```From: jbs@watson.ibm.com
Date: Tue, 19 Sep 95 21:29:19 EDT
Newsgroups: sci.environment
Subject: Effects of global warming

My dispute with Michael Tobis continues.
Tobis noted:

I appreciate Tobis's support on this point.
Tobis continued:
>I haven't figured this out yet, and I am still not inclined to do so in the
>next few weeks. It may not be obvious from the number of postings I made
>recently, but I'm still pretty swamped. However, these aren't postings I
>worked very hard at, and your example may cause me some effort. ...

Well of course one reason for the low signal-to-noise ratio
in this group is a shortage of people willing to work hard on their
posts.
Tobis continued:
>However, if your example is valid, there's something wrong with a big chunk
>of electrical (and, I understand, mechanical) engineering, or at the very
>least, of my understanding of it, so I'm confident it will have some flaw.

I would speculate you are attempting to force things into an
electrical engineering framework which do not fit.
>The output of A is transformed by box B and then combined with the
>forcing and fed back to box A one time step later.  If we allow A and
>B to have memory (specifically to remember their last output, so that
>the current output is a function of the last output and current input)
>it is easy to see that we can chose A and B to emulate the example I
>posted (more precisely the similar difference equations which will
>behave in the same way as the time step goes to zero).  Tobis can
>deny this is a feedback system but then it is hard to see how he can
>argue that the climate system is a feedback system.
Tobis grants:
>It is a feedback system, granted.

Well as noted above it is possible to put my original example
in this form.  Let
output A =  .3 * input A +  .6 * previous output A
output B = -.2 * input B + 1.1 * previous output B
Then if the output of A is fed into B one timestep later and the output
of B is fed into A one timestep later we have the following difference
equations for a(j) and b(j), the outputs of A and B at timestep j.
a(j+1) =  .6 * a(j) +  .3 * b(j)
b(j+1) = -.2 * a(j) + 1.1 * b(j)
Since the eigenvalues of the matrix  .6  .3 are .8 and .9 which lie
-.2 1.1
within the unit circle, the solution of the difference equation will
converge to a=b=0 regardless of the initial conditions.  In other
words a=b=0 is a stable equilibrium point of this system.
Now introduce forcing by adding .1/.3 to the input of A (or
equivalently adding .1 to the output of A).  The difference equations
become
a(j+1) =  .6 * a(j) +  .3 * b(j) + .1
b(j+1) = -.2 * a(j) + 1.1 * b(j)
or
(a(j+1) + .5) =  .6 * (a(j) + .5) +  .3 * (b(j) + 1.)
(b(j+1) + 1.) = -.2 * (a(j) + .5) + 1.1 * (b(j) + 1.)
so as above (a+.5,b+1.) will converge to (0,0) regardless of the
initial values of a and b.  This means a=-.5, b=-1. is a stable
equilibrium point of the forced system.  Note the equilibrium value
of a has moved in a direction opposite the forcing as claimed.
The trajectory of a,b starting from a=b=0 when forcing is
initiated is readily computed.  We obtain
timestep    a value           b value
0      0.0000000000      0.0000000000
1      0.1000000000      0.0000000000
2      0.1600000000     -0.0200000000
3      0.1900000000     -0.0540000000
4      0.1978000000     -0.0974000000
5      0.1894600000     -0.1467000000
6      0.1696660000     -0.1992620000
7      0.1420210000     -0.2531214000
8      0.1092761800     -0.3068377400
9      0.0735143860     -0.3593767500
10      0.0362956066     -0.4100173022
11     -0.0012278267     -0.4582781537
12     -0.0382201421     -0.5038604038
13     -0.0740902064     -0.5466024157
14     -0.1084348486     -0.5864446160
15     -0.1409942939     -0.6234021079
16     -0.1716172087     -0.6575434599
17     -0.2002333632     -0.6889743641
18     -0.2268323272     -0.7178251279
19     -0.2514469347     -0.7442411753
20     -0.2741405134     -0.7683759059
30     -0.4170745935     -0.9164556235
40     -0.4706376183     -0.9705711569
50     -0.4897138583     -0.9897067221
60     -0.4964082781     -0.9964075119
70     -0.4987470893     -0.9987470071
80     -0.4995630775     -0.9995630687
90     -0.4998476481     -0.9998476472
100     -0.4999468775     -0.9999468774
As with the original differential equation example, the initial response
of a to the forcing is in the expected direction.  However the
interaction with b eventually changes the sign of the response of a
which is what Tobis has been claiming cannot occur.  The feedback does
not "turn off" when a returns to 0 because b remains nonzero.
>My guess is that Shearer's example refers to the instantaneous response,
>and not the zero frequency equilibrium. That's just a guess though. My
>point was that the *equilibrium* response must have the same sign as the
>zero frequency open loop gain.

I clearly stated in my original example that the initial
response is in the expected direction but that the equilibrium response
changes sign.
James B. Shearer
```

```From: jshearer@VNET.IBM.COM
Date: Thu, 7 Dec 95 19:34:15 EST
Newsgroups: sci.environment
Subject: climate models

I continue to discuss the following model which I had
proposed in an earlier post.
>         Ok, how about the following model (which I am not claiming is
>physically realistic).  Suppose the ability of the atmosphere to absorb
>visible light (ie shortwave radiation) were temperature dependent
>increasing as the temperature of the atmosphere increased.  Then
>suppose we increase the solar constant.  The initial response will be
>to heat the surface.  The surface will then heat the atmosphere.  The
>hotter atmosphere will absorb more incoming solar radiation causing
>further heating.  Meanwhile the atmosphere will shade the surface
>causing the surface to begin to cool.  If we choose the proper
>parameters I believe we can end up with a hotter atmosphere and a
>colder surface.  Then feedback has reversed the sign of the response
>of surface temperature to forcing which is what Tobis says is
>impossible.

Halliwell observed:
>   Note here that increased absorption of solar radiation by the
>*atmosphere* has been ignored. If we start out with a completely
>transparent atmosphere, this would be appropriate. However, this would
>presume that the "current" atmosphere is at a delicate balance point,
>where there is _currently_ no absorption, but the slightest warming would
>lead to absorption. Such a situation is highly unlikely, so the
>description _should_ include direct atmospheric heating as the result of
>increased solar output.

I realized after posting the original scenario that it was
open to this objection.  I should have chosen a means of heating the
surface that only has indirect effects on the atmosphere.  Assume
say a network of nuclear power stations or as Halliwell suggested in
a later post increased geothermal heat flow.  In what follows I will
discuss such a revised model (ie keep the solar constant constant and
force the surface directly in some way).
First we will look at the equilibrium behavior.  Following
Pierrrehumbert let:
Ta - temperature of isothermal slab atmosphere
Te - temperature of surface
a(T) - shortwave absorption of atmosphere at temperature T
S  - solar flux
c*T**4 - blackbody radiation at temperature T
f  - surface forcing
Assume surface albedo 0 and atmospheric emissivity 1.
Assume radiative energy transfer only.  Then the energy leaving
the atmosphere will be 2*c*Ta**4, the energy leaving the surface
will be c*Te**4, the energy absorbed in the atmosphere will be
a(Ta)*S+c*Te**4 and the energy absorbed in the surface will be
(1-a(Ta))*S+c*Ta**4+f.  At equilibrium the energy emitted and
absorbed will balance in the atmosphere and at the surface.  So
we have the following equations.

a(Ta)*S + c*Te**4     = 2*c*Ta**4                  <1>

(1-a(Ta))*S + c*Ta**4 + f =   c*Te**4                  <2>

Adding <1> and <2> we may solve for Ta**4 ie:

Ta**4 = (S+f)/c                                     <3>

Note Ta is independent of the form of a(Ta).  We now choose a(Ta)
as follows:

a(Ta) = b*((c/S)*Ta**4 - 1) + d                     <4>

Note when f=0, Ta**4=(S/c) and a(Ta)=d.  a(Ta) must lie between
0 and 1 which will be true for values of Ta near (S/c)**.25 if
0<d<1.
Now plug <4> and <3> into <1> and solve for Te.  We
obtain:

Te**4 =  ((2-d)*S + (2-b)*f)/c                      <5>

Hence when b is greater than 2 the surface temperature at
equilibrium moves in a direction opposite to the forcing f.
Note however we have ignored questions of stability.  The
equilibrium solution may not be stable in which case the above
simple analysis is invalid.  Also Halliwell objects:
>   The problem with Shearer's example is that he then analyzes the system
>as if solar forcing only affects surface temperature (it doesn't - there
>is atmospheric absorption in his hypothesized world). He also describes
>the time-dependent response as if the surface warming exerts itself
>without any feedback (solely in response to solar forcing) for a period
>of time, and then the feedback acts alone for a period of time. What
>needs to be done is that all processes act concurrently, and that the
>surface temperature be in balance with all processes that affect it
>(instead of treating one process as if it acts independently).

To investigate stability and deal with Halliwell's second
objection (we already dealt with the first when we changed the way we
introduced forcing) we need to model the nonequilibrium dynamics of
the system.  We do this by assuming when the energy fluxes for the
surface or atmosphere do not balance the temperature of the surface
or atmosphere changes at a rate proportional to the amount of the
imbalance (with constants of proportionality dependent on the heat
capacities).  Let Ta' and Te' be the time derivatives of Ta and Te.
Let Ha and He be the constants of proportionality.  Then <1> and
<2> yield the following differential equations:

Ta' = (       a(Ta)*S + c*Te**4  -  2*c*Ta**4 ) * Ha        <6>

Te' = ( (1 - a(Ta))*S + c*Ta**4 + f - c*Te**4 ) * He        <7>

These equations are nonlinear.  However we are interested in small
perturbations around the f=0 equilibrium solution <3> and <5>.
Hence we may linearize the system as follows.  Let

Ta =       (S/c)**.25 + Ra                             <8>

Te = ((2-d)*S/c)**.25 + Re                             <9>

where Ra and Re are small perturbation terms.  Next plug <8> and <9>
into <6> and <7> using <4> and dropping all higher order terms in
Ra and Re.  If I did the algebra correctly this gives the following
linear system of differential equations in Ra and Rb.

Ra' = (b-2)*g*Ha*Ra + (2-d)**.75*g*Ha*Re               <10>

Re' = (1-b)*g*He*Ra - (2-d)**.75*g*He*Re + f*He        <11>

where g = 4. * (c**.25) * (S**.75)                     <12>

Now the stability of this linear system depends on eigenvalues
of the matrix M:

(b-2)*g*Ha     +(2-d)**.75*g*Ha
(1-b)*g*He     -(2-d)**.75*g*He

The determinant is (g**2)*Ha*He*(2-d)**.75 which is always positive.
Hence the system will be stable iff the trace is negative.  This is
clearly true when b<2.  However we are interested in the case b > 2.
This produces the following stability condition:

(b-2) * Ha < (2-d)**.75 * Hb                      <13>

This means the rate at which the temperature of the atmosphere
responds (Ha) must not be too large compared to the rate at which
the temperature of the surface responds (He).  Intuitively what
going on is this.  When b > 2 the atmosphere considered by itself
is an unstable system.  If it begins to heat, the feedback caused
by increased solar absorption will cause a runaway temperature rise.
However the interaction with the temperature of the surface is a
potentially stabilizing negative feedback loop (since the increased
solar absorption in the atmosphere may cool the surface which in
turn may cool the atmosphere).  However for this loop to succeed
in stabilizing the system the atmosphere must not respond too
quickly compared to the surface.  This is the stability condition
<13>.  Note the larger b is, the more unstable the atmosphere is by
itself and the more stringent the stability condition becomes.
Now consider the effect of the forcing term f.  For small f
we may continue to approximate the nonlinear system <6>,<7> by the
linear system <10>,<11>.  It is easy to verify that the equilibrium
response of Re in the linear system is opposite to the direction of the
forcing when b>2 (just as in the nonlinear system considered above).
It is possible to write down the exact solution of the linear system
with forcing turned on at time 0 and initial conditions Ra=Re=0 in
terms of the eigenvalues and eigenvectors of M which will show how the
system moves to the new equilibrium.  I will not bother as I have
already done this for the original order 2 system I posted as a
counterexample to Tobis and the behavior will be qualitatively
similar.  Intuitively what happens is this.  Suppose the system is
in a stable equilibrium with Ra=Re=0.  When forcing is turned on Re'
and Ra'' immediately become positive.  However Ra' remains 0 (to first
order).  This means the initial response to the forcing will be much
greater for Re than for Ra.  However Ra will eventually respond as
well.  Now once Ra starts to increase it will try to runaway (since
the atmosphere is unstable by itself).  However the interaction with
Re prevents this.  First the increase in Ra will cause the increase in
Re to halt.  However this is not enough to stop the increase in Ra.  As
Ra continues to increase Re will start to decrease.  Eventually the
decrease in Re will halt the rise in Ra.  Note however this cannot
occur until Re becomes negative since when Re is 0, Ra' remains
positive.
The case where the stability condition is not satisfied may
also be of interest.  In this case, I believe Ta will move so that
a(Ta) flips back and forth between 0 and 1 (it can't get stuck in
either position because then the long term energy balance of the earth
will be wrong).  When a(Ta) is 1 the surface will slowly cool reducing
Ta as well until a(Ta) moves below 1 at which point feedback rapidly
cools the atmosphere forcing a(Ta) to 0.  The surface will now begin
to slowly warm eventually warming the atmosphere enough so that a(Ta)
moves above 0.  Then feedback will rapidly warm the atmosphere until
a(Ta) becomes 1.  The cycle can then repeat.  One could even speculate
that ice ages and interglacials might be caused by some similar
mechanism that does not require any external forcing.
James B. Shearer (email jbs@watson.ibm.com)
```

```From: jshearer@VNET.IBM.COM
Date: Tue, 12 Dec 95 17:18:30 EST
Newsgroups: sci.environment
Subject: climate models
Lines: 63

I continue to discuss a model in which the ability of the
atmosphere to absorb shortwave radiation is temperature dependent.
I had posted an analysis of (among other things) when this
situation would be stable (using a two component atmosphere, earth
model suggested by Pierrehumbert).  Halliwell responded by disputing
my stability conclusions based on his numerical calculations showing
instability.
Briefly Halliwell's calculations prove nothing because they
are using too big a timestep (or equivalently too large values for Ha
and He).  This is apparent from the negative temperature values he
obtains.
In more detail Halliwell claimed in part:
>   It is clear that _any_ deviation away from the equilibrium value leads
>to a situation where the system is dynamically unstable. Now, it may be
>that I have introduced a _numerical_ instability by casting the
>differential equation as a difference equation. However, Shearer's
>analysis using a linear approximation should be equally valid in
>determining numerical instability. Any theoretical anlysis of numerical
>stability is easily refuted by a *demonstration* of instability. I
>haven't examined Shearer's linear approximation in detail, but I presume
>that the problem is one where ignoring the higher-order terms leads to
>errors.

This is incorrect, numerical instability can occur when the
original system is stable.  Often a numerical method will only be
stable for sufficiently small timesteps.  (Climate modeling would be
simpler if you could use arbitrarily large timesteps.)  In this case
we are approximating a set of differential equations by a set of
differential equations:

x'(t) = M * x(t)                                  <1>

where x is a vector and M is a matrix.  I have already observed that
0 is a stable solution of this system if all the eigenvalues of M
have real part < 0.  Suppose we approximate x'(t) in <1> by (x(t+h)-
x(t))/h.  Then we obtain the following set of difference equations:

y(n+1) = y(n) + h * M * y(n)                      <2>

where y(0)=x(0) and y(k) approximates x(k*h).  <2> may be
rewritten as:

y(n+1) = (I+ h * M) * y(n)                        <3>

Now the stability condition for <3> is that the eigenvalues of
(I + h * M) must lie within the unit circle.  Now if the eigenvalues
of M lie in the left half plane, a little thought will show that
the eigenvalues of (I + h * M) will lie in the unit circle iff h is
sufficiently small.
Hence I believe if Halliwell repeats his calculations
with a much smaller timestep the instability he is seeing will go
away.
Halliwell also posted:
>   The system Shearer has described is "stable" in the same sense that a
>ball can be balanced on top of another ball: there is a theoretical
>equilibrium that can be demonstrated mathematically, but in practice the
>ball is doomed to fall off eventually.

This would be an unstable equilibrium.  I believe I have
established mathematically that the system has a stable equilibrium.
As noted above you have not yet shown otherwise.
James B. Shearer (email jbs@watson.ibm.com)
```

```From: jshearer@VNET.IBM.COM
Date: Thu, 14 Dec 95 20:57:10 EST
Newsgroups: sci.environment
Subject: climate models

I continue to argue with Halliwell about stability.
>         I continue to discuss a model in which the ability of the
>atmosphere to absorb shortwave radiation is temperature dependent.
>         I had posted an analysis of (among other things) when this
>situation would be stable (using a two component atmosphere, earth
>model suggested by Pierrehumbert).  Halliwell responded by disputing
>my stability conclusions based on his numerical calculations showing
>instability.
>         Briefly Halliwell's calculations prove nothing because they
>are using too big a timestep (or equivalently too large values for Ha
>and He).  This is apparent from the negative temperature values he
>obtains.
Halliwell responded:
>   If you examine the output for b=4 in my tabulated results, you will
>notice that the "correction" value sends the temperatures further _away_
>from the equilibrium value. No change in Ha, He, or time step will alter
>that fact.

So what?  A trajectory which converges to 0 may be moving away
from 0 at some times (even in linear systems).  Think of spiraling
in along near ellipses.
>         Hence I believe if Halliwell repeats his calculations
>with a much smaller timestep the instability he is seeing will go
>away.
Halliwell responded:
>   It can't possibly go away in the case where a positive departure from
>equyilibrium leads to a further positive departure. All that a smaller
>time step will do is make the process take longer for the instability to
>show up.

As noted above this is wrong.  I tried your b=4, d=.5 case with
Ha=.5, He=1.0.  A timestep of 1.0 is quite unstable.  .1 appears to be
stable (although not a good approximation to the differential equations).
.01 seems to be stable and approximate the differential equations.  (I
calculated that timesteps less than .1068 will be stable).
Btw what values of Ha and He were you using?  I was unable to
smaller Ha and He values).  If you still see instability please post
enough details so your results can be reproduced.
James B. Shearer (email jbs@watson.ibm.com)
```

```Article: 81736 of sci.environment
From: fmims@aol.com (FMims)
Newsgroups: sci.environment
Subject: Re: House Global Warming Hearing
Date: 17 Dec 1995 18:59:30 -0500

"R. T. Pierrehumbert" <rtp1@midway.uchicago.edu>
on 17 Dec 1995 15:11:38 GMT (Message-ID:
<4b1bva\$9f0@news.acns.nwu.edu>) wrote, (in part):

>I have not seen any scientific arguments
>published, indicating that the climate should be
>more sensitive to solar variability than CO2.
>This is what Baliunas would have to prove in
>order to support her claims regarding global
>warming.

Many papers have addressed the impact of solar
variability on global warming and cooling. The
latest, which arrived at my desk a few hours
before this post arrived at my PC, concludes
"...solar forcing may have contributed about half
of the observed 0.55C surface warming since 1860
and one third of the warming since 1970." (Judith
Lean, Juerg Beer & Raymond Bradley,
"Reconstruction of solar irradiance since 1610:
Implications for climate change" Geophysical
Research Letters, 22, 3195-3198, 1 Dec 95.)

The significance of Pierrehumbert's comment about
the relative impact of warming due to CO2 and
solar variability is that a satisfactory answer
may be long in coming. In various surveys of
college students and even professional scientists,
respondents generally agree that CO2 is the most
important greenhouse gas. In reality, the
greenhouse effect of CO2 is dwarfed by that of
water vapor. Yet we have scarcely begun to
understand the natural modulation of water vapor.

(The casual observer can readily understand the
impact of water vapor by recalling how cloudy
winter nights are generally much warmer than clear
winter nights. Similarly, clear nights in the
desert southwest or at high altitudes are much
cooler than at more humid sites.)

For example, data collected by the Smithsonian
Astrophysical Observatory in Chile and California
patterns. (Robert Roosen, an occasional
contributor to this forum, has conducted important
studies of the old Smithsonian data.)

I have measured total column water vapor using
various near-infrared hygrometers in Texas almost
every day since 1989. The diurnal changes range
from none to major. About all that can be said is
that column water vapor is usually higher in
summer than in winter.

Other greenhouse gases should also be considered. Methane has
increased considerably, although the rise has moderated recently.
Consider ozone, a greenhouse gas with enormous seasonal and even
daily variability. For example, the last 6 days here at Seguin,
Texas (29.6N) (ozone given in Dobson units or milli-atm-cm):

12 Dec    267
13 Dec    254
14 Dec    252
15 Dec    244
16 Dec    241
17 Dec    283

These changes are actually very common. An extreme case occurred
on 16 March 1990 when ozone exceeded 350 Dobson units for a few
hours (confirmed by TOMS).

Although the general consensus is that global ozone has declined
around 5% since the 1980's, ozone at various sites in the
northern hemisphere increased from 4 to 10% during the 1960's.
These variations hold significance for global temperature
variations.

I have not even mentioned the major problem of isolating the
impact of anthropogenic aerosols. Nevertheless, I hope these
thoughts help illustrate the need to avoid overly simplistic
positions, whether pro or con, on the various climate change
issues now underway. It is unfortunate that even among
professional scientists the floor often becomes dominated by one
particular view, which then proceeds to exclude the other.

Forrest M. Mims III
Sun Photometer Atmospheric network (SPAN)
```

```From: jshearer@VNET.IBM.COM
Date: Wed, 31 Jan 96 20:17:51 EST
Newsgroups: sci.environment
Subject: Re: climate models

I posted (regarding large complicated computer models):
>I suspect if this were done routinely it would often uncover bugs.
Dave Halliwell responded:
>   Here we have it: Shearer is so determined to reject the idea of
>CO2-induced warming that he dismisses over 30 years of work by hundreds
>or thousands of researchers in climatology as "bugs in the code".

This is untrue.  I do not reject the idea of CO2 induced
warming.  Some time ago I posted the following to this group:
>         I will assume your questions are based on a hypothetical
>2*CO2 atmosphere.  I will admit that this group of experts expects
>some global warming to occur and that there appears to be about as
>much expert support for major warming as minor warming.
>         For what it's worth my current estimates are:
>                sensitivity < 0     -   1%
>                sensitivity < 1.5C  -  30%
>         1.5C < sensitivity < 4.0C  -  60%
>         4.0C < sensitivity         -  10%
>These estimates are not firmly held and are subject to change.  I
>would be interested in the estimates of other posters.

These are not the figures someone "determined to reject
idea of CO2-induced warming" would give.  I do not believe I have
posted anything rejecting the idea of CO2-induced warming.  I
suggest Halliwell substantiate his claim or withdraw it.
>         There are psychological factors involved also.  If the program
>results match what the implementer expected he is likely to search less
>vigorously for bugs than when the program results are unexpected.  This
>creates a bias which may cause results of several groups to converge
>to a faulty consensus.  (This has been observed to occur in the
>determination of physical constants by several groups.)
Dave Halliwell responded:
>   Of course, Shearer is the only person that isn't affected by bias.

I have never claimed to be unaffected by bias.  I claim
everybody is affected by bias, sometimes in quite subtle ways.
Some pervasive ways in which people are influenced by bias are the
following:
1.  People tend to believe what it is in their interest
for others to believe.  For example that an auto accident was not
their fault.
2.  People tend to interpret new information in terms of
a preexisting mental model.  They are reluctant to discard a model
before the evidence against it becomes overwhelming.  For example a
pilot may fly a plane into a mountain while thinking he is somewhere
else entirely.  He will have incorporated what might seem like ample
cues that something is wrong into his erroneous mental model of where
he is.
3.  People tend to adjust their opinions so as not to stray
too far from the opinions of their peers.  For example analysts
estimates of company earnings cluster more tightly than justified
by the actual predictability of such earnings.  (Ie the actual
earnings are often far outside the range of expert opinion.)
Scientists can try to minimize the effects of these biases
on their work.  However in my view they can never be entirely
successful.  Furthermore a blind denial that potential problems
exist does not inspire confidence.
Dave Halliwell continue:
>   Regardless of what anybody comes up with in the way of scientific
>evidence supporting CO2-induced warming, Shearer is going to reject it as
>"bug-ridden" or "biased". He's got his head stuck in the sand.

This is again untrue.  I accept that what is popularly called
the "greenhouse effect" warms the surface of the earth.  I accept that
CO2 is a greenhouse gas.  I accept that the observed increase in the
CO2 content of the atmosphere is almost surely of anthropogenic
origin.  I accept that there is a plausible argument that increasing
the CO2 content of the atmosphere will increase the magnitude of the
greenhouse effect thereby warming the surface.  I accept that simple
climate models allow crude estimates of the amount of warming that
can be expected.
I reject (or at least am extremely skeptical of) claims that
very elaborate climate models requiring large computer codes to
implement allow (or will allow anytime soon) us to significantly
refine estimates of climate change due to CO2 available from simpler
models.  I believe it is the people suggesting such models be used
to evaluate policy options who have their heads stuck in the sand.
Consulting the entrails of a goat would be as sensible.
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Fri, 2 Feb 96 20:18:53 EST
Newsgroups: sci.environment
Subject: Re: Half life of global warming

Dave Halliwell and I continue to argue about feedback.
We are now discussing who said what when.
Dave Halliwell posted:
>[On or slightly before Jan 15, 1995, quoted by someone]
>
>In <3f6e6g\$fmr@minotaur.nofc.forestry.ca>, Dave Halliwell
>(dhalliwe@nofc.forestry.ca) wrote:
>
>:    Keep in mind that the presence of many oscillators at various
>: frequencies and delay times also means that one cannot assume a simple
>: DC-type feedback response. It _may_ be possible that an initial warming
>: could lead to _cooler_ temperatures at some time in the future, due to
>: the relative strength and timing of various feedbacks. It is generally
>: not thought that this _will_ happen, but it isn't a 100% bet.

I do not remember seeing this post of yours.  You seem to
agree here that feedback can under some circumstances reverse the
sign of the response to forcing and that this could be true of the
climate system.  I am puzzled then as to why you have been defending
Tobis's claims to the contrary.
You quoted an example of one such contrary claim (11/29/95):
>I do not make quite so strong a claim. I claim that *feedback* cannot
>reverse the sign (at least in a sensibly linearizable situation) of
>the system without feedback. That is, if the output is temperature, there
>is no temperature-dependent phenomenon which can reverse the sign of
>the response. This is a very solid result in elementary systems theory.

There is no restriction to DC systems in this claim.
>  I don't
>think he claimed my example was AC (although he at first claimed
>it wasn't a feedback system, a claim which he eventually withdrew).
Dave Halliwell responded:
>   In the post I quote above, he does explicitly state that he doesn't
>think it is a _linear_ feedback system.

As I noted he withdrew this statement.  The first post you
quoted was from July 1995.  On 9/16/95 Tobis posted in part:
>It is a feedback system, granted.

(I doubt he ever intended to deny the system is linear,
since it clearly is.)
>         If Tobis is lurking in this discussion he could clear some of
>these points up himself.  He has been promising to refute my example
>real soon now for months.
Dave Halliwell responded:
>   You, on the other hand, have never bothered to post any implementation
>of the time dependence of your earlier example, nor have you made any
>attempt that I have seen to demonstrate that your system fits the
>restrictions discussed in Tobis' first post [of the ones quoted above].

As noted above, Tobis later seemed to agree that my example
did meet his conditions.  For example in the same 11/29 post quoted
above:
>At first glance, Shearer's counter-example seems to contradict this.
>I intend to figure out why.

As for posting the time dependence of my example, this seemed
unnecessary since I posted the exact analytic solution.  However to
please Halliwell, I post some points of the time evolution of the
example below.
The system in question is

y'=B*y+a  with y= y1  B= -4 3  and a= 1 (when T>0)
y2     -2 1         0

Recall the system starts in a stable equilibrium at (0,0).
We introduce positive forcing on Y1 at time T=0.  This initially
causes Y1 to increase.  The increase in Y1 causes Y2 to decrease.
The decrease in Y2 causes Y1 to decrease.  This negative feedback
through the interaction with Y2 eventually forces Y1 below 0,
opposite the direction of the forcing.  The system converges to
a new stable equilibrium with Y1=-.5 (and Y2=-1.).  Feedback has
reversed the sign of the response to forcing.
Here columns 2 and 3 are the y1 and y2 variables.  These
are computed from the exact solution.  Columns 4 and 5 are the y1
and y2 variables computed from the equations (Euler's method with step
.1d0).
exact                  numeric
T           Y1          Y2          Y1          Y2
0.000000    0.000000    0.000000    0.000000    0.000000
0.100000    0.081579   -0.009056    0.100000    0.000000
0.300000    0.158419   -0.067175    0.190000   -0.054000
0.400000    0.166647   -0.108689    0.197800   -0.097400
0.500000    0.161242   -0.154818    0.189460   -0.146700
1.000000    0.032756   -0.399576    0.036296   -0.410017
1.100000   -0.000463   -0.445061   -0.001228   -0.458278
1.500000   -0.128420   -0.603527   -0.140994   -0.623402
2.000000   -0.256803   -0.747645   -0.274141   -0.768376
2.500000   -0.345937   -0.842568   -0.362087   -0.860198
3.000000   -0.404144   -0.902905   -0.417075   -0.916456
4.000000   -0.463872   -0.963704   -0.470638   -0.970571
5.000000   -0.486592   -0.986570   -0.489714   -0.989707
6.000000   -0.495052   -0.995049   -0.496408   -0.996408
8.000000   -0.499329   -0.999329   -0.499563   -0.999563
10.000000   -0.499909   -0.999909   -0.499947   -0.999947
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Wed, 7 Feb 96 22:40:28 EST
Newsgroups: sci.environment
Subject: Re: Cooling; was: Re: CFCs in the atmosphere (was Re: Why do

>         William M Connolley posted (regarding a 1971 paper by
>Rasool and Schneider):
>>1. the temperature increase with CO2 found is about 1/3 of Manabe and Wetheral
>>This is accounted for by different CO2 abs coeffs, different lapse rate specs,
>>and different CO2/H20 overlaps.
>
>         So, who was right?

Paul Farrar replied:
>We'll know some time next century, when CO2 doubling is achieved.
>Later we'll find out what happens at 2-1/2X, probably 3X, and maybe
>4X. Perhaps in about 1000 years, when CO2 comes to equilibrium with
>the oceans, we'll have the final answer on this practical experiment.

You misunderstand my question.  I am not asking who was
right about the behavior of the real climate system, rather I am
asking who was right about the behavior of the 1D RCM model of the
real climate system.
Len Evens replied in part:
>Well in science one can never be absolutely certain who or what is
>right or wrong.   However, the general consensus, which includes
>among other people Schneider, is that Manabe was closer to being
>right than Schneider and Rasool were.   ...

Closer to being right about the behavior of the 1D RCM
model?
Len Evens continued:
>However, this is really a rather silly question, I think.    1971
>is at this point ancient history.   If you read the Rasool and Schneider
>paper you would see that the analysis used there is quite rough and
>uses a model of the earth very unrealistic according to present
>standards.    Manabe, also, was of course working with primitive
>models, but it is interesting to note that his predictions for
>temperature sensitivity to CO_2 doubling have remained fairly consistent
>over this period of time.   Perhaps, he and his colleagues, have had
>good physical intuition about what is important and what is not.

Since this is an old dispute about a simple model I would
expect that it is now known exactly who was right and why.  If this is
not the case I would question what climatologists have been doing for
the last 25 years.  It is pointless to fool around with much more
complicated models if you don't know what the correct absorption
coefficients for CO2 are (for instance).
So I ask again, who was right and why?
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Wed, 7 Feb 96 22:41:45 EST
Newsgroups: sci.environment
Subject: Re: climate models

I posted:
>          I reject (or at least am extremely skeptical of) claims that
> very elaborate climate models requiring large computer codes to
> implement allow (or will allow anytime soon) us to significantly
> refine estimates of climate change due to CO2 available from simpler
> models.  I believe it is the people suggesting such models be used
> to evaluate policy options who have their heads stuck in the sand.
> Consulting the entrails of a goat would be as sensible.

>Does this also apply to the econometric models which are used for
>budgeting purposes by CBO, OMB, etc, which have even greater impact
>on policy options and the models used for program trading which
>have enormous impact on our economic well being (well, at least
>my hoped for retirement income)?  If so, what is your position
>as to the posturing in Washington over whose budget proposal is
>honest?  If you hold the econometric models to be useful, then
>why are they more useful for policy decisions than the GCMs.  The
>later appear (at least to me) to be based more on knowledge than
>the former.

I don't trust any elaborate computer model that can't be
convincingly validated.  As I have posted before in this group this
certainly includes many econometric models.
Josh Halpern continued:
>As you might guess, the purpose of asking you this question is to
>point out that most policy decisions today are based on models,
>and comparatively the Global Climate Models are based on a lot
>better data and knowledge than the economic models that we depend
>on.

I don't agree, I believe most policy decisions today are
based on politics.
Josh Halpern concluded:
>Almost without exception, policy decisions are made in the absence
>of perfect (or even good) knowledge of the future consequences of
>that action, and, as has been pointed out elsewhere, not to
>decide is to decide.

It is true that often important decisions have to be made in
the presence of uncertainty.  Policy makers find agonizing over such
decisions painful.  For this reason they are often very susceptible
to claims that there is a way to reduce or eliminate the uncertainty.
In ancient times this might involve consulting an oracle.  Today it
might involve running an elaborate computer model.  In my view the
James B. Shearer (email jbs@watson.ibm.com)
```

```From: jshearer@VNET.IBM.COM
Date: Fri, 9 Feb 96 23:41:35 EST
Newsgroups: sci.environment
Subject: Re: climate models

Here I reply to a post of Rich Puchalsky in which he takes
exception to my using errors in computer calculations by Dave
Halliwell as an excuse to expound on the hazards of buggy computer
calculations in general.  I also respond to Halliwell's comments on
Puchalsky's post.
Rich Puchalsky posted:
>Here Halliwell takes time, purely out of the goodness of his heart, to
>actually set up a spreadsheet to test one of Shearer's propositions.  No
>publication is expected; no special rigor is desired for this off-hand
>Usenet-inspired little task.  Yet when Halliwell makes an error setting
>up the spreadsheet -- which anyone could make, given the non-importance
>of the matter and therefore the lack of careful checking involved --
>Shearer has the *gall* to hold this up as analogous to the work of
>professional modellers that has been checked and reviewed prior to
>publication in a journal.

While posts to this group are not the same as publication
in a professional journal, they may well be seen by as many people.
In my view this means posters should take some care about what they
post, particularly when they are declaring another poster was wrong.
It is true anyone can make programming errors.  (This is
because writing correct programs is hard, much more so for the more
complicated climate models than for the simple model Halliwell
attempted.)  However not everyone has Halliwell's blind faith in
computer calculations.  In the case at issue Halliwell declared
my mathematical argument showing stability was invalid based on a
numerical calculation in which the temperature of the earth went
from 306.6 K to -2659.8 K in one time step.  A more humble individual
might have considered this as an indication that he was doing
something wrong and looked for bugs.
Finally many published papers dependent on computer
calculations are not in fact checked in any meaningful way prior to
publication.  If Puchalsky thinks the results of buggy computer
programs never make it into published papers, he is extremely naive.
Puchalsky continued in part:
>This kind of crap has to be contributing to the exodus of scientists from
>sci.environment.  I note that Pierrehumbert just posted that he no
>longer has time to participate; Grumbine also recently left.  I'll refrain
>from going through the full list.

I have never attempted to drive anyone out of this group by
vilifying them.  I wonder if Puchalsky can say the same.
Dave Halliwell posted:
>   Not only that, but it's _Shearer's_ model. I was implementing the
>model because his original post did not examine the overall
>time-dependence of the system, from initial conditions to equilibrium: he
>only looked at the initial trajectory and the final equilibrium value.
>
>   In a "publication" analogy, Shearer is complaining because the reviewer
>didn't do a perfect job of completing work that the author failed to
>provide. Most reviewers would probably just pull out the REJECT stamp,
>and not bother going into detail.

Ok, let us consider a publication analogy.  I submit a paper
showing (using mathematical arguments) what conditions are needed for
a certain simple model to have a stable equilibrium solution.
Halliwell, as reviewer, rejects the paper based on his totally bogus
numerical calculations which indicate instability.  Eventually I
convince the reviewer that he is wrong.  However he still doesn't
accept the paper.  Instead he invents a new and equally spurious
ground (that a discussion of under what conditions a model has a
stable equilibrium is obligated to include a description of the
trajectories leading to the equilibrium) for rejecting it.  At this
point I would be justified in asking the editor for a different
reviewer.
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Fri, 16 Feb 96 22:06:22 EST
Newsgroups: sci.environment
Subject: Re: Half life of global warming

The feedback discussion drags on.
>          Do you really doubt that it is possible to contrive examples
> with the desired behavior?  Consider for example a house with a single
> zone heating system and the thermostat in a cold spot.  Then it may be
> that the colder it gets outside, the hotter the house will be on
> average (since the thermostat will keep the cold spot at the desired
> temperature and the difference between the hot parts and cold parts
> of the house will increase as it gets colder outside).
Michael Tobis replied:
>This has the nature of Steinn's example - you have more than one
>variable. The temperature at the thermostat is insensitive to the
>temperature outside and that's the only simple feedback loop. It
>ought to be possible to use your pendulum with springs and dashpots
>to accomplish the same with only a single output. It would be a very
>interesting contraption, too. So I'm still puzzled.

that it would involve a nonlinear regime shift.  In my example with
a two room house we can have a completely linear system.  Suppose T1
is the temperature of the room with the thermostat, T2 is the
temperature of the other room.  Cooling the outside tends to reduce
T1 and T2, but reducing T1 may cause T2 to increase so much that the
net effect is a warmer house on average.  If we change variables so
that S1=(T1+T2)/2 and S2=(T1-T2)/2 then we can arrive at a system
of differential equations similar to those I have posted before.  We
force S1 down but the interaction with S2 causes S1 to eventually
rise.  Certainly one can imagine mechanisms whereby heating one
part of the earth causes cooling elsewhere (without a regime shift).
So I am puzzled as to what you think remains of your claim.
The problem with trying to construct an example using
springs is that springs act symmetrically.  For example suppose the
ends of the spring are A and B.  Then if moving A to the right
pushes B to the right, moving B to the right will pull A to the
right.  So this is a positive feedback loop and we need a negative
feedback loop.
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Fri, 16 Feb 96 22:08:17 EST
Newsgroups: sci.environment
Subject: Re: Cooling; was: Re: CFCs in the atmosphere (was Re: Why do

model in a 1971 paper by Rasool and Schneider and an earlier paper by
Manabe.
Michael Tobis replied in part:
>I don't know whether anyone will answer your question, but that is not
>because it is in principle unanswerable.  I think that if you intend to
>cast aspersions on the discipline as a whole, the lack of a clear answer
>to the question you pose is lousy evidence. It's a question of infinitesimal
>significance which 25 year old paper is closer to current understanding.

I think in evaluating how much to trust current models it
is worthwhile to see how well older models have held up.
In this particular case I find the factor of three
difference in model sensitivity suspicious.  I wonder if R&S really
checked that the factors mentioned account for the difference
in model results.  Could it be that the footnote was added at the
last minute to pacify a referee and that the real explanation was
something else?  For example one might suspect a bug in one of
the computer codes.
Michael Tobis continued in part:
>                  ...                                And of course, the
>less objectively decideable question of lapse rate specification is
>irrelevant to 3 dimensional models.

The big models having replaced a few arbitrary assumptions
(such as the lapse constraint) in simple 1D RCM models with a much
larger number of arbitrary assumptions.  I do not see why this should
be considered an improvement.
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Mon, 4 Mar 96 11:40:35 EST
Newsgroups: sci.environment
Subject: Re: Cooling; was: Re: CFCs in the atmosphere (was Re: Why do

I posted:
>          All right, what would you call assumptions for which reasonable
> alternatives exist given the present state of knowledge?  How many such
> assumptions do you believe a typical large climate model contains?  How
> much of the space of reasonable alternative large climate models has
> been explored?  Why should any great weight be given to a single point
> in the space of reasonable large climate models?

Joshua Halpern commented:
>A more interesting question is how sensitive the results are to either
>arbitrary assumptions, or uncertainties in parameters.  Although I
>am not familiar with GCMs, the combustion and atmospheric chemistry
>models I am familiar with carefully include a sensitivity analysis
>The "key" values then tend to get measured, or improved quickly,
>so that at least is a functioning positive feedback loop.
>
>In many cases an arbitrary choice, or a good guess, or an order
>of magnitude estimate suffice.

Well if the results are not sensitive to the details of
the albedo submodel (for example) then it would appear pointless to
have a complicated albedo submodel.
I agree that a sensitivity analysis is important.  I am not
convinced that climatologists are doing an adequate job in this area.
Note also that the more complicated the model the harder it is to
understand what it is sensitive to, another reason I am skeptical
of large complicated climate models.
As for whether things are improving, consider the following
quote from the paper "Climate Sensitivity" (by Robert E. Dickinson,
in Advances in Geophysics, volume 28 (1985), Issues in Atmospheric and
Oceanic Modeling  Part A  Climate Dynamics, p. 99-129, quote starts
p. 110)
"It would also appear that proper modeling of high-latitude
cloud cover and its optical properties is important for obtaining a
correct description of ice-albedo feedback in GCM simulations [as also
in energy balance models, e.g., Golitsyn and Mokhov (1978)].
Unfortunately, even the climatological cover of high-latitude clouds
is poorly known [as reviewed by Barry et al. (1984)], and their
modeling in GCMs is totally speculative.
Thus in summary it appears that the largest sources of
uncertainty for the sensitivity of global average temperature to
external changes in tropospheric energy balance are the magnitude
of the ice-snow albedo feedback processes and the magnitude and
sign of cloud-radiation feedback processes.  These conclusions
have been drawn for over a decade [cf. e.g., Schneider and
Dickerson (1974)].
However, what is especially distressing is that recent GCM
studies have not contributed to narrowing our uncertainty as to those
processes but have suggested that we are rather more ignorant than
we previously thought.  ... "
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Tue, 5 Mar 96 20:27:18 EST
Newsgroups: sci.environment
Subject: Re: Cooling; was: Re: CFCs in the atmosphere (was Re: Why do

Michael Tobis posted:
>I wonder whether Shearer's skepticism regarding such models extends to
>models of the atmospheres of other planets, or the dynamics of stars,
>or even to the pursuit of fluid dynamic modelling of industrial processes,
>all of which are undertaken in an essentially similar way.

As I have said in previous posts, I am extremely skeptical of
any computer model which cannot be easily checked against reality.
Consider the comments of Clifford Stoll regarding his
dissertation (which depended on a computer model of Jupiter's
atmosphere) in his book Silicon Snake Oil (p152-153).
"Yes, but do I believe it today?  That question makes me
squirm.  Complicated computer models are sexy--researchers manipulate
their views of reality to fit their favorite computer program.  They
become invested in their own models.
After years of modeling Jupiter's atmosphere and exploring
parameter space, I'm not certain.  I spent months researching what
ought to go into my model, but I sure didn't include everything.  I
never explored all possible cloud structures, only the most likely
ones.  I checked my software, but couldn't test every possible
programming flaw.
In most research, you keep close track of systematic errors--
numbers are usually perfectly correct, but a bad assumption or simple
bug throws the answer out the window.
Computer models don't convince--they aren't simple and they
sure aren't physical.  I can list my assumptions, show you my data,
and describe my program.  But I hope you'll still be skeptical--
there's plenty of places to goof up.  Probably the only way to
clinch the issue is a visit to the planet with a microscope and
tweezers."
I would guess his model was much simpler than a typical
climate model.
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Tue, 5 Mar 96 20:29:40 EST
Newsgroups: sci.environment
Subject: Re: Cooling; was: Re: CFCs in the atmosphere (was Re: Why do

Scott Nudds posted:
>  The key term in this thread - the one that you now conveniently ignore,
>after having employed it - is the term "arbitrary".  You referred to
>"arbitrary assumptions".

In an earlier post in this thread I explained what I meant by
"arbitrary assumptions" as follows:
> By arbitrary, I mean any assumption for which reasonable
> alternatives exist given the present state of knowledge.
To which Nudds replied:
>  Ok.
Nudds appears to have forgotten this.
Scott Nudds continued:
>  My statements accuse you of assuming that "arbitrary assumptions" are
>used in GCM's.  As usual, the burden of proof is on you to provide
>examples of these "arbitrary assumptions".
>
>  You appear incapable of doing so.  So rail on child.

Regarding "burden of proof" Nudds appears to feel that the
burden of proof is always on anybody who disagrees with him.  In this
case he doesn't even have the guts to actually disagree with me by
posting something like "Shearer is wrong, there are no arbitrary
assumptions in GCMs".  Instead he blathers on about how I have not
proven 2+2=4 to his personal satisfaction.
In any case I provided numerous examples of arbitrary
assumptions in a post in a different thread.  I will repeat one:
>         I recently obtained a "Description of the NCAR Commumity
>Climate Model (CCM2)" from the net (gopher://isis.cgd.ucar.edu/99/
>processor/doc/TN-382.ps.).  Some quotes
>         <numerous other examples deleted>
>         p. 67:  "... the number of layers is arbitrary.  ... we
>arbitrarily chose a constant layer thickness of 50 cm."
James B. Shearer (email jbs@watson.ibm.com)

```

```From: jshearer@VNET.IBM.COM
Date: Fri, 8 Mar 96 19:44:28 EST
Newsgroups: sci.environment
Subject: Re: Demonizing S. Schneider

Well, the man does appear to be a tempting target.
I ran across a book called "The Cooling" (By Lowell Ponte,
Prentice Hall, 1976) in my local public library.  The book worries
about a possible impending ice age (among other things, the book
contains a mishmash of eccentric scientific and political ideas).
And what should I see on the back cover but a plug from Schneider.
Thus:
"The dramatic importance of climate changes to the world's
future has been dangerously underestimated by many, often because
we have been lulled by modern technology into thinking we have
conquered nature.  But this well-written book points out in clear
language that the climate threat could be as awesome as any we
might face, and that massive world-wide actions to hedge against
that threat deserve immediate consideration.  At a minimum, public
awareness of the possibilities must commence, and Lowell Ponte's
provocative work is a good place to start."
--Dr. Stephen H. Schneider, Deputy Head
Climate Project, National Center
for Atmospheric Research

A more prudent man would decline to endorse such books in
view of the adverse affects such endorsements might have on his, not
to mention his profession's, credibility.
In fairness Schneider does appear to have had second