Questions you should be able to answer after reading the material

Module 4 Radiation Energy of the Sun is of large importance in the Earth System, it is the external driving force of the processes in the atmosphere. Without Solar radiation processes in the atmosphere (as Thermodynamics and Microphysics) could not exist. The radiation of the sun is mainly short-wave radiation. On the contrary, the earth and atmosphere itself also emit radiation, which mostly consist of long-wave radiation. This module gives a description of the general aspects of radiation and processes by which gases and particles absorb and scatter radiation. Read the parts of Wallace and Hobbs indicated below: Chapter 4 Radiative Transfer 4.1 The Spectrum of Radiation... 113 4.3 Blackbody Radiation... 117 4.3.1 The Planck Function... 117 4.3.2 Wien s Displacement Law... 118 4.3.3 The Stefan-Boltzmann Law... 119 4.3.4 Radiative Properties of Nonblack Materials... 120 4.3.5 Kirchhoff s Law... 121 4.3.6 The Greenhouse Effect... 121 4.4 Physics of Scattering and Absorption and Emission... 122 4.4.1 Scattering by Air Molecules and Particles... 123 4.4.2 Absorption by Particles... 126 4.4.3 Absorption and Emission by Gas Molecules... 127 4.6 Radiation Balance at the Top of the Atmosphere... 144 Key concepts of the reading material Shortwave or solar radiation Longwave or thermal radiation Blackbody radiation Wien s Law Planck Law Inverse quadratic law of radiation Kirchhoffs Law Scattering Absorption Rayleigh Scattering Mie Scattering Questions you should be able to answer after reading the material Which two wavelength bands make up the spectrum most relevant for the atmosphere? Give a definition or description of the effective emission temperature. Explain why a planet 4 times further away from the sun has a solar constant that is 16 times smaller. Explain the difference between the surface albedo and the planetary albedo. In Figure 4.35, explain why the warm Sahara has a negative net radiation budget? Meteorology and Climate 21 of 93

Exercise 1 Blackbody Radiation 1.1 Do exercise 4.22 of Wallace and Hobbs (page 147). 1.2a Find the flux density of solar radiation of the planet Venus given the following data: Fs,Earth = 1368 W m -2, distance Sun-Venus 0.72 AU. Check your answer with the value in table 4.1 of Wallace and Hobbs (page 120). 1.2b The answer to the previous question was on short wave solar radiation. Now find the flux density of the radiation Venus emits. Assume that the albedo is 0.78 and that the planet is in radiative equilibrium. 1.2c Also find the effective emission temperature of the planet. Check the answer again with the table value. 1.2d What is the difference between the radiation Venus receives and the radiation it emits? Explain with Wien s displacement law (page 118 of Wallace and Hobbs). 1.3 Do exercise 4.56 of Wallace and Hobbs (page 152). Exercise 2 Atmospheric Effects 2.1*a Consider the simplified model of the short wave energy balance shown in figure 4.1. The model atmosphere consists of an upper layer with transmissivity T1, a partial cloud cover layer with fractional coverage fc and reflectivity at the top of Rc (assume no reflectivity at the bottom), and a lower layer with transmissivity T2. The planet s surface has an average reflectivity Rs. Assume that no absorption takes place within the cloud layer and no scattering takes place except in the cloud layer. Find the fraction of short wave radiation that reaches the surface. 2.1b Find an expression for the planetary albedo A. 2.1c For the following values of model parameters, calculate the planetary albedo: fc = 0.5, T1 = 0.95, T2 = 0.90, Rc = 0.5, Rs = 0.125. 2.1d Use the model to estimate the albedo of a cloud free and cloud covered Earth. * This is an exercise at exam level T1 fc Rc T2 Rs Figure 4.1 Simplified atmosphere model. With transmissivity T1 and T2, fractional cloud coverage fc and reflectivity Rc and Rs. Meteorology and Climate 22 of 93

Exercise 3 Solar Radiation 3.1 Wallace and Hobbs (page 385) describe the incoming flux of solar radiation as follows: During daytime, the incoming solar radiation is proportional to the sine of the elevation angle of the sun, which varies with time of day, latitude and season. In this exercise we will examine this relationship. The solar declination angle, δ s, is defined as the angle between the incoming solar radiation and the plane of the Earth s equator. It varies from +23.45 on 22 June to -23.45 on 22 December. The solar declination angle for any day of the year is approximately: 360 ( d - dr ) δ s = φr cos( ) (4.1) d y with the tilt of the Earth s axis: φ = 23.45, the relative Julian day: d (day of year, e.g. r for February 11: d = 31+11= 42days), the day of the summer solstice d = 173(in nonleap years*) and the number of days in a year d = 365 (in non-leap years). Find the solar declination angle for today. * leap year = schrikkeljaar 3.2 The hour angle is the angle between the sun and the observers south (the angle between the plane trough zenith and South and the plane through the celestial north pole). It changes with 360 / 24 = 15 per hour. For a given time (in UTC) and longitude, it can be calculated using: tutc h = 360 + λ -180 (4.2) 24 Calculate the hour angle for Wageningen (51.967 N, 5.667 E) for today at 14.00 local time. λ denotes the longitude (positive east of the Greenwich meridian). 3.3a The local solar altitude above the horizon can now be calculated. This angle, Ψ, often referred to as solar elevation angle is dependent on latitude, φ (positive north of the equator), solar declination, δ s, and time of day. sin( Ψ) = sin( φ) sin( δs ) + cos( φ) cos( δs ) cos( h) (4.3) with the Coordinated Universal Time (UTC) day: t UTC and the length of day: t d = 24h. Calculate the solar elevation angle for Wageningen (51.967 N, 5.667 E) for today at 14.00 local time. 3.3b Make a schematic drawing of the definition solar elevation angle. Also include the zenith angle, which is angle between the sun and the local zenith (vertically upwards from a particular location) and the azimuth angle, the angle between the north and the suns position. 3.4a The path of the sun along an observers view of the atmosphere can now be computed. The distance Earth-Sun is variable, resulting in a varying amount of solar normal beam -2 irradiation S 1368 7 W at the top of the atmosphere, where S0 = 1368 W m -2 0 m is the solar constant. The current distance Earth-Sun is 147.127 10 9 m. Find the value of the solar normal beam irradiation (S). 3.4b Recall that not all of this radiation reaches Earth s surface. The local incoming solar flux is: F S T sin( ) (4.4) s r y r Meteorology and Climate 23 of 93

with T r the net sky transmissivity, which depends on path length through the atmosphere, atmospheric absorption characteristics and cloudiness. Check the website of the Veenkampen weather station and find the incoming solar flux. Estimate with this value and the value calculated in exercise 3.3a the transmissivity under current conditions. Practical 4 Radiation and Radiative Transfer Radiation is the prime source that moves the atmosphere. Understanding its properties, behaviour and distribution is paramount in understanding weather and climate. In this unit we will study solar (shortwave) radiation in some detail in order to understand radiative processes such as absorption and scattering in the atmosphere. The detailed theory of radiative transfer, including long wave radiation, is beyond the scope of this course. Preparation: - Create the folder D:\SMARTS - Copy all files and folders (subdirectories) from the following location W:\PROJECTS\MAQ21806\unit4MC\ to: D:\SMARTS. Exercise 1 Scattering and Absorption of Solar Radiation SMARTS (Simple Model of the Atmospheric Radiative Transfer of Sunshine) is a spectral model to predict at the Earth s surface (a) the direct beam, diffuse, and global irradiance incident on a horizontal surface ( A in Figure 4.2), or (b) the direct beam at normal incidence ( B in Figure 4.2). The direct beam at normal incidence means: only the direct (not the diffuse) sunlight on a plane that is perpendicular to the sun s rays. The cosine effect, which is important for a horizontal surface because of the angle between the sun s rays and the horizontal surface, is eliminated when considering a surface that is always perpendicular at the sun s rays. Note however, that the longer path of the sun s rays through the atmosphere, when the sun is not in the zenith, is still important, also for the direct beam at normal incidence. The model covers the shortwave solar spectrum (280 to 4000 nm), and thus includes the UVA, UVB, Visible and Near-Infrared bands. It can also predict the photosynthetically active components of radiation, the UV index, as well as various UV action weighted spectra. In this unit we will restrict ourselves to irradiances on a horizontal surface and normal beam irradiances. Figure 4.2 The difference between direct beam sunlight incident on a horizontal plane (A) or at normal incidence (B) depends on the value of the Sun s altitude ( ) or on the zenith angle ( = 90 - ). 1.1 Running SMARTS - From the D:\Smarts folder delete, if present, the following two files: Meteorology and Climate 24 of 93

- smarts295.ext.txt - smarts295.out.txt - From the separate file (in BlackBoard) Running SMARTS User Interface read: 1. Running the model. - Start Microsoft Excel and open D:\SMARTS\smarts295.xls - Follow the instructions as mentioned in 1. Running the model: - Select Enable Content (in the horizontal, yellow bar at the top). - Click on Click Here to Start (in the SMARTS Version 2.9.5 window) - Click: Get Config in the SMARTS Configuration window, and get the configuration file named Control.txt in the EDU\Run1 folder. - Click Run Model in the SMARTS Configuration window. The model will run and produce output in the D:\SMARTS folder. - Click Quit in the SMARTS Configuration window, do NOT save any changes. This will complete running the model. - The following three files have been created in the D:\SMARTS folder: - smarts295.ext.txt - smarts295.out.txt - smarts295.inp.txt 1.2 Examining the model results - Move the three files to a folder that you define yourself anywhere in the D:\SMARTS folder. All three files can be inspected using Notepad or Wordpad (for both: use landscape view to facilitate reading this file). Open the file smarts295.out.txt. Locate and write down the following quantities of the broadband irradiances : - Direct beam at normal incidence: 1. Extraterrestrial (in W m -2 ). Extraterrestrial means: outside the Earth, it is the radiation as it is received at the top of the atmosphere when no extinction has yet occurred. 2. Terrestrial (in W m -2 ). Terrestrial means: at (or near) the Earth s surface. 3. Atmospheric Transmittance. - For the horizontal plane: 4. Direct Beam (in W m -2 ). 5. Diffuse (in W m -2 ). 6. Global (in W m -2 ). 7. Why is the direct beam extraterrestrial irradiance at normal incidence (from question 1) not equal to the solar constant of 1366.1 W m -2? 8. What is the mathematical relation of the three broadband irradiances for the horizontal plane? 9. At the direct beam at normal incidence : what is the mathematical relation between Extraterrestrial, Terrestrial and Atmospheric Transmittance? The file smarts295.ext.txt contains the spectral (i.e. wavelength dependent) data of the selected output quantities. Viewing this file in Notepad just shows a large amount of numbers and is quite useless. To view these results graphically, these data must be imported in an Excel spreadsheet. This has been done already, and the results of this so-called control run are in the file D:\SMARTS\EDU\Run1\Practical.xls in the tab labeled Ctl. Check if the data in the spreadsheet are the same as in your smarts295.ext.txt file! If they are NOT the same, the wrong SMARTS configuration has been used in running the model (in 1.1) and subsequent exercises may be wrong! The Excel file practical.xls has three tabs containing the data from smarts.ext.txt: - Ctl: this sheet contains the results of the control run. The control run is used to compare the results of all experiments to be performed. The data should not be changed. Meteorology and Climate 25 of 93

- Exp: this sheet will contain the results of the smarts295.ext.txt file of any exercise to be performed later on. At the moment this sheet should be empty. - Diff: this sheets contains the difference = experiment-control of all fields. The Excel file also contains 11 charts (chart0 - chart10) containing the graphical representation of all data. Briefly glance through the spreadsheets and charts to become acquainted with the contents of the file. 10. Water vapour transmittance (Chart7) shows bands of total transmittance (transmittance = 1) and bands of total absorption (transmittance = 0). For the following wavelength bands indicate the transmittance (either 1 or 0). 11. In which other chart(s) (0 through 10) is the effect of the transmittance spectrum of water vapour also discernible? 12. Ozone (O3, Chart6) has a very sharp cut-off wavelength in the UV part of the spectrum (< 300 nm): shorter wavelengths are absorbed completely, longer wavelengths are transmitted completely. Go to the Ctl sheet and give the wavelength below which more than 50% of the radiation is absorbed. 1.3 Absorption in the shortwave (solar) spectral region - We begin with an experiment where we decrease the amount of ozone (O3) to see what the effects are on the solar radiation received at the Earth s surface. 13. Look in the smarts295.out.txt file of the control run and find the total amount of ozone of the control run (in Dobson Units). - Start the model and load the control configuration. Change the amount of ozone to 0.0 atm-cm (i.e. no ozone). Run the model and store the output in a separate folder. - In the smarts295.out.txt file of this run find and write down the amount of direct, diffuse and global radiation on the horizontal plane. - How much is the amount of each of these quantities relative to the control run? 14. Direct Beam (in %). (Note: 100% indicates the amount has not changed.) 15. Diffuse (in %). (Note: 100% indicates the amount has not changed.) 16. Global (in %). (Note: 100% indicates the amount has not changed.) - Import the data from the smarts295.ext.txt file as follows (for Excel 2010): - start Excel - open the file D:\SMARTS\EDU\Run1\Practical.xls. - (if necessary) remove all data on row 3, 4, on the spreadsheet on the Exp tab - move your cursor to cell A3 - import the data by: - Data > From Text - Find and select the correct smarts295.ext.txt file > Open - Check the bullet: Delimited > Next - Check the tick mark: Space > Finish - Check the bullet: Existing worksheet =$A$3 > OK - now all new data has been imported, the difference with the control run has been calculated and the results can be seen on the various charts in the Excel file. - For the Global horizontal irradiance (Chart 3): 17. What wavelength ranges have been affected by the removal of ozone? 18. At what wavelength is the maximum difference between control and experiment? 19. Is this maximum in the difference in global radiation due to the change in diffuse or in direct radiation? Meteorology and Climate 26 of 93

1.4 The effect of the zenith angle The optical mass or relative air mass is a measure of the relative length that the sun s rays travel through the atmosphere. When the sun is directly overhead (a situation only encountered in the tropics) the sun is in the so-called zenith. Then the length of the sun s rays through the atmosphere reaching the surface is at its minimum and by definition the optical mass M = 1 and the zenith angle = 0 ; the solar altitude (i.e. the angle between the direction of the sun s position and the horizon) = 90. If the earth s surface is assumed to be flat (see Figure 4.2.) the relation between the optical mass (M) and the zenith angle ( ) is given by: 1 M = cosθ This is a good approximation as long as the zenith angle is smaller than 85 ; at larger angles the curvature of the earth and the refraction of sunlight need to be taken into account. As the zenith angle increases the path of the sun s rays through the atmosphere becomes longer and more absorption and scattering will take place. We are going to investigate this with the SMARTS model. - Start the model. - Load the control configuration. - In the Solar Geometry (Card 17) change the Relative air mass (M) model from 1.5 into 1.0. - Run the model and retrieve from the smarts295.out.txt file the following parameters: Zenith angle (in degrees): check if this is indeed equal to 0. For the horizontal plane: write down the amount of direct, diffuse and global radiation. 20. Calculate how much (in %) of the global radiation is in the form of diffuse radiation. - For increasing zenith angle (and increasing air mass): 21. The amount of global radiation (increases/decreases). 22. The percentage diffuse radiation (increases/decreases). 23. The atmospheric transmittance (increases/decreases). 24. Select the correct explanation why the percentage diffuse radiation changes the way it does (question 22) with increasing zenith angle. 25. Which quantity decreases faster with increasing zenith angle? 26. This can be explained by. Meteorology and Climate 27 of 93