Realistic two-box parameters and heat capacity choices for Earth's climate system

This will probably be my final post on this question - however I may append updates if other issues come up. In particular this post will look first at whether the fitted parameter values for two-time-constant fits to temperature vs forcing data for Earth's climate system have a collection of underlying physical two-box models that satisfy the basic physical constraints on such systems, and then whether the range of physical parameters in these matching models appears to correspond roughly with appropriate associated physical properties of the real Earth climate system.

CORRECTION: The following text has been modified significantly due to errors in the preceding post that nullify most of the original discussion here:

Our new garden shed

new_shed.jpgMy summer project is pretty much done. I haven't done much carpentry in the past, and found the construction process surprisingly educational. Constructing the flooring, framing, siding, roof, and putting in the window and door all had their own unique challenges in measurement, cutting, joining, etc. I still have to build some shelving and bins and put up some hooks and other devices to hold our tools - can't do that yet though as the kids have installed a couch and turned it into a play house for now. Another couple of weeks though and our new shed should be fully operational!

Perturbative two-box: applying the constraints

Continuing from the previous post, suppose we want to look at solutions where the (s) box is close to the short-time-constant (τ-) solution, and the (o) box then close to the long-time-constant (τ+) solution. That suggests setting the corresponding inverse time constants perturbatively close to τ- and τ+, respectively. Define dimensionless small numbers εs and εo as follows:

Eq. 27: αs = (1 - εs)/τ-
Eq. 28: αo = (1 - εo)/τ+

Then from the definitions of ν+ and ν- (unnumbered equation between 22 and 23 in the previous post) we find:

Two-box continued: solution space

This is essentially a continuation of the math in the previous post. The same warnings apply!

The previous analysis indicated we have 3 free variables to play with. Let them be αs, αo and Cs (the initial inverse time constants of the two boxes, and the heat capacity of the "surface" box).

Equations 9 and 12 of the previous post show a relationship between w+s and w+o depending on the α's, γ's and τ+, and equations 10 and 13 show the same relationship for w-s and w-o with τ- instead of τ+.

More two-box model: some fun with math

This will probably be painful for anybody who hasn't already been following this (which I'm sure is all but 1 or 2 readers, if that many). So skip this post unless you're really into solving systems of equations...

Playing with R trying to fit the modern temperature record to forcings

Ok, this time I'm going to start with the graph, and explain what's going on after. Seems to work for other folks... :
Global mean temperature and a fit to forcings

Moore's law and its analogues

Kevin Kelly has a great new essay up, "Was Moore's Law Inevitable?", examining a series of examples of exponential growth in technological capability from a wide range of fields - and makes the very interesting point that all these examples are "prisoner[s] of physics, the periodic table, manufacturing technology and economics" - but some of them proceed rapidly and some do not. The interesting question is why?

Transitions in information technology

I recently finished reading Victor Hugo's Notre Dame de Paris (i.e. the Hunchback of Notre Dame). Among his many long asides and discussions setting the tone for the time (it is set in Paris of the late 1400's, well over 300 years before he wrote) I particularly noticed his remarks on the remarkable transition just beginning at the time. As he put it: "The invention of printing is the greatest event in history." The copy of his book that I read was, however, not printed on paper, but electronically downloaded from Project Gutenberg - donated to the world through a scan of the public domain 1880 version translated by Isabel F. Hapgood. If the invention of printing was clearly the greatest historical event by the 1830's when Hugo first wrote those words, the 20th century revolution in information technologies is at least the start of something far greater.

$9.50 - and just who was "Party B"?

Last night, as a holder of a few hundred shares in Sun Microsystems (JAVA is their stock symbol), I finally received voting instructions and an explanation of the proposed merger with Oracle. This is actually the second time I've had the opportunity to vote on a company's proposal to end itself through merger - the first was just last fall, when SpaceDev (SPDV stock symbol) was acquired by Sierra Nevada Corporation. In both cases it's been a somewhat mixed experience emotionally. The acquisition price has been a significant improvement on the recent market price for their shares (for Sun, the $9.50 price is significantly above the roughly $5 it was trading at a few months ago), so that's nice on the money side. On the other hand the reason I was holding the shares in the first place was because I believed the company had great potential for the future.

Some basic climate references

I recently corresponded with a colleague who has acquired a degree of "skepticism" regarding global warming. His comments to me specifically cited Freeman Dyson and Will Happer, distinguished physicists who are also well-known global-warming skeptics, and he contrasted their credentials with those of John Holdren (Obama's new science advisor) and Al Gore. The following is a lightly edited version of my response, which I'm posting here mainly as a place for some useful links on the subject.

On the dimensions of the noosphere

This will necessarily be a somewhat rambling collection of my thoughts as I don't feel I've settled down to any solid conclusions on the matter. Perhaps just writing this down will clarify some of my thinking, or perhaps the ideas here will fetch some comments from others that will help point me in better directions. This is the development of some of the thinking from my earlier comments on measuring wrongness - the science I'm familiar with centers on measurement and quantification, and it certainly seems potentially fruitful to consider ways in which one could impose measures (of "wrongness" or "rightness" or just "uncertainty") on the world of ideas. In a sense that kind of measurement is what we impose under the banner of peer review, though the visible outcome is more a binary (publish/don't publish) than continuous measure.

Whither Scientific Datasets?

Recently at work we've been making some minor changes to the handling of "auxiliary files" - movies, additional information, or data sets provided by the authors that go beyond the normal article text, figures and tables (all XML or PDF format) that we usually publish. The issue of archiving datasets in particular has been on my mind. One motivation is my own past experiences wondering what to do with large collections of (in my case computer-simulated) data generated in the process of doing research. I probably still have some of it, what I thought most significant, stored somewhere on the laptop I'm writing from now. Though I'm not sure what I would do with it after 20 or more years of neglect. Would it even be worth anything to myself or anybody else, to make it available? Recently advocates of scientific openness, for example Michael Nielsen's Physics World article, have made a strong case for sharing with the world.

Measuring Wrongness

One of the great puzzles I feel up against these days in several different contexts is finding a clear way to express how wrong certain expressed views are. This is not (at least usually not) an issue of moral wrongness, but in most cases just simple inconsistency of logic, disagreement with basic scientific understanding of issues, or perhaps abuse of the English language in ways that make no sense whatsoever. Last fall I spent an inordinate amount of time documenting the errors in an article by a climate-change "skeptic", but even then the simple count of the problems doesn't feel like it gives a true picture of the enormity of the misrepresentation of the facts provided by the article in question.

Quotes on Unity

In keeping with the un-theme of this blog, I now present something completely different...

Belonging to a church with a lay clergy, it's my turn to speak once in a while to our ward, a congregation of about 130 on an average week. I seem to get called on every couple of years (more than I would like, but less than some!) Last Sunday (before Memorial Day) was my turn again, under the general topic of "unity". Following are some notes and quotes I gathered for the talk, for anybody interested. No, I did not use all this stuff in the talk... there's only so much you can say in 20 minutes!

New Congressional Budget Office Report on Climate Change

temperature projections 1850 to 2100
Thanks to Michael Tobis I discovered a new report this week from the Congressional Budget Office that has the most dramatic illustration I've seen of projections of temperature for the remainder of this century (right - figure 1 in the report). The PDF of the 33-page report is available for download from CBO.

Exercise

When I was young I naturally had plenty of exercise. It helped that my parents didn't bother to drive me most of the time and there were no buses to my junior high or high school, so I did a lot of walking (high school was well over a mile each way). That included walking through the blinding snow-storms we regularly got in Newfoundland. Even in college and grad school I was mostly car-less; I'd get occasional rides from strangers when they saw me walking home with bags of groceries (in the rain I looked particularly pathetic, I guess), but mostly it was walk, walk walk. Or sometimes take a city bus. I'd occasionally take my bike out for long rides in the hills around Ithaca.

Author identity

The main project I'm focused on at work right now relates to uniquely identifying the people who write and referee articles for our journals. Our referee database is pretty good, but even that has a number of duplicate entries, as I've been finding. In one case the name was the same but with last and first name's switched; in another somehow we'd created a record with a slightly modified version of the surname (and a note that the name was wrong). It's a lot trickier than one might at first imagine, but an open public solution for researcher identification could be a big help. There seem to be several projects in the works in that regard:

Middle school band concert

Rather than say much about it, I'll just let you listen. I thought it was pretty good for a 6th grade band - it's a big band too; Elizabeth loves her teacher. If you listen closely, you can here occasional exclamations from her almost-4 year-old little brother, who loves to hear her play the flute.

Why are some people so easily confused?

Apparently this article of mine on the basic physics and mathematics of radiation on a planet relating to the Greenhouse effect, became somewhat the subject of discussion on a German climate science thread. Given the language difference, I didn't quite follow what they were on about, and so asked for a summary in a related discussion. Note that my article has been discussed at length previously and Google shows lots more references around the 'net.

Hot Spot Redux: analysis of tropical tropospheric amplification

It's been over a month since I completed most of the following analysis, which I've been planning to write up more concretely. This post is intended as a summary of the basic questions I've been trying to address, although there are some mathematical issues I've worked out that I won't cover here. First, a few basic facts and some terminology regarding Earth's atmosphere. If you're already familiar with lapse rate discussions you can skip the next few paragraphs.

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