Chapter 21 Copyright © 2011, 2015 by Roland Stull. Meteorology for Scientists and Engineers, 3rd Ed. Natural Climate proCesses CoNteNts Earth’s average surface temperature has been surprisingly steady over mil- Radiative Equilibrium 793 lennia. Factors that control the tem- Greenhouse Effect 795 21 perature are solar output, Earth orbital characteris- Atmospheric Window 796 tics, ocean currents, atmospheric circulations, plate Average Energy Budget 797 tectonics, volcanoes, clouds, ice caps, gas emissions, Astronomical Influences 797 particulates, aerosols, and life. Milankovitch Theory 797 Some of these factors tend to reduce climate Solar Output 803 change, and are classified as negative feedbacks. Tectonic Influences 804 Others amplify change, and are positive feedbacks. Continent Movement 804 The steadiness of Earth’s surface temperature sug- Volcanism 804 gests that negative feedbacks dominate. Feedbacks 806 Idealized models of climate processes are pre- Concept 806 sented next. These “toy models” are oversimplifi- Idealized Example 807 cations of nature, yet they serve to illustrate funda- Infrared Radiative (IR) Feedback 810 mental climatic controls and responses. Water-vapor Feedback 810 Lapse-rate Feedback 810 Cloud Feedback 811 Ice–albedo (Surface) Feedback 811 Ocean CO2 Feedback 812 radiative equilibrium Biological CO2 Feedback 812 Daisyworld 813 The Earth is heated by shortwave radiation from Physics 813 the sun, and is cooled by longwave (infrared, IR) ra- Equilibrium and Homeostasis 815 diation to space (Fig. 21.1). Geological records show GCMs 815 that the Earth’s surface has had nearly constant Present Climate 816 annual-average temperature (less than 4% change Definition 816 of absolute temperature over the past 100 million Köppen Climate Classification 817 years), suggesting a balance between radiation in- Natural Oscillations 818 flow and outflow. El Niño - Southern Oscillation (ENSO) 818 Incoming minus reflected sunlight, times the Pacific Decadal Oscillation (PDO) 820 interception area, gives the total radiative input to North Atlantic Oscillation (NAO) 824 Earth: Arctic Oscillation (AO) 824 2 Madden-Julian Oscillation (MJO) 824 Radiation In=()1 − A ··SRoπ· Earth •(21.1) Other Oscillations 824 where A = 0.30 is global albedo (see Focus Box), Summary 825 –2 Threads 826 So = 1366 W·m is the annual average total solar irradiance (TSI) over all wavelengths as measured Exercises 826 Numerical Problems 826 Understanding & Critical Evaluation 828 Web-Enhanced Questions 831 *3 Synthesis Questions 832 4VOMJHIU &BSUI “Meteorology for Scientists and Engineers, 3rd Edi- tion” by Roland Stull is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. To view a copy of the license, visit Figure 21.1 http://creativecommons.org/licenses/by-nc-sa/4.0/ . This work is Solar input (white arrows) and infrared output (dark arrows) available at http://www.eos.ubc.ca/books/Practical_Meteorology/ . from Earth. 793 794 chapter 21 NATURAL CLIMATE PROCESSES by satellites, and R is the Earth radius. The area FoCUS • albedo Earth of a disk πR2 rather than the surface area of a sphere The average global reflectivity (portion of incom- 4πR2 is used because the area of intercepted solar ing sunlight that is reflected back to space) for Earth radiation is equivalent to the area of the shadow cast is called the albedo, A. But the exact value of A is dif- behind the Earth. The TSI has fluctuated about ±0.5 ficult to measure, due to natural variability of cloud W·m–2 (the thickness of the dashed line in Fig. 21.2) and snow cover, and due to calibration errors in the during the past 33 years due to the average sunspot satellite radiation sensors. cycle. See the Radiation chapter for TSI details. Trenberth, Fasullo & Kiehl (2009, Bul. Amer. Me- teor. Soc.) report a range of values of 27.9% ≤ A ≤ 34.2%. Assume the Earth is a black body in the infrared, They suggest A = 29.8%. We use A ≈ 30% here. and that it emits IR radiation from its whole surface area (continents and oceans). Multiplying the Ste- fan-Boltzmann law (eq. 2.15), which gives the emis- 3P 8N sions per unit area, times surface area of the Earth (assumed spherical here) gives: m 2 4 •(21.2) P Radiation Out =4 π··RTEarthσ SB· e P TMPQFS 3 –8 –2 –4 8pN where σSB = 5.67x10 W·m ·K is the Stefan- 5F , Boltzmann constant, and Te is the effective radia- , F SFGFSFODFTUBUF 5 tion emission temperature. The real Earth is quite heterogeneous, with oceans, continents, forests, clouds and ice caps of dif- m fering temperatures. Each of these regions emits dif- ferent amounts of radiation. Also, some radiation is P 4 emitted from the Earth’s surface, some from various 8pN heights in the atmosphere, and some from clouds. The effective radiation temperature is defined so that the total emissions from the actual Earth-ocean- atmosphere system equal the theoretical emissions 4 8N P from a uniform Earth of temperature Te. Figure 21.2 For a steady-state climate (i.e., no temperature Thick curved line shows the variation of Earth effective radiation change with time), outputs must balance the inputs. temperature Te with solar irradiance So , assuming an albedo of A = 0.30 . Dashed lines show present conditions, which will Thus, equate outgoing and incoming radiation from eqs. (21.1 and 21.2), and then solve for T : be used as a reference point or reference state (Ro*, Te*). Thin e black straight line shows the slope ro of the curve at the reference 1/ 4 1/ 4 point. R = (1–A)·S /4 is net solar input for each square meter ()1 − AS· R o o T = o = o of the Earth’s surface (see Focus Box, next page). e •(21.3) 4·σSB σSB ≈ 254.8 K ≈ – 18°C Solved Example Find the radiative equilibrium temperature of the Earth-atmosphere system. where Ro = (1–A)·So/4. Fig. 21.2 shows this reference state and shows how the effective temperature var- Solution: ies with total solar irradiance, assuming constant –2 albedo. This effective temperature is too cold com- Given: So = 1366 W·m solar irradiance A = 0.30 global albedo (reflectivity) pared to the observed surface temperature of 15°C. Find: Te = ? K radiative equilibrium temp. Hence, this simple model must be missing some im- portant physics. Use eq. (21.3): This radiation balance is a negative feedback. −2 1/ 4 (.1− 0 3)·(·1366 W m ) Namely, increases of incoming solar radiation are Te = −8 − 2 −4 4·( 5.67 × 10 W· m ·K ) mostly compensated by increases in outgoing IR, yielding only small temperature changes. = 254.8 K ≈ 255 K = – 18°C Because the radiative feedback dominates over all others, the Earth’s climate is relatively stable, Check: Units OK. Physics OK. as geological records demonstrate (Fig. 21.3). Fifty Discussion: The effective radiation temperature does not depend on the radius of the planet. million years ago, the average surface temperature R. STULL • METEOROLOGy FOR SCIENTISTS AND ENGINEERS 795 was about 6°C warmer than now. During the past ten thousand years, the climate has oscillated about *DF ±1°C about the recent 15°C average. Although these "HF temperature changes are small (range of ∆T is of $ZDMFT order 10°C) relative to the Earth’s absolute tempera- ^ å5 $ ture, they can cause dramatic changes in sea level and glaciation. m m m m m m m m m Greenhouse effect m m m m m You can increase the sophistication of the previ- 5JNF .ZS 5JNF LZS ous model by adding a layer of atmosphere (see Fig. Figure 21.3 21.4) that is opaque to infrared radiation, but trans- Paleotemperature estimate (smoothed) as a difference ∆T from parent to visible. Sunlight heats the Earth’s surface. the 1961 to 1990 temperature average. Time is relative to cal- Radiation from the surface heats the opaque atmo- endar year 2000. Scale breaks at the dotted and dashed lines. sphere. Radiation from the top of the atmosphere is Glacial/interglacial oscillations (i.e., ice-age cycles) prior to lost to space, while radiation from the bottom of the 500,000 yr ago have been smoothed out. atmosphere heats the Earth. The incoming radiation from the sun must bal- PTQIFSF ance the outgoing radiation from the atmosphere, in BUN order for the Earth-atmosphere system to remain in 4Pp m" 3P p5 radiative equilibrium. Hence T T T = T = 255 K = –18°C (21.4) A e 5 5" T as before, where Te is the effective emission tempera- ture of the whole Earth-atmosphere system, and T &BSUI A Tp5" Tp5" is the temperature of the atmosphere. For this case, the two temperatures are equal, because the atmo- sphere is opaque. Other energy balances can be made for the atmo- sphere separately, and for the Earth’s surface sepa- rately, with output from one system being the input Figure 21.4 to the other. The opaque atmosphere is assumed Greenhouse effect with an to emit as much IR radiation upward to space, as idealized one-layer atmosphere. Distance between Earth and downward toward the Earth. The amount emitted atmosphere is exaggerated. Assume that the radius of the Earth both up and down from the atmosphere is given by approximately equals the radius at the top of the atmosphere. Ro 4 is the net solar input, and σ is the Stefan-Boltzmann constant. the Stefan-Boltzmann law as σSB·TA . Incoming IR 4 radiation from the Earth’s surface is σSB·Ts , where Ts is the Earth-surface temperature. If the atmosphere FoCUS • Why does ro = (1–a)·so / 4 ? is at steady state, then absorbed IR equals emitted IR: In Figs. 21.4 and 21.5, the net solar input Ro is 4 4 given as (1–A)·S /4 instead of S .