## 19 August 2007

### climate phase lag trickery

Why does it get hot? Because of the sun.

But in temperate climates in the northern hemisphere, the most light from the sun comes around the summer solstice -- June 21 -- and yet the hottest part of the year is the second half of July. In certain places with a lot of maritime influence, the heat comes even later; the canonical northern-hemisphere example is probably San Francisco, where September is the warmest month. Similarly, the hottest time of the day isn't noon (even correcting for daylight savings time; solar noon is generally around 1 PM clock time under daylight savings time), but perhaps two to four hours later.

This phase lag comes about because the atmosphere holds some heat; the temperature as a function of the day of the year could be modeled by a differential equation, where the rate of change of temperature is some decreasing function of the temperature, plus a sinusoidal input. Thus the output should be similar to the input, but phase-lagged.

Furthermore, I am starting to believe (without evidence) that the temperature in my apartment building is lagged by maybe a couple weeks relative to the temperature outside during the day; I believe with somewhat more evidence that the hottest time of day in my apartment is generally around eight or nine in the evening. And so I find myself fantasizing about a world where that phase lag existed to such an extent that it's warm in my apartment at night and cold during the day. (Without using the air conditioner, that is.)

A bit more ridiculously, what if I could exploit that sort of seasonal phase lag to the point where it was cold in the summer and hot in the winter? But I'd need some sort of ridiculously large heat reservoir, something bigger than the ocean. Still, it's an interesting fantasy. The hottest time outside is a month after the time with the most solar radiation; the hottest time inside might be a few weeks after that; what if I had some sort of series of nested boxes each of which could shift the hottest time of year a few more weeks? If I nested enough of those boxes...

of course, it would be cheaper to just run the heat.

Seriously, though, there is some new construction that attempts to use the insulating properties of certain building materials in this way, although not so much to reverse the seasons as to smooth out seasonal variation. One particularly interesting one I heard about a few months ago depended on the thermal properties of a certain type of wood, which underwent a phase change around seventy degrees Fahrenheit; thermally it's very similar to keeping an ice cube in your house, except it's a magical seventy-degree ice cube instead of the thirty-two degrees of a normal ice cube.

#### 1 comment:

Aaron said...

I've been told by a civil engineering student with family in India that passive heating and cooling is very common there; many houses will have bare floors, for example, to expose the high-thermal-mass concrete foundations directly to the interior.

Passive heating and cooling seems to be very common in the U.S. as well... albeit not intentionally! The first morning in my first apartment, for example, I nearly froze to death while taking a shower; when I left the house, the temperature outside turned out to be around eighty degrees! The culprit, I suspect, was a layer of thick clay tiles on the bathroom floor; I covered them up with a carpet the following week, and have never had problems since.