cirrus cloud horizontal and vertical inhomogeneity effects...

Meteorol Atmos Phys 91, 223–235 (2006)DOI 10.1007/s00703-004-0099-2

Department of Atmospheric Sciences, University of California, Los Angeles, CA, USA

Cirrus cloud horizontal and vertical inhomogeneityeffects in a GCM

Yu Gu and K. N. Liou

With 14 Figures

Received April 19, 2004; revised July 15, 2004; accepted August 12, 2004Published online: April 28, 2005 # Springer-Verlag 2005

Summary

A set of the inhomogeneity factor for high-level cloudsderived from the ISCCP D1 dataset averaged over afive-year period has been incorporated in the UCLAatmospheric GCM to investigate the effect of cirrus cloudinhomogeneity on climate simulation. The inclusion of thisinhomogeneous factor improves the global mean planetaryalbedo by about 4% simulated from the model. It alsoproduces changes in solar fluxes and OLRs associated withchanges in cloud fields, revealing that the cloud inhomo-geneity not only affects cloud albedo directly, but alsomodifies cloud and radiation fields. The correspondingdifference in the geographic distribution of precipitationis as large as 7 mm day�1. Using the climatology cloudinhomogeneity factor also produces a warmer troposphererelated to changes in the cloudiness and the correspondingradiative heating, which, to some extent, corrects the coldbias in the UCLA AGCM. The region around 14 km,however, is cooler associated with increase in the reflectedsolar flux that leads to a warmer region above. An inter-active parameterization for mean effective ice crystal sizebased on ice water content and temperature has also beendeveloped and incorporated in the UCLA AGCM. Theinclusion of the new parameterization produces substantialdifferences in the zonal mean temperature and the geo-graphic distribution of precipitation, radiative fluxes, andcloud cover with respect to the control run. The verticaldistribution of ice crystal size appears to be an importantfactor controlling the radiative heating rate and the con-sequence of circulation patterns, and hence must be in-cluded in the cloud-radiation parameterization in climatemodels to account for realistic cloud processes in theatmosphere.

1. Introduction

Satellite mapping of the optical depth in midla-titude and tropical regions has illustrated thatcirrus clouds are frequently finite in natureand display substantial horizontal variabilities(Minnis et al, 1993; Ou et al, 1995). Verticalinhomogeneity of the ice crystal size distributionand ice water content (IWC) has also been de-monstrated in the microphysics balloon soundingobservations (Heymsfield and Miloshevich,1993). Based on three-dimensional (3D) radia-tive transfer calculations, cloud inhomogeneityhas been shown to play a significant role inthe heating rate profile averaged over mesoscalegrids and the result differs from that computedfrom the conventional plane-parallel (PP) ap-proach (Gu and Liou, 2001). However, creatingrepresentations of cloud inhomogeneity in gen-eral circulation models (GCMs) for climatestudy is a difficult task since they generally havespatial scales greater than 100 km due primarilyto computational limitations. Moreover, the rela-tionship between the cloud optical properties (interm of optical depth) and radiative fluxesis nonlinear, leading to biases in the model-simulated flux field caused by the use of an av-erage optical depth to represent cloud spatialinhomogeneity.

The cloud horizontal inhomogeneity effect onsolar albedo has been examined by Cahalan et al(1994), Kogan et al (1995), and more recentlyby Cairns et al (2000). Using data obtainedfrom observations, large eddy simulations, andMonte-Carlo radiative transfer calculations forstratocumulus and cumulus clouds, these authorsfound that cloud inhomogeneity leads to a con-siderably smaller solar albedo, as compared tothe value computed from the PP radiative transfermodel employing a mean liquid water content(LWC). This effect has been taken into accountin climate models by reducing the optical depth,e.g., by a factor of 0.7, for all cloud types.Tiedtke (1996) and Rotstayn (1997) tested theassumption of a uniform adjustment in GCMs,and pointed out that extension of the uniformreduction factor to all modeled clouds appearsunrealistic but might be taken as the lower limitof the adjustment. Rossow et al (2002) used theInternational Satellite Cloud Climatology Project(ISCCP) datasets to obtain a climatology of themesoscale variability of cloud optical depth,emissivity, and temperature to test and refinethe treatment of cloud-radiation interactions.However, these inhomogeneity parameters havenot been tested in a GCM.

The present study focuses on the high-levelcirrus clouds that play a pivotal role in the radia-tive budget of the Earth-atmosphere systemthrough the reflection of solar radiation and thetrapping of outgoing longwave radiation, andhence, significantly affect the atmospheric ther-mal structure and climate (Liou, 1986; 1992;Ackerman et al, 1988; Stephens et al, 1990).Most of the previous studies on cloud inhomo-geneity have focused on quantifying the solaralbedo bias for stratocumulus clouds, where abias as high as 15% has been reported (Cahalanet al, 1994; Barker, 1996; Pincus et al, 1999).Attention has recently been given to high-levelclouds. A bias in the outgoing longwave radiativeenergy budget, up to �15 W m2, has been founddue to the high-level ice cloud inhomogeneity(Fu et al, 2000; Pomroy and Illingworth, 2000).Carlin et al (2002) examined the high ice cloudinhomogeneity using optical depth dataset for themidlatitude, and reported a solar albedo bias ofup to 25% over a low reflective surface at a highsolar zenith angle, and a spherical solar albedobias as high as 11%. The high cloud inhomo-

geneity effect on simulated climate, however,has not been examined.

Cloud vertical inhomogeneity have beenmostly studied in terms of cloud vertical overlap(e.g., Geleyn and Hollingsworth, 1979; Liangand Wang, 1997; Stubenrauch et al, 1997; Chouet al, 1998; Gu and Liou, 2001). Computation ofthe radiative properties of cirrus clouds requiresthe information on ice crystal size distributionand a time-consuming computational light-scat-tering program. Thus, parameterizations (e.g., Fuand Liou, 1993) have been developed to deter-mine the single-scattering properties in terms ofIWC and mean effective ice crystal size. WhileIWC is generally predicted in GCMs, meaneffective ice crystal size is normally prescribed.For example, a value of 75 mm has been usedby K€oohler (1999) and Ho et al (1998). The icecrystal size distribution, however, is a function oftemperature (Heymsfield and Platt, 1984),and significantly interacts with the radiation field(Gu and Liou, 2000; Wu et al, 2000). Thus, itwould be desirable to develop an interactivemean effective ice crystal size parameterizationin connection with radiative transfer calculationsin GCMs and climate models.

The objective of this study is to investigatethe effect of cirrus cloud horizontal and verticalinhomogeneity on climate simulation. We use theUCLA atmospheric GCM (AGCM) described inSect. 2 to perform several numerical experi-ments, whose design is also discussed. In Sect.3, we investigate the effect of the cirrus cloudhorizontal inhomogeneity on the simulated cli-mate in terms of precipitation, temperature,radiation, and cloud patterns, while the sensitiv-ity of the simulated climate to cirrus cloud ver-tical inhomogeneity is discussed in Sect. 4.Finally, a summary is given in Sect. 5.

2. Model description and experimentdesign

2.1 UCLA AGCM

The UCLA AGCM is a state-of-the-art grid pointmodel of the global atmosphere extending fromthe Earth’s surface to a height of 50 km. Themost important features of the model have beendescribed in Gu et al (2003). The model predictsthe horizontal wind, potential temperature,

224 Y. Gu and K. N. Liou

mixing ratios of water vapor, cloud liquid waterand ice water, planetary boundary layer depth,surface pressure, land surface temperature, andsnow depth over land. In this study, we used alow-resolution version, with horizontal resolutionof 4� latitude by 5� longitude and 15 verticallayers from the Earth’s surface to 1 hPa. Therecently updated UCLA AGCM incorporates amore physically based radiation scheme thathas the capability of studying a variety of climateproblems, including the greenhouse gas and aero-sol effects (Gu et al, 2003). This scheme com-bined the delta-four-stream (Liou et al, 1988) andthe delta-two-and-four-stream methods (Fu et al,1997) for solar and thermal infrared flux transfer,respectively. Both methods have been demon-strated to be computationally efficient and, atthe same time, highly accurate in comparisonto exact radiative transfer computations. The cor-related k-distribution method for radiative trans-fer was used to account for gaseous absorptionin multiple scattering atmospheres. The single-scattering properties for ice and water cloudswere parameterized in terms of IWC=LWC andmean effective size=radius. In conjunction withthe preceding radiative scheme, parameteriza-tions for the fractional cloud cover and cloudvertical overlap have also been devised in themodel. The cloud amount is empirically deter-mined from the total cloud water mixing ratio.For radiation calculation purposes, the modelclouds were vertically grouped in terms of low,middle, and high cloud types. Maximum overlapwas first used for each cloud type, followed byrandom overlap among the three groups.

2.2 Parameterization of cloud horizontalinhomogeneity

The general approach to account for cloud spatialinhomogeneity is to adjust the optical depth byan empirical value less than 1. The adjustmentcoefficients must be related to LWC and IWCfields in the cloud and values of 0.5 to 0.85 havebeen employed. To investigate the sensitivity ofthe cloud inhomogeneity factor in the UCLAAGCM, Gu et al (2003) carried out a simulationin which the cloud inhomogeneity factor of 0.7was replaced by 1. This modification reducesOLR by 4.6 W m�2, and simultaneously en-hances the reflected solar radiation by about

12 W m�2. The inhomogeneity effect on solarradiation clearly exceeds that on IR radiation.The corresponding planetary albedo increasesfrom 27.82% to 31.31%, an enhancement ofabout 10%, indicating that the cloud inhomo-geneity has a significant impact on the simulationof planetary albedo. Examination was also madeof the effects of changing the mean effective icecrystal size from 85 mm to 50 mm. A reduction inice crystal size leads to a smaller OLR at TOA,but a larger planetary albedo. The effect of icecrystal size on solar and IR radiation in theseexperiments had the same magnitude.

To investigate the cloud inhomogeneity effecton climate modeling, we performed a number ofmodel simulations. Each simulation is a 5-yearrun with the initial condition corresponding toOctober 1. For the control run (CTRL), a reduc-tion factor of 0.7 to account for cloud inhomo-geneity was introduced to adjust the opticaldepth on each grid point for all cloud types inthe UCLA AGCM simulation. Also, an ice crys-tal size of 80 mm was prescribed uniformly forice clouds. A second simulation, referred to asHORZ, was conducted by replacing the uniformvalue of 0.7 with the five-year mean values of theinhomogeneity factor � for high-level clouds thathave been derived from the ISCCP D1 dataset(Rossow et al, 2002). These values were calcu-lated from: (a) the area-mean optical depth �m

obtained from an area of about 280 km by280 km based on individual satellite pixels, repre-senting an area of about 5 km by 5 km sampled atintervals of about 30 km as follows:

�m ¼ 1

N

XNi¼1

�i; ð1Þ

and (b) the corresponding radiative mean opticalthickness � r that represents a homogeneous cloudhaving the same albedo as the actual inhomoge-neous cloud with �m in the form

�r ¼ R�1

�1

N

�XNi¼1

Rð�iÞ��

; ð2Þ

where R is a radiative transfer operator that deter-mines the radiative flux from the optical thick-ness. The inhomogeneity factor � is thendetermined by

� ¼ 1 � �r=�m: ð3Þ

Cirrus cloud horizontal and vertical inhomogeneity effects in a GCM 225

The effects of cloud inhomogeneity on radiativetransfer can then be approximately accounted forby re-scaling the area-mean optical thickness asfollows:

�r ¼ ð1 � �Þ�m; ð4Þwhere �m is the linear average of varying opticalthickness over the area that is predicted from aGCM, and � r is the ‘‘radiative-average’’ valuethat would yield the correct cloud albedo (Cairnset al, 2000).

Figure 1a and b shows, respectively, the geo-graphic distribution of the annual mean values of� averaged over 1986–90 for high-level cloudsand the differences between 1 � � and a uniformvalue of 0.7. The distribution of � illustrates thepattern of the ITCZ feature, the subtropical jetregions, the generation portion of winter stormtracks, and the clouds over major mountains.The most homogeneous high-level clouds arefound over the eastern edges of the oceans inthe southern hemisphere, north Africa, and themiddle east (Fig. 1a). It is also shown that the

reduction factor 0.7 may be a good approxi-mation for clouds along the equator. However,for the fairly homogeneous areas, use of 0.7may overestimate the cloud inhomogeneity effect(Fig. 1b). The geographic patterns of � are ratherconstant with season. For this reason, we adoptedthe annual mean � values and interpolated to theUCLA AGCM model grid point. Low and middleclouds remain unchanged in this experiment.

2.3 Parameterization of ice crystal sizefor use in climate models

At this point, most of the climate models pre-scribe ice particle size in conjunction with radia-tion calculations. For example, the ice clouds inthe UCLA AGCM assume a uniform ice crystalsize of 85 mm (Gu et al, 2003). Using a two-dimensional cirrus cloud model with the explicitprediction of ice crystal size distribution, Gu andLiou (2000) showed that the lower parts of thecloud possess higher number densities of largeice particles, whereas the cloud top is dominatedby the presence of more small ice particles. Thisresult is consistent with the observed patternpresented by Heymsfield and Platt (1984), andOu et al (1995), in which both IWC and meanice crystal size show systematic relationshipwith temperature. Following the work of Liou(1992) and Ou et al (1995), the temperature-dependent IWC and mean effective ice crystalsize may be expressed by parameterization inthe forms

IWC ¼ expf�7:6

þ 4 exp½�0:2443�10�3ð253� TcÞ�2:445g;ð5Þ

De ¼X3

n¼0

cnðTc � 273Þn; ð6Þ

where 213 K<Tc<253 K, c0¼ 326.3, c1¼ 12.42,c2¼ 0.197, and c3¼ 0.0012. The temperature-dependent De is obtained according to a generalpower relationship between ice crystal size dis-tribution and IWC as reported by Heymsfield andPlatt (1984) who showed that for a given tem-perature, values of the empirical coefficients aresubject to uncertainty due to the observationaldata spread. Therefore, accuracy of the actualmean effective ice crystal size must be further

Fig. 1a. Geographic distribution of the annual mean valuesof the inhomogeneity factor � averaged over 1986–90 forhigh-level clouds (ISCCP), (b) difference between 1 � �and a uniform value of 0.7 used in CTRL


improved based on De. Using the relationshipbetween De and IWC and since the real De andIWC must have the same relationship based ondimensional analysis, we have

De ¼ ðIWC=IWCÞ1=3De: ð7Þ

This formulation has been verified by Ou et al(1995) using the balloonborne replicator dataobtained during the First ISCCP RegionalExperiment, Phase II, Cirrus Intensive FieldObservation (FIRE-II IFO). To implement thisparameterization in the UCLA AGCM, we firstcompute IWC and De from Eqs. (5) and (6),respectively. Then using the IWC predicted fromAGCM, we can determine De following Eq. (7)for each grid point where ice cloud occurs. In thisway, De can effectively interact with radiation aswell as dynamic and thermodynamic fields in theclimate model. The vertical inhomogeneity ofcirrus clouds is then accounted for in the UCLAAGCM by using the varied mean effective icecrystal size calculated from model predictedIWC and temperature for high clouds, an experi-ment referred to as VERT.

3. Effect of cirrus cloud horizontalinhomogeneity

To illustrate the cloud inhomogeneity effects onradiation budget, we show in Table 1 the Januaryand July global mean solar fluxes and OLRs atTOA and the surface for the three AGCM simu-lations described in Sect. 2. Compared to CTRL,HORZ enhances the reflected solar radiation byabout 5 W m�2, and reduces OLR by 2 W m�2

(Table 1). The cloud inhomogeneity effect onsolar radiation clearly exceeds its effect on ther-mal infrared radiation. The corresponding plane-tary albedo increases from 27.82% to 29.12%,showing an improvement of about 4%. Com-

pared to the observed planetary albedo obtainedfrom the Earth Radiation Budget Experiment,which has a value of 29.5% (�1%) for the globalmean (Barkstrom and Smith, 1986), incorpora-tion of a uniform reduction factor of 0.7 inthe UCLA AGCM reduces the reflected solarfluxes at TOA by about 4%. Inclusion of a setof variable reduction values leads to an overallimprovement of solar flux simulation.

Figure 2 shows the zonal mean differencesin the January and July net solar and IR fluxesat TOA between HORZ and CTRL. The zonalmean differences in net solar fluxes at TOAbetween HORZ and CTRL occur mainly in theITCZ and the storm track zones in the northernhemisphere winter, as well as near the pole of thenorthern hemisphere summer. Note that for solarfluxes, most of the changes occur in the summerhemispheres due to the seasonal change of thesun. Changes in the OLR are located in the ITCZand oceanic midlatitudes. These features aredirectly associated with differences in the cloudinhomogeneity factor used in HORZ and CTRL.Carlin et al (2002) studied the relationship be-tween solar albedo and high-cloud optical depthand found that there was normally a convexrelationship between solar albedo and ice cloudoptical depth, except under certain cases suchas low optical depth for an overhead sun anda high reflective underlying surface where aconcave relationship was found. A higher inho-mogeneity factor of 0.7 was used in CTRL, asmaller cloud optical depth, which results in lessreflected solar fluxes and more OLRs at TOA.Rossow et al (2002) obtained a similar conclu-sion based on global radiation calculations usingthe ISCCP data for one particular day in July,1986.

However, this conclusion does not seem to betrue when we examine the geographic radiative

Table 1. Global mean values of the January and July solar (SW) and infrared (LW) fluxes at TOA and the surface (SFC) for thethree AGCM simulations

Variable January global mean July global mean

CTRL HORZ VERT CTRL HORZ VERT

TOA SW (W m�2) 261.5 256.4 263.4 244.7 240.3 245.9TOA LW (W m�2) 230.1 227.5 226.2 236.2 234.2 232.7SFC SW (W m�2) 192.5 187.3 193.0 176.4 171.9 175.8SFC LW (W m�2) 55.47 55.12 54.33 54.43 54.54 53.32


flux distribution. Figures 3–5 display the distri-bution of the January and July mean solar and IRflux differences at TOA, and differences in thecloudiness. In January, differences in the solarflux are as large as 50 W m�2, while more than30 W m�2 are found in OLRs (Figs. 3a and 4a).These differences do not display geographic pat-

terns that resemble differences in the inhomo-geneity field, as shown in Fig. 1b. Changes inthe solar fluxes and OLRs, in fact, are associatedwith changes in the cloud fields (Fig. 5a). Anincrease (decrease) in cloudiness corresponds toa decrease (increase) in solar fluxes and OLRs.Comparing differences in the cloudiness with

Fig. 2. Zonal mean differences in the January and July net shortwave (a and b), and longwave (c and d) fluxes (W=m2) atTOA between HORZ and CTRL

228 Y. Gu and K. N. Liou: Cirrus cloud horizontal and vertical inhomogeneity effects in a GCM

those in the inhomogeneity field (Fig. 1b), theincreased cloudiness, hence more reflected solarflux, in some areas (e.g., along the equator from0� E to the northeast of Australia) is associatedwith a higher inhomogeneity factor which, how-ever, should give a smaller cloud albedo. Thisindirect feedback process could be due to the factthat initially the cloud with a higher inhomo-geneity has a lower albedo and reflect less solarradiation. As a consequence, more heating occursbelow the cloud top and stronger updraft is pro-duced, leading to the formation of more cloudi-ness. Thus, cloud inhomogeneity not only affectsthe cloud albedo directly, but also modifies theglobal cloud field through cloud-radiation inter-action. Similar changes are found in July in whichradiative flux differences are also associated withchanges in the cloudiness (Figs. 3b, 4b, 5b).

Figure 6 displays differences in the January andJuly mean precipitation distribution between theHORZ and CTRL experiments. Differences in theprecipitation are found in ITCZ and the winterstorm tracks with values as large as 7 mm day�1,although the global mean values for the two casesare about the same. Differences in the geographic

Fig. 3. January (a), and July (b) mean net solar flux differ-ences (W m�2) between HORZ and CTRL at TOA

Fig. 4. Same as Fig. 3, except for OLR

Fig. 5. January (a), and July (b) mean total cloud coverdifferences (%) between HORZ and CTRL

distribution of precipitation, as in the case ofradiative flux, do not display patterns that resem-ble those occurred in the inhomogeneity field.However, changes in the precipitation and radia-tive fluxes are closely associated with changes inthe cloud fields (Fig. 5).

Figure 7 shows the January zonal mean differ-ences in total cloud water mixing ratios, solarheating rates, and IR heating rates obtained inHORZ and CTRL. The HORZ experiment pro-duces more cloud water in the middle to uppertroposphere above the ITCZ and in the mid-lower troposphere of the midlatitudes in thenorthern hemisphere winter. Also HORZ pro-duces more liquid water in the lower troposphereof the midlatitude in the summer hemisphere(Fig. 7a). Figure 7b and c show the correspond-ing differences in solar and IR radiative heatingrates. More high clouds result in more solar heat-ing in the cloud layer, whereas it is less in thelayers below due to the reduced downward solarflux (Fig. 7b). Increase in high clouds also leadsto more IR cooling at the cloud top and more IRwarming at the cloud bottom. The heating=

cooling effect produced by IR exceeds the solarheating, resulting in warming of the tropo-sphere. The simulated results for July are simi-lar to those for January and are not shown here.

The January and July zonal mean temperaturedifferences between the HORZ and CTRL ex-periments are illustrated in Fig. 8. In January,HORZ produces a warmer surface and tropo-sphere related to the net radiative warming in thisregion. This warming, to some extent, correctsthe cold bias in the UCLA AGCM. However,the region around 14 km is cooler as a resultof the variable cloud inhomogeneity that in-creases the reflected solar fluxes, as comparedto the use of a uniform value of 0.7. Conse-quently, more upward reflected solar fluxes resultin more absorption above and hence a warmerregion, as shown in Fig. 8a. The July simulationresults, however, differ somewhat with cooling inthe troposphere of the oceanic midlatitudes due

Fig. 6. January (a), and July (b) mean precipitation differ-ences (mm day�1) between HORZ and CTRL

Fig. 7. January zonal mean differences in (a) the total cloudwater mixing ratio (10�6 kg kg�1), (b) shortwave heatingrate (K day�1), and (c) longwave heating rate (K day�1)between HORZ and CTRL


to less latent heat release in those areas asso-ciated with the reduced cloud field.

4. Effect of cirrus cloud verticalinhomogeneity

Using the formulation presented in Sect. 2.3, therelationship between the mean effective ice crys-tal size and IWC and temperature is displayedin Fig. 9. The De values for temperatures from�60 �C to �20 �C (213 to 253 K) and IWCs from0.1 to 2 mg m�3 (left panel) and 2 to 40 mg m�3

(right panel) range between 15 and 150 mm, ingeneral agreement with the mean effective icecrystal sizes retrieved from the FIRE-II IFOobservation (Ou et al, 1995). These values arealso in the size range determined from the 28ice crystal size distributions obtained from sixfield campaigns reported by Fu (1996). The meaneffective ice crystal size is shown to increasewith IWC. However, its relationship with tem-perature appears more complicated. For tempera-tures from �55 to �45 �C, De decreases withincreasing temperature for a given IWC. Outsidethis temperature range, however, De increaseswith increasing temperature.

Fig. 8. January (a), and July (b) zonal mean temperaturedifferences (K) between HORZ and CTRL

Fig. 9. Contour map of the mean effective ice crystal size (mm) as a function of ice water content (a) 0.1 to 2.0 mg m�3, and(b) 2.0 to 40 mg m�3 for temperature from �60 to �20 �C


We now examine the cirrus cloud verticalinhomogeneity effect on the simulated climaticpatterns in terms of mean effective ice crystalsize. The January and July global mean radiativefluxes at TOA and the surface for VERT arelisted in Table 1. At TOP, this experiment pro-duces 1–2 W m�2 differences in the global meansolar radiative flux and 3–4 W m�2 in OLR, ascompared to CTRL. It appears that the new inter-active parameterization tends to generate anoverall smaller mean effective ice crystal size(e.g., the January global mean value is about58.18 mm) as compared to the prescribed 85 mmin CTRL. As a result, more IR radiation emittedfrom the surface is trapped in VERT than inCTRL. However, the global mean reflected solarflux decreases due to the reduced cloudiness. Themean effective ice crystal size appears to havemore direct impact on IR radiation, while thecloudiness has larger impact on solar radiation.

The geographic distribution of the precipita-tion, OLR, and total cloud cover fields alsoshows substantial differences between VERTand CTRL. Increases in the precipitation overthe winter storm track in January and over warmpool in both January and July are seen in VERT,with a maximum value of about 6 mm day�1

(Fig. 10). While CTRL underestimates the con-vection and precipitation in Indo-Pacific (Gu et al,2003), VERT appears to improve the simulationin that area. The January and July global meanvalues of precipitation from VERT also show bet-ter agreement with observations (3.21 mm and3.45 mm for January and July, respectively,according to the data reported in CMAP) thanCTRL (Table 2).

The global mean cloud cover simulated fromVERT is also slightly closer to the ISCCPobserved value of 62.2% for January and62.6% for July (Table 2). Difference in the cloudcover, with a maximum value of about 25%, has

a similar pattern as that in the precipitation, as isexpected (Fig. 11). The corresponding differencein OLR is as large as 35 W m�2 and has an oppo-site sign with respect to precipitation and cloudcover as a consequence of the thermal green-house effect of clouds (Fig 12). Negative valuesare found over warm pool, indicating the en-hancement of the simulated convection in thatregion in VERT.

The January zonal mean ice water mixing ratiodifference between VERT and CTRL showsmore ice water in the high cloud regions overITCZ and the subtropical oceanic area of thesouthern hemisphere (Fig. 14a). Consequently,

Fig. 10. January mean differences in (a) January, and (b)July precipitation (mm day�1) between VERT and CTRL

Table 2. Global mean values of total cloud cover, precipitation, and planetary albedo in the three AGCM simulations forJanuary and July

Variables January global means July global means

CTRL HORZ VERT CTRL HORZ VERT

Total cloud cover (%) 63.85 63.85 63.39 63.92 64.16 63.17Precipitation (60� S–60� N; mm day�1) 3.61 3.58 3.51 3.798 3.776 3.71Planetary albedo (%) 27.4 29.12 27.34 27.56 29.0 27.07


Fig. 11. January (a), and July (b) mean cloud cover differ-ences (%) between VERT and CTRL

Fig. 12. January (a), and July (b) mean OLR differences(W m�2) between VERT and CTRL

Fig. 13. January zonal mean (a) solar, and (b) IR heatingrate differences (K day�1) between VERT and CTRL

Fig. 14. January zonal mean (a) ice water mixing ratio(kg kg�1), and (b) temperature (K) differences betweenVERT and CTRL


more solar heating is found in VERT in thoseareas, while less is shown in the lower atmo-sphere due to decrease in the available solar flux(Fig. 13a). The IR heating rate shows enhancedcooling at the cloud top while more warming atthe cloud bottom in accordance with changes inthe ice cloud field (Fig. 13b). The correspondingzonal mean temperature differences illustratewarming in most areas of the troposphere asso-ciated with net radiative heating (Fig. 14b). Dif-ferences in July show similar patterns and are notpresented here. It is clear that the new interactiveparameterization for the mean effective ice crys-tal size is more physical and that the verticalinhomogeneity of cirrus clouds is an impor-tant factor that can significantly impact climatesimulation.

5. Conclusions

The cirrus cloud horizontal and vertical inhomo-geneity effects have been investigated in thisstudy. The introduction of a cloud inhomogeneityfactor with spatial variations leads to a significantincrease in the net solar fluxes at TOA with aglobal average of about 5 W m�2, compared tothe use of a uniform value of 0.7. It improvesthe simulation of the reflected solar fluxes atTOA and hence the planetary albedo. The cloudinhomogeneity has an impact on the thermalradiative transfer as well, but the effect is quanti-tatively smaller. Differences in the precipitationdistribution are as large as 7 mm day�1, althoughthe corresponding global mean value remainsabout the same. Differences in the geographicdistribution of precipitation and radiative fluxesbetween the two different cloud inhomogeneityparameterizations are shown to be associated withthe patterns of cloud field changes. An increase inthe cloudiness in certain areas, and the consequentincrease in the reflected solar flux and decreasein OLR, is associated with higher cloud in-homogeneity. Thus, cloud inhomogeneity not onlyaffects cloud albedo directly, but also modifies theentire cloud and radiation fields. Using variedcloud inhomogeneity factors also produces tem-perature change in the whole atmosphere relatedto changes in the cloudiness and the correspond-ing radiative heating and latent heat release.

An interactive parameterization for meaneffective ice crystal sizes based on IWC and

temperature has been developed for use in cli-mate models. The mean effective ice crystalsize for a model grid when ice clouds are gen-erated can now be parameterized from the pre-dicted IWC and temperature in climate models.This allows a direct interaction between cloudmicrophysics and radiative transfer. The preci-pitation and cloud cover patterns simulated fromthe new parameterization show better agreementwith the observed global mean values. The glo-bal mean effective ice crystal size calculatedfrom the parameterization shows a smallervalue than the prescribed 85 mm that was usedin the control simulation, resulting in less OLR.In association with the reduced cloudiness,we also find that the reflected solar flux issmaller. The geographic distribution of the pre-cipitation, OLR, and total cloud cover fieldsshows significant differences, as compared tothe control run. More precipitation and lessOLR are found in the winter storm track regionand the Indian Ocean corresponding to changesin the cloudiness. Employing interactive meaneffective ice crystal size results in a warmertroposphere associated with the radiative heat-ing modulated by the cloudiness. The sensitiv-ity of simulated climate to cloud horizontal(optical depth) and vertical (particle size) inho-mogeneity appears to suggest that interactiveparameterizations for these two parameters arerequired in order to improve the overall cloudand radiation physics currently used in climatemodels.

Acknowledgments

This research was supported by National Foundation GrantATM-99-07924 and DOE Grant DE-FG03-00ER62904. Wethank Drs. M. D. Chou and Xiaoqing Wu for constructiveand useful comments on the paper.

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Corresponding author’s address: Dr. Y. Gu, Departmentof Atmospheric Sciences, University of California, LosAngeles, CA 90095, USA (E-mail: [email protected])


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