Environment of Earth

March 9, 2008

RADIATION BALANCE OF EARTH

Filed under: Environment — gargpk @ 2:19 pm
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In every component of the global environment, radiation is constantly coming and a portion of incoming radiation is constantly going out of it. The algebraic sum of radiation fluxes reaching and leaving a place is called its radiation balance. In the study of global environment, following three types of radiation balances are important:

(a) Radiation balance of Earth’s surface (R)

It is the algebraic sum of radiation fluxes reaching and leaving the surface of Earth. Its magnitude is equal to the difference between the amounts of direct and diffused short-wave radiation absorbed by Earth’s surface and the long-wave effective radiation and is given as:

R = Q(1 – A) – I

where, R = Radiation balance of Earth’s surface; Q = Total direct and diffused short-wave radiation reaching Earth’s surface; A = Albedo of Earth’s surface given as a fraction of unity; I = Effective radiation.

Due to ‘green-house effect’ of atmosphere, the average radiation balance of Earth’s surface is always positive. The radiation balance of Earth’s surface is linked to the radiation balance of atmosphere.

(b) Radiation balance of Earth-atmosphere system (Rs)

It is the algebraic sum of radiation fluxes reaching and leaving Earth-atmosphere system as a whole. This it is equal to the difference between radiation solar radiation reaching the upper boundary of atmosphere i.e. incoming radiation (incident solar radiation) and long-wave radiation leaving atmosphere’s upper boundary i.e. outgoing radiation. Its magnitude may be given as:

Rs = Qs(1 – As) – Is

where, Rs = Radiation balance of a vertical column extending from upper boundary of atmosphere to the Earth’s surface; Qs = incoming radiation; As = Albedo of Earth-atmosphere system and Is = outgoing radiation.

The outgoing radiation of Earth-atmosphere system includes that part of Earth’s surface radiation which passes through atmosphere unaltered and goes out of atmosphere’s upper boundary plus radiation of atmosphere itself going out of its upper boundary. The outgoing radiation is much influenced by clouds. In the absence of clouds, Earth’s surface radiation within wavelength range of 900-1200 nm plays important role. In completely cloudy conditions, the radiation from the upper surface of clouds becomes very important and this radiation depends on the temperature of that surface. The temperature at the upper surface of clouds is usually much lower than the temperature at the Earth’s surface. Therefore, clouds substantially reduce the amount of long-wave radiation into the outer space.

(c) Radiation balance of atmosphere (Ra)

It is equal to the difference between radiation balance Earth-atmosphere system and the radiation balance of Earth’s surface i.e. given as:

Ra = Rs – R

or, substituting the expressions for Rs and R, as:

Ra = Qs(1 – As) – Q(1 – A) – (Is – I)

The magnitude of the radiation balance of atmosphere is negative and equal to the absolute value of radiation balance at Earth’s surface. This negative radiation balance of atmosphere is compensated by:

(i) inflows of energy from condensation of water vapor during cloud formation and precipitation and

(ii) flow of heat from Earth’s surface associated with turbulent heat conductivity of lower atmospheric layer.

Geographical distribution of radiation balance

The radiation balance at Earth’s surface is not uniform but varies at different geographical locations. Following two factors have important effect on the variation of radiation balance over Earth’s surface.

1. Relationship between latitude and irradiance: The radiation reaching certain surface area (B) at Earth’s surface depends on the latitude and is given by Lambert’s cosine law:

QB = Qo cos z

where, Qo = Irradiance of solar beam at upper boundary of atmosphere i.e. equal to solar constant; z = solar zenith angle.

Zenith angle of direct solar beam may be defined under any condition of varying latitude, solar declination and solar time is given by:

cos z = sin sin + cos cos h

where, = latitude; = angle of solar declination (angle between solar beam and equator which varies between -23.45 degrees on 22 December and +23.45 degrees on 22 June); h = hour angle of Sun (measure of time from solar noon where one hour equals to 15 degrees).

Maximum monthly range of solar irradiance shows considerable increase with latitudes and is also related to variations in photoperiod (time in hours between sunrise and sunset P). Value of h at both sunrise and sunset may be derived from solar declination and latitude of site by:

cos h = -(tan tan )

so that the photoperiod (P) is gives as:

P = 2/15 cos-1 h

2. Optical effects of atmosphere on solar irradiance: The ideal pattern of solar irradiance at the upper boundary of atmosphere is not realized perfectly at Earth’s surface because of the optical effects of atmosphere on solar beam passing through it. Following three features of the interaction between solar irradiance and the atmosphere determine solar irradiance at the Earth’s surface.

(i) Path length (m): Assuming that the thickness of atmosphere over Earth’s surface is uniform, the length of path, which solar beam traverses from upper boundary of atmosphere to the Earth’s surface i.e. the path length (m) is given as:

m = 1/cos z

The path length (m) is shortest at the place where solar beam and Earth’s surface are perpendicular to each other. The above relation is found to be correct upto zenith angle (z) of about 70 degrees (Robinson, 1966). At greater zenith angles, curvature of Earth and atmospheric refraction cause increasing overestimation of the value of path length.

(ii) Atmospheric transmittance: The radiation of solar beam passing through atmosphere may be absorbed, reflected and scattered by various gases and aerosols in the atmosphere. The effects of these phenomena on the solar irradiance are reflected in mean atmospheric transmittance (). If all the effects of atmosphere on the solar beam are assumed to be constant throughout the depth of atmosphere, then depletion of the irradiance of solar beam at upper boundary of Earth’s atmosphere (Qo) will be simple function of path length (also termed air mass) and mean atmospheric transmittance. Then the solar irradiance reaching Earth’s surface (Q) will be given as:

Q = Qo m

The value of strongly depends on dust and pollutants present in the atmosphere and may vary from 0.4 in polluted atmosphere to 0.8 in very clear and dry atmosphere.

(iii) Cloud cover: The solar beam passing through Earth’s atmosphere is also affected by the cloud cover present in it. Various empirical relationships have been derived which relate solar irradiance reaching Earth’s surface to some measure of cloudiness. No such relation is perfect because of the variations in optical properties of different cloud types. A general relationship derived from global observations at 88 well separated meteorological stations is given as:

Q = Qo (0.803 – 0.34f – 0.458f2)

Where, f = monthly fractional cloud cover.

The variations in mean atmospheric transmittance have not been included in this relationship and the above relationship will show changes with such variations.

The salient features of the geographical distribution of radiation balance of Earth’s surface keeping in view above effects on solar irradiance at upper boundary of Earth’s atmosphere are as follows:

1. Yearly total radiation: It varies substantially within the range of less than 60 to more than 220 kcal/sq. cm/year.

(i) At high and middle latitudes, distribution of total radiation is zonal in nature while in tropical latitudes the distribution deviates from zonality.

(ii) Total radiation is greatest in high-pressure belts in Northern and Southern Hemispheres, especially in desert areas of continents. Highest total radiation is found in Northwest Africa. It is due to almost total absence of clouds in that region. However, total radiation is reduced in low latitudes near equator, in regions of monsoon climates and in certain other regions due to increased cloudiness.

(iii) Total radiation also varies seasonally i.e. in different months of the year. This may be illustrated by considering its values in June and December i.e. the months in which average height of Sun is highest and the lowest in Northern Hemisphere and vice-versa in Southern Hemisphere.

During December, zero isocline passes somewhat to the north of Arctic Circle. At latitudes above it, Sun never rises above the horizon and total radiation is zero. To the south of zero isocline, total radiation increases rapidly. Its distribution in region below Arctic Circle and above tropical latitudes is largely zonal. In low tropical latitudes, the zonal character of distribution is absent and total radiation is determined by the degree of cloudiness in different regions. Further, average zonal changes in total radiation are relatively small from low latitudes in Northern Hemisphere throughout entire Southern Hemisphere. Continuous increase in length of day towards South Pole in Southern compensates for reduction in average height of Sun and so there is negligible reduction in total radiation towards higher latitudes in Southern Hemisphere.

During June, similar situation exists with regard to distribution of total radiation. In Northern Hemisphere, total radiation shows relatively little change except for desert regions where its value is high. At middle and high latitudes of Southern Hemisphere, total radiation decreases with increasing latitudes.

2. Yearly total radiation balance: Yearly total radiation-balance at Earth’s surface is positive over entire surface of oceans and land. Negative yearly sums of radiation balance are found only in regions of permanent snow or ice cover. The yearly radiation balance shows sharp changes from land to ocean areas. As albedo values of ocean surface are lower, radiation balance of ocean areas is usually higher than that of land areas at same latitudes.

On ocean surface, distribution of radiation balance is generally zonal in character. However, some regions particularly where warm and cold currents operate, some deviations from zonality are found. At tropical latitudes, radiation balance of ocean surface shows small changes while in the middle latitudes, there is rapid reduction in corresponding balances from lower to higher latitudes. Greatest value of radiation balance of Earth’s surface is 140 kcal/sq. cm/year, which occurs in Arabian Sea.

On the land surface, changes in yearly radiation-balance values are also partly zonal in nature. However, in certain regions deviation from zonality is found due to difference in their moisture conditions. In the dry regions, radiation balance is lower in comparison with regions of sufficient or excessive moisture at same latitudes. The low radiation balance in dry regions is due to:

(i) Reflection of short-wave radiation

(ii) Higher expenditure of radiation energy on effective radiation owing to high surface temperature, low cloudiness and relatively low air humidity. Thus alongwith general reduction in radiation balance at higher latitudes, there are also found regions of further reduced radiation balance in areas of dry climate. This reduction is particularly observed in Sahara, deserts of Central Asia and in many other deserts and arid regions. In monsoon regions, yearly radiation balance of Earth’s surface is also somewhat reduced due to intense cloudiness during warm season. In humid tropical regions, highest yearly radiation balance values are found on land but even these just reach 100 kcal/sq. cm/year which is quite less than corresponding maximum value for the ocean.

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