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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% An example input file demonstrating the agp option of the SVJour %
+% document class for the journal: Annales Geophysicae %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+\documentclass[agp]{svjour}
+
+\usepackage{graphics}
+\usepackage{epsfig}
+\usepackage{times}
+% \usepackage{mathtime}
+%
+\sloppy
+%
+\journalname{Ann. Geophysicae}
+%
+\begin{document}
+\title{On the regional climatic impact of contrails:}
+\subtitle{microphysical and radiative properties of contrails and
+natural cirrus clouds}
+\author{B. Strauss\inst{1} \and
+R. Meerkoetter\inst{1} \and
+B. Wissinger\inst{1} \and
+P. Wendling\inst{1} \and
+M. Hess\inst{2}}
+\institute{Deutsche Forschungsanstalt fuer Luft- und Raumfahrt (DLR),
+Institut fuer Physik der Atmosphaere, Oberpfaffenhofen, D-82234 Wessling,
+Germany
+\and
+Meteorologisches Institut der Universitaet Muenchen, Muenchen, Germany}
+\mail{B. Strauss\\
+e-mail: pal3@opasul.pa.op.dir.de}
+\date{Received: 17 November 1995 / Revised: 12 May 1997 /
+Accepted: 6 June 1997}
+\titlerunning{On the climatic impact of contrails}
+\authorrunning{B. Strauss \etal}
+
+\maketitle
+
+\abstract{The impact of contrail induced cirrus clouds on regional
+climate is estimated for mean atmospheric conditions of Southern Germany
+in the months of July and October. This is done by use of a regionalized
+one-dimensional radiative convective model (RCM). The influence of an
+increased ice cloud cover is studied by comparing RCM results
+representing climatological values with a modified case. In order to
+study the sensitivity of this effect on the radiative characteristics of
+the ice cloud, two types of additional ice clouds were modelled: cirrus
+and contrails, the latter cloud type containing a higher number of
+smaller and less of the larger cloud particles. Ice cloud parameters are
+calculated on the basis of a particle size distribution which covers the
+range from 2 to 2000\,$\mu$m\,, taking into consideration recent
+measurements which show a remarkable amount of particles smaller than
+20\,$\mu$m. It turns out that a 10\% increase in ice cloud cover leads
+to a surface temperature increase in the order of 1\,K\,, ranging from
+1.1 to 1.2\,K in July and from 0.8 to 0.9\,K in October depending on the
+radiative characteristics of the air-traffic-induced ice clouds.
+Modelling the current contrail cloud cover which is near 0.5\% over
+Europe yields a surface temperature increase in the order of 0.05\,K.
+\keywords{Insert keyword here}}
+
+\strich
+
+%%%%%%%%%%%%%%%
+%% Section 1 %%
+%%%%%%%%%%%%%%%
+
+\section{Introduction}
+\label{sec:1}
+
+Air traffic influences the atmosphere through the emission of various
+gases and particles. Among these, water vapour and aerosol particles
+acting as cloud nuclei are of special interest because they support
+cloud formation thus modifying an important climate factor. Therefore,
+the impact of contrails, or better `air-traffic-induced cirrus clouds'
+was discussed recently within the scope of air traffic and climate in
+general \citep{Schu94}. \citet{Li90} studied the global influence of
+contrails within a case study, using a two-dimensinal climate model.
+They found an increase in surface temperature of 1\,K in the case of an
+increase in cloud cover by 5\% between 20$^\circ$ and 70$^\circ$ N.
+\citet{Po96} studied the influence of an increase in water vapour and in
+cirrus cloud cover induced by air traffic using a three-dimensional GCM.
+They showed that a significant climatic effect is more likely to occur
+on the basis of contrail cloud cover rather than on the basis of
+additional water vapour due to air traffic. The GCM results show an
+increase in surface temperature of 1\,K at 50$^{\circ}$N for a contrail
+cloud cover of 5\%.
+
+However, one may expect contrails to have a stronger impact on a
+regional scale than on a global scale. To estimate this, a case study is
+carried out within this paper for an area of increased air traffic in
+southern Germany. This is done by use of a one-dimensional radiative
+convective model (RCM), originally developed by \citet{Li83} and
+modified to allow modelling of regional climate by taking into account
+advection as a third energy flux besides radiation and convection. The
+effects of an increased ice cloud cloud cover on the equilibrium
+temperature profile of a mean July and October atmosphere were
+simulated.
+
+\begin{figure*}
+\sidecaption
+\unitlength0.9cm
+\begin{picture}(12,7)
+\framebox(12,7){}
+\end{picture}
+\caption{Ice replicator mounted on the DLR research aircraft `Falcon'}
+\label{fig:1}
+\end{figure*}
+
+Special emphasis is laid on the parameterization of the radiative
+characteristics of ice clouds. There are two types of ice cloud used in
+the model: cirrus and contrail. An increase in ice cloud cover is
+modelled twice, using both cloud types, in order to estimate the
+influence of the cloud radiative characteristics on the results.
+Corresponding RCM input parameters are the transmittance and the
+reflectance in the solar, and the emittance, the transmittance and the
+reflectance in the terrestrial spectral range. Values of these
+quantities are obtained by radiative transfer model (RTM) calculations.
+Ice clouds in the model are assumed to consist of particles in the range
+2--2000\,$\mu$m. The size distribution for particles smaller than
+20\,$\mu$m is based on recent in situ measurements which are presented
+in Sect.~\ref{sec:2}, for particles greater than 20\,$\mu$m a parameterization
+of \citet{He84} is used. Contrails are assumed to consist of a larger
+portion of smaller particles and less of the bigger ones compared to
+natural cirrus clouds. The ice water content, however, is assumed to be
+the same in both cloud types, for reasons of better comparability. It is
+anticipated that the portion of small particles has an appreciable
+influence on the radiative properties of ice clouds \citep{Ar94}.
+Section~\ref{sec:3} describes the model modifications, Sect.~\ref{sec:4}
+presents and discusses the resulting equilibrium temperature profiles.
+
+%%%%%%%%%%%%%%%
+%% Section 2 %%
+%%%%%%%%%%%%%%%
+
+\section{Measurements of microphysical properties in cirrus clouds and
+contrails}
+\label{sec:2}
+
+In situ measurements by use of an ice replicator [built by J. Hallett,
+Desert Research Institute (DRI), Reno, Nevada, USA] were carried out in
+both natural cirrus and aged contrails. This was done within the
+campaign `CIRRUS '92' organized by `Deutsche Forschungsanstalt f\"ur
+Luft- und Raumfahrt' (DLR). It took place between 1 and 19 October 1992
+in South Germany. On 15 October measurements were taken in a natural
+cirrostratus cloud located ahead of a frontal system related to a strong
+low over Denmark. On 9 October measurements were taken in contrails with
+ages in the order of half an hour embedded in arising cirrus. In this
+case a high was located over Central Europe, a low over the
+Mediterranean Sea and advection of warm air in southern Germany just
+started from the south. A comparison of these two measurements is of
+special interest with regard to a possible difference in the
+microphysical behaviour of these two cloud types. The question of how
+representative these two clouds were remains open up to now.
+
+The principle of the ice replicator (see Fig.~\ref{fig:1}) is quite easy:
+the particles fly through an inlet situated at the tip of the
+instrument, sized 2 $\times$ 7\,mm$^2$, and impact on a coated leader
+film which is transported just behind that entrance. The impacts of the
+particles are conserved in the coating and are analysed by microscopy,
+digitization of the microscope pictures and image processing software.
+Thus information on particle shapes, sizes, concentration and size
+distribution is obtained. The lower resolution of the instrument is
+about 4\,$\mu$m, depending on the quality of the coating which does not
+always have the same characteristics. A source of uncertainty concerning
+absolute particle numbers is the uncertainty due to the collection
+efficiency for particles smaller than approximately 10\,$\mu$m, which is
+not known accurately. Particles larger than approximately 100\,$\mu$m
+normally break by impaction and information on these particles is
+therefore weak. Regions showing fragments of broken particles were
+excluded from evaluation. Nevertheless, there remains an uncertainty due
+to misclassification of some broken material. This effect is contrary to
+the collection efficiency effect. Figure~\ref{fig:2} shows eight size
+distributions of the cirrus cloud measured on 15 October 1992 taken from
+eight different parts of this cloud, thus representing a measure of the
+natural variability. Also shown is a parameterization for cirrus cloud
+particles larger than 20\,$\mu$m in size for temperatures of
+$-55^{\circ}$C and $-40^{\circ}$C \citep{He84,Li92}. The temperature in
+the cloud was about $-55$ to $-57^{\circ}$C. One can see three important
+features:
+
+\begin{enumerate}
+\item there are many `small' particles, i.e. particles smaller than about
+20\,$\mu$m in size;
+\item the measured size distributions coincide with the parameterization
+of Heymsfield and Platt in the overlap size regime;
+\item the variability is in the order of one magnitude.
+\end{enumerate}
+
+\begin{figure}
+\unitlength0.9cm
+\begin{picture}(8.575,7)
+\framebox(8.575,7){}
+\end{picture}
+\caption{Size distributions in a cirrostratus cloud measured on 15
+October 1992 over Southern Germany. The eight curves represent eight
+different parts of the cloud and thereby give a measure of the natural
+variability. The two lines represent parameterizations for particles
+larger than 20\,$\mu$m for $-55\,^{\circ}$C ({\it solid}) and
+$-40\,^{\circ}$C ({\it dash -- three dots}) after Heymsfield and Platt
+(1984)}
+\label{fig:2}
+\end{figure}
+
+The strong fluctuations at sizes larger than about 20$\mu$m are due to
+the size of sampling volume which is comperatively small for particles
+of this size regime. It is in the order of several thousand cm$^{3}$.
+The collection efficiency is assumed to be 1 for all sizes, i.e. numbers
+for particles smaller than approximately 10\,$\mu$m are probably
+slightly underestimated. Integration gives a mean particle concentration
+of 0.7\,cm$^{-3}$ with values ranging from 0.5 to 1.1\,cm$^{-3}$.
+
+These values can be compared to data obtained by measurements with a
+Counterflow Virtual Impactor (CVI) in natural cirrus clouds, as
+presented by \citet{St93}. The CVI detects ice particles up to
+30\,$\mu$m by measuring the concentration of the nuclei and the ice
+water content of the particles. CVI values range from 0.1 to
+1\,cm$^{-3}$ and therefore confirm the replicator data.
+
+Figure~\ref{fig:3} shows the corresponding results for the aged contrails
+on 9 October. The temperature in these contrails was between
+$-37^{\circ}$C and $-45^{\circ}$C. The mean concentration value is found
+to be 1.3\,cm$^{-3}$, again assuming a collection efficiency of 1, with
+values ranging from 0.8 to 1.6\,cm$^{-3}$. A comparison of the two
+clouds is shown in Fig.~\ref{fig:4}. The two curves represent mean
+values of the size distribution for the two cloud types. One can see
+that the particle concentration for the aged contrails is larger for all
+sizes measured by the ice replicator. But the difference is
+significantly less than the variability of each of the two clouds.
+
+\begin{figure}
+\unitlength0.9cm
+\begin{picture}(8.575,7)
+\framebox(8.575,7){}
+\end{picture}
+\caption{Size distributions measured in aged contrails on 9 October 1992
+over Southern
+Germany. Lines as in Fig.~\ref{fig:2}}
+\label{fig:3}
+\end{figure}
+
+\begin{figure}
+\unitlength0.9cm
+\begin{picture}(8.575,7)
+\framebox(8.575,7){}
+\end{picture}
+\caption{Comparison of size distribution for natural cirrus (15 October 1992,
+{\it thick}) and aged contrails (9 October 1992, {\it thin}). Lines as in
+Fig.~\ref{fig:2}}
+\label{fig:4}
+\end{figure}
+
+%%%%%%%%%%%%%%%
+%% Section 3 %%
+%%%%%%%%%%%%%%%
+
+\section{The radiative convective model and its modification}
+\label{sec:3}
+
+The RCM output of the original model version represents an atmospheric
+state of long-term and global averaging. It divides the atmosphere into
+21 layers containing three cloud layers and calculates a temperature
+profile representing an equilibrium state between radiation and
+convection within each layer. The whole spectral range comprises six
+spectral intervals in the solar and five intervals in the terrestrial
+region.
+
+The temperature profile is computed on the basis of the Curtis matrix
+principle, i.e. starting with an emittance, reflectance and
+transmittance value and a first-guess temperature value for each
+atmospheric model layer and then applying a perturbation scheme. This
+immediately gives the equilibrium state temperature profile, i.e. no
+time-stepping method is used. Values in cloudy layers are assumed to be
+dominated by the cloud particles. Figure~\ref{fig:5} gives an overview of
+the procedure. For more details see \citet{Li83}.
+
+\begin{figure*}
+\sidecaption
+\unitlength0.9cm
+\begin{picture}(12,7)
+\framebox(12,7){}
+\end{picture}
+\caption{Flow diagram showing the principle procedure of the RCM. Each
+iteration repeats the calculations of the vertical exchange coefficient
+and of the profile of the radiative fluxes on the basis of the new
+temperature profile. Advection is taken into consideration as a third
+energy flux besides radiation and convection in the modified version of
+the RCM which is used in this study}
+\label{fig:5}
+\end{figure*}
+
+To permit simulations on a regional scale and for limited time periods,
+advection has to be taken into consideration. Furthermore, the following
+variables have to be specified for the considered region and time: (1)
+solar zenith angle, (2) water vapour profile, (3) ozone profile, (4)
+cloud cover, (5) surface albedo, (6) Bowen ratio.
+
+All of these values except the cloud cover are assumed to be constant in
+the frame of this study. Cloud cover values for mid-level and low clouds
+are fixed, whereas high cloud cover is varied. More details are given in
+Appendix~B.
+
+Special emphasis is given to the parameterization of the optical
+properties of ice clouds. In the model's original version, ice clouds
+consist of cylindrically shaped monodisperse ice particles with a mean
+length of 200\,$\mu$m, a mean radius of 30\,$\mu$m and a mean
+concentration of 0.05\,cm$^{-3}$.
+
+However, recent research results force these assumptions to be modified.
+It turned out that models tend to underestimate the solar ice cloud
+albedo when compared to measurements \citep{St91}. As a consequence, two
+hypotheses are made to explain this discrepancy: in today's models,
+particles are usually described as spheres or hexagons. Hypothesis (1)
+says that particle shapes have to be modelled more precisely with
+respect to multibranched particles which are regularly found in ice
+clouds and which could cause increased backscattering as compared to
+simple hexagonally shaped columns and plates \citep{Wi90}. Hypothesis
+(2) concerns the particle size. Little is known about particles smaller
+than 50\,$\mu$m due to the lower resolution of instruments usually
+employed for in situ measurements of ice particles. Ice cloud models
+usually assume particles with a minimum size of 20\,$\mu$m or even
+larger. Hypothesis (2) says that a significant amount of smaller
+particles have an appreciable influence on the radiative characteristics
+of ice clouds by enlarging the number of backscattered photons and
+herewith increasing cloud albedo. Model calculations
+\citep{Ma93,Ia95,St96} make hypothesis (1) appear unlikely, whereas
+recent in situ measurements as presented in the previous section support
+hypothesis (2). Therefore, the ice cloud parameterization used in the
+RCM was modified by assuming hexagonally shaped ice particles in the
+solar spectral range, and cirrus particle size distributions in the
+small-particle regime as based on our measurements (see Sect.~\ref{sec:2})
+and those of \citet{He84}. In the terrestrial spectral range,
+Mie-calculations were carried out for volume equivalent spheres.
+
+The following two subsections describe the parameterization of the
+optical properties of ice clouds and of the advection in detail.
+
+\subsection{Calculation of the radiative properties of ice clouds}
+
+\subsubsection{Procedure.}
+%
+Radiative properties of ice clouds in the RCM are described by the
+broadband transmittance and reflectance in the solar spectral range and
+in addition the emittance in the terrestrial spectral range. These
+quantities were calculated with a separate radiation transfer model
+(RTM) based on the Matrix Operator Method \citep{Pl73} by the following
+steps:
+
+\begin{enumerate}
+\item Calculation of the phase function $\phi$ (solar region), asymmetry
+factor $g$ (terrestrial region), volume extinction coefficient $\sigma$,
+and single scattering albedo $\omega$ on the basis of the particle-size
+distribution and the spectral complex refractive index of ice \citep{Wa84}.
+In the solar region these parameters are derived for hexagonally shaped
+particles under the assumption of geometrical optics \citep{He94}. In the
+terrestrial spectral range Mie-calculations have been performed for volume
+equivalent spheres.
+\item Calculation of spectral downward- and upward-directed radiative fluxes
+at cloud top and base with an RTM. The ice cloud layer is embedded between
+9.6 and 11.0\,km.
+\item Calculation of broadband transmittance, reflectance and emittance by
+use of wavelength integrated fluxes at cloud top and base within the solar
+and terrestrial spectral range.
+\end{enumerate}
+
+\begin{table}[b]
+\caption[]{Modelled size distribution of cirrus cloud particles. The particle
+concentration is 0.58\,cm$^{-3}$, the ice water content $2.077 \cdot
+10^{-3}$\,gm$^{-3}$}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{-1.75pt}}lcccc}
+\hline
+\noalign{\smallskip}
+size class & represented size range & $A$ & $B$ & particle number \\
+ & $\mu$m & $\mu$m & $\mu$m & m$^{-3}$ \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+I & 2 -- 6 & \phantom{.}1.4 & \phantom{1.}3.5 & $1.69\cdot 10^5 $ \\
+II & \phantom{1}6 -- 20 & \phantom{11}4 & \phantom{11}10 & $3.87\cdot 10^5 $ \\
+III & 20 -- 40 & \phantom{1}10 & \phantom{11}30 & $1.77\cdot 10^4 $ \\
+IV & 40 -- 90 & \phantom{1}22 & \phantom{11}60 & $3.19\cdot 10^3 $ \\
+V & \phantom{1}90 -- 200 & \phantom{1}41 & 130 & $1.40\cdot 10^3 $ \\
+VI & 200 -- 400 & \phantom{1}60 & \phantom{1}300 & $1.75\cdot 10^2 $ \\
+VII & 400 -- 900 & \phantom{1}80 & \phantom{1}600 & $3.16\cdot 10^1 $ \\
+VIII & \phantom{1}900 -- 2000 & 110 & 1300 & $3.99\cdot 10^0 $ \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:1}
+\end{table}
+
+\subsubsection{Microphysical properties of cirrus and contrails.}
+%
+Size distributions are specified for two cloud types: cirrus and
+contrails. Table~\ref{tab:1} gives the discretized cirrus size distribution
+as derived from two separate data sources. A and B designate the half
+width and the length of the representative hexagonal ice particles. For
+cirrus cloud particles smaller than 20\,$\mu$m the size distribution is
+based on in situ measurements as presented in Sect.~\ref{sec:2}. For cirrus
+cloud particles larger than 20\,$\mu$m the size distribution is based on a
+parameterization of \citet{He84} (using a revised version in
+\citet{Li92}), which is a function of temperature. For reasons of
+consistency, the range $-55^{\circ}$C to $-60^{\circ}$C is used here,
+because temperature values within this range were measured during the
+flight in the cloud on 15 October 1992. Taking the particle numbers of
+\citet{He84,Li92} directly, however, leads to a significantly smaller
+ice water content than that measured by these two papers, which is
+$2.077 \cdot 10^{-3}$gm$^{-3}$. We assume that this discrepancy is due
+to the assumption that particles in our model have hexagonal shapes in
+all size classes, whereas the measurements show aggregates in the range
+of larger particles. For a certain diameter, an aggregate contains a
+significantly larger volume than a column. In order to adjust the ice
+water content value in the model to the measured value, particle numbers
+in size classes V to VIII were increased by a factor of 3.47.
+
+For consistency of the following comparison the ice water content within
+contrails is assumed to be the same as that for the natural cirrus case.
+Having no precise information on particle number densities for sizes
+larger than 20\,$\mu$m, we assume that the relative particle size
+distribution is the same as that for the natural cirrus case
+(Table~\ref{tab:1}), through, with an upper size limit of 200\,$\mu$m. This
+gives also qualitative agreement with the measurements of \citet{Ga96}.
+As a result of the adjustment of the ice water content there are more
+small particles in contrails than in natural cirrus, which is consistent
+with our measurements.
+
+\begin{table}
+\caption[]{Modeled size distribution of contrail particles. The particle
+concentration is 1.0\,cm$^{-3}$, the ice water content $2.077 \cdot
+10^{-3}$\,gm$^{-3}$}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{-1.75pt}}lcccc}
+\hline
+\noalign{\smallskip}
+size class & represented size range & $A$ & $B$ & particle number \\
+& $\mu$m & $\mu$m & $\mu$m & m$^{-3}$ \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+I & 2 -- 6 & \phantom{.}1.4 & \phantom{.}3.5 & $2.91\cdot 10^5 $ \\
+II & \phantom{1}6 -- 20 & \phantom{11}4 & \phantom{11}10 & $6.67\cdot 10^5 $ \\
+III & 20 -- 40 & \phantom{1}10 & \phantom{11}30 & $3.05\cdot 10^4 $ \\
+IV & 40 -- 90 & \phantom{1}22 & \phantom{11}60 & $5.51\cdot 10^3 $ \\
+V & \phantom{1}90 -- 200 & \phantom{1}41 & \phantom{1}130 & $2.42\cdot 10^3 $ \\
+VI & 200 -- 400 & \phantom{1}60 & \phantom{1}300 & $0 $ \\
+VII & 400 -- 900 & \phantom{1}80 & \phantom{1}600 & $0 $ \\
+VIII & \phantom{1}900 -- 2000 & 110 & 1300 & $0 $ \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:2}
+\end{table}
+
+\begin{figure}[b]
+\unitlength0.9cm
+\begin{picture}(8.575,7)
+\framebox(8.575,7){}
+\end{picture}
+\caption{Modelled size distributions ({\it steps}) for natural cirrus ({\it
+solid}) and contrails ({\it dashed}). Also shown are replicator measured size
+distributions as indicted in Fig.~\ref{fig:4} for natural cirrus ({\it
+solid}) and contrails ({\it dashed})}
+\label{fig:6}
+\end{figure}
+
+\subsubsection{Radiative properties of contrails and natural cirrus clouds.}
+%
+The radiative transfer model adopted to calculate vertical profiles of
+upward- and downward-directed fluxes is based on the matrix operator
+theory \citep{Pl73}. This RTM accounts for processes of multiple
+scattering, absorption and thermal emission. The cloud optical
+properties are described by $\phi$ (solar), $g$ (terrestrial), $\sigma$
+and $\omega$. Besides the cloud parameters, the RTM needs the
+corresponding optical parameters for aerosol particles. Furthermore, the
+vertical profiles of temperature, pressure and air density, as well as
+the absorber masses of the relevant gases, characterize the atmospheric
+state. These meteorological parameters are given for our model
+atmospheres in Appendix~B. Table~\ref{tab:6} in Appendix~A shows the
+spectral resolution within the solar spectral range as used in the RTM.
+
+In the solar region, the sharp forward peak of the cirrus phase function
+is truncated by applying the delta-function approximation. In the
+terrestrial range, a Henyey-Greenstein approximation of the phase
+function is adopted which depends only on the asymmetry factor. The
+transmission functions of the relevant gases valid in the spectral
+subintervals are approximated by exponential sum fitting.
+
+Table~\ref{tab:7} in Appendix~A gives the values of $C$, $g$ and
+$\omega$ for the cirrus and contrail cloud as calculated for hexagonally
+shaped particles with geometrical optics. $C$ designates the extinction
+cross-section and equals the extinction coefficient normalized to one
+particle per cm$^{-3}$. Note that the $g$ values are shown in the table
+but subsequently are not used. For the model calculations, the complete
+phase function is used. Note that the spectral resolution is not
+identical to that in the RTM (see Table~\ref{tab:6}), however, it accounts
+for a proper representation of the radiative properties which in turn
+mainly follow the spectral behaviour of the complex refractive index of
+ice. Phase functions are calculated at wavelengths 0.550, 1.100, 1.400,
+1.905, 2.600 and 3.077$\mu$m. These wavelengths are chosen as
+representative with respect to the spectral behaviour of the refractive
+index of ice.
+
+To obtain the analogous values for the RTM input spectral intervals
+(Table~\ref{tab:6}), a proper mean value is calculated by
+\begin{equation}
+\overline{x_j} = \frac{\sum_{i} x_i E_i \Delta \lambda_{i,j}}{\sum_{i} E_i
+\Delta \lambda_{i,j}},
+\label{eq:1}
+\end{equation}
+where $x$ represents the variables $\sigma$ and $\omega$,
+$\overline{x_j}$ designates the mean value of the $j$th spectral
+interval $\sum_{i} \Delta \lambda_{i,j}$ within the solar spectral
+range. The variable $E_i$ is the solar constant at the wavelength $i$.
+
+The first column in Table~\ref{tab:8} in Appendix~A shows the spectral
+resolution in the terrestrial region used by the RTM. In order to obtain
+$\sigma$, $g$ and $\omega$ values in the terrestrial region,
+Mie-calculations for corresponding spherical particles were carried out
+within each spectral interval at its central wavelength given in
+Table~\ref{tab:8}, where the conversion from hexagonal particles into
+corresponding spheres is done by calculation of equivalent volume. It is
+expected that such spheres give better $\omega$ values compared to
+spheres of equal surface \citep{Ta89}.
+
+Downward- and upward-directed solar fluxes at cloud top and base result
+from RTM calculations for the isolated cloud layer as radiative transfer
+medium. In a next step, the cloud transmittance is derived by relating
+the downward directed fluxes at cloud top and base, respectively. The
+ratio of upward and downward flux at cloud top correspondingly gives the
+cloud reflectance. Solar zenith angles are cosine weighted means over
+the solar day for July and October in Munich. Results are shown in
+Table~\ref{tab:3}.
+
+\begin{table}
+\caption{Solar radiative properties of cirrus and contrails as derived from
+RTM calculations (Jci: July, cirrus, Jco: July, contrails, Oci: October,
+cirrus, Oco: October, contrails)}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{\fill}}cccc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+case & solar zenith angle & transmittance & reflectance \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+Jci & 58.71 $^{\circ}$ &0.932 & 0.057 \\
+Jco & 58.71 $^{\circ}$ &0.908 & 0.080 \\
+Oci & 69.78 $^{\circ}$ &0.891 & 0.095 \\
+Oco & 69.78 $^{\circ}$ &0.855 & 0.131 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:3}
+\end{table}
+
+As expected, transmittances increase and reflectances decrease with
+decreasing particle concentration. The extinction coefficient value is
+found to be 0.130 and 0.198\,km$^{-1}$ for cirrus and contrails,
+respectively, at a wavelength of 0.55\,$\mu$m. Values of the cloud
+optical thickness at a wavelength of 0.55\,$\mu$m are 0.18 and 0.28 for
+cirrus and contrails, respectively.
+
+To obtain emittance, transmittance and reflectance in the terrestrial
+spectral range, RTM calculations were carried out for two different
+vertical atmospheric segments: (1) the atmosphere between surface and
+cloud top and (2) the cloud layer only. The first serves to obtain the
+upward fluxes at cloud top $f_{top} \uparrow $ and cloud base $f_{base}
+\uparrow $, the latter gives the fluxes emitted by the cloud layer
+itself, designated as $fcl_{top} \uparrow $ and $fcl_{base} \downarrow
+$. The upward-directed emittance is calculated according to $fcl_{top}
+\uparrow $ / $\varsigma T_{top}^4$ , where $\varsigma$ denotes the
+Stefan--Boltzmann constant and $T_{top}$ the temperature at cloud top.
+The downward-directed emittance is calculated analogously. In the RCM
+the mean of these two emittance values is used. The transmittance is
+given by $(f_{top} \uparrow - fcl_{top} \uparrow )/f_{base} \uparrow$,
+the reflectance by $( f_{base} \downarrow - fcl_{base} \downarrow
+)/f_{base} \uparrow$. Table~\ref{tab:4} lists the results, Table~\ref{tab:5}
+presents the derived values for cloud emittance, transmittance and
+reflectance.
+
+\begin{table}
+\caption{Radiative fluxes in the terrestrial spectral range; $f_{top}
+\uparrow$: upward flux at cloud top, $f_{base} \uparrow$: upward flux at
+cloud base, $f_{base} \downarrow$: downward flux at cloud base,
+$fcl_{top} \uparrow$: upward flux at cloud top (cloud only), $fcl_{base}
+\downarrow$: downward flux at cloud base (cloud only), other
+designations as in Table~\ref{tab:3}}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{\fill}}cccccc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+case & $f_{top} \uparrow $ & $f_{base} \uparrow $ & $ f_{base} \downarrow $
+& $fcl_{top} \uparrow $ & $fcl_{base} \downarrow $ \\
+& Wm$^{-2}$ & Wm$^{-2}$ & Wm$^{-2}$ & Wm$^{-2}$ & Wm$^{-2}$ \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+Jci & 245.1 & 286.7 & 75.5 & 57.0 & 59.9 \\
+Jco & 231.8 & 286.7 & 86.3 & 62.2 & 65.3 \\
+Oci & 238.5 & 272.3 & 54.4 & 43.4 & 45.5 \\
+Oco & 227.8 & 272.3 & 62.9 & 48.7 & 51.0 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:4}
+\end{table}
+
+\begin{table}[b]
+\caption{Derived ice cloud radiative properties in the terrestrial spectral
+range}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{\fill}}lccc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+case & emittance & transmittance & reflectance \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+Jci & 0.386 & 0.656 & 0.054 \\
+Jco & 0.421 & 0.592 & 0.073 \\
+Oci & 0.320 & 0.716 & 0.033 \\
+Oco & 0.359 & 0.658 & 0.044 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:5}
+\end{table}
+
+As expected, emittances and reflectances increase with increasing particle
+concentration whereas transmittances decrease with increasing particle
+concentrations.
+
+\subsection{Parameterization of advection}
+
+\subsubsection{Method.}
+%
+In our case study an atmospheric segment with vertical boundaries along
+the region of southern Germany is modelled. For simplicity it is called
+in the following an `atmospheric box'. In contrast to modelling on a
+global scale, net fluxes of energy through the lateral boundaries of
+this atmospheric box have to be taken into account. It is assumed that
+the net energy flux which leaves the top of the box as radiation (in the
+considered time period) equals the energy flux which is gained through
+the lateral faces as advection. The profile of advected energy is set
+proportional to the wind profile. The value of the energy flux leaving
+the atmospheric box at the top is taken from ERBE (Earth Radiation
+Budget Experiment) satellite data. This flux is $-59$ and 97\,Wm$^{-2}$
+in the months of July and October, respectively, the minus sign in the
+July case representing an energy gain for the box. More details
+concerning the satellite data are given in Appendix~B. Values for the
+vertical profile of the wind speed are taken from radiosonde data,
+'Munich' station, averaged for the years 1981--1985.
+
+Within the frame of this study, no feedback mechanisms concerning
+advection are taken into consideration.
+
+\subsubsection{Results of regionalization.}
+%
+Figure~\ref{fig:7} shows RCM results for the reference case, i.e. the case
+with climatological values of cirrus cloud cover in July. Two
+temperature profiles are shown: one results from including advection as
+already outlined, whereas the other results from neglecting it. For
+comparison, the climatological July values as derived from radiosonde
+data are shown.
+
+\begin{figure}[b]
+\unitlength0.9cm
+\begin{picture}(8.575,7)
+\framebox(8.575,7){}
+\end{picture}
+\caption{Modelled temperature profiles for July with ({\it solid}) and without
+({\it dashed}) advection compared to radiosonde measurements ({\it triangles})}
+\label{fig:7}
+\end{figure}
+
+Calculated temperatures fit quite well throughout the whole troposphere.
+A small inversion layer is modelled at the surface but not seen in the
+climatology values. This indicates that the Bowen ratio might not be
+representative for this case, however, in this study only temperature
+differences are of interest.
+
+\begin{figure}
+\unitlength0.9cm
+\begin{picture}(8.575,7)
+\framebox(8.575,7){}
+\end{picture}
+\caption{As in Fig.~\ref{fig:1}., but for October conditions}
+\label{fig:8}
+\end{figure}
+
+Figure~\ref{fig:8} shows corresponding temperature profiles for October
+conditions. Noteworthy is the great influence of advection inducing a
+temperature difference of approximately 25\,K throughout the
+troposphere. It is important to note that the uncertainty of the
+satellite data is in the order of 10\,Wm$^{-2}$ which corresponds to an
+uncertainty in the temperature profile in the order of only 3\,K.
+
+%%%%%%%%%%%%%
+% Section 4 %
+%%%%%%%%%%%%%
+
+\section{Results and discussion}
+\label{sec:4}
+
+The impact of ice clouds induced by air traffic is estimated by
+comparing the RCM results for an increased high cloud cover with those
+for the reference cases in July and October. It is assumed that the ice
+cloud cover increases at the expense of the uncovered area.
+
+The surface temperature results are shown in Fig.~\ref{fig:9}. An ice
+cloud cover increase due to contrails by 10\% causes surface temperature
+increases of 1.1 and 0.8\,K\, in July and October, respectively.
+Assuming that the increased cloud cover is due to clouds which have
+natural cirrus properties, these values are 1.2 and 0.9\,K,
+respectively. Thus, for both months the increase in high cloud cover due
+to natural cirrus warms the surface more than the increase due to
+contrails. Obviously, the primarily larger shortwave albedo of the
+contrails due to more smaller particles leads to less warming than in
+the case of natural cirrus, even if the emittance of contrails is larger
+than that of natural cirrus. Figure~\ref{fig:9} shows a linear relation
+between cloud cover and surface temperature, because the RCM weights
+flux linearly with cloud cover. Part of the contrails certainly will
+occur over mid- and low-level clouds. Since the RCM does not consider
+overlapping effects of several cloud layers, our values for surface
+warming represent an upper limit.
+
+\begin{figure}
+\unitlength0.9cm
+\begin{picture}(8.575,7)
+\framebox(8.575,7){}
+\end{picture}
+\caption{Increase in surface temperature $\Delta T_{surf} $ in
+dependence on additional ice cloud cover $\eta $ due to contrails and
+cirrus in the case of mean July and October conditions over southern
+Germany. {\it Solid}: July, cirrus; {\it dotted}: July, contrails; {\it
+dashed}: October, cirrus; {\it dash-dotted}: October, contrails}
+\label{fig:9}
+\end{figure}
+
+As a further result the radiative forcing at the top of the atmosphere
+with a fixed temperature and humidity profile is obtained. In the July
+case the upward terrestrial flux at the top af the atmosphere is reduced
+by 3.3\,Wm\,$^{-2}$ in the case of a 10\% increase in cirrus cloud
+cover. The corresponding decrease in the solar flux is 0.5\,Wm\,$^{-2}$.
+In the October case, the terrestrial flux is reduced by
+2.6\,Wm\,$^{-2}$, and the solar flux by 0.1\,Wm\,$^{-2}$. The values in
+the contrail cases are slightly lower.
+
+The current cloud cover which is due to contrails and thereby obviously
+due to air traffic is estimated to be in the order of 0.5\% over Europe
+\citep{Ba94}. This increase in cloud cover might be regarded as the
+minimum amount of air traffic induced cloud cover. Therefore it is
+expected that the increases in surface temperature are approximately
+0.06 and 0.05\,K in July and October, respectively.
+
+With regard to the uncertainty in our results, we varied the advection
+term by 10\,Wm$^{-2}$ (that corresponds to an uncertainty of
+10\,Wm$^{-2}$ in the satellite radiation measurement), the resulting
+uncertainty in the surface temperature is about 0.02\,K (change from
+96.75 to 106.75\,Wm$^{-2}$ in the satellite measured net radiative flux
+for the October case). Assuming a doubling of the latent heat flux at
+surface (which is much more than a realistic assumption), the resulting
+uncertainty in the surface temperature is about 0.01\,K (in the October
+case). These values show that these uncertainties have no important
+influence on the results.
+
+In comparison to a corresponding global sensitivity study for the
+climatic effect of an additional contrail cloudiness in the North
+Atlantic region \citep{Po96}, our value for the increase in the surface
+temperature in July is larger (1.2\,K compared to 1\,K). However, in
+this GCM calculation, the ocean temperature was fixed, and so the true
+response of additional cloudiness is slightly underestimated.
+
+The question of the climatic importance is relative: compared to an
+increase in the temperature of 1\,K between the Middle Ages and today,
+our 0.05\,K value is surely not significant. On the other hand, climate
+change is a composite of multiple effects and one should keep air
+traffic in mind as being one of these. Furthermore, our results
+represent equilibrium conditions, and the question of possible effects
+in the non-equilibrium state remains open, e.g. influences in the
+day-to-night differences in temperature.
+
+The results give an idea of how sensitive the regional temperature
+profile reacts on changes in the ice cloud layer which are due to
+changes in cloud cover, radiative properties of the ice clouds and solar
+zenith angle. However, we must keep in mind that our results are based
+on the assumption that the radiation balance on top of the atmosphere is
+fixed to the value that belongs to the undisturbed case and further that
+large-scale advection of energy into the area does not change. In view
+of the small temperature changes induced by the changes in cirrus cloud
+cover, these assumptions are expected to be fulfilled to a first order,
+and our results represent an upper limit of the regional effects of an
+additional cloudiness caused by air traffic. This is also supported by
+the results from a three-dimensional GCM which include feedback
+mechanisms and show the same order of magnitude \citep{Po96}.
+
+\begin{acknowledgement}
+For friendly help concerning the albedo values and discussions on
+aerosol distributions we thank W. Thomas. Concerning ERBE data our
+thanks are given to M. Rieland and K. Standfuss (Meteorologisches
+Institut der Universitaet Hamburg). Last but not least we are very
+grateful to K.N. Liou and S.C. Ou for having made available to us a
+version of their radiative convective model. This work was supported by
+the Bavarian regional climate research programme (BayFORKLIM), which was
+funded by the 'Bayerisches Ministerium fuer Landesentwicklung und
+Umweltfragen'. Their financial support is greatly acknowledged. Topical
+Editor L. Eymard thanks P. Hignett and S. Kinne for their help in
+evaluating this paper.
+\end{acknowledgement}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Correct space for this article! %%
+\vspace{-5pt} %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{table}[b]
+\caption[]{Spectral resolution in the solar spectral range}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{10pt}}cc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+interval number & wavelength range \\
+& $\mu$m \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+1 & 0.20 -- 0.30 \\
+2 & 0.30 -- 0.35 \\
+3 & 0.35 -- 0.40 \\
+4 & 0.40 -- 0.45 \\
+5 & 0.45 -- 0.50 \\
+6 & 0.50 -- 0.55 \\
+7 & 0.55 -- 0.60 \\
+8 & 0.60 -- 0.80 \\
+9 & 0.80 -- 0.90 \\
+10 & 0.90 -- 1.00 \\
+11 & 1.00 -- 1.20 \\
+12 & 1.20 -- 1.60 \\
+13 & 1.60 -- 2.20 \\
+14 & 2.20 -- 3.00 \\
+15 & 3.00 -- 3.40 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:6}
+\end{table}
+
+\begin{appendix}
+
+\section*{Appendix A}
+\label{sec:a}
+
+\subsection*{Tables indicating RTM calculations}
+
+These tables, referred to in the text, are put in an Appendix for
+reasons of clarity and readability.
+
+\begin{table}
+\caption[]{Optical parameters of cirrus and contrail used in the solar
+region. Symbols without a hat denote cirrus parameters, symbols with a
+hat denote contrail parameters}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{-.8pt}}ccccccc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+$\lambda$& $C$ & $\hat{C}$ & $g$ & $\hat{g}$ & $\omega $ & $\hat{\omega}$ \\
+$\mu$m & m$^{-1}cm^3$ & m$^{-1}cm^3$ & & & & \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+0.423 & 2.25$\cdot 10^{-4}$ & 1.99$\cdot 10^{-4}$ & 0.752 & 0.746 & 1.000 & 1.000 \\
+0.550 & 2.25$\cdot 10^{-4}$ & 1.99$\cdot 10^{-4}$ & 0.757 & 0.751 & 1.000 & 1.000 \\
+0.635 & 2.25$\cdot 10^{-4}$ & 1.99$\cdot 10^{-4}$ & 0.760 & 0.753 & 1.000 & 1.000 \\
+0.780 & 2.26$\cdot 10^{-4}$ & 1.99$\cdot 10^{-4}$ & 0.762 & 0.755 & 1.000 & 1.000 \\
+0.830 & 2.26$\cdot 10^{-4}$ & 1.99$\cdot 10^{-4}$ & 0.762 & 0.754 & 1.000 & 1.000 \\
+0.015 & 2.26$\cdot 10^{-4}$ & 1.99$\cdot 10^{-4}$ & 0.764 & 0.756 & 0.999 & 1.000 \\
+1.100 & 2.26$\cdot 10^{-4}$ & 1.99$\cdot 10^{-4}$ & 0.766 & 0.759 & 0.999 & 1.000 \\
+1.200 & 2.26$\cdot 10^{-4}$ & 1.99$\cdot 10^{-4}$ & 0.768 & 0.761 & 0.998 & 0.999 \\
+1.400 & 2.26$\cdot 10^{-4}$ & 2.00$\cdot 10^{-4}$ & 0.771 & 0.764 & 0.995 & 0.997 \\
+1.449 & 2.29$\cdot 10^{-4}$ & 2.02$\cdot 10^{-4}$ & 0.789 & 0.778 & 0.943 & 0.959 \\
+1.504 & 2.32$\cdot 10^{-4}$ & 2.03$\cdot 10^{-4}$ & 0.804 & 0.792 & 0.900 & 0.924 \\
+1.615 & 2.30$\cdot 10^{-4}$ & 2.02$\cdot 10^{-4}$ & 0.791 & 0.779 & 0.939 & 0.956 \\
+1.850 & 2.27$\cdot 10^{-4}$ & 2.00$\cdot 10^{-4}$ & 0.785 & 0.777 & 0.985 & 0.990 \\
+1.905 & 2.31$\cdot 10^{-4}$ & 2.03$\cdot 10^{-4}$ & 0.803 & 0.793 & 0.930 & 0.950 \\
+2.000 & 2.37$\cdot 10^{-4}$ & 2.07$\cdot 10^{-4}$ & 0.831 & 0.819 & 0.844 & 0.874 \\
+2.190 & 2.30$\cdot 10^{-4}$ & 2.02$\cdot 10^{-4}$ & 0.807 & 0.798 & 0.959 & 0.972 \\
+2.600 & 2.35$\cdot 10^{-4}$ & 2.06$\cdot 10^{-4}$ & 0.867 & 0.859 & 0.910 & 0.933 \\
+3.077 & 2.59$\cdot 10^{-4}$ & 2.28$\cdot 10^{-4}$ & 0.941 & 0.938 & 0.534 & 0.534 \\
+3.413 & 2.52$\cdot 10^{-4}$ & 2.21$\cdot 10^{-4}$ & 0.878 & 0.869 & 0.606 & 0.614 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:7}
+\end{table}
+
+\begin{table}
+\caption[]{Optical parameters of cirrus and contrail cloud models in the
+terrestrial region. Symbols without a hat denote cirrus parameters,
+symbols with a hat denote contrail parameters}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{\fill}}ccccccc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+$\lambda$& $\sigma$ & $\hat{\sigma}$ & $g$ & $\hat{g}$ & $\omega $ & $\hat{\omega}$ \\
+$\mu$m & km$^{-1}$ & km$^{-1}$ &-&-&-&-\\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+\phantom{1}4.08 &0.1623 &0.2553 &0.830 &0.820 &0.748 &0.769 \\
+\phantom{1}4.26 &0.1728 &0.2715 &0.852 &0.844 &0.727 &0.746 \\
+\phantom{1}4.40 &0.1696 &0.2669 &0.875 &0.868 &0.693 &0.709 \\
+\phantom{1}4.49 &0.1783 &0.2813 &0.880 &0.874 &0.676 &0.690 \\
+\phantom{1}4.65 &0.1732 &0.2722 &0.874 &0.867 &0.701 &0.718 \\
+\phantom{1}4.88 &0.1938 &0.3082 &0.863 &0.857 &0.783 &0.804 \\
+\phantom{1}5.13 &0.1895 &0.3010 &0.871 &0.866 &0.791 &0.813 \\
+\phantom{1}5.41 &0.1951 &0.3091 &0.886 &0.881 &0.764 &0.785 \\
+\phantom{1}5.71 &0.1748 &0.2768 &0.909 &0.905 &0.684 &0.698 \\
+\phantom{1}6.06 &0.1727 &0.2742 &0.918 &0.914 &0.608 &0.615 \\
+\phantom{1}6.45 &0.1742 &0.2763 &0.904 &0.899 &0.638 &0.648 \\
+\phantom{1}6.90 &0.1639 &0.2574 &0.904 &0.898 &0.634 &0.645 \\
+\phantom{1}7.41 &0.1670 &0.2618 &0.896 &0.889 &0.649 &0.661 \\
+\phantom{1}8.00 &0.1628 &0.2557 &0.891 &0.884 &0.669 &0.683 \\
+\phantom{1}8.70 &0.1485 &0.2300 &0.897 &0.890 &0.671 &0.688 \\
+\phantom{1}9.30 &0.1429 &0.2197 &0.902 &0.894 &0.639 &0.654 \\
+\phantom{1}9.76 &0.1266 &0.2927 &0.913 &0.905 &0.612 &0.625 \\
+10.53 &0.1048 &0.2541 &0.947 &0.938 &0.426 &0.412 \\
+11.76 &0.1399 &0.2138 &0.883 &0.871 &0.441 &0.429 \\
+12.90 &0.1597 &0.2496 &0.846 &0.835 &0.468 &0.460 \\
+13.79 &0.1570 &0.2429 &0.841 &0.829 &0.500 &0.495 \\
+14.81 &0.1845 &0.2889 &0.804 &0.790 &0.547 &0.548 \\
+16.00 &0.1686 &0.2627 &0.798 &0.783 &0.580 &0.586 \\
+18.18 &0.1449 &0.2188 &0.768 &0.747 &0.629 &0.644 \\
+22.22 &0.1193 &0.1747 &0.752 &0.729 &0.732 &0.763 \\
+28.57 &0.0902 &0.1232 &0.793 &0.763 &0.605 &0.631 \\
+40.00 &0.0829 &0.1148 &0.847 &0.811 &0.350 &0.314 \\
+66.67 &0.1107 &0.1511 &0.684 &0.621 &0.406 &0.380 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:8}
+\end{table}
+
+\section*{Appendix B}
+\label{sec:b}
+
+\subsection*{Input parameters for the radiative convective model and the
+matrix operator model}
+
+This appendix summarizes the input parameters describing atmospheric
+conditions for the RCM as well as for the matrix operator model in the
+cases of both months studied, July and October.
+
+Tables~\ref{tab:9} and~\ref{tab:10} list the input parameters concerning
+the atmospheric conditions in the case of July and October, respectively
+from radiosonde data. Temperatures are used as starting point for the
+RCM calculations and data for modelling the optical properties of the
+cirrus cloud layer. The data are taken from radiosonde measurements
+averaged over the years 1981 to 1985, DWD (Deutscher Wetterdienst)
+station Munich, except the humidity values in 100 and 150\,hPa, which
+are averages from 1987 to 1989 due to lack of corresponding values in
+the mentioned time-period.
+
+\begin{table}[b]
+\caption[]{Radiosonde values over southern Germany in the month of July,
+averages from 1981 to 1985}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{\fill}}ccccc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+height & pressure & temperature & air density &
+humidity \\ km & hPa & K & g\,cm$^{-3}$ & \% \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+31.85 & \phantom{1}10 & 233.6 & 14.91 & \\
+27.13 & \phantom{1}20 & 227.4 & 30.64 & \\
+24.43 & \phantom{1}30 & 223.9 & 46.68 & \\
+21.09 & \phantom{1}50 & 220.4 & 79.03 & \\
+18.91 & \phantom{1}70 & 218.5 & 111.6 & \\
+16.62 & 100 & 218.1 & 159.7 & 19.5 \\
+14.01 & 150 & 220.0 & 237.5 & 20.6 \\
+12.15 & 200 & 220.1 & 316.5 & 40.3 \\
+10.70 & 250 & 224.2 & 388.4 & 44.5 \\
+\phantom{1}9.47 & 300 & 232.5 & 449.5 & 44.4 \\
+\phantom{1}7.44 & 400 & 248.1 & 561.5 & 42.9 \\
+\phantom{1}5.78 & 500 & 259.7 & 670.2 & 44.2 \\
+\phantom{1}3.13 & 700 & 275.5 & 883.1 & 58.5 \\
+\phantom{1}1.54 & 850 & 285.2 & 1033.8 & 67.6\\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:9}
+\end{table}
+
+\begin{table}[b]
+\caption[]{Radiosonde values over southern Germany in the month of
+October, averages from 1981 to 1985}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{\fill}}ccccc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+height & pressure & temperature & air density & humidity \\
+km & hPa & K & g\,cm$^{-3}$ & \% \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+31.01 & \phantom{1}10 & 222.5 & 15.66 & \\
+26.50 & \phantom{1}20 & 218.2 & 31.93 & \\
+23.91 & \phantom{1}30 & 216.0 & 48.38 & \\
+20.67 & \phantom{1}50 & 214.3 & 81.28 & \\
+18.55 & \phantom{1}70 & 213.9 & 114.0 & \\
+16.30 & 100 & 213.4 & 163.2 & 18.9 \\
+13.75 & 150 & 213.8 & 244.4 & 20.8 \\
+11.94 & 200 & 215.2 & 323.8 & 33.2 \\
+10.52 & 250 & 220.8 & 394.4 & 35.2 \\
+\phantom{1}9.31 & 300 & 228.7 & 457.0 & 37.6 \\
+\phantom{1}7.32 & 400 & 243.9 & 571.3 & 34.1 \\
+\phantom{1}5.68 & 500 & 255.7 & 681.2 & 35.7 \\
+\phantom{1}3.08 & 700 & 271.2 & 899.2 & 46.3 \\
+\phantom{1}1.51 & 850 & 279.5 & 1059. & 56.1 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:10}
+\end{table}
+
+Humidity values above 100\,hPa as well as all other values above 10\,hPa
+are taken from McClatchey et al. (1972), mid-latitude summer atmosphere,
+1962 and US standard atmosphere for July and October, respectively.
+Surface values are 1981 to 1985 averages from the `Europaeischer
+Wetterbericht' \citep{DWD}, and ozone data are from DWD station
+Hohenpeissenberg (also 1981 to 1985).
+
+\subsection*{Cloud cover and liquid water path}
+
+Cloud cover values are taken from \citet{Wa88}. Values are based on
+ground observation averages between 1971 and 1981. Spatial resolution of
+these data is $5^{\circ} \times 5^{\circ}$, temporal resolution is 3
+months. The following classification is used: Cu, Cb, St, Ns, As, Ac,
+and Ci. To get cloud cover values for the three cloud layers in the RCM,
+Cu, Cb, St, Ns are chosen to give the low cloud cover, Cb, Ns, As, Ac to
+give the mid-level cloud cover and Ci to give the high cloud cover,
+following a procedure used by Liou in the original version of the RCM
+\citep{Li85}. This leads to cloud cover values 0.31, 0.21, 0.07 and 0.41
+for low, middle, high clouds and clear sky, respectively in the month of
+July. The corresponding values for October are 0.56, 0.34, 0.16 and
+0.59, respectively.
+
+The RCM is unable to calculate interactions between clouds. Therefore,
+the radiative flux computations are performed for different atmospheres
+containing one cloud layer each for low, middle and high clouds and one
+clear atmosphere are calculated separately and radiation fluxes are
+weighted afterwards with the corresponding cloud-cover values. For this
+reason, the cloud-cover values given are compacted in the RCM. This is
+done by multiplication with a constant factor (less than 1) in the way
+that the sum of the cloud cover and the clear sky fraction add up to 1.
+Note, however, that the interaction between a single cloud layer and the
+surface is taken into consideration.
+
+The liquid water path value of low clouds is taken from \citet{Li83} as
+60.411\,g\,m$^{-2}$, that for mid-level clouds to 54.06\,g\,m$^{-2}$ in
+the present study. The ice water path for cirrus cloud is assumed to be
+2.908\,g\,m$^{-2}$ according to measurements of \citet{He84}.
+
+\subsection*{Surface albedo}
+
+The surface solar albedo values are taken from \citet{Ko92}. These
+values are based on satellite measurements. In the case of October,
+values from 10:00, 13:00 and 16:00 local time are available,
+corresponding to sun elevations of 26.87$^{\circ}$, 31.06$^{\circ}$ and
+12.29$^{\circ}$, respectively. Interpolation to 20.22$^{\circ}$
+elevation angle which is used in the RCM leads to an albedo of 11.3\%.
+This value is used for the October calculations.
+
+In the case of July, only the 13:00 local time value was available. This
+value is 15.6\%. Due to the fact that the albedo has a minimum value at
+the time of the highest sun elevation angles, an albedo value slightly
+higher than this value was chosen as representative in the July
+calculations. The value was estimated to be 17\% (W. Thomas, personal
+communication).
+
+\subsection*{Aerosol data}
+
+Aerosol data are chosen to represent continental conditions for both
+months studied, July and October (M. Hess and P. Koepke, personal
+communication). Table~\ref{tab:11} shows the assumed aerosol components
+and particle numbers. These values are valid for sea level. The dependence
+on altitude is modeled after
+\begin{equation}
+n(h) = n(0)exp(-h/Z),
+\label{eq:2}
+\end{equation}
+where $n$ denotes the particle number, $h$ the altitude and $Z$ a reference
+altitude which is 8\,km. For more details, including refractive indices,
+see \citet{WM83}.
+
+\begin{table}
+\caption[]{Aerosol conditions used for calculations}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{\fill}}llll@{\hspace{0pt}}}
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+height & aerosol type & number & mode radius \\
+km & & cm$^{-3}$ & $\mu$m \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+- 2 & water soluble (70\%)& 7000 & 0.0285 \\
+& insoluble & 0.4 & 0.471 \\
+& soot & 8300 & 0.0118 \\
+2-12 & water soluble (50\%)& 438 & 0.0262 \\
+& insoluble & 1.24$\cdot 10^{-3}$ & 0.471 \\
+& soot & 292 & 0.0118 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:11}
+\end{table}
+
+\subsection*{Satellite data used for parameterization of advection}
+
+Satellite data are taken from ERBE (Earth Radiation Budget Experiment)
+via the `Meteorologisches Institut der Universitaet Hamburg'. Spatial
+resolution of these data is $2.5^{\circ} \times 2.5^{\circ}$. The data
+are taken from 47.5$^{\circ}$ to 50.0$^{\circ}$N and 10.0$^{\circ}$ to
+12.5$^{\circ}$E and cover quite accurately the area of Bavaria, southern
+Germany. In the case of July, a 5-year average of monthly averaged net
+fluxes (top of atmosphere) is used (1985--1989). Values are 68.75,
+55.96, 54.63, 61.94 and 51.80\,Wm$^{-2}$ for the 5 months, respectively.
+The mean value used is 58.62\,Wm$^{-2}$. For October, corresponding data
+from 2 years 1985 and 1986 are used. Values are $-99.00$\,Wm and
+$-94.50$\,Wm$^{-2}$, respectively, and the mean value
+$-96.75$\,Wm$^{-2}$ is used.
+
+\subsection*{Bowen ratio data}
+
+The relation ship between surface fluxes of sensible and latent heat
+strongly dominates the temperature profile near surface. Values were
+taken from \citet{Be69}. These values were measured in 1964 on the area
+of a meteorological research station of the University of Munich,
+Germany, located in the surroundings of the city. It is not clear how
+representative they are these values are for whole southern Germany and
+how representative they are for a monthly mean averaged over many years.
+However, due to lack of better data these values, given in Table~\ref{tab:12}
+are used in the calculations.
+
+\begin{table}[t]
+\caption[]{Bowen ratios for July and October, southern Germany used in
+the calculations}
+\begin{tabular*}{84.22mm}{@{\hspace{0pt}\extracolsep{10pt}}cc@{\hspace{0pt}}}
+\hline
+\noalign{\smallskip}
+month & sensible heat / latent heat \\
+& $\rm Wm\it^{-2} /\rm Wm\it^{-2} $ \\
+\noalign{\smallskip}
+\hline
+\noalign{\smallskip}
+July & 24 / 130 \\
+October & 9 / 31 \\
+\noalign{\smallskip}
+\hline
+\end{tabular*}
+\label{tab:12}
+\end{table}
+
+\end{appendix}
+
+\begin{thebibliography}{}
+
+\bibitem[Arnott \etal(1994)]{Ar94} {\bf Arnott, W.P., Y.Y. Dong, J.
+Hallett, and M.R. Poellot}, Role of small ice crystals in radiative
+properties of cirrus: a case-study, FIRE II, November 22, 1991, {\it J.
+Geophys. Res.}, {\bf 99}, 1371--1381, 1994.
+
+\bibitem[Bakan \etal(1994)]{Ba94} {\bf Bakan, S., M. Betancor, V.
+Gayler, and H. Grassl}, Contrail frequency over Europe from
+NOAA-satellite images, {\it Ann. Geophysicae}, {\bf 12}, 962--968, 1994.
+
+\bibitem[Berz(1969)]{Be69} {\bf Berz, G.}, {\it Energiehaushalt der
+Bodenoberfl\"ache}, {\it Meteorologisches Institut der Universit\"at
+M\"unchen}, 1969.
+
+\bibitem[Deepak and Gerber(1983)]{WM83} {\bf Deepak, A., and H.E. Gerber
+(eds.)}, Report of the expert meeting on aerosols and their climatic
+effects, {\bf WCP-55}, 1983
+
+\bibitem[Deutscher Wetterdienst(1981)]{DWD} {\bf Europaeischer
+Wetterbericht}, DWD, Amtsblatt des Deutschen Wetterdienstes, D6168, ISSN
+0341-2970, 1981--1985.
+
+\bibitem[Gayet \etal(1996)]{Ga96} {\bf Gayet, J.-F., G. Febvre, G.
+Brogniez, H. Chepfer, W. Renger, and P. Wendling}, Microphysical and
+optical properties of cirrus and contrails: cloud field study on 13
+October 1989, {\it J. Atmos. Sci.}, {\bf 53}, 126--138, 1996.
+
+\bibitem[Hess and Wiegner(1994)]{He94} {\bf Hess, M., and M. Wiegner},
+COP: Data library of optical properties of hexagonal ice crystals, {\it
+Appl. Opt.}, {\bf 33}, 7740--7746, 1994.
+
+\bibitem[Heymsfield and Platt(1984)]{He84} {\bf Heymsfield, A.J., and
+C.M.R. Platt}, A parameterization of the particle size spectrum of ice
+clouds in terms of the ambient temperature and the ice water content,
+{\it J. Atmos. Sci.}, {\bf 41}, 846--855, 1984.
+
+\bibitem[Iaquinta \etal(1995)]{Ia95} {\bf Iaquinta, J., H. Isaka, and P.
+Personne}, Scattering phase function of bullet rosette ice crystals,
+{\it J. Atmos. Sci.}, {\bf 52}, 1401--1413, 1995.
+
+\bibitem[Koepke(1992)]{Ko92} {\bf Koepke, P., R. Meerkoetter, W. Thomas,
+and B. Vogel}, Albedo in Mitteleuropa aus METEOSAT-Minimumcounts, {\it
+Meteorologisches Institut der Universit\"at M\"unchen, Forschungsbericht
+`MIM-FB92-S4'}, 1992.
+
+\bibitem[Liou(1992)]{Li92} {\bf Liou, K.N.}, {\it Radiation and cloud
+processes in the atmosphere}, Oxford University Press, Oxford, 1992.
+
+\bibitem[Liou and Ou(1983)]{Li83} {\bf Liou, K.N., and S.C. Ou}, Theory
+of equilibrium temperatures in radiative-turbulent atmospheres, {\it J.
+Atmos. Sci.}, {\bf 40}, 214--229, 1983.
+
+\bibitem[Liou \etal(1985)]{Li85} {\bf Liou, K.N., S.C. Ou, and P.J. Lu},
+Interactive cloud formation and climatic temperature perturbations, {\it
+J. Atmos. Sci.}, {\bf 42}, 1969--1981, 1985.
+
+\bibitem[Liou \etal(1990)]{Li90} {\bf Liou, K.N., S.C. Ou, and G.
+Koenig}, An investigation on the climatic effect of contrail cirrus, in:
+{\it Air traffic and the environment -- background, tendencies and
+potential global atmospheric effects, Ed. U. Schumann, Proc. DLR Int.
+Coll., Bonn, Germany}, Springer, Berlin Heidelberg New York 1990.
+
+\bibitem[McClatchey \etal(1972)]{MC72} {\bf McClatchey, R.A., R.W. Fenn,
+J.E.A. Selby, F.E. Volz, and J.S. Garing}, Optical properties of the
+atmosphere (third edition), {\it Air Force Systems Command, United
+States Air Force, AFCRL-72-0497}, 1972.
+
+\bibitem[Macke(1993)]{Ma93} {\bf Macke, A.}, Scattering of light by
+polyhedral ice crystals, {\it Appl. Opt.}, {\bf 32}, 2780--2788, 1993.
+
+\bibitem[Plass \etal(1973)]{Pl73} {\bf Plass, G.N., G.W. Kattawar, and
+F.E. Catchings}, Matrix operator theory of radiative transfer. 1:
+Rayleigh scattering, {\it Appl. Opt.}, {\bf 12}, 314--329, 1973.
+
+\bibitem[Ponater \etal(1996)]{Po96} {\bf Ponater, M., S. Brinkop, R.
+Sausen, and U. Schumann}, Simulating the global atmospheric response to
+aircraft water vapour emissions and contrails: a first approach using a
+GCM, {\it Ann. Geophysicae}, {\bf 14}, 941--960, 1996.
+
+\bibitem[Schumann(1994)]{Schu94} {\bf Schumann, U.}, On the effect of
+emissions from aircraft engines on the state of the atmosphere, {\it
+Ann. Geophysicae}, {\bf 12}, 365--384,\break 1994.
+
+\bibitem[Stackhouse and Stephens(1991)]{St91} {\bf Stackhouse, P.W., and
+G.L. Stephens}, A theoretical and observational study of the radiative
+properties of cirrus: results from FIRE 1986, {\it J. Atmos. Sci.}, {\bf
+48}, 2044--2059, 1991.
+
+\bibitem[Strauss(1996)]{St96} {\bf Strauss, B.}, On the scattering
+behaviour of bullet-rosette and bullet-shaped ice crystals, {\it Ann.
+Geophysicae}, {\bf 14}, 566--573, 1996.
+
+\bibitem[Stroem(1993)]{St93} {\bf Stroem, J.}, Numerical and airborne
+experimental studies of aerosol and cloud properties in the troposphere,
+{\it Dissertation, Dep.\break Meteorology, Stockholm University, ISBN
+91-7153-168-8},\break 1993.
+
+\bibitem[Takano and Liou(1989)]{Ta89} {\bf Takano, Y.,and K.-N. Liou},
+Solar radiative transfer in cirrus clouds. Part I: single--scattering
+and optical properties of hexagonal ice crystals, {\it J. Atmos. Sci.},
+{\bf 46}, 3--19, 1989.
+
+\bibitem[Warren(1984)]{Wa84} {\bf Warren, S.G.}, Optical constants of
+ice from the ultraviolet to the microwave, {\it Appl. Opt.}, {\bf 23},
+1206--1223, 1984.
+
+\bibitem[Warren \etal(1988)]{Wa88} {\bf Warren, S.G., C.J. Hahn, J.
+London, R.M. Chervin, and R.L. Jenne}, Global distribution of total
+cloud cover and cloud type amounts over land, {\it NCAR, Technical
+Notes}, 1988.
+
+\bibitem[Wielicki \etal(1990)]{Wi90} {\bf Wielicki, B.A., J.T. Suttles,
+A.J. Heymsfield, R.M. Welch, J.D. Spinhirne, M.C. Wu, D.O'C. Starr, L.
+Parker, and R.F. Arduini}, The 27--28 October 1986 FIRE IFO cirrus
+study: comparison of radiative transfer theory with observations by
+satellite and aircraft, {\it Mon. Wea. Rev.}, {\bf 118}, 2356--2376,
+1990.
+
+\end{thebibliography}
+
+\end{document}