assessing 1d atmospheric solar radiative transfer models ...j. li meteorological service of canada,...

2676 VOLUME 16J O U R N A L O F C L I M A T E

q 2003 American Meteorological Society

Assessing 1D Atmospheric Solar Radiative Transfer Models: Interpretation andHandling of Unresolved Clouds

H. W. BARKER,a G. L. STEPHENS,b P. T. PARTAIN,b J. W. BERGMAN,c B. BONNEL,d K. CAMPANA,e

E. E. CLOTHIAUX,f S. CLOUGH,g S. CUSACK,h J. DELAMERE,g J. EDWARDS,h K. F. EVANS,i Y. FOUQUART,d

S. FREIDENREICH,j V. GALIN,k Y. HOU,e S. KATO,l J. LI,m E. MLAWER,g J.-J. MORCRETTE,n W. O’HIROK,o

P. RAISANEN,p V. RAMASWAMY,j B. RITTER,q E. ROZANOV,r M. SCHLESINGER,r K. SHIBATA,s P. SPORYSHEV,t

Z. SUN,u M. WENDISCH,v N. WOOD,b AND F. YANGr

aMeteorological Service of Canada, Downsview, Ontario, CanadabColorado State University, Fort Collins, Colorado

cNOAA–CIRES Climate Diagnostics Center, Boulder, ColoradodLaboratoire d’Optique Atmospherique, Lille, France

eNational Centers for Environmental Prediction, Camp Springs, MarylandfThe Pennsylvania State University, University Park, PennsylvaniagAtmospheric Environmental Research, Lexington, Massachusetts

hMet Office, Bracknell, Berkshire, United KingdomiUniversity of Colorado, Boulder, Colorado

jGFDL, Princeton University, Princeton, New JerseykDNM, Moscow, Russia

lHampton University, and NASA Langley Research Center, Hampton, VirginiamMeteorological Service of Canada, Victoria, British Columbia, Canada

nECMWF, Reading, United KingdomoUniversity of California, Santa Barbara, Santa Barbara, California

pUniversity of Helsinki, Helsinki, FinlandqDeutscher Wetterdienst, Offenbach am Main, Germany

rUniversity of Illinois at Urbana–Champaign, Urbana, IllinoissMeteorological Research Institute, Ibaraki-ken, Japan

tVoeikov Main Geophysical Observatory, St. Petersburg, RussiauBureau of Meteorology, Melbourne, Australia

vInstitute for Tropospheric Research, Leipzig, Germany

(Manuscript received 8 April 2002, in final form 12 February 2003)

ABSTRACT

The primary purpose of this study is to assess the performance of 1D solar radiative transfer codes that areused currently both for research and in weather and climate models. Emphasis is on interpretation and handlingof unresolved clouds. Answers are sought to the following questions: (i) How well do 1D solar codes interpretand handle columns of information pertaining to partly cloudy atmospheres? (ii) Regardless of the adequacy oftheir assumptions about unresolved clouds, do 1D solar codes perform as intended?

One clear-sky and two plane-parallel, homogeneous (PPH) overcast cloud cases serve to elucidate 1D modeldifferences due to varying treatments of gaseous transmittances, cloud optical properties, and basic radiativetransfer. The remaining four cases involve 3D distributions of cloud water and water vapor as simulated bycloud-resolving models. Results for 25 1D codes, which included two line-by-line (LBL) models (clear andovercast only) and four 3D Monte Carlo (MC) photon transport algorithms, were submitted by 22 groups.Benchmark, domain-averaged irradiance profiles were computed by the MC codes. For the clear and overcastcases, all MC estimates of top-of-atmosphere albedo, atmospheric absorptance, and surface absorptance agreewith one of the LBL codes to within 62%. Most 1D codes underestimate atmospheric absorptance by typically15–25 W m22 at overhead sun for the standard tropical atmosphere regardless of clouds.

Depending on assumptions about unresolved clouds, the 1D codes were partitioned into four genres: (i)horizontal variability, (ii) exact overlap of PPH clouds, (iii) maximum/random overlap of PPH clouds, and (iv)random overlap of PPH clouds. A single MC code was used to establish conditional benchmarks applicable toeach genre, and all MC codes were used to establish the full 3D benchmarks. There is a tendency for 1D codesto cluster near their respective conditional benchmarks, though intragenre variances typically exceed those forthe clear and overcast cases. The majority of 1D codes fall into the extreme category of maximum/randomoverlap of PPH clouds and thus generally disagree with full 3D benchmark values. Given the fairly limitedscope of these tests and the inability of any one code to perform extremely well for all cases begs the questionthat a paradigm shift is due for modeling 1D solar fluxes for cloudy atmospheres.

1. Introduction and objectives

Much of the rich structure of the earth’s climate canbe traced to interactions between radiation and the four-

Corresponding author address: Dr. Howard Barker, Cloud PhysicsResearch Division (ARMP), Meteorological Service of Canada, 4905Dufferin St., Downsview, ON M3H 5T4, Canada.E-mail: [email protected]

dimensional distribution of the three phases of water.While representation in large-scale atmospheric models(LSAMs) of all such interactions deserves attention andwork, those involving clouds are recognized generallyas notoriously difficult and in need of much work (e.g.,Houghton et al. 1995). This recognition stems from theobvious limitations of modeling unresolved clouds andradiative transfer in LSAMs along with numerical ex-periments that show that seemingly small systematic

15 AUGUST 2003 2677B A R K E R E T A L .

changes in cloud properties have significant impacts onsimulated regional and global climate (e.g., Senior1999). Moreover, studies that intercompared cloud ra-diative feedbacks in LSAMs (Cess et al. 1996, 1997)came to the conclusion that different representations ofcloud-related processes in LSAMs may account formuch of the uncertainty associated with estimates ofclimate sensitivity.

Preceding and overlapping the Cess et al. studies, andother LSAM intercomparisons (Lambert and Boer2001), was the Intercomparison of Radiation Codes inClimate Models (ICRCCM) program (World ClimateResearch Programme 1984; Ellingson and Fouquart1991; Fouquart et al. 1991). Fouquart et al. (1991) dem-onstrated that when several 1D atmospheric solar ra-diative transfer codes operated on the same atmosphericprofile, the range of estimated irradiances often ex-ceeded 20% with root-mean-square differences relativeto medians of typically 4%–10%; single-layer homo-geneous overcast clouds and aerosols showed the largestdisparities.

ICRCCM’s main message to climate modeling groupswas that their solar codes may be imparting fictitiousradiative forcings that, in all likelihood, have adverseeffects on simulated climate. A logical question leadingfrom these results is as follows: since different radiationcodes operating on identical (and simple) atmosphericcolumns yield significantly different irradiance profiles,how much of the disparity in estimates of climate sen-sitivity is due to different treatments of radiative trans-fer? To this day, this question remains unexplored.

Since ICRCCM, most codes have been modified tobetter resolve the solar spectrum, spectroscopic data-bases have been updated [high-resolution transmissionmolecular absorption database (HITRAN) upgrades],and new gaseous transmittance and cloud optical prop-erty parametrizations have become active (e.g., Hu andStamnes 1993; Fu and Liou 1993; Edwards and Slingo1996). Yet, most codes are built on the extreme, ide-alistic, systematic assumption of maximum/randomoverlap of homogeneous clouds (Geleyn and Hollings-worth 1979). Over the past two decades, however, sev-eral studies have demonstrated that different overlapconfigurations have major impacts on simulated radia-tion budgets (e.g., Morcrette and Fouquart 1986; Stu-benrauch et al. 1997; Barker et al. 1999). Likewise,when horizontal fluctuations in cloud are neglected, es-timates of domain-averaged irradiances can be in seriouserror (e.g., Cahalan et al. 1994a; Barker et al. 1996,1999; Pincus et al. 1999). There are far fewer, and in-conclusive, assessments of ensuing dynamical impacts(Tiedtke 1996; Liang and Wang 1997; Morcrette 1993).This is because multilayer 1D solar codes that handlecloud horizontal and vertical variability have only begunto be tested (e.g., Barker and Fu 2000), and also becausethe additional input they require is unavailable as yet.Clearly, there is a need to develop both parameteriza-

tions for characterizing unresolved clouds and 1D ra-diative transfer algorithms that utilize them.

Given developments in modeling radiative transfersince ICRCCM and given no formal indication of how1D solar codes respond to the general scenario of mul-tiple layers of nonovercast clouds, it seems timely toinitiate a follow-on to ICRCCM. Thus, the primary ob-jective of this study is to assess how well operational,and experimental, 1D solar radiative transfer codes pre-dict broadband irradiances and heating rate profileswhen they operate on columns of information pertainingto partially cloudy atmospheres generated by 3D cloud-resolving models.

Before this objective can be realized, however, it isessential that clear-sky (i.e., cloud and aerosol free) andplane-parallel, homogeneous (PPH) overcast clouds beconsidered first. This is because variances and biasesfor simple cases carry over to complicated cloud cases.As it was never the intention of this study to repeatICRCCM, the number of clear-sky and homogeneousovercast cloud cases considered here is minimal. Hence,this study is more an extension of ICRCCM rather thana repeat.

The second section outlines some details of this in-tercomparison. The third and fourth sections present themodel atmospheres, benchmark calculations, and inter-comparison results for simple and complex atmo-spheres. The fifth section contains conclusions.

2. Participation and general conditions

Tables 1–4 list participants and properties of theirmodel(s). Results were submitted for 25 1D solar codesand four 3D Monte Carlo (MC) codes. Most partici-pants completed calculations for 12 atmospheric pro-files, though results for only 7 cases are presented here.For all cases, calculations were performed for solarzenith angle cosines m 0 from 0.05 to 1.0, in incrementsof 0.05, with spectrally invariant (Lambertian) surfacealbedo as of 0.2. In contrast, ICRCCM used m 0 of 0.26and 0.866 with as of 0.2 and 0.8. Each participant wasasked to provide top-of-atmosphere (TOA) albedo ap ,total atmospheric absorptance aatm , and surface ab-sorptance asfc for each m 0 integrated spectrally acrosswavelength intervals 0.2–0.7, 0.7–5.0, and 0.2–5.0 mm,neglecting terrestrial emission. Upwelling and down-welling irradiances were also requested at each modellevel for the spectral range 0.2–5.0 mm at m0 5 0.25,0.5, and 1.0.

In all cases, cloud optical properties were modeledas pure liquid water spheres with effective radius re 510 mm, even when it was obvious that cloud watershould have been either ice or precipitation. This avoid-ed ambiguity in specifying ice crystal structure, precip-itation size distributions, and associated spectral opticalproperties. Another intercomparison might inform par-ticipants about the presence of clouds and have themset the optical properties. This may work with codes


TABLE 1. Participants that submitted results for 1D codes.

Participant Affiliation Code abbreviation

H. Barker Meteorological Service of Canada, Downsview, ON, Canada MSC1J. Bergman NOAA–CIRES Climate Diagnostics Center, Boulder, CO CDCJ. Edwards and S. Cusack Met Office, Bracknell, Berkshire, United Kingdom MOY. Fouquart and B. Bonnel Laboratoire d’Optique Atmospherique, Lille, France LOAS. Freidenreich and V. Ramaswamy GFDL, Princeton University, Princeton, NJ GFDLV. Galin DNM, Moscow, Russia DNMY. Hou and K. Campana National Centers for Environmental Prediction, Camp

Springs, MDNCEP

S. Kato NASA Langley, Hampton, VA LaRCJ. Li Meteorological Service of Canada, Victoria, BC, Canada MSC2E. Mlawer, J. Delamere, and S. Clough Atmospheric Environmental Research, Lexington, MA AERJ.-J. Morcrette ECMWF, Reading, United Kingdom ECMWFP. Raisanen University of Helsinki, Helsinki Finland UOHB. Ritter Deutscher Wetterdienst, Offenbach am Main, Germany DWE. Rozanov and M. Schlesinger University of Illinois at Urbana–Champaign, Urbana, IL UIUCK. Shibata Meteorological Research Institute, Ibaraki-ken, Japan MRIP. Sporyshev Voeikov Main Geophysical Observatory, St. Petersburg,

RussiaVMGO

Z. Sun Bureau of Meteorology, Melbourne, Australia BOMM. Wendisch Institute for Tropospheric Research, Leipzig, Germany IFTG. Stephens, P. Partain, and N. Wood Colorado State University, Fort Collins, CO CSU

TABLE 2. Participants that submitted results for 3D Monte Carlo codes.

Participant Affiliation Code abbreviation

H. Barker Meteorological Service of Canada, Downsview, ON,Canada

MSC

E. E. Clothiaux The Pennsylvania State University, University Park, PA PSUK. F. Evans University of Colorado, Boulder, CO UCW. O’Hirok University of California, Santa Barbara, Santa Barbara, CA UCSB

used in operational LSAMs, but many participatingcodes lacked such automation. On the other hand, hadspecific optical properties been assigned, numerous setswould have been required to facilitate all combinationsof spectral intervals (see Table 3). Finally, while allcloud particles were assumed to be liquid spheres withre 5 10 mm, individuals were free to generate corre-sponding spectral optical properties but requested to usethe Henyey–Greenstein (1941) phase function when ap-plicable.

3. Clear-sky and homogeneous overcast clouds

The purpose of this section is twofold. First, it isessential to demonstrate that the 3D Monte Carlo al-gorithms used to set benchmarks for the complex 3Dcloud fields agree both among themselves and with adetailed line-by-line (LBL) model that was designatedas the benchmark for the simple atmospheres. As yet,LBL models cannot perform 3D radiative transfer cal-culations for complicated atmospheres to benchmarkstandards (Partain et al. 2000). Therefore, 3D radiativetransfer codes must be compared to LBLs for simpleconditions. If the 3D codes perform well for simpleconditions, this bolsters confidence in them as providersof benchmarks for complex cloud cases. The second

point of this section is to establish ranges of 1D coderesults for simple conditions.

a. Description of cases

For the single clear-sky (denoted as CLEAR) and twohomogeneous overcast clouds, the McClatchey et al.(1972) tropical (TRO) atmosphere was used. This at-mospheric profile consists of 64 layers, extends fromthe surface to ;100 km, and has prescribed values ofpressure, temperature, density, water vapor, and ozonemixing ratios. Carbon dioxide mixing ratio was set to360 ppm and it was suggested that oxygen be includedtoo.

The first cloudy case, denoted as CLOUD A, usedthe TRO clear-sky atmosphere, but the layer between3.5 and 4 km was filled with a uniform overcast cloudwith c 5 0.159 g kg21. For pure liquid spherical drop-qlets with re 5 10 mm, visible optical depth was ;10(Slingo 1989). The second cloudy case, CLOUD B, wasa uniform overcast cloud positioned between 10.5 and11 km with c 5 0.034 g kg21, which gives a visibleqoptical depth of ;1. Thus, CLOUDs A and B resembleclosely cases 49 and 46 of Fouquart et al. (1991).


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TABLE 4. Characteristics of 3D Monte Carlo codes. Here Ns denotes the number of spectral intervals. Participant abbreviations expandedin Table 2.

Participant Ns Spectral gas transmission Cloud optics References

MSCUCPSUUCSB

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MieMieMieMie

Barker et al. (1999)Benner and Evans (2001)Kato et al. (1999)O’Hirok and Gautier (1998); S Yang et al. (2000)

FIG. 1. (a) Difference between direct-beam spectral irradiancesestimated by AER’s LBL radiative transfer model (LBLRTM) andmeasured by the RSS spectrometer; (b) difference between diffusespectral irradiances estimated by AER’s CHARTS model and mea-sured by the RSS spectrometer. Shaded regions represent confidencelimits (after Mlawer et al. 2000). Measurements were made at ARM’sSGP site on 18 Sep 1997. Cosine of solar zenith angle was 0.21 andthere was 4.2 cm of precipitable water.

b. Benchmark calculations

It is essential for this study to demonstrate that resultsdesignated as benchmarks are indeed such. Mlawer etal. (2000) compared the LBL developed at AtmosphericEnvironmental Research, Inc. (AER), known as theCode for High-Resolution Accelerated Radiative Trans-fer (CHARTS), to high-quality spectral surface irradi-ance measurements made at the U.S. Department of En-ergy Atmospheric Radiation Measurement (ARM) Pro-gram Southern Great Plains (SGP) site (e.g., Stokes andSchwartz 1994) by the Rotating Shadowband Spectro-radiometer (RSS; Harrison et al. 1999) and the AbsoluteSolar Transmittance Interferometer (ASTI; Murcray etal. 1996; Mlawer et al. 2000). In these comparisons,atmospheric profiles were based on coincident sound-ings (cf. Brown et al. 1999; Clough et al. 1989). Whileaerosol optical properties were unknown, values of sin-gle-scattering albedo and asymmetry parameter requiredby CHARTS to yield errors in spectral diffuse irradiancealways less than 5% were consistent with recognizedaerosol models (Kato et al. 1997).

Figure 1 shows an example of how well CHARTSperformed for a small m0 and heavy water vapor burden.While these experiments had adequate radiometric mea-surements available only at the surface, photons con-tributing to surface irradiance typically experience thelongest paths and most scattering events. Thus, it is

difficult to imagine being able to predict spectral surfaceirradiance as well as in Fig. 1 and have poor corre-sponding estimates of ap and aatm. It may, therefore, besafe to say that CHARTS represents the modeling stan-dard for clear skies; identification of such a standardwas not possible during ICRCCM.

For the current study, CHARTS employed opticalproperties for homogeneous overcast clouds based onMie scattering calculations (Wiscombe 1979, 1980) us-ing refractive indices from Segelstein (1981) integratedspectrally over 5-nm intervals for a gamma distributionof droplets with re 5 10 mm and effective variance of0.1.

Due to time and resource constraints, CHARTS com-pleted only a limited set: m0 5 0.25, 0.5, and 1.0 forthe simple cases. Figure 2a shows broadband values ofap, aatm, and asfc as functions of m0 for the CLEARexperiment from CHARTS and the four MC codes. Thisshows that the MC codes agree extremely well amongthemselves and that relative deviations from CHARTSrarely exceed 62%. These results are corroborated inTable 5a, which lists broadband, visible, and near-IRvalues of ap, aatm, and asfc for m0 5 0.5.

Establishing cloudy-sky benchmarks was more dif-ficult. First, since three of the four MC codes have mod-erate spectral resolution, their cloud optical propertiesdepend on spectral weighting (e.g., Li et al. 1997). Sec-ond, underlying assumed droplet size distributions var-ied slightly though all used re 5 10 mm. Despite theseuncertainties, Figs. 2b,c show that the MC codes andCHARTS agree almost as well as in the CLEAR ex-periment. For CLOUD A, estimates of ap and aatm differslightly and stem from different droplet optical prop-erties and spectral weightings. The mean number of pho-ton scattering events (averaged over all m0 and wave-lengths) for CLOUD B is ;3, while for CLOUD A itis ;17. This explains why minor differences in cloudoptical properties are apparent in results for CLOUD A.

Tables 5b,c list broadband, visible, and near-IR valuesfor CLOUDs A and B at m0 5 0.5 for the MC codesand CHARTS. While broadband MC results differ fromCHARTS by always ,4%, differences climb to ;9%for the near-IR band. Table 6 lists heating rates in thecloudy layers of CLOUDs A and B for the MC codesand CHARTS. Overall, these results suggest that theMC codes can be used to assess the 1D codes.

c. Contrast with ICRCCMFigure 3 shows root-mean-square (rms) differences

relative to the median for all 1D results, as well as the


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←

FIG. 2. Broadband values of TOA albedo ap, atmospheric absorp-tance aatm, and surface absorptance asfc predicted by the four MCmodels and CHARTS as functions of m0 for the CLEAR, CLOUDA, and CLOUD B atmospheres.

range of broadband values of ap, aatm, and asfc. Availablecorresponding values for aatm and asfc from ICRCCMare also indicated. For the CLEAR case, both rms andrange are remarkably similar to ICRCCM values. Note,however, that most of the codes documented here werelow spectral resolution while in ICRCCM about halfwere classified as high resolution.

For CLOUD A, estimates of aatm are much more con-sistent than they were in ICRCCM. This may be due tothe current widespread use of a small number of cloudoptical property parameterizations (e.g., Slingo 1989;see Table 2), though it is interesting to note that par-ticipants here were only told to use re 5 10 mm, whilein ICRCCM they were given exact size distributions.The cohesion of ap seen for CLOUD A degrades forCLOUD B and the corresponding range increases by afactor of ;2. It is not clear why this is the case as bothCLOUDs A and B were both specified to be liquid phasewith re 5 10 mm. Save for aatm for CLOUD A, rms’sand ranges for aatm and asfc for CLOUDs A and B areup slightly from ICRCCM levels.

d. Results: Clear sky

Figures 4a–c show median values and interquartileranges (the range containing 25% of all results eitherside of the median) for ap, aatm, and asfc as functions ofm0 for the 1D models in the CLEAR experiment. It alsoshows results from the Pennsylvania State University(PSU) MC as it could be partitioned at ;0.7 mm. AsTable 5 shows, the PSU model represents the other MCswell. Broadband ap for the 1D codes agree very wellwith the benchmarks though they show a tendency tounderestimate aatm and overestimate asfc. Compared tothe models of 10–15 years ago, most 1D codes in usetoday predict slightly more aatm and slightly less asfc andap [see Table 9 in Fouquart et al. (1991)]. The over-estimates of asfc shown here are, however, similar inmagnitude to those shown by Kinne et al. (1998). Theparticularly good agreement in the visible portion of thespectrum probably stems from better parameterizationsof Rayleigh scattering [cf. Fouquart et al.’s (1991) Fig.4]. For the near IR, however, there is a marked under-estimation of aatm in step with an equally severe over-estimation of asfc. This makes sense for when surfacealbedos are low (as in this case); transmitted photonstend to have longer optical pathlengths than reflectedphotons. Hence, weak atmospheric absorptance is ex-pected to show more in the transmitted field than thereflected field.


TABLE 6. Heating rates (K day21) for the cloudy layer in theCLOUD A (low cloud) and CLOUD B (high cloud). Results for UCwere not directly applicable and so were omitted. MSC, UCSB, andPSU defined in Table 2.

CLOUD A

m0

1D overall

(25%) Median (75%) CHARTS

3D Monte Carlo

MSC UCSB PSU

0.250.51.0

(2.30)(6.25)

(14.70)

2.566.81

16.56

(2.89)(7.48)

(18.33)

2.216.23

15.79

2.506.94

17.20

2.086.12

15.77

2.587.03

17.16

CLOUD B0.250.51.0

(3.40)(5.25)(6.93)

4.026.298.30

(4.23)(6.71)(8.63)

4.066.477.96

4.086.588.09

3.555.917.47

3.896.187.45

The difference between benchmark and 1D medianvalues of broadband aatm can be described by

1D 3Da 2 a [ Da ø 20.012m ,atm atm atm 0 (1a)

which has a (spherical) mean value of1

Da 5 2 Da m dm ø 20.008. (1b)atm E atm

0

This implies that, when integrated over the sun-up pe-riod, a typical 1D code in use today underestimates aatm

by ;11 W m22 for clear-sky tropical conditions. Sincethe linear relation Daatm 5 bm0 is so well defined, thissuggests that the magnitude of b will apply for some-what smaller water vapor burdens too. Thus, the un-derestimations shown here tend to echo those reportedby Arking (1999) and are almost certainly due to lackof a water vapor continuum (Mlawer et al. 2000). Sev-eral models using gaseous transmittance parameteriza-tions based on old spectroscopic databases and no watervapor continuum follow closely Daatm ø 20.02m0,which translates into underestimates of diurnal meanatmospheric absorption of about 18 W m22. For over-head sun, some models underestimate atmospheric ab-sorption by 40 W m22.

Figure 4d shows the three quartiles for 1D heatingrates at m0 5 0.5 as well as the mean and standarddeviation for the benchmark codes. Below ;350 mb,benchmark values are systematically larger than the vastmajority of 1D estimates. This points to water vaporlines and continuum not included, or represented poorly,in old spectroscopic databases upon which many 1Dmodels are based. The 3D codes used here employ pa-rameterizations based on newer databases that includethe continuum.

e. Results: Planar, overcast clouds

Figures 5 and 6 show quartiles of ap, aatm, and asfc

as functions of m0 for the 1D models for CLOUDs Aand B. For both clouds, ap predicted by most 1D codes

are greater than the benchmarks for high sun and lessfor low sun regardless of spectral range. The overesti-mation at large m0 is particularly evident in the near IRand is likely tied to too little aatm, which carries overfrom CLEAR. It may also be associated with widespreaduse of Slingo’s (1989) parameterized asymmetry param-eter, which, as discussed later, is too small across mostof the solar spectrum. Also, about 1–2 W m22 of thisunderestimation likely stems from extensive use of two-stream approximations (Raisanen 2002). Likewise, un-derestimation of ap at small m0 resembles errors inherentin delta-two-stream approximations (King and Harsh-vardhan 1986).

Regarding aatm, the 1D codes do fairly well in thevisible range, but in the near IR and integrated over theentire spectrum, they underestimate systematically rel-ative to both the 3D codes and CHARTS by amountssimilar to those for CLEAR, the exception beingCLOUD B at small m0 where cloud transmittances (i.e.,asfc) are too large due again to the predominance of deltatwo streams.

Table 6 lists heating rates for the cloud layer for all3D models and CHARTS, as well as the quartile rangesfor the 1D codes. Somewhat contrary to aatm, as shownin Figs. 5 and 6, heating rate estimates for clouds by1D models are quite good. Clear relations could not beidentified between spectral resolution, optical propertyparameterization, and cloud heating rate. It is possiblethat empirical alterations to droplet single-scattering al-bedos in low-resolution codes have countered excessiveabsorption that is known to plague these models (Slingo1989).

A comment on cloud optical property parameteri-zation is warranted at this stage. Figure 7 shows high-resolution values of single-scattering albedo v 0 andasymmetry parameter g computed by Mie theory(Wiscombe 1979, 1980) using refractive indices fromSegelstein (1981) for a gamma droplet size distri-bution with re of 10 mm and effective variance of 0.1.Also shown are estimates from Slingo’s (1989) andHu and Stamnes’s (1993) parameterizations at re 510 mm. Though differences are fairly minor for v 0 ,Slingo’s values for g are systematically low by ;0.02across the entire visible and near IR, which will yieldclouds that are too reflective. A difference of 0.02may sound small, but re 5 6 mm is required to bringHu and Stamnes’s estimates of g into agreement withSlingo’s at re 5 10 mm. A difference of 4 mm in re

is larger than what is expected to have occurred inthe most polluted regions over the industrial era dueto increased sulphate aerosol concentrations (e.g.,Lohmann and Feichter 1997).

As Table 2 shows, Slingo’s parameterization is es-pecially popular despite Hu and Stamnes’s being ap-plicable over a wider range of re. This is likely due toHu and Stamnes’s use of noninteger exponents, whichdegrade computational efficiency to a point that is, ap-


FIG. 3. (left) The rms differences relative to the median among all 1D codes and (right) ranges of 1Dmodel results for ap, aatm, and asfc as functions of m0 for the (top) CLEAR, (middle) CLOUD A, and (bottom)CLOUD B atmospheres (as indicated on the left of the plots). Lines are for the present study while dotsrepresent corresponding ICRCCM values of aatm and asfc.

parently, unacceptable for GCMs and numerical weatherprediction (NWP) models. There exists, however, anunpublished third-order polynomial version of Hu andStamnes’s parameterization (Y. Hu 1996, personal com-

munication) that is efficient when Horner’s algorithm isapplied. Finally, Hu and Stamnes’s parameterization ex-hibits minor discontinuities at certain re where fittedcoefficients change.


FIG. 4. (a) Median (50% quartile) values for 1D models of TOA albedo ap as functions of m0 for the CLEAR atmosphere for three spectralranges: 0.2–0.7 mm (blue), 0.7–5.0 mm (red), and 0.2–5.0 mm (black). Also shown are corresponding 25% and 75% quartiles and benchmarkvalues for one of the MC codes and CHARTS. (b) As in (a) except for atmospheric absorptance aatm. (c) As in (a) except for surfaceabsorptance asfc. (d) Three quartile values (25%, 50%, 75%) for 1D model heating rates as a function of pressure at m0 5 0.5. Also shownis the median value for the 3D MC codes with error bars representing standard deviation.

4. Realistic 3D cloud fields

This section is the apex of this study: to assess howwell 1D solar codes interpret and handle unresolvednonovercast clouds. Cloud fields produced by 3D cloud-resolving models (CRMs) were used to represent com-plicated, realistic cloudy atmospheric columns. Fromthe 3D CRM fields, 1D columns of cloud properties

were produced to represent fields generated by a hy-pothetical LSAM. As the LSAM was assumed to havedone a perfect job at estimating unresolved cloud, all1D models were provided with perfect profiles of what-ever they needed to operate. Most required profiles ofcloud fraction, mean cloud water mixing ratio qc, andmean water vapor mixing ratio inside and outside ofclouds. Some models required profiles of mean loga-


FIG. 5. Same as Figs. 4a–c, but for CLOUD A. Quartile values forheating rates in the cloudy layer are listed in Table 6.

rithmic qc and cumulative upward and downward cloudfractions. The former gives an indication of horizontalvariability of cloud water, while the latter provides in-formation on cloud overlap.

Having established that for simple atmospheres allfour Monte Carlo codes agree extremely well amongthemselves and with CHARTS, this bolsters confidencein them being used as benchmarks for the complex cloudcases. A novelty of this study is its use of conditionalbenchmarks. These are discussed in detail in the fol-lowing section, which is followed by descriptions of thecloud fields and then by results.

a. Benchmark calculations

It is worth noting that an infinite number of 3D cloudfields can all give rise to the same set of 1D profilesof cloud information. Thus, the full 3D benchmarkirradiances produced by the MC models are, in prin-ciple, only a single sample from a potentially diversepopulation (Barker et al. 1999). Moreover, all 1D codesmake explicit simplifying assumptions about unre-solved clouds and thereby, knowingly, omit aspects ofunresolved cloud structure. So to provide 1D modelerswith only full 3D MC results would not be too infor-


FIG. 6. Same as Fig. 5, but for CLOUD B. Quartile values forheating rates in the cloudy layer are listed in Table 6.

mative. For example, a sound a priori assumption isthat 1D codes using PPH clouds with maximum/ran-dom overlap and 3D MC codes will produce resultsthat generally disagree. So, while full 3D results areinformative as representatives of the truth, it would beequally informative to have benchmarks for maximum/random overlap of PPH clouds too.

It is a simple task to create benchmark irradiances forPPH clouds following maximum/random overlap (andother idealized scenarios) with an MC code, though itis likely a luxury that most 1D modelers do not have.As such, one MC code was used to establish conditionalbenchmarks for the 3D fields. The 1D codes were thensorted according to how they handled unresolved clouds

and compared to their respective conditional bench-marks. The following series of benchmark calculationswas performed (cf. Barker et al. 1999).

1) FULL 3D

In this case, the actual CRM fields with inherent hor-izontal grid spacings Dx were used by all MC algorithmsalong with cyclic horizontal boundary conditions. Theseexperiments provided benchmark estimates of broad-band, domain-averaged ap, aatm, asfc, and heating rateprofiles. All results were averaged around solar azimuthf by injecting each photon at f 5 2pR, where R is auniform random number between 0 and 1.


FIG. 7. Cloud droplet single-scattering albedo and asymmetry parameter as a function of wavelength based on Mie calculations for agamma droplet size distribution with re 5 10 mm and effective variance of 0.1. Also shown are values from Slingo’s (1989) and Hu andStamnes’s (1993) parameterizations.

Four independent 3D MC algorithms were used toestablish these benchmarks (see Table 4). This redun-dancy was primarily to convince all that the benchmarkresults are trustworthy and that only a single MC wasneeded to compute conditional benchmarks.

2) INDEPENDENT COLUMN APPROXIMATION

These cases used the exact 3D CRM fields exceptthat Dx was infinite. In so doing, all information aboutspatial distributions of cloud was available but therewas no indication that clouds had finite horizontal ex-tent, including sides. The independent column approx-imation (ICA) has often been shown to be a very goodapproximation to the full 3D solution for both single-layer, planar clouds (Cahalan et al. 1994b) and mul-tilayer, towering clouds (Barker et al. 1998, 1999). Thelargest differences between ICA and the full 3D so-lution are at small m 0 .

3) EXACT OVERLAP

With this model the exact positions of cloudy cells,as dictated by the CRM, are retained, but Dx is infiniteand all clouds in a layer have the same mean cloudmixing ratio defined as

F[q (i, j, k)]q (i, j, k)O c ci, j

q (k) 5 , (2)cF[q (i, j, k)]O c

i, j

where

1; x . 0F[x] 5 50; x 5 0,

and qc(i, j, k) is the mixing ratio in the (i, j)th cell ofthe kth layer. Therefore, this model represents the ideal1D PPH model that is capable of handling a continuumof cloud overlap rates (e.g., Barker et al. 1999).

4) MAXIMUM/RANDOM OVERLAP

For this model, when clouds occur in adjacent layersthey are maximally overlapped and any excess cloud ispositioned at random across its layer. If a clear layerseparates two cloudy layers, they are assumed to overlaprandomly. Also, Dx is infinite. This model was advo-cated in the observational study of Tian and Curry(1989) and proposed initially by Geleyn and Hollings-worth (1979).

These fields are created by first randomly distributingthe Nc(k) cloudy cells, all of which have c(k), acrossqthe uppermost cloud layer. Moving down, if Nc(k 2 1), Nc(k), randomly position cloudy cells in the (k 21)th layer beneath cloudy cells in the kth layer. If Nc(k2 1) . Nc(k), place Nc(k) cells in layer k 2 1 beneaththe cloudy cells in layer k and randomly distribute theremaining Nc(k 2 1) 2 Nc(k) cloudy cells in layer k 21 among the remaining N 2 Nc(k) cloudless cells inlayer k 2 1, where N is the total number of cells perlayer. If a cloudless layer is encountered, position cloudycells of the next cloud layer that is encountered ran-


TABLE 7. Summary of radiative transfer (cloud field) models used in this study. All four Monte Carlo codes generated benchmark resultsfor the full 3D model, while just one generated results for the other conditional models. First column indicates the model; second indicateswhether it is defined uniquely (i.e, ‘‘no’’ implies dependence on random number generation); third tells whether cloudy cells are positionedas in the CRM fields or whether they have been shifted horizontally; the fourth column indicates whether clouds have been homogenizedacross layers; and the last column lists the horizontal grid spacing. The maximum overlap model saw minimal use.

Model UniqueClouds positioned as

in CRMHorizontal variations

in cloud water Dx

Full 3DICAExact overlapMax/random overlapMax overlapRandom overlap

YesYesYesNoYesNo

YesYesYesNoNoNo

YesYesNoNoNoNo

Finite`````

domly across the layer, just as was done for the upper-most cloud layer.

Limited use was made of this category’s close rela-tive: maximum overlap. With maximum overlap, cloudycells are always placed into the minimum number ofvertical columns in a domain. Total cloud fractions formaximum overlap are always less than or equal to thosefor maximum/random overlap.

5) RANDOM OVERLAP

These fields were created by simply taking the Nc(k)cloudy cells containing c(k) and redistributing them atqrandom across the layer regardless of cloud state inadjacent layers. Again, Dx is infinite. Though LSAMsdo not apply this model globally, it is an interestingextreme case that isolates the random component of themaximum/random model, and one that a few groupsimplemented here for diagnostic reasons. Table 7 sum-marizes the models just presented.

b. Description of cases

The fields used here were simulated by several verydifferent CRMs. When selecting these fields, the inten-tion was to capture a range of demanding tests, not torepresent clouds with the largest globally averaged ra-diative impacts.

In all cases, water vapor was averaged horizontallywithin a layer into clear- and cloudy-sky portions. Both1D and 3D codes used these fields. Though this aver-aging can have significant impacts on local heating rates,it had very little impact on domain averages. Abovemodel domains up to ;100 km, skies were cloudless,temperature profiles followed the TRO atmosphere, andwater vapor was set almost to zero, which tests theability of codes to represent sharp vertical moisture gra-dients such as off the west coasts of midlatitude con-tinents. Ozone followed the TRO profile through theentire atmosphere.

1) MARINE STRATOCUMULUS

This marine boundary layer cloud was provided byB. Stevens (1998, personal communication) and was

generated with conditions during the Atlantic TradeWind Experiment (ATEX). The cloud extends fromabout 0.7 to 1.6 km above the surface with the top ofthe model domain at ;3.2 km. Vertical grid spacingranges from 0.02 to 0.04 km, domain size is (6.8 km)2,and Dx 5 0.1 km. At the time, it was necessary toconsider such a small domain in order to address small-scale variability.

Figure 8a shows the field and summarizes key radi-ative properties. At about 1.5 km, where most of thecloud sits in a layer about 150 m thick, mean visibleextinction coefficient ^b& is ;100 km21. Cloud lowerdown is likely precipitation, as fractional amounts Ac

are typically less than 0.05 and ^b& are huge at ;200km21. Also shown is

2^b&

n 5 , (3)b 1 2sb

where sb is standard deviation of b across a layer. Themore inhomogeneous the cloud, the smaller nb. Throughuse of a single value for re, nb is identical to nqc. Forthis case nb ø 1, though for the entire cloud nt, forvisible optical depth t, is only 0.45. Had the clouds inthis case overlapped maximally, nt would have beencloser to 1 but as Fig. 8a shows, overlap falls betweenmaximum and random; total cloud amount is 0.565 withthe cloudiest layer Ac ø 0.3. Also, had maximum over-lap occurred, mean visible optical depth ^t&, which is14.4, would have been larger.

2) OPEN CELLS

This field represents a cold-air outbreak over warm wa-ter (Anderson et al. 1997). As Fig. 8b shows, this fieldconsists of vigorous open cellular convection with cloudsfrom about 0.8 to 7.5 km, which is the top of the modeldomain. Vertical grid spacing is 0.15 km, domain size is(50 km)2, and Dx 5 0.39 km. This domain size is similarto those in numerical weather prediction models. Theamount of water vapor in this case is roughly one thirdthat of the others. Though much of the cloud in this sim-ulation should be mixed phase, cloud water was treatedas liquid droplets with re 5 10 mm. In the main body ofthe cloud between 4 and 7 km, ^b& is ;30 km21. Below


FIG. 8. (a) (upper left) A plan view of vertically integrated cloud optical depth for the ATEX cloud field (B. Stevens 1998, personalcommunication); (upper right) the field in three-quarter view; (lower left) profiles of cloud fraction Ac, mean cloud visible extinction coefficient

, and a variability parameter n as defined in (3); (lower right) downward accumulated cloud fraction according to CRM data and twobidealized overlap assumptions applied to the profile of Ac on the left. (b) Same as in (a) but for the OPEN CELLS cloud field (Anderson etal. 1997); (c) same as (a) but for the GATE A cloud field (Grabowski et al. 1998); (d) same as (a) but for the GATE B cloud field (Grabowskiet al. 1998).


FIG. 9. (upper row) Broadband TOA albedos as functions of m0 for the ATEX cloud field. The title of each plot indicates genre of cloudtreatment by 1D clouds. Each plot shows the mean and std dev of full 3D benchmarks as computed by four MC codes (heavy solid lines),the conditional benchmark computed by one of the MC codes (heavy gray lines), and all the 1D codes in a particular class (dashed lines).(lower row) Corresponding heating rate profiles.

the main body ^b& increases to about 70 km21 but Ac aresmall. As a result, ^t& for the entire cloud is 52.9. Again,due to cloud overlap being between random and maxi-mum, nt is only 0.53 while nb . 1 for the cloudiest layers.Moreover, total cloud fraction is 0.9 though the cloudiestlayer has Ac 5 0.7.

3) DEEP TROPICAL CONVECTION

Figures 8c,d summarize two fields extracted fromGrabowski et al.’s (1998) simulation of phase III of theGlobal Atmospheric Research Programme AtlanticTropical Experiment (GATE). GATE A (Fig. 8c) con-sists of nonsquall clusters of organized convection withthe anvil removed so as to mimic towering, or devel-oping, clouds. Only liquid phase hydrometeors wereconsidered. GATE B (Fig. 8d) is a squall line and bothliquid and ice phases were considered. The ice crystals(referred to as ice A by Grabowski et al.) were, however,treated as though they were liquid spheres. The fieldscontain deep convective clouds reaching up to 16 km,domains are (400 km)2 and rival those in global climatemodels, and Dx 5 2 km. There are 35 layers of unequalgeometric thickness extending up to ;20 km. Domainsthis large represent the coarsest GCMs. Rain, snow, andgraupel were neglected with little radiative conse-quence.

For GATE A, ^b& are typically ;60 km21 and nb ø1. Owing again to overlap of inhomogeneous layers, nt

is quite small at only 0.25. Thus, this field is extremelyvariable and represents a demanding test for 1D codes.Note that clouds overlap almost maximally above 6 kmbut acquire a substantial random component at loweraltitudes. Total cloud fraction is 0.46 and ^t& ø 59.

GATE B’s profiles are similar to those of GATE Aat altitudes less than 4 km. GATE B is, however, dom-inated by near-overcast clouds above 8 km where ^b&are less than 10 km21 and nb ø 0.3. These small valuesof nb are due to cohabitation of anvil and dense coreregions. Thus, with ^t& ø 85 and nt ø 0.3, this case isas demanding as GATE A.

5. Results: 3D cloud fields

Figures 9–12 show ap as a function of m0 and heatingrate profiles for m0 5 0.5 for the four 3D cloud fields.For each field, values are shown for full 3D, exact over-lap, maximum/random overlap, and random overlap asdocumented in section 4. The 1D models were parti-tioned into their respective class and plotted anony-mously. Benchmark values for the specific genre ofcloud treatment are shown on each plot. For reference,full 3D benchmarks are shown on each plot too (means6 standard deviations for the four MC codes). In thefollowing sections, results for each genre are discussed.By referring to Table 3, one can deduce the genre intowhich each model falls. The focus here is on ap andheating rate profiles.


FIG. 10. As in Fig. 9, except for the OPEN CELLS cloud field.

a. ICA

The 1D codes included in the ICA genre are thosethat attempt to deal with horizontal variations in cloudbeyond cloud fraction Ac. As Figs. 9–12 reveal, the ICAbenchmarks are consistently closest to the full 3D val-ues. In each case though, characteristic ICA biases forap are apparent: too reflective at large m0 and too trans-missive at small m0. Clearly, this class of 1D code isstill very much in the experimentation phase as the var-iance of results from case to case is large. For example,for GATE A they agree among themselves fairly welland follow the conditional benchmark, although obviousproblems exist for heating in the lower reaches of cloud.In fact, the outlier in this case is the European Centrefor Medium-Range Weather Forecasts (ECMWF) mod-el, which uses maximum/random overlap and representshorizontal variability by simply reducing cloud opticaldepth everywhere all the time by a factor of 0.7 (Cahalanet al. 1994a; Tiedtke 1996). Results for this model areapparent in the other fields for it is the one that resemblescorresponding maximum/random benchmarks.

GATE B exemplifies the importance of addressinghorizontal variability of cloud, as the ap benchmarksfor exact, maximum/random, and random overlap areall similar and much larger than the full 3D values,which are tracked well by the ICA. The same can besaid for heating rates. This is because GATE B is dom-inated by a thick, yet highly variable, near-overcast anvilthat renders choice of overlap scheme irrelevant. Con-trary to GATE A’s results, consistency of ap and heatingrate estimates by 1D ICA-like models are terrible.

The OPEN CELLS case proved to be a challenge forboth the 1D codes and the ICA benchmark. For full 3Dtransfer at large m0, substantial amounts of radiationleak out cloud sides in a downward direction (Welchand Wielicki 1984). It is unlikely that 1D codes willever address this successfully. The 1D codes tend toperform well for ATEX with the ECMWF code still anoutlier. Had the cloud in ATEX been represented by oneor two layers at typical LSAM vertical resolution (i.e.,hundreds of meters rather than tens of meters), theECMWF code, and the other 1D codes in this class,would have performed well. The rest of the codes thatdo not account for horizontal fluctuations would havedone worse, for they would have been blind to implicithorizontal variability inherent in the overlap of manyhomogeneous, partially cloudy layers.

Despite its crude, empirical treatment of overlap, theMeteorological Service of Canada (MSC1) code (Or-eopoulos and Barker 1999) performs fairly well. It ap-plies a downward reduction to cloud t, thereby recog-nizing that irradiances are variable in the horizontal andthat they tend to be small in dense cloud beneath otherdense clouds. The MSC1 code requires an estimate ofhorizontal variability [i.e., Eq. (3)] and techniques thatprovide it are beginning to emerge (Considine et al.1997; Jeffery and Austin 2003). Nevertheless, this code,like other 1D codes, is rigid in the sense that alteringassumptions about unresolved cloud is difficult, and thatto include systematic (known) relations such as hori-zontal variations in droplet size may be next to impos-sible.


FIG. 11. As in Fig. 9, except for the GATE A cloud field.

b. Exact overlap

The 1D codes in this category were those that didnot address horizontal variability of cloud but did utilizeprofiles of accumulated cloud fraction. Thus, they at-tempted to capture the main features of cloud overlap(i.e., a profile of cloud fraction presented to the directbeam). Figures 9–12 show that, as expected, exact over-lap benchmarks of ap are systematically greater thanthose for full 3D and ICA on account of homogenizedclouds that cover the sky to the same extent as those inthe full 3D and ICA.

As the 1D codes in this class agree well for CLEARand CLOUDs A and B, most of the variance for the 3Dclouds arises from different handling of cloud overlap.For GATE B and OPEN CELLS these codes agree fairlywell, for cloud was quite extensive and details aboutoverlap are minor. For ATEX and GATE A, however,overlap is important (see Figs. 8a,c) and disagreementamong 1D codes is large for both ap and heating rate.

Like the ICA-style models, 1D models that require,or at least those that can utilize, information about exactoverlap are requesting information that is currently un-available in LSAMs. For a discussion on the overlappingstructure of real clouds derived from cloud-profiling ra-dar, see Hogan and Illingworth (2000).

The large spike in heating rate at 350 mb for OPENCELLS is due to the sudden encounter of downwellingirradiance with water vapor in the top layer of the cloudmodel domain. This is associated with correlated-k dis-tribution models that use relatively few k values and werenever expected to be applied to such extreme conditions.

This feature was also present for ATEX, but above 800mb, so it does not appear on the plots in Fig. 9.

c. Maximum/random overlap

All the 1D codes in this class use horizontally ho-mogeneous clouds in conjunction with the maximum/random overlap assumption. It is the most populatedclass, which signifies the growing popularity of thisscheme. Nevertheless, this scheme is risky for it is anextreme approximation that, when applied systemati-cally, can be expected to underestimate ap and over-estimate asfc (see Fig. 8). Figures 9–12 show that useof homogeneous clouds often fortuitously counter thisbias and result in overall radiative responses that are inbetter agreement with the full 3D benchmarks than arethe exact overlap benchmarks. It is important to note,however, that derivatives of radiative fluxes with respectto cloud properties are almost minimized for this model;surely this will impact estimates of climate sensitivity.

For the most part, 1D codes that employ maximum/random overlap track their conditional benchmark val-ues reasonably well in magnitude, but more so indap/dm0. What is interesting, however, is that all of thesecodes, save for those that underestimate water vaporabsorptance severely, underestimate ap for GATE A andATEX, the cases where the maximum/random overlapassumption has a large impact. Figure 13a is a replotof ap as a function of m0 for maximum/random overlapof GATE A (i.e., Fig. 11), but it also shows the con-ditional benchmark for maximum overlap as defined in


FIG. 12. As in Fig. 9, except for the GATE B cloud field.

FIG. 13. (a) Broadband TOA albedo as a function of m0 for the maximum/random overlap rendition of the GATE A cloud field. This isa replot of Fig. 11 but it includes the MC benchmark for maximum overlap (denoted as max overlap) as described in section 4a(4). (b)Dashed lines represent broadband TOA albedos for the homogeneous CLOUD A (gray lines) and CLOUD B (black lines) predicted by all1D codes that assume maximum/random overlap. Solid lines are corresponding values for one of the MC codes.

section 4a(4). While the benchmark maximum overlapvalues of ap are slightly less than those for maximum/random, they are still greater than most 1D model val-ues.

Figure 13b shows ap for CLOUDs A and B as pre-dicted by all 1D codes that use maximum/random over-

lap and corresponding values for a MC code. Note thatfor homogeneous clouds the 1D models tend to reflectmore than the benchmark while the opposite is true forthe 3D cloud cases. To answer why this occurs is beyondthe scope of this report. It is an important issue, however,for if the 1D codes were to begin addressing horizontal


variability, their estimates of ap would be suppressedeven more than those in Figs. 9–12. Furthermore, notethat the relative range of 1D results is roughly doublethat for the homogeneous clouds. This suggests differ-ences, or errors, in the interpretation of maximum/ran-dom overlap by 1D codes.

There is a tendency for the 1D models to underes-timate heating rates beneath layers with maximum Ac

yet rally back respectably, often overestimating, nearthe surface. The explanation for this is that low-levelclouds are shielded too much by clouds aloft. A similarproblem afflicts the 1D codes in the ICA class.

d. Random overlap

Although operational 1D codes do not invoke randomoverlap everywhere all the time, it is invoked whencloud layers, or blocks of cloudy layers, are separatedby at least one clear layer. Thus, when a 1D code revertsto random overlap for the cloud fields used here, itshould agree with the conditional benchmarks. As Figs.9–12 show, this is not always the case. Particularly puz-zling are estimates of ap for GATE A. First, the curvethat cuts diagonally across the plot (across the plot forATEX too) utilizes Briegleb’s (1992) scheme, whichuses overcast clouds with optical depths scaled by afactor of . This scheme does, however, produce max-3/2Ac

imum heating near the correct altitude. The other twomodels underestimate benchmark values of ap by sig-nificant amounts, not withstanding the fact that theyunderabsorb in the CLEAR and overcast tests. It is notclear whether the 1D codes are trapping too much up-welling radiation via multiple internal reflections orwhether they are not presenting enough cloud to thedirect beam. Judging by the heating profiles, photonsappear to be getting absorbed at the proper altitude,despite one of the codes seriously underestimating ab-sorption by droplets.

It is unlikely that the benchmarks are incorrect orunrepresentative (cf. Barker et al. 1999). Overall, theseresults are a bit disconcerting for they suggest that theseemingly routine treatment of random overlap in 1Dcodes may often be incorrect. This may not bode wellfor models using maximum/random overlap.

e. Climatological context

To put these results into a climatological context, con-sider cloud radiative forcing (CRF) at the TOA, whichis defined as

clr cldCRF(m ) 5 S (u, J )m [a (m ) 2 a (m )], (4a)0 0 p 0 p 0(

where is TOA albedo from the CLEAR experiment,clrap

is the corresponding value from one of the cloudycldap

experiments; and S ( is normal TOA irradiance, whichdepends on latitude u and day number J. DefiningCRF3D(m0) as CRF for any of the 3D codes, let the errorfor a particular 1D code be defined as

DCRF(m ) 5 CRF (m ) 2 CRF (m ). (4b)0 1D 0 3D 0

The diurnal-mean error in CRF for a 1D model is, there-fore,

1^DCRF& 5 DCRF[m (u, J, t)] dt, (4c)u,J E 0Dt(u, J )

Dt(u,J )

where Dt is time between sunrise (or sunset) and solarnoon, and DCRF in the integrand of (4c) was fit withcubic splines for easy numerical integration.

The left column of Fig. 14 shows annual marches ofCRF3D for the four 3D cloud fields. The other threecolumns show contour plots of ^DCRF&u,J for three 1Dmodels that address clouds differently; one is from theICA genre that attempts to capture both horizontal var-iability and overlap, while the two others represent clas-ses using homogeneous clouds with exact overlap andmaximum/random overlap. The three 1D codes usedhere tracked their respective conditional benchmarksbest. While the results in Fig. 14 are highly idealized,they nevertheless give indications of the annual marchof errors in CRF to be expected from different as-sumptions about unresolved clouds.

The ICA genre performs best with ^DCRF&u,J errorsrarely exceeding 10%; for GATE A and ATEX they areless than 5%, or 2 W m22. While the 1D code repre-senting exact overlap performed well relative to itsbenchmarks, it is clear that use of such a code in anLSAM would result in a systematic, and rather severe,enhancement of CRF by as much as 20–50 W m22

(assuming clouds were predicted accurately). The 1Dcode representing the maximum/random overlap genredoes well for ATEX, though it would have done poorlyhad there not been so much vertical resolution workingin its favor, and poor for GATE B due to omission ofhorizontal variability. When cloud overlap has a fairlystrong maximum component, as in ATEX, or when the1D bias as a function of m0 is both positive and negativeas in OPEN CELLS, errors in CRF can be small andcomparable to ICA errors.

6. Summary and conclusions

The primary objective of this study was to assess howwell current 1D radiative transfer codes interpret andhandle unresolved clouds. The philosophy adopted herewas to use 3D cloud-resolving model (CRM) fields assurrogates for fields that a large-scale atmospheric mod-el (LSAM) would have produced had it sufficient spatialresolution. Applying 3D Monte Carlo (MC) photontransport algorithms to the CRM fields yielded profilesof benchmark irradiances that were used to asses 1Dcodes. In addition, conditional MC benchmarks weregenerated according to each method, or genre, of han-dling cloud horizontal variability and cloud overlap by1D codes. Conditional benchmarks allowed 1D codesto be evaluated against results within the same genrerather than simply against full 3D results.


FIG. 14. (left column) Annual march of broadband CRF at the TOA for the four CRM fields based on mean values obtained from thefour MC codes. Remaining columns show CRF errors due to a representative 1D code from the ICA, exact overlap, and maximum/randomoverlap genres. All units are W m22.

To achieve the objective stated above, it was neces-sary to consider a small number of clear-sky and ho-mogeneous overcast cloud cases. The cases consideredrevealed that most 1D codes used for research and byweather and climate models underestimate atmosphericabsorption of solar radiation. For overhead sun and thestandard tropical atmosphere, this underestimation was;20 W m22 relative to the benchmark models, whichincluded an LBL code that has been compared exten-sively to detailed observations. The majority of this biasalmost certainly results from the lack of water vaporcontinuum absorption in 1D models. Clearly, these er-rors carry over to, and complicate assessments involv-ing, the 3D cloud fields.

The most common class of 1D model in this study

assumes maximum/random overlap of homogeneousclouds. The adoption by many large-scale modelinggroups of codes hard-wired with this scheme suggeststhe emergence of a maximum/random overlap paradigm.Results presented here imply that not all 1D codes ofthis variety are performing exactly as intended for theytend to systematically underestimate albedo relative totheir conditional benchmark. Moreover, maximum/ran-dom overlap of homogeneous clouds is simply an ex-treme and incorrect set of assumptions (e.g., Hogan andIllingworth 2000; Mace and Benson-Troth 2002) thatcan result in substantial biases even when the code isknown to perform perfectly. Forcing a code based onmaximum/random overlap of cloud to acknowledge hor-izontal fluctuations should not be considered a solution


either, for it will inevitably result in even greater un-derestimates of albedo due to increased transmittanceof too few clouds exposed to direct beam.

There was a marked paucity of avant-garde 1D mod-els that were able to use the independent column ap-proximation as their conditional benchmark. This wouldstill be the case if this study were initiated today. Whilethose that did participate often performed best, by nomeans do they agree among themselves, and often theyexhibit nonnegligible biases. While the ideal 1D codewould account for horizontal variable cloud amid a gen-eralized overlap scheme, there is no guarantee that bi-ases would be reduced to satisfactory levels and that itwould be flexible enough to deal with increasingly de-tailed portrayal of unresolved optical properties (be theycloud or other constituents including the surface). In-deed, it is difficult to imagine how 1D codes that re-semble those tested here could even begin to addressissues such as horizontally variable droplet sizes, ver-tical correlations in condensate, and cloud-surface typecorrelations. Furthermore, it can be expected that in-creasingly complex codes will demand more compu-tation time. This is an issue that 1D modelers mustaccept if they intend their codes to be used operationally.

This study has generalized King and Harshvardhan’s(1986) assessment of single-layer, monochromatic, two-stream approximations: no single multilayered, broad-band, 1D solar code performs well for all conditions.This is partly due to gaseous transmittance parameter-izations, cloud optical property parameterizations, andthe two-stream approximation (as employed by most),but mostly because of inappropriate cloud overlap as-sumptions, incorrect application of overlap assumptions,neglect of horizontal variability of cloud, and inappro-priate assumptions about horizontal variability. It maybe that there are far too many nonlinear aspects to theproblem to be able to satisfy all needs with a singleapplication of a code that operates on tangible infor-mation and uses a justifiable amount of computationtime. As pessimistic as this sounds, it should be seenas a challenge by begging the question that the paradigmof constructing 1D radiative transfer codes that directlyincorporate assumptions about unresolved cloud struc-ture is inadequate. As such, the nature of subgrid-scaleparameterization should be reconsidered and new meth-odologies invented for computing radiative heating inlarge-scale models.

Acknowledgments. HWB thanks J. Abraham (DirectorMRB-MSC) for financial support and B. A. Wielickifor computing resources at NASA Langley. While par-ticipants appear alphabetically in the author list, addi-tional acknowledgement goes to those at AER for per-forming additional benchmark testing, S. Cusack forwork in the initial stages that helped smooth the pro-cedure, J.-J. Morcrette, P. Raisanen, and B. Bonnel forperforming additional computations, and E. E. Cloth-iaux for extensive proofreading of this manuscript.

Thanks also to G. L. Potter for initial motivation, R. G.Ellingson, and W. B. Rossow for presenting our case,W. J. Wiscombe for encouragement, R. Pincus for dis-cussions, and an anonymous reviewer for comments thatimproved the readability of this manuscript. Providersof cloud-resolving model data are also acknowledged:W. Grabowski, V. Grubisic, M. Moncreiff, B. Stevens,and X. Wu.

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