The phase transition from water vapor to small ice crystals is commonly described by classical nucleation theory. This theory assumes that thermal fluctuations in supersaturated water vapor lead to the spontaneous formation of water clusters of various sizes. As soon as a cluster exceeds the critical radius, further growth of that cluster is energetically favored. However, to reach the critical radius, the energy barrier ∆F∗ has to be overcome. Preexisting ice nuclei lower this energy barrier, thus facilitating the nucleation process. For the formation of mesospheric ice particles, MSPs are believed to serve as ice nuclei. However, classical nucleation theory relies on several assumptions, which might not be applicable to mesospheric conditions. Additionally, critical parameters have not been experimentally determined for the extreme conditions of the polar summer mesopause. This leads to an uncertainty of the nucleation rate of several orders of magnitude.
In classical nucleation theory, it is assumed that the temperature of the ice nucleus is equal to the temperature of the surrounding gas. This assumption might not be true for MSPs at the summer polar mesopause, since these MSPs could be warmer than the ambient atmosphere. Thus, the classical nucleation theory has been extended to account for a possible temperature difference between MSPs and the ambient atmosphere. A positive temperature difference increases the critical radiusr∗ as well as the nucleation barrier ∆F∗. Only those MSPs which are larger than r∗ can act as ice nuclei, so that an increase of r∗ due to warmer MSPs reduces the number of possible ice nuclei.
The increase of the nucleation barrier ∆F∗ results in generally lower nucleation rates.
The overall effect of a positive temperature difference between MSPs and ambient atmosphere is that the nucleation process takes longer and that fewer MSPs can act as ice nuclei.
In this chapter the microphysical model CARMA is introduced. The setup for the simulations presented in this thesis is described, as well as the background fields required by the CARMA model. Additionally, the capabilities of the microphysical model are demonstrated with a set of exemplary simulations.
3.1 Community Aerosol and Radiation Model for Atmospheres
CARMA, the Community Aerosol and Radiation Model for Atmospheres, is a micro-physical model with a flexible setup, which can be applied to a variety of aerosol and cloud problems. The original one-dimensional CARMA code developed by Turco et al.
(1979) and Toon et al. (1979) was later extended to three dimensions (Toon et al., 1988) and adapted to mesospheric conditions (Turco et al., 1982; Jensen and Thomas, 1989) for NLC studies (e.g., Rapp et al., 2002; Merkel et al., 2009; Stevens et al., 2010;
Russell III et al., 2010; Siskind et al., 2011; Chandran et al., 2012).
The CARMA model for NLC studies comprises three constituents: MSPs, ice particles and water vapor. These constituents are able to interact via the following reactions:
nucleation of MSPs to form ice particles, deposition of water vapor onto ice particles for their growth, sublimation of ice particles with release of water vapor (and in the case of total evaporation with release of MSPs), and coagulation. Coagulation of MSPs is considered, coagulation of ice particles and also coagulation of MSPs with ice particles.
Water vapor is additionally dissociated by Lyman-α radiation. These processes are visualized in Fig. 3.1.
Ice particles and aerosols are calculated as number densities, which are resolved in grid boxes and radius bins. The above mentioned processes are calculated individually for each gridbox and size bin. The nucleation process is calculated via the heterogeneous nucleation rate given by Eq. 2.42. The growth and evaporation of ice particles is treated via the kinetic growth rates (see Eq. 2.45). Coagulation is determined using a Brownian coagulation kernel (see Pruppacher and Klett, 1997, Ch. 15 and Jacobson et al., 1994). Photodissociation of water vapor is parametrized as described by Jensen (1989).
Figure 3.1: Schematic diagram of CARMA showing the basic constituents and their interactions (drawn after Jensen and Thomas, 1989).
An Eulerian transport scheme handles the transport of particles and water vapor due to background winds, eddy diffusion and sedimentation (particles only). The piecewise parabolic method by Colella and Woodward (1984) calculates advection in physical space and radius space (growth of particles). In a one-dimensional setup (as in this study), a divergence correction is applied in order to fulfill the continuity equation according to Jensen and Thomas (1989): A divergent vertical flow is thereby compensated by horizontal advection from virtual neighboring boxes with identical properties, which brings aerosol particles and water vapor into the considered gridbox (and vice versa for a convergent vertical flow).
The size distribution of aerosol particles is resolved in 40 size bins with mass doubling between adjacent bins, starting from minimal radii of 0.2 nm for MSPs and 2 nm for ice particles. The model domain covers the altitude range from 72 km to 102 km in 120 equidistant levels of 250 m thickness. The time step is set to 100 s for all slow processes
like transportation and coagulation. The fast microphysical processes nucleation and growth are calculated on shorter time scales, where the time step is adjusted according to the current microphysical conditions of each grid box. The length of each simulation was set to 48 h.
From the model output, the total number density and mean radius of the ice particles is calculated via
ntot =Z ∞
0
dN
dr dr (3.1)
and
rmean =Z ∞
0
rdN
dr dr, (3.2)
respectively, where dN/dr denotes the ice particle size distribution. The backscatter coefficientβ is calculated via
β =Z ∞
0
πr2Qsca(λ, r, n)dN
dr dr (3.3)
with the scattering efficiency Qsca as a function of wavelength λ, particle radius r and refractive index n. The backscatter coefficient always refers to a wavelength of λ= 532 nm, which is a frequently used wavelength for lidar detection of NLCs (e.g., Baumgarten et al., 2008; Thayer et al., 2003). The scattering efficiency is calculated from Mie theory (Bohren and Huffman, 1983) for spherical ice particles, or from T-matrix calculations (Mishchenko and Travis, 1998) for spheroids. If not mentioned otherwise, the ice particles are assumed to be spherical.
The modeled NLCs are classified by their backscatter coefficient β into different brightness classes (Fiedler et al., 2011): Faint NLCs (in units of 10−10m−1sr−1) refer to those with 1< β < 4, weak NLCs have 4< β <7, medium NLCs are characterized by 7< β <13, and strong NLCs by β >13.
This study builds on the CARMA model used by Rapp and Thomas (2006) with several improvements:
• The background state of the mesopause region can either be described by cli-matological profiles as in the setup by Rapp and Thomas (2006) or with wave driven profiles taken from KMCM (Kühlungsborn Mechanistic general Circulation Model, see Sec. 3.2.2). The KMCM profiles of temperature, density, pressure and wind are updated in CARMA every 600 s. The climatological and wave driven background profiles is shown in Figs. 3.2 and 3.3, respectively.
• The updated dust profile from the global and seasonal MSP model by Megner et al. (2008b) for July conditions at 68◦N has been incorporated into CARMA (see Sec. 3.2.3).
• Some minor changes in the code, providing more consistency in the microphysical calculations or the stability of the model, are listed in the Appendix A.1.
As in the setup of Rapp and Thomas (2006) CARMA is operated in a one-dimensional setup. This 1D setup is necessary in order to run the large number of sensitivity runs for this study in reasonable computation time.