3. Radiation Components and Atmospheric Attenuation a. Direct i. scattering and turbidity b. Diffuse i. standard and uniform overcast skies

Transcription

1 Lecture 7, Solar Radiation, Part 1, Principles Instructor: Dennis Baldocchi Professor of Biometeorology Ecosystem Science Division Department of Environmental Science, Policy and Management 345 Hilgard Hall University of California, Berkeley Berkeley, CA September 16, 2004 This set of Lectures will discuss A. Solar Radiation 1. Solar Constant 2. Spectral Composition of Sunlight a. Planck s Law b. Wien s Law c. absorption, reflection and transmission d. uv,par, NIR, IR 3. Radiation Components and Atmospheric Attenuation a. Direct i. scattering and turbidity b. Diffuse i. standard and uniform overcast skies B. Terrestrial Radiation 1. Long wave radiation: Stefan-Boltzmann Law 2. Kirchoff s Law 3. Spectral Distribution 4. Emissivity C. Net Radiation Balance L7.1 Introduction The sun is the source of energy that drives the cycle of life and death on earth. It is also the energy source that gives us warmth and evaporates water and melts snow. Obviously, no course on biometeorology could proceed without a thorough discussion of solar radiation. The sun is our nearest star. It is about 150,000,000 km away from the Earth. Due to its immense, but finite size, it has an angular diameter of 0.5 degree (32 minutes), as viewed 1

2 from Earth. The Sun burns continuously via thermonuclear reactions (fusion). Inside the sun, radiative processes transfer this energy from 0.3 to 0.7 radii. Convection transfers solar energy to its exterior surface. Despite the extremely high temperatures needed at the core of the sun, to sustain its thermonuclear reactions, the sun has a black body temperature of 5770 K. Consequently, we receive a relatively constant flux density of energy, defined as the Solar Constant. Its mean value is 1366 W m -2 +/- 3. Table 1 Solar Properties (after Lean, 1997, the sun course ( Property Value Age years Magnitude 4.8 Mass kg Radius 696,000 km Mean Distance from Earth (1 AU) m (8 light minutes) Surface Gravity 274 m s -2 Effective Temperature 5785 K 1 arc second 726 km Luminosity W Solar constant, viewed from Earth 1366+/- 3 W m -2 The sun emits a spectrum of electromagnetic radiation. Electromagnetic Radiation consists of discrete packets of photons. Radiation is an electromagnetic mechanism that allows energy to be transported, at the speed of light, through regions of space devoid of matter. Radiation is the 3 rd manner by which energy is transferred, convection and conduction being the other means. Radiant energy transfer is not dependent upon contact between the source and sink, as are conduction and convection. Consequently, radiative transfer is much different for the other forms of mass, heat and momentum transfer, that we deal with and are proportional to driving gradients. Electromagnetic radiation moves at the speed of light, c, m s -1, in a vacuum, with wave-like motion. The speed of light is proportional to the product of the wavelength of the radiation (λ) and the frequency at which it oscillates (ν), λν = c. Radiation has origins in the absorption and release of energy by electrons. Molecules possess energy in the form of kinetic energy and electrostatic potential energy due to the orbiting of electrons around the nucleus. Molecules also possess rotational and vibrational energy. According to quantum mechanics theory, unique electron configurations occur around each nucleus. The energy level is due to the orbit, and the vibration and rotation of the electrons. A molecule will transfer to a higher energy level by absorbing electromagnetic radiation. Electromagnetic radiation is emitted when electrons drop an energy level. The radiation energy emitted is in discrete packets, called photons. A spectrum of radiation is emitted because the excitation of electrons differs 2

3 when they are associated with rotational, vibration and electronic states of the molecules and atoms. L7.2 Solar Radiation and Its Spectrum The Sun emits a nearly continuous spectrum of energy, ranging from very short wave and high energy packets of quanta, to low energy and long wave lengths. Table 7.1 lists the various wave bands that are intercepted by Earth and their sources S(λ) (W m -2 µm -1 ) λ (µm) Figure 1 Electromagnetic spectrum of sunlight above and below the atmosphere (Web page for radiation calculations 3

4 Table 2 Various spectral wavebands have different sources of origin Name waveband Mechanism Radio waves Mm to km Electrical conductor carrying alternating energy Far infrared 2.7 to 100 micron Molecular rotation Near infrared micron Molecular vibration Visible 0.4 to 0.7 micron Displacement of outer electrons of an atom Ultraviolet Sub micron Displacement of outer electrons of an atom Xrays Displacement of inner electrons of an atom Gamma rays Angstroms Displacement of nucleons in an atomic nucleus On earth, there are 4 wavebands of electromagnetic radiation that are of particular interest. These are the ultraviolet, photosynthetically active, near infrared and infrared bands (see Ross, 1980). 1) Ultraviolet (0.29 to 0.38 µm). This band possess high energy. It can damage molecular bonds. Its presences leads to the photochemical formation of ozone in the troposphere. It has a moderate impact on photomorphogenesis. Its flux density is relatively low since most ozone is absorbed in the stratosphere. Therefore, about zero to 4% of incoming solar radiation is in this band. 2) Photosynthetic Active band (PAR), also know as photosynthetic photon flux density (PPFD) (0.38 to 0.71 µm) This band is the visible band. It contains visible energy across the primary colors of purple, blue, green, yellow, orange, red. It provides the energy for photosynthesis. Between 21 and 46 per cent of solar radiation is in this band. Table 3 color and waveband, nm Color Waveband violet Blue Cyan Green Yellow Orange Red ) Near Infrared band (NIR) (0.71 to 4.0 µm). This wave band is not visible, but contributes to the heat budget of organisms. 4

5 4) Long wave or terrestrial radiation (3.0 to 100 µm). This is the radiation emitted by bodies on earth. Its flux density is a function of the surfaces temperature and emissitivity. Table 4 Distribution of Solar energy by Waveband (Monteith and Unsworth) Waveband Energy % , ultra-violet , visible/par , near 38.8 infrared 1500 to infinity 12.4 The spectral quality of light incident to the ground is affected by selected absorption by water vapor gases and aerosols. Water vapor is a strong absorber of light with wavelengths of 100, 1400, 1600 and 1900 nm. Ozone absorbs ultraviolet light (λ < 300 nm), CO2 absorbs strongly in the 2750 and 4250 nm bands and oxygen absorbs 690 and 760 nm sunlight (Bonhomme, 1995). The spectral quality of sunlight varies with the direct/diffuse fraction of sunlight and the solar elevation angle. Ross (1976) provides a algorithm for the conversion factor between PAR and R g as a function of the direct beam and diffuse components (this algorithm is for daily integrated fluxes of solar energy): f par: R g Rbeam / R = 1+ R / R beam diffuse diffuse On a clear day with 10% diffuse radiation, f par:rg is On a cloudy day with 90% diffuse radiation, f par:rg is On an hourly basis, the PAR:Rg ratio, for direct radiation, ranges from 0.2 to 0.43 as solar elevation goes from 0 to 40 degrees. It then remains relatively constant with higher elevation angles. For diffuse radiation, this ratio ranges from about 0.6 to As a quick rule of thumb, the PAR:Rg, for total radiation, is rather conservative, being on the order of 0.46 to 0.50 (these computations assume that PAR conversion factor between quanta and energy is 4.6 umol quanta per J). Electromagnic radiation is measured or quantified, interchangeably in terms of quanta or energy. Therefore, certain terminology is used to describe the transfer of this energy to the surface. 5

6 Table 5 Term symbol and unit Description number of photons Mole photons photon flux mole s-1 dq/dt photon flux density mole m -2 s -1 net radiant flux per unit area, normal to the area photon intensity mole s -1 st -1 radiant flux though a solid angle photon radiance mole m -2 s -1 radiant flux pass through a unit area of surface 1 di in the direction of the unit solid angle cosθ da photon irradiance mole m -2 s -1 number of photons incident on a surface per unit area and time Table 6 term symbol and unit Description radiant energy Q (J) Energy radiant flux J s -1 dq/dt radiant flux density J m -2 s -1 net radiant flux per unit area, normal to the area radiant intensity J s -1 st -1 radiant flux though a solid angle radiance J m -2 s -1 radiant flux pass through a unia area of surface 1 di in the direction of the unit solid angle cosθ da irradiance J m -2 s -1 energy incident on a surface per unit area and time da (note: solid angle, dω = r 2 intensity (Watts per steradian) I df = ) d ω The relation between energy and the wavelength or frequency of light, attributed to Planck, is: E = hυ = hc / λ vacuum where h is Planck's constant, J s, 6

7 5.5e e-19 Photon energy (J) 4.5e e e e e-19 4e-7 5e-7 6e-7 7e-7 wave length photoen.spw 7/22/99 Figure 2 spectra of energy with wavelength Mean wavelength of sunlight is about 550 nm. This sunlight has a photon energy of J mol -1. The inverse of this value yields a convenient conversion coefficient between photon flux density and radiant flux density (4.6 µmol J -1 ). L7.2.1 Radiation Laws attributed to Planck s, Stefan-Boltzmann and Wein Planck's Law is one of the most important concepts in modern physics. It has much importance for biometeorology for it gives us information about the spectral emission of energy from the Sun. Planck s Law s defines the amount of energy emitted as a function of the temperature and the wavelength of the source. E( λ,t ) = 2 2πhc 5 hc λ (exp( λkt ) 1) 7

8 k is the Bolzmann constant, J molecule -1 K -1 Mathematical manipulation of Planck s Law yields other useful insights about the transfer of electromagnetic radiation. Integrating Planck s distribution with respect to wavelength, for instance, yields the Stefan-Boltzmann Law, which states that the radiant energy emitted by a surface is proportional to its temperature taken to the fourth power. E( λ, T ) dλ = L = σt 4 (W m -2 ) σ is the Stefan-Bolztmann constant ( W m -2 K -4 ). This equation is especially useful for it helps us gauge the radiative temperatures of the sun. Luminosity equals the solar constant, measured at the Earths surface times the area of a sphere with a radius equal to the distance between the earth and sun. L= S * 4π R L= 1366 x 4 x x ( ) 2 = W Knowing that that radius of the sun is m, we can form a balance between the black body radiation law and the emittance of the sun, to calculate its temperature 2 σt = 2 4πr 26 yields a surface temperature of 5770 K. By examining the sun s or Earth s spectrum we are inclined to ask, what is the wavelength of that radiating source when E is maximal? This question can be answered with Wien s Law. Wien s Law is derived by examining the maximum of a function. This equation is derived by solving for wavelength when the partial derivative of Planck s Law with respect to wavelength equals zero: ET (, λ) = 0 λ The solution yields: 2897 λ max = (µm) T k 8

9 For the case where the sun is about 5700 to 5800 K, the maximum wavelength is 483 nm which falls in the blue-green portion of the spectrum. Climatological records show that the mean earth surface temperature is about 288 K, therefore the earth emits radiation at 10 um, which is in the infrared portion of the electromagnetic spectrum. L7.2.2 Photon Interactions with the Surface When photons, interacting with material, are either absorbed (as with a black surface), reflected (as with a bright white surface) or transmitted (as with the passage of sunlight through glass. Absorptivity: the fraction of incident radiation flux absorbed by a surface Reflectivity: the fraction of incident radiation flux density that is reflected by a surface Transmissivity: the fraction of incident radiation flux density that is transmitted through a surface. Since the absorptivity, reflectivity and transmissivities are fractions of incident sunlight, their sum, with respect to their behavior for a given wavelength, equals one. α( λ) + ρ( λ) + τ( λ) = 1 Because E is not a linear function of wavelength, the average reflectance, absorptance and transmittance must be determined by weighting a surface s reflectance according to the light spectrum, to compute these variables across a broad band portion of the spectrum. ρ α τ =z z ( ) ( ) ρλe λdλ E( λ) dλ α λ E λ dλ = z z ( ) ( ) E( λ) dλ τ λ E λ dλ = z z ( ) ( ) E( λ) dλ The reflectance in the visible portion of the EM spectrum is called albedo. Typical values for common surfaces are listed below 9

10 L7.2.3 Albedo Albedo is not only the name of our dog, but it is defined as the fraction of incident radiation that is reflected by a surface. It is derived from the Latin word albus for white. Figure 3 Albedo I. Albedo is a fundamental parameter used in weather models and models that compute the radiative balance of the Earth s surface. The Earth, as viewed from space, has an albedo of 30%. Figure 4 Picture of Earth from space The albedo of different vegetation surfaces varies widely. Deserts and snow are highly reflective, as seen in Figure 4. By contrast, forests are optically dark. Crops and short vegetation tend to have medium albedos. 10

11 Table 7 List of Reflectances for a range of vegetation and soil types (Campbell and Norman, 1998, Davies and Idso, 1979, Oke, 1987) Surface Reflectivity Grass Wheat Maize Beets 0.18 Potato 0.19 Rain Forest 0.12 Deciduous forest Coniferous forest SubArctic Savanna Steppe 0.20 Fresh snow Old snow Wet dark soil 0.08 Dry dark soil 0.13 Dry sand 0.35 Boreal forest with snow The role of snow and forest landscapes is particularly interesting. The presence of snow in the Boreal zone does not lead to as bright an albedo as was presumed by weather forecasters. 11

12 Figure 5 Snow covered fen and adjacent black spruce forest. Notice the bright fen, as it consists of low level herbaceous vegetation. In contrast the adjacent spruce forest is quite dark, despite the presence of snow. Boreas project Figure 6 James Bay, Canada, MODIS Satellite. Notice the dark spots from the interception of light by the boreal forest, even though the landscape is covered with snow, a larger scale example of the one demonstrated in Figure

13 Figure 7 Dark, low albedo of old age redwood stand, next to clear cuts and forest regrowth. Orick, CA. In this situation, we can observe how albedo decreases with canopy rugosity (see Oygumjimbo and Roberts, 2004 GRL). Figure 8 Brighter landscape of oak savanna, open vegetation with dead and highly reflective grass underneath. In the BOREAS experimental region, the winter background albedo of the forest is on the order of 0.12 to 0.30, while over grass it was Computations of temperature using an 13

14 older version of the European Center Medium Range Weather Forecasting (ECMWF) model predicted temperatures that were up to 10 o C too cold, as they assumed that a forest with snow was highly reflective. When the regional albedo was reset to 0.2 there became good agreement between measured and forecasted temperatures. Life history is another issue affecting albedo. Figure 8 shows the reflectivity of visible light over a grazed grassland when it was green and photosynthesizing and dead and dry. Albedo more than triples, at midday, when the grass changes from being green and dry green grass, D50-60 dead grass D PAR Albedo time (hours) Figure 9 Reflectivity of visible light (photosynthetically active radiation) over a grazed grassland near Ione, CA. L7.2.4 Long wave Emittance Black body radiation is another important concept to grasp. Photons emitted by a energy transition emit photons at a single wavelength. A similar relation holds for photons and energy that are absorbed. When spectral lines merge, as with an infinite combination of absorption and emission lines, the spectra becomes continuous. A black body radiator thereby is defined as a surface that perfect absorbs and emits radiation. In reality, no surface truly exists. But many surfaces are close to being black body radiators for infrared radiation. We can define emissivity, the fraction of black body emittance at a given wavelength by a material. If the surface is a true black body then Kirkoff s Law applies: α( λ ) = ε( λ ) ρλ ( ) = 0 τ( λ) = 0 For a black body surface, absorptivity equals emissivity in the long wave band and they equal one. Reflectance and transmissivity are zero. 14

15 Not all surfaces are perfect black body emitters (ε=1). α( λ) = ε( λ) ρλ ( ) = 1 ελ ( ) τλ ( ) = 0 Substances such as aluminum have low emittance factors. In this situation the Stefan- Boltzmann law is redefined as: LA = εσt 4 Most plants and soils of interest have high emissivities (> 0.9). A list of values is presented in the following Table. Table 8 List of Infrared Emissivities (Campbell and Norman, 1998) Surface Emissivity Plant leaves Glass Aluminum 0.06 Aluminum 0.30 paint Soil Water 0.96 For non-black bodies we can still assume transmission is zero. To calculate reflectivity we use: ρ( λ) = 1 ε( λ) = 1 α( λ) So the infrared reflectivity of water, that has a 0.96 emissivity, is L7.3. Solar Radiation at the Earth s Surface The flux density of solar radiation at the Earth s surface, on a horizontal plane, is comprised of a fraction of direct beam and diffuse radiation Rg = Rbeam + Rdiffuse The beam component is a function of the flux density of the plane normal to the sun s incoming rays and the solar elevation angle: R = R sin β + R g normal diffuse 15

16 a. direct radiation Sunlight incident at the Earth s surface passes through a gas, dust and aerosol filled atmosphere, which can absorb, reflect and scatter sunlight. Radiation reaching the Earth s surface is thereby a function of the depth of the atmosphere and the amount of attenuating particles and gases. Water vapor, ozone and aerosols are the main absorbers of solar radiation. Gas molecules and aerosols scatter light. Measurements of sunlight, orthogonal to the solar beam rarely exceed 75% of the solar constant. Beer s Law is often used to evaluate the attenuation of monochromatic sunlight by the atmosphere R g ( τ, λ) = R ( 0, λ)exp( τ ( λ) m) g R g (0) is the radiation flux density of an aerosol free atmosphere, τ is the turbidity coefficient or optical depth and m is mass of the air, computed as the secant of the solar zenith angle or the reciprocal of the sine of the solar elevation angle (m = 1/sinβ). P m = 101.( 3 kpa )cosθ Photons encounter two types of scattering in the atmosphere Rayleigh scattering and Mie scattering. The type of scattering that occurs relates to the relation between the wavelength of the radiation and the radius of the scattering material, r: s r = 2π λ Rayleigh scattering occurs as photons strike gas molecules in the atmosphere, cases where the s ratio is much less than one. Rayleigh scattering pertains to scattering where the medium is smaller than the lights wavelength. This scattering is proportional to the inverse of the fourth power of the wavelength and is associated with forward and backward scattering. Shorter wavelength radiation, such as blue light is scattered more than longer radiation such as red light. If we examine scattering across the visible portion of the EM spectrum we reveal that 400 nm radiation is scattered 9 times more than 700 nm radiation (700/400) 4. It is Rayleigh scattering that is responsible for the blue color of earth s Atmosphere. The sun s yellow/redness color is observed because blue light is depleted from the sun s beam by the time it reaches our eyes. Dust and aerosols are much bigger than gas molecules (micron) (s values between 0.1 and 50). Mie scattering pertains to these elements and is proportional to the ratio of the molecular diameter and the inverse of the lights wavelength, d/λ. The optical depth is determined by integrating across the depth of the atmosphere the mass absorption (k) and scattering coefficients: 16

17 zz τλ ( ) = ρ( k( λ) + s( λ)) dz 0 In practice, the optical depth is the linear sum of the optical depths for ozone, water vapor, Rayleigh scattering and aerosol Mie scattering: τ( λ) = τ ( λ) + τ ( λ) + τ ( λ) + τ ( λ) o3 ho Rayleigh aerosols 2 Long term and high quality measurements of atmospheric transmission are becoming more important, to assess another aspect of global change. Figure 10 stanhill and cohen, 2001 b. diffuse radiation Diffuse radiation is radiation from the sky, exclusive of the sun. There is a component of diffuse radiation on clear and cloudy days. The amount of diffuse radiation reaching the surface will depend on cloud type, the sun s elevation angle, and the amount of reflected surface radiation that is reflected downward again. The fraction of diffuse light is increasing as more aerosols are loaded in the atmosphere due to pollution or after volcanic eruptions. Stanhill and Cohen (2001) have reported that the transmissivity of the atmosphere is decreasing. They report that the maximum rate of decrease in solar radiation was -1.7 W m -2 per year, or -1.2% per year. The location of this trend was centered around 35 N, a region with high insolation, fossil fuel use and population. 17

18 Figure 11 The spectral composition of diffuse light is altered from that in the sun s direct beam. The mean spectrum of diffuse light in a clear sky is shifted towards shorter wavelengths and has a mean of 450 nm. Under clouds, scattering cause the sky to be grayish. The zonal distribution of sunlight under a clear sky can be described with the uniform overcast sky distribution (Wallace and Hobbs, 1977): The amount of energy available to the hemisphere can be evaluated using solid geometry. First we start with the definition of the solid angle, ω, in terms of the zenith and azimuth angles: dϖ = sin φdφdθ and its integral over the upper hemisphere z z = π/ 2 0 2π sinφdφdθ dθ 2π 0 The flux density of diffuse radiation contributed across the sky is z z 2π π / 2 E = Lcosφsinφdφdθ 0 0 z π / 2 E = 2L Lcosφsinφdφ 0 So for a given sky sector the fractional radiation is: 18

19 Rd ( γ ) R d = 2cosγ sin γ = Γ ( γ) Under cloudy skies the standard overcast sky distribution is used. Rd ( γ ) R d 6 = ( + sin γ)cosγ sin 5 1 γ It shows that the sky near the zenith is 3 times brighter than near the horizon. 1.0 Relative Sky Brightness uniform sky 0.2 standard overcast sky Zenith Angle Figure 12 Calculations of sky brightness for a uniform sky and standard overcast sky L7.4 Terrestrial Radiation According to Kirchoff s law, gases that absorb radiation emit radiation. Gases in the atmosphere that absorb and emit radiation are water vapor, ozone and carbon dioxide. Nitrogen and Argon absorb little if no radiation. Oxygen, though it is considered to absorb no radiation, does disassociate by absorbing ultraviolet radiation to form ozone. 19

20 Figure 13 meted.ucar.edu/satmet/goeschan/ media/graphics/sm5cm92.gif Several empirical functions have been developed to compute downward longwave radiation for cloudless skies (Monteith and Unsworth, 1990). 4 LB = εσ a Ta, K where the longwave flux density and the emissivity are a function of air temperature and humidity, respectively. 20

21 IR incoming (W m -2 ) Tair (C) Figure 14 Measurements of incoming longwave radiation, near Ione, CA. Based on work by Monteith and Unsworth, the emissivity can be estimated as a function of precipitable water in the atmospheric column, p. ε a = a+ b(ln( p) ) Brutsaert recommends an algorithm for clear sky emissivity that is a function of the vapor pressure of the atmosphere ε sky e =172 T a 1 7. ( ) / a where ea is vapor pressure (kpa) and Ta is air temperature (K). On the basis of empirical field data, numerous algorithms exist for estimating downwelling longwave energy flux density. Monteith and Unsworth advocate: 4 LB = σ T a where T is in degrees Kelvin 21

22 With further manipulation we can arrive at the equation: LB = T a where T is in Celsius. Evaluation of these functions show that longwave radiation ranges between about 150 and 450 W m -2 in the temperature range of -10 and 40 C. 500 Downward Longwave Radiation Flux Density (W m -2 ) T k Figure 15 Model computations of Infrard flux density as a function of temperature Other functions are attributed to Swinbank (1963) LB = T 6 a The upward emitted long wave radiation is a function of the surface temperature (to the fourth power) and the downward longwave radiation that is reflected upward. A = s + B 4 L εσt ( 1 ε ) L 22

23 L7.5 Net Radiation Balance The surface energy budget provides the conceptual guide for investigating energy exchange over a landscape. The net radiation (R n ) absorbed by a forest, crop, fen or lake is equal to the sum of incoming short wave (R g ) and long wave radiation ( L ) minus the reflected shortwave and emitted long wave radiation. R ( 1 α ) R L L n = g + B A Rn = ( 1 α) Rg + εlb εσt s 4 Before we close, it will be instructive to use some of the principles of the radiation, at hand, to examine the radiation balance of earth. As biometeorological studies can contribute to our understanding of Earth s greenhouse effect. Case 1. Case with no atmosphere. Equilibrium balance between radiation intercepted by Earth and that radiated back into space. 2 2 π r ( 1 α) S * = 4π r σt 4 earth earth k ( 1 α ) S * 4 = σ 4 T k S*= 1366 W m -2 α=0.30, mean Earth Albedo 23

24 E=241 W m -2 T rad =255K, mean radiative temperature of the Earth 2. Radiative balance over planet with atmosphere, the Zero Dimensional Case Everyday experience, the presence of liquid water and a network of climatological temperature sensor tells us that the surface temperature is way above 255 K (-36 C). Greenhouse gases partially close the atmospheric window and trap heat more efficiently at the surface and in the lower atmosphere. To balance this effect, the surface and lower atmosphere must warm and emit thermal radiation at a greater intensity. Greenhouse Effect is caused when the atmosphere absorbs thermal radiation in the spectral regions where the atmosphere is opaque. In accordance with the conservation of energy, the amount of energy absorbed equals that emitted. With the case of an atmosphere overlying the earth, approximately half of the emitted radiation is re-directed towards the surface and the other half is lost to space. Top of atmosphere, 342 W m -2 received from sun, 105 W m -2 is reflected for a net of 237 W m -2. Yet 390 W m -2 of radiation is received and emitted at Earth s surface since its surface temperature is 288K, causing long wave radiation to peaks at about 10 um. To enable this much energy to be received at the surface the atmosphere must absorb and reradiate 153 W m -2, the difference between the surface emission and that lost to space The direct radiative forcing of long-lived trace gases is about 2.45 W m -2 CO 2 forcing: 1.56 Wm -2 CH 4 forcing: 0.47 Wm -2 N 2 O forcing: 0.14 W m -2 The direct radiative forcing of CFC and HFC is about 0.25 W m -2, but the net forcing is 0.1 W m -2 due to a negative feedback associated with ozone depletion in the stratosphere. Tropospheric aerosols, due to fossil fuel and biomass combustion, have a negative forcing of about 0.5 W m -2. These aerosols are short-lived and easily washed out of the atmosphere. This forcing adjusts rapidly to changes in emissions. DISCUSSION QUESTIONS/POINTS TO PONDER Is it a coincidence that our vision and the waveband for photosynthesis evolved to utilize light in the peak spectral range of the sun? SUMMARY POINTS Planck s Law defines the spectral distribution energy radiating of a black body surface of a given temperature. 24

25 The main broadband wave bands of solar energy are ultraviolet, visible and near infrared. Integrating Planck s Law with respect to wavelength from zero to infinity produces the Stefan-Boltzmann Law which states that the amount of energy radiativing from a black body is proportional to its temperature to the fourth power. Differentiating Planck s Law with respect to wavelength and solving for the maximum value (the wavelength when the derivative is zero) produces Wien s Law, which states that the maximum wavelength is inversely proportional to surface temperature One can derive how hot the sun is by knowing its spectral distribution and solving for Wien s Law. It can also be derived from geometrical considerations knowing the solar constant, the distance between Earth and the Sun, the Sun s radius and the Stefan-Bolzmann law. Incident radiation is absorbed, reflected or transmitted. The albedo of land is a function of vegetation leaf area and height, soil exposure, and its moisture content. Longwave emission of energy is proportional to its emissivity, as defined by Kirkoff s Law The net radiation balance is a equal to the sum of incident solar radiation minus the fraction reflected (albedo times incoming solar radiation) plus incoming longwave energy minus the energy emitted from the surface that is proportional to its temperature to the fourth power. ASSIGNMENT 1. Using Planck s Law, compute and plot the IR spectrum for temperatures of 250, 273, 303 K. Compare these with a spectrum computed at 6000 K. 2. Using Planck s Law and the solar spectrum (computed at 6000 K) to compute the mean leaf reflectance for 3 cases: a. weighted arithmetic mean (without Planck s Law) b. spectrum with low reflectance in the visible and high reflectance in the near infrared Wave band (nm) Reflectivity

26 c. spectrum with high reflectance in the visible and low reflectance in the near infrared Wave band (nm) Reflectivity In the future, research is developing in the areas of astrobiology and concepts learn here may be useful to study the environment of other planets. Using information from standard astronomical tables, compute the solar constant on Mars. Then compute its black body radiative temperature. 4. An infrared thermometer senses outgoing longwave radiation, not the temperature. Consequently, it must be corrected for the reflected sky radiation A = s + B 4 L εσt ( 1 ε ) L For a value of 500 W m -2, compute the surface temperature for cases of incoming longwave radiation of 400, 300 and 200 W m -2, for emissivity cases of 1.00, 0.98, 0.95 and References Bonhomme, R The solar radiation: characterization and distribution in the canopy. In: Crop Structure and Light Microclimate. INRA. Varlet-Grancher, Bonhomme and Sinoquet (eds) pp Campbell, GS and JM Norman An Introduction to Environmental Biophysics. Springer. Chandrasekhar, S Fundamentals of Radiative Transfer. Dover Press 26

27 Davies, J.A. and S.B. Idso Estimating the surface radiation balance and its components. In: Modification of the Aerial Environment of Crops. ed. B.J. Barfield and J.F. Gerber. ASAE. St. Joseph, MO. pp Hess, S.L Introduction to Theoretical Meteorology. Holt, Rinehart and Winston, New York. 362 pp. Lean, J The sun's variable radiation and its relevance for earth. Annual review of Astronomy and Astrophysics. 35: Monteith, J.L. and M.H. Unsworth. Principles of Environmental Physics, 2 nd edition Oke, T.R Boundary Layer Climates. Metheun. Ross, J The Radiation Regime and Architecture of Plant Stands Stanhill, G. and Cohen, S., Global dimming: a review of the evidence for a widespread and significant reduction in global radiation with discussion of its probable causes and possible agricultural consequences. Agricultural and Forest Meteorology, 107(4): Wallace J.M and P.V Hobbs Atmospheric Science, An Introductory Survey. Academic Press. Data Resources Sunphotometer data and atmospheric optical depth information 27