The Surface Energy Budget | Watts Up With That?


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.

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

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 and must have always remained within certain limits. 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.

Conduction

The surface loses absorbed energy by conduction: a warm surface loses sensible heat to the cooler air above. 24 W/m2 or 14.3% 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 at 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 thermal energy from 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 absorption of radiation by abundant water vapor. Because of this, direct radiation to space is inhibited. Radiation into space on the average takes place from about 5 kilometers above the Earth’s surface where radiation absorbing water molecules are rare. Above the clouds radiation to space becomes easier.

The transport to higher altitudes of a total of 128 W/m2 of latent and other 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 extra warming is neutralized. Surface cooling is a daily occurring dynamic process that works harder at higher temperatures and less at lower temperatures. Dynamic daily cooling follows dynamic daily warming. Surface heating is always followed by surface cooling.

Theory
An object in space, like a planet, is cooled by radiation. On a rock planet without a greenhouse atmosphere all cooling takes place from the surface and no surface radiation is absorbed after release from the surface. But in the case of a planet surrounded by greenhouse gases effective radiation to space only takes place from elevations where greenhouse gases are sufficiently absent.

On an ocean planet water vapor dominates the greenhouse atmosphere and energy absorption in the lower atmosphere delays surface heat loss, so the surface is warmer than the surface of a rock planet. Convection has to take over the transport of energy to higher elevations in order to restore unhindered radiation to space.

From a rock planet without greenhouse gases to a full ocean Earth that is dominated by water and water vapor, the share of radiation in surface cooling diminishes. The surface of the rock planet is cooled 100% by radiation transport. The surface of ocean planet is mostly cooled by convection which transports sensible and latent heat from the surface to higher elevations. See Figure 2.

Figure 2. Surface cooling for two extremes. A 100% Rock Planet (without greenhouse gases) and a 100% Ocean Planet (with greenhouse gases). On the Rock Planet all surface energy disappears by surface radiation straight into space, no radiation is absorbed by an atmosphere. On the Ocean Planet greenhouse gases absorb all surface radiation with an appropriate frequency. Radiation to space mostly takes place from higher elevations, lacking significant water vapor. On Ocean Planet convection transports sensible and latent heat from the surface upward to elevations required for escape to space. The red line represents present Earth: convection is involved in the upward transport of more than three quarters of all surface energy.

General rule: the more greenhouse gases an atmosphere contains, the smaller the role of radiation in surface cooling. And the higher the role of convection.

Conclusions

The Earth’s surface is mostly cooled by convection, not by radiation. Most surface radiation is absorbed by greenhouse gases and radiation transport 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 transports it as latent heat to higher altitudes where it is released when the vapor condenses into liquid water droplets. There it is more easily emitted to space. 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 warmer.

When greenhouse gases are absent from the atmosphere, radiation to space provides 100% of surface cooling. When the content of greenhouse gases rises the role of radiation diminishes in favor of the role of convection.

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 about three quarters dependent on convection.

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 3. Source: IPCC TAR WG1 (Kiehl and Trenberth 1997).

** In figure 3 ‘Thermals’ are mentioned where ‘conduction’ is meant. Table 1 in Kiehl-Trenbert 1997 mentions “surface sensible heat” and NASA shows in their energy budget ‘Conduction/convection’. Neither ‘thermals’ nor ‘convection’ are correct: convection should involve all sensible heat resulting from absorption and should involve all latent heat of evaporation. Sensible and latent heat have to be transported to higher elevations in order to be radiated to space.

A remark has to be made about the vertical scale used in fig. 3. Absorption of surface radiation and radiation back to the surface takes place very close to the surface, often within a few meters. The vertical scale as used in the figure 2 does not represent reality.

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

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