to be elongated in adirection perpendicular to their rotational axis;that is, they are oblate. Typical aspect ratios fordust particles observed during studies in China(Okada et al., 2001) and the PRIDE field expe-riment (Reid et al., 2003) are in the range of1.4–1.9. Previous studies have made many ass-umptions regarding the shape of dust particles.Dust is commonly composed of quartz crystalsthat are typically tetrahedral in shape. Particlescomposed of clays have been observed to exhibitflat, platelike structures. The scattered intensityof irregular aerosols could be a factor of 1.5larger and a factor of 2 smaller at forward scat-tering and backscattering angles, respectively,than those of volume-equivalent spheres (Kalas-hnikova and Sokolik, 2002).

Many studies have been dedicated to quan-tifying the size distribution of dust particlesfrom varied global locations over the years, butdata interpretation and problems with sizingtechniques have large uncertainties (Reid et al.,2003). d’Almeida et al. (1991) characterizedthe size spectrum assuming a lognormal dis-tribution, which can often be bimodal. Some


typical size distributions cited in contem-porary works on dust research also suggested agamma distribution with an effective radius ofabout 2µm.

Satellite remote sensing of the optical depthand size of dust particles can be used to cons-train GCM simulations concerning the impact ofdust outbreaks on climate and climate change.As discussed above, dust particles are exclu-sively nonspherical. However, it has been acommon practice to use the phase functioncomputed from the Lorenz–Mie theory for“equivalence” spheres in retrieval and ana-lysis. On the basis of the scattering resultsfor spheroids, Mishchenko et al. (1995) illus-trated that the spherical equivalence assumptioncan result in substantial errors in the aerosoloptical depth retrieved from satellite observa-tions. Dubovik et al. (2006) further showed thatthis assumption can lead to unrealistic retrievalsin aerosol size distribution and the spectraldependence of the refractive index inferredfrom ground-based AERONET measurements.It appears that the significance of aerosol nons-phericity in remote sensing and climate studyhas been increasingly recognized.

In the following, we present an exampleof the importance of aerosol nonsphericity forsatellite remote sensing and radiative forcinganalysis. Figure 2 displays the phase functionsat a wavelength of 0.63µm and with a sizeparameter of 10 for three types of aerosol par-ticles — a randomly oriented dustlike particlewith 10 surface faces, a spheroid, and a sphere —computed with the finite-difference time domain(FDTD) approach (Yang and Liou, 2000), theT-matrix method (Mishchenko et al., 1996),and the Lorenz–Mie theory, respectively. Thetwo top panels are for oceanic particles at thetwo satellite sensing wavelengths of 0.63 and0.86µm, while the bottom panels are for mineraland soot particles using a wavelength of 0.63µm.As shown, significant differences are evidentin the backscattering directions where satelliteradiometers see the atmosphere, except in the

case of soot with large absorption, denoted bya significant value in the imaginary refractiveindex. These differences can be as large as afactor of 10 between dustlike and sphere at mostof the scattering angles greater than 120◦. Ifthe retrieval uncertainty for optical depth, τ , is50%, defined as [τ(dust)−τ(sphere)]/τ(sphere),the aerosol solar radiative forcings at the topof the atmosphere (TOA) and the surface differby 8 and 12W/m2, respectively, based on cal-culations from the Fu and Liou (1992, 1993)radiative transfer model using the standardatmospheric profiles for water vapor and othergases along with a solar constant of 1366W/m2,a surface albedo of 0.1, and a solar zenith angleof 60◦. A retrieval uncertainty factor of 2 yieldsradiative forcing differences of 15 and 23W/m2

at TOA and the surface, respectively. Theseare hypothetical large numbers for illustrationpurposes but nevertheless a physically reliableremote sensing of aerosol optical depth mustaccount for the aerosol nonsphericity, particu-larly in the case of dust.

(b)Carbonaceous particles. Carbonaceous par-ticles in the atmosphere, which are of spe-cific interest to the climate and climate changestudy, strongly absorb sunlight, heat the air,and contribute to global warming (Menon et al.,2002). Recent investigations indicated that themagnitude of the direct radiative forcing dueto BC exceeds that from CH4 and may bethe second most important component of globalwarming, after CO2, in terms of direct forcing(Jacobson, 2001). In addition to the directclimate effect, BC particles, acting as CCN, caninhibit cloud formation (Koren et al., 2004).The magnitude of BC absorption depends highlyon its refractive index (especially its imaginarypart), shape, and size distribution. It alsodepends on the mixing state of BC particles.

Carbonaceous compounds make up a largebut highly variable fraction of the atmos-pheric aerosols. Carbonaceous materials are by-products of solid, liquid, or vapor combustion,


Figure 2. Phase functions at a wavelength of 0.63 µm and with a size parameter of 10 for three types of aerosolparticles: a randomly oriented dustlike particle with 10 surface faces, a spheroid, and a sphere computed with thefinite-difference time domain (FDTD) approach, the T-matrix method, and the Lorenz–Mie theory, respectively.

generated either directly through aggregation ofmolecules formed in combustion processes fromcoal, biomass burning, and biofuel, leading tosoot particles (primary carbon), or indirectlythrough condensation from a supersaturated gasproduced by chemical reactions and resulting insecondary organics (secondary carbon). The by-products of fossil fuel burning are injected intothe atmosphere from both stationary sources,such as factories and power plants, and mobilesources, such as motor vehicles. Aerosol particlesproduced by fossil fuel burning are concentratedover North America, Europe, China, Japan,India, and other industrialized regions. The

primary aerosol particles released from fossilfuel burning generally fall into two categories:soot and fly ash. Soot includes both elemental(BC) and organic compounds, and is generallyin the fine particle mode. Fly ash is the nonor-ganic by-product of coal burning. Coal containssubstantial residual mineral material, includingclays, shale, sulfides, carbonates, chlorides, andvarious trace metals. When coal is burned, theseparent materials are released unreacted or ther-mally transformed. They take the form of sphe-rical glassy particles in the coarse particle mode.The combination of soot and fly ash releasedfrom coal furnaces results in a bimodal size


distribution of primary aerosol particles. Dieselengines are the dominant source of soot insome urban environments, but worldwide, coalburning releases about ten times as much BCinto the atmosphere as diesel fuel combustion.

Primary carbon or soot aerosol consists oftwo subcomponents with different absorbing fea-tures: graphitic carbon with a high absorbingproperty and primary organics with a ratherweak absorbing property (Rosen and Novakov,1984). The number and mass concentrations ofthe single subcomponents are highly variablefunctions of space and time, as in the case of theparameters determining their size distribution.Given this importance, measurements of BCand the differentiation between BC and organiccarbon still require improvement (IPCC, 2001).Recent estimates place the global emission of BCaerosols from biomass burning at 6–9Tg/yr andfrom fossil fuel burning at 6–8Tg/yr (Scholesand Andreae, 2000). The emission of BC hasbeen especially large in China, owing to thelow temperature household burning of coal andbiofuels (Streets et al., 2001). Giorgi et al.(2002) carried out a series of simulations usinga coupled regional climate-chemistry/aerosolmodel and showed that anthropogenic fossil fuelsoot exerts a positive radiative forcing of 0.5–2W/m2 TOA. Using a regional climate modeldeveloped in China, Wu et al. (2004) alsoreported that BC induces a positive radiativeforcing at TOA and a negative forcing at thesurface. Reducing uncertainties in the radiativeforcing due to BC must account for its funda-mental absorption and scattering properties.

BC particles can be internally and exter-nally mixed with other nonabsorbing materials(Martins et al., 1998). The same amount of BCunder different types of mixing can result infairly different absorption properties. The effi-ciency of absorption of a certain amount ofBC is determined by its mass absorption coef-ficient, which depends on the size of particlesand the type of mixing between BC and non-absorbing components such as organic matter

and sulfates. In the case of an external mixturewhere individual pure BC particles are in par-allel with nonabsorbing particles, the BC massabsorption efficiency is about the same for pureBC particles. However, it is likely that BC par-ticles that form at relatively high temperaturewill be coated by a nonabsorbing shell to forman internal mixture. Another type of internalmixture is a long-chain aggregate of BC particlesformed at high temperature, which can also becoated with nonabsorbing materials to form aninternally mixed heterogeneous structure. Theseopened clusters usually collapse to form closelypacked sphertlike structures as a result of inter-actions with water vapor and clouds.

Owing to their production mechanisms, car-bonaceous materials, including BC, are con-fined to the submicrometer size range. However,aggregation of freshly produced particles mayyield particle sizes above that range. Small sphe-rical soot particles coagulate to form chainlikeaggregates. These irregularly shaped particleshave been found to be fractal, and have specialoptical properties. The mass median diameterof BC in the atmosphere is very small, between0.1 and 0.5µm. In urban air, two size modescan often be detected; a smaller mode resultingfrom freshly formed primary aerosol and a largermode resulting from coagulation processes. Themore remote the location, the more dominantthe larger size mode, reflecting the importanceof coagulation during the aging of carbonaceousaerosol as it is transported from the site ofcombustion. BC aerosols normally have a longlifetime in the atmosphere because of their smallsize, usually less than 1 µm. Identifying andquantifying the purely carbonaceous materialremains a difficult task. Effects of the aggre-gation of soot aerosols on their scattering andabsorbing properties have recently been studiedby Liu and Mishchenko (2005).

The state-of-the-art radiative transferschemes that have been used in climate modelshave not taken into account the effects of aerosolnonsphericity and inhomogeneous structure


(e.g. Gu et al., 2006, and the preceding GCMexample). The neglect of these effects could sub-stantially underestimate or overestimate aerosolradiative forcing. For example, the asymmetryfactor of realistic aerosols, which is directlyrelated to the albedo effect, can be quite dif-ferent from that of their spherical counterparts.It follows that a spherical “equivalence” ass-umption can lead to erroneous assessment of theaerosol radiative forcing. In the preceding dis-cussion, we have demonstrated the nonsphericalshape effect of dust particles on the scatteringphase function and the consequence of remotesensing of their optical depth and particle size.In the case of BC particles, we have showedthe complexity of inhomogeneity associated withinternal inclusions, external attachments, andcluster structures. Indeed, accurate and efficientdetermination of the scattering and absorptionproperties of these two major types of nonsphe-rical and inhomogeneous aerosols is a subjectthat will require in-depth research efforts.

3. The Effect of Mountains onRadiation Fields

The energy emitted by the Sun and receivedby the Earth’s surface is determined by threesets of factors. The first includes the latitude,the solar hour angle, and the Earth’s positionrelative to the Sun, which determine incomingsolar radiation at the top of the atmosphereand can be precisely calculated (Liou, 2002).The second involves the attenuation of thesolar beam by scattering and absorption causedby atmospheric gases, aerosols, and cloud par-ticles. The last comprises terrain characteri-stics including elevation, slope, orientation, andsurface albedo. On a sloping surface in moun-tainous terrain, the total solar radiation can beseparated into five components according to theSun-to-surface path (Fig. 3): (1) the direct fluxcontains the photons arriving on the grounddirectly in line from the Sun to the surface,unscattered by the atmosphere; (2) the diffuse

Fdiffuse Fdirect

Fdirect-reflected

Fdiffuse-reflected

Fcoupling

Target

12

3

4

5

Figure 3. Schematic representation of the flux com-

ponents received by the target on a sloping surface inmountainous terrain. (1) direct, (2) diffuse, (3) direct-reflected, (4) diffuse-reflected, and (5) coupling fluxes(after Chen et al., 2006).

flux is composed of photons scattered by theatmosphere; (3) the direct-reflected flux is asso-ciated with photons traveling directly throughthe atmosphere unscattered but subsequentlyreflected to the target surface by neighboringslopes; (4) the diffuse-reflected flux is similarto the direct-reflected irradiance except that itis composed of photons already scattered bythe atmosphere and then reflected by neigh-boring slopes; and (5) the coupling flux is com-posed of photons that have experienced multiplesurface reflections and atmospheric scatterings.The direct, diffuse, and coupling componentsare produced when solar radiation interacts witha flat surface. However, over mountains, addi-tional components are generated by the direct-reflected and diffuse-reflected fluxes throughinteraction with rough topography that areabsent for the flat surface.

A variety of models of varying sophisti-cation and complexity have been developedto compute most of these solar flux com-ponents in rugged terrain in which the directincident beam is computed by introducing acosine correction of the local zenith angle andconsidering the shadow caused by topography


(e.g. Olyphant, 1986). Diffuse radiation has beenmodeled as being proportional to the area ofthe sky dome visible to the target surface (e.g.Dozier and Frew, 1990). Factors contributingto terrain-reflected flux have generally not beenconsidered explicitly, but are approximated byassuming a first-order reflection between sur-rounding terrain and the target surface. Theterrain-reflected radiation is particularly signi-ficant over snow surfaces (Dozier, 1980). Mieschet al. (1999) used a Monte Carlo approach tocompute flux components at ground level andthe radiance reaching the satellite-borne sensorover a very simple 2D rugged terrain with homo-geneous atmospheric layers above, and con-cluded that a 10% error may occur when theterrain-reflected and coupling components mayplay a dominant role in the signal measured bya satellite sensor over poorly exposed or sha-dowed areas. As this brief literature survey illus-trates, the effect of complex 3D mountainousterrain on the surface flux components of Fig. 3has not been systematically and rigorouslystudied.

Chen et al. (2006) developed a 3D MonteCarlo radiative transfer model that calculatesthe flux components exactly given a realisticdistribution of scatterers and absorbers in theatmosphere and provided the first definitiveassessment of the relative importance of theflux components in a clear-sky atmosphere.The 3D Monte Carlo method for the transferof radiation from the Sun as a point sourcewith application to clouds has been presentedin some detail by Marshak and Davis (2005).Chen et al. (2006) also characterized the factorscontrolling diurnal, seasonal, and geographicalvariability in the flux components and deter-mined the significance and sources of errorsin conventional radiative transfer schemes inareas of intense topography by applying the3D radiative transfer model to a real 3Dmid-latitude mountainous surface. Errors inradiative transfer schemes that have been usedin GCM’s with smoothed topography were

assessed by comparing 3D results with themountainous surface to identical calculations fora flat surface with the same mean elevation. Itwas shown that the errors are on the order of 5–20W/m2, depending on the time of the day, andstem from the fact that the atmosphere absorbsa different amount of solar radiation when thetopography underneath it is smoothed.

The Tibetan Plateau, which covers about2.4 million square kilometers with an averageheight of over 4 km, has a profound influenceon the general circulation of the atmosphere,owing to its uplift of large scale flow patternsand its insertion of heating with a confininglower boundary at high levels. The win-tertime dynamic effect enhances the southwardtransport of the Siberian high and leads to alarge trough in the jet stream extending into thePacific (e.g. Charney and Eliassen, 1949). Thesummertime elevated heat source has been reco-gnized by meteorologists since early papers byT. C. Yeh (Ye, 1979) in conjunction with the for-mation and maintenance of the Asian summermonsoon, the onset of Meiyu, or the East Asiansummer monsoon rainfall period, and the sum-mertime heavy rainfall frequently occurring incentral China. At lower levels the mechanismis similar to but more powerful than that ofthe summer near surface jet of the US’ GreatPlains. However, our knowledge of the TibetanPlateau heating and its interactions with thecomplex regional dynamics and the consequenteffects has remained rather limited. Althoughreanalysis data have been used to provide tem-poral and spatial distributions of differentialheating, these results are severely limited by ina-dequacies in the formulations of diabatic pro-cesses in the models. Problems associated withthe vertical profile of radiative heating ratesover the mountainous region, the coupling ofthe surface to the lower atmosphere throughboundary layer convection, and the snow albedofeedback in regional and global climate changeappear to be largely unresolved and oftenignored.


We applied the 3D solar radiative transfermodel constructed by Chen et al. (2006) toa domain of 200km × 200km centered atLhasa over the Tibetan Plateau and carried outan analysis of the topography effects on thesurface and atmospheric radiation fields. Forthe terrain information, we used the HYDRO1kdatabase that was developed at the US Geo-logical Survey’s EROS Data Center to providecomprehensive and consistent global coverage oftopographical datasets. The required data forradiation calculations include digital terrain ele-vation, slope, and orientation. Employing theISCCP 2.5◦ by 2.5◦ resolution surface albedomap, we obtain one surface albedo value forradiation calculations. Figure 4 displays thedistributions of the surface downward (upper

Figure 4. Distributions of the surface downward (upper panels) and net (lower panels) solar fluxes at a 1 km ×1 km resolution over the domain.

panels) and net (lower panels) solar fluxes ata 1 km × 1 km resolution over the domain.The standard atmospheric water vapor andother trace gaseous profiles were used as inputin the calcuation along with a solar zenithangle of 64◦ and two azimuthal angles corre-ponding to early morning and late afternoon.The results displayed in these diagrams illus-trate the effect of terrain and its orientationwith respect to the Sun’s position. We see sub-stantial different flux values along the rivervalleys (two heavy solid lines). The net surfacesolar flux for a flat surface at an average heightof abour 4 km is 400W/m2, but it varies fromabout 40 to 500W/m2 in the 200km × 200kmdomain. Figure 5 illustrates a 3D atmosphericheating rate distribution in the domain, with the


Figure 5. 3D atmospheric heating rate distribution in a 200 km × 200 km domain, with the terrain height shownat the bottom as a black shade.

terrain height shown at the bottom as a blackshade. A substantial variability of the atmo-pheric heating rate ranging from about 0.2 to1.2K/day is shown. The inhomogeneous surfacefeature affects not only surface radiation butalso the atmospheric radiation field above.

For application to regional weather andclimate models, we are most interested in theflux averaged over a domain. Figure 6 illus-trates the domain-averaged fluxes for flat andmountain surfaces as a function of time of dayusing horizontal resolutions of 50×50km2, 100×100km2, and 200×200km2. Two surface albedosof 0.2 and 0.7, representing a snow condition,were used in the calculations. The domain-averaged fluxes were obtained by averaging theresults from the 1× 1 km2 3D radiative transfercalculations. Net flux differences between thepreceding resolutions appear to be small but, incomparison with the flat surface counterpart, adifference of 5–20W/m2 is shown. Figure 7 illus-trates the averaged atmospheric solar heatingrate over a horizatal domain of 200 km × 200km

for the case of a flat surface with an averageheight of 4.7 km and two mountainous casesrepresenting morning and afternoon conditions.Heating rate results for the two mountaineouscases are close because of the large domainaverage. However, significant variations fromabout 0 to about 0.76K/day are shown inthe regions from the lowest elevation of 2.3 kmto about 6 km, resulting from the effect ofmountain slopes associated with the solar zenithangles used in the calculations. These differenceswould have a substantial effect on the energybalance of the planetary boundary layer in GCMsimulations over the Tibetan Plateau.

In summary, we have demonstrated the signi-ficance of topographical effects on surface andatmospheric radiation fields in clear atmos-pheres. Clouds and aerosols are anticipated tohave a profound influence on the radiationbudget over mountain terrain and are subjectfurther investigation. Moreover, the thermalinfrared (long wave) radiation emitted fromrugged terrain with nonhomogeneous surface


Figure 6. Domain-averaged fluxes for flat and mountain surfaces as a function of time of day using horizontalresolutions of 50 × 50 km2, 100 × 100 km2, and 200 × 200 km2. Two surface albedos of 0.2 and 0.7 (snow condition)were used in the calculations.

temperatures is another subject that requires in-depth study.

4. Radiative Transfer in theAtmosphere–Ocean System

The climatological value of solar flux pene-trating the mixed layer can reach 40W/m2 inthe tropical regions and produce a difference inthe heating rate of a 20m mixed layer by about0.33◦C a month (Ohlmann et al., 1996). Thevertical distribution of solar flux also influencesthe stability and stratification of the mixed layerand the sea surface temperature. Consequently,a quantitative understanding of the ocean solarflux profile is important to ocean model simu-lations. The surface albedo, which includes thesurface reflectivity and the upwelling radiationfrom the water surface, is critical to the energybudget in the atmospheric planetary boundarylayer. However, the reflectivity of the wind-blown surface is difficult to evaluate. The surfacereflectance may be reduced by 50% when thesolar zenith angle is 70◦ and the wind speedincreases from 0 to 20m/s (Mobley, 1994).

Figure 7. Averaged atmospheric solar heating rate

over a horizatal domain of 200 km× 200 km for the caseof a flat surface with an average height of 4.7 km (denotedby the horizontal dashed line) and two mountainouscases representing morning and afternoon conditions.

The surface roughness also affects the upwellingradiation from the water surface and its deter-mination requires accurate radiative transferanalysis. In addition, the oceanic pigment onradiative transfer in the ocean is also significant.A change of 0.10mg/m3 in the phytoplankton


concentration in the mixed layer can result ina corresponding change of the penetrative solarflux by about 10W/m2 at a level of 20m depth(Siege et al., 1995). Because solar radiation isthe energy source for photosynthesis, it alsodirectly affects the marine productivity.

A typical coupled radiation model deals withparametrized and simplified radiative transfer inthe atmosphere and ocean separately by consi-dering one medium as the boundary conditionor the other. Computationally expensive modelshave also been developed for solar flux calcu-lation (Jin et al., 2002), but they are not com-patible with coupled atmosphere–ocean modelsfor climate simulation.

Lee and Liou (2007) developed a coupledatmosphere–ocean broadband solar radiativetransfer model based on the analytic delta-four-stream approach originally derived by Liou(1974) and Liou et al. (1988). This approachis computationally efficient and at the sametime can achieve acceptable accuracy for fluxand heating rate calculations in the atmosphereand the oceans. Figure 8 illustrates a coupled

Figure 8. A coupled atmosphere–ocean system with the solar beam reflected and refracted by a wind-blown seasurface. For an optically inhomogeneous system, the atmosphere and the ocean can be divided into a number ofseparate homogeneous layers such that each layer can be characterized by a single-scattering albedo, a scatteringphase function, and an extinction coefficient.

atmosphere–ocean system with the solar beamreflected and refracted by a wind-blown seasurface. For an optically inhomogeneous system,the atmosphere and the ocean can be dividedinto a number of separate homogeneous layerssuch that each layer can be characterized bya single-scattering albedo, a scattering phasefunction, and an extinction coefficient. Theentire radiative transfer system can be solvedby matching the continuity equations for dis-crete intensities at the interfaces. To take intoaccount the reflection and transmission of thewind-blown air–water interface, a Monte Carlomethod (e.g. Preisendorfer and Mobley, 1985)has been employed to simulate the travelingof photons and to compute the reflectance andtransmittance of direct and diffuse solar fluxesat the ocean surface using Cox-Munk’s (1954)surface slope distribution. For the ocean part,existing bio-optical models, which correlate theconcentration of chlorophyll and the absorptionand scattering coefficients of phytoplankton andother matter, have been integrated into thiscoupled model.


Lee and Liou’s model was first compared tothe values computed by a more exact modelemploying more discrete streams and illustratesthat the relative accuracies of the surface albedoand total transmission in the ocean determinedfrom the present model are generally within 5%,except in cases of the solar zenith angle beinglarger than 80◦. The observational data col-lected at the CERES Ocean Validation Expe-riment (COVE, Jin et al., 2002) site have alsobeen used to validate this model and the resultsshow that the relative differences of downwardand upward short wave fluxes and albedo arewithin 10% of the observed values.

As an example, Fig. 9(a) shows the surfacesolar albedo as a function of the wind speedand the cosine of the solar zenith angle (SZA),µ0, for the clear sky condition with the chlo-rophyll concentrations of 0 and 12mg/m3. Anocean depth of 200m with an ocean bottomalbedo of 0.1 was used in the calculation and thechlorophyll concentration was considered uni-formly in the whole layer. The sea surface albedogenerally increases with the SZA for µ0 > 0.1,because the Fresnel reflectance increases with anincreasing incident angle. However, the surfacealbedo decreases with the SZA for µ0 < 0.1,because when the Sun’s altitude becomes lower,the intensity of direct solar radiation decreasesmore rapidly than that of diffuse radiation.Thus, the addition of the proportion of diffuseradiation reduces the effective SZA, leadingto decrease in the surface albedo. The windeffect on the surface albedo is strong only whenµ0 > 0.4. The surface albedo increases withchlorophyll concentration owing to increase inthe scattering coefficient. However, this effectis not significant because increase in backscat-tering is canceled out by increase in the par-ticulate absorption in sea water. Figure 9(b)shows the transmission (z = 5m) using the chlo-rophyll concentrations of 0 and 2mg/m3. Trans-mission decreases significantly with increasingchlorophyll concentration owing to increase inabsorption. The transmission minimum occurs

at µ0 ∼ 0.25. Owing to Rayleigh scattering,the intensity in the blue light region of directsolar radiation decreases with increase in opticaldepth. Sea water has a minimum absorptioncoefficient in the blue light region and forthis reason the transmission decreases with anincreasing SZA. Because there is more radiantintensity in the blue light region for diffuseradiation than the direct counterpart, the trans-mission increases with the SZA for the low Sun’selevation associated with more energy for diffuseradiation.

The existing bio-optical models, which cor-relate the concentration of chlorophyll andthe absorption and scattering coefficients ofphytoplankton and other matter, are highlyempirical and require verification by funda-mental theory and observations. For example,absorption by phytoplankton and the associatedliving or nonliving derivatives and absorptionby the dissolved yellow matter are directly cor-related with that by phytoplankton withoutrigorous physical fundamentals. Moreover, theRayleigh scattering theory is not applicable towater because the distance between water mole-cules in the liquid phase is too short. TheEinstein–Smoluchowski theory (Mobley, 1994)of scattering states that fluctuation in themolecular number density due to random mole-cular motions causes fluctuation in the indexof refraction, which gives rise to scattering.An empirical form for the volume scatteringfunction and the scattering coefficients between200 and 800 nm for pure sea water have beenused in the field of ocean optics (Smith andBaker, 1981). In addition, the scattering coef-ficients for phytoplankton and other matterhave been determined simply from the bio-optical model (Morel and Maritorena, 2001).The correct scattering and absorption propertiesfor irregular phytoplankton and other speciesin the ocean must be determined from thetheory of electromagnatic scattering along withappropriate scattering experiments in the labo-ratory — an exciting research area.


(a)

(b)

Figure 9. (a) Sea surface albedo for radiation between 0.2 and 4.0µm as a function of the wind speed and thecosine of the solar zenith angle for the clear sky condition with chlorophyll concentrations of 0 (left panel) and 12(right panel) mg/m3. (b) Transmission at the ocean depth of 5 m with chlorophyll concentrations of 0 (left panel) and2 mg/m3 (right panel) (after Lee and Liou, 2007).

5. Summary

In this paper, we have presented three con-temporary and largely unsolved problems inatmospheric radiative transfer with application

to the Asian–Pacific region. Although it hasbeen written in a review format, some newresults have also been presented to illustrateimportant points in climate and remote sensingapplications.


Aerosols are undoubtedly the most uncertainclimate element in the Earth’s atmosphere atthe present time. Analysis and understandingof the radiative forcings owing to the directand indirect aerosol climate effects require thebasic scattering and absorption properties. Thedust storms originating in China during thespringtime and their global transport havea profound impact on the climate of EastAsia. Moreover, China is the largest underde-veloped country in the world and has beenobtaining 80% of its energy from coal com-bustion. The emission of BC has been espe-cially large owing to low-temperature householdcoal burning. Dust and BC are nonspherical andinhomogeneous particles. Reliable and efficientdetermination of the scattering and absorptionproperties of these particles based on theoreticalapproach, numerical solution, and controlledlaboratory experiment must be undertaken inorder to reduce uncertainties in their radiativeforcings by means of global and regional climatemodels.

The effect of terrain inhomogeneity on theradiation fields of the surface and the atmo-sphere above has not been accounted for inweather and climate models at this point. Onthe basis of a 3D radiative transfer programwe illustrated that without consideration oftopographical variability in typical midlatitutemountainous regions in the United States, netsolar flux at the surface can be off by 5–20W/m2, assuming a flat surface. Many lands-capes on the continents exhibit significantterrain features and in particular, the TibetanPlateau has a profound influence on the generalcirculation of the atmosphere and climate in theEast Asia region. The temporal and spatial dis-tributions of surface radiation over this intensivetopography determine surface dynamic pro-cesses and atmospheric radiative heating. Thus,accurate calculations and parametrizations ofradiative transfer including both the solar andthe thermal infrared spectra in clear and cloudyconditions must be developed for incorporationin regional and global models.

The last unsolved radiative transfer area weidentified is associated with the transfer of solarradiation in the atmosphere–ocean system. Theocean covers about 70% of the Earth’s surface,and the radiation interface between the atmo-sphere and the ocean is rather intricate. Wepointed out that the vertical distribution of solarflux influences the stability and stratification ofthe mixed layer and the sea surface temperature.The surface roughness produced by the winds isthe predominating factor controlling the pene-tration of solar flux into the ocean mixed layerand it must be correctly modeled for radiationcalculations. Finally, we pointed out the lackof fundamental scattering and absorption infor-mation on irregular phytoplankton and otherspecies in the ocean for heating rate calculationand remote sensing application.

Acknowledgements

The research for this work has been supportedin part by NSF Grants ATM-0331550 and ATM-0437349 and DOE Grant DE-FG03-00ER62904.We thank Yoshihide Takano and Rick Hansellfor their assistance during the preparation ofthis article.

[Received 4 January 2007; Revised 28 April 2007;Accepted 30 April 2007.]

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