Ventana software support forum

Posted: **Fri Apr 03, 1998 11:19 pm**

Dear George Backus:
Your analysis on climate change is interesting, but I think you should add =
the extreme uncertainty concrning climate change mechanisms [non anthrop=
ic]. A prof of meteoroly at MIT [name escapes me, but I have the refer =
at home] stated that"science does not predict climate".
Pls find enclosed my analisis of C02 Mauna Loa data, which sheds a differ=
ent light.
Best
Roberto Vacca
Research Projects Leader
ISIS - Istituto di Studi per lInformatica e i Sistemi
Rome, Italy

THE 1976 DISCONTINUITY IN ATMOSPHERIC CO2 AND A CURVE FITTING EXERCISE =
ON 1959-76 DATA AND ON 1976-95 DATA.
by Roberto VACCA - Project Leader at ISIS, Istituto di Studi Per l Infor=
matica e i Sistemi, Rome, Italy - mc4634@mclink.it - December 27, 1997

The following table gives the annual averages of atmospheric CO2 concentr=
ation in Mauna Loa, Hawaii, as measured by C.D. Keeling and T.P. Whorf =
of the Scripps Institution of Oceanography of the University of Californi=
a

Annual Average
ppm

1959
315.83

1960
316.75

1961
317.49

1962
318.3

1963
318.83

1964
319.04

1965
319.87

1966
321.21

1967
322.02

1968
322.89

1969
324.46

1970
325.52

1971
326.16

1972
327.29

1973
329.51

1974
330.08

1975
330.99

1976
331.98

1977
333.73

1978
335.34

1979
336.68

1980
338.52

1981
339.76

1982
340.96

1983
342.61

1984
344.25

1985
345.73

1986
346.97

1987
348.75

1988
351.31

1989
352.75

1990
354.04

1991
355.48

1992
356.29

1993
356.99

1994
358.88

1995
360.9

In these 36 years atmospheric CO2 concentration has increased, but a clea=
r discontinuity took place in 1976. The average increase between 1959 and=
1976 was of .95 ppm/year, whereas between 1976 and 1995 it was of 1.522=
ppm/year. This increase in the slope of CO2 concentration has been const=
rued by some as a sign that said concentration is now aiming (faster) at =
ultimate higher levels. The forecast, however, is based on rather naive =
extrapolation procedures.

I have made an attempt to fit to the two time series 1959-76 and 1976-95 =
a three variable logistic Volterra equation of the form;

x =3D A/[1 + e(B t + C)]

since very often similar relationships have been found to describe accura=
tely growth processes of variables expanding to fill an ecological niche.
The following table gives the results of this exercise.

Data from : 1959-76 1976-95
Asymptote 486 ppm 400 ppm
Stand.Error 6.41 E-04 5.65 E-04
Time constant 468 years 124 YEARS
D-factor 1.45 E-04 2.38 E-03
B .9388 3.518
C -.8914 -4.639

This appears to indicate that from 1976 the atmospheric CO2 concentration=
is increasing - faster than in previous years - towards the lower asympt=
ote of 400 ppm which should be reached in the first decades of the 22nd =
century..

The time constant is defined here as the time to go from 10% to 90% of =
the final asymptote value. The values of the constants B and C given in =
the tables have been determined using a standardized time scale in which =
the time for the year 1950 is 1.5 and the time for the year 2050 is =
2.5.

The D-factor is an indicator of the unicity of the equation (see Franchin=
a, V. and Vacca, R. - "Logistic Curves: Construction and Unicity", Intern=
ational Conference on the Diffusion of Technologies and Social Behaviour,=
IAASA, 1989). Values of the D-factor much lower than 10-4 would indica=
te that the data do not point towards a sharply defined asymptote, but =
admit a wide range of plausible asymptotes - all featuring quite close =
values of the standard error in the fit.

The 2 strikingly low standard errors in the equations fits and the fairly=
high values of the D-factor indicate that the analysis is quite credible=
. If future observations will confirm that the current trend aims at the =
400 ppm asymptote (only 10% higher than the present level), dangers of =
global warming due to increases of atmospheric CO2 would have to be asses=
sed as much lower than judged by some - or, perhaps, as non existent.

From: Roberto Vacca <mc4634@mclink.it>

Posted: **Mon Apr 13, 1998 10:28 am**

Please find enclosed my answer to JSterman SD1528 and GBackus SD1532

The aim of my note [SD1524] was to call attention to the 1976 DISCONTINUI=
TY in atmospheric CO2 [average yearly growth of .95 ppm from 1959 to 76 =
and of 1.522 ppm from 76 to 95 --- but I hear now from Mauna Loa that =
growth from 95 to 96 was 1.67 ppm: so continuing the new trend]. I do not=
claim that my second logistic represent a tool to forecast a determinist=
ic future. I just want to call attention to a possible explanation [and =
a counterintuitive one: slow growth aims high, fast growth aims low]. Any=
other explanations around?

It is certainly true that in SOME cases Volterra equations fit very well =
time series of growth processes. These equations have also a very good =
record of permitting very accurate forecasts -- again in SOME cases. I =
have been producing for years [sometimes for a decade] very good forecast=
s in : epidemics [cancer deaths in Italy - which aimed at 50k up to 1944 =
and at 230k from 1944 to present {and for 12 years this second asymptote =
is computed with minimal variations based on the growing time series}], =
growth of populations of human artefacts, growth of human populations. =
A large number of cases has been published by Marchetti and Nakicenovic =
at IIASA, Laxenburg.

I have developed analytical methods which permit not only of finding the =
best fitting equation, but also of assessing how credible it is that said=
equation is unique. In some cases it can be shown that an infinity of =
equations fit the data equally well so that no sensible forecast can be =
supplied in this way.

So I intend the exercise of fitting logistic curves to time series only =
as a tool to make explicit regularities possibly stable over long periods=
and also to assess the quality of data. In fact the presence of noise =
above a certain level stultifies any search for descriptive equations or =
for any kind of model [if our knowledge of present and past is to inaccur=
ate, there is little we can say about the future]. We have carried out =
an attempt to model most urban variables by means of SD, of Volterra equa=
tions and of Input/Output Leontieff matrixes. The use of some logistics =
within the SD model has proved quite effective. [The study was named ACT-=
VILL4, carried out for DGXII of the European Commission in Brussels: I =
can send a 10 page abstract and the complete report can be ordered from =
DGXII].

The points made by GBackus are well taken. I think it is useful to rememb=
er that on the planet atmospheric CO2 represents 700 Gtons of carbon, bio=
sphere CO2 2,000 Gtons and oceanic CO2 37,000 Gtons.

best
Roberto Vacca
mc4634@mclink.it

Posted: **Sat Apr 18, 1998 1:25 pm**

Many thanks to Tom Fiddaman for the various refs [especially Lindzen].

He is right I standardise time on a scale that has:
1900 =3D 1 2000 =3D 2 2050 =3D 2.5

I dissent on the comment of Maunaloa CO2 data showing a lot of noise: the=
RMS errors of the order of 5E-04 in the fit appear to indicate the oppos=
ite.

Best

Roberto Vacca

Posted: **Wed Apr 22, 1998 11:20 am**

Hi folks,

I am wondering if any of you are familiar with the Energy 2020 model,
which (at my first glance) appears to be a system dynamics model of the
energy-economy sector.

If so, Id like to hear from you (and pick your brains a little...

Dean

******************************************************************
Dean Stinson OGorman

Policy Analyst
Energy Economics Branch
Saskatchewan Energy and Mines
1914 Hamilton Street
Regina, Saskatchewan
Canada S4P 4V4
phone: 306-787-3378
fax : 306-787-2333
email: deanso@cs.uregina.ca OR semee@gov.sk.ca
WWW: http://www.gov.sk.ca/enermine

"You must be the change you wish to see in the world."
-Gandhi

Posted: **Sun Apr 26, 1998 9:14 am**

Hi George,

Interested to hear about the model of energy implications etc. Australia
went to Kyoto with the "Megabare" and Gigabare" models of our economy, and
the sob-story that reductions in emmissions would cost mega- or giga- jobs.
Unfortunately, it seems that that particular modelling approach (based on
computable general equilibrium [CGE] modelling) had a number of problems.
In particular, the politicians seized on one or two simplistic predictions
and used these to argue for an INCREASE in Australias emmisions. (The
-abare suffix in the model names is because the work was done by ABARE -
the Australian Bureau of Agricultural and Resource Economics - the (last?)
bastion of neoclassical-economics deterministic modelling).

I am interested to know about the political correctness of energy 2020.
Does it give some unpalatable predictions that cause the pollies to get
into a flap? How does it deal with sectoral impacts such as: a 5%
reduction in emmissions will cause the x industry to lose y,000 jobs and $z
million etc? What about the role of innovation and adaptation? As far as
I know, the CGE models either ignore these sorts of dynamics, of at best
allow the stock of capital goods to change (grow?) over time.

John

------------------------------------------------------------------
John Wolfenden
(http://metz.une.edu.au/~jwolfend/index.htm)
New England Ecological Economics Group
(http://www.une.edu.au/cwpr/NEEEG/neeg.html)
Centre for Water Policy Research
University of New England, Armidale, NSW, 2351, Australia

Phone (02) 67732420 Fax (02) 67733237
International 61 2 67732420 (ph); 61 2 67733237 (fax)
email jwolfend@metz.une.edu.au; Mobile 0412 245 234

Committee Member and Postgraduate Coordinator, Australia New Zealand
Society for Ecological Economics

Posted: **Tue Jun 23, 1998 5:10 pm**

Hi Dean,

I worked with Abha Bhargava on her (now old) version of the SEM model. Jeff
Amlin and
I are the primary co-authors of the last decades set of incarnations,
although a large number of system dynamicists who went through Dartmouth
College and MIT in the late 1970s and early 1980s get to take credit or
blame for part of the model -- depending on the point of view. NRCan in
Ottawa (Neil McIlveen, Wally Geekie, and Nick Macaluso) is currently testing
a new all-province (plus US) version of the model to look at Kyoto and
deregulation issues. BC Hydro and BC Gas also use the model.

We have tried to maintain it as an SD model in the extreme. So far, so good
(or bad -- depending, again, on your point of view.) My guess is that you
are actually looking for someone else to talk to you about ENERGY 2020 --
who does not have the developers bias. Nonetheless, if you want any more
(biased) information or documentation, please contact me again.

George

George Backus, President
Policy Assessment Corporation
14604 West 62nd Place
Arvada, Colorado, USA 80004-3621
Bus: +1-303-467-3566
Fax: +1-303-467-3576
email: George_Backus@ENERGY2020.COM

Posted: **Fri Jun 26, 1998 9:46 am**

Im afraid Im coming in at the end of this discussion, but Im also very
interested in taking a look at an electric utility (energy) deregulation
model. Is there one that is available for downloading or text that I can
refer to?

----------------------------
lovitte@detroitedison.com

"Let DC Energize Your Project!"

Posted: **Mon Jun 29, 1998 12:36 pm**

Regarding John Wolfendens question about modelling costs of CO2
abatements.
While general equilibrium models (CGE) of course miss all points about
dynamics, they still can produce interesting and relevant answers to
given questions. The answers depend on what goes into CGE-models, just
as for SD-models.

The Megabare and Gigabare models might miss important points regarding
the tax system. See the literature on "double dividend". When CO2 is
taxed, other taxes can be reduced (a green tax system). Typically these
other taxes have negative allocational implications. For example, a
reduced tax on labour will lead to increased use of this resource.
Consequently, at least in equilibrium, CO2 taxes could imply more,
rather than fewer jobs. If beneficial local effects of CO2-taxes are
added (for instance due to reductions in NOx-emissions), and if
technological progress is added, even more good results could come out
of these models.

In a recent report by Mathiesen and Moxnes (in Norwegian), using a
CGE-model, we show that a welfare index peaks at CO2 emission reductions
around 30 percent. This could even happen if certain energy intensive
industries are protected to avoid that they emmigrate.

Best regards, Erling Moxnes
From: Moxnes Erling <Erling.Moxnes@snf.no>
SNF, Breiviken 2, N-5035 Bergen, Norway

Posted: **Tue Jun 30, 1998 2:20 pm**

We have some "hype" and other documentation that I can send to anyone who
requests it. Our Web page is in really bad shape until we can "come up for
air." Therefore, it is NOT a good place to look for now.
...

I agree that the CGE models are not all bad and they can pick up many of the
important considerations. I do, however, see a BIG difference between just
saying equilibrium (as in current markets do clear) and clairvoyant
optimization (the thrust of most Climate Change models used today). I
find it hard to claim that humans will make the optimal decisions today to
affect a perfectly known year 2020. The world will always do worse than
optimal and that is the problem. (Why didnt we start worrying about Climate
Change in 3000 BC when we "knew" that England would eventually cause an
industrial revolution and all this trouble?) If a policy model focuses on
the limitations to "perfect" policy and helps design mechanisms to
compensate, then we can meet goals -- almost any goals. This is how
feedback control works -- it corrects for errors and unknown(able)
conditions. (Geez, sounds like SD...) If we simply assume "problems"
optimally away, than we will clearly not meet any goals.
...

We do have "troubled minds" with the simplistic assumptions, unsubstantiated
data (and theory), and the clairvoyant optimization aspect of the "ABARE"
models. We are at a sectoral level (26 separate economic classifications)
causally simulating fuel and technology choice by end-use. We also have
detailed supply and pollution simulations. We link to a third-party
multi-region econometric (!) feedback model, but that model is consistent
with SD principles in terms of feedback and lags. It does cause us some
consternation in its iterations to make supply and demand balance each
period but the "errors" in this appear to be insignificant.

We capture the impacts of new technologies that could be made available --
and the change in economic structure. We can test assumptions of further
innovations and technological change. A new technology tends to make it
less expense to do something then it would have otherwise been. (When it
comes right down to it, this is the only reason for developing the new
technology.) The reduction in overall economic costs actually stimulates
either the industry or the energy use -- despite improved efficiency. It
also reduces the "pain" of disincentive programs and the economic clout of
incentives. Thus, technology improvement can both help and hurt depending on
what it stimulates more -- efficiency or growth capabilities.

When we run Kyoto related scenarios we do see the shifts in industry. And
depending on how any taxes are recycled (e.g. to reduce labor taxes), the
local and "neighboring" economies can be hurt or benefit. The heart burn of
the "pollies" occurs from our myopic (or even "imperfect" adaptive
expectation) "assumptions.They say, "If we all know what needs to be done
by the year 200, why wouldnt the world make all the optimal decisions
necessary to get there?" Our arguments that we have absolutely no historical
evidence that humans have ever responded until the pain actually hits them
just causes their glazed of eyes to ask back "What does reality have to do
with good policy?"

Another problem (which may be with our model), is that it shows humans to be
very resilient to change. They are very good at finding ways of avoiding it
(that old feedback stuff...

. Therefore, our work indicates that
incentives and disincentives (taxes) to meet Climate-Change goals are almost
twice what many expect.

Thanks,

George

George Backus, President
Policy Assessment Corporation
14604 West 62nd Place
Arvada, Colorado, USA 80004-3621
Bus: +1-303-467-3566
Fax: +1-303-467-3576
email: George_Backus@ENERGY2020.com

Posted: **Sun Jul 05, 1998 10:24 am**

In SD 1526 Roberto Vacca analyzes trends in global CO2 concentrations by
fitting a logistic curve to the Keeling et al. Mauna Loa CO2 data. As is
often the case with data showing exponential-like growth, the equation fits
reasonably well. Roberto finds a good fit with an asymptote of 400 ppm
CO2. He then makes the following claim:

"If future observations will confirm that the current trend aims at the 400
ppm asymptote (only 10% higher than the present level), dangers of global
warming due to increases of atmospheric CO2 would have to be assessed as
much lower than judged by some - or, perhaps, as non existent."

With all due respect, this analysis is not credible and cannot be taken
seriously. Other plausible growth models such as the Gompertz, Richards,
and others will fit the data equally well and give vastly different
predictions of ultimate CO2 levels. Indeed, there is an infinite number
of alternative models that can fit any data set arbitrarily well and still
will give different predictions of the behavior outside the range of the
historical data. Historical fit alone cannot give us confidence in the
utility of a model.

More important, fitting a logistic model - or any model - in this fashion
to a data set - any data set - is a black box, atheoretical procedure.
Curve fitting of this type is not grounded in a causal analysis of the
underlying system dynamics. The global climate/economy system is far too
complex, with far too many feedback processes, delays, and nonlinearities,
to be captured by a three parameter curve fit, or by any black box model.
It is true that logistic-type models can fit some data series for growth
processes well. It is also true, however, that there are many, many more
for which such models have failed.

The history of black box curve fitting is replete with examples of such
failed predictions - beginning with the predictions of Verhulst for
various populations. Later, Pearl and Reed (1924), based on the same type
of model used here, that the US population would reach a maximum of 197.27
million people. The population of the US in 1990 was about 250 million and
it is still growing. They also estimated an upper limit to world
population of about 2 billion. World population today is about 6 billion
and growing. One might suppose that a factor of three error would provide
sufficient reason to abandon such black box curve fitting methods, but
instead, many aficionados of the logistic curve only concluded that there
had been a shift in parameters, or that the curve fit had to be done at a
more disaggregate level, or a different functional form used, or some other
ad hoc adjustment was required. Epicycles continue to be added to
epicycles. (A good review of the inappropriate use of the logistic and
other black box curve fitting models in the context of population growth is
found in Cohen, Joel (1995) How Many People can the Earth Support? New
York: WW Norton, my source for the Pearl and Reed predictions).

Black box modeling is the antithesis of good system dynamics practice. Far
too many people are still wasting far too much time and money in vain
attempts to find a simple equation that can be fit to some data set and
then make predictions without bothering with the tiresome and difficult
work of developing an actual theory of the underlying dynamics of the
process and testing it in the field. Further, far too much effort is
devoted to the generation of unconditional forecasts (such as Robertos
forecast of CO2 concentration) and far too little to the development of
causal models that can help us design policies to change the dynamics for
the better and realize our deepest aspirations for a better world. I
believe it was St. Exupery who said "As for the future, your task is not to
foresee, but to enable it." Black box modeling is not only scientifically
unsupportable but emotionally disempowering.

My comments here are methodological and not ideological or political - I
would have written the same response had Robertos conclusion been that
atmospheric CO2 concentration would treble and posed a grave threat to the
survival of humanity. Besides the work of George Backus, readers interested
in a thoughtful analysis of the global climate/economy system from a
structural perspective are directed to the work of Tom Fiddaman, who has
not only developed an original system dynamics model of the climate/economy
system, but also replicated and critiqued many of the most important such
models in the literature. Tom has a web site containing these models.

John Sterman
J. Spencer Standish Professor of Management
Director, MIT System Dynamics Group
MIT Sloan School of Management
E53-351
30 Wadsworth Street
Cambridge, MA 02142
617/253-1951 (voice); 617/258-7579 (fax), jsterman@mit.edu
http://web.mit.edu/jsterman/www

Posted: **Mon Jul 06, 1998 3:51 pm**

I was gone over the US holiday and just saw got back to find SD 1524 =
note on asymptotic CO2 levels. I also saw John Stermans SD 1528 =
response and am afraid I agree with John. =20

I must also confess here about our work. As I looked at the CO2 data, I =
could find no compelling evidence for or against significant anthropic =
causes of increased CO2 concentration. Thus, even though I wanted to =
add a climate feedback loop "for kicks to the model so that I could =
"see" some secondary damage and counter-response, I left the loop(s) out =
because I thought it would bias results more than I was (possibly) doing =
so already.

There is compelling evidence that the CO2 levels are rising dramatically =
(with asymptotic assumptions now being what is highly questionable). =
The question then becomes, "Could we create an anthropic "cause" for =
reduced or stabilize CO2 via policy?" The evidence for human abilities =
to "correctly" control the climate is non-existent. This then raises the =
question of whether we should consider letting fate takes its course and =
focus policy on preparing to move millions from the coastal areas of the =
world and developing new agricultural practices needed for a warmer and =
more tumultuous climate. Here I chickened out. The ENERGY2020 model =
can test "mitigation" policies that reduce anthropic CO2 emission =
related to energy -- and no more. For $, we were asked to look at =
energy and economic CO2-mitigation policies. For $, that is what we =
did... period. Consulting -- the second oldest profession.

George Backus, President
Policy Assessment Corporation
14604 West 62nd Place
Arvada, Colorado, USA 80004-3621
Bus: +1-303-467-3566
Fax: +1-303-467-3576
email: George_Backus@ENERGY2020.com

Posted: **Thu Jul 16, 1998 2:01 pm**

>A prof of meteoroly at MIT [name escapes me, but I have the refer >at home]
stated that"science does not predict climate".

His name is Richard Lindzen. I dont have any recent citations, but the
following is a start: Lindzen, R. S. (1990). =93Some Coolness Concerning=
Global
Warming.=94 Bull. Am. Meteorol. Soc. 71(3): 288-299.
You can find links to other credible critics and a few cranks on my web=
pages.

Im afraid I have to weigh in on the side of George Backus and John Sterman=
on
the issue of CO2 concentration. A few points:

>The aim of my note [SD1524] was to call attention to the 1976=20
>DISCONTINUITY in atmospheric CO2 [average yearly growth of .95=20
>ppm from 1959 to 76 =3D and of 1.522 ppm from 76 to 95 --- but I=20
>hear now from Mauna Loa that =3D growth from 95 to 96 was 1.67 ppm:=20
>so continuing the new trend].

To me, the data looks like a trend with a lot of noise that just happens to
look like a discontinuity over a short period. This is especially apparent=
if
you combine the Mauna Loa data with the Siple ice core data, which covers a
much longer historical period. In that case, the annual change in CO2
concentration looks like exponential growth, not a discontinuity.

Going beyond "eyeballing" the data, there is also a fundamental problem with
logistic equation used:

>I have made an attempt to fit to the two time series 1959-76 and 1976-95 a
three variable logistic Volterra equation of the form;
>
> x =3D A/[1 + e(B t + C)]

If CO2 is increasing over time, B should be negative, and A is the=
asymptotic
CO2 concentration. Roberto estimates positive coefficients for B (.9388 and
3.518), so I assume he must be normalizing time in some way. I tried to
replicate the estimates myself, with the following results:

Data=A0=A0=A0=A0=A0=A0=A0 59-76=A0=A0=A0=A0=A0=A0 76-95=A0=A0=A0=A0=A0=A0=
59-95=A0=A0=A0=A0=A0 1744-1996*
A=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 494=A0=A0=A0=A0=A0=A0=A0=A0 730=A0=A0=A0=
=A0=A0=A0=A0=A0 700=A0=A0=A0=A0=A0=A0=A0 584
B=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 -.0086=A0=A0=A0=A0=A0 -.0080=A0=A0=A0=A0=A0=
-.0072=A0=A0=A0=A0 -.0027
C=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 16.3=A0=A0=A0=A0=A0=A0=A0 16.0=A0=A0=A0=
=A0=A0=A0=A0 14.4=A0=A0=A0=A0=A0=A0 5.15
X(1750)=A0=A0=A0=A0=A0 111=A0=A0=A0=A0=A0=A0=A0=A0=A0 88=A0=A0=A0=A0=A0=A0=
=A0=A0 106=A0=A0=A0=A0=A0=A0=A0 244
X(2100)=A0=A0=A0=A0=A0 422=A0=A0=A0=A0=A0=A0=A0=A0 506=A0=A0=A0=A0=A0=A0=A0=
=A0 484=A0=A0=A0=A0=A0=A0=A0 382

* Includes Siple ice core data

If you backcast this equation to its historic asymptote, its clear that the
CO2 concentration would have to have started at 0 at some point. This=
violates
our understanding of at least the last 100,000 years history of CO2
concentrations. Indeed, the forecasts for X in 1750 supplied are wildly off
the
accepted "preindustrial" CO2 concentration (~280 ppm), unless the Siple data
are included, in which case the fit is very poor over much of the period.

I tried to salvage things by adding a 4th term:

Y =3D Y0 + D / (1 + EXP( E*time + F ))

In this case, the historical fits are better, but the forecasts are wild
unless
the Siple data are included:

Data=A0=A0=A0=A0=A0=A0=A0 59-76=A0=A0=A0=A0=A0=A0 76-95=A0=A0=A0=A0=A0=A0=
59-95=A0=A0=A0=A0=A0 1744-1996
Y0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 310=A0=A0=A0=A0=A0=A0=A0=A0 329=A0=A0=A0=A0=
=A0=A0=A0=A0 310=A0=A0=A0=A0=A0=A0=A0 280
D=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 42.2=A0=A0=A0=A0=A0=A0 4950=A0=A0=A0=A0=
=A0=A0=A0 3083=A0=A0=A0=A0=A0=A0 1863
E=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 -.111=A0=A0=A0=A0=A0 -.085=A0=A0=A0=A0=A0=A0=
-.051=A0=A0=A0=A0=A0 -.019
F=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 220=A0=A0=A0=A0=A0=A0=A0=A0 175=A0=A0=A0=
=A0=A0=A0=A0=A0 106=A0=A0=A0=A0=A0=A0=A0=A0 41
Y(1750)=A0=A0=A0=A0=A0 310=A0=A0=A0=A0=A0=A0=A0=A0 329=A0=A0=A0=A0=A0=A0=A0=
=A0 310=A0=A0=A0=A0=A0=A0=A0 280
Y(2100)=A0=A0=A0=A0=A0 352=A0=A0=A0=A0=A0=A0=A0 5192=A0=A0=A0=A0=A0=A0=A0=
2766=A0=A0=A0=A0=A0=A0=A0 721

Whent the Siple data are included, the forecast of 721 ppm in 2100 suggests
that we should be concerned.

>I do not claim that my second logistic represent a tool to=20
>forecast a determinist ic future. I just want to call attention=20
>to a possible explanation [and a counterintuitive one: slow=20
>growth aims high, fast growth aims low]. Any other explanations=20
>around?

Regardless of the data available, I think these forecasts are misguided.=
There
are really two components to the forecast: what will happen with emissions,
and
how the carbon cycle will respond. These need to be considered separately,=
and
with causal models.

The logistic equation makes sense when you have a system that can be broadly
described as growth (from a positive loop) towards a limit (from a negative
loop). This makes sense for epidemics (infection spreads until susceptibles
are
exhausted) and maybe cumulative CO2 emissions (emissions grow fueled by
economic growth until fossil resources and forests are exhausted and/or
competing energy technologies take over).

Atmospheric CO2 is more like a leaky tub, filled by emissions and drained by
storage in the oceans and biosphere. The structure of the carbon cycle
suggests
an obvious behavior mode, not captured by the logistic equations above:
overshoot. If emissions peak and decline, and CO2 storage processes have=
long
time constants, then it seems likely that atmospheric CO2 will also peak
before
returning to some long-term equilibrium.

Wed like to know the time constants of the draining processes, and the
nonlinearities or sink limits associated with them. Wed also like to know
about positive or negative feedbacks through the climate system. There are
already many simple and complex physical, causal models of these features,=
so
it seems more productive to debate the specifics of these models than
arbitrary
curve-fits.

>The points made by GBackus are well taken. I think it is useful to rememb=
=3D
>er that on the planet atmospheric CO2 represents 700 Gtons of carbon, bio=
=3D
>sphere CO2 2,000 Gtons and oceanic CO2 37,000 Gtons.

Its also important to remember that fossil resources contain on the order=
of
10,000 Gtons and that the ocean behaves more like it contains only 3700=
Gtons
because of the chemistry of CO2 absorption. Big sinks arent all that=
helpful
when theyre matched by big sources and have time constants of centuries.

Those interested in pursuing this further might turn to the links on my web
pages, or look to the following references:

Bj=F6rkstrom, A. (1986). One-Dimensional and Two-Dimensional Ocean Models=
for
Predicting the Distribution of CO2 Between the Ocean and the Atmosphere. The
Changing Carbon Cycle: A Global Analysis. J. R. Trabalka and D. E. Reichle.
New
York, Springer-Verlag.

Bolin, B. (1986). Requirements for a Satisfactory Model of the Global Carbon
Cycle and Current Status of Modeling Efforts. The Changing Carbon Cycle: A
Global Analysis. J. R. Trabalka and D. E. Reichle. New York,=
Springer-Verlag.

Fung, I. (1991). Models of Oceanic and Terrestrial Sinks of Anthropogenic=
CO2:
A Review of the Contemporary Carbon Cycle. Biogeochemistry of Global
Change. R.
S. Oremland. New York, Chapman & Hall.

Goudriaan, J. and P. Ketner (1984). =93A Simulation Study for the Global=
Carbon
Cycle, Including Mans Impact on the Biosphere.=94 Climatic Change 6:=
167-192.

Keller, A. A. and R. A. Goldstein (1995). =93Oceanic Transport and Storage=
of
Carbon Emissions.=94 Climatic Change 30: 367-395.

Oeschger, H., U. Siegenthaler, et al. (1975). =93A Box Diffusion Model to=
Study
the Carbon Dioxide Exchange in Nature.=94 Tellus XXVII(2): 167-192.

Rotmans, J. and M. G. J. denElzen (1993). =93Modelling feedback mechanisms i=
n
the
carbon cycle: balancing the carbon budget.=94 Tellus 45B(4): 301-320.

Townsend, A., S. Frolking, et al. (1992). Report: Carbon Cycling in
High-Lattitude Ecosystems. Modeling the Earth System. D. Ojima. Boulder, CO,
UCAR/Office for Interdisciplinary Earth Studies: 315-323.

Regards,

Tom Fiddaman

****************************************************
Thomas Fiddaman, Ph.D.
Ventana Systems http://www.vensim.com
34025 Mann Road Tel (360) 793-0903
Sultan, WA 98294 Fax (360) 793-2911
Tom@Vensim.com http://home.earthlink.net/~tomfid/
****************************************************