Intruduction Of Earth Surface

The Sun is a dwarf main-sequence star with an age of about 4.6 Byr (billion years) whose luminosity has increased slowly, by about 30%, from the time it joined the main sequence. At the same time, the XUV (1-1200 A) and ultraviolet emission decreased as the rotation rate of the Sun became slower, and its magnetic activity declined. Thus, the incoming solar radiation (ISR) at the Earth's orbit is determined by solar evolution on timescales of billions of years. Luminosity variations affect climate directly, while variations in the ultraviolet flux affect the molecular composition of the atmosphere, and so indirectly affect climate through the concentrations of greenhouse gases. The ultraviolet flux also has a direct effect on biological evolution that can also indirectly influence climate by controlling land weatherability (§12.2), surface cover and surface reflectivity.

According to analyses of stratigraphic distributions of oxidized and reduced mineral deposits, the atmosphere of the early Earth (4 Byr ago) was anoxic near the surface, with the O2 mixing ratio less than 10~4, and it is generally accepted that today's oxygen-rich atmosphere is the product of photosynthesis and organic-carbon burial. An anoxic early atmosphere implies no ozone layer, and hence no associated ultraviolet screen to shield early life from the Sun's lethal ultraviolet radiation. Heavy bombardment of the Earth's surface is thought to have occurred between 4.5 and 3.8 Byr ago, based on the lunar-cratering record, so that life became extant about 4 Byr ago, as evidenced by the microfossil record. Thus understanding the evolution of solar ultraviolet flux on timescales of billions of years, which is related to solar activity, is of paramount importance to the biological evolution on Earth.

On timescales of about a million years to thousands of years, changes in the Earth's orbit can produce significant changes in ISR. On human life timescales, there are variations in the luminosity and ultraviolet flux arising from the 11-year solar cycle related to the coverage of the solar surface by sunspots. Solar-cycle luminosity variations are relatively small, but the variation in ultraviolet flux is significant.

The seasonal-latitudinal distribution of the ISR determines the global distribution of the Earth's shortwave radiation budget. This distribution is determined by the tilt of the planet's axis and the eccentricity of its orbit. These in turn determine the duration of the polar winter (or night) and the polar ice caps. The distribution of Earth's total, both shortwave (solar) and longwave (terrestrial), radiation budget determines both atmospheric and oceanic dynamics and hence climate. We shall examine the Earth's radiation budget in Chapter 8 and the evolution of the Earth's climate in §12.2.

5.2 The Sun as a main—sequence star 5.2.1 Stellar properties

Main-sequence (dwarf) stars like the Sun are referred to as late-type stars and burn H to He. These stars have relatively low effective temperatures and stellar radii. The smallest of these stars are classified as spectral types G, K and M, and have effective temperatures ranging from 5980-5370 K (G0-G9), 5230-4350 K (K0-K5), and below 3840 K for M0-M2 stars. In our galaxy the most numerous are the M stars, then the K stars followed by the G stars.

The colour index B-V of a star is defined as

where mB and mv are the apparent magnitudes of the star in the blue and visual, respectively. To a good approximation the mass of a late-type star can be computed from log(M/MQ) = 0.28 — 0.42(B — V), (5.2)

so that the radius of the star can be calculated from

where G = 6.626 x 10-8 dyn cm2 g-2, is the universal gravitational constant and g the gravitational acceleration at the stellar surface. The effective temperature of a late-type star can be approximated from log Teff = 3.908 — 0.234(B — V). (5.4)

The Sun is a main-sequence dwarf star of spectral type G2V (V being the luminosity class of the main-sequence stars) according to the effective temperature classification shown in Table 5.1. The present properties of the Sun are given in Table 5.2, where Mq is the solar mass, Rq the radius, Lq the luminosity, Tq the effective surface temperature, and tQ its age. The present composition of the solar surface is given in Table 5.3.

The effective temperature of the Sun corresponds to a surface temperature of a blackbody that has the equivalent luminosity. The surface of the Sun is referred

Table 5.1 Thermal parameters for late-type main-sequence stars. (Data from Cram and Kuhi 1989)

Spectral-type M/Mq

logg

Teff(K)

B-V

GO

1.15

4.32

5980

0.583

Gl

1.10

4.34

B900

0.60S

G2

1.07

4.3B

BSOO

0.62B

G3

1.04

4.37

B710

0.642

G4

1.00

4.3S

B690

0.6B7

GB

0.9S

4.40

B620

0.672

G6

0.93

4.42

BB70

0.690

G7

0.90

4.44

BB00

0.713

GS

0.S7

4.46

B4B0

0.740

G9

0.S4

4.4S

B370

0.776

KO

0.S1

4.49

B230

0.S19

Kl

0.79

4.B0

BOSO

0.S66

K2

0.76

4.B2

4920

0.912

K3

0.74

4.B3

4S10

0.966

K4

0.70

4.B4

4640

1.030

KB

0.67

4.BB

43B0

1.1B0

MO

0.B2

4.63

3S40

1.420

Ml

0.49

4.66

3710

1.47B

M2

0.44

4.70

3620

1.512

Table 5.2 Present solar mass, radius, luminosity, effective temperature, age and log(g).

Mq( g)

Rq (cm) Lq (erg/s)

Tq (K)

to (Byr)

log(g)

1.989x 1033

6.96x 10lu 3.845x 1033

5777 K

4.6

4.44

Table 5.3 Per cent abundance by volume (%v) and by mass (%m) of elements in the solar surface.

Element

%v

%m

H

92.0

73.4

He

7.S

2B.0

C

0.02

0.20

N

0.00S

0.09

O

0.06

0.S

Ne

0.01

0.16

Mg

0.003

0.06

Si

0.004

0.09

S

0.002

0.0B

Fe

0.003

0.14

to as its photosphere whose mean temperature is Tq. The concept of a surface of course is a matter of definition. In Chapter 3, we derived the following variation of temperature with mean all-wave optical depth for an atmosphere in radiative equilibrium

where To is the atmospheric skin temperature, corresponding to t = 0. We also saw that the skin temperature and effective temperature are related by

so that To = 0.84Tq. Thus, for the Sun the atmospheric skin temperature is 4859 K. We also noted that the effective temperature is located at r = which defines, essentially, the photospheric surface. Above the photosphere we expect the atmospheric temperature to decrease to the skin temperature. In fact for the Sun as we move outwards magnetic-field effects heat the atmosphere so, analogous to the Earth's stratosphere that is heated by solar ultraviolet radiation due to ozone absorption, the Sun's atmospheric temperature begins to rise above the skin temperature in what is called the solar chromosphere where the temperature goes through a temperature minimum and that has a mean value of about 4600 K. If it were not for the non-radiative heating, associated with the magnetic-field activity of the Sun, the temperature of the outer solar atmosphere would decrease to zero at infinity due to dilution of the radiation field according to the inverse square law. The temperature at 'infinity' is in fact not zero but 2.725 K, the blackbody temperature corresponding to the cosmic microwave background radiation. The temperature in the chromosphere is of the order of 104 K, due to non-radiative heating, and rises to about 106 K (corresponding to X-ray emission) in the outer atmosphere, called the solar corona. The chro-mospheric temperature is sufficient for atomic hydrogen, the main constituent, to have appreciably populated excited states. This fact is very important to the ultraviolet radiation that reaches the Earth, and hence to the photochemistry of the atmosphere.

5.2.2 Total solar irradiance

The mean Sun-Earth distance is r = 1.496 x 1013 cm = 1 AU, and the mean flux arriving at the Earth's orbit at this mean distance is called the solar constant or total solar irradiance (TSI) and it is denoted by Sq. Measurements give a mean value of

Sq = 1366 W m~2 over several solar cycles. Thus, according to the inverse square law of radiation where Lq is the solar luminosity. When we consider the relatively long, on human timescales, characteristic time for radiative perturbations in the solar core to reach the solar surface, we can appreciate the historical terminology of solar constant.

Free escape of photons from the centre of the Sun would take only Rq/c = 2.3 s. However, the mean free path of photons in their random path outwards is very small. If we let l represent the mean free path then l = 1/t = 1/aN (5.8)

where t is the optical depth, and a = 2 x 10-24 cm-2, is the absorption cross-section. Now the number of particles per unit volume, N is given by i (5.9)

where Na = 6.022 x 1023 is the Avogadro number, m = 0.6 is the solar mean molecular weight (§5.4.1), and p is the solar mean density equal to 1.409 g cm-3. Thus, N = 1.4 x 1024 and hence l = 0.36 cm. Now since each photon absorption/reemission event takes about tae = 10-8 s, then the travel time to escape is taenc, where nc is the number of such absorption/re-emission events to reach the surface given by (Rq/1)2, so that the travel time to escape is of the order of 10 Myr. Thus, perturbations to the photon flux in the solar core take a long time to be reflected in its luminosity. As we shall see, there are radiative perturbations at the solar surface due to photospheric magnetic field activity that result in areas of reduced radiative emission called sunspots that are controlled by the 11-year solar cycle. The total solar irradiance thus varies over the solar cycle.

5.2.3 The solar cycle

The 11-year cycle of solar activity manifests itself in significant variation of sunspot (easily observable regions of reduced visible radiation flux) numbers on the solar photosphere. The Sun undergoes a period of very few sunspot numbers, of the order of 10, called the solar minimum to a period of sunspot numbers of the order of 100, called the solar maximum. The period between the solar minima or between the maxima is about 11 years. Annual mean sunspot numbers since 1730 AD, clearly show the 11-year cycle, as seen in Fig. 5.1 (data given by the NASA Marshall Space Flight Center, based on the International Sunspot Numbers). It is worth noting that between 1645 and 1715 AD, the evidence is that there was very few sunspots, the cycle was unclear during this period, referred to as the Maunder minimum.

The current solar cycle is Cycle 23 that commenced with a minimum in October 1996. Measurements of the total solar irradiance, or solar constant Sq, over the solar cycle have been performed by various satellites, such as NIMBUS-7,

FlG. 5.1. Sunspot number variation since 1750 AD. (Data from NASA)

SMM (Solar Maximum Mission), ERBS (Earth Radiation Budget Satellite), and ACRIM (Active Cavity Radiometer Irradiance Monitor). In Fig. 5.2 is shown the solar constant for the period 1978-2003, based on the ACRIM Composite TSI (Total Solar Irradiance) data, based on ACRIM 1,2,3, Nimbus 7/ERB and VIRGO measurements. The long-term mean value, according to the ACRIM composite is 1366.25 ±0.71. The SOLCON experiment, which was part of the ATLAS 1 & 2 Missions on the space shuttles Atlantis and Endeavour, measured the solar constant between 9-11 April 1993 and found a mean value of 1366.31 W m~2. There is also a solar-cycle variation, as can be seen in Fig. 5.2, where the minimum in the solar constant in October 1996 corresponds to the minimum in sunspot number. This arises because although sunspots reduce the solar luminosity, they are surrounded by bright regions called faculae that increase in number along with sunspots during solar maxima. The overall radiation balance is dominated by the faculae. The variation in solar luminosity over the solar cycle, is about 0.1%, which according to simple climate models would correspond to a < 0.1 K variation in the Earth's mean global surface temperature, a quantity too small to affect climate. However, ultraviolet and energetic-particle flux variations are much larger and play a significant role in upper-atmospheric chemistry.

200-

150-

200-

150-

100-

n—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—r

1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Year

100-

n—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—r

1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Year o O

1370-, 136913681367136613651364136313621361 -

1360

Solar Minimum October 1996

Mean=1366.26 SD=0.71

1975

1980

1985

1990 Year

1995

2000

2005

FlG. 5.2. Total solar irradiance (TSI), or solar constant, variation between 1978 and 2003 AD, based on ACRIM Composite data.

5.2.4 Solar spectral irradiance

The solar spectral irradiance, Sq\, reaching the Earth is shown in Fig. 5.3 and comprises mostly a Planck function distribution on which are superimposed emission lines that are generated in the solar chromosphere. The most important of these is the Lyman-a of H, which corresponds to the transition between the ground and first excited state, as shown in Fig. 5.4. Transitions originating from the second level are known as the Balmer series, while those originating from the third level are called the Paschen series. For the H atom, the energy difference between any two levels is given by

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