The Surface Energy Budget

Guest post by Wim Röst

Abstract

The energy budget for the surface is different from Earth’s energy budget. A look at the surface energy budget reveals that radiation is not the main factor in cooling the surface. The dominant factor in surface cooling is convection, responsible for the removal of more than three quarters of the surface’s energy. Thinking only in terms of radiation is misleading.

Introduction

People live on the surface; thus, we are interested in surface temperatures. Surface temperatures result from the energy flux absorbed and released by the surface. Those energy fluxes are shown by the surface energy budget presented below in Table 1 and Figure 1. The energy budget of the surface is simple. Only two factors play a role in cooling the surface.

The surface

The surface energy budget is different from the Earth as a whole. For Earth, as a planet, it is most important to know how much energy is entering the upper atmosphere and how much energy is leaving the upper atmosphere. However, for the surface and for surface temperatures it is important to know how much energy is entering and leaving the surface.

For billions of years life has survived on or near the surface of the Earth. Surface temperatures must have been very stable. One big temperature anomaly during those billions of years would have killed all life on Earth. A closer look at energy flux at the surface shows which processes must be responsible for that stability.

Definition of ‘the surface’

For energy flux at the surface normally a broader definition of ‘the surface’ is used. Strictly speaking ‘the surface’ is just the contact layer between land and ocean with air. But for measuring ‘surface temperatures’ a level about 1.80 meter above the surface is used. Furthermore, absorption of solar energy ‘by the surface’ includes the absorption of solar energy by oceans to a depth of 200 meters. This indicates that for surface energy flux a broader definition of ‘the surface’ is needed.

Warming and cooling

To understand developments in surface temperatures both warming and cooling processes are important. The numbers used for the surface energy budget are derived from Kiehl-Trenberth’s 1997 Earth’s Energy Budget (Kiehl and Trenberth 1997).*

The solar shortwave energy flux warming the surface is 168 W/m2. The surface cooling fluxes observed are as follows.

Evaporation

Evaporation is the primary surface cooling process. Evaporation causes the fastest moving water molecules to escape from the surface, leaving the slower moving molecules behind and the surface cools. The escaping molecules carry ‘latent heat of evaporation’ with them and account for 78 W/m2 or nearly half (46.4 %) of total surface cooling. The amount of evaporation is a function of the thermal energy striking the ocean surface.

Conduction

The surface loses absorbed energy by conduction: a warm surface loses sensible heat to the cooler air above. 24 W/m2 or 14.5% of total surface cooling results from conduction.

Radiation

Most of the energy that leaves the surface in the form of radiation (390 W/m2) returns as back radiation, mostly from greenhouse gases: 324 W/m2. This part is not cooling the surface, it is not a net loss. This energy is going ‘from one pocket to the other’ without cooling the surface.

Part of the radiative energy leaving the surface directly reaches space. 40 W/m2 or 23.8% of all net surface cooling is radiated from the surface straight into space. It reaches space by about the speed of light, much faster than other processes.

The remaining 26 W/m2 of surface radiation is the part that is leaving the surface as radiation but is absorbed by greenhouse gases and not returned to the surface in the form of back radiation. This 26 W/m2 warms the air where it became absorbed: very near to the surface. After absorption this 26 W/m2 is thermalized: the absorbed energy is transmitted to other air molecules (mainly N2 and O2) and continues as sensible heat.

Total surface cooling

Total surface cooling by each factor is shown in Table 1.

Surface warming

168 W/m2 of the Sun’s incoming shortwave energy warms the surface as it is absorbed. The total of all cooling factors in Table 1 add to the same amount of 168 W/m2. Back radiation is adding many W/m2 to the surface (324 W/m2) but the same quantity of radiation leaves the surface as part of the 390 W/m2 radiative heat loss. The result is a net surface warming / cooling by back radiation of zero W/m2.

Surface cooling

‘Energy In’ must equal ‘Energy Out’ to keep temperatures stable. Any change in factors that are warming or cooling the surface will affect surface temperatures. Factors that are cooling and are warming the surface are shown in Figure 1.

Figure 1. The Earth’s Surface Energy Budget. Numbers derived from Kiehl-Trenberth 1997. The surface of the Earth is cooled 40 W/m2 by radiation; this part of surface radiation is radiated straight into Space. 324 W/m2 of all outgoing surface radiation returns nearly simultaneously as back radiation. The remaining 26 W/m2 of surface radiation is absorbed by greenhouse gases and results in the warming of the atmosphere near the surface (the Greenhouse Effect). Conduction cools the surface by 24 W/m2. The largest single factor that cools the surface is the evaporation of water vapor. The latent heat of evaporation removes 78 W/m2 of energy from the surface. Total surface cooling by all cooling factors together: 168 W/m2. Total solar heat gain: 168 W/m2.

Conduction and net absorbed radiation provide the lower atmosphere with 50 W/m2 of sensible heat. Together with the 78 W/m2 latent heat this sensible heat must be transported high in the atmosphere where it can be radiated into space. At the surface, there is a high rate of thermal energy absorption by abundant water vapor. Direct radiation to space is not very effective. Radiation into space on the average takes place from about 5 kilometers above the Earth’s surface where absorbing water molecules are rare. Above the clouds radiation to space becomes effective. Clouds exist at an altitude where water condenses (and sometimes freezes) and evaporates simultaneously, some of the energy released by condensation or freezing, usually near the top of the cloud, is radiated to space. This works like an air conditioner, but water is the cloud’s coolant.

The transport to higher altitudes of a total of 128 W/m2 of latent and sensible heat (or thermal energy) takes place via convection. Convection is the main player in surface cooling. Net surface radiation to space is only responsible for 40 W/m2 of the total surface heat loss. As surface temperatures rise, more evaporation takes place and convection works harder to cool the surface.

Three forms of energy transport cool the surface. But all surface energy is transported away from the surface (broad definition) in just two ways: by convection and by radiation. See Table 2.

Convection which is responsible for three quarters of all upward transport of surface energy is a very dynamic process. Convective heat loss varies from hour to hour, from day to day, from season to season, from year to year, and varies by geological period. It also constantly varies from place to place. Both quantity and speed of convection are constantly varying, adapting to local circumstances.

To understand changes in surface temperatures, understanding dynamics of convective heat loss is important.

The mechanism that sets the level of surface temperatures

When temperatures rise (which happens every day as soon as the Sun starts shining) more water vapor fills the air. This lowers the density of the air column. Water vapor is lighter (less dense) than dry air, so evaporation lowers the local air density and convection starts spontaneously. Convection carries latent heat of evaporation and all surface sensible heat from the surface upward to a higher altitude. Rising temperatures and rising water vapor cause convective cooling. But when temperatures go down the whole process of convective cooling slows down.

The surface stops the extra cooling at the point where warming is neutralized. Surface cooling is a daily occurring dynamic process that works harder at higher temperatures and less at lower temperatures. 24 Hours a day the ‘warmest moment of the day’ is reached at a great number of locations. Dynamic daily cooling follows dynamic daily warming. Surface cooling always follows surface heating.

Conclusions

The surface of the Earth is mostly cooled by convection, not by radiation. Most surface radiation becomes absorbed by greenhouse gases and therefore radiation becomes ineffective in cooling the surface. Only 23.8% of all surface energy is lost by direct radiation from surface into space.

The remaining three quarters of surface energy remains in the atmosphere just above the surface in the form of latent and sensible heat. This energy must be transported upward by convection. Energy can only effectively be radiated into space from higher altitudes because the upper air lacks the main greenhouse gas, water vapor. Water vapor absorbs most surface-emitted radiation near to the surface and radiates a lot of it back to the surface. For effective surface cooling, the upward transport of thermal energy, via convection, is key. Without convection the surface would not be cooled to present temperatures and would become much warmer than it is now.

Incoming solar radiation has a lot of frequencies, up into the ultraviolet and higher. The radiation emitted by the surface is mostly infrared radiation with the peak frequency determined by the surface temperature. The surface emitted frequencies are absorbed by water vapor and other greenhouse gases. The air is transparent to many incoming solar radiation frequencies and when they strike the Earth’s surface they are absorbed, warming the surface.

Most of Earth’s surface is water, which evaporates when warmed. A high rate of evaporation causes clouds to form. Thus, surface ocean water, under the Sun, will find a natural temperature where the heat or thermal energy carried away equals the energy absorbed from the Sun. The overall ocean, to the ocean floor, has an average temperature of less than five degrees Celsius on average and acts as a thermostat on global surface temperature. More input energy causes more evaporation, less energy, less evaporation. Thus, the cloud-free spot where the most sunlight is absorbed, in the tropical oceans, has a maximum temperature. This temperature varies a few degrees depending upon local factors, such as currents and proximity to land, which has no maximum temperature. But, the maximum temperature in the central tropical oceans is about 30 degrees Celsius as determined by Newell and Dopplick in 1979 (Newell and Dopplick 1979).

In the tropics, at around 26°C evaporation will increase to the point that clouds begin to form. By the time the surface temperature reaches 30°C, the clouds have severely restricted sunlight and the surface temperature stops increasing (Xie and Roemmich 2017). At higher latitudes, where sunlight is striking the oceans at an angle, temperature is often not the limiting factor on temperature, there wind can play a larger role in cooling the surface. Some think this maximum temperature will change due to global warming, but this seems unlikely, the physical properties of water and the atmosphere will not change as the world warms or cools. If the atmosphere warms, the average cloud cover will just increase.

On Earth, the main greenhouse gas, water vapor, absorbs most surface radiated energy. Radiation, therefore, cannot cool the surface effectively. The cooling of the surface of the Earth is mainly dependent on convection. Thunderstorms are the most dramatic convection event and are giant air conditioners for the surface, transporting huge amounts of thermal energy high in the atmosphere very quickly.

The process of convection is very dynamic: it increases as temperatures rise and subsides as temperatures fall. Dynamic convective surface cooling follows surface heating, which stabilizes surface temperatures.

With regards to commenting, please adhere to the rules known for this site: quote and react, not personal.

About the author: Wim Röst studied human geography in Utrecht, the Netherlands. The above is his personal view. He is not connected to firms or foundations nor is he funded by government(s).

Thanks to Andy May who was so kind to correct and improve the text where necessary and useful.

  • The Earth’s Energy Budget by Kiehl-Trenberth 1997:

Figure 2. Source: (Kiehl and Trenberth 1997).

Works Cited

Kiehl, J., and Kevin Trenberth. 1997. “Earth’s Annual Global Mean Energy Budget.” BAMS 78 (2): 197-208. https://journals.ametsoc.org/bams/article/78/2/197/55482

Newell, R.E., and T.G Dopplick. 1979. “Questions Concerning the Possible Influence of Anthropogenic CO2 on Atmospheric Temperature.” J. Applied Meterology 18: 822-825. http://journals.ametsoc.org/doi/pdf/10.1175/1520-0450(1979)018%3C0822%3AQCTPIO%3E2.0.CO%3B2.

Xie, Shang-Ping, and Dean Roemmich. 2017. Voyager: Is there a limit to how much sea temperatures can rise? July 18. Accessed July 21, 2020. https://scripps.ucsd.edu/news/voyager-there-limit-how-much-sea-temperatures-can-rise#:~:text=At%20the%20present%20time%2C%20the,C%20(88%C2%B0%20F).