a three-dimensional radiative transfer model to...

1 OCTOBER 1998 3065O ’ H I R O K A N D G A U T I E R

q 1998 American Meteorological Society

A Three-Dimensional Radiative Transfer Model to Investigate the Solar Radiationwithin a Cloudy Atmosphere. Part II: Spectral Effects

WILLIAM O’HIROK AND CATHERINE GAUTIER

Institute for Computational Earth System Science and Department of Geography, University of California, Santa Barbara,Santa Barbara, California

(Manuscript received 16 January 1997, in final form 21 January 1998)

ABSTRACT

In this second part of a two-part paper, the spectral response of the interaction between gases, cloud droplets,and solar radiation is investigated using a Monte Carlo-based three-dimensional (3D) radiative transfer modelwith a spectral resolution of 0.005 mm. Spectrally resolved albedo at the top of the atmosphere, transmissionto the surface, and absorption throughout the atmospheric column between 0.25 and 4.0 mm are computed andcompared for 3D and independent pixel approximations at various solar zenith angles.

Analysis of a tropical cloud field shows that for overhead sun, the effects of cloud morphology reduceabsorption in the UV and increase absorption in the water-vapor absorption bands. At steep solar zenith angles,the enhanced absorption shifts spectrally to the near-infrared atmospheric windows, where increases up to 50%in absorption by cloud droplets are obtained. While there is no change in absorption in the visible, the 3D effectis shown to produce false estimates of cloudy-column absorption based on residual net fluxes in this spectralregion. Alterations to the albedo and enhanced absorption in the 3D computations generate reduced estimatesin remotely sensed cloud optical thickness and overestimates in cloud-droplet size distribution. Finally, a bandratio of 0.94 to 1.53 mm downwelling irradiance at the surface is proposed as a possible measure of 3D enhancedatmospheric absorption.

1. Introduction

In Part I of this paper (O’Hirok and Gautier 1998,henceforth referred to as OG98), we described the var-ious spatial mechanisms by which cloud morphologycan impact the shortwave radiative field. Examinationof a tropical cloud field showed that the assumption ofplane-parallel clouds leads to underestimates in broad-band shortwave atmospheric absorption in the presenceof clouds, increased transmission to the surface, and areduction in top of the atmosphere (TOA) albedo. Anoriginal motivation for this research was to determineif 3D cloud effects could account for the 25–30 W m22

discrepancy between theoretical estimates and recentobservations of atmospheric absorption in the presenceof clouds as reported by Cess et al. (1995), Ramanathanet al. (1995), and Pilewskie and Valero (1995). Althoughwe found that the 3D cloud effect alone could not ac-count for the magnitude of enhanced absorption, we willshow in this second paper that it may explain some ofthe difficulties associated with assessing cloudy-columnabsorption.

Corresponding author address: Dr. William O’Hirok, Institute forComputational Earth System Science, University of California, SantaBarbara, Santa Barbara, CA 93106–3060.E-mail: [email protected]

Part of the debate on enhanced cloud absorption cen-ters on the reliability of broadband absorption estimatesbased on residuals of net fluxes from measurementsgathered within a spatially complex environment. Spec-tral measurements of albedo and reflectance that areeasier to perform, suggest that the discrepancy betweentheory and observation is much smaller than recentlyreported by Cess and others (Stephens and Tsay 1990),or that the enhanced absorption may merely be an ar-tifact of the performed analysis (Imre et al. 1996). How-ever, as the word spectral implies, such measurementscannot provide direct broadband absorption, but canonly be used to infer absorption based on a combinationof theoretical models and measurements in selectedspectral bands. Hence, conclusions about absorption de-pend, to a degree, on the very models that are beingdeliberated upon. In this paper, we examine the spectraldistribution of the 3D radiative field and investigate ifand how the plane-parallel assumption can bias conclu-sions made about cloudy-column absorption derivedfrom spectral measurements. Furthermore, we discusshow measurements could be used to evaluate the im-portance of 3D effects.

2. BackgroundClouds primarily scatter incident radiation in the ul-

traviolet and visible (,0.7 mm) and both scatter and

3066 VOLUME 55J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S

FIG. 1. Spectral transmission to the surface for all gases (dark gray) and water vapor (lightgray). Overlay of cloud-droplet single-scattering albedo for effective radii of 4, 8, and 16 mm.

absorb in the near- and middle infrared (0.7–4 mm). Theamount of energy absorbed within a cloud depends onthe cloud droplet microphysics (i.e., single scatteringalbedo, phase function, and extinction coefficient), thedensity of cloud particles and their spatial distribution,interstitial aerosol and gas properties, and the spectraldisposition of the impinging radiation. All optical prop-erties vary spectrally. For cloud droplets, the single-scattering albedo is a function of wavelength, dropletsize, and the complex index of refraction. The spectralvariation of the single-scattering albedo is generally co-herent with the spectral variations of the extinction co-efficient of water vapor (Fig. 1). Exploiting this theo-retical knowledge, cloud spectroscopy techniques havebeen established to infer cloud properties from remotesensing. Based on results from remote sensing, en-hanced cloud absorption has been raised as an issue butdismissed as relatively insignificant (Stephens 1996).

The ratio of the near-infrared albedo to the visiblealbedo of a cloud field provides a direct indication ofpotential problems in the numerical modeling of ab-sorption by clouds. It is generally assumed that the al-bedo in the visible portion of the shortwave spectrumis well understood and that discrepancies occur in thenear-infrared. For a stratus layer, Hayasaka et al. (1995)obtained ratios of near-infrared albedo to visible albedoranging from 0.67 to 0.81 that are inconsistent withmodel results showing values near 0.85. For the morehomogeneous clouds encountered in their observations,it is possible to model the observed albedo in the visibleand near-infrared with a single cloud-droplet distribu-tion. However, for the more heterogeneous clouds, nosingle cloud-droplet distribution can account for the al-

bedo simultaneously observed in both spectral regions.Similar findings were obtained by Hignett (1987), whopresented observations of near-infrared albedo lowerthan results from plane-parallel radiative transfer mod-els. While these results suggest an ‘‘anomaly,’’ the near-infrared to visible albedo ratio has been employed byStephens (1996) to demonstrate the difficulties in rec-onciling the reported 25–30 W m22 discrepancy. Basedon model computations, Stephens shows that the near-infrared to visible albedo ratio would need to drop by50% to a level below 0.5 for the 25–30 W m22 reportedenhanced absorption. To date, however, the value of 0.5for the near-infrared to visible albedo ratio is inconsis-tent with reported observations.

Based on spectral reflectance, the assumption that theenhanced absorption is water related, and thus occursin the near-infrared, is not unreasonable. Stephens andPlatt (1987) demonstrated that theory overestimatesnear-infrared reflectance predominantly in atmosphericwindow regions and only slightly underestimates re-flectance near the visible at 0.75 mm. At 2.25 mm,Twomey and Cocks (1982) demonstrated that to matchremotely sensed droplet size distributions with in situcloud physics measurements, a three- to five-fold in-crease in the absorption coefficients is required. Na-kajima and King (1991) showed comparable results within situ measurements being 2–3 mm less than effectiveradii estimated from 2.16-mm reflectance data. To matchthe predicted drop size with the measured size, an anom-alous water-vapor absorption correction term needed tobe entered into the calculation. Stephens (1996) suggestthat for a plane-parallel cloud, a 50% reduction in near-infrared reflectance at 2.16 mm is equivalent to an in-


FIG. 2. Cloud-top height model input.

crease in droplet effective radius from 10 to 50 mm.Again, analogous to the albedo ratio, such droplet sizesare inconsistent with observations for stratus clouds.

Partially due to spatial sampling issues, most com-parisons between observations and theory are limitedto layered clouds—either solid stratus or less homo-geneous stratocumulus. For these clouds, the plane-par-allel assumption is not unreasonable. However, the newresults of Ramanathan et al. (1995), Pilewskie and Val-ero (1995), and to some extent Cess et al. (1995) arebased on tropical clouds, for which this assumption issuspect. To place an upper bound to potential 3D effectsand to evaluate the problems associated with the plane-parallel assumption within the context of these morerecent studies, all the 3D and 1D radiative computationsare performed for a tropical cloud field.

3. Method

The atmospheric radiative transfer model used in thisstudy is based on the Monte Carlo method. This tech-nique and other 3D radiative transfer methods used insimilar investigations has been extensively described inOG98. The model includes all major atmospheric gasesand aerosols. Cloud microphysical properties are basedon calculations derived from Mie scattering theorywhile gaseous absorption is computed using the k-dis-tribution method from LOWTRAN 7 (Kneizys et al.1988). Complete Monte Carlo computations are per-formed for the entire solar spectrum (0.25–4.00 mm) at0.005-mm resolution. Comparisons with a discrete-or-dinate radiative transfer model (Ricchiazzi et al. 1998)for clear sky and various plane-parallel clouds dem-onstrates that there is good agreement both spectrallyand broadband (OG98).

The model spatial environment consists of a synthe-sized cloud scene embedded within a typical tropical

atmosphere partitioned into 47 layers. From the surfaceto 10 km the thickness of the layer is 400 m becomingprogressively thicker with altitude above that height.Horizontally, it is partitioned into 800 m 3 800 m cellsarranged on an 80 3 50 grid. Cloud geometry is syn-thesized from cloud-top heights derived from satelliteimagery (Fig. 2). Cloud-base altitude of the convectivecells is fixed at 1200 m with a maximum cloud thicknessof 8800 m. Clouds that are difficult to detect from sat-ellite imagery because of pixel resolution or multiple-cloud layering have been included to more closely re-semble an actual cloud field. Numerous small cumuluscongestus clouds with a maximum areal extend of 1600m and cloud thickness of 1200 m are added near thebase of the large convective cells. Scattered altostratuscloud layers 800–1200 m thick at a base altitude of 6000m were also included, their total areal coverage beingapproximately 12%.

Internally, along the horizontal plane, the liquid watercontent (LWC) and effective radius (re) remain constantwithin the modeled clouds. Vertically, LWC varies withthe slope of the adiabatic curve. The effective radiusalso varies vertically and ranges from 4.2 mm near thebase of the convective cells to 16 mm at 2400 m abovethe cloud base and held constant to the cloud top. Forthe cumulus congestus clouds, re ranges from 4.4–10mm, and for altostratus clouds, 5.5–8.0 mm. The meaneffective radius of the field is 11.7 mm. For the entirefield the maximum optical thickness is 220, with a meanof 92.

Model computations are performed in a 3D mode(3DM) and independent pixel mode (IPM). The IPMessentially performs a plane-parallel computation ateach grid cell. Photons are confined in the horizontaldirection and are allowed vertical travel only throughthe atmospheric column. The 3DM more closely sim-ulates the flow of radiation through the atmosphere by


FIG. 3. Spectral ratio of 3DM to IPM model results for (a) TOAalbedo and (b) transmission to surface at solar zenith angles of 08,308, and 608. Beneath each plot is 3DM model results for TOA albedoand transmission to the surface expressed as a fraction of TOA in-solation.

FIG. 4.(a) Schematic of the flow of radiation along the direct beamfor a steep solar zenith angle as it intercepts the top and side of acloud in the 3DM computations. (b) Flow of radiation for the IPMcomputations where the direct beam intercepts the cloud top or sur-face only.

allowing both vertical and horizontal photon travel. Forboth modes, the actual distribution of atmospheric prop-erties is precisely the same, and thus differences in theresults can be directly attributed to the plane-parallelassumption.

From Part I (OG98), the 3D results showed a 7%reduction in albedo, an 18 W m22 increase in surfacedownwelling irradiance, and a 12 W m22 increase intotal atmospheric absorption for broadband solar radi-ation (0.25–4.00 mm). These values represent daylightmeans for the entire spatial domain of the model. Atsolar noon, peak differences occur for the upwelling anddownwelling fluxes, but interestingly, the peak absorp-tion takes place at a 458 solar zenith angle. For variousmanifestations of the tropical cloud field expressed asa single-layered homogeneous cloud (more typical ofthe representations used in climate models), the differ-ence from the 3D computations ranges from 216 to 38W m22.

4. Spectral results

To examine the 3D effect on normalized measuredquantities, such as spectral albedo or transmission, the

ratio of the 3DM to IPM results are presented in Fig.3. As a reference, the 3DM albedo and transmission areshown in the lower portion of each panel. The quantitiesare averages for the entire spatial domain. Gaps in theplots represent points where either the IPM or 3DMresults are at, or close enough to zero, that the signif-icance of the ratio is lost in the noise introduced byMonte Carlo computations.

For the TOA albedo, the 3DM is smaller at all wave-lengths and for all sun angles. Within the visible, andextending into the near-infrared, the albedo ratio re-mains constant and ranges between 0.95 and 0.98. Thehighest value occurs at 608 since the direct beam inter-cepts not only the top of the cloud, but the sides as well,effectively increasing the areal coverage of the 3D cloudfield (Fig. 4a). For the IPM, which treats clouds as hav-ing a zero aspect ratio, the direct beam cannot intercept


FIG. 5. Variation of spectral absorption with altitude for 3DM computations at solar zenith angles of (a) 08 and (b) 608. Difference inspectral absorption between 3DM and IPM computations at solar zenith angles of (c) 08 and (d) 608. Spectral location of main gaseousabsorption bands are noted along horizontal axis.

the side of a cloud, and the exposure to the direct beamdoes not change with solar zenith angle (Fig. 4b). Be-yond approximately 1.2 mm, however, proportionallymore of the radiation intercepted by cloud sides becomesabsorbed rather than scattered. The net effect is a changein the solar zenith angle of maximum albedo from 608to 08 above a pivot point near 1.2 mm. At wavelengthswhere the cloud-droplet single-scattering albedo is rel-atively low, the effects on the TOA albedo can be dra-matic. At 1.53 mm the albedo is reduced by 15% to25% depending on the solar zenith angle. At 1.98 mmthe reduction is from 25% to 40%. And for wavelengthsgreater than 3.4 mm, the reduction approaches 50% fora solar angle of 608.

The transmission of solar radiation to the surface isalso subject to 3D effects. For overhead sun, the 3DMtransmission is enhanced by as much as 20%. Spectrally,the variation is relatively constant with the lowest valuesoccurring beyond 3.4 mm. At 308, the transmission isalso higher from the ultraviolet wavelengths to 2.0 mm.Beyond this wavelength, however, the transmission forthe 3DM drops by as much as 20% near 3.4 mm. Forthe 608 solar zenith angle, the transmission is greater

by 5%–10% in the ultraviolet and visible, but dramat-ically falls off in the near-infrared with attenuation atthe surface as high as 20% to 40% for the wavelengthsof 1.65 and 2.25 mm, respectively. This reduction intransmission is directly attributable to increases in ab-sorption by cloud droplets.

To examine the spectral nature of 3D-enhanced ab-sorption in the atmosphere, the absorption of solar ra-diation has been integrated along the horizontal planeof the model domain and plotted as a function of alti-tude. In Fig. 5, the upper panel represents absorptionobtained from the 3DM computations, whereas the low-er shows the difference between the 3DM and IPM forsolar zenith angles of 08 (Fig. 5c) and 608 (Fig. 5d). Thedashed lines define the vertical boundaries of the cloudfield. It should be noted that within upper reaches ofthe cloud field, most of the cells are void of clouds.Overall, 9% of the field is completely clear of cloudsfrom the surface to the top of the atmosphere. Accord-ingly, there may be some transmission to the surface atwavelengths that are normally opaque to an overcastsky.

Readily apparent for both solar zenith angles (Figs.


5a,b) is the absorption of ultraviolet radiation by strato-spheric ozone. At 0.30 mm, the high-extinction coeffi-cient of ozone produces peak absorption of 40 and 21mW m23 mm21 at 08 and 608, respectively. Because ofthe higher albedo of the IPM at solar noon, more photonspass through the stratospheric ozone layer a second timethan for the 3DM causing slightly (1.3 mW m23 mm21)more energy to be absorbed for the IPM case. Furtherinto the visible region, the spectrally broader but weakerabsorption feature caused by the Chappuis ozone bandsis revealed. The sharp line at 0.76 mm extending fromthe surface to approximately 20 km is indicative of ab-sorption by molecular O2. For both solar zenith angles,the peak absorption (65 mW m23 mm21 at 08) occursabove and within the upper half of the cloud field. Abovethe clouds, at solar noon, the higher albedo of the IPMproduces slightly greater absorption. In contrast, the 3Denhancement of absorption occurs lower in the cloudfield where higher concentrations of oxygen combinedwith greater downwelling radiation. At 608, however,much of the radiation that would have reached the lowerlevels of the atmosphere has already been reflected orabsorbed, resulting in slightly higher IPM absorption.

In the upper troposphere, the lightly shaded peak at2.0 mm and the broader feature centered at 2.7 mm arecaused by absorption from CO2. The strong absorptionby CO2 in the 2.7-mm band tends to remove most ofthe radiation before it interacts with water vapor lowerin the atmosphere. However, the implementation of thek-distribution method for a mixture of gases within theframework of this model may produce an inherent errorat this wavelength (see OG98). But the combination ofthe low TOA insolation, complete absorption above 4km, and the lack of any demonstrable differences be-tween the 3DM and IPM computations at this wave-length makes this error, if distinguishable, likely to beinsignificant.

Naturally, the strongest absorption features are causedby water vapor and cloud droplets. Since these two con-stituents represent different phases of water, substantialoverlap occurs in their spectral signature (Fig. 1). Still,the absorption by gases primarily takes place in thesebands, and this concentration dominates the image. Ab-sorption caused by the minor water-vapor absorptionbands is observed in the lower troposphere at 0.59, 0.65,0.72, and 0.82 mm with peaks as high as 48 mW m23

mm21. The major water-vapor bands centered at 0.94and 1.12 mm appear as broad lines producing peak ab-sorption of 58 and 61 mW m23 mm21, respectively.

For these wavelengths at solar noon, peaks in 3D-enhanced absorption reach nearly 10 mW m23 mm21 atan altitude of 2.5 km. Since the 3DM allows photonsto leak from the sides of clouds, there is an increase indownwelling radiation in the lower layers of the at-mosphere. Combined with a greater abundance of watervapor, absorption is increased in these layers. As thesolar zenith angle steepens, however, this effect is re-duced since the direct beam intercepts not only the top

of the cloud, but also the side, effectively increasing theareal coverage of the cloud (Fig. 4a). For spectralregions with substantial absorption, the downwelling en-hancement is further reduced as cloud leakage is damp-ened. For the IPM, as noted previously, the direct beamcannot intercept the side of a cloud, and thus comparingthe two modes, the IPM now allows a larger transmis-sion of energy to the lower portions of the atmospherewhere it can be absorbed by water vapor.

As the single-scattering albedo generally decreasesfurther into the near-infrared at 1.38, 1.87, and 2.7 mm,the task of discerning the separate effects of water vaporand cloud droplets becomes more formidable. At solarnoon, absorption is maximized in the upper portion ofthe cloud field to the extent that little radiation is trans-mitted below 4 km. At 608, the longer pathlength raisesthis cutoff level by a kilometer. Since virtually all theradiation is absorbed in the upper reaches of the cloudfield, differences between the 3DM and IPM are neg-ligible. The continuous features appearing between theabsorption bands are caused by cloud droplets.

For both solar zenith angles of 08 and 608, greaterabsorption by the 3DM is caused by a combination ofwater vapor and cloud droplets. Naturally, the highestabsorption levels (75 mW m23 mm21 at 08) arise wher-ever the cloud is exposed to the direct solar beam. Forthis cloud field, a large proportion of the cloud tops areabove 8 km. The altostratus cloud layer located at analtitude of 6 km is responsible for intense line spreadacross the spectrum from 1.0 to 4.0 mm. Generally,enough energy is available in the near-infrared spectralregions between the atmospheric windows for absorp-tion to occur in all cloud layers between 1 and 10 km.However, for wavelengths greater than 3.0 mm, the lowsolar input and strong absorption properties of clouddroplets prevents the transmission of radiation belowthe altostratus cloud layer.

Most of the 3D-enhanced cloud-droplet absorptiontakes place within the spectral ranges of 1.15–1.30 and1.5–1.8 mm with minor absorption effects between0.95–1.05 and 2.0–2.4 mm. At solar noon, the 3DM hasgreater absorption in the lower half of the cloud fieldwith maximum increases over the IPM ranging between2 and 4 mW m23 mm21. Most of this increase is causedby energy being focused into these regions by leakagefrom clouds at higher altitudes. This leakage out of theclouds, however, actually causes the IPM to produceslightly more absorption at these higher altitudes. Butthe effect is gradually dampened as the wavelength in-creases. At 608, the 3D enhanced absorption is shiftedtoward the upper half of the cloud field with maximumvalues reaching 5 mW m23 mm21. Here, 3D computa-tions allow for the impinging solar beam to strike thecloud side at a higher angle than the IPM. The result isfor some photons to travel farther into the cloud wherethey can become ‘‘trapped’’ and eventually absorbed.

By additionally integrating the absorption along thevertical axis, the spectral dichotomy responsible for the


FIG. 6. Difference between 3DM and IPM spectral computations for (a) total atmosphericabsorption, (b) gaseous absorption, and (c) cloud-droplet absorption at solar zenith angles of 08,308, and 608. Fluxes are integrated for the entire spatial domain.

3D peak enhancement that occurs between 308 and 608becomes clearer. Figure 6 shows the atmospheric ab-sorption partitioned between gases and cloud droplets.For overhead sun, the lower albedo of the 3DM reducesabsorption in the ultraviolet by 8 W m22 mm21, but thisloss is insignificant compared to the enhancement fromabsorption by water vapor in the near-infrared. Withinthe 0.94-mm water-vapor band, increases of 30 W m22

mm21 are observed. For steeper sun angles, the absorp-tion enhancement caused by gases is reduced. However,it is partially compensated by increases in absorption

by cloud droplets. At 608, the 3DM enhancement reach-es 50% at 1.24 and 1.62 mm.

Spectrally integrated, the net compensation is not azero sum since much of the enhancement by gases anddroplets occurs within different spectral regions. Below1.2 mm, for example, the enhancement due to water-vapor absorption is reduced as the solar zenith angleincreases. This reduction is not caused by greater ab-sorption from cloud droplets, but merely is the responseto an increase in 3D albedo. Further into the near-in-frared, a large amount of the enhanced absorption by


FIG. 7. Computations by 3DM for net flux (downwelling–upwelling) at 0.42 mm as a fraction of the TOA insolation. Net flux at eachhorizontal grid cell for altitudes of (a) 11 km, (b) 0.4 km, (d) 20 km, and (e) 15 km. Atmospheric absorption estimate from difference innet fluxes between (c) 11 km and 0.4 km and (f ) 20 km and 15 km. The dark line highlights absorption estimate averaged over 20 km 2 box.

cloud droplets occurs within the atmospheric windowand has no direct effect on absorption by gases. But asthe sun progresses toward the horizon, some of the en-hanced absorption by cloud droplets occurs along theedges of the water vapor bands causing a decrease inabsorption by water vapor.

5. 3D effects on measurements

a. Residual absorption

The measurement of atmospheric absorption cannotbe made directly, but estimated only through the residualof the differences of broadband net fluxes or inferredfrom spectral measurements of albedo, transmission, orboth. All methods, to a degree, are impacted by thespatial characteristics of the cloud fields. An example

of the spatial problems inherent in using the residual ofthe differences of net fluxes is demonstrated in Fig. 7for atmospheric-column absorption between 400 m and11 km and between 15 and 20 km. At each of thesealtitudes, the net flux (downwelling 2 upwelling) as afraction of the TOA insolation is computed. To highlightthe difficulties associated with the residual method,computations are made at 0.42 mm where conservativescattering is dominant. The only absorption occurringat this wavelength is by oceanic aerosol, for which themaximum total atmospheric column absorption is lessthan 0.5% of the TOA insolation. Hence, any valuesabove this level or those that are negative may be con-sidered as an estimate of the error associated with thisspecific cloud morphology. The fluxes for this field arebased on runs of 40 000 000 photons.


TABLE 1. Visible, near-infrared ratio of near-infrared (NIR) to visible albedo and atmospheric absorption for 3DM, IPM, Type II, ISCCP,and Stephens-Cb cloud types.

Cloud type Visible Near-infrared albedo NIR/Vis ratioAtmospheric absorption

(W m22)

3DMIPMType IIISCCPStephens-Cb

0.710.730.770.740.81

0.520.560.630.670.59

0.740.770.830.890.72

214202200176230

max 2 min 0.10 0.15 0.17 54

For the residual method to be applicable, the as-sumption must be made that energy flows vertically andthat horizontal fluxes can be neglected. Since the IPMis based on this assumption, the absorption inferred fromthe net flux agrees with the actual absorption compu-tations. However, for the 3DM, horizontal diffusion dra-matically alters absorption estimates. At 11 km, the netflux appears diffused with the darkest patches emanatingfrom the highest cloud tops where much of the down-welling irradiance is reflected back toward space. Thebrightest areas are represented by columns that are voidof clouds. Although the values approach 50% of theTOA insolation, the maximum would be much greaterif photons were not scattered into these columns fromadjacent cloudy cells. At 400 m, the diffusion is lesspronounced since the variation in the distance betweenthis layer and the cloud base is much smaller than it isbetween the 11-km layer and the cloud tops. Peak valuesnear 1.2 occur for clear columns where the direct beamsolar radiation is supplemented by the downward leak-age of radiation from adjacent cloudy cells.

By subtracting the net flux at 400 m from the net fluxat 11 km, the absorption is obtained. Since the actualmaximum absorption is less than 0.5% of the TOA in-solation, it is obvious that for the horizontal scale ofindividual columns (800 m 3 800 m) the use of theresidual of the differences of net fluxes for determiningabsorption is impossible. As shown, the absorption rang-es from a positive 20% to a negative 80% in the clearcolumns. This pseudo-production of energy in clear skycomes at the expense of radiation diffused out of theclouds. On a larger spatial scale of 20 km 3 20 km foran entirely cloudy column (outlined box), an absorptionof 7% is still indicated. Taken over the entire spatialdomain the absorption is only 0.2% since the modelemploys cyclic boundaries to maintain continuity offluxes.

Even for layers completely void of clouds, the effectsof an underlying cloud field on the estimate of absorp-tion can be significant. Comparing the net fluxes at 15and 20 km, it is clear that the degree of diffusion oc-curring in a given layer depends on the distance betweenthat layer and the scattering location of the radiation.Thus, in the presence of clouds in the atmosphere, notwo different vertical layers can share the same radiationpattern. This assured spatial incoherence produces ab-

sorption estimates up to 10% for atmospheric layersbetween 15 and 20 km where nominally the absorptionis nil. The results presented here represent a rather ex-treme case, and for less complex cloud fields andthrough prudent spatial and temporal averaging, the er-rors associated with estimating absorption based on theresidual of the differences of net fluxes can presumablybe reduced.

b. Near-infrared to visible albedo ratio

As proposed by Stephens (1996), the near-infrared tovisible albedo ratio provides a criterion on the effectsclouds have on the absorption of solar radiation. Directmeasures of this ratio for layered clouds range between0.68 and 0.95 (Hayasaka et al. 1995; Stephens 1996).In Table 1, the visible and near-infrared albedo, the al-bedo ratio, and the atmospheric absorption are listed forthe 3DM and IPM computations. Additionally, resultsfrom three plane-parallel tropical cloud parameteriza-tions are included. As explained in Part I, it is not pos-sible to produce exact plane-parallel equivalents to the3D cloud field. Thus, different parameterizations usedare: ISCCP (Fig. 9b in Rossow and Schiffer 1991), Ste-phens-Cb (Stephens 1978), and a plane-parallel cloudusing the mean cloud-base altitude, geometric thickness,effective radius, and liquid water content of the 3Dcloud field (Type II). The results from each cloud rep-resentation are combined with those for the 9% clearsky. The outcomes listed in the table represent quantitiesaveraged over daylight hours.

As shown in Table I, all of the ratios for the near-infrared to visible albedo fall within the limits of ob-servations. The 3DM and IPM albedo results are rela-tively close at 0.74 and 0.77, respectively. Without theslight compensatory effect of a lower visible albedo forthe 3DM, the difference between the two would be 0.06rather than 0.03. Since the 3D-enhanced absorption rep-resents much less than half the values recently reported,the ratio is not expected to approach the 0.5 ratio sug-gested by Stephens (1996) as the maximum level ca-pable of reproducing these findings. However, a com-parison between the plane-parallel results for the Ste-phens-Cb and ISCCP representation reveals an intrigu-ing element of Stephens (1996) assertion.

Both of these clouds represent large convective cells,


FIG. 8.(a) Inferred mean optical thickness of cloud field from thematching of plane-parallel computations of 0.62-mm TOA albedo tothat of IPM (light gray) and 3DM (dark gray) model results. Effectiveradius of plane-parallel cloud is held constant at 11.7 mm. Inferredmean effective radius of cloud field from the matching of plane-parallel computations of (b) 2.13-mm TOA albedo to that of IPM(light gray) and 3DM (dark gray) model results. Optical thickness ofplane-parallel cloud is held constant at t 5 102. Results are shownfor solar zenith angles of 08, 308, and 608.

FIG. 9. Ratio of 0.94 to 1.53 mm spectral bands for (a) columnabsorption, (b) transmission to surface, and (c) TOA albedo. Resultsof 3DM and IPM computations are expressed as the cosine of thesolar zenith angles 08, 158, 308, 458, 608, and 758.

but because the Stephens-Cb (re 5 32 mm) has largercloud droplets than the ISCCP (re 5 10 mm), it absorbs54 W m22 more solar radiation (daylight average). Al-though this difference in absorption is near the level ofthe discrepancy between model computations and ob-servations recently suggested, the ratio for the Stephens-Cb is 0.72: only 0.17 less than that for ISCCP. Thus, itbecomes clear that not all plane-parallel clouds areequal, and that the means by which clouds are repre-sented may account for part of the discrepancy betweenmeasurement and theory.

c. Inferred cloud microphysical properties

As noted in the background, part of the impetus be-hind the issue of enhanced absorption arose from thedifficulty in reconciling in situ measurements of cloudmicrophysical properties from those inferred from re-flectance data. To examine the issue further, the simu-lated spectral albedo from the IPM and 3DM compu-tations are compared to those from a plane-parallel cloudmodel (Type II) to infer cloud microphysical properties.In reality, such methods would employ reflectance at aspatial resolution higher than that used in this exercise,but the results should provide a gauge on the upperbounds of the error associated with the plane-parallelassumption for retrieving cloud microphysical proper-ties.

To estimate cloud optical thickness, the liquid water

content of the plane-parallel cloud is adjusted until thealbedo at 0.62 mm matches that computed from eitherthe IPM or 3DM. As shown in Fig. 8a, the use of theplane-parallel assumption can have a dramatic effect onthe retrieval of cloud optical thickness for a morpho-logically complex cloud field. From Table 1, the dif-ference between the plane-parallel and either the IPMor 3DM computations represent less than a 10% reduc-tion in the visible albedo. Due primarily to the nonlinearrelationship between bulk radiative properties and op-tical thickness, however, the estimated optical thicknessvalue retrieved is approximately one-half that of theactual optical thickness of the cloud field, t 5 102. Inaddition, the inferred optical thickness increases withsolar zenith angle. This tendency agrees with the resultsof Loeb and Davies (1996), who found a systematic biaswith solar zenith angle using a plane-parallel model to


retrieve cloud optical thickness from Earth RadiationBudget Experiment satellite observations.

To estimate cloud-effective radius, the same tech-nique is used, but the wavelength is changed to the near-infrared, and the effective radius of the plane-parallelcloud is varied while the optical thickness is held con-stant. At 2.13 mm, the effective radius inferred from theIPM albedo is virtually identical to the mean effectiveradius (11.7 mm) of the 3D cloud field (Fig. 8b). Thisfinding is rather surprising, considering that the effectiveradius of cloud droplets in the cloud tops within thisfield varies between 4.4 and 16 mm. Based on the 3DMalbedo at 2.13 mm, the estimated effective radius is 17mm at solar zenith angles of 08 and 308 and reaches 23mm at 608. It is not the nonlinear relationship betweenbulk radiative properties and optical thickness that isimportant here. Rather, the 3D enhancement of absorp-tion by cloud droplets produces the discrepancy betweeninferred and actual cloud microphysical properties.

d. Enhanced absorption

As demonstrated in model simulations, the effect ofcloud morphology on the radiative field varies spectrallyand according to the angle of the sun. For high solarangles, cloud morphology produces an increase in ab-sorption in the spectral regions of gaseous absorptionand to a smaller degree, enhances absorption by clouddroplets within the near-infrared atmospheric windows.As the sun approaches the horizon, the absorption bycloud droplets increases and encroaches upon the water-vapor absorption bands to the point where a reductionin absorption by water vapor occurs at several wave-lengths. As shown in Fig. 9a, the 0.94 to 1.53 mm ab-sorption ratio shows a strong divergence between theIPM and 3DM fluxes with increasing solar zenith angle.When related to the angle of the sun, this spectral ab-sorption differential provides an observable spectral sig-nature in atmospheric transmission (Fig. 9b) and albedo(Fig. 9c) ratios. These ratios can serve as an indicationof the 3D effect, but they should be convolved with anestimate of the cloud field optical thickness, as a signalof the same magnitude could theoretically be producedby variations in the optical properties of a plane-parallelcloud over time.

6. Conclusions

For the cloud field used in this investigation, it isshown that cloud morphology reduces absorption in theUV and increases absorption in the gaseous absorptionbands for overhead sun. At steeper solar zenith angles,the enhanced absorption spectrally shifts to the near-infrared atmospheric windows, where increases up to50% in absorption by cloud droplets are obtained. Whilethere is no change in absorption in the visible, the 3Deffect is shown to produce false estimates of cloudycolumn absorption based on residual net fluxes in this

spectral region. Therefore, it is not unreasonable to as-sume that part of the cloud absorption ‘‘anomaly’’ maybe tied to the issue of spatial sampling. Although thisproblem is not unknown, the approaches taken to min-imize this effect are debatable. Additionally, as dem-onstrated, spectral measurements of cloud albedo, whichare considered to be more reliable, are not immune tocloud heterogeneity. Hence, to understand the radiativeeffects of clouds, broadband and spectral, it is essentialto have an appreciation of the interdependent nature ofcloud microphysical and macrophysical properties. Theconvoluted interaction between processes occurring atthese two extremely different scales provides a partialexplanation for the differences found between theoryand observation of atmospheric absorption in the pres-ence of clouds and for the related discrepancies betweenremotely sensed estimates of cloud microphysical prop-erties and in situ measurements.

Acknowledgments. We are grateful to Dr. Paul Ric-chiazzi for his valuable insight and assistance with im-plementation of the LOWTRAN-7 routines. This re-search has been funded in part by Department of EnergyGrants 90ER61062 and 90ER61986, National ScienceFoundation Grant ATM-9319483, and National Aero-nautics and Space Administration Grant NAGW-31380.

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