The climate sensitivity of the CSIRO Global Climate Model is investigated using uniform sea surface temperature perturbation experiments. One experiment (denoted DIAG) uses a diagnostic treatment of clouds, with fixed cloud radiative properties that vary with height. The other experiment (denoted CTRL) uses a recently introduced prognostic treatment of stratiform clouds, with interactive calculation of cloud radiative properties.
The DIAG experiment has a positive shortwave (SW) cloud feedback and a negative longwave (LW) feedback, due to an overall reduction of midlevel and high cloudiness in the warmer climate. The signs of both the SW and LW feedbacks are opposite in the CTRL experiment due to an overall increase of cloud water content in the warmer climate. Because of cancellation between the SW and LW components, there is not a large difference in the net cloud feedback between the two experiments, with both having a modest negative cloud feedback, as measured by the change in cloud radiative forcing.
The CTRL experiment has a larger clear-sky climate sensitivity than the DIAG experiment. Off-line radiative calculations are used to show that this is primarily because of a stronger water vapor feedback. This is caused by differences in upper-tropospheric cloud radiative forcing that give a stronger upward shift of the tropopause on warming when the prognostic scheme is used. A sensitivity test shows that an artificial restriction on the maximum height of high clouds that exists in the diagnostic scheme is the reason for the different behavior.
The robustness of the result obtained in the CTRL experiment is investigated via 18 perturbation experiments, in which key parameters in the prognostic cloud scheme are varied, while retaining the overall approach used in the CTRL experiment. As far as possible, theory and observations are used to constrain the ranges within which these parameters are varied. It is found that the behavior of the scheme under climate change is generally robust, with no statistically significant changes in LW cloud feedback and only modest changes in SW cloud feedback. Overall, larger differences (both in control climate and in climate sensitivity) result from parameter changes that affect cloud formation than from changes that affect precipitation processes or cloud radiative properties.
The effect of clouds on the sensitivity of global climate models to radiative perturbations has attracted considerable attention, especially since the study by Cess et al. (1990) in which the authors found that different cloud feedbacks were the main cause of a threefold variation in climate sensitivity among 19 GCMs tested. Cess et al. used idealized experiments in which the sea surface temperature (SST) was uniformly perturbed by ±2 K, and the resulting changes in the top-of-atmosphere (TOA) radiation budget were used to evaluate the climate sensitivity of each model. These experiments can be regarded as the inverse of conventional climate-change experiments, in which climate sensitivity is evaluated from the change in surface temperature that results from a radiative perturbation (such as that due to an increase of atmospheric CO2).
In a follow-up study, Cess et al. (1996) found that more recent models showed considerably smaller differences in net cloud feedback, with most producing modest values. There were still, however, substantial differences in the longwave (LW) and shortwave (SW) feedback components among the models tested. The tendency toward smaller net cloud feedbacks was associated with cancellation between the LW and SW feedback components in 12 of the 18 models. (Of the remaining six models, four had both feedback components positive, while two had one feedback component negligibly small.) However, the authors questioned whether the convergence was due to a general increase in the accuracy of GCM cloud parameterizations or whether there had merely been a convergence toward similar errors in the models.
One limitation of this type of intercomparison is that, in view of the wide range of parameterizations employed by the various models, it is difficult to ascribe the different climate sensitivites of any two models to specific differences in model formulation. Indeed, it is possible that the differences in cloud feedbacks among the models tested are substantially due to other differences in model formulation, rather than differences in the cloud parameterizations themselves (Colman and McAvaney 1997).
Early studies of the effects of clouds on the climate sensitivity of GCMs considered feedback effects due to the inclusion of simple diagnostic cloud treatments with fixed cloud radiative properties. Hansen et al. (1984) found that the inclusion of cloud feedbacks increased the sensitivity of their model to a doubling of CO2 by about 30%. Wetherald and Manabe (1988) performed doubled-CO2 experiments using both fixed and diagnostic clouds and found that the inclusion of diagnostic clouds increased the sensitivity of the model by 25%, in broad agreement with the result of Hansen et al. The positive cloud feedback of Wetherald and Manabe was principally due to an increase of cloudiness around the tropopause, which was higher in the warmer climate. The effect of this increase outweighed the effects of a decrease of high cloudiness below the tropopause and an increase of low cloudiness at high latitudes. The increase of cloudiness around the tropopause on global warming has been found in many studies and can be explained by the penetration of moist tropospheric air to levels that were previously above the tropopause. Wetherald and Manabe explained the lifting of the tropopause in terms of an increase of latent heating due to convection in the warmer climate; this result is also consistent with a simple conceptual model based on the lifting of a parcel of near-surface air along a moist adiabat (Mitchell and Ingram 1992).
Since then the treatment of clouds in models has become more complex, and most models now include prognostic cloud water and/or interactive calculation of cloud radiative properties. More recent studies have therefore tended to focus on differences between diagnostic and prognostic treatments or on the effects of changes to cloud microphysical treatments or cloud radiative properties.
Aside from the model intercomparisons of Cess et al., several recent studies have emphasized the uncertainties inherent in cloud parameterization in GCMs. Senior and Mitchell (1993) performed doubled-CO2 experiments using a diagnostic cloud scheme and three versions of Smith’s (1990) prognostic cloud scheme. They found that the surface warming due to a doubling of CO2 was 5.4 K using the diagnostic cloud scheme and varied from 1.9 K to 3.3 K with the prognostic scheme. Li and Le Treut (1992) and Le Treut et al. (1994) found that changes to the treatment of precipitation had a marked effect on the cloud feedbacks in their GCM. Morcrette (1995) showed results from 12 experiments with a global model, comparing diagnostic and prognostic cloud schemes, and the effects of changes to cloud–radiation interactions, model resolution, and the treatment of frozen precipitation. He found that the 12 model versions yielded an almost threefold variation in climate sensitivity. Many of the model changes examined by these authors actually resulted in a change in the sign of the net cloud feedback.
A result obtained in a number of studies that have used the SST-perturbation method (Taylor and Ghan 1992; Del Genio et al. 1996; Lee and Somerville 1996;Lee et al. 1997) is that replacement of height-dependent cloud radiative properties with interactive calculation of cloud radiative properties results in a change in the sign of both the LW and SW cloud feedback components. In each of these studies, the use of height-dependent cloud radiative properties gave negative LW and positive SW feedbacks, whereas inclusion of cloud water feedbacks gave positive LW and negative SW feedbacks due to an overall increase of cloud water content on warming. The latter result is qualitatively consistent with adiabatic calculations (Betts and Harshvardhan 1987) and with radiative–convective model calculations by Somerville and Remer (1984) in which the variation of cloud water content with temperature was based on observations. However, different schemes can give different results; an interesting example was presented by Lohmann and Roeckner (1996b), who found that the treatment of frozen precipitation formation in the prognostic scheme of Lohmann and Roeckner (1996a) results in a decrease of global-mean ice-water path on warming, and hence a negative LW cloud feedback.
In summary, there is still little consensus on the effect of clouds on the climate sensitivity of GCMs, or even on the effect of particular treatments, such as diagnostic versus prognostic approaches. The only real consensus so far is that changes to the treatment of clouds can significantly affect the modeled cloud feedbacks.
Recently, the treatment of clouds in the CSIRO GCM has been substantially upgraded, with replacement of the diagnostic scheme used previously (based on Slingo 1987) by a prognostic scheme (Rotstayn 1997). Unlike the diagnostic scheme, the prognostic scheme integrates the clouds into the model’s hydrological cycle, differentiates between the properties of ice and liquid-water clouds in a consistent manner, and includes interactive calculation of cloud radiative properties. Rotstayn (1998) also found that the cloudiness and LW cloud radiative forcing (LWCF) obtained with the prognostic scheme were overall in better agreement with observations than those obtained with the diagnostic scheme. The more realistic physical basis of the prognostic scheme and the improvements obtained in the simulation of the present climate both suggest that the prognostic scheme is a more appropriate tool for the study of climate change. They also suggest that the climate sensitivity of the model might be substantially altered due to inclusion of the new scheme.
The purpose of the present study is to answer two questions. First, what is the effect of the introduction of a prognostic cloud scheme on the climate sensitivity of the CSIRO GCM? Second, how robust is this result in the face of perturbations to key parameters in the prognostic scheme? Perturbation studies of this type—as distinct from studies that explore the sensitivity of simulations of the present climate to model parameters—are rarely carried out. The fact that there are no observations that can be used to validate the future climates simulated by GCMs underlines the need for more perturbation studies, in addition to those that consider simulations of the present climate.
To evaluate the climate sensitivity of the model, inverse climate-change experiments based on uniform ±2 K SST perturbations are used. A big advantage of these experiments is that equilibrium is attained much more quickly than in conventional climate-change experiments, allowing the effect of a number of parameter changes to be investigated at reasonable computational cost. Another advantage is that feedbacks due to changes in surface albedo are suppressed, which makes it easier to isolate the effects due to clouds. Also, the results can be readily compared with those obtained using other GCMs. The main disadvantage of the inverse experiments is their idealized nature, and the climate sensitivites derived from such experiments can differ significantly from those obtained from doubled-CO2 experiments (Senior and Mitchell 1993) or from nonuniform SST pertubations (Del Genio et al. 1996). However, despite their idealized nature, they provide valuable insights into the physical processes occurring in the model and can point toward parameters worthy of further investigation in the context of more realistic climate change experiments.
The organization of the paper is as follows. The model and experimental design are described in section 2. The results obtained with the diagnostic cloud scheme and with the control version of the prognostic scheme are presented and discussed in section 3. The uncertainties in key parameters in the prognostic cloud scheme are discussed in section 4, and the effects of perturbations to the prognostic scheme are considered in section 5. Section 6 contains discussion and section 7 contains a summary and conclusions. Whereas Rotstayn (1997) used SI units almost exclusively in the description of the scheme, in the present study commonly used (non-SI) units are used for some quantities, even though they are implemented in SI units in the model.
2. Model description and experimental design
a. The CSIRO GCM
The CSIRO GCM is a spectral model that utilizes the flux form (Gordon 1981) of the primitive equations. Advection of water vapor (and of cloud water when the prognostic cloud scheme is in use) is now handled via a semi-Lagrangian scheme in which the departure points of the flow trajectories are calculated following McGregor (1993) and a quasi-monotonic interpolation scheme (Bermejo and Stanifort 1992) is used to prevent the generation of spurious oscillations and ensure nonnegativity of the advected quantities. The version of the model used in the present study has 18 sigma levels in the vertical and horizontal resolution of R21 (approximately 5.6° long × 3.2° lat), the same as that used by Rotstayn (1997, 1998). The 18 levels are at σ = 0.996, 0.978, 0.946, 0.900, 0.843, 0.776, 0.702, 0.623, 0.541, 0.459, 0.377, 0.298, 0.224, 0.157, 0.100, 0.054, 0.022, and 0.004.
The treatment of radiative transfer in the model follows Schwarzkopf and Fels (1991) in the longwave and uses an improved version of Lacis and Hansen (1974) in the shortwave. Clouds are treated by either a diagnostic scheme or a prognostic scheme (described in the next two subsections). Vertical turbulent fluxes of heat, momentum, and moisture (both in and above the surface layer) are calculated as a function of atmospheric stability using the method of Louis (1979). The treatment of shallow convection follows the approach of Tiedtke (1988) and entails a simple adjustment to the diffusion coefficients used in the turbulent mixing scheme. Deep convection is parameterized via a moist convective adjustment scheme that generates a mass flux, based on the ideas of Arakawa (1972). Large-scale precipitation is treated by one of two methods depending on which cloud scheme is in use (see below). Other components of the model’s physics package include a soil–canopy scheme (Kowalczyk et al. 1991) and a gravity wave drag scheme (Chouinard et al. 1986). Model-specific details of the implementation of the physics package are given by McGregor et al. (1993) and Rotstayn (1997).
b. The diagnostic cloud scheme
The diagnostic cloud scheme consists of methods for (i) calculation of the cloud fraction, (ii) specification of the cloud radiative properties, and (iii) the formation of large-scale precipitation.
The calculation of the cloud fraction is loosely based on Slingo (1987) and includes some features of the adaptation of Slingo’s scheme described by Hack et al. (1993). There are three cloud layers (low, midlevel, and high). Low cloud consists of that which forms in model layers centered below σ = 0.8 (but excluding the lowest model layer); midlevel cloud consists of that which forms in model layers centered between σ = 0.8 and σ = 0.43; high cloud consists of that which forms in model layers centered between σ = 0.43 and σ = 0.15. The cloud in each model layer is calculated as a combination of the large-scale (stratiform) and convective cloud in that layer; these are then overlapped randomly in the vertical to arrive at the low, midlevel, and high cloud amounts. The three cloud layers that are passed into the radiation scheme are each only one model layer thick; for each cloud layer, the cloud is placed in the model layer that has the highest relative humidity of those making up the cloud layer. The convective cloudiness in each column increases slowly as a function of the convective rainfall rate (Slingo 1987); this is then distributed across the convectively active layers following Hack et al. (1993) so that, when randomly overlapped, the individual layers combine to give the correct total column amount. The stratiform cloud fraction in each layer is calculated as
where RHe is the environmental relative humidity outside any convective cloud that has formed in the grid box. The critical relative humidity RHcrit is calculated differently for each of the three cloud layers and also varies as a function of atmospheric static stability, with lower values of RHcrit specified for each layer under unstable conditions than under stable conditions. For low cloud over land areas, RHcrit is also reduced as a function of the subgrid variability of the surface topography, increasing the amount of cloud in mountainous areas. In addition, the scheme allows the formation of explicit stability-dependent low cloud in very stable conditions (based on Slingo 1987). This cloud is calculated as a function of the strength of the inversion, but is only invoked if the relative humidity exceeds 0.5.
The cloud radiative properties are specified as a function of height, with different values of the SW reflectivities and absorptivities and the LW emissivity prescribed for the three cloud layers (low, midlevel, and high). The SW properties decrease with height, while the emissivity has a lower value for high clouds than for low and midleve1 clouds (see Table 1). The shortwave properties are specified separately for band 1 (approximately 0.1–0.7 μm) and band 2 (approximately 0.7–4.0 μm). There is assumed to be no cloud absorption in band 1.
Large-scale precipitation is calculated via the removal of any supersaturation, and is not closely coupled to the clouds used for the radiation calculation. In particular, the precipitation calculation occurs at every model time step (every 24 min), whereas the diagnosis of cloud fraction occurs only at radiation time steps (every 2 h). More details of the diagnostic cloud scheme are given in appendix A of Rotstayn (1998).
c. The prognostic cloud scheme
The prognostic cloud scheme (Rotstayn 1997) differs from the diagnostic scheme in that the stratiform clouds used in the radiation scheme are integrated into the model’s hydrological cycle. The scheme incorporates prognostic variables for large-scale cloud liquid water and cloud ice, physically based treatments of precipitation processes in stratiform clouds, and interactive calculation of cloud radiative properties. A diagnostic treatment of convective cloudiness similar to that used in the diagnostic cloud scheme has been retained at present. Figure 1 gives a schematic overview of the microphysical processes included in the scheme. Also included (but not shown in Fig. 1) are vertical turbulent mixing and semi-Lagrangian advection of cloud liquid water and cloud ice.
Cloud formation and dissipation are calculated using an assumed triangular subgrid distribution for the mixing ratio of total (vapor plus cloud) water in a grid box. Cloud water then forms in the part of each grid box in which the total-water mixing ratio exceeds the saturated value. This scheme (Smith 1990; Rotstayn 1997, 1998) retains the use of a prescribed critical relative humidity that controls the onset of cloud formation; it is this critical relative humidity that defines the standard deviation of the probability distribution function (PDF) for the moisture distribution within each grid box. The cloud fraction and the amount of condensate depend on (i) the difference between the total-water mixing ratio and the saturated value in a grid box, and (ii) the critical relative humidity.
The ice fraction in mixed-phase clouds is calculated by a novel method, driven primarily by the relative difference between the saturation mixing ratios with respect to ice and liquid water at a given temperature. This method differs from the approach commonly used in GCMs, in which the ice fraction is determined by interpolation as a function of temperature. A feature of the method is that it involves no “tunable” parameters.
Cloud liquid water is depleted by autoconversion (i.e., collision and coalescence of cloud droplets), collection of cloud liquid water by falling rain, and accretion of cloud liquid water by falling ice. Precipitation of cloud ice is calculated using an observationally based fall speed, based on the assumption that ice particles grow quickly by diffusion to sufficient size to acquire appreciable fall speeds. Evaporation of rain and sublimation of falling ice (loosely, snow) are included, using parameterizations that account for the different properties of raindrops and falling ice particles. In the development of the scheme, considerable emphasis was placed on the physical basis of the parameterizations of the various precipitation processes, most of which are treated along similar lines to microphysical schemes that have been used in mesoscale models, as distinct from the relatively crude treatments characteristic of earlier schemes used in GCMs. Also, fractional cloudiness is taken into account in the parameterizations, based on the assumption that clouds are randomly overlapped in the vertical.
The prognostic scheme differs from the diagnostic scheme in that radiatively active clouds are allowed to form in all layers of the model. The clouds, which are each one model layer thick, are randomly overlapped in the vertical. Instead of being prescribed as in Table 1, the cloud radiative properties required for input to the model’s shortwave code are calculated using a delta-Eddington scheme (Slingo 1989; Francis et al. 1994). The properties are essentially a function of the cloud visible optical depth, which depends on the liquid- or ice-water path and the droplet or particle effective radius. The liquid- and ice-water paths in stratiform clouds are calculated by the scheme, based on the mixing ratios of cloud liquid water and cloud ice, respectively. The liquid- and ice-water paths in convective clouds are based on a prescribed cloud water content of 0.2 g m−3, with the liquid fraction increasing linearly with temperature from zero at −35°C to 1 at 0°C. The effective radius is calculated following Martin et al. (1994) for liquid-water clouds and Platt (1994) for ice clouds. The cloud emissivities are calculated as a function of the infrared optical depth, which depends linearly on the visible optical depth (Rotstayn 1997).
The control version of the prognostic cloud scheme used in this study includes some minor changes relative to the version described by Rotstayn (1997). Over land areas, the critical relative humidity RHcrit has been reduced from 0.8 to 0.75, while retaining the value of 0.85 over oceans. This change gives slightly larger average cloud amounts over land, which are overall in better agreement with observations. The use of a smaller value of RHcrit over land than over oceans is a crude way to account for greater subgrid variability over land. As in the earlier version of the scheme, there is no variation of RHcrit with height. The other significant change involves the method used to compensate for the treatment of clouds as plane parallel by the radiation scheme. Without such compensation, a GCM with realistic global cloudiness and liquid-water paths would have excessive shortwave cloud forcing (SWCF) since plane-parallel clouds have higher albedos than real clouds (Harshvardhan and Randall 1985). Details are given in section 4. Also, to reduce the excessive amounts of snow and sea ice that were noted by Rotstayn (1998) after increasing the number of vertical levels from 9 to 18, the albedos of melting snow and sea ice have been reduced in the seasonally varying run that was used to initialize the SST-perturbation experiments (described below). However, for the SST-perturbation experiments, the albedos of snow and sea ice are held fixed, regardless of surface temperature, to suppress any feedbacks due to changes in surface albedo.
d. Experimental design
This study uses uniform ±2 K SST-perturbation experiments in the spirit of Cess et al. (1990) to provide a surrogate climate change that is used to evaluate the climate sensitivity of the model. As in previous studies, perpetual July (but diurnally varying) simulations are used, and the soil moisture, deep soil temperature, snow, and sea ice extent are held fixed at mid-July values obtained from a seasonally varying run performed using the control version of the prognostic cloud scheme. Each simulation is run for 15 months and is forced with SSTs obtained by increasing or decreasing by 2 K the climatological mid-July SST field used in the seasonally varying run. Data from the last 12 months of each run are analyzed; that is, the model is allowed to equilibrate for three months at the start of each run. Experiments are performed using the diagnostic scheme, the control version of the prognostic scheme, and a number of perturbed versions of the prognostic scheme. Each perturbation experiment (to be described in section 4) uses a version of the model in which a single change is made with respect to the control version. The philosophy adopted is to vary key parameters in the scheme, while retaining the overall approach used in the control version of the scheme. In other words, it is the robustness of the scheme that is being investigated, rather than the effect of replacing one cloud scheme by another. Rotstayn (1997) discussed the uncertainty of a number of parameters in the cloud scheme, drawing on both theory and observations to demonstrate that the parameter values chosen were reasonable. As far as possible, similar considerations are used in the present study to constrain the ranges within which the various parameters are perturbed.
Following other studies that have used the SST-perturbation technique, the change G in the TOA radiation balance that results from the change in surface temperature ΔTs is used to evaluate the climate sensitivity of the model. Here, Δ denotes the difference between the +2 K and −2 K simulations, that is, the change resulting from the 4-K SST increase. The radiative perturbation G can be partitioned into its LW and SW components as
where F and Q are, respectively, the global-mean outgoing LW flux and net downward SW flux at the TOA. The climate sensitivity parameter
is used to quantify the climate sensitivity of the model. In the context of a SST-perturbation experiment, a larger value of λ corresponds to a smaller radiative perturbation G that results from the imposed surface warming. In the context of a conventional climate change experiment, such as a doubled-CO2 experiment, a larger value of λ would correspond to a larger surface warming that results from the imposed TOA radiative perturbation G.
Again following Cess et al. (1990), the effect of clouds on the model’s climate sensitivity is quantified by λ/λc, that is, the ratio of the sensitivity parameter to the clear-sky sensitivity parameter. The clear-sky sensitivity parameter is calculated by using the model’s clear-sky fluxes Fc and Qc in place of F and Q, respectively, in (2). The clear-sky fluxes are calculated using method II of Cess and Potter (1988), that is, by repeating each radiation calculation with all cloud amounts set to zero. As shown by Cess et al.,
where ΔCF is the change in cloud radiative forcing induced by the SST increase. The cloud radiative forcing measures the impact of clouds on the TOA radiation budget, and is defined as
where, by definition, Fc − F = LWCF and Q − Qc = SWCF. Equation (4) shows that, for positive G, λ/λc > 1 corresponds to ΔCF > 0 (interpreted as positive cloud feedback), whereas λ/λc < 1 corresponds to ΔCF < 0 (interpreted as negative cloud feedback). The cloud feedbacks derived by this method differ slightly from those obtained by an alternative method (Zhang et al. 1994; Colman and McAvaney 1997) in which fields from the “perturbed” run are substituted one by one into the “control” run to calculate the partial radiative perturbation from each field. This is because of the different temperature and moisture distributions between a clear-sky and a cloudy-sky atmosphere (Zhang et al. 1994).
3. Effect of the change of cloud scheme on the model’s climate sensitivity
To understand the different behavior of the two cloud schemes under climate change, four SST-perturbation experiments are considered in this section.Table 2 shows that there are substantial differences in the climate sensitivity of the model depending on which cloud scheme is in use. Not only does λ differ between CTRL and DIAG, but so does λc. Most of this section is devoted to consideration of the cloudy-sky and clear-sky differences between CTRL and DIAG. The NOCON experiment, which is identical to CTRL except for the omission of convective cloudiness, is used in the next paragraph to illustrate the effect of the diagnosed convective cloud on the results obtained with the prognostic cloud scheme. The DIAGH experiment is used later to clarify the reasons for some of the differences between CTRL and DIAG.
Cloudiness and cloud water data shown in this section and subsequent sections include the (relatively small) convective component. Feedbacks due to any changes of convective cloud-water content are suppressed in the present version of the model, due to the use of a prescribed cloud water content in convective clouds. This means that the only permitted feedbacks related to convective cloudiness are those resulting from changes of convective cloud fraction. These changes are small, since the convective cloud fraction varies only slowly with convective rainfall rate. This is illustrated by the cloud feedbacks obtained in the NOCON experiment, which are almost identical to those obtained in the CTRL experiment (Table 2). Even though the convective cloudiness has little effect on the model’s climate sensitivity at present, it does have a significant effect on the model’s control climate. For example, the −2 K simulation of the NOCON experiment has globally averaged cloudiness of just 52.0%, compared to 58.4% in CTRL.
a. Cloudy-sky differences between CTRL and DIAG
The sign of ΔQ is opposite in the two experiments, with the net difference of 2.1 W m−2 between the two experiments being approximately accounted for by the difference of 2.2 W m−2 in ΔSWCF. There is a positive SW cloud feedback in DIAG (ΔSWCF > 0) and a negative SW cloud feedback in CTRL (ΔSWCF < 0).
The positive SW feedback in DIAG is principally due to a 2.2% reduction in midlevel cloudiness on warming (Table 3 and Fig. 2a, where midlevel cloud is that which lies between σ = 0.81 and σ = 0.42). There is also a 1.0% decrease in global-mean high cloudiness, despite some regions of increased high cloudiness near the tropopause, and a 0.8% increase in low cloudiness. Overall, the changes in cloudiness in the middle and upper troposphere have the character of an upward shift. (The region of reduced cloudiness near the tropical tropopause is discussed below.) The changes in cloudiness are generally consistent with the changes in relative humidity (Fig. 3a), but there is a “layering” effect in the cloudiness field because the three cloud layers are each only one model-layer thick (section 2b). Note that the prescribed cloud reflectivities for midlevel cloud are only slightly smaller than those for low cloud (Table 1), so the marked reduction in midlevel cloudiness has a stronger effect on SWCF than the smaller overall increase in low cloudiness.
The negative SW cloud feedback in CTRL is primarily driven by changes in cloud water content rather than changes in cloudiness. In global-mean terms, the changes in cloudiness at different levels are small (Table 3). As in DIAG, there is a general upward shift of cloud in the middle and upper troposphere (Fig. 2b). The changes in cloudiness are again generally consistent with the changes in relative humidity (Fig. 3b), except in the lower troposphere in the Tropics where there is a slight reduction in cloudiness despite an increase in relative humidity. As noted by Mitchell and Ingram (1992), changes in cloudiness and relative humidity are not tightly coupled, when averaged over time and space, due to the nonlinear relationship between them. Despite a small reduction in global-mean low and midlevel cloudiness, an increase in the amount of cloud liquid water in the warmer atmosphere (Fig. 4a) results in a net increase in SWCF. Although there are some regions of reduced cloud liquid water, the global-mean vertically integrated liquid-water path increases from 84 g m−2 in the −2 K run to 101 g m−2 in the +2 K run. Figure 5a shows the zonally averaged ΔSWCF from both experiments. The largest difference between the experiments occurs in the Tropics, just north of the equator, where DIAG has positive ΔSWCF and CTRL has negative ΔSWCF. In DIAG the positive ΔSWCF is associated with a reduction of cloudiness (Fig. 2a), whereas in CTRL the negative ΔSWCF is associated with an increase of cloud liquid water (Fig. 4a), which occurs despite a reduction of low cloudiness in the warmer atmosphere. The overall pattern of changes in cloud liquid water is complex, with increases aloft but also regions of decrease in the lower troposphere at low and midlatitudes. The regions of decreased cloud liquid water are not wholly accounted for by decreases in cloudiness since there are still substantial regions of decreased cloud liquid water even when the changes shown in Fig. 4a are normalized by the cloud changes shown in Fig. 2a. There is some observational evidence to support decreases of cloud liquid-water content with temperature in warm regions (Feigelson 1978; Gultepe et al. 1996; Tselioudis et al. 1998).
In DIAG, ΔF is 4.4 W m−2 larger than in CTRL. Of this, 3.4 W m−2 is accounted for by the difference in ΔLWCF. The remaining 1.0 W m−2 represents the difference in the change of clear-sky LW absorption between the two experiments; this is discussed in the next subsection.
The negative LW cloud feedback in DIAG is due to an overall reduction in the amount of high and midlevel cloudiness (Table 3 and Fig. 2a). The midlevel clouds contribute significantly to LWCF; although they are emitting LW radiation at warmer temperatures than the high clouds, their larger emissivities (Table 1) increase their contribution to LWCF. Tests with the model show that the high clouds contribute a little more than two-thirds of the LWCF, and that the midlevel clouds contribute a little less than one-third.
In CTRL, there is a positive LW cloud feedback, which is again driven primarily by increases of cloud water content on warming. While there is a small increase in high cloudiness associated with an upward shift of cloud (Fig. 2b), the changes in high and midlevel cloudiness are small in global-mean terms (Table 3). Importantly, there is an increase of cloud ice at higher levels (Fig. 4b), which results in an increase of cloud emissivity. There is also an increase of cloud emissivity at lower levels in the warmer atmosphere due to the replacement of ice clouds by liquid-water clouds, which have greater optical depth. This positive LW cloud feedback is not present in DIAG, in which cloud emissivity is fixed.
The difference in the sign of the change in high cloudiness between DIAG and CTRL is mainly due to a large difference in the Tropics (Fig. 6). In CTRL, the largest increase in high cloudiness occurs near the tropical tropopause at the σ = 0.100 level (Fig. 2b). This increase in cloudiness near the tropopause in a warmer climate is consistent with the findings of a number of other studies (Wetherald and Manabe 1988; Mitchell and Ingram 1992; Zhang et al. 1994). However, the diagnostic cloud scheme does not allow cloud to form at this level since its highest cloud layer is one level lower, at σ = 0.157. This artificial restriction is less significant in the extratropics since the tropopause is lower there. The difference in the change of high cloudiness between the two experiments results in a large difference of up to around 10 W m−2 in ΔLWCF in the Tropics (Fig. 5b). To illustrate the impact of the artificial restriction on the high cloudiness, another experiment has been performed, identical to DIAG except that the restriction on the maximum height of clouds in DIAG was removed. This experiment (denoted DIAGH) has changes in high cloudiness similar to those in CTRL (Fig. 6), and in common with CTRL, the global-mean high cloudiness in DIAGH shows a small increase (0.1%) on warming. Despite this, DIAGH still has a negative LW cloud feedback due to a 2.3% decrease in midlevel cloudiness (Table 3).
b. Clear-sky differences between CTRL and DIAG
Perhaps more surprising than the differences in ΔSWCF and ΔLWCF between the two experiments is the difference in the clear-sky sensitivity parameter λc. This implies that the change of cloud scheme has altered the distribution of water vapor and/or temperature in the model. In the absence of feedbacks other than that due to surface temperature, λ ≈ 0.3 K m2 W−1, representing a balance between the surface warming and increased LW emission from the surface (Cess et al. 1990). Since feedbacks due to surface albedo changes are excluded by the experimental design, the clear-sky feedbacks that need to be considered are those due to water vapor and temperature lapse rate. Water vapor feedback is generally strongly positive in GCMs since the warmer atmosphere contains more moisture, resulting in a large increase in LW absorption and a smaller increase in SW absorption. Lapse rate feedback is usually weakly negative in GCMs, with stronger warming in the upper troposphere than at the surface increasing the LW emission relative to that expected from the change in surface temperature alone. The combination of water vapor and lapse rate feedbacks is positive and typically increases λc in GCMs to about 0.5 K m2 W−1 (Cess et al. 1990). The 19 GCMs intercompared by Cess et al. had values of λc ranging from 0.40 to 0.57, with an average value of 0.47.
While the values of λc obtained in the two experiments are within the range of values from Cess et al. (1990), CTRL has a relatively high clear-sky sensitivity, whereas DIAG has a clear-sky sensitivity that is lower than average. The much larger increases in humidity around the tropopause in CTRL compared to DIAG (Fig. 3) suggest that there is a stronger water vapor feedback in CTRL. Also, the zonally averaged temperature changes (Fig. 7) show that CTRL has a marked cooling above the tropopause, particularly in the Tropics, which is not present in DIAG. This suggests that the lapse rate feedbacks could also differ between the two experiments. Both the moisture and temperature changes are consistent with a more substantial lifting of the tropopause in CTRL than in DIAG.
The most obvious way that the change of cloud scheme can affect the lifting of the tropopause is via atmospheric cloud radiative forcing (ACRF), defined as the difference of the cloudy-sky and clear-sky heating rates. The ACRF is dominated by the LW ACRF, rather than the SW, which is felt mainly at the surface [Slingo and Slingo (1988), who also give a useful elementary discussion of the factors controlling LW ACRF]. The ACRF is shown for the −2 K simulations of the CTRL and DIAG experiments in Fig. 8. The ACRF is broadly similar in both experiments, with strong LW cooling near the surface and warming aloft, particularly in the Tropics. However, there are significant differences that depend on the details of the two cloud schemes. For example, the ACRF in the DIAG experiment shows the layering effect discussed previously. The stronger upward shift of the tropopause in CTRL is related to the increase in tropical upper-troposperic ACRF that results from the increase of high cloudiness in the warmer atmosphere (Fig. 9). In CTRL, the peak increase in ACRF occurs near the tropical tropopause at the σ = 0.100 level (Fig. 9a), whereas in DIAG it is restricted to occur one level lower at σ = 0.157 (Fig. 9b). Except near the tropical tropopause and in the boundary layer, the changes in ACRF are small.
These results suggest that the artificial restriction on the maximum height of high clouds in DIAG is the main cause of the different clear-sky responses of the two schemes. Indeed, it turns out that the DIAGH experiment (described above) has changes in ACRF similar to those in CTRL (not shown). Importantly, the changes in relative humidity (Fig. 3c) and temperature (not shown) around the tropopause in DIAGH are more similar to those from CTRL (Fig. 3b) than those from DIAG (Fig. 3a). This shows that DIAGH has a relatively strong upward shift of the tropopause, in common with CTRL. The stronger upward shift gives DIAGH a value of λc similar to that from CTRL (Table 2). These changes also give DIAGH a weaker negative LW cloud feedback than DIAG, and a net climate sensitivity close to that of CTRL. This shows how a seemingly minor artificial constraint on the modeled clouds can have a significant effect on the model’s climate sensitivity. It also echoes the findings of Gage et al. (1991) and Lohmann and Roeckner (1995) that cloud radiative processes in the upper troposphere have an important role in regulating interactions between the troposphere and the stratosphere.
c. Off-line radiative calculations
The large humidity changes shown in Fig. 3 suggest that the higher clear-sky sensitivity obtained in the CTRL experiment are related primarily to a stronger water vapor feedback. However, it is possible that the lapse rate feedback is important too.
To determine the relative contributions of the water vapor and lapse rate feedbacks, the method of Zhang et al. (1994) can be used. In this method, instantaneous temperature, moisture, and cloud fields are saved from the model experiments at some time interval, and off-line radiative calculations are performed using these fields. The individual feedback contributions are computed by substitution of each field, one by one, from the +2 K simulation into the −2 K simulation of each experiment. This gives the contribution of each field to the total feedback parameter δ = Δ(F − Q)/ΔTs, which is the reciprocal of the climate sensitivity parameter λ. A refinement of the method (Colman and McAvaney 1997) requires substitution of each field in both directions (from the +2 K simulation into the −2 K simulation, and also from the −2 K simulation into the +2 K simulation), followed by averaging the results obtained from the two substitutions. This gives a more accurate evaluation of the individual contributions, as it removes the effect of the loss of correlation between fields when substitutions are made from one run into another.
Results from off-line radiative calculations that have been performed on fields from the CTRL, DIAG, and DIAGH experiments are shown in Table 4. The fields were saved from the last 12 months of each experiment at intervals of 18 h (to include the effect of the diurnal cycle), and the method of double substitution described in the previous paragraph has been used. Positive (negative) numbers in Table 4 represent negative (positive) feedback contributions, and the magnitude of each number is proportional to the strength of the feedback contribution.
The results confirm that the higher clear-sky climate sensitivity in CTRL is related primarily to a stronger water vapor feedback in that experiment. Of the clear-sky feedback contributions, the biggest difference between the CTRL and DIAG experiments is in their LW water vapor feedbacks. There are also smaller differences in the lapse rate and surface temperature feedbacks from CTRL and DIAG that contribute to the higher clear-sky climate sensitivity in CTRL. The effect of the strength of the upward shift of the tropopause is shown by the DIAGH experiment, which has an LW water vapor feedback similar to (actually slightly stronger than) that in CTRL.
The results also show that the method used gives very good accuracy. First, the reciprocal of the total feedback parameter obtained from the off-line radiative calculation for each experiment is in excellent agreement with λ as given in Table 2. Second, the individual feedback contributions add to give the total feedback parameter almost exactly (provided that the method of double substitution is used). The slightly worse result obtained with the prognostic cloud scheme is because there are small SW contributions (ΔQ/ΔTs)Ts and (ΔQ/ΔTs)Γ that are not shown in Table 4. These terms arise because instantaneous values of the mixing ratios of cloud liquid water and cloud ice were saved from the CTRL experiment, whereas the calculation of effective radius is based on cloud water contents. The cloud water contents are obtained by multiplying the corresponding mixing ratios by the atmospheric density, which is a function of temperature. When these terms are included, the sum of the individual contributions agrees with the total feedback parameter to two decimal places.
As Zhang et al. (1994) pointed out, the cloud feedbacks obtained by this method differ from those calculated using Eq. (4). Recall that use of Eq. (4) gave negative net cloud feedbacks for all three experiments. According to Table 4, CTRL and DIAGH have positive net cloud feedbacks, whereas the strength of the negative cloud feedback in DIAG is reduced to almost zero. In other words, there is a positive shift in the net cloud feedback for each experiment when the off-line radiative calculations are used instead of Eq. (4). However, the off-line calculations still give positive LW cloud feedback and negative SW cloud feedback in CTRL and negative LW cloud feedback and positive SW cloud feedback in DIAG.
4. Uncertainty of key cloud scheme parameters
All of the key parameters in the prognostic cloud scheme may be considered “uncertain,” despite the efforts made to use theory and observations to constrain the form of the various parameterizations adopted. These parameters can be grouped according to whether they are concerned with cloud formation, precipitation processes, or cloud radiative properties, and are discussed in the following subsections.
a. Cloud formation
Within the framework of the simple PDF-based approach used in the scheme, two obvious choices that have to be made are the critical relative humidity RHcrit that controls the onset of stratiform cloud formation, and the shape of the PDF itself. Even once these have been chosen, different variations are possible (Le Treut and Li 1991; Smith 1993). More complex PDF-based schemes are also possible (Ricard and Royer 1993; Xu and Randall 1996a). In the present study, the investigation will be restricted to the effect of simple changes to RHcrit and the shape of the PDF.
1) Critical relative humidity RHcrit
The values of RHcrit used in the control version of the scheme were chosen by trial and error to give reasonable distributions of cloudiness and cloud radiative forcing. RHcrit is one of the most uncertain parameters in the scheme because there are few observations that indicate what is an appropriate choice of RHcrit (and, really, there is no observational basis to justify the assumption that cloud formation is dependent on a fixed critical relative humidity). However, due to the lack of an obviously better approach, the use of such arbitrary critical relative humidities to parameterize fractional cloudiness has been widespread in GCMs, although some interesting alternative approaches have recently been proposed (Ricard and Royer 1993; Tiedtke 1993; Xu and Randall 1996b). Of these, Tiedtke’s scheme does not completely avoid the use of a critical relative humidity. A wide range of critical relative humidities has been employed in GCMs. For example, the diagnostic scheme in the Australian Bureau of Meteorology Research Centre (BMRC) GCM employs critical relative humidities as low as 0.55 (Colman and McAvaney 1997), whereas some of the models compared by Cess et al. (1990) only allowed stratiform clouds to form in saturated grid boxes; that is, they used critical relative humidities of unity. The obvious uncertainty in the choice of RHcrit, combined with the fact that most GCMs employ critical relative humidities in their cloud schemes, reinforces the need to assess the effect of changes in RHcrit on the climate sensitivity of the model.
Due to the relatively unphysical nature of the parameter, it is difficult to specify a range of uncertainty within which to perturb RHcrit based purely on physical considerations. However, Rotstayn (1998) found that the low and midlevel cloudiness in the model (and hence the SWCF) is sensitive to changes in RHcrit, and it is desirable that the error in the model’s globally averaged SWCF, relative to the observed value from the Earth Radiation Budget Experiment (ERBE), be acceptably small. Regarding what is acceptable, one subjective criterion is that the error lies within the range found for other GCMs, such as the 19 GCMs tested in the Cess et al. (1990) intercomparison. Recall that the control version of the scheme uses RHcrit = 0.85 over oceans and RHcrit = 0.75 over land. Sensitivity tests have shown that RHcrit can be perturbed by ±0.1, while keeping the error in the global-mean SWCF within the range found by Cess et al., so this range is used in the present study to investigate the effect of changes in RHcrit.
2) Shape of PDF
The scheme uses a symmetric triangular PDF for the subgrid distribution of moisture to calculate the formation and dissipation of stratiform cloud. The other simple PDF that has been used in conjunction with a critical relative humidity is the “top hat” function (Le Treut and Li 1991; Smith 1993). Replacing the triangular PDF with the top-hat PDF in the model, while retaining the same critical relative humidities, gives larger liquid-water paths and hence stronger SWCF, because the top-hat PDF has thicker “tails”; that is, it has a larger standard deviation than the triangular PDF. This is the perturbation of the scheme that will be used to investigate the effect of changes in the shape of the PDF.
b. Precipitation processes
In the scheme, precipitation is calculated differently for liquid water and ice clouds. In liquid-water clouds, an important precipitation process when ice falls into the cloud from above is accretion of cloud liquid water by falling ice (Rotstayn 1997). When falling ice is not present (in particular at temperatures above 2°C) autoconversion is the main process that initiates rain formation since collection of cloud liquid water by falling rain requires autoconversion to have occurred first to generate the rain. The efficiencies of both the accretion and autoconversion processes in the model depend on parameters that are specified based on observations, but are still uncertain. In ice clouds, the precipitation rate is controlled by the fall speed for ice particles, which, though based on observations, is again somewhat uncertain.
1) Critical cloud droplet radius rcrit
This parameter controls the onset of autoconversion in liquid-water clouds. The critical mixing ratio qcrit at which autoconversion begins is given by
where ρl is the density of liquid water, ρ is the air density, and Nd is the cloud droplet concentration (discussed below). The cubic dependence of qcrit on rcrit in (6) suggests that the amount of liquid water retained in the modeled clouds will be strongly dependent on rcrit, a finding that is reinforced by sensitivity tests performed with the model. Physically, rcrit can be thought of as the mean droplet radius at which the droplets are large enough for coalescence to become significant. In the development of the parameterization, Manton and Cotton (1977) used rcrit = 10 μm, based on Manton (1974), who showed that the effect of coalescence becomes comparable to that of condensational growth when the droplets are larger than about 10 μm. A slightly smaller value (9 μm) is used in the control version of the present scheme. As explained by Rotstayn (1997), it is not difficult to justify the use of a smaller value in a model of much coarser resolution than the mesoscale models that Manton and Cotton had in mind. Considering perturbed versions of the scheme, it is not entirely clear from physical considerations what constitutes a “reasonable” range of values for rcrit, but changing it by ±3 μm represents a substantial perturbation of the control value, and in any case perturbing rcrit outside of this range results in poor agreement between modeled and observed liquid-water paths.
2) Cloud droplet concentration Nd
In the scheme, Nd affects the autoconversion process in two ways: the rate constant in the autoconversion parameterization [Eq. (15) of Rotstayn (1997)] is inversely proportional to N1/3d and the critical cloud-liquid-water mixing ratio at which autoconversion begins (qcrit) is directly proportional to Nd for a given value of rcrit [Eq. (6)]. Of these two, the latter has a much more potent effect on the model simulations. The dependence of the autoconversion rate and the onset of autoconversion on Nd are consistent with theory that predicts that the development of precipitation will occur more readily in maritime clouds (which have relatively low cloud droplet concentrations) than in continental clouds (which have relatively high cloud droplet concentrations). It has also been suggested that the dependence of precipitation efficiency on cloud droplet concentration is a mechanism by which aerosols can affect cloud albedo and lifetime, and hence the earth’s radiation budget (Albrecht 1989). Although it is possible to relate Nd to the concentration of aerosols if the latter quantity is available in the model (e.g., Jones and Slingo 1996), aerosols have not yet been included in the CSIRO GCM, so Rotstayn (1997) adopted the simpler approach of prescribing reasonable values for Nd. The selected values (Nd = 500 cm−3 over land and Nd = 100 cm−3 over oceans) were chosen to be broadly realistic for continental and maritime clouds, respectively (e.g., Twohy et al. 1995). While these values may be regarded as“typical,” the use of constant values for land and ocean areas is obviously a simplification, and even as mean values they are uncertain. For example, Boers et al. (1996) measured droplet number concentrations of 10–40 cm−3 in unpolluted air over the Southern Ocean, whereas in polluted air droplet concentrations in excess of 1000 cm−3 have been observed (Leaitch et al. 1992). Considering perturbed versions of the scheme, uniformly increasing or decreasing Nd by a factor of 2 would represent the most that could be justified on the basis of retaining a reasonable level of agreement with observations.
3) Bulk density of falling ice particles ρf
In the scheme, ρf appears in the parameterization of accretion of cloud liquid water by falling ice and in the parameterization of sublimation of falling ice. Both the accretion rate [Eq. (29) of Rotstayn (1997)] and the sublimation rate [Eq. (30) of Rotstayn (1997)] are inversely proportional to ρf, for a given mass flux of falling ice. An increase (decrease) in the sublimation rate will decrease (increase) the amount of falling ice available to accrete liquid water, so the true dependence of the accretion rate on ρf is less than linear. As discussed by Rotstayn (1997), ρf has typically been assigned a constant value of 100 kg m−3 for parameterization purposes, but in reality it can vary dramatically for different types of ice particles. For example, in a modeling study, Clough and Franks (1991) found mass-weighted mean densities of falling ice particles to vary from around 20 kg m−3 to 400 kg m−3. These different types of particles, including pristine ice crystals, snowflakes (i.e., aggregates of ice crystals), and graupel (i.e., “rimed” ice particles that have grown by accretion of liquid water) are all represented by the one variable (“falling ice”) in the present scheme. Considering perturbations to the scheme, increasing or decreasing ρf by a factor of 4 would be the most that could be justified on the basis of remaining within the range of values found by Clough and Franks.
4) Fall speed of ice particles Vf
The scheme calculates the precipitation of cloud ice via the use of an observationally based fall speed (Heymsfield 1977)
where Wi is the ice-water content (in kg m−3). The fall speeds of real ice particles depend in a complex way on particle morphology (Locatelli and Hobbs 1974), but in the scheme it is necessary to use a simplified approach since there is only one variable to represent all forms of frozen precipitation. Equation (7) gives fall speeds that increase slowly with ice water content from 0.31 m s−1 when Wi = 10−6 kg m−3 to 0.67 m s−1 when Wi = 10−4 kg m−3, and only approach 1 m s−1 at very large ice-water contents (Wi = 10−3 kg m−3). It is the same parameterization as that used in one experiment by Senior and Mitchell (1993); the other experiments they performed with the prognostic cloud scheme used a constant fall speed of 1 m s−1. Heymsfield and Donner (1990) used a very similar parameterization, and stated that the fall speed is “probably accurate to ±20%.” According to data shown by Rogers and Yau (1988), pure ice crystals typically fall at about 0.4–0.5 m s−1, dry snowflakes at about 1 m s−1, and graupel at speeds greater than 1 m s−1. So the use of (7), which gives fall speeds close to 0.5 m s−1 over a wide range of ice-water contents, effectively assumes that frozen precipitation is dominated by pure ice crystals, except at large ice-water contents. On the other hand, a constant fall speed of 1 m s−1, as used by Senior and Mitchell, is more representative of snowflakes. Considering perturbed versions of the scheme, one straightforward method is to use the error estimate given by Heymsfield and Donner to uniformly perturb the fall speed by ±20%. Another obvious experiment is to try Vf = 1 m s−1, which effectively assumes that frozen precipitation occurs as snowflakes (aggregates) at all temperatures. Although this is somewhat unrealistic, because aggregation of ice crystals only becomes efficient at warmer temperatures [cf. the parameterization of Lin et al. (1983)], it is of interest to consider the effect of a relatively large perturbation to the fall speed.
c. Cloud radiative properties
The cloud radiative properties required for input to the model’s SW radiation scheme are the reflectivities (for the visible and near-infrared bands) and absorptivities (for the near-infrared band only, since clouds are assumed to be nonabsorbing in the visible band). For the LW radiation scheme, the cloud emissivities are required. All these quantities depend on the cloud optical depth, which depends on the liquid- (or ice-) water path and the effective radius of the cloud droplets or particles. The optical depth for liquid-water (or ice) clouds is
where W is the liquid- (or ice-) water content, Δz is the cloud thickness, ρw is the density of liquid water (or ice), and re is the effective radius. For liquid-water clouds, the effective radius depends on the calculated liquid-water content and the prescribed cloud droplet concentration, which, as discussed previously, is an uncertain parameter. For ice clouds, calculation of the effective radius is even more uncertain since it depends on crystal morphology as well as ice crystal number concentration, which is itself very uncertain. A key parameter concerning ice clouds is the asymmetry parameter, which controls the ratio of forward-scattered to back-scattered radiation. Another uncertainty, affecting all types of clouds, is the method used to account for cloud inhomogeneities.
1) Cloud-droplet concentration Nd
The specification of this parameter was discussed previously, as it affects the autoconversion process, in addition to the cloud radiative properties. The cloud optical depth [Eq. (8)] in liquid-water clouds is proportional to N1/3d because of the dependence of the droplet effective radius on Nd; namely,
where Wl is the liquid-water content, and κ = 0.67 in continental air masses or 0.80 in maritime air masses (Martin et al. 1994). In the model, it is assumed that clouds over land are continental, whereas those elsewhere are maritime. Equations (8) and (9) imply that for a given amount of liquid water, a cloud comprising a large number of small droplets will have a larger optical depth, and hence a higher albedo, than one comprising a smaller number of larger droplets. This has been proposed as a mechanism by which aerosols can have an indirect cooling effect on the earth’s radiation budget (Twomey 1977). It is in addition to the effect of aerosols on precipitation efficiency discussed previously.
2) Effective radius re for cloud ice particles
Previously, most schemes in GCMs have assumed a constant value for the effective radius re in ice clouds. However, observations suggest that average ice particle sizes increase with temperature, and hence with ice-water content (Platt 1989). This effect is included in the present scheme, based on calculations by Platt (1994), with the ice particle effective radius increasing with ice-water content Wi according to
where a = 0.051 and b = 0.667 if re and Wi are specified in SI units. These values were calculated on the assumption of spherical ice particles. A more detailed parameterization, which accounts for ice crystal morphology, is presented by Platt (1997). This parameterization is equivalent to the use of a = 0.0016 and b = 0.32 in (10), and gives a more gradual increase of re with Wi than that given by the earlier scheme. Obvious perturbations to the scheme are the use of the parameterization from Platt (1997), as well as the use of a constant re for ice clouds, as has been customary in GCMs until recently. A value of re = 30 μm is chosen, as this gives globally averaged LWCF close to that obtained using (10).
3) Asymmetry parameter for ice clouds gi
The asymmetry parameter affects the ratio of forward-scattered to back-scattered SW radiation. Smaller values of gi increase the amount of back-scattered radiation (and hence the cloud albedo), whereas larger values decrease the amount of back-scattered radiation. There is considerable uncertainty regarding the specification of gi (e.g., Francis et al. 1994). Stephens et al. (1990) suggested that gi = 0.7, whereas Francis et al. found that gi = 0.8 gave slightly better agreement with radiation measurements. The latter value is adopted in the control version of the present scheme. The value for spherical ice particles (about 0.85) serves as an upper limit on the reasonable range of values for gi. This larger value represents one obvious perturbation of the scheme, whereas an equal reduction to give gi = 0.75 would give a value still comfortably within the “reasonable” range.
4) Reduction of plane-parallel cloud albedo
As was mentioned in the introduction, the plane-parallel cloud albedos calculated in GCMs are larger than those of real clouds with the same average microphysical properties. It is necessary to apply a correction to compensate for this effect if a model with realistic liquid-water paths is to provide realistic SWCF. Guided by the results of Cahalan et al. (1994) and Kogan et al. (1995), Rotstayn (1997) reduced the cloud optical depth by a factor ξ, which varied from 0.5 to 0.9 depending on cloud type and cloud fraction. The effect of the factor ξ is to reduce both the cloud reflectivities and absorptivities that are calculated for input to the radiation scheme. However, the effect of inhomogeneities on cloud absorption is much more uncertain than the effect on cloud albedo. For example, modeling by Byrne et al. (1996) has shown that the presence of broken cloud actually enhances the absorption of solar radiation, in contrast to the effect of the reduction of cloud optical depth. On the other hand, Hignett and Taylor (1996), based on aircraft observations and 3D Monte Carlo modeling, found that internal cloud inhomogenities result in a reduction of cloud absorption. In view of this uncertainty, the scheme has been modified to retain the plane-parallel values of cloud optical depth (and hence the cloud absorptivities), but the computed cloud reflectivities are reduced by a factor ξ′, which is set to 0.9 for stratiform cloud or 0.7 for convective cloud. (Note that, using either method, energy conservation is ensured because cloud transmission increases.) Considering perturbations of the scheme, the uncertain nature of this correction suggests that it would be wise to investigate the effect of removing the correction altogether, that is, that of retaining the plane-parallel cloud reflectivities. Another obvious perturbation is to revert to the use of the factor ξ as used by Rotstayn (1997).
d. Summary of sensitivity experiments
The preceding discussion suggests the following list of sensitivity experiments. Although no claim is made that the list is exhaustive, it does include perturbations to almost all the parameters that were varied while “tuning” the scheme during its development. Each sensitivity experiment consists of a single change relative to the version of the prognostic cloud scheme as used in the CTRL experiment:
RH+: Increase all critical relative humidities by 0.1 to 0.95 over ocean points and to 0.85 over land
RH−: Decrease all the critical relative humidities by 0.1, to 0.75 over ocean points and to 0.65 over land
PDF: Change the shape of the PDF used in the calculation of cloud formation from triangular to top hat
RAD+: Increase rcrit from 9 μm to 12 μm
RAD−: Decrease rcrit from 9 μm to 6 μm
ND+: Increase Nd by a factor of 2 to 1000 cm−3 over land and to 200 cm−3 over oceans
ND−: Decrease Nd by a factor of 2 to 250 cm−3 over land and to 50 cm−3 over oceans
RHOF+: Increase ρf from 100 kg m −3 to 400 kg m−3
RHOF−: Decrease ρf from 100 kg m −3 to 25 kg m−3
VF+: Increase Vf by 20% by multiplying (7) by 1.2
VF−: Decrease Vf by 20% by multiplying (7) by 0.8
VF1: Use a constant Vf = 1 m s−1
RE30: Use a constant effective radius of 30 μm for ice clouds
REP97: Account for ice crystal morphology in the parameterization of re for ice clouds following Platt (1997)
GI+: Increase gi from 0.8 to 0.85
GI−: Decrease gi from 0.8 to 0.75
PLANE: Use the plane-parallel values of cloud SW radiative properties
XI: Reduce the cloud optical depths by the factor ξ as in Rotstayn (1997) instead of reducing the reflectivities as in CTRL.
5. Perturbation experiments with the prognostic cloud scheme
Before comparing the changes associated with the 4 K SST increase in each of the 19 experiments performed with the prognostic cloud scheme, it is of interest to consider some aspects of the control climate produced by each of these model versions. For ease of comparison with Cess et al. (1990), the −2 K simulation is taken to be the “control” for this purpose. Table 5 shows a number of relevant globally averaged quantities from the −2 K simulation of each of the experiments. The quantities shown are total cloudiness (TC), low cloudiness (LC), high cloudiness (HC) liquid-water path (LWP), ice-water path (IWP), net downward shortwave flux (Q), and outgoing longwave flux (F) at TOA, shortwave cloud forcing (SWCF), and longwave cloud forcing (LWCF). A number of observations can be made about the data in Table 5.
In all the experiments, TC, Q, F, SWCF, and LWCF are within the ranges obtained from the 19 GCMs intercompared by Cess et al. (1990). (Data for LC, HC, LWP, and IWP were not given by Cess et al.) In other words, the perturbations made to the scheme do not appear to have resulted in simulations that lie outside the range of those obtained with other GCMs, at least in a globally averaged sense. However, bearing in mind that a perpetual July −2 K simulation is not exactly comparable to a conventional July simulation, some of the model versions have SWCF or LWCF that is in worse agreement with observations from ERBE than the CTRL version, which agrees closely with ERBE in the global mean.
Variations of Q among the experiments are almost entirely accounted for by corresponding variations of SWCF; the clear-sky SW flux Qc (i.e., the difference between Q and SWCF) varies by only 0.2 W m −2 among the experiments. Variation of the clear-sky LW flux Fc is slightly larger (0.7 W m−2), but still much smaller than the variation of F.
Excluding the last five experiments, which only involve changes to cloud radiative properties, linear regression between the columns of Table 5 yields some strong correlations. SWCF is well predicted by TC (correlation coefficient R = −0.90) and LC (R = −0.87), and very well predicted by LWP (R = −0.96). This makes sense physically because it is the optically thick liquid-water clouds (which usually occur at low altitudes) that most strongly affect SWCF. LWCF is well predicted by IWP (R = 0.90) and very well predicted by HC (R = 0.97). This also makes sense physically because it is the high clouds (which consist mainly of ice) that most strongly affect LWCF.
The first seven perturbation experiments listed in Table 5 (RH+ to ND−) mainly involve changes in LC, LWP, and SWCF, rather than HC, IWP, and LWCF. Rotstayn (1998) noted that changes to RHcrit mainly affect low cloud rather than high cloud in the model, and evidently the same is true of changes to the shape of the PDF. Experiments RAD+, RAD−, ND+, and ND− involve changes to warm rain processes and consequently affect mainly the liquid-water clouds. The next five experiments (RHOF+ to VF1) involve changes to the properties of falling ice, but affect LWP through the accretion process. The last six experiments (RE30 to XI) involve changes to the cloud radiative properties, and have minimal affects on cloudiness and cloud water paths, although some of them have substantial effects on SWCF or LWCF.
Experiments RAD+, RAD−, ND+, and ND− have noticeable effects on SWCF via their effects on LWP, even though the corresponding changes in low cloud and total cloud are small. Although the changes in cloud droplet concentration have a smaller effect on LWP than do the changes to the autoconversion threshold rcrit, they have a larger effect on SWCF, because cloud droplet concentration directly affects cloud albedo [through Eqs. (9) and 8], as well as the efficiency of rain formation.
Overall, the changes to the treatment of cloud formation (RH+, RH−, and PDF) and the large increase in the fall speed of frozen precipitation (VF1) have the strongest effects on the simulation. Experiments RH+, RH−, and PDF have large effects on low cloud and LWP, and a small effect on high cloud. Experiment VF1 has a large effect on high cloud and IWP, and some effect on low cloud and LWP. Of the other experiments, REP97 has a relatively large effect on LWCF (showing that the newer parameterization gives, on average, larger effective radii in ice clouds), whereas the treatment of clouds as plane parallel in PLANE has a relatively large effect on SWCF.
Table 6 shows the radiative flux changes at TOA and the climate sensitivity parameters calculated from the 19 experiments performed with the prognostic cloud scheme. Values that differ significantly from those in the CTRL experiment are denoted by a superscript s (significant at 5%) or a superscript S (significant at 1%). Statistical significance was assessed using Student’s t-test, with the monthly mean values from each of the 12 months taken as the individual samples. Because quantities from consecutive months of each experiment may not be truly independent, the conservative assumption was made that only alternate months are independent; that is, the test was performed using 10 degrees of freedom (2 × 6 − 2) rather than 22 degrees of freedom (2 × 12 − 2). The following observations can be made about the data in Table 6.
Overall, the differences among the experiments are modest compared to the intermodel differences found by Cess et al. (1990, 1996). For example, considering the ratio λ/λc, Cess et al. (1990) found values ranging from 0.70 to 2.47, and Cess et al. (1996) found values ranging from about 0.74 to 2.0. Here λ/λc ranges from 0.86 to 1.09. Some of the differences found by Cess et al. probably result from other differences in model formulation (Colman and McAvaney 1997).
All experiments other than RH+ have negative ΔSWCF and ΔQ and a negative net cloud feedback (λ/λc < 1). All experiments have positive ΔLWCF.
The largest differences (relative to the CTRL experiment) in λ/λc are in the experiments that involve changes to the PDF used in the calculation of cloud formation (RH+, RH−, and PDF). These are also the only experiments that have differences from the CTRL experiment significant at the 1% level. The differences in λ/λc result from differences in ΔSWCF. Senior and Mitchell (1995) also found that changing the PDF significantly affected the climate sensitivity of their model.
Other experiments with statistically significant differences from the CTRL experiment are VF1, PLANE, and XI. Experiment VF1 differs from the others in that its differences are related to clear-sky LW flux changes rather than ΔSWCF.
On the whole, the experiments with significant differences from the CTRL experiment are those that also differ substantially in their −2 K simulation (Table 5), although to some extent experiments ND+ and XI defy this generalization. In other words, there is a tendency for relatively large changes in the “control” climate to be associated with relatively large changes in climate sensitivity.
There is less variation in the LW flux changes than in the SW flux changes among the experiments. For example, ΔLWCF varies by only 0.6 W m−2, whereas ΔSWCF varies by 2.1 W m−2. Also, there are no statistically significant differences in ΔLWCF or ΔF among the experiments
Although the range of variation of ΔQc is less than 0.1 W m−2, the small difference in ΔQc in the RH+ experiment is statistically significant due to the small standard deviation of the monthly mean values for this quantity.
Despite the expectation that the parameterization of ice-cloud effective radius might affect the LW cloud feedback in the model (Platt 1989), there are no significant differences from the CTRL experiment in either the RE30 or REP97 experiments.
Further insights into these results are provided by Table 7, which shows the changes in cloudiness and cloud water paths from the 19 experiments. The statistical significance of the differences from the CTRL experiment was assessed in the same way as described previously for the data in Table 6. The following observations can be made.
All experiments show an increase of LWP and IWP resulting from the SST increase, whereas changes in cloudiness are mixed, with both increases and decreases occurring. The latter result is in contrast to that found by Cess et al. (1990), where all models gave a decrease of average cloudiness as a result of the SST increase. However, Del Genio et al. (1996) obtained an increase of global-mean cloudiness with their prognostic scheme.
Excluding the last five experiments, ΔSWCF is well predicted by ΔTC (R = −0.88) and ΔLWP (R = −0.77), and very well predicted by ΔLC (R = −0.97). Similarly, ΔLWCF is well predicted by ΔHC (R = 0.90), but poorly predicted by ΔIWP (R = −0.15). The last result can be explained by the lack of information regarding the height of clouds in the IWP diagnostic—in some experiments, the differences in ΔIWP may occur at low levels, where they do not have much impact on ΔLWCF. It also reflects the fact that none of the ΔIWP changes are statistically significant.
Significant differences in ΔTC, ΔLC, and ΔLWP in experiments RH+, RH−, and PDF result in the significant differences in ΔSWCF noted previously. Conversely, significant differences in ΔLWP in experiments RAD+, RAD−, ND+, and ND− and in ΔTC and ΔLC in experiment VF1 do not result in significant differences in ΔSWCF. In other words, significant changes in SWCF occur as a result of concomitant changes in cloudiness and LWP.
In the PLANE and XI experiments, significant differences in ΔSWCF are associated with significant differences in ΔLWP, despite the fact that the experiments only involve changes to cloud radiative properties. This suggests that feedbacks due to cloud radiative forcing have altered the distribution of cloud liquid water in the model.
The robustness of the behavior of the prognostic cloud scheme is encouraging. Indeed, it would be disturbing if the change in climate sensitivity resulting from inclusion of the scheme were not reasonably robust. Perturbations of the cloud scheme related to the treatment of precipitation and cloud radiative properties result in little change to the model’s climate sensitivity, whereas perturbations related to the treatment of cloud formation result in somewhat larger changes. (Note that the cloud formation scheme calculates both the cloudiness and the cloud-water mixing ratio, and differs in that respect from the approach of Xu and Randall (1996b), who parameterize the cloudiness on the assumption that the amount of cloud water is already available.) This finding argues for an increased research effort into the parameterization of cloudiness and echoes the comments of Xu and Randall (1996a), who pointed out the lack of a physical basis for the schemes used to calculate cloudiness in most GCMs. The importance of this problem is further underlined by the results of Cess et al. (1997), who found that seasonal changes in observed cloud radiative forcing are mainly related to changes in cloudiness, rather than changes in cloud radiative properties or cloud height. It is probably also not a coincidence that the other experiments that give statistically significant changes in shortwave cloud feedback are those that involve changes to the method used to compensate for the treatment of clouds as plane parallel by the radiation scheme. In common with the treatment of cloud formation, this aspect of the scheme suffers from the lack of a strong underlying physical basis.
It is interesting to compare the present study with that of Morcrette (1995), who found relatively large variations of climate sensitivity in 12 SST-perturbation experiments that employed different cloud treatments. It is possible to gain some insights into the reasons for the differences between the two studies. Of his experiments, the five that used a diagnostic cloud scheme gave lower climate sensitivities than the seven that used versions of the prognostic scheme of Tiedtke (1993). Of those that used the prognostic scheme, the largest changes were in one that involved the replacement of an observationally based treatment of frozen precipitation (similar to that used in the present study) with a treatment following Sundqvist (1988), and in another in which all clouds were assumed to be composed entirely of liquid water for radiation purposes. The other experiments that used the prognostic scheme involved changes to model resolution and cloud vertical-overlap assumptions, and gave relatively modest differences in climate sensitivity. So, the two experiments with the prognostic scheme that gave relatively large differences involved, respectively, a substantial change of approach to a key component of the scheme, and an idealized change to cloud radiative properties that was more heuristic than realistic. These experiments are in contrast to the approach adopted in the present study, where observations and theory were used as far as possible to constrain the perturbations within realistic ranges, while retaining the overall approach of the original scheme.
Another aspect of Morcrette’s results is that the variation of globally averaged quantities such as cloudiness and cloud radiative forcing from the −2 K simulation is much larger than in the present study. This echoes the tendency noted in the present study for larger variations in climate sensitivity to be associated with larger variations in control climate. In Morcrette’s results, there is a strong negative correlation between Q and ΔQ (R = −0.80) and between F and ΔF (R = −0.84). This implies the existence of similar correlations between SWCF and ΔSWCF and between LWCF and ΔLWCF since, as expected, his results show little variation in the clear-sky fluxes. In the present study, there is a fairly strong positive correlation between Q and ΔQ (R = 0.65). However, F and ΔF are poorly correlated (R = 0.22), although it should be remembered that there is relatively little variation in F and ΔF among the experiments. It would be interesting to know to what extent these correlations exist when the cloud treatments (or other parameterizations) in other models are perturbed. If they do, they could be explained by the idea that, if (for example) the clouds in a particular model have a tendency to produce a negative SW feedback, then substantially increasing (decreasing) the SWCF in the model’s control climate is likely to increase (decrease) the negative SW feedback provoked by a shift to a warmer climate. An argument of this type was used by Cess et al. (1996) to explain how the strong positive SW cloud feedback obtained with the ECHAM GCM in the 1990 intercomparison had resulted from an improper choice of the prescribed cloud-droplet effective radius that caused the clouds to be too bright. However, Del Genio et al. (1996) found that when they modified the critical relative humidities in their model to increase the amount of high cloud (which was deficient in the extratropics), they obtained little difference in the model’s climate sensitivity. They asserted that “validation of the mean state itself contains no information about a GCM’s response to perturbations.” This issue deserves further investigation. Correlations between aspects of a model’s control climate and its climate sensitivity emphasize the importance of validation of models before they are used to make inferences about climate change. They also suggest that one could justify using large-scale observations, such as those from ERBE, to provide additional constraints on some of the parameter ranges investigated in the present study.
The climate sensitivity obtained with the diagnostic cloud scheme in this study differs from that obtained with the Mark 1 version of the CSIRO GCM that was featured in the Cess et al. (1996) intercomparison. That version of the model gave λ/λc = 1.03, compared to λ/λc = 0.85 as obtained with the diagnostic cloud scheme in the present study. The Mark 2 model used in the present study differs from Mark 1 in a number of respects (Rotstayn 1997). Sensitivity tests with the model suggest that the different cloud feedbacks are largely explained by the increase of vertical resolution from 9 to 18 levels, and a different treatment of shallow convection, which followed Geleyn (1987) in the earlier model. An experiment, similar to the DIAG experiment, but with nine vertical levels and using Geleyn’s shallow convection scheme, gave λ/λc = 1.06; that is, the result from Cess et al. was approximately recovered. Further sensitivity experiments have shown that both the change of vertical resolution and the change of shallow convection scheme contribute to the change of cloud feedback. This result suggests that much of the intermodel variation in cloud feedbacks found by Cess et al. (1990, 1996) could be due to other model differences. Further support for this idea comes from the study of Colman and McAvaney (1997), who found that large differences in cloud feedback resulted from changes to the model’s convection scheme and vertical resolution, as well as changes to the experimental boundary conditions regarding soil moisture. This points toward the importance of controlled experiments in which different parameterizations are compared within a single model, in addition to model intercomparisons.
7. Summary and conclusions
Uniform SST-perturbation experiments have been used to compare the feedbacks resulting from diagnostic and prognostic cloud treatments in the CSIRO GCM. The diagnostic scheme uses cloud radiative properties prescribed as a function of height, whereas the prognostic scheme includes interactive calculation of cloud radiative properties.
With the diagnostic scheme, a negative LW and positive SW cloud feedback is obtained. In other words, both the positive LW forcing (mainly due to high and midlevel clouds) and the negative SW forcing (mainly due to low and midlevel clouds) decrease in magnitude in the warmer climate. With this scheme, feedbacks due to changes in cloud radiative properties are suppressed. The cloud feedbacks that do occur result from changes in cloudiness; a decrease in midlevel cloudiness contributes to both the LW and SW feedbacks, and a smaller decrease in high cloudiness contributes to the LW feedback. A small increase in low cloudiness is insufficient to counter the positive SW feedback due to the decrease in midlevel cloudiness.
Use of the prognostic scheme gives a change in the sign of both the LW and SW cloud feedback components. This different behavior is primarily due to the explicit dependence of the cloud radiative properties on the cloud liquid-water and cloud ice contents, which increase overall in the warmer climate. Because of this increase, both the warming LW cloud forcing and the cooling SW cloud forcing increase in magnitude in the warmer climate. The changes in global-mean low, midlevel, and high cloudiness on warming are small with this scheme, so the cloud feedbacks are dominated by the changes in cloud water content. A larger reduction of cloudiness on warming (cf. Cess et al. 1990) could have offset the effects of cloud water increases. Also, although the overall increases in cloud water content obtained here (and in several other GCMs) are qualitatively consistent with the predictions of simpler models (Somerville and Remer 1984; Betts and Harshvardhan 1987), a different result has been obtained with at least one GCM (Lohmann and Roeckner 1996b).
Due to cancellation between the LW and SW components, there is not much difference between the net cloud feedbacks given by the two schemes. The finding of cancellation between LW and SW components is consistent with most of the models tested by Cess et al. (1996). As measured by the change of cloud radiative forcing, the prognostic scheme gives a weak negative net cloud feedback, and the diagnostic scheme gives a slightly stronger negative net cloud feedback. If an artificial restriction on the maximum height of high clouds that exists in the diagnostic scheme is removed, the diagnostic scheme gives a net cloud feedback almost identical to that obtained with the prognostic scheme. This is because removal of the artificial restriction allows the cloudiness around the tropical tropopause to increase on warming, thus reducing the strength of the negative LW cloud feedback.
The change of cloud scheme also affects the clear-sky feedbacks, with the prognostic scheme giving the model a higher clear-sky climate sensitivity. Off-line radiative calculations have been used to show that this is mainly because of a stronger LW water vapor feedback that results from a stronger upward shift of the tropopause on warming. The artificial restriction on the maximum height of high clouds in the diagnostic scheme is the reason for the weaker upward shift of the tropopause when this scheme is used, because it is cloud radiative forcing close to the tropical tropopause that drives this shift. When this artificial restriction is removed, the diagnostic scheme gives a clear-sky climate sensitivity similar to that obtained with the prognostic scheme.
The results obtained with the prognostic scheme are generally robust in the face of perturbations to key parameters in the scheme. The 18 perturbed versions of the scheme all give modest positive LW cloud feedbacks, and all except one give modest negative SW cloud feedbacks. The remaining version, which gives a weak positive SW cloud feedback, involves an increase of the critical relative humidity used to control the onset of cloud formation. Overall, larger differences (both in control climate and in climate sensitivity) result from parameter changes that affect cloud formation than from changes that affect precipitation processes or cloud radiative properties. This suggests that future work should focus on improving the parameterization of cloud formation and fractional cloudiness.
Two limitations of the scope of this study are worth noting. First, only feedbacks resulting from changes in stratiform clouds have been considered, as the simple diagnostic treatment of convective cloud largely suppresses any feedbacks resulting from changes in convective cloud (section 3). It is planned to include a more physically based treatment of convective cloud in the next version of the CSIRO GCM, probably together with a new convection scheme. Second, the effects of simultaneous changes in two or more cloud-scheme parameters have not been considered. It is possible that the behavior of the scheme (or of other schemes) could be less robust in the face of multiple simultaneous changes.
The response of the prognostic scheme to an imposed warming—an overall increase of cloud-water content, combined with small changes in global-mean low, midlevel, and high cloudiness—resulted in SW and LW cloud feedbacks of opposite sign, and hence a modest net cloud feedback. An intriguing question is “What changes to the physics are required to reverse the signs of the SW and LW cloud feedbacks obtained with this scheme?” Although the scheme was shown to be generally robust in the face of perturbations to various parameters, the overall approach was not changed. There is a need for further studies to investigate the effects of changing the methods used to parameterize the cloud fraction and the formation of precipitation.
This work contributes to the CSIRO Climate Change Research Program and is partly funded through Australia’s National Greenhouse Research Program. It constitutes a part of the author’s Ph.D. thesis under the supervision of Dr. Brian Ryan of CSIRO Division of Atmospheric Research and Prof. David Karoly of the Cooperative Research Centre for Southern Hemisphere Meteorology. The author thanks both supervisors for their advice and encouragement and Martin Dix for numerous helpful discussions. Thanks are also due to Dr. Robert Colman of BMRC and an anonymous reviewer for their constructive comments on this paper.
* Additional affiliation: Cooperative Research Centre for Southern Hemisphere Meteorology, Clayton, Victoria, Australia.
Corresponding author address: Dr. L. D. Rotstayn, Division of Atmospheric Research, CSIRO, PMB1, Aspendale, Victoria 3195, Australia.