11
$\begingroup$

In the morning, Google shows the temperature from four or five hours ago (around 2:00 a.m.). But then I update the report, and I get the temperature slightly lower than before.

Why is the temperature at 2:00 a.m. higher than the temperature at 7:00 a.m.?

$\endgroup$
12
  • $\begingroup$ Whilst User123 answer mostly covers the reason why, it would be interesting to see if the temperature difference between 2am and 7am is always the same i.e is the difference always 5° or is it higher or lower somedays? This might indicate other factors influence the difference. $\endgroup$ May 10 at 13:13
  • 1
    $\begingroup$ @MattBartlett If there is clear sky, the difference is bigger, but when clouds are present, the difference is smaller. That's why anticyclones in the winter usually bring dry and freezing cold days (as opposed to anticyclones in the summer which usually bring dry and scorching hot days). $\endgroup$
    – User123
    May 10 at 14:18
  • 2
    $\begingroup$ Heat does not travel back in time. $\endgroup$
    – TylerH
    May 10 at 18:34
  • 2
    $\begingroup$ @Universal_Learner. I'm not entirely sure on scale of the effect, but at night plants burn the fuel reserves they make during the day. So during the day they are Endothermic and take in heat (which is why grass feels cool to lie down on) and during the they are Exothermic and give out heat. Depending on the wind and size of the forest the evening air could be warmer. $\endgroup$ May 11 at 10:31
  • 1
    $\begingroup$ You may have noticed that the sun is missing overnight. $\endgroup$
    – J...
    May 11 at 15:12
30
$\begingroup$

The Earth is always radiating heat to the space. But in the day the Sun delivers some heat. The net heat flux is then defined as the sum of those two factors. If the energy delivered by the Sun is bigger than the cooling rate, the Earth is net warming (positive net flux – we can imagine it like heat is travelling "to us"), as opposed to the opposite case (cooling; negative net flux – heat is travelling "away").

In the day, the Sun warms the ground until the evening. The Sun's heating rate is higher than the cooling rate, so the temperature is rising until it gets to a point where the heating rate is same as cooling rate. This happens in the evening, so the temperature is steady at that point. But the Sun goes even lower, so the net flux becomes negative. In the night there is only cooling of Earth, so the temperature is falling steadily until the Sun is high enough that it balances the cooling. This happens at a point of a minimum temperature.

Of course, this is valid for most of the days, but we can have some other effects that can change the time of the minimum temperature (clouds, fronts or advection, for example).

On graph:

T(t)

So, the temperature is falling over night after the sunset, but rises again after the sunrise. Thus, the temperature is at its lowest point in the morning.


Appendix for all you loving calculations:

Note: Simplified to toy model, no atmosphere

The cooling rate of the Earth is approximatelly given by the Stefan-Boltzmann equation:

$$j_E=\sigma\cdot T^4=5.670 \cdot 10^{-8} \frac{W}{m^2 K^4} \cdot (288.15 K)^4 = 390 \frac{W}{m^2}$$

The maximum heating rate of Sun in the zenith is $j_{\text{S max}}=1361 \frac{W}{m^2}$. So, the heating rate of Sun at altitude $\alpha$ is: $$j_S=j_{\text{S max}}\cdot \sin{\alpha}=1361 \frac{W}{m^2}\cdot \sin{\alpha}$$

When is the heating rate equal to zero?

$$0=j_S-j_E=1361 \frac{W}{m^2}\cdot \sin{\alpha} - 390 \frac{W}{m^2}$$ $$1361 \frac{W}{m^2}\cdot \sin{\alpha} = 390 \frac{W}{m^2}$$ $$\alpha = 17 °$$

So, with our calculations, the minimum temperature is at the time when the altitude is equal to 17°.

$\endgroup$
8
  • 8
    $\begingroup$ I would argue that the concept of "warmed by the ground" is almost correct, but i think that the main point is not the interaction between the gound and the atmosphere, but, rather, the distinction between heat rate (positive in the day and negative in the night() and internal energy (temperature) of the system. Ths system keeps cooling while the heat rate is negative (night) and reached the coolest point when the heat rate becomes positive again. $\endgroup$ May 10 at 9:31
  • 8
    $\begingroup$ This is nitpicky; I upvoted your answer. However, with regard to your statement the lowest temperature is right at the sunrise: I suggest changing that to "the lowest temperature is typically very close to sunrise". Your own graph shows the lowest temperature occurring shortly after sunrise. In addition, there are times (e.g., a warm front that arrives in the evening) when the lowest temperature of the day occurs before sunset. $\endgroup$ May 10 at 11:01
  • 2
    $\begingroup$ I was just going to say "it's been cooling off since the sun went down, the sun has been set longer at 7:00am than it has at 2:00am" - glad you gave a 'real' answer! $\endgroup$
    – TCooper
    May 11 at 0:16
  • 2
    $\begingroup$ Can this also explain why June gets the most irradiance but August is the warmest month, in many places in the northern hemisphere? $\endgroup$ May 11 at 10:57
  • 2
    $\begingroup$ @EricDuminil Yes, in the August, the mean cooling rate is equal to the mean warming rate, so the temperature is at its maximum. $\endgroup$
    – User123
    May 11 at 14:55
-1
$\begingroup$

Your question is a bit ill-formed. There are more precise statements that we might take you as asking, for instance you might be claiming that the low takes place after sunrise, and be asking why that is. A very basic model of the temperature is that it is a sinusoidal function of time, and it is driven by the intensity of solar energy, also modelled as a sinusoidal function of time (that is, the net power, when the heat radiating from the Earth is subtracted from the heat coming from the Sun, is modelled as a sin function). If we had that the solar power is $P(t) = -\cos(t)$ where midnight is considered to be both $0$ and $2\pi$, and temperature is $T(t)$ where $T'(t) = P(t)$, then we would actually have $T$ and $P$ being $\pi/2$ (that is, six hours) out of phase with each other. That is, solving for $T(t)$ gives us $\sin$, and $\sin(t)$ is the same as $P(t-\pi/2)$.

The actual equation will be much more complicated: solar power isn't a sine wave, there are heat reservoir effects, radiative cooling depends on the current temperature, etc. The actual displacement between the minima will depend on all of those factors, but the general principle that the forcing function and the response function tend to be out of phase holds.

$\endgroup$
3
  • 1
    $\begingroup$ Is solar power really maximum at $\frac{\pi}{2}$? (= 6:00 a.m.) Think about this again. $\endgroup$
    – User123
    May 11 at 20:22
  • 1
    $\begingroup$ And of course it's not nearly a sin function because solar energy itself is never negative... $\endgroup$ May 11 at 21:18
  • 1
    $\begingroup$ @JeopardyTempest Maybe he wanted to give the approximate function of heat flux. If he wanted to do that, it would be $P(t)=-\cos{t}$ and thus the integral $T(t)=-\sin{t}+T_0$. With this function we can see the minimum temperature at $\frac{\pi}{2}$ (= 6.00 a.m.) Otherwise, I think he has just overcomplicated the situation without making it better. $\endgroup$
    – User123
    May 12 at 14:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.