Formula for temperature change over one day?

Question

I am looking for a formula that describes the temperature over one day (24 hours). I was thinking about something like

T(t) = (Tmax - Tmin)*cos( 2*pi* (t-t0)/24 ) + Tmin

with

t in hours

t0~15 hottest moment of the day

Tmax and Tmin the extremal temperatures over the day

And I would like to express Tmin in Tmax. In that way I only need to know the daily maximum to extent it to the entire day.

Thanks,

Answer 1

That's a fairly decent model.  But note that the hottest part of the day happens 2 or 3 hours after noon and a few hours before sunset, while the coldest part of the day happens just before sunrise (i.e. 6 a.m.).  So your cos function needs to be a little funkier than that.  Like multiply your cos function by some weighting function so you can drive the temp up more certain hours or beat it down more than a cos normally would at other hours.  But then it's getting heavy handed, and those weights would change with season.  

I think you have the right idea though and I usually think of it the same way you have expressed it in your formula, roughly.

If I were you I would set the time offset so max temp and min temp are achieved at 5 p.m. and 5 a.m.  I think that's the closest you can get to the first order.