Discussion of the Question 01/98

DELAYED WEATHER

The question was:

Summer (winter) solstice in the Northern hemisphere, i.e. the date when the sun is highest (lowest) in the sky, is on June 21 (December 21). Yet the hottest (coldest) weather is a month or two later. Give a quantitative explanation of this delay.

Since a qualitative answer has already been published in the New Scientist (22 Nov. 97 issue) we may as well give it to you. A. Westwood and S. Collins from the University of Leeds said that "the Earth has certain heat capacity, which leads to a thermal time lag." Now we know the reason! All we need is a (semi)quantitative estimate of the time lag.


(6/98) Michael Bertschik (e-mail mbertsch@urz-mail.urz.uni-heidelberg.de), a Ph.D. sudent at University of Heidelberg suggested the following solution:

Mass of atmosphere to heat (thickness ~10km, constant pressure) is M=5*1018m3*density(air) = 6,5*1021g.
Difference of extraterrestrial solar constant and "ground" solar constant: (1400-970) W/m2 = 430 W/m2; hence absorbed energy E (irradiated surface of earth * solar constant) is
E = Pi*R(earth)2 * 430 W/m2 = 5,5*1016 W = 5,5*1016 J/s.
Heat capacity of air: cv = 0,73 J/(g*K).
Heating per second in Kelvin: H = E/(cv*M) = 1,16 * 10-5 K/s. So the heating per day is ~ 1 Kelvin.

Y. Kantor: This solution disregards daily fluctuations of temperature, which could be explained using similar arguments. In addition the energy flux in a calculation of this type must be positive or negative depending on the season. The "jury" was not convinced by the argument...

(2/99) Bill Bruml (e-mail Wbruml@star21.com), wrote the following message which may give us some hints regarding the correct solution:

Very crudely: Model solar input as varying from some average value by (1+a*sin(t)) over the course of the year. Model heat losses as constant and ignore any heat transfer between the latitudes. If the earths long term average temperature stays the same, the heat loss is the same as the average heat input so the net heat input is just a*sin(t) and the integrated excess heat (which is the temperature) is just (-1/a)*cos(t).
At the winter solstice sin(t) (solar input) is at its minimum value and -cos(t) (temperature) is at its mid point. At the vernal equinox, sin(t) (solar input) is at its mid point and -cos(t) (temperature) is at its minimum.
So, I get (semi)quantitative (about as semi as it can get) information about the date of the coldest day without needing needing to know the magnitude of the heat flows. With this first order model, the question for more sophisticated models is not, "Why is the coldest day after the winter solstice?" but, "Why is the coldest day before the vernal equinox?"

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