METR 104:
Our Dynamic Weather
(Lecture w/Lab)
The Daily Temperature Cycle:
Why and How
Dr. Dave Dempsey
Dept. of Geosciences
SFSU, Fall 2012

We observe that the temperature at the earth's surface typically varies more or less cyclically over the course of a day:

This is the daily temperature cycle. Although we naturally tie this cycle to the sun, the daily temperature cycle differs in some significant ways from the daily cycle of solar radiation:

These differences tell us that there is more going on with the daily temperature cycle than just the daily cycle of the sun.

The Principle of Energy Conservation, written as a heat budget relation, helps us understand what is going on. This basic physical principle tells us:

Also, it tells us that:

This is true for the earth's surface, our own physical bodies, and any other physical object or material. Hence, to understand when and why the earth's surface warms and cools, we have to identify and quantify the various ways in which it gains and loses heat.


How does the earth's surface gain and lose heat?

We can get insight about the combined effects of these simultaneous means of gaining and losing heat by building a mathematical model of the daily temperature cycle based on the Principle of Conservation of Energy, seeing how the model behaves, and comparing it to observations of the real world. We've done this in several METR 104 labs.

As an example, we performed a model simulation of the daily temperature cycle that includes only absorption and emission of radiative energy, which are typically the the most important ways by which the earth's surface gains and loses heat. The accompanying graph shows some results of this simulation, in particular:

  1. the rate at which the surface loses heat by emitting LWIR radiation (blue curve, #1); and
  2. the total rate (that is, added together) at which the surface gains heat by (a) absorbing solar radiation, and (b) absorbing LWIR radiation emitted downward by greenhouse gases (mostly water vapor and also carbon dioxide), without clouds (red curve, #2).

This graph covers a period of 2.5 days (60 hours). The LWIR radiative emission (plot #1) also tells us about what the temperature is doing, since the hotter an object is, the more radiative energy it emits. From the LWIR emission plot, we can see that:

So, we see that:

The bottom line is, to understand the daily temperature cycle: