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   pdfauthor = {Jan\ Hollan}%,
   pdftitle  = {No soon glaciation!},
   pdfsubject= {Milankovich forcing past and future},
   %pdfkeywords={Ice Age, insolation, glaciation}
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\title{No soon Ice Age, says astronomy}
\author{\www{Jan Hollan}{http://astro.sci.muni.cz/pub/hollan}}
\date{December 18., 2000}
\maketitle

I've read many times, that the onset of large climate changes is governed
by changes in insolation of various latitudes on the Earth due to changes
in the geometry of Earth movement
(Milanković theory, see
 \www{www.mpae.gwdg.de/EGS/egs\_info/milankovic.htm}
     {http://www.mpae.gwdg.de/EGS/egs_info/milankovic.htm}). 

I also remember an old misunderstanding, that as the Holocene is here for
ten thousand years already, it should end soon, as the last interglacial
(and also previous warm periods) did not last as long. 

However, if the driving factor is a change of insolation, we are not
limited to guessing that the present post-glacial period will be similar to
the previous ones, but we can rely on astronomical ephemerides of future
insolation.  They say clearly, that the present warm period is to last at
least as long as the past cold period! This holds for sure even with no
anthropogenic enhancement of the greenhouse effect.   

For the future one hundred thousand years the Earth orbit will be almost
circular, and therefore no very cold summers can appear in northern
latitudes. Cold summer millennia occur just then, when the Earth goes
through apohelion (farthest point of its orbit from the Sun) during the
northern warmest months, and when this apohelion is far indeed. The latter
condition is true only in times, when the orbital eccentricity is large.
It will be large only half a million years later, so there is no danger of
a glaciation before that.


%\begin[h]{figure}
\centerline{
\includegraphics[width=0.8\textwidth]{insolr}
}
%\caption{Global temperature and northern latitude insolation during 
% the last two glacial cycles} 
%\end{figure}

Now, let's visualise the correspondence between insolation and global
temperatures. To do that, data from \http{www.ngdc.noaa.gov/paleo} are
needed. The above picture made from them displays three curves. 
The top one gives the average insolation of 65 degrees northern latitude
(Watts per one square meter of a horizontal atmosphere) in mid-July. As
seen, it varies from some 390 to 490\,W/m$^2$ (the data are taken from
\cite{Berger}). 

The middle curve represents well the global temperatures. More accurately,
it partly neglects northern hemisphere, as the data are from the Antarctic
Vostok ice core \cite{Vostok}.

The bottom curve is from Greenland GRIP core; not the temperatures
themselves are given, but just relative abundances of an O$^{18}$ isotope. 
These are indicators of the ruling temperatures in the northern Atlantic. 
It is apparent that many abrupt changes appeared there, almost surely
caused by different states of warm northward Atlantic conveyor belt.
However, a smoothed curve would be quite similar to the middle one, i.e.,
the long-period temperature changes are really global.

%begin{latexonly}
 \parbox{0.45\textwidth}
%end{latexonly}
 {
 %\begin{figure}
\includegraphics[width=0.5\textwidth]{eiszeit}
 %\caption{Variation of methane and carbon dioxide atmospheric 
 %concentrations, enabling large temperature changes} 
 %\end{figure}
 }\hfill
%begin{latexonly}
 \parbox{0.45\textwidth}
%end{latexonly}
{The correspondence of insolation of northern latitudes and global
temperatures is striking. How is that possible? The answer is in trends of
glaciation. Warm northern summers tend to diminish the ice sheet, whereas
during cold ones (and warm winters with more precipitation) the permanent
snow cover grows. This affects not only the Earth albedo, but somehow also
the methane concentration in the atmosphere -- much methane is contained
in hydrates in permafrost and sea bottom in northern latitudes, and
warming can release much methane into the air. The large global
temperature changes are just triggered by changing insolation, their large
amplitude is however possible just through a large change in greenhouse
gases concentration, as figure 2 shows. 
The methane data are from \cite{Chapellaz}, 
CO$_2$ ones from \cite{Barnola}.
}

\bigskip
Now, the future. To get the insolation of the northern 65 degrees
parallel, I have employed the programme insola from \cite{Laskar}.
The result is in the following figure. 

\vfill

%\begin{figure}
\centerline{\includegraphics[width=0.9\textwidth]{insol65n}}
%\caption{Summer insolation of northern latitudes 
%during the last 0.26 and next 0.70 million years} 
%\end{figure}

You may note, that the values for the past 260 thousand years are a bit
higher than in the first figure. This is mostly due to a different 
part of summer for which the data hold (and to a different ``solar
constant'', I took 1366.3\,W/m$^2$). 

The main result is, that the mid-summer insolation of relevant northern
latitudes will be not as low as at the onset of the last glaciation
(110\,ka before) another 0.6\,Ma. The first ever pronounced fall of summer
insolation happens some 130 thousands years from now, but it is not at all
so deep as those ones that started the last two Ice Ages. So, we can say
there is no conceivable cause for another glaciation for at least those
130\,ka. Quite probably, another glaciation cannot come sooner that 620
thousand years from now. 

To be worried that ice sheets will spread soon is really a queer attitude. 
We should be more concerned with the possibility of a runoff greenhouse effect 
which could turn our Earth to another Venus before that half-a-million years!


\begin{thebibliography}{9}
\raggedright

\bibitem{Berger} Berger, A., 1992, Orbital Variations and Insolation
Database.  IGBP PAGES/World
 Data
Center-A for Paleoclimatology Data Contribution Series \# 92-007.
NOAA/NGDC
Paleoclimatology Program, Boulder CO, USA.
See \ftp{ftp.ngdc.noaa.gov/paleo/insolation}, file orbit91.

\bibitem{Vostok} Many authors, perhaps shortly J. Jouzel et al.; the file
with all explanation and data is \www
{ftp.ngdc.noaa.gov/paleo/icecore/antarctica/vostok/vostok\_deld.txt}
{ftp://ftp.ngdc.noaa.gov/paleo/icecore/antarctica/vostok/vostok_deld.txt}

\bibitem{GRIP} 
See  GRIP Ice Coring Effort, see file gripinfo.htm in
\http{www.ngdc.noaa.gov/paleo/icecore/greenland/summit/document/}

The O18 data, giving the past temperatures, are in the file gripd18o.txt in 
\ftp
{ftp.ngdc.noaa.gov/paleo/icecore/greenland/summit/grip/isotopes/}.
The first cited (most recent) paper on them is

Johnsen, S.J., H.B. Clausen, W. Dansgaard, N.S. Gundestrup, C.U. Hammer,
U.
Andersen, K.K. Andersen, C.S. Hvidberg, D. Dahl-Jensen, J.P. Steffensen,
H.
Shoji, A.E. Sveinbjörnsdóttir, J.W.C. White, J. Jouzel, and D. Fisher.
1997. The d18O record along the Greenland Ice Core Pproject deep ice core
and the problem of possible Eemian climatic instability. Journal of
Geophysical Research 102:26397-26410.

\bibitem{Chapellaz}
Chappellaz et al, Nature 345, 127-131 (1990). Data from 
\ftp{ftp.ngdc.noaa.gov/paleo/icecore/antarctica/vostok/ch4.txt}

\bibitem{Barnola}
Barnola et al,Nature, 329, 408-414 (1987). Data from 
 \ftp{ftp.ngdc.noaa.gov/paleo/icecore/antarctica/vostok/co2.txt}

\bibitem{Laskar}
\ftp{ftp.bdl.fr/pub/ephem/sun/la93}. The citation given there is:

Laskar, J., Joutel, F., Boudin, F.: 1993, Orbital, precessional
                  and insolation quantities for the Earth
                  from -20 Myr to + 10Myr
                  Astron. Astrophys. 270, 522

\end{thebibliography}

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