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diff --git a/macros/latex/contrib/springer/svjour/agp/example/example.tex b/macros/latex/contrib/springer/svjour/agp/example/example.tex new file mode 100644 index 0000000000..90fc830bbf --- /dev/null +++ b/macros/latex/contrib/springer/svjour/agp/example/example.tex @@ -0,0 +1,1277 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% 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. 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