2.5.2: Surface Energy Balance
- Page ID
- 46148
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Arguably the most important aspect to consider about the Earth-Sun system is the energy balance. In steady-state, the amount of incoming energy should equal the amount of outgoing energy (Net Radiative Flux=\(F ^*=0\)).
Let’s start with the incoming solar radiation. The solar constant “\(S\)” is approximately equal to 1361 W·m-2. This value is a rough estimate of the amount of energy per area received by the Earth from the Sun, but it is not exact. We call it a solar “constant” but it can be slightly lower or higher at times. Radiation emitted from a spherical source, like the sun, decreases by the square of the distance from the sphere’s center. This is called the inverse square law.
The following equation is a basic budget equation. Net radiation (\(F ^*\)) is equal to the incoming solar radiation (\(K\downarrow\)), the reflected solar radiation (\(K\uparrow\)), the longwave radiation emitted by the Earth (\(I\uparrow\)), and the downwelling longwave radiation emitted from the atmosphere (\(I\downarrow\)) received by the Earth’s surface.
\[F^*=K \uparrow+K \downarrow+I \uparrow+I \downarrow \nonumber \]
Some of the sunlight that reaches the surface of the Earth is reflected, depending on the albedo, \(K\uparrow\) is often written in the following way:
\[K \uparrow=-\alpha \times K \downarrow \nonumber \]
This is a brief introduction to a surface energy balance model. As you may imagine, it can become much more complicated depending on the factors involved. It also strongly depends on the number of layers considered in the model. We will discuss this further in a later chapter.
For now, you should understand that incoming solar radiation is called shortwave radiation and is in the ultraviolet and visible portions of the electromagnetic spectrum because of the emission temperature of the Sun. When solar radiation interacts with the Earth, it is partially absorbed by the Earth’s surface, and partially reflected, depending on the albedo of the surface. In the diagram above, you can see that some of the incoming solar radiation is reflected by clouds, some is reflected by the Earth’s surface, but most is absorbed by the Earth’s surface or the atmosphere.
You should also understand that Earth emits radiation too. However, it is at a lower intensity and a much longer wavelength, which is called the infrared portion of the electromagnetic spectrum because of the lower emission temperature of the Earth. Radiation is emitted by the Earth’s surface, and by the atmosphere. We’ll go into more detail on this later.
Pro Tip: Many synonyms were discussed above. When referring to radiation from the sun you may hear the following words used: solar radiation, shortwave radiation, and ultraviolet radiation. When referring to radiation from the Earth you may hear the following words used: infrared radiation, longwave radiation.
Earth’s average temperature remains relatively constant as there is a balance of outgoing radiation and incoming radiation.