
FN may not necessarily be very efficient ice nuclei (particles that already form ice at a few percent supersaturation with respect to ice or at rather warm temperatures.) Throughout this work, we define FN as ice-nucleating aerosols. This is partly caused by the lack of information about the origin, spatial distribution, and chemical nature of the FN. In contrast, knowledge about ice formation caused by heterogeneous freezing nuclei (FN) at low temperatures are poorly understood. The processes involved in ice formation in cirrus clouds seem to be largely understood only in the case of homogeneous freezing of supercooled droplets. Ice nucleation is a fundamental cloud process. The change in longwave radiation in these simulations only amounted to 0.1–0.2 W m −2. The only link to ice clouds is heterogeneous freezing of cloud droplets. In these models the changes in anthropogenic aerosol concentration have no direct impact on ice clouds.

The estimates for both indirect aerosol effects in these studies range from −1.1 to −2.1 W m −2. predicted cloud droplet number concentration and parameterized cloud droplet nucleation for an internally as well as an externally mixed aerosol. Whereas Rotstayn used an empirical relationship between sulfate aerosol mass and cloud droplet number, Lohmann et al. These studies consider both the effect of increasing cloud albedo due to more but smaller cloud droplets for a given liquid water path and the increase in cloud lifetime due to the reduced precipitation efficiency. Several studies have estimated the indirect effect of anthropogenic aerosols by conducting numerical experiments with preindustrial and present-day emissions. Meteorological Office Unified Model that allows subsaturation or supersaturation with respect to ice by explicitly solving the growth equation for a single ice particle. Only recently, Wilson and Ballard introduced an ice phase scheme into the U.K. All of these schemes apply the saturation adjustment scheme for condensation and deposition that is, no supersaturation with respect to ice is allowed. State-of-the-art general circulation models (GCMs) represent cirrus clouds either by diagnosing the ice water portion from the predicted total water content as a function of temperature or by separately predicting cloud ice mixing ratio. In contrast, very little information is available concerning the interaction of aerosols and cold cirrus clouds (consisting of ice crystals), despite the fact that cirrus clouds exert a significant potential climatic impact. Considerable progress has been made in representing the indirect effect of aerosols on warm clouds (consisting of water droplets), either by developing empirical relationships between aerosol mass and cloud droplet number or by deriving approximate analytic expressions to calculate the fraction of particles acting as CCN in a given ensemble of aerosols.

Quantifying the relationship between aerosol and cloud properties is a challenging enterprise. The latter influences cloud properties such as droplet number and size, albedo, precipitation rate, and lifetime. An important component of this uncertainty is related to the indirect forcing, associated with the link between aerosol properties such as particle number and size, chemical composition, and ability to act as cloud condensation nuclei (CCN). The largest uncertainties in the prediction of climate forcing from anthropogenic changes in atmospheric composition arise from attempts to quantify the climatic effects of aerosols on clouds in global climate models.

The potential role of aerosol size and heterogeneous freezing processes in altering the predicted cirrus properties is briefly addressed. The derived parameterization is validated with parcel model simulations, and its applicability for use in climate models is discussed. In such cases, applicable in many situations, the number of crystals formed via homogeneous freezing of aqueous solution droplets is rather insensitive to details of the aerosol size distribution, but increases rapidly with updraft velocity and decreases with temperature. The analysis explains the dependence of the number density of ice crystals on the vertical velocity and temperature seen in numerical simulations of cirrus formation when the timescale of depositional growth of the pristine ice particles is fast compared to the timescale of the freezing event. The nucleation and initial growth of ice crystals in cirrus clouds at low (<235 K) temperatures prevailing in the upper troposphere and in the tropopause region is theoretically considered.
