G. IORGA
Department of Physics and Applied Mathematics, Faculty of Chemistry, University of Bucharest,
Regina Elisabeta, No. 4-12, 030018 Bucharest, Romania
Corresponding author e-mail: giorga@gw-chimie.math.unibuc.ro

S. STEFAN
Department of Atmospheric Physics, Faculty of Physics, University of Bucharest,
P. O. Box MG-11, 077125 Bucharest, Romania

RESUMEN

La reflectividad nubosa a nivel regional puede modificarse tanto por el aumento en el número de concentración del aerosol, como por el incremento en la dispersión de la distribución relativa del tamaño de las gotas de las nubes. Este trabajo se enfoca en el papel que tienen los aerosoles prenubosos en la reflectividad de las nubes. Para describir dos tipos de aerosoles, los marinos y los rurales, se utilizaron tamaños de distribución logarítmica normales. El número de aerosoles que se activan como gotas se obtuvo con base en la parametrización de activación de Abdul-Razzak y Ghan (2000). Se calculó el albedo nuboso considerando el efecto de dispersión espectral en la parametrización del radio efectivo de nubes y en el factor de asimetría de dispersión. Para considerar la dispersión se utilizaron dos factores de escalamiento diferentes. También se investigó la sensibilidad del albedo nuboso a la relación entre la dispersión espectral y el número de concentración del aerosol, en función del contenido de agua líquida (LWC) y del radio efectivo de gotas. Al considerar la dispersión se obtuvieron valores altos de radio efectivo con respecto al caso base, en el que no se considera la dispersión. Las diferencias absolutas inferidas en los valores del radio efectivo son menores a 0.8 um al calcularlas con cada uno de los dos factores de escalamiento ya que el LWC está entre 0.1 y 1.0 g m^-3. Cuando la dispersión es considerada tanto en el radio efectivo como en el factor de escalamiento (factor de escalamiento (βLDR) la profundidad óptica disminuye hasta 14% en el caso de los aerosoles marinos y hasta 29% en el de los continentales. En correspondencia, el cambio relativo en el albedo nuboso es de hasta 6% en el caso de las nubes marinas y hasta 11% en las continentales. Para las nubes continentales, el radio efectivo calculado considerando la dispersión se ajusta bien al rango de las mediciones de radio efectivo realizadas en el proyecto SCAR-B. El albedo nuboso calculado considerando la dispersión muestra una mejor concordancia con el albedo estimado a partir de las mediciones de radio efectivo del proyecto SCAR-B que el albedo calculado sin dispersión. En condiciones marinas despejadas de nubes, solamente el albedo escalado βLD se ajusta de manera satisfactoria al rango de validez del albedo calculado utilizando la relación radio efectivo contenido de agua líquida propuesta por Reid et al. (1999) en el proyecto ASTEX. El bajo coeficiente de correlación de la parametrización del radio efectivo contenido de agua líquida, también puede tener un papel.

ABSTRACT

Both the enhancement of the aerosol number concentration and the relative dispersion of the cloud droplet size distribution (spectral dispersion) on a regional scale can modify the cloud reflectivity. This work is focused on the role that pre-cloud aerosol plays in cloud reflectivity. Log-normal aerosol size distributions were used to describe two aerosol types: marine and rural. The number of aerosols that activate to droplets was obtained based on Abdul-Razzak and Ghan's (2000) activation parameterization. The cloud albedo taking into account the spectral dispersion effect in the parameterization of cloud effective radius and in the scattering asymmetry factor has been estimated. Two different scaling factors to account for dispersion were used. The sensitivity of cloud albedo to spectral dispersion-cloud droplet number concentration relationship in connection to the changes in liquid water content (LWC), and the cloud droplet effective radius has been also investigated. We obtained higher values of effective radius when dispersion is taken into account, with respect to the base case (without considering dispersion). The inferred absolute differences in effective radius values between calculations with each of the scaling factors are below 0.8 |am as LWC ranges between 0.1 and 1.0 g m^-3. The optical depth decreased by up to 14% (marine), and up to 29% (continental) when dispersion is considered in both effective radius and asymmetry factor (β_LDR scaling factor). Correspondingly, the relative change in cloud albedo is up to 6% (marine) and up to 11% (continental) clouds. For continental clouds, the calculated effective radius when dispersion is considered fits well within the measured range of effective radius in SCAR-B project. The calculated cloud albedo when dispersion is considered shows better agreement with the estimated cloud albedo from measured effective radius in SCAR-B project than the cloud albedo calculated without dispersion. In cleaner conditions of marine clouds, only β_PL-scaled albedo fits satisfactory within the validity range of albedo inferred using an effective radius-liquid water content relationship proposed by Reid et al. (1999) from ASTEX project. The low correlation coefficient of the effective radius-liquid water content parameterization in ASTEX may also play a role within.

Keywords: Aerosol size distribution, spectral dispersion, effective radius, cloud albedo, indirect aerosol effect.

1. Introduction

Aerosols have a direct radiative forcing (e.g. Charlson et al., 1992; Haywood and Shine, 1995) by scattering and absorbing solar radiation and by absorbing and emitting thermal radiation. This can lead to either a cooling (e.g. sulfates, nitrates...) or a warming (black carbon) of the atmosphere depending on the proportion of scattered light to that absorbed. In addition to the direct forcing, aerosols perturb the radiation balance indirectly, through the formation of clouds because aerosols can serve as cloud condensation and/or ice nuclei. In polluted regions, an increased aerosol concentration can modify the microphysical and radiative properties of clouds (first aerosol indirect effect; Twomey, 1974), as well as the precipitation efficiency and hence the cloud lifetime (second aerosol indirect effect; Albrecht, 1989; Pincus and Baker, 1994). Both, first and second indirect effects of aerosols on climate are believed to increase the amount of solar radiation that is reflected into space without reaching the Earth's surface, resulting in a cooling effect. The third climatic effect of aerosols is linked to the presence of absorbing components in aerosol particles; these particles absorb radiation and the resulting radiative heating in elevated layers can perturb the temperature profile, which can lead to the evaporation of low-level clouds (semi-direct effect; Hansen et al., 1997; Ackerman et al., 2000). The Intergovernmental Panel on Climate Change report (2001) estimated the direct forcing of anthropogenic aerosols to be -0.5 W m^-2 and the total indirect forcing to lie between 0 and -2 W m^-2, in global mean. The resulting total radiative forcing (well-mixed greenhouse gases, solar activity, ozone, direct aerosol effects and Twomey effect) has a 75-97% probability of being positive (McFiggans et al., 2006). This latest estimate neglects the cloud lifetime effect and aerosol effects on mixed-phase and ice clouds because the scientific knowledge about these latter effects is not sufficient to predict their magnitudes yet.

Recent reviews of theoretical and observational evidence for the aerosol effects can be found for instance in the work of Haywood and Boucher (2000), in IPCC (2001), in the works of Kanaki-dou et al. (2005), Lohmann and Feichter (2005), and Yu et al. (2006); while McFiggans et al. (2006) review the currently-available observational evidence for the compositional complexity of atmospheric aerosol, and the derived properties of their size distributions and composition that are thought to affect aerosol ability to act as cloud condensation nuclei (CCN). All these studies point out that amongst aerosol effects, the indirect one is currently credited with the greatest range of uncertainty.

Existing GCM-based calculations tend to overestimate the indirect aerosol effect as they use many simplifications imposed by the large number of coupled processes, over a large range of spatial and temporal scales that need to be addressed, in order to deal with the associated computational burden. Lohmann and Feichter (2005) estimate for the cloud albedo effect values between -1.9 and -0.5 Wm^-2, and between -1.4 and -0.3 Wm^-2 for the cloud lifetime effect. The poor aerosol characterization in GCM is in part due to the lack of a comprehensive global database of aerosol concentrations, chemical composition and optical properties; subtle aspects of the interaction between aerosols and clouds are not entirely captured (Haywood and Boucher, 2000). Therefore, the uncertainty in the estimations is mostly attributed to the complex issues regarding the link aerosol particles-cloud droplets, like the aerosol and aerosol precursor emissions from a given emission inventory, like the representation of aerosol size distribution (Ghan et al., 2001a), and the cloud nucleation parameterization (e.g., Boucher and Lohmann, 1995), the relationship between effective radius and volume mean radius (Chen and Penner, 2005) and the representation of the microphysics of mid-level clouds (Lohmann et al., 2000). The great computational expense associated with detailed simulations of relevant phenomena also prevents reliable assessments of the forcing with regional and global atmospheric models.

Currently, there are two categories of approaches to relate the aerosol properties (concentration, size and composition) to the cloud microphysical properties (number concentration and effective radius): the empirical approach and the mechanistic one.

First approach uses an empirical relationship between cloud droplet number and aerosol mass concentration (Boucher and Lohmann, 1995; Roelofs et al., 1998; Menon et al., 2002; Lowenthal, 2004). At present, such relationships can only be derived between sulfate aerosols, sea salt, organic carbon and cloud droplet number, but data are not available yet for dust or black carbon and cloud droplet number. These methods are based on observations and are easy to use in global forcing calculations, but they do not reflect the physical and chemical processes that occur during cloud nucleation, which depend on the size, chemical composition of the aerosol, as well as the updraft velocity. In addition, they are based on measurements at particular regions and times, therefore it is questionable if they could be used for a global calculation or used to simulate future climates.

As the primary source of cloud droplets is droplet nucleation, which depends on the aerosol size distribution, composition and the updraft velocity, the mechanistic approach considers these important aspects. Abdul-Razzak et al. (1998) and Abdul-Razzak and Ghan (2000) developed a parameterization based on Koehler theory that can describe the cloud droplet formation for a mono-and a multi-modal aerosol consisting of few chemical species. This approach has been extended by Nenes and Seinfeld (2003) to include kinetic effects for aerosols that do not have time to grow to their equilibrium size. As the aerosol composition is important in cloud droplet activation in warm clouds, the effect of surface-active organics has recently been included in the parameterization of cloud droplet formation by Abdul-Razzak and Ghan (2004), while other effects of organics, such as their film-forming ability are considered by Rissman et al. (2004), and Fountoukis and Nenes (2005). Lance et al. (2004) explored the relative importance of the chemical effects of film forming compounds and of updraft velocity on cloud droplet number.

Current uncertainties in model treatments of the aerosol effects also include limitations due to dispersion of the resulted cloud droplets. Recently, Liu and Daum (2002) and Rotstayn and Liu (2003) showed that the dispersion of the cloud droplet spectrum is related to the cloud droplet number concentration. They compiled measurements in polluted and unpolluted warm stratiform and shallow cumulus clouds southwest of San Diego, over the northeastern Pacific, the northeastern Atlantic, the Southern Ocean, the eastern Florida coast, west of California, and over the northern Indian Ocean. From there, they concluded that polluted clouds with a higher droplet concentration tend to have a larger relative dispersion, other factors being the same. This simultaneous increase of the relative dispersion and droplet concentration with the increased aerosol loading may be due to a more complex chemical heterogeneity of anthropogenic aerosols, a broader size distribution, more small droplets competing for water vapor in polluted clouds compared to clean clouds, or a combination of the three (Srivastava, 1991; Wood et al., 2002; Hudson and Yum, 1997; Feingold and Chuang, 2002). Pre-cloud aerosol and dynamical properties of clouds, such as updraft velocity and turbulence, may also affect the cloud droplet concentration and spectral dispersion. A relationship to include them has been proposed by Liu et al. (2006) very recently. However, how aerosol loading affects the cloud droplet dispersion is not clear yet, as Lu and Seinfeld (2006) provide reasons for a decrease of relative dispersion of droplet spectrum with increasing aerosol concentration when this is below 1000 cm^-3.

Most GCM-based calculations of indirect forcing do not consider the effect of cloud droplet dispersion and there are only few simulations (Liu and Daum, 2002; Peng and Lohmann, 2003; Rotstayn and Liu, 2003; Chen and Penner, 2005) that made it. All are focused on global mean value of indirect forcing and show that the change in the indirect forcing associated to a change from the fixed coefficient β (a coefficient between volume mean radius and effective radius (Martin et al. 1994)) to a β that is related to droplet number is of some importance. The reduction of the indirect effect by including the dispersion effect is 15% by Peng and Lohmann (2003), between 12 and 35% by Rotstayn and Liu (2003), and 18% by Chen and Penner (2005).

While all estimations are within the range (10-80%) suggested by Liu and Daum (2002), there are differences in the applied methodology, the used models, parameterizations and input data. We point out here only the most important differences. The Rotstayn and Liu's (2003) model uses assumed values for pre-industrial and modern-day emissions of sulfate as a surrogate for all aerosols and infers droplet number from Boucher and Lohmann's (1995) parameterization, includes an interactive treatment of the tropospheric sulfur cycle and a physically based cloud scheme. Peng and Lohmann's (2003) model uses cloud droplet data from RACE and FIRE.ACE field campaigns, and ECHAM4 GCM. Chen and Penner (2005) assumed a single mode log-normal size distribution for the aerosol (pure ammonium sulfate) with a total aerosol number concentration of 1000 cm^-3, mode radius of 0.05 μm and a standard deviation of 2, and the sectional representation of the activation scheme of Abdul-Razzak and Ghan (2002). There are differences between the parameterizations of β coefficient, as well. In all simulations, the asymmetry factor has been considered having a fixed value. None included the variation of βin the asymmetry factor.

2. Data description and methodology

 2.1 Aerosol size representation and chemical composition

Due to the spatial and temporal variability of anthropogenic aerosols (Andreae, 1995; Jonas, 1995) the forcing has strong regional character (Kiehl and Rodhe, 1995; Ramanathan, 2001; Chameides et al., 2002), and the result is a regionally heterogeneous climate response (Taylor and Penner, 1994). In view of the large regional variability of aerosol, it is questionable whether the global mean forcing is sufficient to characterize the radiative impact of aerosols and the regional scale would not be more appropriate. Therefore, two aerosol types: marine and rural (as clean-continental) have been considered. The multimode log-normal aerosol number size distributions are given by:

where n_a,i, a_mi and σ_i are the total number concentration, geometric mean dry radius, and geometric standard deviation of aerosol mode i, respectively, and a represents the aerosol particle radius.

The modal representation has been used in regional and global aerosol models (e.g., Giorgi, 1986; Binkowski and Shankar, 1995; Environmental Protection Agency (EPA), 1999; Ghan et al., 2001a, 2001b, 2001c).

Measurements reported in literature show that the continental aerosol contains 15-30% sulfate, while marine aerosol contains somewhat more (30-60%), percentages that assure that fine aerosols at usual humidities are hygroscopic ones and they behave as optically ideal droplets. Beside chemical species that dissolve easily into water, atmospheric aerosol particles contain numerous substances, which are partially or completely insoluble. In this respect, we assumed that rural aerosol is a mixture of ammonium sulfate (75%) and mineral dust (25%), and pure ammonium sulfate for marine aerosol. The corresponding coefficients of the aerosol number size distributions are shown in Table Ia and result from measurements (Jaenicke, 1988; Hoppel and Frick, 1990; Bott, 2000).

The curvature parameter A and the hygroscopicity B were obtained considering the properties of each chemical component presented in Table Ib (from Qian et al., 2003); for the mixed composition of rural aerosol, A and B were obtained following the procedure explained in section 2.2.

2.2. Aerosol activation model

The processes that determine aerosol activation and droplet nucleation have been well understood and the Koehler theory expresses the number of particles activated in terms of supersaturation S, and predicts the time evolution of S in a rising air parcel (Pruppacher and Klett, 1997). A number of numerical models have been developed to implement this theory (e.g. Lee et al., 1980; Flossman et al., 1985; Heymsfield and Sabin, 1989), but they require detailed calculations over multiple size sections and multiple time steps between initial saturation and peak supersaturation, Smax, and thus they are computationally too expensive to be used in multi-dimensional atmospheric models. Therefore, several parameterizations with simplifying assumptions have been developed (e.g. Twomey, 1959; Ghan et al., 1993; Abdul-Razzak et al., 1998).

This study uses the parameterization of Abdul-Razzak et al. (1998) and Abdul-Razzak and Ghan (2000). An air parcel having specified aerosol size distribution and initial temperature, pressure and relative humidity (slightly below 100%) rises adiabatically with a specified updraft velocity. The particles whose critical or activation supersaturations (Scrit) are below S_max (achieved by the rising air parcel) are then assumed to be activated (Nenes et al., 2001). This S_max is then used to compute the number (or the mass) of activated particles. Hereby the computational problem reduces to the calculus of S_max.

The generalized Abdul-Razzak and Ghan (2000) parameterization is fully described in Abdul-Razzak and Ghan (2000), therefore we revisit here only the basics, keeping in mind that for multi-mode aerosol we need to add over all modes " i " of the aerosol size distribution.

For a single aerosol type, and a single log-normal mode, the fraction of aerosol particles that activate to droplets, following Abdul-Razzak and Ghan (2000) parameterization, is given by:

N is the droplet number concentration, N_ap is the total aerosol number concentration, a_c is the dry radius of the smallest activated aerosol, a_m is the geometric mean radius, σ is the geometric standard deviation of the size distribution and erf(u) is the error function. The radii a_c and a_m are calculated from Koehler theory through their corresponding critical supersaturations: the maximum supersaturation S_max corresponding to the smallest activated particle a_c is given by:

and the critical supersaturation S_m of a particle with radius a_m, which is given by:

and the critical supersaturation S_m of a particle with radius a_m, which is given by:

In the equations (3) and (4), the coefficient A counts for the curvature effect on the droplet surface and the coefficient B describes, depending on the particle composition, the hygroscopic properties of the aerosol population:

and

For the multimode version of the activation, the Abdul-Razzak and Ghan (2000) parameterization assumes that internal mixtures of material compose each mode; this involves that only the hygroscopicity B changes in a mean hygroscopicity parameter, averaged over all components j in aerosol mode i:

where r_ij is the mass mixing ratio of component j and mode i.

The maximum parcel supersaturation is obtained in Abdul-Razzak and Ghan (2000) parameterization using two functions f₁( 1n σ) = 0.5 exp{2.5 (1n σ)²}, and f₂(1n σ)=l+0.251n σ which are used to fit the ratio of S_m and S_max to a numerical solution of the governing equations:

where:

Here V is the updraft velocity, G accounts for diffusion of heat and moisture to the particles, a and y are coefficients in the supersaturation balance equation (Abdul-Razzak et al. (1998) and Abdul -Razzak and Ghan (2000) or Pruppacher and Klett (1997) for full description).

2.3 Simple cloud model: effective radius, optical depth and albedo calculations

In a global or in a regional climate model, the properties of clouds are computed in terms of optical depth, single-scattering albedo, and asymmetry factor over a number of spectral intervals (e.g., Slingo, 1989). These properties depend on the effective droplet radius and the cloud liquid water path.

The cloud droplet effective radius r_eff,defined by Hansen and Travis (1974) as the ratio between the third to the second moment of a droplet size distribution, depends on droplet number concentration (N) and LWC (Martin et al., 1994):

where β is a scaling coefficient frequently used in GCM to obtain r_eff from volume mean radius. Rotstayn and Liu (2003) suggest that β to be called spectral shape factor as it describes the width of the cloud droplet size distribution (eq. 12).

Martin et al. (1994) have shown that the relationship between r_eff and volume mean radius varies from ocean to land, and they proposed for β a value of 1.077 over ocean and of 1.143 over land, as this resulted from measurements in warm stratocumulus clouds during observations in Pacific, Atlantic and around British Isles. The cloud droplet number concentrations up to 200 cm^-3 in clouds over ocean areas and up to 450 cm^-3 in clouds over land were encountered.

From analysis of measurements in polluted and unpolluted warm stratiform and shallow cumulus clouds over worldwide, Liu and Daum (2002) and Rotstayn and Liu (2003) have shown that P is an increasing function of the relative dispersion s of cloud droplet spectrum:

They propose λ = 0.001, 0.003, 0.008 for the lower bound, average and upper bound of this variation respectively. The cloud droplet number concentrations they compiled were up to 800 cm ^-3.

Peng and Lohmann (2003) had cloud data from two field campaigns: The Radiation, Aerosol and Cloud Experiment (RACE), which took place from August to October 1995 off the coast of Nova Scotia, and the First ISCCP Regional Experiment-Arctic Cloud Experiment (FIRE.ACE), that was conducted in April 1998 in the Canadian and the United States, Arctic; data that encompasses cloud droplet number concentrations up to 300 cm^-3. They propose to use for p its direct dependence of cloud droplet number:

For warm stratocumulus cloud we considered, the cloud optical depth can be approximated (e.g., Peng et al., 2002) as:

where H is the thickness of model layer (cloud thickness) and can be related to r_eff and cloud droplet number concentration N as:

The cloud albedo (A) was computed taking into account the two-stream approximation of a non-absorbing, horizontally homogeneous cloud (Lacis and Hansen, 1974):

First, we considered that the scattering asymmetry factor g has a fixed value (0.85), and second, we included the dependence of g of the cloud droplet effective radius, as in some GCM or regional climate models may be implemented. We used the parameterization in ECHAM GCM (Boucher and Lohmann, 1995) for visible range of electromagnetic spectrum:

The exact procedure used in the present study is as follows: 1) specify the average aerosol physical and chemical characteristic for two typical environments (rural as clean continental and marine) based on published observations, 2) determine a likely droplet number concentration based on the ARG parameterization and determine the scaling coefficient p counting for dispersion of the cloud droplet spectrum, 3) calculate the cloud effective radius, optical depth and cloud albedo in two pairs of calculation: β-scaled (denoted in figures as +β) and non-scaled (denoted in figures as - β), and estimate the differences.

3. Results and discussion

3.1 Comparison of the observed cloud droplet concentrations and model results

The number size distribution for marine, and rural aerosol calculated from parameters in Table Ia are represented in Figure 1. The number concentration of droplets nucleated in a cloud has been estimated following the procedure in section 2.2. The computations based on equations (1) ÷ (10) consider a temperature of 21 ºC, and an updraft velocity of 0.5 m s^-1 (within the expected range of stratiform clouds (Paluch and Lenschow, 1992; Seinfeld and Pandis, 1998)). The other coefficients are listed in Tables, Ia and b, and the coefficients counting for gas kinetic effects being that used by Abdul-Razzak and Ghan (2000). Using a single updraft velocity for the entire grid cell is a simplification, since the updraft velocity varies over the grid cell (Lohmann et al., 1999); but we assumed it constant, since we are only interested in the cloud drop activation process, which generally occurs on the order of seconds.

As a dataset on measured droplet concentrations was not available for the size distributions considered by us, we compared our results with reports from field campaigns. Table II lists the cloud droplet number concentration values calculated using the aerosol concentration-cloud droplet concentrations relationships based on five field measurements reported by Gultepe and Isaac (1999). There were more than ten thousand observations collected over a period of 11 years in primarily stratus and stratocumulus, therefore they cover a wide range of conditions of cloud formation. We also have chosen to compare our results with that inferred from the Gultepe and Isaac (1999) correlations as these are currently being used in GCM.

Mean values from a comprehensive observational database for marine and continental stratus and stratocumulus clouds performed by Miles et al. (2000) are also indicated. A comparison of our cloud droplet number concentrations with that inferred from Gultepe and Isaac (1998) correlations and datasets compiled by Miles et al. (2000) shows a good agreement.

3.2 Dispersion effect on effective radius

We investigated the influence of dispersion on droplet effective radius as LWC ranges from 0.1 to 1 g m^-3 using the value of 0.42 for relative dispersion (s) for marine case and that of 0.73 for rural case. The relative dispersions were inferred from the cloud droplet concentrations using first Liu and Daum (2002) and Rotstayn and Liu (2003) relationships, i.e. eqs. 12 and 13, and second using Peng and Lohmann (2003) relationship, i.e. eq. 14. This means that scaling factor β_LDR (respectively β_PL) ranges from 1.16 (1.207) for marine to 1.41 (1.324) for rural air masses; when dispersion is not considered β = 1.

The database of Miles et al. (2000) reveals that droplet size distributions measured in ambient conditions have relative dispersions between 0.15 and 0.83 for marine clouds, with 55% distributions having s above 0.4, and 74% having s above 0.3. From the same database, for clouds over land, the relative dispersions range from 0.21 to 0.9, with only 10% distributions having s above 0.7 and 31% having s above 0.5.

Figure 2 shows the comparison of the calculated p-scaled effective radius and non-scaled effective radius for marine and continental clouds using the above method. For an LWC ranging from 0.1 to 1 g m^-3, the β_LDR-scaled effective radius increases from 8.5 to 18.4 μm for marine clouds, and from 5.9 to 12.8 |a,m for continental clouds. The estimated β_PL-scaled effective radius is higher than β_LDR-scaled effective radius for marine clouds; for continental clouds, the situation is reversed. This is due to the difference in the mathematical form of the β-N relationship (for N between about 130 and 970 cm^-3, β_PL > β_LDr)- In both cases, the absolute differences are below 0.8 μm as LWC ranges between the specified limits.

We estimate a measure of the dispersion effect on effective radius by defining the percentage difference 5r_effas:

where r_eff, _p is effective radius value when the dispersion is considered. The dispersion presence (through scaling factor β_LDR) leads to an increase in effective radius of 16% (marine) and respectively of 41% (continental). When scaling factor p_PL is used, the 5r_eff changes to 20% (marine) and to 32% (continental). This means the effect of dispersion is more pronounced as the cloud droplet number concentration (determined by the aerosol number concentration) has higher values but the option of the β-scaling factor also plays a role.

In the Earth's atmosphere a large variety of droplet sizes can be found depending very much on the type of cloud they are embedded in. Stephens (1978) quotes radii ranging from 2.25 µm for stratus clouds to 7.5 µm for stratocumulus. Han et al. (1994) derived radii for water clouds from satellite measurements ISCCP between 8.2 and 12 μm, but is difficult to use them for comparison with our data as information about the value of LWC is necessary. An example of a more appropriate comparison is the following: Miles et al. (2000) reports effective radius of 11.4 μm for marine stratocumulus when LWC = 0.28 g m^-3, and we calculated a β_LDR-scaled value of 12.3 µm at LWC = 0.3 g m^-3; for continental stratocumulus, Miles et al. (2000) provides effective radius of 9.1 μm for an LWC = 0.4 g m ^-3 for marine stratocumulus, and we calculated a β_LDR-scaled value of 9.43 μm. But from the same database, we extracted for LWC = 0.11 g m^-3, measured values of 12.7 and 4.85 μm, while we calculated β_LDR-scaled value of 5.94 μm and anon-scaled value of 4.21 μm. This is as indication that while the differences between the measurements can be attributed to the different sampling locations, methods and the meteorological parameters, our simulations can not be directly compared with this database. A further comparison is performed in section 3.5.

3.3 Dispersion effect on cloud albedo

According to equations (11-17), an increase in s acts to decrease the optical depth and the cloud reflectivity. In the following calculations the cloud albedo is calculated in the assumption that the scattering asymmetry factor has a fixed value of 0.85.

In both cloud types, there is a decrease in optical depth (Fig. 3) and cloud albedo (Fig. 4), as liquid water increases and as spectral dispersion increases. This behaviour varies with aerosol type, the decrease (defined in the same way like δr_eff) in optical depth being of up to 14 (17%) in the marine case, and up to 29 (24%) in the rural case for a cloud of 100 m thickness (β_LDR, respectively β_PL were used). When spectral dispersion is represented by β_LDR, the decrease in cloud albedo (Fig. 5) is between 6 and 10% (marine) and between 11 and 21% (continental). Therefore, in both clouds the dispersion effect on cloud albedo can be seen counting for more than 5%.

3.4 Albedo computations with dispersion included in scattering asymmetry factor

In the previous sections, we performed the calculations taking into account the dispersion only in the effective radius, and cloud albedo has been obtained considering a constant value of 0.85 for the scattering asymmetry factor g. We have repeated calculations but considering that dispersion to be also included in g through Eq. 18. The corresponding relative decrease in cloud albedo for both cloud types is also plotted in Figure 5. It can be seen the important effect that inclusion of dispersion in both r_eff and g has on cloud reflectivity: in both types of clouds, the dispersion effect could lead to a relative change in cloud reflectivity for more than 20%. For the same liquid water content, the variability in cloud droplet concentration (from 60 to 319 cm-^-3) determines variability in albedo of up to 3%.

3.5 Comparison with SCAR-B and ASTEX results

The calculated cloud albedo, when relative dispersion has been considered, shows better agreement with the estimated cloud albedo from measured effective radius in SCAR-B project than the cloud albedo calculated without dispersion, for clouds over continental areas (Fig. 7a). In cleaner conditions of marine clouds (Fig. 7b), albedo values when relative dispersion has been considered are higher than those inferred using an effective radius-liquid water content relationship proposed by Reid et al. (1999) from ASTEX project when LWC exceeds 0.5 g m^-3; only β_PL-scaled albedo fits satisfactory within the validity range. The low correlation coefficient of 0.36 of the parameterization obtained Reid et al. (1999) may also play a role within.

3.6 Implications for the aerosol first indirect effect

As the first indirect effect is directly related to changes in cloud reflectivity (e.g. Seinfeld and Pandis, 1998), it can be characterized quite well as follows: assuming a constant LWC, a change in droplet number (N) can be roughly related to a change in cloud reflectivity (Δ A):

where F₀ is the incident solar flux (W m²), C_c is the fractional cloud cover, T_a is the fractional transmittance of the atmosphere, ΔA is the change in cloud albedo. This rough approximation shows that a diminished cloud albedo, due to an enhanced dispersion of cloud droplet spectrum with absolute values (Table III) up to 0.13 (marine) and up to 0.16 (continental), are expected to correspondingly diminish the estimated indirect forcing. Thus, spectral dispersion effects could help to explain the high end of the simulated aerosol first indirect forcing.

4. Conclusions

This study assesses the variability in cloud albedo that may result from the variability of relative dispersion of cloud droplet spectrum. Using the observed aerosol characteristics, the detailed ARG parameterization to obtain the number of cloud droplets, and a simple cloud model, we found that spectral dispersion may diminish cloud reflectivity by up to 28 (marine) and 31% (continental), with respect to the case when cloud albedo is calculated without considering the dispersion of cloud droplet spectrum.

The calculated cloud albedo scaled by a parameter, which is a function of the relative dispersion of cloud droplet spectrum, shows better agreement with the estimated cloud albedo from measured effective radius in SCAR-B project than the cloud albedo calculated without scaling, for clouds over rural areas. In cleaner conditions of marine clouds, only β_PL-scaled albedo fits satisfactory within the validity range of albedo inferred using an effective radius-liquid water content relationship proposed by Reid et al. (1999) from ASTEX project. The low correlation coefficient of the parameterization may also play a role within.

Even if our simple estimate of the aerosol effect on cloud reflectivity cannot take all the feedbacks operating in a general or a regional climate model into account, our result shows that spectral dispersion may have important significance for the indirect aerosol effect. We propose that ARG parameterization to be tested in a global or regional climate model when dispersion effect (included in both effective radius and in scattering asymmetry factor) is investigated. The effect produced by the enhancement of ε on cloud reflectivity is evidently large enough to be considered in assessing the indirect aerosol effect, and understanding the relation between ε, N and A will help to reduce the large uncertainty inherent in this effect.

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