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**:

The following proved a little long to be just an update to the previous post; I guess one should never say never. Nevertheless I don't anticipate a need for anything more on this model.

I've been discussing in some detail here a mathematical model of the response of Earth's climate to radiative forcings, trying to address some of the concerns expressed elsewhere on the need for such a model to be "physically realistic". In the case of the two-box model, a given fit of the response function to a two-time-constant decay curve could come from one of many different underlying physical models that correspond to a partitioning of Earth's climate system into two parts with different response rates. So the question has been whether any of these possible underlying physical models are in some way "realistic" or not. That essentially reduces to criteria on the magnitude of the various constants and partial outcomes in the model relative to real components of our planet.

Buy high, sell low. Works every time. The other day I sold stock for $1800 that I had originally purchased for $12,000, and was happy to do it. Read on for the details!

Most of our "playground" investment portfolio (as opposed to the serious ones in retirement and college funds) is invested in renewable energy and energy efficiency-related company stocks. It's actually doing pretty well this year, up almost 85%. Of course, that doesn't quite make up for the 55% drop in 2008, but anyway... I'm fairly confident that these companies are doing things that are essential for the future of our nation and our world, so I'm happy to invest in them even when that investment ends up being at a loss. But Daystar Inc (DSTI) was a bit of a special case.

One of my more recent posts on the two-box model explored the space of possible underlying models for a given empirical fit by fixing heat capacities of the two boxes and varying the heat transfer rate. Keeping the time constants positive restricts the range of allowed heat capacities considerably, while forcing fraction (x) and temperature measurement fraction (y) also provide some constraints given the expectation they must lie between 0 and 1 (and must have actual solutions). Even among solutions satisfying those constraints, there is a further condition that the results look reasonable - as pointed out there and by Lucia here, some of the solutions produce wildly different response levels for the two boxes, which seems unrealistic for systems that should roughly correspond to sub-components of Earth's climate.

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Update - January 29 2013

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Given the extremely large number of spam comments I'm seeing (at least 10 to 1 over real comments), comments on articles are not posted automatically unless you are a registered site user (see the "Create New Account" link on the left-hand side).

Last year (2008) we were starting to look at alternatives to our oil-fired burner for heating our house. The house is an almost rectangular 35x60 ft ranch a little over 30 years old, and came with a 1000-gallon buried oil tank, no longer allowed in town codes, so we knew we had to at least get rid of that some time. We finally got that taken care of a few weeks ago. How we're going to heat our house this winter we're still not quite sure. Anyway... one of the interesting options then (and now) was a geothermal heat pump system, and we had several contractors come in and give us quotes. Not cheap at all, mainly because we would have to switch from baseboard radiators to forced air, and putting in the ductwork and vents would take a lot of labor. But there's a 30% federal credit available so we may still go that route.