Chapter 8. Earth’s Energy
Recommended article : 【Earth Science】 Earth Science Table of Contents
2. Solar and Terrestrial Radiation
4. Internal Energy of the Earth
1. Solar Radiation Energy
⑴ Light and Energy
① Electromagnetic Waves
○ Waves propagated by the vibration of electric and magnetic fields in space
○ Includes gamma rays, X-rays, ultraviolet rays, visible light, infrared rays, and radio waves
○ Speed of 3 × 10^8 m/s in a vacuum
② Radiant Energy
○ Energy propagated by electromagnetic waves
○ Absorbed by matter and converted into thermal energy
⑵ Insolation (Incoming Solar Radiation)
① Solar Constant : Energy incident on 1 cm^2 of a surface perpendicular to solar rays at the upper boundary of Earth’s atmosphere for 1 minute, usually 2 cal / cm^2·min
② Solar Radiation Energy Received by Earth : If the total solar radiation energy of πR^2I is incident on Earth, then if it is evenly distributed over the entire Earth’s surface, the amount of solar radiation energy incident on a unit area of the Earth’s surface is
○ Where I is the solar constant, 2.0 cal / cm^2·min
2. Solar and Terrestrial Radiation
⑴ (Reference) Blackbody Radiation
① Definition : Phenomenon where all objects with energy emit light
② Blackbody : Object that absorbs all incident energy and emits all absorbed energy completely
③ Number of States for Waves (number of modes)
○ Based on Normal Modes
○ 1D Normal Modes : For a wave with length L, various normal modes of vibration exist depending on the state number n (where n is a natural number)
○ 3D Normal Modes : Various waves (in this case, light) exist based on the state vector (l, m, n) of the wave, where l, m, n are integers
○ State vectors can correspond to orthogonal coordinates : Considering the octant due to l, m, n being positive integers
○ Number of states for waves : If the number of grid points in the 1/8 sphere with a radius of p centered at the origin is N*(p),
○ Relationship between state count (N*) and frequency (ν)
○ The equation does not consider that two waves with opposite phases can exist for the same state count
○ Conclusion : Volume V = L^3, Number of states per unit volume N = N* / V,
④ Rayleigh-Jeans Law
○ Overview : In analyzing blackbody radiation in terms of waves, UV catastrophe must be observed
○ Average vibrational energy of the system in Thermodynamics
○ Average radiant energy per unit volume at frequency ν
○ UV Catastrophe : The phenomenon where blackbody radiation emits light very close to wavelengths of 0
○ In reality, light with wavelengths close to 0 converges to zero intensity
⑤ Planck’s Law
○ Max Planck introduced the concept of quanta and assumed E = hν, successfully explained in 1900
○ Energy of a single photon
○ Probability of having n photons with frequency ν : Inspired by the exponential distribution in Maxwell-Boltzmann Distribution
○ Average energy of the system
○ Average radiant energy per unit volume at frequency ν
○ Planck’s Curve : Distribution of radiant energy emitted by a blackbody based on wavelength. Blackbody’s radiant energy distribution depends only on temperature
Figure. 1. Planck’s Curve
○ Total energy per unit volume of the system
○ Flux of photons
⑥ Stefan-Boltzmann Law : The energy radiated per unit area per unit time from a blackbody is proportional to the fourth power of the blackbody’s absolute temperature T(K)
○ Often modified for real objects by introducing the emissivity ε in the equation
○ Where σ : Stefan-Boltzmann constant, 8.22 × 10^-11
⑦ Wien’s Displacement Law : The wavelength λmax (μm) at which the maximum radiant energy is emitted is inversely proportional to the absolute temperature T(K) of a blackbody
○ Where α : Wien’s constant, 2.89 × 10^3
⑧ Pauli Exclusion Principle
○ Definition : No two or more identical electrons can exist in the same quantum state on a single orbit
○ Reason for the continuous graph of the Planck’s Curve
○ Many atoms gather, and energy levels overlap slightly, leading to a continuous appearance of energy levels as they
slightly shift
Figure. 2. Splitting of Energy Levels Due to Orbital Overlap
Figure. 3. Formation of Energy Bands Due to Orbital Overlap
⑵ Solar Radiation
① Solar radiation curve is similar to the radiation curve of a 5,800 K blackbody
② Solar maximum radiation wavelength : 0.47 μm - visible light (shortwave radiation)
③ 95% of the total solar radiation energy is distributed in the wavelength range of 0.25 ~ 2.5 μm
○ Visible light : Wavelength 0.4 ~ 0.7 μm, about 45% of solar radiation energy
○ Ultraviolet light : Wavelength 0.15 ~ 0.4 μm, about 9% of solar radiation energy
○ Infrared light : Wavelength 0.7 ~ 4.0 μm, about 46% of solar radiation energy
④ Scattering of Solar Radiation
○ Classification 1. Elastic Scattering : No change in energy during scattering, incident and scattered wavelengths are the same
○ Rayleigh Scattering
○ When the wavelength is much larger than the size of particles
○ Scattering becomes stronger as the wavelength gets shorter
○ Reason why the sky appears blue
○ Mie Scattering : When the wavelength is similar to the size of particles
○ Classification 2. Inelastic Scattering : Energy change occurs during scattering, incident and scattered wavelengths are different
○ Also known as Raman Scattering
○ If a substance gains energy, it is called Stokes Scattering
○ If a substance loses energy, it is called anti-Stokes Scattering
⑶ Terrestrial Radiation
① Terrestrial radiation = Surface radiation + Atmospheric radiation
② Average temperature of the Earth’s surface is 288 K (15 ℃)
③ Maximum terrestrial radiation wavelength : 10 μm - infrared region (longwave radiation)
④ 95% of total terrestrial radiation energy is distributed in the wavelength range of 2.5 ~ 25 μm
3. Earth’s Heat Budget
⑴ Absorption by the Atmosphere
① X-rays, gamma rays → Absorbed by atoms in the upper atmosphere
○ Wavelengths below 0.2 μm : Oxygen, nitrogen molecules absorb
○ Wavelengths of 0.24 ~ 0.30 μm : Ozone absorbs
○ Wavelengths of 5 ~ 10 μm : Water vapor absorbs
○ Wavelengths of 10 ~ 20 μm : Carbon dioxide absorbs
○ Wavelengths longer than 20 cm → Absorbed in the ionosphere
② Electromagnetic Waves that pass through the atmosphere
○ Solar radiation energy
○ Visible light (0.3 ~ 1.2 μm) : Optical window
○ Radio waves (1 mm ~ 20 m) : Radio window
○ Terrestrial radiation energy
○ Infrared radiation (8 ~ 13 μm) : Infrared window (atmospheric window)
③ Greenhouse Effect
○ Greenhouse gases : Water vapor, carbon dioxide, methane, freon gases, etc.
○ Greenhouse effect : Effect of warming the atmosphere near the Earth’s surface
○ Principle 1. Greenhouse gases do not absorb much of the Sun’s shortwave radiation
○ Principle 2. Greenhouse gases absorb most of Earth’s longwave radiation
Figure. 4. Earth’s Energy Balance
⑵ Earth’s Thermal Equilibrium
① Earth’s Radiative Equilibrium
○ Definition : State where Earth’s temperature is maintained at a constant level
○ Reason : Over long periods, the amount of incoming solar radiation and outgoing terrestrial radiation achieve a nearly equal balance
○ Also known as heat balance or radiative equilibrium
② Albedo
○ Definition : Energy reflected or scattered back to space by the Earth’s surface, clouds, dust, or air particles from the Sun’s radiation
○ Reflectivity : Depends on the angle of incidence when light strikes the object
○ If the angle of incidence is less than 60 degrees, 96% of the incident light passes through the object
○ Earth has an average albedo of 31%, while the Moon has 12%
○ Desert ＞ Forest ＞ Ocean in terms of albedo
③ Heat Energy Budget
○ Solar Insolation (100%) = Surface Absorption (50%) + Atmospheric Absorption (20%) + Earth’s Reflection (30%)
○ Solar insolation : 0.5 cal / cm^2 · min
○ Surface absorption : 0.25 cal / cm^2 · min, re-emitted into space
○ Atmospheric absorption : 0.1 cal / cm^2 · min, re-emitted into space
○ Earth’s reflection : 0.15 cal / cm^2 · min
⑶ Thermal Budget and Heat Transport by Latitude
① Thermal Budget by Latitude
○ Low Latitude : Incoming energy > Outgoing energy → Energy surplus
○ Mid Latitude : Incoming energy ≒ Outgoing energy → Energy equilibrium
○ High Latitude : Incoming energy < Outgoing energy → Energy deficit
② Heat Transport
○ Equatorial ocean circulation to Mid Latitude
○ Mid-latitude atmospheric circulation to High Latitude
○ Results in maintaining radiative equilibrium by latitude
4. Internal Energy of the Earth
⑴ Geothermal Gradient : 3 ℃ / 100 m, geothermal gradient decreases as depth increases
⑵ Radioactive Decay Heat
① Granite (constitutes continental crust) ＞ Basalt (constitutes oceanic crust) ＞ Gabbro (constitutes mantle)
⑶ Geothermal Flux
① The amount of heat energy emitted from the Earth’s interior to the surface per unit area and per unit time.
○ Influenced by radioactive decay and volcanic activity
○ Global average value : 1.5 HFU = 1.5 × 10^-6 cal / cm^2 · s
② Continental Geothermal Flux : Mainly due to the decay heat of radioactive isotopes in granite
③ Oceanic Geothermal Flux : Heat transferred from the Earth’s interior and released
○ Ridge crest ＞ Oceanic trench ＞ Seamounts
○ Submarine ridges, seamounts, island arcs, and volcanic arcs show high geothermal flux
○ Submarine trenches, abyssal plains, and stable continental regions show low geothermal flux
Input : 2016.06.22 20:54
Modified : 2022.09.12 19:34