Abstract

A parameterization is introduced for the prediction of cloud water in the National Center for Atmospheric Research Community Climate Model version 3 (CCM3). The new parameterization makes a much closer connection between the meteorological processes that determine condensate formation and the condensate amount. The parameterization removes some constraints from the simulation by allowing a substantially wider range of variation in condensate amount than in the standard CCM3 and tying the condensate amount to local physical processes. The parameterization also allows cloud drops to form prior to the onset of grid-box saturation and can require a significant length of time to convert condensate to a precipitable form, or to remove the condensate. The free parameters of the scheme were adjusted to provide reasonable agreement with top of atmosphere and surface fluxes of energy. The parameterization was evaluated by a comparison with satellite and in situ measures of liquid and ice cloud amounts. The effect of the parameterization on the model simulation was then examined by comparing long model simulations to a similar run with the standard CCM and through comparison with climatologies based upon meteorological observations.

Global ice and liquid water burdens are higher in the revised model than in the control simulation, with an accompanying increase in height of the center of mass of cloud water. Zonal averages of cloud water contents were 20%–50% lower near the surface and much higher above. The range of variation of cloud water contents is much broader in the new parameterization but was still not as large as measurements suggest. Differences in the simulation were generally small. The largest significant changes found to the simulation were seen in polar regions (winter in the Arctic and all seasons in the Antarctic). The new parameterization significantly changes the Northern Hemisphere winter distribution of cloud water and improves the simulation of temperature and cloud amount there. Small changes were introduced in the cloud fraction to improve consistency of the meteorological parameterizations and to attempt to alleviate problems in the model (in particular, in the marine stratocumulus regime). The small changes did not make any appreciable improvement to the model simulation.

The new parameterization adds significantly to the flexibility in the model and the scope of problems that can be addressed. Such a scheme is needed for a reasonable treatment of scavenging of atmospheric trace constituents, and cloud aqueous or surface chemistry. The addition of a more realistic condensate parameterization provides opportunities for a closer connection between radiative properties of the clouds, and their formation and dissipation. These processes must be treated for many problems of interest today (e.g., anthropogenic aerosol–climate interactions).

1. Introduction

Clouds are extremely important regulators of the earth’s climate. They strongly affect the earth’s radiation budget, they are sites for rapid transport of heat and mass, they are regions where important chemistry takes place, and they are reservoirs of heat and moisture within the atmosphere. Yet because of their complexity, and the vast range of scales in time and space over which they operate, it is difficult to accurately represent their role in climate within today’s atmospheric models. Rather severe simplifications must be made to most processes entering into a cloud’s description in order to be incorporated into an atmospheric model.

The importance of a reasonable representation of clouds in atmospheric models today and the associated difficulties in parameterizing them are well known. Three recent complementary discussions of the issue can be found in Sundqvist (1993b), Fowler et al. (1996), and Del Genio et al. (1996). They point out the difficulties and design criteria required to construct, calibrate, and verify the correct behavior of a scheme for the representation of clouds in a global atmospheric model.

In this paper we introduce a new parameterization of cloud condensate in the National Center for Atmospheric Research (NCAR) Community Climate Model version 3 (CCM3) and discuss some initial results from Atmospheric Model Intercomparison Project (AMIP) style simulations using the new parameterization. The formulation has been adopted for the next version of the CCM, which was released in the latter half of 1997. Our formulation for cloud water combines a representation for condensation and evaporation similar to that of the pioneering work of Sundqvist, with a bulk microphysics parameterization closer to that used in cloud-resolving models. Our reasons for departing from the Sundqvist formalism are discussed in more detail in section 3. The parameterization adds one additional predicted variable to the model, which we call cloud condensate. It is assumed to have a negligible fall velocity and thus to be suspended within a parcel. The condensate is currently assumed to be sufficiently short lived that resolved (i.e., advective) processes have little influence upon it, but unresolved processes (i.e., convective and turbulent processes in the boundary layer) can effect it (advection by resolved processes can be enabled with a switch). The neglect of advection is not necessarily a safe assumption, and we will explore the simulation sensitivity to this process in a future paper. The condensate can evaporate back into the environment or be converted to a precipitating form (which we assume to be either rain above a freezing temperature or a graupel-like snow below the freezing point) depending upon its in-cloud value and the forcing by other atmospheric processes. The precipitating components of the parameterization are treated in diagnostic form [i.e., the time derivative has been neglected, following Sundqvist (1988) or Ghan and Easter (1992)].

The parameterization currently takes about 12% of the total model run time, a relatively small fraction when compared to the more elaborate formulations of Fowler et al. (1996) or Ghan et al. (1997), who cite factor of 2 increases in computer time, and similar to that of Del Genio et al. (1996), who use a somewhat simpler formulation than ours for the transformation of condensate to precipitate. It falls somewhere between the “first class” of cloud water parameterizations defined in Fowler et al. (1996) that use very simple microphysical formulations and the “third class” parameterization, which maintains the time-dependent forms of the evolution equations for at least five classes of cloud particles.

The NCAR CCM3 has a quite realistic model climatology when considered in the context of current general circulation models (GCMs). Its simulation properties have been evaluated in a variety of ways (Kiehl et al. 1998; Hack et al. 1998; Hurrell et al. 1998, hereafter HU98) in a special issue of the Journal of Climate (Vol. 13, issue 6) devoted to articles about the NCAR Climate System Model (CSM) effort. One example of the quality of the simulation is the fact that the CSM model (consisting of the CCM3 coupled to a full depth ocean model, and interactive sea-ice parameterization) has now been run for a 300-yr simulation without any correction of the fluxes and no evidence of globally averaged surface temperature drift (there are still local temperature drifts). We are aware of no other coupled climate system model today that is capable of such a simulation. Imbalances between the atmosphere, ocean, and ice components generally imply relatively rapid drifts in surface temperature unless the model is constrained through a flux correction at the surface, or by prescribing the ice amount. The lack of drift with respect to today’s climate in this model suggests that both top of atmosphere and surface fluxes of energy, momentum, and moisture are quite realistic (and implicitly that the dynamics of the atmosphere itself are also reasonable).

It has been our goal during the initial development of this parameterization to achieve a simulation of approximately equivalent (or better) quality to the standard CCM3, and to minimize the number of changes made to other parameterizations in the GCM. This implies that, at least in a time-mean sense, the climatology of the simulation with the predicted condensate must be quite similar to that of the standard CCM3, since its general circulation is already quite good. Nevertheless, the addition of the cloud water parameterizations has relaxed some constraints within the climate system, and changes are evident in some aspects of the CCM climate. Perhaps more importantly, we have designed the parameterization with a number of other goals in mind. These goals are to introduce a more physically realistic representation of cloud processes while keeping the parameterization explainable, and computationally rather inexpensive. We were seeking a parameterization that allowed for the following:

  1. A local response of condensate amount to forcing by other processes (advection of heat and moisture, convection, and turbulent boundary layer processes). The standard CCM3 allows only for a very broad response over a whole column to changes in the column-integrated water vapor amount.

  2. The storage of water in the form of condensate, and the associated latent heat exchanged with the atmosphere when the condensate undergoes a phase change.

  3. An explicit representation of the conversion of condensate (ice or cloud water) to precipitate, in terms of easily understood physical properties.

  4. An explicit representation of differences in cloud properties over oceans and land associated with the different sources providing cloud condensation nuclei (CCN).

The new condensate parameterization removes some “constraints” from the simulation by allowing a substantially wider range of variation in condensate amount than in the standard CCM3. The parameterization also allows cloud drops to form prior to the onset of grid-box saturation and can require a significant length of time to convert condensate to a precipitable form or to remove the condensate. It therefore introduces a new set of feedbacks and processes with timescales not present in the standard CCM3. So it is expected that the temporal or spatial variability of the model might change.

We note that the parameterization was designed not only to include interactions between the model’s water vapor, temperature, and radiative fields as emphasized by Fowler et al. (1996) and Del Genio et al. (1996), but also because they are important when considering the interactions between clouds and aerosols and other soluble atmospheric trace species (e.g., Lohmann and Roeckner 1996; Feichter et al. 1996; Berge 1993). The parameterization provides some additional opportunities for including new feedbacks in the model (e.g., Boucher and Lohmann 1995). For example, by using the predicted mass of condensate, and the number density of cloud particles, it is possible to predict the effective radius of the cloud particles and allow aerosol–cloud interactions.

In this paper we will first briefly outline the CCM3 (section 2), and the few changes made to other parameterizations of the CCM (section 2b), then describe the new parameterization (section 3). Section 4 provides some documentation of the similarities and differences between the control and the simulation including the new parameterization.

2. Description of CCM3

a. Control

The standard NCAR CCM3 is described in Kiehl et al. (1996). The model climatology is described in a series of papers by Kiehl et al. (1998), Hack et al. (1998,hereafter HA98), HU98, and Bonan (1998, hereafter BO98)

The evolution equations for heat and momentum use a spectral representation for the horizontal treatment and first-order vertical finite differences for vertical gradients. The horizontal resolution is approximately 2.8° × 2.8°. A hybrid vertical coordinate is used that is terrain following in the lower troposphere, and gradually makes a transition to a pressure following coordinate in the lower stratosphere. Eighteen vertical levels are used extending from the surface to approximately 35 km. The time integration scheme used for the dynamical and thermodynamic equation is a semi-implicit, leapfrog time integration scheme. A 20-min time step is used for the model dynamics. The transport of moisture and other tracer species is done using a three-dimensional “shape preserving” semi-Lagrangian transport formalism. The physical parameterizations and transport are time split (i.e., applied sequentially). Because both the semi-Lagrangian transport and the physical parameterization are two-time-level schemes, a 40-min time step is used for them, with the solution advanced from time level tn−1 to tn+1. The planetary boundary layer parameterization is a nonlocal scheme, in which the boundary layer depth is calculated explicitly and the profile of diffusion coefficients is prescribed below that depth. The parameterization includes the typical downgradient diffusion throughout the depth of the atmosphere, as well as a less typical nonlocal transport term within the convective boundary layer. Above the boundary layer a local vertical diffusion scheme is used, with a local Richardson number–dependent diffusion coefficient. A parameterization of momentum flux divergence (produced by stationary gravity waves arising from flow over orography) is included.

Convection is represented by two schemes. A deep penetrative convection scheme (Zhang and McFarlane 1995) is applied first. This scheme acts to reduce any convective available potential energy (CAPE) present within the column extending from the surface to the upper troposphere over a short time period. Subsequently a local convective transport scheme (Hack 1994) is used to remove any local instabilities that remain. The Hack convection scheme typically represents the shallow subtropical convection and midlevel convection whose origins do not occur in the boundary layer. The parameterizations both move heat, moisture, and trace species in a self-consistent way.

The cloud fraction parameterization is philosophically based upon the work of Slingo (1987). Cloud fraction depends upon relative humidity, vertical motion, static stability, and convective properties. Clouds are permitted at all tropospheric levels above the surface layer. Stratiform condensation in the standard CCM3 takes place when a grid box is completely saturated. The in-cloud water distribution (Hack 1998) used in the radiative transfer calculation is prescribed as a function of column-integrated water vapor and height. That is,

 
formula

where ρc is the in-cloud water content, qv is water vapor specific humidity, and pt and ps represent the pressures at top of the atmosphere and surface, respectively. Thus clouds in the near-surface layers always have about the same water content, but values in the upper troposphere can differ—particularly between the Tropics and extratropics. A distinction is made within the radiation parameterization between ice and liquid phases of water. The cloud water is assumed to be liquid above a temperature of 263 K. Below 243 K it is assumed to be pure ice. The fraction of liquid to total water varies linearly with temperature between these two regimes. A 10-μm (5 μm) effective radius is assumed for warm clouds over ocean (land). Ice clouds are assumed to have a 10-μm effective radius for the radiatively active ice particles (not the snow) below 800 mb and to increase linearly in pressure to a 30-μm effective radius above 400 mb. These properties are then used in the calculation of cloud albedos, absorptivities, and emissivities. The solar radiative heating is computed using a δ-Eddington parameterization with 18 spectral bands. The longwave calculation includes a Voigt line shape correction (incorporated to increase cooling rates in the upper stratosphere and mesosphere). Clouds are assumed to be plane parallel and randomly overlapped between layers. Condensate is assumed to be uniformly distributed within the cloudy volume.

The atmospheric model is coupled to an interactive land surface model that predicts snow cover, albedo, and fluxes of moisture, heat, and momentum across the surface (BO98).

In the version of the model run for this study, the sea surface temperatures have been prescribed using estimated monthly mean estimates for the years of 1979–93. Thus the simulation is an extension of an AMIP style integration.

b. Modification to the standard CCM3

In spite of the general quality of the simulation discussed above, there are significant biases in the model simulations. There is a persistent polar cold bias of 2–6 K in the lower troposphere in both hemispheres when compared to analyses from the European Centre for Medium-Range Weather Forecasts (ECMWF) or National Centers for Environmental Prediction (NCEP) (see HA98 and following text). There are corresponding general cold biases in midlatitude surface temperatures, particularly in the Northern Hemisphere summer. The marine stratocumulus clouds often tend not to be bright enough, and the marine stratocumulus cloud amount west of Peru does not show a large enough seasonal cycle (Kiehl et al. 1998). Precipitation tends to be too persistent in the warm pool region and is located south of the equator over Indonesia rather than north of it over the Phillipines during June–August (JJA). A secondary maximum exists in the model over the date line, north of the equator, which is not seen in the observational estimates. While we have not put an all out effort on alleviating these biases, we have made some minor modifications to the model in an attempt to improve the simulation of these features, and monitored the effect of the cloud water revisions on these problems.

To introduce a consistent formulation for a predicted cloud water amount, it was necessary to make a few minor modifications to the CCM in addition to the cloud water parameterization itself. For example, the standard CCM3 does not permit the formation of clouds in the lowest model layer. This restriction was designed to circumvent potential problems in earlier versions of the CCM, which showed an abundance of very bright, low clouds when they were permitted there. This feature can be explained in part by the fact that the prescribed cloud water amounts have their maximum in the lowest model level by design, assuring the maximum brightness per unit amount of cloud in that layer [see Eq. (1)]. In the standard CCM3 it is possible to have condensation occurring within a grid volume even in the absence of any diagnosed cloud, because condensation processes are decoupled from cloud fraction, which influences only the radiation. On the other hand, the prognostic cloud scheme described here is strongly tied to the cloud amount. It is not possible for condensation to occur in the absence of a diagnosed cloud fraction. This constraint highlights the improved consistency required and enforced between processes when the prognostic cloud water scheme is used. For this reason we have modified the standard cloud fraction parameterization to permit clouds in the surface layer and require that at least 1% cloud fraction is diagnosed in any grid box exceeding 99% relative humidity. This latter modification makes virtually no difference to the standard model but does permit the cloud water scheme to prevent supersaturation.

Furthermore, we felt that improvements were needed to the formulation for convective cloud fraction parameterization used in the standard CCM3, which makes convective cloud proportional to the logarithm of the vertical integral of the convective mass flux, from the level of free convection to the level of neutral buoyancy, as diagnosed by the two convective parameterizations. An examination of the convective cloud distribution showed very little spatial coherence, with essentially the same (i.e., within a factor of 2) 10% convective cloud cover diagnosed over subsidence regions with suppressed convection and those areas (e.g., the warm pool Pacific) with very strong convection. Most of the radiatively important cloud fraction within the CCM3 is determined by the stratiform cloud formulation based primarily on relative humidity. On the other hand, Xu and Krueger (1991) have shown that relative humidity is not a good predictor for clouds in the upper troposphere connected with convection. For our formulation of condensate formation to work, cloud fraction and local moistening must be strongly correlated. For this reason we have replaced the standard convective cloud fraction in CCM3 with an expression documented in the appendix that makes convective cloud depend upon the rate at which mass detrains from the convective updraft.

The CCM3 diagnosis of marine stratocumulus depends upon a local measure of the vertical stability (Slingo 1987). Because this parameterization may be sensitive to vertical resolution, and because the CCM3 does not show the correct seasonal cycle in marine stratocumulus cloud amounts, or the associated cloud forcing in those regions, we modified the calculation of cloud fraction in marine stratocumulus regimes. A very strong correlation has been shown to exist in observations between the mean stratification in the lower troposphere (defined by the difference between potential temperature at 700 hPa and the surface) and the cloud fraction in those regions (Klein and Hartmann 1993). Kiehl et al. (1998) demonstrated that although the seasonal cycle of the basic thermal structure is correct in the CCM3, the correct seasonal in-cloud fraction is not diagnosed from the Slingo (1980) scheme. For this reason we have replaced that scheme with one determined from the regression relationship found by Klein and Hartmann (1993). The precise forms used in the parameterization are expressed in appendix A.

Finally we have made minor modifications to the Zhang convection scheme to eliminate inconsistencies between the mass fluxes used to transport trace constituents and those used to calculate heat and moisture tendencies, and we removed a minor bug in the code. The convection changes had only a tiny effect on the model climate but improve the model’s internal consistency.

3. Description of the new condensation parameterization

In this section we describe the form of the new parameterization. As mentioned in the introduction, the conversion of water vapor to and from condensate follows the work of Sundqvist (1978) and Sundqvist (1993b) (and references therein) although we perform the manipulations in the context of the water vapor mixing ratio, rather than the relative humidity, which simplifies the development somewhat. The conversion from condensate to precipitate is quite different from that of Sundqvist. We have chosen forms more similar to those used in regional models of the atmosphere, which usually retain explicitly the constants arising from assumptions about the size distributions of the cloud water and precipitation. This provides a ready opportunity to modify the cloud properties in the future for, for example, aerosol–climate interactions. It is also easier to isolate the role of different processes in controlling the condensate distribution in formulations in which each process is explicitly and separately represented, rather than one in which many processes are represented by enhancements or reductions to terms already present as is done in Sundqvist (1993b).

While the standard CCM3 “stratiform” condensation parameterization has been completely overhauled, condensation processes within the convective parameterizations themselves are unmodified. We have chosen this approach for a number of practical reasons.

We will tend to discriminate between the cloud processes occurring within regions of vigorous upward or downward motion with vertical motions of order a meter per second or larger and those occuring outside those regions, but connected with the convection, composed of decaying cloud elements or cirrus outflow regions. We view the convective parameterizations as representing the influence that the small-scale convective up- and downdrafts have on the larger-scale environment (decaying cloud elements and cloud-free regions). These up- and downdrafts are thought to occupy only very small areas (less than 5%) with respect to the total cloud fraction occupied by the convective cloud systems. Because of this, one can argue that the volume (or fraction seen from above) of these cloud systems is dominated by the passive component of the cloud systems. This passive region is in turn controlled by the rate at which these elements are spawned by the active cores and mixed with the cloud-free environment. The cloud properties within the passive region are predicted by our parameterization.

We also note the properties of the convective parameterizations themselves are strongly controlled by the assumptions about the formation of cloud water and its conversion to precipitating forms. Changing these assumptions within the convection changes the way in which they move heat and moisture and can have very significant effects on the simulation. In accord with our desire to minimize the changes to other model parameterizations, we have deferred modifying the convective parameterizations for another time.

The calculation of terms controlling the rate of exchange of mass between water vapor and cloud water (and the associated latent heat release) arises through a manipulation of the equations for water vapor and heat, and assumptions about how the heat and moisture partitioning occurs within the cloudy and cloud-free parts of the grid volume. This is described in section 3a. The conversion of cloud water to falling precipitate is achieved by a very simple bulk microphysics parameterization, described in section 3b.

a. Moisture and heat budget closure—Condensation and evaporation

Schematically, the evolution equation for water vapor may be described as

 
υ̇ = 𝒜υ + 𝒮υ + 𝒞υ − (QE),
(3)

where υ is the mixing ratio of water vapor, (˙) = ∂/∂t, 𝒜 is the resolved transport by horizontal and vertical advection, and 𝒞 is the tendency term associated with convection. Here, QE represents the tendencies by the (as yet undetermined) condensation and evaporation of cloud water, and 𝒮 represents the tendencies associated with all other subgrid-scale parameterizations affecting the water vapor distribution (e.g., vertical diffusion and planetary boundary layer parameterizations). In a similar way we write the tendency equation for heat:

 
= 𝒜T + ℰ + 𝒮T + 𝒞T + β(QE),
(4)

where T is temperature and β = L/Cp. Here L is the latent heat of vaporization/sublimation and Cp the gas constant for dry air, and is the radiative forcing. The corresponding equation for the cloud water mixing ratio qc is

 
c = 𝒜qc + 𝒮qc + 𝒞qc + QEP,
(5)

where P is the precipitation term; that is, the conversion of cloud water to precipitate. The calculation of this term is dealt with in the next subsection. We express the Clausius–Clapeyron equation schematically as

 
υs = υs(T, p).
(6)

One can differentiate υs in time to form

 
formula

The volume-averaged quantity υ can in principle be partitioned into a mean value for the cloudy fraction of the volume υc (=υs) and a cloud-free value υe:

 
υ = (1 − f)υe + s,
(8)

where f is the cloud fraction. In (8) we have assumed that the water vapor within the cloudy fraction of the grid box is just saturated. We will neglect the variation in temperature within the volume. By differentiating (8) in time, substituting (7), (6), (3), and (4), and rearranging we get

 
formula

The right-hand side of (9) (hereafter identified as M) contains all the known tendency terms, that is, those determined by processes external to the cloud water formulation. Those terms on the left-hand side contain unknown terms. This formulation is quite similar to Sundqvist (1993b), although he partitioned relative humidity into cloudy and cloud-free values, which changed the subsequent development somewhat. The condensation–evaporation terms are now fixed through a sequence of closure assumptions, similar to those of Sundqvist.

Closure assumption 1: The fraction of M operating within the cloud part of the volume acts to condense/evaporate cloud water. This statement can be expressed through an appropriate choice of terms from (9) as

 
(1 + fαβ)(QE)cloudy = fM.
(10)

We use the notation (QE)cloudy to denote condensation and evaporation of cloud water within the cloud part of the volume. We also acknowledge the possibility of condensation/evaporation occuring within the cloud-free part of the grid volume [denoted by (QE)clear]. This can take place, for example, when clouds grow or erode (both the cloud fraction will change and the cloud water content can change). Equation (10) is very similar to part of the formulation of Sundqvist (1993b), except that the relative humidity, RH, appeared instead of f on the left side of the equation.

The difference between (9) and (10) gives

 
formula

This equation is an expression of the relationship between changing the size of the cloud (the term), moistening the cloud-free part of the volume (the υ̇e term), condensing or evaporating cloud water [the (QE)clear term], and the forcing term arising from other processes in the model [(1 − f)M]. In Sundqvist’s formulation f is a straightforward function of the relative humidity—that is, f = f(RH)—so can also be considered a known function of other variables and processes. In our case the calculation of the cloud fraction is sufficiently complex that one cannot write an analytic expression for ḟ. (The description of how f is determined is described in appendix A.) One can however approximate as the difference between f calculated on two adjacent time steps; that is,

 
= (fnewfold)/Δt,
(12)

and this has been our choice. The remaining undetermined processes are (QE)clear and (υ̇e), which we construct according to the following closure assumptions.

Closure assumption 2: When the cloud is growing ( ≥ 0), the new cloud water increases to match that within the cloudy part of the grid box. Conversely, when the cloud is eroding ( < 0), the cloud water goes to zero in that region. These two statements can be expressed as

 
(1 + fαβ)(QE)clear = ḟq̂c,
(13)

where c = qc/f is the in-cloud mixing ratio.

From closure assumptions 1 and 2, it is straightforward to show that the remaining large-scale forcing term (1 − f)M acts to change the water vapor amount in the grid volume

 
formula

The reader will note in our derivation that QE in (3) may be written as the sum of three terms

 
QE = (QE)cloudy + (QE)clear + (QE)rain,
(15)

where the terms on the right-hand side are determined by (10), (11), and Qrain ≡ 0. The term Erain is discussed in more detail below.

b. Prognostic cloud water formulation—Bulk microphysics

Because the condensation process itself has been determined by forcing terms and closure assumptions described in the previous subsection rather than an approach in which a supersaturation is calculated, and CCN nucleate and grow, the whole microphysical calculation reduces to modeling the process of conversion of cloud water to precipitating water. For this process to occur, we construct a formulation that follows in some ways the bulk microphysical formulations used in smaller scale cloud-resolving models, rather than those of Sundqvist (1993b). We do this because the former method makes an explicit connection between individual physical quantities like droplet number, shape of size distribution of precipitate, etc., and the formation of precipitate, and (as will become evident) it also separates the various processes contributing to precipitation more strongly and makes diagnosis more straightforward. Because these quantities must represent an ensemble of cloud types in any given region (or grid volume), the new formulation still involves gross approximations, but it is much easier to control (tune) the parameterizations and understand their individual impact when the processes are isolated from each other.

As in the cited references of Sundqvist the parameterization is expressed at times in terms of a single predicted variable. Within the parameterization, however, we actually represent four types of condensate: a liquid and ice phase for suspended condensate with no appreciable fall speed (ql and qi) and a liquid and ice phase for falling condensate (precipitation, qr and qs). Currently, only the total suspended condensate qc (qc = ql + qi) is integrated in time; the other quantities are diagnosed as described below. Before beginning the microphysical calculation, the total condensate is decomposed into the liquid and ice phases assuming the fraction of ice is

 
wice = max{0, min[1, (TfT)/20]},
(16)

where T is the grid volume temperature, and Tf (=273.16 K) is the temperature at which freezing begins. Thus, wice is assumed to vary linearly between the freezing point and −20°C. Observations and more detailed microphysical models show a broad range of ratios of liquid to ice in clouds, and it is difficult to be certain of an appropriate range for this parameter. We have chosen a range we consider intermediate in nature and have not explored the model sensitivity to this formulation. The in-cloud liquid water mixing ratio is

 
= (1 − wice)qc/f,
(17)

and the in-cloud ice water mixing ratio is assumed to be

 
= (wice)qc/f.
(18)

[It is straightforward to extend the formulation to include predicted separate cloud liquid and cloud ice categories by replacing (5), the evolution equation for qc, with corresponding equations for separate production and loss terms for ice and liquid.] The precipitate falling from above is assumed to be snow (rain) at temperatures below (above) freezing. The grid volume mean quantities have been converted to in-cloud quantities by dividing the mean mixing ratios by a “cloudy volume” fraction.

We now seek to express the evaporation term (E) and the precipitation term (P) in (5). First, evaporation can, in general, be split into three parts, following (15):

 
E = Ecloudy + Eclear + Erain.
(19)

We assume that Ecloudy ≡ 0, since no evaporation can take place in saturated air. The term Eclear represents evaporation of cloud water in a cloud that is shrinking;this is treated according to (11). The last term, Erain, is parameterized as in Sundqvist et al. (1989); that is,

 
Erain = kE(1 − RH)(1 − f)0.5,
(20)

where kE = 10−5 in SI units, and RH is the relative humidity. The factor 1 − RH expresses the subsaturation, and the 1 − f factor expresses the fact that evaporation takes place only in the cloud-free part of the grid box. The term represents the flux of precipitation coming into the grid box from above.

It is assumed that there are five processes that convert condensate to precipitate:

  • The conversion of liquid water to rain (PWAUT) follows a formulation originally suggested by Chen and Cotton (1987) and often used subsequently by Cotton and colleagues. Modified versions have been suggested by Liou and Ou (1989) and Boucher et al. (1995): 
    formula
    Here ρa and ρw are the local densities of air and water, respectively, and N is the assumed number density of cloud droplets. Here Cl,aut = 0.55π1/3k(3/4)4/3(1.1)4, and k = 1.18 × 106 cm−1 s−1 is the Stokes constant. We have assumed N is 400 cm−3 over land near the surface, and 150 cm−3 over ocean. A transition region of 1000 km is defined, where the number density varies linearly with distance from the nearest land point. Here r3l and r3lc are the mean volume radii of the droplet, and a critical value below which no autoconversion is allowed to take place, respectively. Here H is the Heaviside function; H(x) = (0, 1) where x (<, ≥) 0.

The volume radius r3l = [(3ρaq)/(4πNρw)]1/3. Our standard value for the critical radius at which conversion begins is 5 μm. Baker (1993) has shown that this parameterization results in collection rates that far exceed those calculated in more realistic stochastic collection models. This has been explained by Austin et al. (1995) as due to the choice of a collection efficiency appropriate to a cloud droplet distribution that has already been substantially modified by precipitation. They suggest that a much smaller choice is appropriate prior to precipitation onset. Therefore we have modified the parameterization by making Cℓ,aut ← 0.1Cℓ,aut when the precipitation flux leaving the grid box is below 0.5 mm day−1.

  • The collection of cloud water by rain from above (PRACW) follows Tripoli and Cotton (1980): 
    PRACW = Cracwρ3/2qr,
    (22)
    where Cracw = 0.884[g/(ρw 2.7 × 10−4)]1/2 s−1 is derived by assuming a Marshall–Palmer distribution of rainwater falling through a uniformly distributed cloud water field.
  • The autoconversion of ice to snow (PSAUT) is similar in form to that originally proposed by Kessler (1969) for liquid processes and Lin et al. (1983) for ice, but we have imposed a temperature dependence quite similar to that proposed in Sundqvist (1988): 
    PSAUT = Ci,autH(iqic).
    (23)
    The rate of conversion of ice (Ci,aut) to snow is set to 10−3 s−1 when the ice mixing ratio exceeds a critical threshold qic. The threshold is set to 4.0 × 10−4 at T = 0°C and 5.0 × 10−6 at T = −20°C. The threshold varies linearly in temperature between these two limits.
  • The collection of ice by snow (PSACI) follows Lin et al. (1983) precisely, although its computational form is somewhat different, for efficiency; 
    PSACI = Csaceii.
    (24)
    The coefficient of collection is 
    Csac = c7ρc8ac5.
    (25)
    Here, c5, c7, and c8 are constants arising from the assumed shape of the snow distribution (they are expressed in gory detail in appendix B); ei is assumed to be 1.0.
    The collection of liquid by snow (PSACW) also follows Lin et al. (1983): 
    PSACW = Csacew.
    (26)
    Lohmann and Roeckner (1996), citing some work by Levkov et al. (1992), suggest that the riming process is too efficient using the standard values, and we achieve a reduction by decreasing the collection efficiency by an order of magnitude over the suggested value in Lin et al. (1983) that is, we set ew equal to 0.1.

Figure 1 displays a measure of the relative role of each term in the conversion of condensate to precipitate in the model over a summer season (the model run is described in detail in the next section). This quantity was calculated by first time averaging PSAUT, PWAUT, PRACW, PSACW, PSACI, then zonal averaging them, and finally normalizing each term by the sum of the processes as a relative measure of their importance. A number close to unity implies the term dominates the condensate conversion. One near zero implies the process is not important. The figure suggests that the autoconversion term (PWAUT) dominates for warm clouds below about 700 mb in the Tropics and subtropics. The rain accretion term PRACW becomes more important in midlatitudes and the middle troposphere. PRACW has a strong seasonal cycle with a maximum in the summer hemisphere (not shown). There is a range of altitudes where all terms play a role in the conversion. The range is between 400 and 600 mb in the Tropics, and it descends as one moves poleward. Typically, the accretion of supercooled liquid by snow (PSACW) has the least importance as a conversion mechanism, and this is perhaps due to the reduction of the collection efficiency we mention above. In the upper troposphere the autoconversion terms for ice (PSAUT) and the accretion of ice by snow (PSACI) play an equally important role.

Fig. 1.

The relative importance of the microphysical terms in the conversion of condensate to precipitate. See text for an explanation of the calculation. Contour interval is 0.1.

Fig. 1.

The relative importance of the microphysical terms in the conversion of condensate to precipitate. See text for an explanation of the calculation. Contour interval is 0.1.

4. Results

a. Description of model runs

The new parameterizations were inserted into the standard CCM3 and the cloud water parameterization tuned through a series of short runs by adjusting the choice of the thresholds for the onset of precipitation for rain and snow (i.e., N, r3lc, and qic). Only these parameters were explicitly adjusted to tune the model climate. The parameters were tuned to make globally averaged top of atmosphere radiative fluxes balance (i.e., energy in = energy out), and have the cloud forcing be reasonably close to Earth Radiation Budget Experiment (ERBE) estimates. The only parameter that required significant adjustment with respect to the nominal values suggested in the cited literature from which we have developed the parameterizaton was the threshold for autoconversion of ice qic at very cold temperatures. The values we have used are somewhat smaller than the nominal values suggested by Sundqvist (1993a); however, he did not attempt to tune the model for reasonable radiative properties, nor test the parameterization in the Tropics. The physics of ice crystal formation and conversion to a precipitating form is extremely complicated, and poorly understood—and in our opinion still inadequately represented in all bulk microphysical models in use today. Hence we acknowledge the somewhat arbitrary formulation and tuning procedure we have adopted, which was merely to achieve a reasonable top of atmosphere flux within the model.

After the tuning, the model was run for 14 yr (1979–92), using estimated monthly mean sea surface temperatures appropriate for an AMIP-style simulation. The first year of the simulation was ignored to allow the model to equilibrate more fully to the model modifications.

We will refer to the run that included the new cloud water parameterization as PCW (prognostic cloud water), and the run using the standard model configuration as CONTROL.

b. Evaluation of cloud water distribution

We begin by showing differences in the variable we are explicitly changing—the condensate amount. Figures 2 and 3 display the December–February (DJF) and June–August (JJA) averaged zonal average of cloud water (upper panel), and the absolute (middle panel) and relative (lower panel) change between the predicted and diagnosed cloud water amounts in the same (PCW) model run. The contour intervals in each of the panels are spaced approximately logarithmically (1, 2, and 5 × 10n). The differences are most apparent in absolute amount near the surface with a notable decrease in the predicted cloud water amount below 850 mb and a corresponding increase above (850–400 mb). There is also a small area in the tropical upper troposphere (about 300 mb and again at 100 mb) where cloud water decreases. As seen below, the increases occur where convection detrains water.1 The areas where condensate decreases in the Tropics are where convection will not support it. The differences are largest in a relative sense in polar regions where the predicted cloud water exceeds the diagnosed value aloft by a factor of 5 in the Southern Hemisphere in both seasons.

Fig. 2.

DJF averages of (upper panel) predicted cloud water (weighted by cloud fraction, 106 kg kg−1), (middle panel) difference of predicted–diagnosed cloud water for the same run (106 kg kg−1), (lower panel) difference in predicted and diagnosed cloud water normalized by the diagnosed cloud water.

Fig. 2.

DJF averages of (upper panel) predicted cloud water (weighted by cloud fraction, 106 kg kg−1), (middle panel) difference of predicted–diagnosed cloud water for the same run (106 kg kg−1), (lower panel) difference in predicted and diagnosed cloud water normalized by the diagnosed cloud water.

Fig. 3.

As in Fig. 2 but for JJA averages.

Fig. 3.

As in Fig. 2 but for JJA averages.

The Northern Hemisphere predicted condensate parameterizations show a very different seasonal cycle than the diagnosed cloud water parameterization. During the summer the two parameterizations predict about the same condensate loading (i.e., they agree to about 20% in the zonal seasonal average). During the winter, however, the predicted condensate parameterization generates much less condensate near the surface and much more at higher altitudes. As seen later, this change in condensate loading is manifested by significant changes in optically important cloud amount, and radiative fluxes. This is precisely the signature required to improve the CCM3 signature in the north polar region, in which winter clouds have too much optical importance (Briegleb and Bromwich 1998).

The general conclusion is that the prognostic condensate parameterization will predict more condensate above, and less below for cold regimes, and about the same as the diagnostic condensate parameterization for warm midlatitude regimes. The changes suggest that the relationship between cloud water and the model climate is significantly more complex than that suggested by Eqs. (1) and (2) in the standard CCM3.

The horizontal distribution of cloud water amount for both parameterizations and their difference can be seen in Fig. 4. The fields are displayed by partitioning the cloud water into the mass contained between the surface and 750 mb (upper row), 750 mb and 500 mb (second row from top), 500 and 250 mb (third row from top), and above 250 mb (bottom row). The cloud water mass in the upper layer (lowest row) has been multiplied by 10 to allow use of the same color tables for all levels. The figure suggests that near the surface (top row) the predicted cloud water contents are lower than the diagnosed cloud water in the areas of marine stratus, and over the polar continental regions, and somewhat higher in the storm track regions. The prognostic cloud water parameterization is higher (5–20 g m−2) over the eastern Pacific ITCZ, and slightly lower (2–5 g m−2) in the warm pool region and Indian Ocean near the surface. The substantial decrease in cloud water near the surface in polar regions suggested in Figs. 2 and 3 is also evident in panel c. Higher up, the predicted cloud water is almost uniformly higher than the diagnosed cloud water amounts. Clear signatures are seen of increases with respect to the diagnostic parameterization in the storm track regions and in the South Pacific convergence zone. Above 250 mb there is as much as a factor of 2 (2–5 g m−2) increase in regions of strong convection.

Fig. 4.

Annual averages of layer-averaged cloud condensate path weighted by cloud fraction: (upper row) mass between the surface and 750 mb, (second row) mass between 750 and 500 mb, (third row) mass between 500 and 250 mb, (last row) mass above 250 mb. The masses in the last row have been multiplied by 10 to allow use of the same color table throughout.

Fig. 4.

Annual averages of layer-averaged cloud condensate path weighted by cloud fraction: (upper row) mass between the surface and 750 mb, (second row) mass between 750 and 500 mb, (third row) mass between 500 and 250 mb, (last row) mass above 250 mb. The masses in the last row have been multiplied by 10 to allow use of the same color table throughout.

It is important of course to compare the model cloud water amounts with observations. Perhaps the most comprehensive measurements in space and time have been gathered using microwave techniques, which provided estimates of integrated cloud liquid water over oceans. The retrieval method is sensitive to the presence of precipitation and cannot see ice. This introduces great uncertainties in the accuracy of the retrieval method. Figure 5 compares estimates for January cloud (liquid only) water paths for the two model versions and that estimated using the inversion techniques from Weng and Grody (1994) and Greenwald et al. (1993). The large differences between the observational estimates highlight the difficulties and uncertainties associated with the retrieval using the microwave measurements. Corresponding global annual averages for these fields are shown in Table 1. More discussion of this table appears in section 4c(1). The fundamental spatial structures between all four distributions are quite similar. Both model versions tend to look quite like each other. They severely underestimate the cloud liquid water compared to Greenwald et al. (1993) and are much closer to the Weng and Grody (1994) estimates, which have global (ocean only) annual averages of 81, and 44 g m−2, respectively. The predicted condensate parameterization tends to predict somewhat higher water paths (32 g m−2) than does the diagnosed parameterization (30 g m−2), particularly in the winter hemisphere [see also section 4c(1)].

Fig. 5.

The cloud liquid water path for the two model simulations and as estimated from Weng and Grody (1994) and Greenwald et al. (1993).

Fig. 5.

The cloud liquid water path for the two model simulations and as estimated from Weng and Grody (1994) and Greenwald et al. (1993).

Table 1.

Global annual averages for the 5-yr simulations compared to two recent model studies and observations. Abbreviations follow:GSEA = Greenwald et al. (1993), WG = Weng and Grody (1994), FRR96 = Fowler et al. (1996), DG96 = Del Genio et al. (1996).

Global annual averages for the 5-yr simulations compared to two recent model studies and observations. Abbreviations follow:GSEA = Greenwald et al. (1993), WG = Weng and Grody (1994), FRR96 = Fowler et al. (1996), DG96 = Del Genio et al. (1996).
Global annual averages for the 5-yr simulations compared to two recent model studies and observations. Abbreviations follow:GSEA = Greenwald et al. (1993), WG = Weng and Grody (1994), FRR96 = Fowler et al. (1996), DG96 = Del Genio et al. (1996).

The condensate paths above 500 mb seen in Figs. 4g–l suggest that the ice amounts in the PCW run will be higher than in CONTROL (often by a factor of 2) but have a similar spatial distribution. There are no global estimates of ice water path from observed variables to compare. Instead we resort to variables with which in situ measurements from relatively recent field campaigns for ice (and some liquid measurements also) to compare with the parameterizations. In mixed phase regimes it is difficult to isolate one phase of condensate from the other in field campaign measurements. For example, the recent study of Gultepe and Isaac (1997) in northeastern North American clouds attempted to isolate the liquid from ice phase, but at the same time they compared their estimates directly with those of Mazin (1995) and Feigelson (1978) over the former Soviet Union, who were unable to isolate the phases. Similarly, Heymsfield (1993), Heymsfield and McFarquhar (1996), and McFarquhar and Heymsfield (1996) have sumarized measurements over the central Pacific during the field campaign the Central Equatorial Pacific Experiment (CEPEX) field program where measurements in tropical cirrus anvils were taken in March of 1993 that are believed to be primarily ice, but also contain the liquid phase. Thus, to facilitate a comparison we will use total (ice + liquid) condensate in mixed phase temperature regimes when comparing to observations. Figures 6 and 8 (later in this section) show scatter diagrams of total (ice + liquid) in-cloud water over a North American region and a central tropical Pacific region, respectively, as a function of temperature. The North American region corresponds approximately to the area described in Gultepe and Isaac (1997), who analyzed more than 200 000 measured liquid water contents in midlatitude clouds at altitudes below 500 mb from a variety of field programs during all seasons. The central Pacific region corresponds approximately to the CEPEX region.

Fig. 6.

Scatter diagrams for in-cloud water from prognostic parameterization (left panels) and diagnostic parameterization (right panels). The upper panels represent in-cloud water contents sampled once every 3 h for January from the model run. The lower panels contain corresponding samples from July. Superimposed on each panel is the line of best fit of mean LWC to temperature from measurements used in Gultepe and Isaac (1997) (for all seasons).

Fig. 6.

Scatter diagrams for in-cloud water from prognostic parameterization (left panels) and diagnostic parameterization (right panels). The upper panels represent in-cloud water contents sampled once every 3 h for January from the model run. The lower panels contain corresponding samples from July. Superimposed on each panel is the line of best fit of mean LWC to temperature from measurements used in Gultepe and Isaac (1997) (for all seasons).

Fig. 8.

Scatter diagrams for (upper panel) prognostic cloud water, (middle panel) diagnostic cloud water, (lower panel) measurements from CEPEX. Superimposed on each panel is the line of best fit of mean LWC to temperature from measurements used in Gultepe and Isaac (1997) (for all seasons).

Fig. 8.

Scatter diagrams for (upper panel) prognostic cloud water, (middle panel) diagnostic cloud water, (lower panel) measurements from CEPEX. Superimposed on each panel is the line of best fit of mean LWC to temperature from measurements used in Gultepe and Isaac (1997) (for all seasons).

Figure 6 shows the temperature–liquid water content (LWC) relationship for both predicted and diagnosed parameterizations for the midlatitude data, along with with a line of best fit between the mean LWC and temperature from Gultepe and Isaac (1997). The most evident differences between the parameterizations are the much larger range of variation in the predicted cloud water content and the larger values, particularly at temperatures above 0°C, in the prognostic condensate parameterization. The points in both parameterizations tend to cluster along the x (temperature) axis (particularly in summer) due to the sampling at discrete levels, each with an associated characteristic temperature. The clustering in diagnosed cloud water content (particularly in summer) arises because the parameterization depends only on the layer height, and the vertical integral of water vapor [see (2) and (1)]. Variations in column water vapor are smaller in summer and hence the diagnosed cloud water clusters more during that season. Both parameterizations generate mean water contents, which match the observations reasonably for the warmest clouds. Where temperature variations are larger (near the surface, where z/hl is small) the cloud water dependence implied from (1) is small. Both parameterizations tend to underestimate the water content compared to the observations (however, see next paragraph) for colder clouds, with the mean diagnosed cloud water content differing slightly more with respect to observations than the predicted cloud water parameterization.

Statistical characterization of mean cloud water amounts are quite uncertain. Gultepe and Isaac (1997) note a discrepancy in characteristic mean values of a factor of 2 for warmer clouds and of 4 or 5 for cold clouds between their estimates and those of Mazin (1995) and Feigelson (1978) (see Fig. 7). They suggest a variety of reasons for the discrepancy in estimates: there has been no calibration between the various instruments used during the different field campaigns; the detection limits of the instruments making the measurements are believed to affect the estimated cloud water properties, with higher LWC inferred from instruments having a higher threshold; they indicate that some measurement strategies have attempted to isolate liquid water from total water content and this effects the estimates; they also show that the averaging interval used to composite the measurements can significantly affect the estimates. They suggest that the instruments’ ability to isolate small suspended particles from larger precipitating particles is uncertain and differs between instruments. Finally, they speculate that interannual variability may contribute to the discrepancies. We note that the most sensitive of the instruments cited by Gultepe and Isaac (1997) has a detection limit of 0.032 g m−3, and thus many of the cloud water contents displayed in the figures could not be detected from those instruments. The mean values from the aforementioned studies and the model are shown in Fig. 7. Both model cloud water distributions tend to match the estimates of Mazin (1995) (who used the most sensitive measurement technique of those cited) most closely at cold temperatures. The only observational study cited here that included condensate measurements at very warm temperatures near 20°C was Gultepe and Isaac (1997), and agreement between model and observations is quite reasonable there as well.

Fig. 7.

Mean values of in-cloud water content for the two model parameterizations and the three observational studies cited in the text.

Fig. 7.

Mean values of in-cloud water content for the two model parameterizations and the three observational studies cited in the text.

Differences between cloud water contents can also be seen in the CEPEX region (Fig. 8). The very large scatter of measured values in ice water content makes comparison between models and measurements difficult. The clustering of points in the diagnostic parameterization arises for the same reasons cited above and is even more striking. Rather than comparing a line of best fit to the CEPEX observations, we have chosen to display histograms for the parameterization and observations in Fig. 9. There is a substantial increase in the spread of the ice water contents provided by the prognostic parameterization (about two orders of magnitude) compared to its diagnostic counterpart (two to four orders of magnitude). The measured spread is still larger (typically four or five orders of magnitude), although these are representative of very small spatial scales, which might explain some of the discrepancy. The modes of the parameterized and measured water correspond reasonably well for most temperature ranges (there are no layers in this region occupying the −70° to −60°C temperature range, and this accounts for the lack of points there). They agree to one bin (i.e., a factor of 2). Nevertheless, there seems to be a general underestimation of cloud water at temperatures below freezing. This is also the case over North America, according to Fig. 7, except for the data of Mazin (1995). Both model versions also show a bias toward higher water contents than the CEPEX observations in the warmest temperature range.

Fig. 9.

Histograms of the in-cloud water content (ICW) as a function of temperature from the CEPEX data (left black bar of each cluster), the prognostic parameterization (middle gray bar of each cluster), and the diagnostic parameterization (right light bar of each cluster).

Fig. 9.

Histograms of the in-cloud water content (ICW) as a function of temperature from the CEPEX data (left black bar of each cluster), the prognostic parameterization (middle gray bar of each cluster), and the diagnostic parameterization (right light bar of each cluster).

c. Evaluation of model climate

1) Comparison of global annual averages between models and observations

Table 2 summarizes the globally averaged results for the two model configurations and the observational estimates. Both model configurations and observational estimates were analyzed for the simulated period of 1985–89, to correspond to the period the Earth Radiation Budget Experiment (ERBE) was operating.

Table 2.

Global annual averages for the 5-yr simulations compared to observations where available. Abbreviations for observations follow: LW90 = Legates and Willmott (1990), KT97 = Kiehl and Trenberth (1997), TOA = top of atmosphere.

Global annual averages for the 5-yr simulations compared to observations where available. Abbreviations for observations follow: LW90 = Legates and Willmott (1990), KT97 = Kiehl and Trenberth (1997), TOA = top of atmosphere.
Global annual averages for the 5-yr simulations compared to observations where available. Abbreviations for observations follow: LW90 = Legates and Willmott (1990), KT97 = Kiehl and Trenberth (1997), TOA = top of atmosphere.

The statistics suggest the model runs are similar in most respects, and they are more alike than either is to the observations. The globally averaged top of atmosphere radiative forcing from the two model runs differs by order 0.5 W m−2. Both model configurations are very near a radiative equilibrium, with the revised model slightly further from an exact balance between incoming and outgoing energy at the top of atmosphere and surface. This may be due to the additional storage term for energy-related quantities associated with the predicted cloud water parameterization. Differences for all quantities are generally less than the uncertainty in the estimates based on observations and are within the natural variability of the models. The most significant differences apparent are in surface fluxes. Latent heat fluxes are significantly lower (order 4 W m−2). The corresponding decrease in evaporation is balanced in the water budget by a reduction in precipitation, and in the energy budget by an enhancement in the net longwave radiation escaping the surface. There has been a reduction in the convective precipitation and enhancement in the stratiform precipitation. This is presumably due in part because the new parameterization does not require a grid volume to be saturated in order for precipitation to take place. There are also differences in the burden of liquid and ice condensate in the two model runs, consistent with the analysis of the previous section.

The liquid and ice water amounts from our simulation may be comparedd to those obtained by Fowler et al. (1996) and Del Genio et al. (1996) in Table 1. We note that our values are quite similar to those of Fowler et al. (1996), but much lower than those of Del Genio et al. (1996), in particular for the ice phase. There is at present no algorithm for obtaining ice water paths from satellites, but it should be noted that Lin and Rossow (1996) estimated a ratio of 0.7 between ice water paths and liquid water paths from nonprecipitating clouds over sea, using Special Sensor Microwave/Imager (SSM/I) data.

In the previous subsection, we pointed out that there were indications that our ice water paths might be rather low. Since our longwave cloud forcing is quite realistic (see Table 2 and Figs. 15–16), it is not an easy task to retune the model to give higher ice water paths and still provide reasonable radiative budgets. Another study is under way, where we seek improvements to the treatment of ice optics by, for example, taking into account the observed temperature dependency of ice crystal sizes (e.g., Ou and Liou 1995). Preliminary findings suggest that with this treatment, somewhat larger ice water paths are obtained without any harmful impact on the radiative budgets or LWCF.

Fig. 15.

DJF top of atmosphere fluxes for the control simulation (dotted line), the PCW simulation (dashed line), and the ERBE estimates (solid line).

Fig. 15.

DJF top of atmosphere fluxes for the control simulation (dotted line), the PCW simulation (dashed line), and the ERBE estimates (solid line).

2) Seasonal and regional differences between model simulations

Table 2 suggests some differences in fluxes of energy and moisture at the surface and top of atmosphere. The seasonal mean zonal-mean differences in some of these fields are shown for DJF and JJA in Figs. 10 and 11, respectively. Observational estimates of zonal averages of many of these quantities are still uncertain, but generally either model version compares quite well with existing estimates [see BO98, Kiehl et al. (1998), or Hack et al. (1998) for comparisons of the control with observations]. For brevity we generally show only model difference fields, with occasional reference to observations for a few fields.

Fig. 10.

Ensemble mean differences between the PCW and control model simulations for DJF (a) convective precipitation, (b) stratiform precipitation, (c) latent heat flux, (d) sensible heat flux, (e) net longwave surface flux, (f) net solar surface flux, (g) net longwave top of atmosphere flux, and (h) net top of atmosphere solar flux. Shaded regions indicate ±2σ estimates for interannual variability.

Fig. 10.

Ensemble mean differences between the PCW and control model simulations for DJF (a) convective precipitation, (b) stratiform precipitation, (c) latent heat flux, (d) sensible heat flux, (e) net longwave surface flux, (f) net solar surface flux, (g) net longwave top of atmosphere flux, and (h) net top of atmosphere solar flux. Shaded regions indicate ±2σ estimates for interannual variability.

Fig. 11.

As in Fig. 10 but for JJA.

Fig. 11.

As in Fig. 10 but for JJA.

The shaded regions show the ±2σ estimate of variability of the (13) individual seasons about the ensemble means. The difficulty in assessing statistical significance in situations like this is well known. Fields are correlated in space and time, and the number of realizations are small. We have not attempted a rigorous statistical characterization, but we consider ensemble mean differences outside the shaded regions as very likely to be significant, those on the edge of the shaded regions as probably significant, and those well within the shaded regions likely to be within the “noise” generated by interannual variability.

There is a marked reduction (by about 1 mm day−1) in the peak (of 6–7 mm day−1, not shown) in convective precipitation in the Tropics in both seasons (indeed over the whole year) that is probably significant. There are also significant changes in midlatitude precipitation, particularly during JJA. The small increase in stratiform precipitation in both seasons in the Tropics is quite significant with respect to the shaded region. Much larger differences occur in the midlatitudes but the amplitude of precipitation and its variability is also higher there, and the importance of the change is uncertain. The dipole structure in the Southern Hemisphere during DJF (also seen in the longwave and shortwave fluxes at the surface and top of atmosphere in Figs. 10e–h) suggests a small (5° lat) equatorward shift of the southern summertime storm track. The reduction in latent heat flux, needed to balance the reduction in precipitation, is significant during both seasons. The changes of 5–10 W m−2 at 40°–60° of latitude, where the latent heat flux itself is only 20–40 W m−2, are probably relatively more important than those in the Tropics where the zonally averaged heat fluxes reach 150 W m−2.

There are reductions in the sensible heat flux into the atmosphere during winter in both hemispheres. This is probably associated with the warmer winter atmospheric temperatures in the lower troposphere discussed in more detail below. The warmer winter atmospheric temperatures reduce the vertical gradient between the surface and lowest model layer, and with this goes a reduction in sensible heat flux. The signature over Antarctica is similar to that seen generally in the winter midlatitudes, but it occurs year-round (again, see below). A very significant increase in the sensible heat flux is evident over oceans during summer in mid- and polar latitudes in both hemispheres. The 5–10 W m−2 difference seen there represents a near doubling of the flux in the midlatitude values compared to the control simulation.

Perhaps the most significant signature seen of all the differences occurs in the radiative fluxes in polar regions. There are decreased top of atmosphere longwave fluxes (Figs. 10g and 11g) over Antarctica (all year-round) and over midlatitudes and polar regions in winter, and a corresponding increase in the net surface longwave fluxes (Figs. 10e and 11e). Both the Antarctic signature, and the winter midlatitude and polar signatures can be explained by the substantial increase in cloud ice water content at higher altitudes in the cloud water maximum seen in Figs. 2 and 3. The differences in surface and top of atmosphere fluxes in the extratropics can perhaps be most easily explained in terms of changes in the model meteorological fields of Figs. 12 and 13.

Fig. 12.

Ensemble mean differences between the PCW and control model simulations for DJF: (a) temperature, (b) zonal wind, (c) moisture, (d) a near-surface reference height temperature (2 m over land, 10 m over ocean), (e) cloud fraction, (f) effective cloud (cloud fraction weighted by its emissivity). Shaded regions indicate regions where differences in simulations are less than ±2σ estimates for interannual variability.

Fig. 12.

Ensemble mean differences between the PCW and control model simulations for DJF: (a) temperature, (b) zonal wind, (c) moisture, (d) a near-surface reference height temperature (2 m over land, 10 m over ocean), (e) cloud fraction, (f) effective cloud (cloud fraction weighted by its emissivity). Shaded regions indicate regions where differences in simulations are less than ±2σ estimates for interannual variability.

Fig. 13.

As in Fig. 12 but for JJA.

Fig. 13.

As in Fig. 12 but for JJA.

There are very small (<10%) changes in the zonally averaged cloud cover itself (Figs. 12e and 13e) except at the surface, where formation of clouds is now allowed. Except near the poles, we believe the changes in cloud amount are small compared to our uncertainty in the corresponding observational climatology. However, near the poles, the increase in height of the emitting surface (with a corresponding decrease in temperature) caused by the upward shift in height of condensate, and the increased ice amounts there result in a change of emissivity of the clouds. This can be seen in the change in effective cloud (the cloud fraction weighted by its emissivity) in Figs. 12f and 13f. High polar ice clouds tend to have a higher optical thickness in PCW than in the control. The change in emissivity in the clouds results in a decrease in the net (outgoing) longwave radiation in the top of atmosphere flux and an increase in the net outgoing longwave flux at the surface (panels f and h of Figs. 10 and 11).

Figure 14 shows the time series of monthly mean low cloud cover over the arctic basin for the two model simulations and an observational estimate. Cloud fraction estimates over polar regions are notoriously difficult to make. Satellites are unable to discriminate between ice, snow, and cloud, and ground-based measurements are few, and highly subjective. One of the more comprehensive datasets available is that of Warren et al. (1988). The thick dashed line is a sinusoid fitting their data for total cloud cover over the Arctic at 12–15 sites over the period 1952–80. We have constructed an approximate model cloud fraction (using a random overlap assumption) for clouds below 700 mb from the archived monthly mean three dimensional cloud distributions. The thick lines show low cloud cover for the PCW run, and thin lines show the control simulation. The solid lines show the cloud fraction independent of the cloud optical properties, and dotted lines show the low cloud fraction using the effective cloud cover, which weights the cloud fraction by the cloud emissivity. The effective cloud cover and standard low cloud amount for the control simulation lie upon each other, suggesting that Arctic clouds in that simulation are basically black to longwave radiation. They have the wrong phase compared to the observations, indicated by a minimum in the May–June time frame. The PCW simulations’ standard low cloud cover is virtually identical to that of the control, but the effective low cloud amount looks very different. It shows the right phase with a minimum in the DJF time frame, and maximum in August–September. The amplitude of the seasonal cycle is still a factor of 2 smaller than the observations. The underestimate may be explained by a number of factors. One explanation is that observational estimates may be off in amplitude;there is speculation that surface observers often underestimate cloud fraction during the polar night because of the difficulty of estimation from moonlight. Another possibility is that meteorological terms that determine the cloud fraction (water vapor convergence and temperature structure) may be wrong. Lastly, it is likely that some aspects of cloud fraction, cloud water content, or optical properties continue to be unrealistic.

Fig. 14.

The seasonal cycle of low cloud cover over the Arctic basin. Thick dashed line is a sinusoid fitting of the data for total cloud cover over the arctic for 1952–80 from Warren et al. (1988). Thick lines are the model PCW run. Thin lines are control. Solid lines show the approximate model cloud fraction (using a random overlap assumption) independent of optical properties. Dotted lines show the corresponding effective cloud cover, which weights the cloud fraction by the cloud emissivity.

Fig. 14.

The seasonal cycle of low cloud cover over the Arctic basin. Thick dashed line is a sinusoid fitting of the data for total cloud cover over the arctic for 1952–80 from Warren et al. (1988). Thick lines are the model PCW run. Thin lines are control. Solid lines show the approximate model cloud fraction (using a random overlap assumption) independent of optical properties. Dotted lines show the corresponding effective cloud cover, which weights the cloud fraction by the cloud emissivity.

Figures 15 and 16 show the zonally averaged top of atmosphere fluxes for the two model configurations and the estimates from ERBE, for the composite DJF and JJA seasons between 1985 and 1989. We show the short- and longwave cloud forcing (defined as the difference between total fluxes and clear sky fluxes) and the net top of atmosphere longwave flux. Both models agree quite well with the observations and again are more similar to each other than to the observations. Top of atmosphere longwave fluxes have decreased over each winter pole by about 10 W m−2. This puts the PCW run closer to the observations than the control simulation for outgoing longwave radiation (OLR) (Briegleb and Bromwich 1998) and farther in terms of longwave cloud forcing. Because of difficulties in distinguishing between cloudy and cloud-free regions near the poles (due to the presence of ice- and snow-covered surfaces), the cloud forcing is much less certain than the total longwave flux, and we believe the PCW simulation is more realistic in these regions.

Fig. 16.

As in Fig. 15 but for JJA.

Fig. 16.

As in Fig. 15 but for JJA.

The changes in top of atmosphere and surface fluxes produce temperature changes in the model (Figs. 13a and 12a). There is a small but significant decrease (1 K) in the temperature at the tropical tropopause during DJF. There are more important temperature increases in the model in winter polar regions. The zonally averaged temperature has increased in cold regions (i.e., winter in the Northern Hemisphere, and summer and winter over Antarctica) in the lower troposphere, and this improves the simulation significantly there. Figure 17 compares the zonally averaged and seasonally averaged temperature distributions between the model and observational estimates from the NCEP reanalysis. Polar cold biases in both hemispheres below 400 mb in the control run are substantially reduced, particularly in the winter hemisphere. The 2°–6° cold bias seen near the surface in DJF near the north pole has been replaced by a 0°–1° warm bias. A large reduction in the cold bias near the surface in Antarctica is also evident.

Fig. 17.

Model minus NCEP analysis temperature difference for case PCW and control for the JJA composite and the DJF composite of 1989–95. Temperature differences between 2° and 4° are lightly shaded. Those between 4° and 6° are more darkly shaded. Dotted lines indicate negative contours (cold biases).

Fig. 17.

Model minus NCEP analysis temperature difference for case PCW and control for the JJA composite and the DJF composite of 1989–95. Temperature differences between 2° and 4° are lightly shaded. Those between 4° and 6° are more darkly shaded. Dotted lines indicate negative contours (cold biases).

It is difficult to assess the importance of other changes to the model climatology. The substantial reduction in OLR over Antarctica has also dramatically changed the model near-surface temperatures (Figs. 11d and 10d), but we are uncertain of our ability to characterize the real temperature there. The Northern Hemisphere summer temperatures are reduced slightly, but probably significantly, and this increases a preexisting small bias in CCM3 (B097). Changes in zonal wind (Figs. 13b and 12b) are small everywhere, except during DJF at 40°S, where there is an equatorword shift of the upper-troposphere jet. This shifts the westerly bias in this region compared to the control (HU98), but does not improve or degrade its basic character. Time series of regional diagnostics of surface temperature, precipitation, and top of atmosphere radiative fluxes have been examined for both models and compared to observations. The differences between simulations are generally small, and the model modifications improve the simulations in some regions slightly, and degrade it slightly elsewhere.

Some coherent regional differences can be found in the surface energy fluxes for the two models (Fig. 18). We have chosen to highlight regional changes exceeding 15 W m−2, a number of which exceed 2σ of the models’ natural variability for most regions for these fields. The figures suggest a seasonal cycle to some of the changes in simulation that cannot be discerned from the annually averaged perspective described by Table 2. There are relatively large (15–45 W m−2) changes in solar insolation reaching the surface over the year. Many of the changes are within the stratocumulus regime. During JJA there is a reduction in solar insolation reaching the surface near the California coastline and an enhancement farther offshore. There are similar signatures off the coast of Namibia and northwestern Africa. The signature is reversed off the coast of Chile and Peru in summer. We believe these differences are primarily connected with the revisions to the marine stratocumulus, but they reflect only small changes to significant biases already present in the CCM3, and we do not examine them further here. The result suggests that it may be necessary to thoroughly revise the parameterizations controlling this region (i.e., boundary layer, surface flux, and turbulent diffusion) in order to improve this area. Interestingly, although there are large changes to the global longwave flux leaving the surface (Table 2) of 5 W m−2, those changes are not apparent in the longitude–latitude distribution, suggesting that the increase is relatively small and uniform over the globe. Changes to the sensible heat flux are likewise relatively small, and reflect small differences in the precipitation pattern. The latent heat flux decreases are spatially coherent and tend to follow the regions of maximum precipitation.

Fig. 18.

Differences between DJF (left panels) and JJA (right panels) surface energy fluxes for case PCW: (top row) surface shortwave flux (positive downward), (second row) surface longwave flux (positive upward), (third row) sensible heat flux (positive upward), (bottom row) latent heat flux (positive upward).

Fig. 18.

Differences between DJF (left panels) and JJA (right panels) surface energy fluxes for case PCW: (top row) surface shortwave flux (positive downward), (second row) surface longwave flux (positive upward), (third row) sensible heat flux (positive upward), (bottom row) latent heat flux (positive upward).

5. Summary and conclusions

We have introduced a new parameterization for the prediction of cloud water into the NCAR CCM3. The new parameterization makes a much closer connection between the meteorological fields that determine condensate formation, and the condensate amount than the previous diagnostic parameterization. The free parameters of the scheme were adjusted to provide reasonable agreement with top of atmosphere and surface fluxes of energy. The parameterization was evaluated by a comparison with satellite and in situ measures of liquid and ice cloud amounts. The effect of the parameterization on the model simulation was then examined by comparing long model simulations to a similar run with the standard CCM, and through comparison with climatologies based upon meteorological observations.

The new parameterization introduced significant changes into the cloud water distributions. Global ice and liquid water burdens are about 30% higher than in the control simulation. The center of mass of cloud water was raised. Zonal averages of cloud water contents were 20%–50% lower near the surface, and much higher above. Regional mean cloud water often differed by a factor of 2 or more between the two simulations. The range of variation of cloud water contents was much broader in the new parameterization but was still not as large as measurements suggest. The agreement between model and observations was better in midlatitudes than in the Tropics.

Like Lohmann and Roeckner (1996) only small improvements are apparent in the simulation through the addition of a more realistic model formulation. Differences in the simulation were found to be relatively small for most meteorological fields, and we have omitted showing many fields that were virtually identical. The largest significant changes found to the simulation were seen in polar regions (winter in the arctic, and all seasons in the antarctic). The new parameterization drastically changes the Northern Hemisphere winter distribution of cloud water. High clouds are now blacker to OLR, and low clouds allow more radiation to leave the surface. This changes the seasonal cycle of outgoing radiation, cloud fraction, and temperature in the polar regions significantly. The model is 2°–8° warmer in the near-surface layer at the poles during winter, and this reduces a long-standing bias in both the Arctic and Antarctic simulations.

Small changes were introduced in the cloud fraction parameterization to improve consistency of the meteorological parameterizations and to attempt to alleviate problems in the model (in particular, in the marine stratocumulus regime). These changes did not (unfortunately) make any appreciable improvement to the model simulation.

The new condensate parameterization removes some“restoring springs” from the simulation, by allowing a substantially wider range of variation in condensate amount than in the standard CCM3, and tying the condensate amount to the local physical processes. The parameterization allows cloud drops to form prior to the onset of grid-box saturation and can require a significant length of time to convert condensate to a precipitable form or to remove the condensate. It therefore introduces a new set of feedbacks and processes with timescales not present in the standard CCM3. So it is expected that the temporal or spatial variability of the model might change. We have looked for signatures of this change to the model in interannual variability, and in model variance on timescales from 3 h to 30 days. The differences are difficult to find, and more difficult to quantify with respect to statistical significance. We will defer a discussion of these issues to another paper.

Perhaps most importantly, the new parameterization adds significantly to flexibility in the model and the scope of problems that can be addressed. A cloud water parameterization is required for a reasonable treatment of scavenging of atmospheric trace constituents, and aqueuous or surface chemistry taking place on or within cloud particles. The addition of a more realistic condensate parameterization provides many opportunities for making a closer connection between radiative properties of the clouds, and their formation and dissipation. For example, the parameterization can predict an “effective radius” for liquid and ice clouds, based on assumptions about the number density of cloud particles and knowing the mass of condensate, and its assumed size distribution. The current prescription of 5- and 10-μm radii for warm clouds used in the standard CCM3 can be replaced with this predicted value. This adds another feedback to the GCM that is now being explored. By tying aerosol evolution to cloud droplet (or ice crystal) number density it is possible to examine the potential indirect effects of aerosols of anthropogenic origin that can effect the radiative properties of clouds, their lifetime, and their precipitation properties. All of these topics are actively being worked on and we anticipate reports of these studies in the near future.

This parameterization is not as elaborate as some current state-of-the-art bulk microphysical parameterizations. We have limited the number of types of frozen precipitate, prescribed a temperature-dependent expression for the ratio of ice to liquid condensate, and ignored a number of potentially important processes, for example, the mixed phase Bergeron–Findeisen conversion process. As justification for having neglected these processes we remind the reader that we have constructed a parameterization that is relatively simple, quite inexpensive, yet captures many of the processes represented in the more complex parameterizations and uses relatively few “free parameters.” Others have indeed included a mixed phase Bergeron–Findeisen-like representation in their formulations; we have not. We believe that our assumptions about the fraction of ice in the condensate and the temperature dependence assumed in PSAUT in the mixed phase regime are so crude as to overwhelm the more subtle aspects of the mixed phase as represented in such a simple formulation. We believe our simpler parameterization allows the exploration of many aspects of the simulation that will also be important to those more complex and expensive parameterizations (i.e., advection of condensate, or those topics mentioned in the previous paragraph). Our parameterization may be considered a first step down the path toward their implementation.

Acknowledgments

This work was begun by PJR during a one year visit to the Meteorological Institute of Stockholm University and the ECMWF in 1991. It is a great pleasure to finally acknowledge the time spent there. PJR greatly benefitted from discussions with H. Sundqvist, M. Tiedtke, M. Miller, and others at both institutions. We also benefitted from discussions with M. Barth, A. Heymsfield, J. Hack, J. Hurrell, J. Kiehl, M. Lawrence, G. McFarquhar, J. Petch, C. Zender, and other colleagues and visitors to NCAR. The two anonymous referees made constructive comments that helped the manuscript materially. Thanks go to B. Eaton for help in analysis of the runs and to him and Pawel Smolarkiewicz for help in preparation of the figures. JEK acknowledges support from The Research Council of Norway (Programme for Supercomputing) through a grant of computer time.

REFERENCES

REFERENCES
Austin, P., Y. Wang, R. Pincus, and V. Kujala, 1995: Precipitation in stratocumulus clouds: Observational and modeling results. J. Atmos. Sci., 52, 2329–2352.
Baker, M. B., 1993: Variability in concentrations of cloud condensation nuclei in the marine cloud-topped boundary layer. Tellus, 45B, 458–472.
Berge, E., 1993: Coupling of wet scavenging of sulphur to clouds in a numerical weather predition model. Tellus, 45B, 1–22.
Bonan, G. B., 1998: The land surface climatology of the NCAR Land Surface Model (LSM) coupled to the NCAR Community Climate Model (CCM3). J. Climate, 11, 1307–1326.
Boucher, O., and U. Lohmann, 1995: The sulfate-CCN-cloud albedo effect. A sensitivity study with two general circulation models. Tellus, 47B, 281–300.
——, H. Le Treut, and M. B. Baker, 1995: Precipitation and radiation modeling in a general circulation model: Introduction of cloud microphysical processes. J. Geophys. Res., 100 (D8), 16 395–16 414.
Briegleb, B. P., and D. H. Bromwich, 1998: Polar radiation budgets of the NCAR CCM3. J. Climate, 11, 1246–1269.
Chen, C., and W. R. Cotton, 1987: The physics of the marine stratocumulus-capped mixed layer. J. Atmos. Sci., 44, 2951–2977.
Del Genio, A., M.-S. Yao, W. Kovari, and L. W. Lo, 1996: A prognostic cloud water parameterization for global climate models. J. Climate, 9, 270–304.
Feichter, J., E. Kjellström, H. Rodhe, F. Dentener, J. Lelieveld, and G.-J. Roelofs, 1996: Simulation of the tropospheric sulfur cycle in a global climate model. Atmos. Environ., 30, 1693–1707.
Feigelson, E. M., 1978: Preliminary radiation model of a cloudy atmosphere. Part I: Structure of clouds and solar radiation. Beitr. Phys. Atmos., 51, 203–229.
Fowler, L., D. A. Randall, and S. A. Rutledge, 1996: Liquid and ice cloud microphysics in the CSU general circulation model. Part I: Model description and simulated microphysical processes. J. Climate, 9, 489–529.
Ghan, S. J., and R. C. Easter, 1992: Computationally efficient approximations to stratiform cloud microphysics parameterization. Mon. Wea. Rev., 120, 1572–1582.
——, L. R. Leung, and Q. Hu, 1997: Application of cloud microphysics to NCAR CCM2. J. Geophys. Res., 102, 21777–21799.
Greenwald, T. J., G. L. Stephens, and D. L. Jackson, 1993: A physical retrieval of cloud liquid water over global oceans using Special Sensor Microwave/Imager (SSM/I) observations. J. Geophys. Res., 98, 18 471–18 488.
Gultepe, I., and G. A. Isaac, 1997: Liquid water content and temperature relationship from aircraft observations and its applicability to GCMs. J. Climate, 10, 446–452.
Hack, J. J., 1994: Parameterization of moist convection in the NCAR Community Climate Model, CCM2. J. Geophys. Res., 99, 5551–5568.
——, 1998: Sensitivity of the simulated climate to a dianostic formulation for cloud liquid water. J. Climate, 11, 1497–1515.
——, J. T. Kiehl, and J. Hurrell, 1998: The hydrologic and Thermodynamic Characteristics of the NCAR CCM3. J. Climate, 11, 1179–1206.
Heymsfield, A., 1993: Microphysical structures of stratiform and cirrus clouds. Aerosol-Cloud-Climate Interactions, P. V. Hobbs, Ed., Vol. 1, Academic Press, 97–119.
——, and G. M. McFarquhar, 1996: High albedos of cirrus in the tropical Pacific warm pool: Microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands. J. Atmos. Sci., 53, 2424–2451.
Hurrell, J. W., J. T. Kiehl, and J. J. Hack, 1998: The dynamical simulation of the NCAR Community Climate Model version 3 (CCM3). J. Climate, 11, 1207–1236.
Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulations. Meteor. Monogr., No. 32, Amer. Meteor. Soc., 84 pp.
Kiehl, J. T., and K. T. Trenberth, 1997: Earth’s annual global mean energy budget. Bull. Amer. Meteor. Soc., 78, 197–209.
——, J. Hack, G. B. Bonan, B. A. Boville, B. P. Briegleb, D. L. Williamson, and P. J. Rasch, 1996: Description of the NCAR Community Climate Model (CCM3). NCAR Tech. Note, NCAR/TN-420+STR, 151 pp. [Available from National Center for Atmospheric Research, Boulder, CO 80307.]
.
——, ——, and J. W. Hurrell, 1998: The energy budget of the NCAR Community Climate Model (CCM3). J. Climate, 11, 1151–1178.
Klein, S. A., and D. L. Hartmann, 1993: The seasonal cycle of low stratiform clouds. J. Climate, 6, 1587–1606.
Legates, D. R., and C. J. Willmott, 1990: Mean seasonal and spatial variability in global surface air temperature. Theor. Appl. Climatol., 10, 11–21.
Levkov, L., B. Rockel, H. Kapitza, and E. Raschke, 1992: 3D mesoscale numerical studies of cirrus and stratus clouds by their time and space evolution. Beitr. Phys. Atmos., 65, 35–58.
Lin, B., and W. B. Rossow, 1996: Seasonal variation of liquid and ice water path in nonprecipitating clouds over oceans. J. Climate, 9, 2890–2902.
——, R. R. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 1065–1092.
Liou, K.-N., and S.-C. Ou, 1989: The role of cloud microphysical processes in climate: An assessment from a one-dimensional perspective. J. Geophys. Res., 94, 8599–8606.
Lohmann, U., and E. Roeckner, 1996: Design and performance of a new cloud microphysics scheme developed for the ECHAM general circulation model. Climate Dyn., 12, 557–572.
Mazin, I. P., 1995: Cloud water content in continental clouds of middle latitudes. Atmos. Res., 35, 283–297.
McFarquhar, G. M., and A. J. Heymsfield, 1996: Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment. J. Atmos. Sci., 53, 2401–2423.
Ou, S.-C., and K.-N. Liou, 1995: Ice microphysics and climatic temperature feedback. Atmos. Res., 35, 127–138.
Slingo, J. M., 1980: A cloud parameterization scheme derived from GATE data for use with a numerical model. Quart. J. Roy. Meteor. Soc., 106, 747–770.
——, 1987: The development and verification of a cloud prediction scheme for the ECMWF model. Quart. J. Roy. Meteor. Soc., 113, 899–927.
Sundqvist, H., 1978: A parameterization scheme for non-convective condensation including prediction of cloud water content. Quart. J. Roy. Meteor. Soc., 104, 677–690.
——, 1988: Parameterization of condensation and associated clouds in models for weather prediction and general circulation simulation. Physically Based Modelling and Simulation of Climate and Climatic Change, M. E. Schlesinger, Ed., Vol. 1, Kluwer Academic, 433–461.
——, 1993a: Inclusion of ice phase of hydrometors in cloud parameterization for mesoscale and largescale models. Beitr. Phys. Atmos., 66, 137–147.
——, 1993b: Parameterization of clouds in large-scale numerical models. Aerosol-Cloud-Climate Interactions, P. V. Hobbs, Ed., Vol. 1, Academic Press, 175–203.
——, E. Berge, and J. E. Kristjánsson, 1989: Condensation and cloud parameterization studies with a mesoscale numerical weather prediction model. Mon. Wea. Rev., 117, 1641–1657.
Tripoli, G. J., and W. R. Cotton, 1980: A numerical investigation of several factors contributing to the observed variable intensity of deep convection over south Florida. J. Appl. Meteor., 19, 1037–1063.
Warren, S. G., C. J. Hahn, J. London, R. M. Chervin, and R. L. Jenne, 1988: Global distribution of total cloud cover and cloud type amounts over the ocean. NCAR Tech. Note NCAR/TN-317+STR, 140 pp. [Available from National Center for Atmospheric Research, Boulder, CO 80307.]
.
Weng, F., and N. Grody, 1994: Retrieval of cloud liquid water using the Special Sensor Microwave/Imager (SSM/I). J. Geophys. Res., 99, 25 535–25 551.
Xu, K.-M., and S. K. Krueger, 1991: Evaluation of cloud models using a cumulus ensemble model. Mon. Wea. Rev., 119, 342–367.
Zhang, G. J., and N. A. McFarlane, 1995: Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate Centre general circulation model. Atmos.–Ocean, 33, 407–446.

APPENDIX A

Modifications to the CCM3 Cloud Fraction Formulations

Section 2b describes our motivation for modification to the CCM3 cloud fraction diagnosis. This section documents the revisions we made. First, clouds were allowed to form in any layer, including the lowest model layer.

Then, to tie diagnosis of cirrus anvils very strongly to the regions of outflow, we made convective cloud fraction proportional to the rate at which mass is detrained from the parameterized convective updrafts above 500 mb:

 
fc = min〈RH1, min{1, max[0, Du(5.0 × 104)]}〉,
(A1)

where RH1 is the local relative humidity and Du is the rate of detrainment of mass from the convective updraft. This results in a very clear signature in the cloud fields and a strong correlation between deep convection and convective clouds.

Klein and Hartmann (1993) deduced an empirical relationship between marine stratocumulus cloud fraction and the stratification between the surface and 700 mb. We have replaced the standard CCM3 stratus cloud fraction formulation with a dependence utilizing their relationship:

 
fst = min{1, max[0, (θ700θs)(0.057 − 0.5573)]}
(A2)

over oceans. Here θ700 and θs are the potential temperatures at 700 mb and the surface, respectively.

Finally, to assure some clouds exist in volumes near saturation, we diagnose a minimum fraction fmin occupied by clouds. Here fmin is set to 0.01 whenever the relative humidity exceeds 99%. Otherwise it is assumed to be zero.

The total cloud ftot within each volume is then diagnosed as

 
ftot = max(fRH, fc, fst, fmin),

where fRH is the standard CCM3 cloud prescription, which depends basically upon relative humidity. This is equivalent to a maximum overlap assumption of cloud types within each grid box. The condensate value is assumed uniform within any and all types of cloud within each grid box.

APPENDIX B

The Constants Arising in the Cloud Microphysics

The coefficients of Eq. (25) arise from some algebraic manipulation of the expressions appearing in Lin et al. (1983). They in turn depend upon the specification for parameters describing an exponential size distribution for graupel-like snow. The choices used in Lin et al. (1983) (and followed here) are the “slope parameter” d = 0.25; an empirical parameter c = 152.93 controlling the fall speed of graupel-like snow; and Ns = 3 × 10−2, the assumed integrated number density of snow. The constants appearing in Eq. (25) can be expressed as

 
formula

Here ρs = 0.1 is the density of snow and ρ0 = 1.275 × 10−3 a reference air density at the surface. All constants have been expressed in cgs units. The constants arise by assuming a geometric sweepout by the snow size distribution of a uniform distribution of suspended cloud liquid or ice after integration over all snow sizes.

Footnotes

Corresponding author address: Dr. Philip J. Rasch, National Center for Atmospheric Research, Climate and Global Dynamics Division, P.O. Box 3000, Boulder, CO 80307-3000.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation.

1

The convection parameterization of (Zhang and McFarlane 1995);calculates cloud water by lifting parcels from cloud base in a manner designed to reduce CAPE at a prescribed rate, through their lifting condensation level and on to the level of neutral buoyancy. At each level environmental air is entrained into the updraft, and saturated air is detrained. The amount of water vapor flowing into the layer in excess of its saturation value determines the condensate production rate at that level. The condensate is converted to precipitate within the convective plume in proportion to the vertical mass flux. The production and loss terms for convective condensate are used with the updraft mass fluxes and detrainment rate to produce a profile of cloud water, and the source of cloud water by detrainment to the environment. See Zhang and McFarlane (1995) for details.