Email correspondence between Matthew Marler and Vaughan Pratt during March-May 2015 (37 emails)

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NEW SUBJECT: another estimate of climate sensitivity
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Date: Sun, 15 Mar 2015 23:38:45 -0600
From: Matthew Marler 

Hi Vaughan,

I thought I would share this simple calculation with you before I submit
it for review.

yours truly,
Matthew

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Date: Mon, 16 Mar 2015 23:54:13 -0700
From: Vaughan Pratt 

Hi Matthew,

Thank you for your short note.  Can you use feedback on it?  And if so
would you prefer feedback from my perspective or from that of likely referees?

Best,
Vaughan


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Date: Tue, 17 Mar 2015 00:02:58 -0700
From: Vaughan Pratt 

Hi Matthew,

I ran into a problem calculating climate sensitivity as a function of SH,
LH, and UWLWIR.  Do you have a formula for this as a function of those
three variables, so I can just plug in their values?

Vaughan

--------------------------
Date: Tue, 17 Mar 2015 01:10:44 -0600
From: Matthew Marler 

Nope.  I have worked on diverse versions of this idea, and I knew about
what I would get if I did the calculation with a 0.5C.  To me, the most
important points are not the calculated sensitivity, but the approach to
calculating it, and the particular assumptions that go into it.
I appreciate feedback about actual errors, but I already know that a lot of
other approaches get different values; that does not show me to be in
error, but that different approaches produce different results.

Thank you for reading and responding.
Matt

--------------------
Date: Tue, 17 Mar 2015 09:27:22 -0700
From: Vaughan Pratt 

Can you at least give the sequence of arithmetic operations (plus, minus,
times, divide) that you used for your approach to calculating it, in the
order they are applied, and to what they are applied?  This would be very
helpful in understanding your approach.

Vaughan

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Date: Tue, 17 Mar 2015 10:37:41 -0700
From: Vaughan Pratt 

Never mind, I worked out the formulas, portions of which you already 
gave in your write-up.

I agree that it is reasonable to ask what is the increase in each of SH, 
LH, and UWLWIR in response to a given rise in surface temperature.
I also don't see any major problem with the values you've computed for 
each of them, given that you've allowed for considerable uncertainty in 
each of them.  David Romps would be much more qualified than me to 
estimate those values.

What I do see missing however is what happens to all that upward flux. 
100% of the LH is dumped into the clouds, raising their temperature. 
Likewise 100% of the SH serves to warm the troposphere in general.  And 
where there are clouds, 100% of the UWLWIR is absorbed by those clouds, 
while in a clear sky a large fraction of the UWLWIR is absorbed by the 
various greenhouse gases, most notably water vapor but also CO2 and 
ozone, and a little by methane.

As a result the troposphere warms up.  In order to maintain the lapse 
rate, all altitudes of the troposphere must warm by essentially the same 
amount, including the air close to the surface.

Yet the only warming of the surface that your model takes into account 
is an increase in downward radiation attributable to an increase in CO2.
This grossly underestimates the total increase in surface warming 
resulting from increases in the three fluxes you've estimated.

Vaughan

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Date: Tue, 17 Mar 2015 13:20:10 -0600
From: Matthew Marler 

Vaughan: *Yet the only warming of the surface that your model takes into
account is an increase in downward radiation attributable to an increase in
CO2.  This grossly underestimates the total increase in surface warming resulting
from increases in the three fluxes you've estimated.*

Right now, pending better estimates, I think that I have a slight
underestimate, not a gross underestimate.  The hydrological cycle, for
example, takes the energy from the surface to a high altitude, where almost
none of it is radiated back to the surface.  Of the people to whom I have
emailed this (I expect most recipients to trash it, given my lack of
standing in the profession), you are the first to have noticed this
limitation in my model.

Thank you again.
Matthew

---------------
Date: Tue, 17 Mar 2015 20:56:33 -0700
From: Vaughan Pratt 

On 3/17/2015 12:20 PM, Matthew Marler wrote:
> The hydrological cycle, for example, takes the energy from the surface
> to a high altitude, where almost none of it is radiated back to the surface.

Four points:

1.  LH cannot be radiated anywhere, either up or down, because it is 
latent, not sensible.  Instead it stays in the atmosphere until it 
condenses out to clouds, thereby turning LH into SH *in clouds*, which 
then *can* radiate (see 3 below).

2.  However little SH heat is radiated back to the surface, even less is 
radiated out to space because there is more air between a cumulus cloud 
and space than between that cloud and the surface.  The converse is only 
true for clouds higher than 5.6 km (see the third paragraph of the section

https://en.wikipedia.org/wiki/Atmosphere_of_Earth#Pressure_and_thickness

on "Pressure and thickness").  The latter are mainly cirrus clouds, but 
according to Franks (4th line on p.566 of the attached) even those have 
a net heating effect.

3.  Have you ever noticed that cloudy nights are much warmer than clear 
nights for cumulus clouds?  (Less so for cirrus clouds.)  This is 
because the sensible heat dumped into cumulus clouds by condensation 
radiates considerable heat down to the surface.

4.  The mechanism I gave for redistribution of the heat attributable to 
SH, LH, and ULR was as follows. "In order to maintain the lapse rate, 
all altitudes of the troposphere must warm by essentially the same 
amount, including the air close to the surface."  This is a purely 
convective effect.  In particular it does not depend at all on 
radiation.  Whatever radiation there may be on a day to day basis is 
irrelevant because lapse rate totally dominates on a year to year basis.

> Of the people to whom I have emailed this (I expect most recipients
> to trash it, given my lack of standing in the profession), you are
> the first to have noticed this limitation in my model.

I'm not surprised.  Traditional theories such as the Sun goes round the 
Earth, global warming is caused by back radiation, etc die hard.  It's 
going to take a few years for the role of lapse rate to sink in.

An interesting experiment would be to submit your write-up as a post to 
Climate Etc (Judy is pretty good about taking on all points of view---if 
she has any misgivings let me know and I'll tell her I think your [SH,LH,UWLIR]
numbers are within reasonable bounds) and see how many different 
responses you get.  If you do so, let me know and if I have time (my 
calendar is filling up with projects) I'll sit on the sidelines and try 
to evaluate the responses, without interjecting anything about lapse 
rate (other than perhaps to agree with anyone stating that it is an 
important consideration here).

Vaughan

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Date: Wed, 18 Mar 2015 01:17:41 -0600
From: Matthew Marler 

*An interesting experiment would be to submit your write-up as a post to
Climate Etc*

All of the elements have been posted at Climate Etc, RealClimate, and WUWT
with diverse wording, sometimes using the flow diagram from Trenberth et
al.  Prof. Curry has the pdf that I sent to you.

Come back to my main question: SH and LH are pushed to the upper
troposphere where, after transferring their energy to the gases at that
height, their energy is radiated to space.  The air in the thermals  is
pushed up in columns, each surrounded by a toroid of cooler, drier, denser
air that is descending.  The energy flows of those processes are summarized
by Stephens et al and by Trenberth et al.  How do those energy flows change
if the surface warms by 1C (or any other particular value)?


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Date: Wed, 18 Mar 2015 17:52:05 -0700
From: Vaughan Pratt 

On 3/18/2015 12:17 AM, Matthew Marler wrote:
> /An interesting experiment would be to submit your write-up as a post to
> Climate Etc/
>
> All of the elements have been posted at Climate Etc, RealClimate, and
> WUWT with diverse wording, sometimes using the flow diagram from
> Trenberth et al.  Prof. Curry has the pdf that I sent to you.

A URL containing responses to your post at CE would be great.  (Or RC for
that matter, though I rarely go there---if I need to hear preaching to the
choir or testimonials of faith I can go to church on Sunday.)

> Come back to my main question: SH and LH are pushed to the upper
> troposphere

Do you have a source for this, or is it an understanding you've arrived at
on your own?

SH: The only reason SH rises at all is because it increases the lapse rate
locally, thereby destabilizing the atmosphere.  The SH rises only to the
extent necessary to bring the lapse rate back down to the environmental
lapse rate (ELR).  ELR is the only thing governing the distribution of SH.
The idea that SH "is pushed to the upper troposphere" is highly unphysical.
More on this below in connection with thermals and plumes.

LH: This resides in water vapor (WV, to distinguish it from H2O which even in
the atmosphere can be in any of its three phases).  On its initial entry into
the atmosphere, namely via evaporation, LH is (perhaps counterintuitively)
colder than the surrounding air (the mechanism behind a Coolgardie safe),
but equilibrates rapidly in temperature, thereby cooling the air slightly,
with the side effect of stabilizing the atmosphere locally and therefore
not rising, contrary to your intuition about LH.  Until WV condenses to
water droplets it remains a well-mixed gas just like CO2.

Whereas the average molecular weight of dry air is 28.97 grams per mole, CO2
is heavier at 44 g/mol while WV is lighter at 18 g/mol.  One might imagine
therefore that CO2 would sink to the bottom while water vapor would rise to
the top of the atmosphere.  However those weights only impact diffusion, a
very slow process, and therefore play a negligible role in the respective
vertical distributions of these gases, which are driven primarily by
convective processes whose effect is to mix them well.

The upshot is that the WV (and hence LH) has no particular preference for
whether it rises or falls once its initial cooling effect has worn off,
and is simply mixed in by convective processes.

The main difference between CO2 and WV in the atmosphere is that whereas CO2
remains a gas, WV can undergo phase changes between any of the four phases
shown in the figure on p.560 of the Franks paper I sent you.  The most

relevant phase changes are the two at the top of the figure labeled
condensation and its inverse "boiling" (which I would have labeled as
"evaporation"---the transition he labeled "evaporation" I would have labeled
"sublimation").

As I said above, WV does not rise in any significant sense, it is merely
mixed in to even out the distribution.  However its phase is governed by
lapse rate (and also pressure): any given quantity of WV is experienced as
a higher relative humidity (RH) in colder air.  Up to 11 km, ELR averages
6.5 K/km (and above 11 km there is essentially no WV even though exp(-11/8)
= 25% of the mass of the atmosphere is above 11 km).

Most WV condenses out at between 2 and 4 km, forming cumulus clouds comprised
of water droplets.  A very small amount of WV forms cirrus clouds comprised
of ice crystals at altitudes of 6-11 km and temperatures of -30 to -50 C
(243-223 K), see

Since (223/288)^4 = 0.36, the already small quantity of heat in the cirrus
clouds at 11 km is radiated only 0.36 as strongly as heat from the surface.

Furthermore clouds are hotter at the bottom than at the top, by a considerable
amount for thick clouds like cumulonimbus, and therefore radiate more
heat down than up.  Also half the atmosphere is above 5.6 km and contains
greenhouse gases (CO2, ozone, methane) that trap a considerable amount of
the radiation from clouds before it can reach space.

> where, after transferring their energy to the gases at that
> height, their energy is radiated to space.

About a quarter of what little energy remains at that altitude is radiated
to space.  At any height, radiation from a point is distributed uniformly in
all directions.  Half the radiation from a point is to the lower hemisphere
below the point.  Total radiation to the upper hemisphere is given by
the integral of cos(t)*exp(-a/sin(t)) for t from 0 (horizontal) to pi/2
(vertical) where a is the optical depth of the atmosphere for a vertical
ray to space from that point (details if interested).  For optical depths
in the range 0.1 to 1 this turns out to be roughly half of what it would
be for radiation straight up.  Hence including the downward radiation, a
reasonable estimate of the total radiation to space from a point is about
a quarter of what it would be were all of it to be directed straight up.

> The air in the thermals  is
> pushed up in columns, each surrounded by a toroid of cooler, drier,
> denser air that is descending.

As an aside, that describes a plume of hot air.  A thermal is more like
a bubble of hot air.  Thermals becomes plumes when the surface becomes
sufficiently hot to support a steady plume.  The distinction is not
particularly relevant here.

More importantly, as noted above hot air rising from the ground loses
6.5 degrees for every kilometer due to adiabatic expansion, more for air
that is drier than average.  It is therefore much colder when it reaches
a significant altitude.  This is of course only relevant to SH, not to LH,
which cannot cause thermals.

> The energy flows of those processes are
> summarized by Stephens et al and by Trenberth et al.  How do those
> energy flows change if the surface warms by 1C (or any other particular
> value)?

Figure 5 in Section 5 of the attached paper by David Romps plots the
theoretical impact of a 10 degree rise in surface-air temperature on RH and
temperature profiles at altitudes up to 25 km.  Note that the profiles retain
their basic shape while moving up.  For 100% precipitation efficiency the
altitude at which RH reaches 100% rises from 15.5 to 17.5 km as surface-air
temperature rises from 300 to 310 K, and corresponds to the altitude where
lapse rate abruptly reverses, aka the tropopause.  Figure 6 is also based
on theory, while Figures 7 and 8 perform the corresponding analysis using
a cloud-resolving model.

The main take-away here is that RH and T (temperature) are tied together.
As the climate warms, both RH and T at any given altitude climb by the same
height to a new altitude.

It follows that using the Planck feedback to calculate the temperature at
a given altitude resulting from a given warming also lets you calculate
the RH at that altitude.

I'm dubious that the rates of flow change much, but I would gladly defer
to Romps on that question.

Vaughan 


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Date: Wed, 18 Mar 2015 19:26:56 -0600
From: Matthew Marler 

> Do you have a source for this, or is it an understanding you've arrived at
> on your own?

That comes from standard texts, such as Salby Physics of the Atmosphere and
Climate; Randall Atmosphere, Clouds and Climate; and Ambaum Thermal Physics
of the Atmosphere.  The warm surface-layer air expands adiabatically so
that it has a lower density than the air above it, and columns of air are
formed rising through the inversion.  The columns of warm air are pushed
upward by the toroidally shaped much larger columns of descending cool dry
denser air; CAPE is the energy imparted to the rising air by the descending
air that is pushing it up.  There is some heat exchange at the surface
between the inner and outer column (over their full height), but most of
the energy carries upward until the cooling central column is equal to the
surrounding air.  The effect of extra heat and water vapor at higher
surface temperatures is to raise the height (and surface area) of the
clouds.

I have read the Romps et al relative humidity paper, but thank you.  
An analytical model is derived for tropical relative humidity using only
the Clausius-Clapeyron relation, hydrostatic balance, and a bulk-plume
water budget.

You can see the problem right away: they have an equilibrium model for a
process where *almost all of the energy transport occurs in the conditions
farthest from equilibrium.*  Where there is hydrostatic balance there is no
energy transport: where there is energy transport, the water rises as
vapor, accumulates at the condensation level as ice, and then later returns
to the surface in rainfalls (sometimes called "torrents").
To me the most significant aspects of the Laliberte et al paper and the
Romps et al lightning paper is that they get past the equilibrium
approximation.  Where there is equilibrium there is no lightning!

Matt

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Date: Wed, 18 Mar 2015 19:44:53 -0700
From: Vaughan Pratt 

On 3/18/2015 6:26 PM, Matthew Marler wrote:
>
> That comes from standard texts, such as Salby Physics of the Atmosphere
> and Climate;

Page number, please.

I thought Salby's book was quite good.  I would not have thought so if 
he'd claimed anywhere that either SH or LH are "pushed to the upper 
troposphere".  Meteorologists would have cracked up over that.

Vaughan

--------
Date: Wed, 18 Mar 2015 20:10:17 -0700
From: Vaughan Pratt 

On 3/18/2015 6:26 PM, Matthew Marler wrote:
> Where there is equilibrium there is no lightning!

Do you have a page number for this?

You might have noticed that whenever I give you a reference I don't 
merely quote the title of a book or paper, I include a page or figure 
number.  Less than that is useless.

Vaughan

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Date: Wed, 18 Mar 2015 21:10:46 -0600
From: Matthew Marler 

Reread the presentation of CAPE: the less dense hot air rises because
the denser, cooler air pushes it up; the other word used is "lifted".
"Upper troposphere" is a tad inaccurate, perhaps, but definitely up high.
A worked example in Ambaum gives a representative height for LFC (level of
free convection) of 550 hPa, ca 6km.  The tropopause is at 10 km.

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Date: Wed, 18 Mar 2015 21:17:33 -0600
From: Matthew Marler 

"Equilibrium" is when maximum entropy occurs, and there are no more energy
transfers.  Much of the theory treats of "local thermodynamic equilibrium",
where for short distances and small energy changes the processes are
reversible.

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Date: Wed, 18 Mar 2015 22:04:17 -0700
From: Vaughan Pratt 

On 3/18/2015 8:10 PM, Matthew Marler wrote:
> Reread the presentation of CAPE: the less dense hot air rises because
> the denser, cooler air pushes it up; the other word used is "lifted".

Yes, certainly.  Nothing I said contradicts this.

>   "Upper troposphere" is a tad inaccurate, perhaps, but definitely up
> high.  A worked example in Ambaum gives a representative height for LFC
> (level of free convection) of 550 hPa, ca 6km.

That's one extreme example.  At

is an example where the LFC is at 809 hPa, ca 2.1 km.  In a tornado the 
LFC can be at the opposite extreme, practically at the surface.

> The tropopause is at 10 km.

It varies greatly with latitude:
https://en.wikipedia.org/wiki/Tropopause#/media/File:Jetcrosssection.jpg

In the tropics it's at around 17-18 km, about three times Ambaum's LFC, 
eight times the above example, and a hundred times the LFC of a tornado.

Vaughan

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Date: Wed, 18 Mar 2015 22:05:51 -0700
From: Vaughan Pratt 

So regarding lightning, no page number?

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Date: Wed, 18 Mar 2015 23:26:17 -0600
From: Matthew Marler 

Good stuff.  For now we work with means, but the geographic and other
variation becomes more and more important as greater and greater accuracy
is required.  Thanks again.

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Date: Wed, 18 Mar 2015 22:50:41 -0700
From: Vaughan Pratt 

Over the past four billion years, has there been a day when the planet 
was in equilibrium?

If not, that would tend to make your claim vacuously true.  :)

Vaughan

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Date: Wed, 18 Mar 2015 23:55:30 -0600
From: Matthew Marler 
*If not, that would tend to make your claim vacuously true.  :)*

A truth ignored by all who make equilibrium assumptions -- eg, assuming the
accuracy of the Calusius-Clapayron relationship.  Sometimes there is merit
in pointing out that what is obvious has been ignored.

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Date: Wed, 18 Mar 2015 23:27:38 -0600
From: Matthew Marler 

To my knowledge, no one but me has noticed that lighting only occurs in
non-equilibrium conditions.

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Date: Wed, 18 Mar 2015 23:02:05 -0700
From: Vaughan Pratt 

Wouldn't equilibrium destroy the kite industry, wind power, and wave 
power?  We'd be left with solar power as the only sustainable energy source.
Certainly an interesting hypothesis...

-v

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Date: Thu, 19 Mar 2015 11:36:47 -0600
From: Matthew Marler 

Not to worry.  With a round and rotating Earth, circling the sun, and with
axis of rotation tilted with respect to the sun, no equilibrium is
possible, not even a steady-state.

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Date: Sat, 21 Mar 2015 23:51:46 -0700
From: Vaughan Pratt 

Hi Matthew,

Looking again at your paper, I noticed a point I'd overlooked before. You wrote

"According to the theory, a doubling of the CO2 concentration will result
in an increase in the power carried by the downwelling long wave infrared
radiation (DWLWIR) ... by 4 W/m^2 (2)"

Your source (2) is RPH's book.  Where does Ray claim this?  I don't know
anyone that claims it.

There is broad agreement that doubling CO2 increases radiative forcing by
3.7 W/m2.  But that refers to the reduction in OLR when the temperature is
held constant.  There is no reason why DLR should increase by that amount.

Vaughan 

----------------------
Date: Sun, 22 Mar 2015 11:26:21 -0600
From: Matthew Marler 

Good catch.  I can't find it.  On p 623 he says that the net effect of
doubling CO2, with positive water vapor feedback, is to increase mean
surface temperature by 2K.  I may have to substitute the short book by
Randall: Atmosphere, Clouds, and Climate.  3.7 is the common figure, but I
round it to credible significant figures, following him: p 48.  The standard
calculations assume equilibrium, meaning surface and atmosphere are treated
as though at equal temperatures.  Randall calculates equilibrium temp
increase of 1.2K. If you separate the surface from the atmosphere, as in
the flow diagram, then the accumulation of CO2 in the atmosphere does not
increase the surface temperature unless there is an increase in the DWLWIR
-- if increased CO2 in the troposphere does not do anything except reduce
the spaceward flow of radiant energy, then only the troposphere warms.
The derivations assume a constant climate sensitivity.  My short one does
not: it takes the flows as they are and looks at the changes in those flows
as the surface temp increases from its present value.

I submitted it to Science Magazine as a letter to the editor or short note.
Because everyone else has calculated a different sensitivity using the
equilibrium-to-equilibrium scenario, and has gotten a higher estimate, and
because Science publishes few letters, I don't expect it to be published.
It does not even have an introduction to the notion of climate sensitivity
or reference to the multitude of different values.  I wanted it kept short
and focused.

I have shown it to about 20 others, including Nicholas Lewis and Judith Curry.
A statistician I showed it to assured me that I am not a crank, something
I am worried about, being clearly a novice.  Feel free to share it, if you
decide that it has any merit.

Matthew

------------------------
Date: Sun, 22 Mar 2015 23:35:31 -0700
From: Vaughan Pratt 

On 3/22/2015 10:26 AM, Matthew Marler wrote:
> if increased CO2 in the troposphere does not do anything except reduce
> the spaceward flow of radiant energy, then only the troposphere warms.

What is your argument that the ocean does not warm?

Here is a counterargument.  There is a constant flux of insolation into 
the ocean, which is balanced by a flow of latent heat from the ocean to 
the atmosphere.

If the atmosphere warms by one degree, the resulting disequilibrium 
causes less heat to flow from the ocean to the atmosphere.  The mixed 
layer of the ocean therefore warms until equilibrium is restored, namely 
when the mixed layer is a degree warmer.

Vaughan

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Date: Mon, 23 Mar 2015 10:37:50 -0600
From: Matthew Marler 

"Warms until the equilibrium is restored" is what I calculated.  The word
"equilibrium" here is common, but in this case the balance of inflow and
outflow is an "approximate steady state".  Where did I say that the oceans
don't warm?  All I calculate is that the temperature at which balance is
achieved is limited by the evaporative heat flow, so that the computed result
is lower than with other modeling.  If the ocean surface warms by one degree,
the water vapor pressure increases by 7%.  That may be why the estimated
rainfall increase for tropical ocean reported in O'Gorman et al (a survey)
is 7% per degree.  I picked 4%, the low end of the empirical estimates,
but if 7% is more accurate an approximation, then the temperature increase
due to doubling CO2 is even slower.

-------------

========================
NEW SUBJECT: novel calculation of climate sensitivity
========================

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Date: Fri, 10 Apr 2015 13:02:11 -0600
From: Matthew Marler 

Dear Vaughan

I took your advice and put my "novel" calculation up at RealClimate here:

and you can read some comments here:


http://www.realclimate.org/index.php/archives/2015/04/reflections-on-ringberg/

Thanks for your help.

Matthew


========================
NEW SUBJECT: latest revised "sensitivity" paper
========================

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Date: Sat, 16 May 2015 10:48:15 -0700
From: Matthew Marler 

Notice that I specifically call it "Earth surface sensitivity", and I added
a short estimate of the feedback of the feedback effect.

comments welcome.

yours truly,

Matthew R. Marler

------------------
Date: Sat, 16 May 2015 11:44:19 -0700
Subject: Re: latest revised "sensitivity" paper
From: Matthew Marler 

1.  Other calculations of climate sensitivity, those based on equilibrium
and TOA imbalace/balance, implicitly assume that the sensitivity is the
same at all levels; and they do not specifically take into account the
non-radiative transport of energy from the surface.

2. Using these flux estimates I can not estimate the sensitivity of past
climate to past  CO2 increase.  What else it might have been is a more
pressing question if this estimate is accurate, but it is beyond the scope
of this paper.

----------------
Date: Sun, 17 May 2015 04:30:19 +1000
From: Vaughan Pratt 

Thanks for that, Matthew.

On 17-May-15 3:48 AM, Matthew Marler wrote:
> Notice that I specifically call it "Earth surface sensitivity"

That certainly makes it clear.  But since Arrhenius' 1896 paper 
introducing the notion of climate sensitivity was titled "On the 
Influence of Carbonic Acid in the Air upon the Temperature of the 
Ground" it's not clear to me how much clearer "surface" in place of 
"ground" makes the notion.

> comments welcome

While your theoretical estimate of sensitivity at 0.3 C/doubling is 
interesting, I didn't see any mention of actual temperature rise in 
response to observed CO2 rise over the last 70 years (the period for 
transient climate response, TCR), which is closer to 1.8 C/doubling.  
That is, according to you, 5/6 or 83% of observed TCR is due to 
something other than CO2.   What might that something be if not CO2?

Vaughan

--------------
Date: Sun, 17 May 2015 08:08:07 +1000
From: Vaughan Pratt 

Spoken like a true statistician.  :)

1.  Had global climate remained flat over the past 200 years while CO2 
rose from 280 to 400 ppmv, I would say your estimate of 0.3 C/doubling 
was a trifle on the high side...

2. ...and I would therefore not know what to make of a calculation that 
bore no relation to physical reality.

Vaughan

-------------
Date: Sun, 17 May 2015 18:23:19 -0700
From: Matthew Marler 

2.  Can you show that the calculation bears less resemblance to physical
reality than the standard equilibrium-based calculations such as those in
the book by Randall?  Everything in my calculation is from published
summaries of measured processes,

1.  All of the estimates of the effects of CO2 in the recent past depend
upon guesses as to what would have happened without CO2 increase, and
scientists have proffered lots of guesses.

0.  There is no reason to think that the sensitivity now is the same as it
was in, say, 1880.  It would be a baseless assumption in any case, and the
nonlinearities in the effects (radiation, advection/convection, hydrologic
cycle) are evidence against it.

--------------------
Date: Mon, 18 May 2015 10:42:08 -0700
From: Matthew Marler 

I don't see what those comments have to do with my calculations.

Whatever the process was that caused surface temperature oscillations in
the past, that might be continuing.  If so, and if Scafetti or others have
modeled it accurately, then the warming since 1880 would have happened
anyway in the absence of an increase in CO2.  I don't think it did or
didn't, but I do not think that the hypothesis can be rejected on current
evidence.

---------------
Date: Mon, 18 May 2015 10:54:44 -0700
From: Matthew Marler 

It is the back of the envelope calculation, pp 45 - 49.  He does say that
it is simplified: he treats climate change as a change from one equilibrium
to another equilibrium, ignores the non-radiative transfer of energy from
surface to atmosphere (in that calculation -- he addresses it elsewhere),
and ignores the possibility of different changes at different levels.  His
conclusion is modest: "the system adjusts by warming", with which I concur.

-----------
Date: Mon, 18 May 2015 14:41:32 +1000
From: Vaughan Pratt 

On 18-May-15 11:23 AM, Matthew Marler wrote:
> 1.  All of the estimates of the effects of CO2 in the recent past 
> depend upon guesses as to what would have happened without CO2 
> increase, and scientists have proffered lots of guesses.

Common sense suggests that if CO2 remains constant then the effect of 
CO2 on surface temperature will be zero, i.e. no change attributable to CO2.

That's not the same as saying that the surface temperature won't change 
since there are other effects that can change surface temperature.

That said, if you can cite someone who has claimed that CO2 can vary the 
surface temperature when it is held constant, I'd be very interested in 
seeing it.

Vaughan

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Date: Wed, 20 May 2015 09:21:03 +1000
From: Vaughan Pratt 

My comments were in response to your item 1, which was about "All of the 
estimates of the effects of CO2".  I'm guessing you meant to say 
something more like "All the estimates of the effects of natural 
contributions to climate change".  I know of no one who estimates the 
effects of CO2 on climate change to be nonzero when CO2 remains constant.

Assuming that's what you meant to say, one estimate by the skeptical 
community is that of Loehle and Scafetta, 2011.  If you know of another 
that you consider to be of equal or better quality let me know.  In the 
meantime let me address that one.

Back in 2013 I looked very closely at L&S.  I began by checking all the 
arithmetic, algebra, graphs, and fits, all of which panned out very 
nicely.  The upshot was that I was able to reproduce their Figure 5 
exactly in MATLAB based on their formulas for their four components, 
which you can see at http://clim.stanford.edu/LNSFig5.jpg.

Any fault in their model therefore can only lie in the assumptions of 
the model itself.

I am in full agreement with their 20-year cycle, which I would modify 
only very slightly to give it a period closer to 20.5 years, which gives 
a better fit to the data.  I agree with their estimates of both phase 
and amplitude for that component.  While they don't say much about the 
heating mechanism, my best guess is that the temperature peaks at the 
time Bz (the "vertical" component of the Interplanetary Magnetic Field) 
flips from north to south, which happens shortly after the odd-numbered 
solar maxima, impacting cloud formation as proposed back in 1954.

I also agree with them that tropospheric aerosols play no significant 
role in multidecadal climate, albeit for a different reason, namely that 
given in Part I of

which shows that land-sea difference supports (quite convincingly in my 
view) the theory that the "AMO" is of internal (via the ocean) rather 
than radiative (via the troposphere) origin.  There are by the way a 
number of subscribers to each of the radiative and internal explanations 
of the AMO, with the latter being more recent.

As many people have pointed out in the context of the AMO, there are too 
few cycles in the record to reliably infer a 60-year oscillation.  I 
agree with those (e.g. WHT) who find that LOD is a better explanation of 
the "AMO" phenomenon.  My AGUFM14 poster develops a physical basis for 
this explanation, which I've since improved considerably.

However the 60-year component of L&S's model is bounded by its amplitude 
of 0.121 C and long-term mean of zero, making it hard to see how it 
could contribute to any alternative explanation of global warming 
besides anthropogenic effects.  That task therefore devolves to the two 
remaining components of their model, both linear, which they attribute 
to respectively natural and anthropogenic causes.

The latter is assumed to be constant up to 1942 on the ground that CO2 
was changing too little then to have any impact on temperature, whence 
100% of the observed rise for that period must of natural, albeit 
unspecified, origin, which they model as increasing linearly at 0.16 
C/century and continuing as such to 2100.  Starting in 1942 they assume 
that CO2 switches from not changing perceptibly to doubling every 70 
years (i.e. increasing at 1%/year) on the ground that this is the basis 
for the IPCC definition of TCR, whence log(CO2), and hence temperature 
attributable to CO2, increases linearly at 0.66 C/century, making the 
net linear increase for 1942-2100 equal to 0.16 + 0.66 = 0.82 C/century.

I have the following problems with their reasoning about the piecewise 
linear components of their model, which are the only components 
supporting their primary thesis that CO2 contributes relatively little 
to global warming.

1.  Law Dome measurements permit an estimate of the increase of 
temperature attributable to CO2 for 1850-1942 that is an excellent match 
to their 0.16 C/century slope.  This gives an alternative explanation of 
what they attribute to natural causes, with the additional advantage of 
having a physical explanation, unlike their attribution.

2.  Saying that CO2 doubles every 70 years is like saying that the time 
is noon.  During the 70 years starting in 1942 CO2 increased by 27%, 
which is nowhere near doubling.  The CO2 model of Hofmann, Butler and 
Tans based on exponentially increasing CO2 emissions predicts that for 
the 70 years 2030-2100 CO2 will increase by a factor of over 2.6, 
considerably more than doubling.

The conclusion I draw from 1 and 2 is that a model that is (a) simpler, 
(b) a much better fit to the data, (c) has a physical explanation 
(unlike their attribution of the rise of 1850-1942 to natural causes) 
and (d) does not have the C1 (tangent) discontinuity at 1942, can be 
obtained simply as log(CO2) for the known CO2 from 1850 to 2015, 
extended by the Hofmann-et-al model of future CO2 based on exponentially 
rising emissions.

It seems to me that this model is in much better agreement with the 
IPCC, as well as with common sense.  If you know of a model that does 
not have the above shortcomings of the L&S model and that predicts a 
temperature rise more in line with what you expect I'd be very 
interested in seeing it.

Note that none of the above makes any mention of equilibrium climate 
sensitivity or depends on it.  L&S do estimate TCR, but since there is 
no temperature data available for any period in which CO2 has increased 
at 1%/yr (even today the rate of increase has reached only 0.7%/yr) they 
have no basis for estimating TCR, making their estimate meaningless.

Vaughan