tests and improvements of gcm cloud parameterizations ...qfu/publications/ar.yuan.2006.pdftests and...

2 (2006) 222–238www.elsevier.com/locate/atmos

Atmospheric Research 8

Tests and improvements of GCM cloud parameterizations using theCCCMA SCM with the SHEBA data set

Jian Yuan a,⁎, Qiang Fu a, Norman McFarlane b

a Department of Atmospheric Sciences, University of Washington, Seattle, WA 98195, USAb Canadian Centre for Climate Modeling and Analysis, Victoria, British Columbia, Canada

Accepted 4 October 2005

Abstract

A GCM cloud microphysics parameterization is tested and improved using the CCCMA single-column model with cloudproperties obtained at the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) during the period of November 1997 toSeptember 1998. The ECMWF reanalysis water vapor profile is scaled with rawinsonde data so that the new relative humidityprofiles are compatible with rawinsonde data for nudging purposes. This study demonstrates that the treatment of ice nucleationnumber concentration is the controlling factor of the overestimation of monthly mean ice water path originally produced by thismodel. The parameterizations of accretion processes are modified to consider the accumulation due to an increase of precipitationflux through a model layer related to accretion processes. The horizontal inhomogeneity effect of cloud liquid water is consideredin parameterization of autoconversion process. A new method developed for mixed-phase clouds to determine the water vaporsaturation and partitioning of the condensed water into different phases is also tested in this model.

When using a nudging technique with the adjusted ECMWF water vapor profile the model can well simulate the monthly totalcloud cover and daily precipitation rate for the SHEBA period. Using the modified cloud microphysics parameterizations includingimproved treatments for accretion processes, ice nucleation number concentration, and auto-conversion, the monthly mean cloudliquid water path and ice water path are suitably simulated and compare reasonably well to those derived from measurements.© 2006 Elsevier B.V. All rights reserved.

Keywords: Cloud; Microphysics; Parameterization; GCM; Single-column model; SHEBA

1. Introduction

Clouds cover about 60% of the Earth's surface andplay an important role in regulating the Earth's radiationbudget. In current climate modeling, the lack ofunderstanding of cloud is still a major uncertainty(Houghton et al., 1996). Inter-comparison studies ofgeneral circulation model (GCM) simulations (e.g.,

⁎ Corresponding author. Tel.: +1 206 685 9303.E-mail address: [email protected] (J. Yuan).

0169-8095/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.atmosres.2005.10.009

Randall et al., 1998) indicate that different modelssimulating polar processes show large discrepancies inthe Arctic. Curry and Ebert (1992) and Zhang et al.(1996) have demonstrated the importance of specificcloud macro- and micro-physical properties, includingcloud amount, cloud base height, cloud phase, particlesize and shape, and cloud ice/water contents, on cloud-radiation and ice-albedo feedback mechanisms. Thecloud-radiation feedback (CRF) in the Arctic signifi-cantly influences the way heat passes through the Arcticsystem. Because of the complexity and importance of

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http://dx.doi.org/10.1016/j.atmosres.2005.10.009

223J. Yuan et al. / Atmospheric Research 82 (2006) 222–238

polar cloud radiative effects, it is necessary to gain aninsight into them through a combination of modelingand observational studies.

The difficulties associated with simulating cloudradiative effects in GCM studies exist because of thecurrently inadequate understanding of cloud processesincluding the related dynamic, thermodynamic andmicrophysics processes. The microphysics processesare particularly important because the factors determin-ing cloud optical properties are directly related to theseprocesses. It is crucial to improve parameterizations ofmicrophysics processes in GCMs to ensure reasonableatmospheric optical parameters for the simulation ofradiative energy budget.

Due to the complexity of GCMs, it is difficult toisolate specific processes and study them in GCMsimulations. The single-column model (SCM) has beenpromoted as a useful testbed for cloud parameterizations(Randall et al., 1996), but providing suitable boundaryconditions to SCM is extremely challenging (Zhang andLin, 1997; Mace and Ackerman, 1996; Randall et al.,1996).

The Surface Heat Budget of the Arctic Ocean(SHEBA) project is motivated by the large discrepanciesamong simulations by global climate models of thepresent and future climate in the Arctic and byuncertainty about the impact of the Arctic on climatechange (Moritz et al., 1996). The period of the SHEBAexperiments is from 1997 to 1999 at the North PoleSHEBA ice station, which include rawinsonde, lidar,radar, meteorological surface and a microwave radiom-eter observations, etc. Accompanied by ECMWFprovided hourly column output of the water vapor andtemperature forcing data, this integrated observationdata set is well suited for testing GCM cloudparameterizations through SCM simulations in theArctic region.

In this study, we applied a recent version of theCanadian Centre for Climate Modeling and Analysis(CCCMA) single-column model (CSCM) (Lohmann etal., 1999) to the SHEBA year to test and improve GCMcloud parameterization in the Arctic region. The CSCMannual cycle simulation is carried out using theECMWF forcing (Beesley et al., 2000) with a nudgingtechnique. We describe this model and the data usedalong with nudging techniques in Section 2. In Section3, we present the problem in nudging using ECMWFreanalysis water vapor profile and discuss our modi-fication of the data to alleviate this problem. The testand improvement of cloud microphysics parameteriza-tion using SHEBA data are shown in Section 4. Wediscuss the effect of a new partitioning method for

water vapor in mixed-phase clouds, as derived from in-situ measurements in Section 5. The conclusions aregiven in Section 6.

2. Descriptions of model and data and nudgingtechnique

2.1. Model description

The CCCMA single-column model (CSCM) usedin this study is adapted from the second-generationCCCMA GCM (McFarlane et al., 1993). It predictshorizontal wind components, temperature, water vaporand total condensed water. The turbulence schemecontains a prognostic equation for the turbulentkinetic energy (TKE) (Abdella and McFarlane,1997). Other second-order quantities are determineddiagnostically through a parameterization of the third-order moments based on a convective mass-fluxargument. Cumulus clouds are represented by a bulkmodel including the effects of entrainment anddetrainment on the updraft and downdraft convectivemass fluxes (Zhang and McFarlane, 1995). Theradiation code is based on two-stream solutions ofthe radiative transfer equation with six spectralintervals in the infrared spectrum (Morcrette, 1989)and two in the solar spectrum (Fouquart and Bonnel,1980). Gaseous absorption due to water vapor, CO2,O3, CH4, N2O, and CFCs is included.

Two kinds of cloud schemes are available as optionsin the CSCM. One is an explicit cloud scheme; the otheris a statistical cloud scheme. The explicit cloud schemeis used in this study, which is described in detail byLohmann and Roeckner (1996). It has prognosticvariables for liquid water content (ql) and ice watercontent (qi) and uses an explicit approach for conden-sation and cloud cover based on Sundqvist (1978). Inexplicit cloud scheme, cloud fraction (A) is a diagnosticfunction of relative humidity (Sundqvist et al., 1989).

A ¼ 1−ffiffiffiffiffiffiffiffiffiffiffi1−A0

pð1Þ

A0 ¼ ðRh−Rh0Þ=ð1−Rh0Þ ð2Þ

Rh0 ¼ Rhtop þ Rhsfc−Rhtop� �

exp 1−psfcp

� �4" #

ð3Þ

where psfc and p are the air pressure at surface and inatmosphere, respectively. Rh is the grid-mean relativehumidity; Rh0 is a threshold specified as a function ofheight based on the work of Xu and Krueger (1991). Itdecreases from 0.95 near the surface to 0.6 at top of theatmosphere.

224 J. Yuan et al. / Atmospheric Research 82 (2006) 222–238

Condensation only occurs in the cloudy part of thegrid box if moisture convergence due to advection/turbulence/adiabatic cooling occurs. The grid meancondensation rate Qcnd is

Qcnd ¼ Ad ATC qvð Þ−AqsatAt

� �ð4Þ

where ATC(qv) is the growth of grid mean water vapormixing ratio caused by the moisture convergence due toadvection or turbulence, qsat is the water vaporsaturation mixing ratio, and qv is the grid mean watervapor mixing ratio.

The implementation of the statistical cloud scheme isdescribed in detail by Lohmann et al. (1999). Themicrophysics processes are the same for these twoschemes. According to Lohmann and Roeckner (1996),the prognostic equations include

AqvAt

¼ ATC qvð Þ−A Qccnd þ Qc

dep

þ 1−Að Þ Qo

evp þ Qosub−Q

ocnd−Q

odep

ð5Þ

AqlAt

¼ ATC qlð Þ þ A Qccnd−Q

caut−Q

cracl−Q

csacl

�−Qc

frc−Qcfrh−Q

cfrs þ Qc

mltÞ þ 1−Að ÞQocdn

ð6Þ

AqiAt

¼ ATC qið Þ þ A Qcdep−Q

cagg−Q

csaci þ Qc

frc

þ Qc

frh þ Qcfrs−Q

cmltÞ þ 1−Að ÞQo

dep:ð7Þ

The superscripts (c) and (o) refer to the cloudy andcloud-free part of the grid box. The microphysicalprocesses parameterized in CSCM are condensational(depositional) growth of cloud droplets (ice crystals),Qcndc (Qdep

c ); homogeneous (Qfrhc ), heterogeneous (Qfrs

c ),and contact (Qfrc

c ) freezings of cloud droplets; auto-conversion (aggregation) of cloud droplets (ice crystals),Qautc (Qagg

c ); accretion of cloud droplets (Qsaclc ) and cloud

ice (Qsacic ) by snow and of cloud droplets by rain (Qracl

c );evaporation/sublimation of cloud liquid water and rain(cloud ice and snow), −Qcnd

c , Qevpo (−Qdep

o , Qsubo ); and

melting of cloud ice, Qmltc . The precipitation formation

rates are based on Levkov et al. (1992) that include theautoconversion rate for warm clouds derived from thestochastical collection equation (Beheng, 1994) andaggregation rate for cold clouds based on Murakami(1990). qv, ql and qi are grid mean mass mixing ratio ofwater vapor, cloud liquid water contend and cloud icewater content in kg/kg.

The CSCM also includes prognostic equations for thenumber concentrations of cloud droplets, Nl, and ice

crystals, Ni with unit of (1/m3), following Levkov et al.(1992) and Lohmann et al. (1999):

ANl

At¼ Qnucl þ A

Ni

qiQc

mlt−Nl

qlQc

aut þ Qcracl þ Qc

sacl

��þ Qc

frc þ Qcfrh þ Qc

frs−QccdnÞ�−Qnself þ ATC Nlð Þ

ð8Þ�
ANi
At¼ Qnuci þ A

Nl

qlQc

frc þ Qcfrh þ Qc

frs

� �−Ni

qiQc

agg þ Qcsaci þ Qc

iaci þ Qcmlt−Q

cdep

�þATC Nið Þ

ð9Þ

where Qnucl is grid mean nucleation rate of the numberconcentration of cloud droplets; Qnuci is grid meannucleation rate of number concentration of cloud iceparticles; Qnself is the grid mean rate of depletion ofcloud droplet number due to self-collection; ATC(Nl)and ATC(Ni) are the advective and turbulent transportsof Nl and Ni.

The full description of the microphysics parameter-izations in Eqs. (5)–(9) is given by Lohmann andRoeckner (1996) and Lohmann et al. (1999).

2.2. Data description

The data needed to drive the CSCM are large-scaleforcing data and surface observations. Also to test themodel's ability to predict properties of clouds based on arealistic atmospheric state we use the nudging techniquefor horizontal velocities, temperature and water vaporprofiles toward the profiles obtained from objectiveanalysis of observed data.

The location of the simulated column is in the Arctic.Simulated values of the prognostic variables correspondto averages over a horizontal area of approximately60km×60km located at the latitude of 76.373N and thelongitude of 166.994W. The simulated period is fromNovember 1997 to September 1998.

The forcing data is derived from ECMWF reanalysishourly output including the total adiabatic tendencyprofiles of temperature and water vapor. The ECMWFreanalysis hourly output of surface temperature andhumidity and atmosphere profiles of horizontal veloc-ities, temperature and water vapor are used for nudging.

The observational data we use to validate modelpredictions for cloud cover, liquid water path and icewater path are provided by Shupe et al. (2001) based onradar observation, microwave radiometer retrieving, andradar-Doppler radar estimation, respectively. The pre-cipitation data are provided by Moritz (personal


communication 2001) based on a nipher shielded snowgauge system. We also used the SHEBA rawinsondedata provided by de Roode (personal communication2001).

2.3. Nudging

The nudging technique we used in the CSCM isbased on Newtonian relaxation (Jeuken et al., 1996). Werelax the model predicted horizontal velocities towardECMWF reanalysis data based on fixed relaxation time;and relax temperature and water vapor toward ECMWFdata based on the relaxation time determined from meanhorizontal velocities, as follows

AYVAt

¼ TEv þYV obs−

YV CSCM

s0ð10Þ

ATAt

¼ TET þ Tobs−TCSCMs

ð11Þ

AqvAt

¼ TEq þ qv obs−qv CSCM

sð12Þ

s ¼ Lnd=jV j ð13Þ

Nov Dec Jan Feb Mar Apl May Jun Jul Aug Sep0

0.2

0.4

0.6

0.8

1

To

tal

Clo

ud

Co

ver

SHEBA Year

Nov Dec Jan Feb Mar Apl May Jun Jul Aug Sep

SHEBA Year

0

50

100

150

200

250

300

Liq

uid

Wat

er P

ath

(g

/m2 )

RadarModel-ori wv

MWRModel-ori wv

Fig. 1. Comparisons of monthly mean Total Cloud Cover (TCC), Daily Precbetween CSCM simulations and observations at SHEBA site.

where |V | is the horizontal wind speed, τ0 is a typicaltime scale, Lnd (250km) is a typical length scale. TEx isthe tendency of variable x. The subscripts (obs andCSCM) refer to the observed and model simulatedvalues for those variables.

3. Nudging using ECMWF reanalysis H2O profilewith modification

The CSCM annual cycle simulations are first carriedout using the explicit cloud scheme and the ECMWFforcing (Beesley et al., 2000) with a nudging technique.The simulated period is from November 1997 toSeptember 1998.

Fig. 1 shows that the simulated monthly mean totalcloud cover (TCC) is much lower than the radarobservations. The simulated monthly mean dailyprecipitation rate (PREP) is too low compared to theSHEBA surface observations. In contrast, the simulatedmonthly mean liquid water path (LWP) is of the samemagnitude or larger than observed and the monthlymean ice water path (IWP) is systematically larger thanobserved (Shupe et al., 2001).

Since microphysics processes (condensation/depo-sition, autoconversion/aggregation, accretions, etc.) aredependent upon cloud fraction and/or in-cloud water


SHEBA Year


SHEBA Year

Ice

Wat

er P

ath

(g

/m2 )

0

50

100

150

200

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Dai

ly P

reci

pit

atio

n (

mm

/day

)

RetrievedModel-ori wv

ObservedModel-ori wv

ipitation (PREP), Liquid Water Path (LWP) and Ice Water Path (IWP)


contents. Microphysics parameterizations can not bewell evaluated by comparing observed and predictedprecipitation and cloud water predictions based on thepredicted cloud cover that is much lower thanobserved. Therefore, our first focus was to attemptto improve the prediction of the total cloud for theSHEBA year.

Typically, SCMs with explicit cloud schemes havetwo basic types of approaches to predict cloud coverand parameterize microphysics processes in cloudschemes (Fowler et al., 1996). One approach startsfrom microphysics processes and predicts cloudcoverage in the model layer based on the presenceof cloud water. This type of model cannot predictpartial cloudiness. The other approach predicts cloudfraction first within each layer and then parameterizesthose microphysics processes for given cloud fraction.Some previous works (Slingo, 1980, 1987; Xu andRandall, 1996) show that most clouds are subgrid-scale and fractional cloud cover must be considered,even for mesoscale models. Slingo (1980), Sundqvist(1978), Smith (1990) and Xu and Randall (1996)developed different parameterizations for predictingfractional cloud cover in large-scale models. All ofthem use the grid mean variable relative humidity(RH) to parameterize fractional cloud cover. In theCSCM, the Sundqvist (1978) parameterization ischosen for the explicit scheme.

An obvious possibility for underprediction of thetotal cloud cover is that the parameterization, which wasdeveloped for middle latitude or tropic region simula-tions, is not suitable in the Arctic Region. However,because we used nudging based on ECMWF profiles fortemperature and water vapor mixing ratio, underpredic-tion of the cloud cover could also be due to the humidityprofiles used for nudging being dryer than the observedatmosphere.

Due to the insufficient measuring frequency ofrawinsonde data, the nudging used in the CSCMsimulations is based on ECMWF reanalysis temperatureand water vapor profiles. Since these are a blend ofobservations and short-range forecast values resultingfrom the data assimilation process, a possible problem isthat they may have biases associated with thisassimilation process. Such a bias is revealed in Fig. 2which compares monthly mean vertical integrated watervapor path between rawinsonde data and ECMWFreanalysis data.

Fig. 2 shows that the ECMWF reanalysis under-estimates the water vapor path systematically during theSHEBA year. This bias may be related to the use of thefollowing temperature-dependence partitioning method

to determine the water vapor saturation mixing ratio instratiform clouds (Tiedtke, 1993):

Qsat ¼ RQsatw þ ð1−RÞQsati ð14Þ

R¼0 T < 250:16 K½ðT−250:16Þ=ð23:16Þ�2 250:16 KVTV273:16 K1 T > 273:16 K

8<:

ð15Þwhere Qsat, Qsatw and Qsati are water vapor saturationmixing ratio, water vapor saturation mixing ratio withrespect to liquid water and ice, respectively. On the otherhand, in the CSCM Qsat is set to Qsatw or Qsati when thetemperature is higher than 273.16K or lower than235.16K, respectively. For temperature values between273.16K and 235.16K Qsat is chosen to be Qsatw orQsati when ice water mixing ratio is less or more than10−5kg/kg, respectively.

In low-temperature regimes, typical of Arctic condi-tions using the ECMWF method could constrain vapormixing ratio values to be no larger than the saturationwater vapor mixing ratio with respect to ice, which isfrequently too dry. Additionally, the comparisons of incloud water vapor saturation mixing ratio betweenaircraft data and ECMWF formula (Fu and Hollars,2004) reveal that using this formula in such circum-stances leads to a significant underestimation of thewater vapor saturation mixing ratio. Thus, too muchwater vapor would be removed from the atmosphere tobe converted to clouds.

Because the rawinsonde measurements usually haveone measurement per 6 (occasionally) or 12h, theycannot be used directly to nudge the model simulations.In addition, the model predicted cloud is based on therelative humidity but not the absolute value of watervapor mass. In view of these factors, we have developeda scheme to scale the ECMWF water vapor profile asoutlined below while keeping the ECMWF temperatureprofile unchanged:

• Calculate the relative humidity with respect to liquidwater based on ECMWF reanalysis data (RHwecm)and rawinsonde measurements (RHwraw) separatelyand determine the ratio r=RHwraw/RHwecm for eachlevel at time which rawinsonde measurement isavailable;

• Linearly interpolate the ratio r to those times whenrawinsonde data is not available;

• Use those ratios to scale the ECMWF water vapormixing ratio at each time and each level.

0

2

4

6

8

10

12

14

16

Wat

er V

apo

r P

ath

(m

m)

Rawinsonde

ECMWF


SHEBA Year

Fig. 2. Comparison of column integrated water vapor path during SHEBAyear between rawinsonde measurements and ECMWF reanalysis results.


This procedure provides a modified set of profilesthat have the same temperature profile as before buta new water vapor profile, which has a relativehumidity profile that is compatible with rawinsondedata.

The new simulations based on modified ECMWFwater vapor profile shown in Fig. 3 indicate that thesimulated monthly mean total cloud cover agrees well

RadarModel-ori wvModel-new wv

MWRModel-ori wvModel-new wv


0.2

0.4

0.6

0.8

1

To

tal

Clo

ud

Co

ver

SHEBA Year


SHEBA Year

0

50

100

150

200

250

300

Liq

uid

Wat

er P

ath

(g

/m2 )

Fig. 3. Comparisons of TCC, PREP, LWP and IWP between CSCM simulatithose from observations.

with radar observations. The simulated monthly meandaily precipitation is also compared reasonably well tosurface measurements. Thus, the modified profile isconsistent with the physical components of the moistureand thermal forcing based on ECMWF data withnudging. Therefore, we are able to evaluate themicrophysics processes with well-simulated total cloudcover and surface precipitation.

ObservedModel-ori wvModel-new wv

RetrievedModel-ori wvModel-new wv


SHEBA Year


SHEBA Year

Ice

Wat

er P

ath

(g

/m2 )

0

50

100

150

200

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Dai

ly P

reci

pit

atio

n (

mm

/day

)

ons using original and modified water vapor profiles for nudging, and

5 10 15 20 25 30

2

4

6

8

Dec 97 cloud fraction simulated by CCCMA based on Original Qv profile

Dec 97 cloud fraction simulated by CCCMA based on Modified Qv profile

Hei

gh

t (k

m)

Hei

gh

t (k

m)

Hei

gh

t (k

m)

0.2

0.4

0.6

0.8

5 10 15 20 25 30

2

4

6

8

Day of Dec. 97

0.2

0.4

0.6

5 10 15 20 25 30

2

4

6

8

Dec 97 cloud fraction from Radar observation

0.2

0.4

0.6

0.8

Fig. 4. Comparisons of simulated cloud cover with radar observations (lower panel) in the December 1997 at the SHEBA site. The upper and middlepanels are CSCM simulations using the original and modified ECMWF reanalysis H2O profiles for nudging, respectively.


Cloud fractions for December 1997 and July 1998,respectively, are shown in Figs. 4 and 5). Comparedwith radar observations, it is apparent that for

5 10 15

2

4

6

8

Jul 98 cloud fraction simulated by CCCMA

Hei

gh

t (k

m)

5 10 15

2

4

6

8

Jul 98 cloud fraction simulated by CCCMA

Hei

gh

t (km

)

5 10 15

2

4

6

8

Jul 98 cloud fraction from Ra

Hei

gh

t (km

)

Day of Jul.98

Fig. 5. As in Fig. 4 bu

December 1997 the model was unable to predictthe presence of low clouds when using the originalwater vapor profile. However, using the modified data

20 25 30

based on Original Qv profile

0.2

0.4

0.6

0.8

20 25 30

based on Modified Qv profile

0.2

0.4

0.6

0.8

20 25 30

dar observation

0.2

0.4

0.6

0.8

t for July 1998.


the CSCM allowed low clouds to be simulated,especially from December 17th to December 30th.Sensitivity of the cloud cover to the water vaporprofile was not as pronounced in the summer (July1998).

However, Fig. 3 shows that the simulated cloud waterpaths (LWP and IWP) are much larger than the valuesderived from measurements. In the model, both liquidand frozen precipitation (rain and snow) are formed byconversion from cloud water, and the amounts of cloudwater are always much smaller than the total timeintegrated condensational (depositional) water andprecipitation. Usually, these microphysical processesare parameterized in terms of the initiation and growthof precipitation as nonlinear functions of cloud watercontent. Mass conservation implies that the total timeintegrated condensation plus deposition are equal tothe precipitation if the evaporation (sublimation) ofrain (snow) and the temporal variation of cloud waterin the atmosphere are neglected. In the Arctic region,these components are much smaller than the precip-itation. Thus, statistically the mean cloud water in theatmosphere presents the equilibrium state at which thetime integrated condensational/depositional water pro-duction can be balanced by the precipitation processes.Consequently, the results shown in Fig. 3, in whichthe CSCM produced reasonable monthly precipitationbut a much larger cloud water path as compared toobservations, indicate that the parameterizations ofprecipitation processes in the model may have somedefects.

4. Testing and improving microphysicsparameterizations

The GCM cloud microphysics parameterizationstested in this SCM, according to Levkov et al.(1992), Lohmann and Roeckner (1996) and Lohmannet al. (1999), are based on Beheng (1994) and Lin etal. (1983) for the precipitation processes (autoconver-sion, accretion and aggregation, etc.). These para-meterizations were originally developed for cloudresolving model simulations but some of them maynot be suitable in the circumstances under consider-ation here. In the following, we will examine keyaspects of these parameterizations beginning withaccretion processes.

4.1. Accretion

According to Lohmann and Roeckner (1996), thethree accretion processes in CSCM are parameterized

following Beheng (1994) and Lin et al. (1983) in theforms:

Qcracl ¼ 6qqclqr ð16Þ

Qcsacl ¼ 0:1

� p� 3� 106 � 4:83� qclCð3:25Þ4� k3:25s

q0q

0:5

ð17Þ

Qcsaci ¼

p� exp½0:025� ðT−T0Þ� � 3� 106 � 4:83� qciCð3:25Þ4� k3:25s

�q0q

0:5 ð18Þ

where ks ¼�p� ql � 3� 106

qqs

�0:25

, qcl and qci are the in-cloud liquid water and ice water mixing ratios,respectively; qr and qs are rain water and snow mixingratios, respectively; ρ, ρ0, ρi, and ρl are the densities ofair, air at surface (1.3kg/m3), cloud ice (500kg/m3) andcloud water (1000kg/m3), respectively.

In the CSCM, the accretion processes are implemen-ted based on a “pass through” assumption, whichassumes that all precipitation contributions from eachlayer can reach the surface within one time step (15minin this study). This assumption is retained here. It isacceptable for rain but may over estimate the precipi-tation of snow.

In the original scheme, the precipitation mixing ratiosare derived from the precipitation fluxes through therelations:

qr ¼ 1q

Fr

Dz=Dtð19Þ

qs ¼ 1q

Fs

Dz=Dtð20Þ

where Fs and Fr are the precipitation fluxes for snow andrain, respectively, calculated based on the “passthrough” assumption; Δz and Δt are the model layerthickness and time step, respectively. These treatmentsare of dubious validity and obviously have anunphysical dependence on the vertical resolution andtime step. In effect, changing the time step or the verticalresolution of the model layers leads to changes in themean terminal velocities of rain and snow followingEqs. (19) and (20). When the pass through assumption isjustifiable a consistent way to estimate the averagemixing ratios of precipitations is to use physicallyrealistic mean terminal velocities (rather than Δz/Δt) inEqs. (19) and (20). The use of Δz/Δt to convert


precipitation mixing ratios to fluxes is only valid whenattaining the resultant fluxes produced by a layer withina time step.

To test the sensitivity of model simulations to thevertical resolution, we did not apply the nudging onwater vapor and directly used the ECMWF temperaturesso that the simulations have the same atmosphere statewith the same temperature profile and water vaporforcing. Because we fixed the temperature profile for allof these simulations, the effects of differences caused byradiation calculations (i.e. heating rate effect) fordifferent simulations were eliminated. We also let themodel determine the saturation mixing ratio andpartitioning of condensate only based on temperatureso as to minimize differences associated with cloudprediction and partitioning of cloud water. Thus, we canisolate and evaluate the vertical resolution effect.Because the integrated ECMWF forcing is too strong(simulated precipitation is too large; also see Morrisonand Pinto, 2004) and the water vapor was notconstrained, the CSCM produced overcast cloudinessin all simulations. Fig. 6 shows results of a verticalresolution sensitivity study using these original treat-ments. (Only results shown in this figure are based onthe original accretion parameterizations. All others arebased on new accretion parameterizations that wediscuss later. Figs. 1 Figs. 3–5 are based on newaccretion parameterizations but without considering

Model-oldAcc-30Model-oldAcc-95Model-oldAcc-154



0.2

0.4

0.6

0.8

1

To

tal

Clo

ud

Co

ver

SHEBA Year


SHEBA Year

0

100

200

400

300

Liq

uid

Wat

er P

ath

(g

/m2 )

Fig. 6. Vertical resolution dependence of CSCM simulation

accumulation effects.) Three vertical resolutions wereused in the simulations. The legend “Model-oldacc-N”refers to the simulation with N vertical layers. Thetypical layer thickness in the troposphere for 30, 95 and154 layers is 40–50mb, 7–8mb and 3–4mb, respec-tively. Fig. 6 shows that the predicted LWP and IWPsystematically decrease when the vertical resolutionincreases.

An additional compounding problem is that theoriginal scheme considers the accretion processes as aconstant rate within each layer by using the fluxes(precipitation mixing ratio) at the top of each layer forthe whole layer. A more physical way is to consider theaccumulation effect within each layer, accounting foreffects due to changes of precipitation within the samelayer (precipitation flux increases as accretion occurs inthe same layer). Here, we replaced the Beheng (1994)parameterization for accretion of cloud droplets by rainusing Levkov et al. (1992) parameterization:

Qcracl ¼

32qwDRM

Frqcl ð21Þ

where ρw is the density of liquid water; DRM=5.4×10−4m. The only thing we changed from Levkovet al. (1992) parameterization is to use the rain fluxdirectly instead of the product of the rainwater mixingratio and the mean terminal velocity of raindrops and airdensity.




SHEBA Year

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We changed the parameterization of accretion ofcloud droplets by snow to the Rotstayn (1997)parameterization:

Qcsacl ¼

Eackf2qs

Fsqcl ð22Þ

where Eac is the mean value of collection efficiencywhich we set to 1 based on Rogers and Yau (1989) andLin et al. (1983); λf =1.6×10

3 ·100.023(T0−T) is the slopefactor with T0=273.16K and T is the absolute temper-ature of the atmosphere layer; ρs is the bulk density ofsnow which is set to 100kg/m3.

The parameterization of the accretion of snow by icecrystals according to Levkov et al. (1992) is based on Linet al. (1983):

Qcsaci¼pd qcid Esinosd 3:078d ½qqs=ðpqsnosÞ�0:8125

d ðq0=qÞ0:25 ð23aÞwhere nos = 3 · 10

6/m4 is the intercept parameterobtained from measurement (Gunn and Marshall,1958) Esi=exp[0.025 · (T−T0)] is the collection effi-ciency of snow for cloud ice. Eq. (23a) can be writtenin a form:

Qcsaci ¼ pd qcid Esinosd 3:078d ½q=ðpqsnosÞ�0:8125

d ðq0=qÞ0:25ðFs=VtÞ0:8125 ð23bÞwhere Vt is the terminal velocity of snow which weset as 1m/s. In order to account for the accumulationeffect in a simple analytical way, we modified Eq.(23b) so that the flux is expressed as a linear factorin the parameterization:

Qcsaci ¼ pd qcid Esid nosd 3:078d ½1=ðpqsnosÞ�0:8125

d ðq0=qÞ0:25d Fsd C ð24Þ

where C=Vt− 0.8125 ·Fs

− 0.1875 is assumed to beapproximately constant with a numerical value thatis about 7 for Fs with units of kg/m2 s and Vt equalto 1m/s.

A general equation for growth of the precipitationflux due to accretion processes is then of the followingform:

dF=dz ¼ aðqxÞ þ bd Fd qx ð25Þ

where F is the precipitation flux, a(qx) is the increaseof flux caused by either autoconversion or aggrega-tion, qx is the cloud water content which is assumed tobe constant within one layer, and the second term ofthe right-hand side accounts for the accretion effect.

For example, for the growth of rain flux the a(qx) isthe autoconversion rate Eq. (34) and b is 3

2qwDRMbased

on Eq. (21). Taking all quantities except the flux to beconstant for given layer, we can solve this equationanalytically for the flux and thereby explicitlyconsider the accumulated effect of accretion. Thesolution for the flux at the bottom of a layer based onEq. (25) is:

F ¼ F0d exp bd qxd Dzð Þ þ aðqxÞbd qx

d exp bd qxd Dzð Þ−1½ �ð26Þ

where F0 is the flux at the top of the layer and Δz isits thickness.

Fig. 7 shows the sensitivity of the modifiedparameterization for the accretion processes as wellas the accumulation effects. Here we show the resultsusing the new accretion parameterizations with andwithout applying the analytic solution (Eq. (26)) withdifferent vertical resolution. Comparing Figs. 6 and 7shows that the modified treatments of accretionprocesses have much less sensitivity to the modelvertical resolution. However, the accumulation effectfrom the predicted LWP and IWP is clearly evident.The simulation with 30 layers (low vertical resolution)using the new parameterizations but without consid-ering the accumulation effect systematically producedlarger values of the LWP and IWP than the others, butthe results of simulations with 95 and 154 layers showevidence of convergence. By applying Eq. (26) in themodified parameterizations, the simulated LWP andIWP show little sensitivity to the model verticalresolution, which achieving a magnitude slightlysmaller than that using 154 layers without applying(26). This demonstrates that unphysical dependence ofthe accretion parameterization on the vertical resolu-tion is eliminated by considering the accumulationeffect. A similar effect, discussed by Rotstayn (1997),which needs to be considered when using a largertime step, is that cloud water content decreases withtime when accretion processes are active. This is notconsidered in our study since we use a relative shorttime step.

4.2. Ice nucleation number concentration

Generally, there are three kinds of ice nucleationprocesses: Deposition and condensation-freezing nucle-ation, contact freezing and other secondary ice produc-tion. In the CSCM, the ice crystal nucleation isparameterized in terms of the newly deposited/frozen

Model-anaAcc-30Model-newAcc-30Model-anaAcc-95Model-newAcc-95Model-anaAcc-154Model-newAcc-154





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Fig. 7. As in Fig. 6 but using modified treatment of accretion processes with and without considering the accumulation effect.


ice water and a mean ice crystal radius derived from theeffective ice crystal radius rie which is parameterized asa function of temperature based on observations (Ou andLiou, 1995):

rie ¼ 0:5� 10−6½326:3þ 12:4ðT−T0Þþ 0:2ðT−T0Þ2 þ 0:001ðT−T0Þ3� ð27Þ

where T0=273.16K. The mean volume radius riv isdetermined based on an empirical relation with theeffective ice crystal radius rie from simultaneousmeasurements of the two radii (Lohmann et al., 1999):

riv ¼ 10−6ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffibþ ðgþ dr3ieÞ1=3

3

qð28Þ

where β=−2.261×103, γ=5.113×106, δ=2.809×103.Following Lohmann et al. (1999), the rate of new ice

crystals nucleation for given time step Δt is then givenby

Qnuci ¼ 3q0qdepi

4pqir3iv

1Dt

þ Qnfr ð29Þ

where qidep is the increase in the ice mixing ratio due to

deposition of new ice crystals in a layer during the timestep, ρi (500kg/m

3) is the ice crystal density and ρ0 isthe air density. Qnfr is the increase of ice particles due tothe freezing of cloud water in 1/m3 s.

However, many GCM cloud microphysics schemesincluding those used in UK Met-Office Unified Model(Wilson and Ballard, 1999), ARCSCM (Morrison et al.,2003), and CSIRO GCM (Rotstayn, 1997), usediagnostic parameterizations for ice nuclei numberconcentrations based on observations (Fletcher, 1962;Meyers et al., 1992). The parameterization developed byMeyers et al. (1992) considers the number concentrationof ice nuclei due to deposition and condensation-freezing nucleation along with contact freezing:

Nnuci; dep ¼ 1000exp½−0:639þ 0:1296ð100ðSi−1ÞÞ� ð30Þ

Nnuci; con ¼ 1000exp½−2:8þ 0:262ðT0−TÞ� ð31Þ

where T0 is 273.16K and Si is the super-saturation ratiowith respect to ice. Nnuci, dep and Nnuci, con, are in the unitof 1/m3. Eq. (31) applies only if cloud liquid water ispresent. After comparing the Lohmann et al. (1999)treatment with Meyers et al. (1992) parameterization,we found that the Lohmann et al. (1999) treatmentoverestimates the number concentration of ice nucleisignificantly and thus the CSCM produces much moreice particles with smaller sizes. This reduces conversionof ice particles to snow through the aggregation process.Consequently, the CSCM predicts much larger IWPsthan those observed.


Fig. 8 shows the comparison of ice nucleationnumber concentration simulated by using Lohmann etal. (1999) treatment (Eqs. (27)–(29)) and Meyers et al.(1992) parameterization (Eqs. (30) and (31)). Thesolid line refers to the mean ice nucleation numberconcentration produced following Meyers et al. (1992)and the dash line with circles refers to Lohmann et al.(1999) treatment. They are the mean values of icenucleation number concentration produced in eachstep versus temperature by the model during onesimulation. It is evident that using Lohmann et al.(1999) treatment overestimates the nucleation numberconcentration significantly.

Fig. 9 shows results of the sensitivity study forice nucleation number concentration. We useddifferent treatments for ice nucleation numberconcentration with new accretion parameterizations(accumulation effects are not considered here).Simulations are based on general conditions (nudg-ing on temperature and water vapor with adjustedwater vapor profiles). The “Model-Meyers” refersthe simulation using Meyers et al. (1992) parame-terization and “Model-Lohmann” refers the simula-tion using Lohmann et al. (1999) treatment. Fig. 9clearly shows that using Meyers et al. (1992)parameterization decreases the simulated IWP ascompared to using Lohmann et al. (1999) treatment.With similar TCC and PREP prediction, the use ofMeyers et al. (1992) parameterization brings thesimulated IWP into a better agreement with thatderived from measurements.

235 240 245 250

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Fig. 8. Comparisons of the ice nucleation number concentration simulated bMeyers et al. (1992).

4.3. Autoconversion

Autoconversion is a highly nonlinear process.GCMs usually parameterize this process as a nonlinearfunction of in-cloud liquid water content. In the GCMcloud scheme tested in this study, the Beheng (1994)parameterization is used. As discussed by Pincus andKlein (2000) and Wood et al. (2002), this kind ofnonlinear parameterization based on the mean cloudwater content underestimates the autoconversion ratedue to GCM sub-grid scale variability. Because thedistribution of cloud water is not homogenous, usingthe linear averaging of water content to calculate suchnonlinear process rate usually produces less precipi-tation. A more consistent way is to integrate theautoconversion rate by considering the probabilitydistribution function (PDF) of cloud liquid watercontent. We have evaluated the sensitivity to such aprocedure by using Gaussian PDF for total water toderive the factor that accounts for the effect of sub-grid variability as a function of cloud fraction. Wethen apply this correction factor to Beheng (1994)parameterization for auto-conversion in GCM gridscale.

For given GCM grid size, the cloud fraction A andgrid mean total cloud water content qc (Smith, 1990;Richard and Royer, 1993) can be expressed as:

A ¼Z l

�Q1

GðtÞdt ð32Þ

255 260 265 270

ture (K)

y using the parameterization of Lohmann et al. (1999) and that from

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Fig. 9. Comparisons of TCC, PREP, LWP and IWP between observations and CSCM simulations using Meyers et al. (1992) and those usingLohmann et al. (1999) for ice nucleation number concentration. The adjusted water vapor profiles are used for nudging in these simulations.


qc ¼ rZ l

�Q1

ðQ1 þ tÞGðtÞdt ð33Þ

where t, σ and Q1 are a normalized variable, its standarddeviation, and a variable which states the threshold ofcondensation, respectively. The Beheng (1994) param-eterization for autoconversion is:

Qcaut ¼ 6� 1028 � 10−1:7ð10−6NlÞ−3:3ð10−3qqclÞ4:7=q ð34Þ

where qcl is the in-cloud liquid water mixing ratio and ρis the density of air. We define the ratio R for the effect ofhorizontal inhomogeneity:

Raut ¼r4:7

Z l

�Q1

ðQ1 þ tÞ4:7GðtÞdt

ðqc=CFÞ4:7

¼

Z l

�Q1

ðQ1 þ tÞ4:7GðtÞdt"Z l

�Q1

ðQ1 þ tÞGðtÞdt=Z l

�Q1

GðtÞdt#4:7 ð35Þ

Consequently, we can numerically derive a relationbetween Raut and A because from (32) and (35) we

know they are both functions of G(t) and Q1. Byassuming G(t) is the Gaussian distribution function,we find that:

Raut ¼ −40d A3 þ 89d A2−93d Aþ 47 ð36Þ

Fig. 10 shows the comparisons of CSCM simulationswith modified microphysics parameterizations at differ-ent levels. They include the results using the Meyers etal. (1992) parameterization with modified treatments foraccretion processes (“Model-Meyers”), the results using“Model-Meyers” but with treatments of accumulationeffect (“Model-Meyers-ana”), and the results of furtherconsidering horizontal inhomogeneity effect (“Model-Meyers-ana-inhomo”).

With the consideration of accumulation effects, thepredicted IWP decreases systematically. In November,March and April, the decreases are about 40% and insummer time (July–September 1998) the decreases areabout 25%. The LWP decreases about 10% in thesummer. We also see that, after accounting for the sub-grid variability effect on the Beheng (1994) autoconver-sion parameterization, in July and August the simulatedLWP decreases additionally about 10% but simulatedIWP increases a little bit. The TCC and PREDpredictions agree with observations well for all

RadarModel-MeyersModel-Meyers-ana-inhomoModel-Meyers-ana

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Fig. 10. Comparisons of TCC, PREP, LWP and IWP between CSCM simulated based on new accretion parameterizations with and withoutconsidering the accumulation effect and the inhomogeneity effect.


simulations, which are insensitive to the microphysicsprocesses. We conclude that the simulated IWP withmodified microphysics parameterizations (i.e., Model-Meyers-ana-inhomo) agree with the observations withinobservational uncertainties (Shupe, personal communi-cation). The simulated LWP is also greatly improved.But it is noted that there still exist significantdiscrepancies between the simulated LWP and observa-tions in July and August.

5. Partitioning of condensate in mixing clouds

The condensation/deposition of mixed phase cloudsis a common source of difficulty in large-scale models.How to determine the total condensate and thepartitioning between different phases is not wellunderstood. This involves two separate issues. One ishow to determine the water vapor saturation mixingratio in mixed phase clouds in climate models. The otheris how to partition the condensate between liquid andice. Many existing cloud schemes first define saturationmixing ratio and then partition the super-saturated watervapor between ice and water using a simple formula thatdepends on the temperature below freezing point(Smith, 1990; Rotstayn, 1997; Fowler et al., 1996;Ose, 1993). The CSCM employs the saturation mixingratio with respect to pure liquid or pure ice based on a

threshold of cloud ice water content. So the accuracy ofprediction of ice water content also affects thecondensation/deposition and partitioning processes.Since condensation and evaporation processes aremuch faster than deposition and sublimation processes,it is commonly assumed the water vapor saturationpressure should always be that with respect to liquid aslong as liquid water is present. But Fu and Hollars(2004) have shown, using in-situ aircraft observationsfrom Canadian NRC Convair 580 during SHEBA/FIRE.ACE project, that the measured in-cloud water vaporpressure is in good agreement with the cloud-waterweighed saturation pressure. One explanation for thisresult is that in mixed phase clouds there are smallpatches with liquid cloud parcels and ice cloud parcelsintermingled so that the sampling counts the mean watervapor pressure of these patched clouds as a mixture. Wehave examined the sensitivity to the effect of thepartitioning of mixed clouds in CSCM simulations bycomparing the effect of using the original CSCMrepresentation for total condensate and its partitioningto the one that is based on Fu and Hollars (2004) result.We did not nudge water vapor so that the twosimulations have the exactly same forcing profiles forwater vapor. We also scaled the moisture forcing data tofit the precipitation. Thus, we have the water vaporforcing whose integrated value is same as the


precipitation measured. The nudging on temperature isstill retained so as to inhibit possible drifts associatedwith changes in temperature that may render interpre-tation of the results more difficult.

Fig. 11 shows the difference between the twosimulations. Here all previous modifications onparameterizations are applied (Eqs. (21), (22), (24),(26), (30), (31) and (36)). We ignored the nudging onwater vapor and scale the forcing using observedprecipitation so that the integrated forcing is similar toobserved precipitation. Providing a reasonable forcingand without constraining on water vapor we can testhow well the microphysics parameterization works ascompared with measurements. The ‘Model-ori-par’refers to the results using original partitioning method(Lohmann and Roeckner 1996; Lohmann et al., 1999)and ‘Model-mass-par’ refers to the mass-weightedpartitioning method (Fu and Hollars, 2004). Usingmass-weighted partitioning parameterization, theCSCM can produce LWP and IWP that agree wellwith observations, especially in the summer time forLWP. Although these results do not confirm unam-biguously that the mass-weighted partitioning methodis more reasonable, it clearly has the potential toexplain why CSCM simulates an excessively largeLWP in summertime in the SHEBA year.

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Fig. 11. Comparisons of TCC, PREP, LWP and IWP between CSCM simulatall improvements on microphysics parameterization. Water vapor is not coprecipitation.

6. Conclusions and summary

We have described some improvements of GCMcloud parameterizations and tested them in the contextof the annual-cycle simulations for the SHEBA study.Using nudging techniques in CSCM simulations allowsthe CSCM to produce cloud and condensation based onthe atmosphere that is close to the real atmosphere state;while allowing evaluation of simulated cloud properties(LWC, IWC, etc.) and their dependence on microphys-ics parameterizations. The main results are thefollowing.

The CSCM simulations are very sensitive to thewater vapor profile used for the nudging. Because theCSCM procedure for determining the saturation watervapor mixing ratio differs from that used for theECMWF analyses, directly nudging using the SHEBAECMWF reanalysis data results in a dryer backgroundatmosphere during the simulations. In order to alleviatethis bias for the Arctic simulations using the CSCM, weadjusted the water vapor profiles and used these for thenudging while retaining the original ECMWF reanalysisvelocities and temperature profiles along with theadjusted water vapor profiles having similar relativehumidity as rawinsonde observations. The simulationbased on the new water vapor profiles leads to

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ed using old partitioning and mass-weighted partitioning methods withnstrained and the moisture forcing is scaled to be close to observed


reasonable predictions of cloud cover and surfaceprecipitation.

The treatments of accretion processes were found tobe flawed in various ways, resulting among other thingsin an unphysical dependence on vertical resolution. Wechanged and modified the parameterizations of theaccretion processes to eliminate this artificial depen-dence on resolution as account as well for the effect ofaccumulation within layers.

The CSCM systematically tends to produce exces-sively large values of the IWP regardless of what watervapor profile is used in the nudging. This was found tobe sensitive to the parameterization of the ice nucleationnumber concentration. The treatment following Loh-mann et al. (1999), used in the standard version of theCSCM, results in an overestimation of ice nucleationnumber concentration in comparison with anothercommonly used parameterization (Meyers et al.,1992). This results in underestimate of mean ice particlesize that decreases the aggregation rate evidently.Replacing the original treatment with the Meyers et al.(1992) parameterization results in more realistic simu-lated values of the IWP.

The CSCM uses the Beheng (1994) parameterizationfor autoconversion based on the average in-cloud liquidwater content. As suggested by Pincus and Klein (2000),we considered the effect of sub-grid variability, whichaccounts the effect of unevenly distributed cloud water,in the context of an assumed Gaussian distribution forthe totals water. Although the effect of doing this isrelatively small, it does act to make the simulated LWPand IWP more realistic (smaller).

With modified cloud microphysics parameterizationsincluding improved treatments for accretion processes,ice nucleation number concentration, and autoconver-sion, the CSCM simulated LWP and IWP are muchimproved as compared with observations. Furthermore,we find that the simulated LWP and IWP are alsosensitive to the assumptions used to define saturatedwater vapor pressure and partition total cloud conden-sate in mixed phase clouds.

Using a partition and definition of the effectivesaturation vapor pressure based on Fu and Hollars(2004) resulted in substantially improved simulations ofthese quantities for the SHEBA location and period.

Acknowledgements

This study is supported by NSF Grant OPP-0084259,and partly by the Canadian CCAF fund, DOE Grant(Task Order 355043-AQ5 under Master Agreement325630-AN4), LANL IGPP Awards, and NASA Grant

NNG05GA19G. We thank U. Lohmann for providingthe single-column model.

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