Below is a response I wrote in the sci.environment newsgroup regarding parameterization. It might be preferable to write specifically regarding the what and how of parameterizations, but I have since decided that the context is important in illustrating why there's even a question. Robert Grumbine, bobg@radix.net
From rmg3@access5.digex.net Fri Feb 14 13:23:32 EST 1997
Article: 127698 of sci.environment
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From: rmg3@access5.digex.net (Robert Grumbine)
Newsgroups: sci.environment
Subject: Re: Global warming/climate change: a new appoach
Date: 14 Feb 1997 13:02:28 -0500
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In Message-ID: <19970213.221631.393@watson.ibm.com>
From: jbs@watson.ibm.com (James B. Shearer)
Felt compelled to state:

>         The problem here is that the free parameters in these models
>are generally not constants but instead are complicated (and unknown)
>functions of the amount of CO2 in the atmosphere.  Consider the
>earth's albedo for example.  There are any number of choices for
>albedo as a function of CO2 which will match the current albedo but
>differ substantially in a 2*CO2 world.  This leads to significant
>uncertainty in the temperature change expected in 2*CO2 world.
>The only way to eliminate this uncertainty is to somehow derive
>these functions.  However this is beyond the state of the art.  More
>complicated models may hide this uncertainty but they do not
>eliminate it.  For example a model may compute albedo as a function
>of cloud distribution, snow cover and sea ice cover but these items
>are themselves functions of the CO2 content of the atmosphere.  These
>items may themselves be expressed as functions of other items but
>this is not eliminating the uncertainty it is just moving it around
>(and perhaps obscuring it).  I prefer simple models where the
>limitations are obvious instead of more complicated models which
>have obscured with complexity equally bad or worse problems.

  I've left the paragraph untouch, tempting as it was to 
try to take it pointwise.  In brief, Mr. Shearer is dreadfully
incorrect as to what parameterizations are and how they are
implemented.  Most simply, albedo, et al., are _NOT_ functions
are carbon dioxide concentration.  This is fundamental both to
his errors and to the fact that one _can_ make parameterizations.

  Albedo of a surface (or volume, in the case of a cloud) is a 
function of its physical state.  I'll take sea ice for an example.
At the most highly detailed, sea ice albedo is a function of the
snow cover (grain size distribution, depth, age, angle of incidence
of the solar radiation, and portion of incident radiation which is
diffuse versus direct beam, temperature), water ponds if any (size, 
depth, shadowing by snow cover or ice, temperature), and the sea ice 
(grain size, thickness, brine pockets, temperature).  As I said, highly 
detailed.  But notice: None of these mentions CO2.  CO2 just doesn't 
affect the albedo of the ice.  

  What we do (the above gory function being both unknown and far too
ugly to use) is to find a function which represents the sea ice 
albedo well as compared to the observations.  The sea ice albedoes
commonly used include one or more: temperature dependence, snow thickness
dependence, ice thickness, and ponding.  The modelled albedo can
then be compared to observed albedoes, see Grumbine 1994 and references
therein.  The comparison isn't too bad, though not as good as we'd
like, hence (among other things) the SHEBA expedition (http://sheba.
apl.washington.edu/) which will observe sea ice albedo and state
intensely for a year.

  So we have a parameterization which isn't too bad, and are going
to work on finding one that is better.  Mr. Shearer believes, from
the above, that the whole enterprise is useless since we're not making
the parameterizations functions of CO2.  He is simply and emphatically
wrong.  The parameterization means that the albedo is related to
physical quantities.  We can use this relation with confidence, even
under changed climates, because the albedo of ice depends on things
like temperature and there is no reason to believe that warm ice will
behave differently 50 years from now than it does this year.

  Almost everything in a weather or climate model has this character
of being independant of CO2 (or other greenhouse gases).  Cloud formation
is not a function of CO2; it depends on dynamics, available moisture,
heat release in condensation, avilable condensation nuclei, and a number
of things - other than CO2.  Similarly for soil physics, sea ice dynamics,
ocean dynamics, etc.

  In other words, as long as water still freezes at zero and boils at 
100 C, the parameterizations are not going to fail magically with a 
climate change.  As long as the driest deserts in the future aren't dryer
than the driest deserts today, or the wettest rain forest is no wetter
than the wettest today, those parameterizations will continue to be 
as reliable as they are now.  And so on.  

  We'd always like better parameterizations.  The standard, contrary
to Mr. Shearer's assertions, for determining whether a parameterization
is better is whether it represents the modelled quantity better.  i.e.,
a sea ice albedo parameterization is better if it represents observed
sea ice albedo better.  It is _also_ usually the case that a better
parameterization makes for a better model (weather or climate).    

Reference:
Grumbine, R. W., A sea ice albedo experiment with the
  NMC Medium Range Forecast Model, Weather and Forecasting,
  9, 453-456, 1994.
-- see the references therein regarding the albedo parameterization
tested. 

-- 
Bob Grumbine rmg3@access.digex.net
Sagredo (Galileo Galilei) "You present these recondite matters with too much 
evidence and ease; this great facility makes them less appreciated than they 
would be had they been presented in a more abstruse manner." Two New Sciences