4 Radiation Budget of Earth

Sunayan Saha

TABLE OF CONTENTS

1. Learning Outcomes

2. Introduction

3. Basics of global radiation balance

3.1. Important physical laws governing radiative heat transfer

3.2. Components of global energy balance equations-theoretical appraisal

3.2.1.Radiation balance concept

3.2.2.Energy balance concept

4. Sun-The major energy source of earth

    4.1.       Factors influencing earth radiations budget

4.2.       Dynamics of incoming and outgoing radiation

5. Summary

1. Learning Outcomes

After studying this module, you shall be able to:

• Know the concept of radiation and energy balance
• Know the incoming and outgoing radiation/energy components, their spatiotemporal variability on the earth
• Know important physical laws, terminologies and units related to energy transfer through the atmosphere

2. Introduction

Earth’s primary energy source is the solar energy that is considered as one of the fundamental energy of nature, which maintain the dynamics of energy flow for natural ecosystem services. Every entity of natural world radiates and absorbs electromagnetic radiation. As photon flux from the sun (insolation) enters into the earth’s atmosphere, it interacts with atmospheric aerosols, cloud particles and other atmospheric molecules (both macro and micro). Thereafter, the residual resultant fractions are redistributed within the earth’s atmosphere system (Fig 1a). The stratified layers of earth’s atmosphere regulate the net energy dynamics in terms of maintaining a thermodynamic equilibrium at any particular location over an extended period of time. Scientists refer the process as global radiation budget that is primarily based on the law of energy conservation.

The main source of incoming shortwave radiation (Rs↓) on earth’s surface is the sun. The amount of radiation received depends on solar altitude and the transmissivity of the atmosphere. In the absence of clouds, a major fraction of incoming shortwave solar radiation reaches the surface and part of it is reflected back into outer space (albedo). The rest portion gets absorbed by the earth’s surface. Earth subsequently emits a fraction of this absorbed energy as infrared radiation (Fig 1b).Energy exchange processes between the earth surface and atmosphere entrails warming of atmosphere close to the earth surface and also provides energy to drive the general circulations within atmosphere. The net absorbed radiative energy in the earth-atmospheric system is transformed into non-radiative forms that get partitioned to heat up the air, ground and provides the energy to hasten evaporation. In particular, the earth’s radiation budget determines the earth’s climate regimes, oceanic circulation pattern and the dynamics of hydrological cycle. Meteorologists often consider the entire process as the possible indicator for climate change. Therefore, it is highly essential to quantify the basic components of earth’s radiation budget towards the effective monitoring and prediction of the major atmospheric phenomenon in climate change studies.

3. Basics of global energy balance

3.1. Physical laws governing radiative energy transfer

3.1.1 Energy Conservation law:

When radiation falls on any surface, three possible interactions are likely to occur. viz. (a) absoption (b) reflection and (c) transmission. According to the law of energy conservation,

Q = Qa + Qr + Qt …………(1)

Where, Q = total energy of the incident radiation, Qa = energy absorbed; Qr = energy reflected; Qt = energy transmitted.

Therefore, (Qa/Q) + (Qr/Q) + (Qt/Q) = 1

or, α + β + t   = 1 ……………(2)

Where,α = absorption power; β = reflection power; t = transmission power. 3.1.2 Planck’s spectral distribution law:

3.1.2 Planck’s spectral distribution law:

3.1.4 Rayleigh-Jeans Radiation Law:

At terrestrial temperatures (T), for longwave spectrum (low frequency) of the electromagnetic radiation (microwave; λ > 0.5 cm), the exponent factor of Planck’s spectral distribution expression becomes small, and hence the exponential approximation may be expressed as,…. (5)

ec2⁄λT = 1 + λcT2

Therefore, following the asymptotic expansion of Planck’s spectral distribution law the expression becomes:

In atmospheric physics, this expression is called the Rayleigh-Jeans law of radiation and the spectral region λ > 0.5 cm is called the Rayleigh-Jeans region where the Planck function is linear to T. The approximation of Planck’s spectral distribution law with Rayleigh–Jeans law and Wien radiation law is displaced in Fig. 2.

3.1.5 Stefan–Boltzmann law:

Planck’s spectral distribution law confirmed that the blackbody radiant intensity increases with the absolute temperature and the wavelength of maximum intensity decreases with increasing blackbody temperature. If we integrate the total emittance over the entire electromagnetic spectrum, the emitted blackbody radiant flux density (Eλ) is obtained by integrating the Planck function over the entire wavelength region is expressed as Stefan–Boltzmann law:

The abovementioned equation states that flux density emitted from a blackbody is proportional to the fourth power of the absolute temperature. The derived relationship is useful for analysis of broadband infrared radiative transfer.

Now, emissivity of any blackbody surface is defined as the ratio of observed monochromatic radiance (Iλ) to the blackbody radiance predicted by the Planck function (Bλ) at a specific temperature

to the top of the atmospheric blanket of earth, the total available radiant energy undergoes several types of losses before reaching the ground (absorbed and reflected/ scattered back by clouds and other atmospheric macromolecules) during the daytime. A fraction of this available radiant energy gets transmitted within the atmosphere and reaches to the earth surface as available net radiation (Rn).

R = α1 × Rn…………………(11)

Where, α1 is a proportionality factor; not necessarily a constant.

3.2.1.   Radiation balance concept

The Surface Radiation Budget of the earth is divided into four major components (a) downward shortwave radiation (Rs↓), (b) reflected shortwave radiation (Rs↑), (c) downward longwave radiation (RL↓) and (d) upward longwave radiation (RL↑).

The major sub-components of shortwave radiation fractions are:

Rs↓ = Direct beam solar radiation (Rsdirect↓) + Diffuse solar radiation (Rsdiffuse↓)

Rs↑ = Direct beam solar radiation (Rsdirect↑) + Diffuse solar radiation (Rsdiffuse↑)

= αS [Direct beam solar radiation (Rsdirect↓) + Diffuse solar radiation (Rsdiffuse↓)] Now, it is evident that αS = Rs↑/ Rs↓ (Short wave reflectivity i.e. albedo)

Therefore, the net shortwave radiation (Rns) can be expressed as:

Rns = (Rs↓- Rs↑)

Rns = (1+ αS) [Direct beam solar radiation (Rsdirect↓) + Diffuse solar radiation (Rsdiffuse↓)] …. (12)

Net terrestrial longwave radiation (Rnl) = (RL↓- RL↑)

Where,

RL↓ = Radiation emitted by atmosphere (determined by air temperature)

RL↑ = Radiation emitted by earth surface (determined by surface temperature)

According to Stefan-Boltzman law, incoming longwave radiation (RL↓) is determined by apparent sky temperature (Ts) and sky emissivity (εs). Therefore after equation 7, the relation may be expressed as:

RL↓= εs σ Ts4………….(13)

 Where, Ts and εs: cumulative impact of all layers of the atmosphere; depend on cloud cover, humidity, temperature structure and σ is the Stefan-Boltzman constant (eqn. 7)

In similarity, the outgoing longwave radiation (RL↑) depends on true surface radiative temperature (T0) and surface emissivity (ε0) and according to Stefan-Boltzman law it can be expressed as,

RL↑= ε0 σ T04………………….(14)

Finally, the net available radiant energy at earth surface (net radiation; Rn) can be rewritten as:

Rn= Rns + Rnl

= (Rs↓- Rs↑) + (RL↓- RL↑)

= [(1- α) (Rsdirect↓ + Rsdiffuse↓)] + σ (εsTs4 – ε0T04) …. (15)

3.2.2.   Energy balance concept

The net available radiative energy (Rn) at surface get absorbed on the earth’s surface. The absorbed radiative energy is converted to thermal or heat energy facilitating the natural transfer of water from the topsoil to the nearby atmosphere (latent heat flux due to evaporation, LE); heat the air (sensible heat flux; H), and moves into the ground (ground heat flux; G).The sensible heat flux is responsible for heating the atmosphere from the surface up to about1000 m during the day, except for days with strong advection effect. Consequently, the net radiation energy becomes the driver of the land surface energy fluxes as given below:

Rn = G + H + LE + M………..(16)

 In a nutshell, net radiation (Rn) which is actually balanced by G (Ground heat flux), H (sensible heat flux) and LE (latent heat flux) and usedas plant’s metabolic energy (M; balancing photosynthesis and respiration process, may be ignored as it constitutes < 1% of the net quantity of available energy (Rn), therefore are often neglected). Sensible heat is defined as the energy that we can sense that is measured in terms of air temperature. LE is the product of the evaporative flux (E) and the latent heat of vaporization (L, latent heat of vaporization: 2.5×106 J kg-1). All the energy components in this equation is expressed as flux density unit i.e. energy per unit time per unit surface area (W m2).

Under isothermal condition,

Rn = G + H + LE + M ………….(17)

Over 24 hours in a day, cumulative G = 0 and net assimilation of photosynthates are very small those may be ignored. Therefore,

Land surface features often control the relative partitioning of net radiation into LE and H components based on available surface moisture. At thermal equilibrium, the energy budget at any individual leaf surface may be expressed as,

Rate of energy absorption = Rate of energy loss

Therefore,

[αL. cos(θL).Rsdirect] + [αL. Rsdiffuse] + ε L RL = [ε L. σ. (TL+ 273)4] + [hc. (TL – Ta)]  + [k’. L. (eL – ea). gL] …. (19)

Where,

Rsdirect = Direct incident solar radiation available on leaf surface

Rsdiffuse = Diffuse incident solar radiation available on leaf surface

RL = Terrestrial longwave/ infra-red radiation (sky and ground component)

cos (θL) = cosine of leaf orientation angle to direct solar beam

αL= absorption coefficient of leaf (300-4000 nm)

ε L = emission coefficient of leaf towards IR radiation (> 4000 nm) hc = convection coefficient = f (leaf characteristics, wind velocity)

gL = total conductance (includes stomata and boundary layer conductance)

(eL – ea) = water vapor pressure difference between leaf surface (eL) and air (ea) in mbar unit T = temperature of leaf surface (TL) and air (Ta)

σ = Stefan-Boltzman constant

L = latent heat of vaporization (energy required to maintain transpiration pull)

k’ = 216.68 (vapor pressure to vapor density conversion factor)

[Note: hc = cp. ϱ / ra ; where cp = volumetric heat capacity of air; ϱ = density of air; ra = boundary layer resistance = k1 √(leaf width/ wind velocity)]

3.3.       Dynamics of incoming and outgoing radiation

Sign convention:

Components of the radiation and energy balance equations must accompany either a +ve or a – ve sign based on the direction of energy transfer. Radiation and energy fluxes are considered as –ve to the surface, if they transport energy away from the surface that is removes energy, while downward energy movement towards the earth’s surface is considered as +veto the surface.

Shortwave radiation reaching the ground either from sun or sky is considered as +ve and its reflected fractions are considered as –ve to the surface. For longwave radiation, similar sign conventions are used. The sign for net radiation is as per the resultant sum of gains and losses (to and from the surface). During day time, the domination of shortwave incoming solar radiation over outgoing longwave radiation (OLR) from earth’s surface results +ve Rn availability on soil surface (Fig. 4a). In contrast, the absence of Rs↓ during night leads to the dominance of OLR over incoming longwave radiation that turns Rn into –ve entity (Fig. 4b).

For any real surface, the heat capacity of the surface objects such as building, plant canopy etc. play a crucial role for balancing the energy dynamics of earth surface. A finite section of energy is often partitioned into the change in stored energy content of different physical objects (ΔQs) present in the atmospheric layer adjacent to the earth surface (boundary layer). Therefore, the energy balance equation becomes,

Rn = G + H + LE + M + ΔQs …………(20)

However, over an open field the ΔQs fraction is negligible. The observed variability in radiation and surface energy balance dynamics over 24 hrs in a day is displayed in Fig. 5 a and b. The energy partitioning often experiences a high degree of spatiotemporal variability that determines the mean climate condition and its associated variability, worldwide. The detailed spatial distribution across the different latitudes and longitudes are displayed in Fig 6a. The year around daily-averaged solar radiation intercepted at the top of the earth’s atmosphere across different latitudes is displayed in Fig. 6b.

In addition to previously discussed poleward transport mechanism of radiation balance (Meridional Heat Transport), tropical regions harvest maximum solar radiation, thus higher Rn, especially during summer months. Lower shortwave radiation availability during winter often reduces the magnitude of Rn that is got further hastened during summer months in a cyclic mode. Southward facing hill slopes in northern hemisphere receive more shortwave radiation, thus have higher Rn values than north facing hill slopes. Dark surface has more absorption for shortwave radiation (lower albedo), thereby increases Rn value than white surfaces.

4. Sun- The major energy source of earth

The most important and widely accepted principle of climate science relies on the fact that solar energy is the main source of energy for earth’s climate system controlling the net energy budgeting and the hydrological cycle. The energy is generated from the fusion reactions with conversion of four hydrogen (H) atoms into single helium (He) atom in the core portion of the sun that results in minute reduction of the sun’s mass. The solar radiation is comprised of ultraviolet (~5%), visible (~40%) and infrared (~55%) regime of electromagnetic radiation. Upper air ozone layer absorbs radiation with < 0.29 μm wavelengths, thus protects the life form on earth from the detrimental effect of harmful cosmic and UV rays.

If we consider the total shortwave radiation received at the top of the atmosphere as 100 per cent, then while passing through the atmosphere under clear sky condition, ~35% are reflected back to space. Cloud droplets (27%), atmospheric gas molecules (6%) and snow or ice-covered areas of the earth (2%) majorly contributes in to the shortwave scattering into space. The remaining 65% gets absorbed by the earth atmosphere system;14% by earth’s atmosphere and 51% by earth surface (Fig. 7a).As 35% of the total insolation is reflected back as albedo, the balance of longwave radiation accounts for the remaining 65% of shortwave radiation. For long wave radiation, earth surface radiates back 51% of longwave terrestrial radiation out of which, 17% are radiated to space directly and the remaining 34% are absorbed by the atmosphere (6% directly by the atmosphere, 9% through convection and turbulence and 19% through latent heat of condensation). Daytime insolation is the major source for rest 14% of longwave radiation. Finally, 48% of terrestrial long wave radiation gets absorbed by the atmosphere (14% from insolation +34% from terrestrial radiation absorbed by atmosphere) that is also radiated back into space. Thus, the total radiation returning from the earth and atmosphere is (17+48) % = 65% that balanced the net 65% shortwave radiation received from the sun. (Fig. 7b)

Cloud cover often reduces the earth surface energy availability from the solar radiation. The Clouds and the Earth’s Radiant Energy System (CERES) installed on aboard NASA’s Aqua and Terra satellites are used for the quantification of reflected shortwave and emitted longwave radiation aiming to determine the total radiation budget of earth. The amount of radiation received on earth’s surface is often affected by the nature of surface (reflectivity of the surface), incident sun angle, nature of output from sun, and the cyclic seasonal variations of earth’s orbit.

4.1.       Factors affecting global radiation balance

1. Earth’s rotation: Earth’s rotation causes daily variations in net radiation. During daytime, the net radiation is positive while during nighttime it becomes negative because of no incoming shortwave radiation (Rs).
2. Earth-Sun geometry: It causes annual variations in net radiation thereby affects global radiation balance. During winter, the amount of incoming shortwave radiation (Rs↓) received is less which leads to less net radiation (Rn) and the vice-versa happens during the summer.
3. Latitude: Equator receives more incoming shortwave radiation (Rs↓) which leads to more net radiation (Rn) than near poles.
4. Altitude: With increase in altitude, there is less atmospheric reflection/scattering/absorption which leads to more incoming shortwave radiation (Rs↓) received at the surface as well as less  incoming longwave radiation (RL↓). This leads to more positive net radiation (Rn) during day than at sea level while during night it becomes more negative than at sea level.

1. Surface color: Darker surface has lower albedo which leads to lower Rs↑ and higher Rn.
2. Clouds, dust and pollution factor: Clouds, dust, pollutants absorb Rs↓and RL↑, and have direct

4.radiative forcing which varies between -0.2 to -1.1 W m-2. Under cloudy skies, daytime Rn at surface is less positive than clear skies while it is less negative at nighttime as cloud acts as barrier to RL↑ and reradiates back to earth surface.

5.. Meridional Heat Transport: Rn is surplus at low latitudes (< 40° N/S) and deficit at high latitudes (> 40° N/S). Energy is transported from the surplus to the deficit regions (pole-ward transport) by ocean currents (~1/3), warm/cold winds (sensible heat) (~1/3) and moisture in air (latent heat) (~1/3). Thus it prevents overheating at low latitude and over cooling at high latitude; this is known as meridional heat transport (Fig. 8a and b).

5. Summary

The global energy balance approach encompasses the delicate budgeting providing the information on the role of positional influence, vertical structure of temperature and energy profile of atmosphere to maintain the radiative equilibrium between atmosphere and earth surface. It explains the natural greenhouse effect and provides the skeleton for numerical models formulation based on the natural feedbacks system aiming to improve the understanding of ecosystem energy exchange processes. The near surface radiation balance of earth is useful in the fields of agro-meteorology and climatology

• To determine the climate of any region
• To determine the surface radiative properties (albedo, emissivity etc.)
• To determine the net radiation as the input component of surface energy budget
• To determine apparent surface temperature from space
• To study radiative cooling or warming processes of the Planetary Boundary Layer (PBL).
• To parameterize the surface heat fluxes to soil and air in terms of net radiation