Lecture 2 Slide Show .pdf

Earth System Dynamics: Energy Balance OCN 310 August 30 2024 Quick review Formation of the solar system and Earth (~14.5 bya) included sun at the center, “heavy” planets in near-orbit, gas giants farther away Earth cools, chemical differentiation occurs, water from out-g...

Earth System Dynamics: Energy Balance OCN 310 August 30 2024 Quick review Formation of the solar system and Earth (~14.5 bya) included sun at the center, “heavy” planets in near-orbit, gas giants farther away Earth cools, chemical differentiation occurs, water from out-gassing and comets Atmosphere progresses in three stages to be what it is today (chemical composition-wise) Most recent transition was from “snowball Earth”, about 750-500 mya to now; tectonics, volcanoes, greenhouse gases, photosynthesis play roles in getting out of frozen Earth  Past temperature records and proxies show variations on several different time-scales What is causing the “mean state” or “equilibrium?” Outline It’s all about balance First some background (temperature, waves, energy) Incoming energy à solar constant Outgoing energy à black body Frequency dependence What does it all mean Earth’s Energy Balance Earth’s climate, or temperature, has been relatively stable for recent geological time Represents a balance: Energy in = Energy out How to we define these, i.e., what is Energy in? Energy out? Total incoming energy The Sun is a huge nuclear fusion reactor producing energy. The amount received depends on distance; the Earth is about 150 million km from the Sun, and at this distance solar flux is relatively small. The energy intercepted by the Earth over a period of one year is equal to the energy emitted by the Sun in just 14 milliseconds. To put it another way, solar energy captured by the Earth over a period of 1000 years is equal to the energy produced by the Sun in just only 14 seconds. Important concepts Climate change is fundamentally based on energy balance (temperature). Energy (light/radiation) travels in waves. Waves  Waves Amplitude: distance from peak/trough to mean (vs height) Wavelength: distance from peak to peak Frequency: number of peaks passing a fixed point in a certain time Period: time for successive peaks to pass a fixed point Speed: wavelength/period More terms… Force = mass x acceleration Energy = force x distance aka “work”, aka “heat” Units are “Joules” Power = energy / time Units are Watts (= joules/second) The energy of a unit “parcel” of light (aka a photon) is given by: hc E = hf = λ Where h is Planck’s constant and equals 6.63 x 10-34 J sec, f is frequency and lambda is wavelength; c is the speed of light (3 x 108 m/s) What this equation means: Long wavelength = low frequency = low energy Short wavelength = high frequency = high energy  Energy travels in waves, frequency makes a difference: lower frequency (longer wavelength) = lower energy Energy from the Sun Electromagnetic radiation is emitted from the sun via spherical waves. These waves (spheres) expand as you move farther from the Sun, so Solar flux decreases with increasing distance from the Sun The inverse square law: The flux of (solar) energy decreases as the inverse square of the distance (from the sun). Total Solar Irradiance (TSI) Total solar irradiance (TSI) is the amount of power, on average, that strikes the outermost atmosphere of the Earth. 1,366 W/m2 TSI depends only on the total energy per second produced by the Sun (its absolute luminosity) and the distance from the Sun to the Earth, 93 million miles or 150 million kilometers. Solar radiation impacting the Earth’s surface The total solar radiation intercepted by the Earth is the Solar Constant multiplied by the cross section area of the Earth. If we now divide the calculated number by the surface area of the Earth, we obtain the average solar radiation S per square meter of the Earth’s surface: 2 Sπ r 2 2 = 342W / m 4π r Summing it up Amount of energy reaching the Earth (atmosphere) from the Sun is about 342 Watts/m2 This is a function of: The amount of energy produced by the sun, The distance between the Earth and sun, and The surface area of the Earth Energy Balance: outgoing All things with a temperature emit what is called “blackbody radiation” The Earth surface and atmosphere lose heat via blackbody radiation based on their temperature Blackbody Radiation Things emit radiation based on their temperature according to the Stefan-Boltzmann equation (law): Q = sT4 Where, s is the Stefan-Boltzmann constant (5.67 x 10-8 W/m2/K4) and T is temperature (in oK) NOTE: hot bodies emit much more energy than cold Earth’s Energy Balance Incoming from the Sun minus reflection Outgoing from blackbody radiation Difference? à wavelength: incoming shortwave, outgoing longwave Bringing it all together Wait a sec.. Earth radiative balance: Incoming heat = Outgoing heat shortwave from sun = longwave blackbody 4 Qi = σT 342 o o 4 = T = 279 K = 5 C σ Reflection Quantity called “albedo”, essentially the ratio of reflected radiation to incoming radiation Highly reflective surfaces have very high albedo Examples: Snow 0.80 – 0.95 Thick cloud 0.70 – 0.80 Grass/sand 0.25 – 0.30 Forest 0.10 – 0.20 Asphalt 0.05 – 0.10 But still.. Earth radiative balance: Incoming heat = Outgoing heat shortwave from sun = longwave blackbody 4 Qs (1− α ) = σ T 342(1− 0.3) o 4 = T = −18 C σ Energy Balance: incoming About 342 W/m2 is entering the top of the atmosphere: 69% absorbed (mostly by land) 31% reflected back to space (mostly by atmosphere)  Energy travels in waves, frequency makes a difference: lower frequency (longer wavelength) = lower energy Energy as function of wavelength (frequency)  IPCC 5th Assessment Report Figure 1 Radiative balance between incoming solar shortwave radiation (SWR) and outgoing longwave radiation (OLR) What does it all mean?  Dinosaur extinction (~66,000,000 years ago) Human migration out of Africa (~120,000 years ago) What’s next? Natural variability: yes, things are changing, but how much is “natural” and how much is anthropogenic?