Lecture 1: Climate and the 1st Law of Thermodynamics Quick Review of Monday s main features: Lapse rate, Hydrostatic Balance <T> surface = 288K (15 C). In lowest 10 km, the lapse rate, Γ, averages: T Γ z 6.5K / km Hydrostatic Balance: For an isothermal atmosphere (and this is true to ~20%) at rest: P z = P o exp(- [(M a g)/rt]z) = P o exp(- z / H) where H, the scale height, is about 7 1/2 km. The current climate epoch: The Holocene The climate during the last 10,000 years has been notably quiescent Ice core record from Greenland Emergence of civilization (see Diamond "Guns, Germs, and Steel") Figure to follow Some variability, however Climate record of 20th century Figure to follow Nevertheless, recent (and relatively small) local climate shifts have had significant influence. Dust Bowl 1930s Recent (last several decades): abnormal strength and consistency of Indian monsoon 1816 - "year without a summer" (Tambora eruption)
Figure 2. Paleoclimate record for last 150,000 yrs. Ruddiman, 2001. The current climate epoch - the Holocene Figure 3. NOAA global surface temperature, Ruddiman, 2001. The current climate epoch - the Holocene
Climate Puzzles: Faint Sun more later Warm Ages - Cretaceous (100 Ma) Eocene (50 Ma) smaller pole-equator gradient(?) Glaciation - No ice first 2.5 Ga; generally ice free until 0.1 Ga. Transition from 40 Kyr to ~100 Kyr glaciation ~0.7-1 million years ago. Present - warm extratropics / ice covered poles Earth's Orbit Figure 6. Earth s Orbit Climate Puzzles: The Solar "Constant"
The Sun The sun is a relatively small star whose projected lifetime on the main sequence is ~ 11 billion years. Theory and observations of stars similar to the sun suggest that the luminosity has increased 25-30% over the last 4.5 billion years, which as we will see leads to the so-called faint-sun paradox. figure to follow The current solar luminosity, L o, is presently 3.9 x 10 26 W. This energy is emitted by the sun's photosphere whose radius is ~7 x 10 8 m. The flux density at the photosphere is then: Flux Density = flux/area = L o /(4 π r 2 ) = 6 x 10 7 W m -2 Compare San Onofre Nuclear Station 1 or 2 or 3 = 1 x 10 9 W Figure 4. Variation in Solar luminosity on main sequence. Associated T e. Ruddiman, 2001 The Sun
The Solar "Constant" Since space is effectively a vacuum, the amount of energy passing outward through any sphere centered on the sun will be equal to the solar luminosity, L o. If the radiation is isotropic: Flux = L o = S d 4 π d 2 S d, the Solar Constant (at distance d) = L o /(4 π d 2 ) see figure to follow At the mean distance of Earth from Sun (1AU = 1.5 x 10 11 m): S o = 1368 W m -2. For a rotating sphere at 1 A.U., average radiance: S o / 4 = 342 W m -2 [c.f. average new refrigerator (or average person) ~ 100 W.] In addition to 25-30% change in L o over 4.5 billion years, S o changes on various timescales: 1. Annual due to orbital eccentricity (~3% change in d between perihelion - presently Jan. 3 rd - and aphelion) 2. "11-year" (solar cycle) (0.25% change in L o ) 3. Numerous attempts to link decadal solar variation with climate have been (largely) unsuccessful. Figure 5. Ruddiman 2001 Emission Temperature of Planets
Figure 6. Earth s Orbit Climate Puzzles: The Solar "Constant" Figure 7. Ruddiman 2001.
Figure 7. Ruddiman 2001. The Solar "Constant" Cavity Radiation - Stefan-Boltzman Law. Blackbody Radiation. The radiation field within a closed cavity in thermodynamic equilibrium has a value uniquely related to the temperature of the cavity wall, regardless of the material of which the cavity is made. [This radiant intensity is called the blackbody radiation, since it corresponds to the emission from of a surface with unit emissivity (later)]. Intuition: consider two blocks of different material each with an internal cavity; they are placed together such that the cavities connect thru a small hole. The radiation passing in each direction must be the same total intensity (and also of the same color) The intensity of cavity radiation (and therefore blackbody emission) follows the Stefan-Boltzmann Law: E BB = σ T 4 ; σ = 5.67 x 10-8 Wm -2 K -4
Emission Temperature of the Sun The solar flux density of the photosphere is about 6.4 x 10 7 W m -2. We can equate this to the Stefan-Boltzmann formula and derive: T e (photosphere) = [6.4 x 10 7 / σ] 1/4 = 5800 K Emissivity For an arbitrary body at equilibrium with an measured emission of E R we define the emissivity, ε, as: ε = E R / (σ T 4 ) The emissivity of an object is wavelength dependent and related to the reflectivity as (Kirchhoff s Law): ε = 1 - R Metals such as tungsten have emissivities ~ 0.25 in the near IR; liquid water has an emissivity near 1 at all wavelengths - which as we will see later is critical for Earth's climate]. Emission Temperature of Planets The emission temperature of a planet, T e, is the temperature with which it needs to emit in order to achieve energy balance (assuming the average temperature is not decreasing c.f. Jovian planets). We equate the absorbed solar energy with the energy emitted by a blackbody: Solar radiation absorbed = planetary radiation emitted Absorbed Solar Radiation = S p π r p2 (1-α p ) α p is the planetary reflectivity or albedo. For Earth, α p is ~ 0.3. For Venus, α p is ~ 0.7 and so solar energy input per unit area is less despite being at 0.7 AU. Emitted radiation = σ T 4 4 π r p 2 The 4 π r p2 accounts for the fact that emission occurs over the entire area of the sphere. Equating the absorbed and emitted radiation: S p π r p2 (1-α p ) = σ T e 4 4 π r p 2 T e = [(S p / 4)( 1-α p )/ σ] 1/4
Today: Emission Temperature of Earth T e = [(1367 W m -2 / 4) (1 0.3) / (5.67 10-8 W m -2 K -4 )] ¼ = 255 K = -18 C (O o F) Obviously this is not the emission temperature of the surface! As we will see next lecture, the greenhouse effect warms the surface significantly above T e (fortunately). The problem is even more severe early in the solar evolution: 4 Billion years ago: T e = [(1000 W m -2 / 4) (1 0.3(?)) / (5.67 10-8 W m -2 K -4 )] ¼ = 235 K = -38 C (-36 o F) Contrast with Jupiter: Jupiter is 7.8 10 8 km from the sun. Its albedo is 0.73. S Jupiter = 3.9 x 10 26 W / (4 π d Jupiter2 ) = 50 W m -2 T e = [(50 W m -2 / 4) (1 0.73) / (5.67 10-8 W m -2 K -4 )] ¼ = 88 K Actual emission temperature of Jupiter is ~ 134 K. Most of the energy emitted by Jupiter today (> 80% - note T 4 dependence) is associated with cooling from gravitational accretion.