1 the Earth's Energy Budget and Climate Change

1 1 The Earth’s Energy Budget and Climate Change 1.1 Introduction The scattering and absorption of sunlight and the absorption and emission of infrared radiation by the atmosphere, land, and ocean determine the Earth’s climate. In studies of the Earth’s atmosphere, the term solar radiation is often used to identify the light from the sun that illuminates the Earth. Most of this radiation occupies wavelengths between 0.2 and 5 μm. Throughout this book the terms “sunlight, solar radiation, and shortwave radiation” are used interchangeably. Light perceivable by the human eye, visible light, occupies wavelengths between 0.4 and 0.7 μm, a small portion of the incident sunlight. Similar to the terminology used for solar radiation, throughout this book the terms “emitted radiation, terrestrial radiation, thermal radiation, infrared radiation, and long- wave radiation” are used interchangeably for thermal radiation associated with terrestrial emission by the Earth’s surface and atmosphere. Most of the emission occupies wavelengths between 4 and 100 μm. Sunlight heats the Earth. Annually averaged, the rate at which the Earth absorbs sunlight approximately balances the rate at which the Earth emits infrared radiation to space. This balance sets the Earth’s global average temperature. Most of the incident sunlight falling on the Earth is transmitted by the atmosphere to the surface where a major fraction of the transmitted light is absorbed. Annually averaged, the surface maintains its global average temperature by balancing the rates at which it absorbs radiation and loses energy to the atmosphere. Most of the loss is due to the emission of infrared radiation by the surface. Unlike its relative transparency to sunlight, the atmosphere absorbs most of the infrared radiation emitted by the surface. The atmosphere in turn maintains its average vertical temperature profile through the balance of radiation absorbed; the release of latent heat as water vapor condenses, freezes, and falls as precipitation; the turbulent transfer of energy from the surface; and the radiation emitted by clouds and by the greenhouse gases, gases that absorb infrared radiation. This chapter begins with the global annually averaged balance between the sunlight absorbed by the Earth and the infrared radiation emitted to space. A simple radiative equilibrium model for the Earth renders a global average Atmospheric Radiation: A Primer with Illustrative Solution, First Edition. JamesA.CoakleyJrandPingYang. © 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA. 2 1 The Earth’s Energy Budget and Climate Change temperature that is well below freezing, even if the Earth absorbed substantially more sunlight than it currently absorbs. The Earth’s atmosphere is modeled as one that allows sunlight to pass through but blocks the infrared radiation that is emitted by the surface. This simple model produces the Earth’s greenhouse effect leading to a warm, habitable surface temperature. The model provides an estimate of the radiative response time for the Earth’s atmosphere, about a month. The month-long response time explains the atmosphere’s relative lack of response to the day–night variation in sunlight and also its sizable response to seasonal shifts as the Earth orbits the sun. The model also leads to estimates of changes in the average temperature caused by changes in the incident sunlight and in atmospheric composition, such as the buildup of carbon dioxide in the atmosphere from the burning of fossil fuels. Some of the change in temperature is due to feedbacks in the atmosphere and surface that alter the amounts of sunlight absorbed and radiation emitted as the Earth’s temperature changes. This chapter then describes more realistic models for the Earth’s atmosphere considered as a column of air with a composition close to the global average composition. It describes how forcing the atmosphere to be in radiative equilibrium leads to turbulent heat exchange between the atmosphere and the surface. The combination of radiation and the exchange with the surface largely explains the vertical struc- ture of the Earth’s global average temperature. In addition, the chapter describes realistic estimates for the various sources of heating and cooling for the surface and the atmosphere and the roles played by clouds and the major radiatively active gases. The chapter ends by noting that the distribution of the incident sunlight with latitude leads to the complex circulations of the atmosphere and oceans. The winds associated with the atmospheric circulation and the accompanying pattern of precipitation and evaporation contribute to the circulation of the oceans. The winds and ocean currents carry energy from the tropics to high latitudes. This transfer of energy moderates the temperatures of both regions. 1.2 Radiative Heating of the Atmosphere The first law of thermodynamics states that energy is conserved. According to this law, an incremental change in the internal energy of a small volume of the atmosphere dU is equal to the heat added dQ minus the work done by the air dW. dU = dQ − dW (1.1) Air behaves similarly to an ideal gas. For an ideal gas the internal energy is pro- portional to the absolute temperature. An incremental change in internal energy is given by dU = mCV dT with m the mass of air undergoing change and CV the heat capacity of air held at a constant volume. Of course, the atmosphere is free to expand and contract. It is not confined to a volume. Held at constant pressure, air will expand if its temperature rises. The work done by the air is PdV with P the pressure of the air and dV the incremental change in its volume. Combining the 1.3 Global Energy Budget 3 equation of state for an ideal gas PV = mRT with the conservation of energy gives mRT mC dT = dQ + dP (1.2) p P −1 −1 with Cp = 1005 J kg K being the heat capacity of air held at constant pressure, −1 −1 CP = CV + R,andR = 287 J kg K the gas constant for dry air. Throughout this book, the small changes sometimes applied to the temperature in order to account for the effects of water vapor on the heat capacity and gas constant will be ignored. For a small increment in time, dt, dT dQ mRT dP mC = + (1.3) p dt dt P dt with dT∕dt often referred to as the heating rate and often expressed in units of Kelvin per day, dQ∕dt being the rate at which energy is being added or removed from the air (J s−1 or W), and dP∕dt the rate at which the pressure of the air is changing. The pressure changes give rise to motion. Air responds to heating by changing its temperature and moving. Most of the radiative heating in the atmosphere goes to changing the thermodynamic state, such as the temperature changes experienced in high latitudes in response to changes in solar heating as the Earth orbits the sun. There are, however, some instances in which the radiative heating nearly balances the dynamical response. The rate of downward motion referred to as subsidence approximately matches the radiative cooling in the troposphere of subtropical high pressure systems. For annual mean, global average conditions, there is no net movement of air, dP∕dt = 0. Consequently, dT dQ mC = (1.4) p dt dt 1.3 Global Energy Budget Annually averaged, the Earth approximately maintains a state of radiative equilibrium. Under such conditions, the annually averaged, global mean temperature remains constant with time. For radiative equilibrium, the rate at which the Earth absorbs sunlight equals the rate at which the Earth emits radiation. −2 Let Q0 be the solar constant in units of power per unit area (W m ), the sunlight reaching the “top” of the Earth’s atmosphere at the average distance between the Earth and the sun, one astronomical unit (AU). There is, of course, no “top” of the atmosphere. Instead, the top represents the surface of an imaginary sphere that contains the Earth and most of the atmosphere. Here, the sphere contains the atmosphere that absorbs or reflects a major fraction of the incident sunlight and also absorbs and emits a major fraction of the infrared radiation. A sphere with a radius that extends to 30 km above the Earth’s surface serves as an imaginary “top.” Such a sphere contains 99% of the Earth’s atmosphere. The solar constant has been measured with high accuracy (∼0.1%) from satellites. The measured values range roughly from 1360 to 1370Wm−2.The 4 1 The Earth’s Energy Budget and Climate Change Fraction of sunlight reflected α, albedo θ 0 Incident sunlight Q –2 0 = 1360 Wm Radiation Area blocked πR 24× σT emitted = 4 E e πR 2 = E Radiative equilibrium Sunlight absorbed = Radiation emitted Q α × πR 2 πR 24× σT 0(1 – ) E = 4 E e Q 0 (1 – α) = σT 4 4 e Figure 1.1 Radiative equilibrium for the absorbed sunlight is balanced by the emit- Earth. The rays from the sun are parallel as ted infrared radiation. The Earth rotates they strike the Earth. To a distant viewer sufficiently rapidly that its radiative equi- in space, the Earth casts a shadow as if it librium temperature, Te, is assumed to be were a circle having a radius equal to that the same for both day and night sides. The of the Earth. The Earth reflects a fraction angle between the incident sunlight and of the sunlight that is blocked and absorbs thenormaloftheEarth’ssurfacewherethe the remainder. In radiative equilibrium, the sunlight strikes is the solar zenith angle 0. most recent measurements [1] are thought to provide the most accurate value, 1361 W m−2.

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