We observe that the temperature at the earth's surface typically varies more or less cyclically over the course of a day:
- The temperature at the earth's surface is usually coldest near sunrise.
- It warms through the morning and into the early afternoon to a peak sometime in the middle of the afternoon.
- It then cools through the late afternoon and through the night until it reaches a minimum again near sunrise the next 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:
- Solar radiation peaks near noon, not in midafternoon as temperature usually does.
- Solar radiation is zero (and unchanging) all night, while temperature typically falls through the night.
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:
- For an object to warm, it must gain heat (by various means, added together) faster than it loses heat (by various means, added together).
- For an object to cool, it must lose heat (by various means combined) faster than it gains heat (by various means combined).
Also, it tells us that:
- The bigger the difference between the rate at which an object gains and loses heat, the faster the objects temperature will change.
- When an object gains heat just as fast as it loses heat, its temperature won't change. (We say that the object's heat budget is balanced.)
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?
- The earth's surface gains heat by:
- absorbing solar radiation
- daytime only, varies over the course of each day
- absorbing longwave infrared (LWIR) radiation emitted downward by greenhouse gases (notably water vapor, and also carbon dioxide)
- happens continuously, day and night
- conduction of heat from the atmosphere
- happens when the surface is cooler than the atmosphere next to it, usually late at night after the surface has cooled
- The earth's surface loses heat by:
- emitting LWIR radiation
- happens continuously, day and night
- conduction of heat to the atmosphere
- happens when the surface is warmer than the atmosphere next to it, which is most of the time
- evaporation of water from the surface
- happens when liquid water is present
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:
- the rate at which the surface loses heat by emitting LWIR radiation (blue curve, #1); and
- 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:
- The surface temperature reaches a minimum not far from sunrise (when total absorption and LWIR emission are equal).
- Temperature (and LWIR emission) rises through the morning and into the afternoon (when the total absorption is greater than the LWIR emission, so the surface is gaining heat faster than it loses heat).
- Temperature reaches a peak in the afternoon (when total absorption and LWIR emission are again equal).
- Temperature then falls through late afternoon and all night (because LWIR emission is greater than total absorption, so that the surface is loseing heat faster than it gains it).
So, we see that:
- The temperature continues to rise for a while after noon because total absorption is still greater than LWIR emission then, even though total absorption has begun to decrease. Eventually the temperature peaks in midafternoon when the absorption falls enough to match the rising LWIR emission, and the temperature stops rising.
- The temperature falls through the night, even though solar absorption is zero and not changing, because LWIR emission is greater than absorption of LWIR from greenhouse gases. That is, the surface cools at night because it loses heat faster than it gains heat.
The bottom line is, to understand the daily temperature cycle:
- We have to consider not just solar radiation, but also radiative emission by the surface.
- We can use idealized models of the physical world to help us understand (and predict) things that we observe.