Appendix D.1 – Sample Midterm Lab Exam Questions: UNBC ENSC 201 Appendix D.1: Sample Lab Midterm Exam ANSWERS Use the equation sheet supplied with the Lab Midterm Review materials (Appendix D.1) when you are preparing as this is what you can expect to see with the exam. 1. What is a contour line (i.e. define the concept of a contour line). A contour line is a line of “equal value” on a map or spatial image. In meteorology, these lines take various forms, for example: isotherms are lines of equal temperature; isohyets are lines of equal precipitation; isobars are lines of equal pressure; etc.. (For most people, the contour lines seen on topography maps are most familiar. They are called “contour lines” and this can be confusing as in this context these lines represent lines of equal elevation, not just lines of equal value. ) 2. A site has the following characteristics. It is night. Note the “percentage of the site” values given below represent both L↑ and L↓ down values. a. Calculate L*. b. Under these conditions, how does L* relate to Q*? c. Answer qualitatively (calculations aren’t required). i. How would L*change if the sky were to become clear? ii. What would happen to the air temperature at the surface? Type Clear sky Clouds Buildings Trees ground Temperature % of site -40 0C 0% 0 -10 C 100% 5 0C 10% 0 0 C 10% 0 5 C 80% Answer Comments At this site these make up L↓ values and sum to 100%. The clear sky value is obviously not used. At this site, these make up L↑ values and sum to 100%. The cloud value at 100% would be how you could know if the buildings or trees were considered to be L↑ or L↓ values. ANSWER: For all calculations: MAKE SURE TO SHOW YOUR UNITS AND HOW THEY CANCEL. a. Method: determine the energy emitted for L↓ and L↑ using StephenBoltzman’s Law (L↓ = σ T4 and L↑ = σ T4) and then compute L* using L* = L↓ - L↑ . To compute L↓ and L↑: L↓ = σ T4 Where: T = 100% @ -100C in Kelvin = 273.15 + (-100C) = 263.15 K L↓= (5.67 x 10-8 W m-2 K-4)(283.15 K)4 L↓= 271.89 W m-2 L↑ = σ T4 Where: T = (80% @ 50C + 10% @ 50C + 10% @ 00C + 10% @ 50C) T = (90% @ 50C + 10% @ 00C) = (0.9 x 50C + 0.1 x 00C) = 4.50C T in Kelvin = 273.15 + 4.50C = 277.65 K L↑ = (5.67 x 10-8 W m-2 K-4)(277.65 K)4 L↑ = 336.96 W m-2 Then L* = L↓ - L↑ : L* = L↓ - L↑ = ( 271.89 W m-2 - 336.96 W m-2 ) = - 65.07 W m-2 1 Appendix D.1 – Sample Midterm Lab Exam Questions: UNBC ENSC 201 b. Under these conditions (i.e. nighttime – given in the questions preamble), Q* =L*. c. If the sky were to become clearer: i. L* would become a larger negative number as the value for L↓ would be smaller, but L↑ would not change as much or as quickly so L* would be more negative. ii. the temperature at the surface would decrease since L*=Q* will be a larger negative number, cooling the air to a greater extent. 3. Given that the radiation temperature of the Earth-Atmosphere is about 254 K, and assuming it is a black body: a. Calculate the flux density of longwave radiation (Wm-2) emitted by the EarthAtmosphere. ANSWER: L↑E-A = σ T4 where T = 254 K L↑ E-A = (5.67 x 10-8 W m-2 K-4) (254 K)4 L↑ E-A = 236 W m-2 b. What is the total flux emitted (W) by Earth? ANSWER: The flux emitted by Earth is equal to the flux density times the surface area of Earth. L↑ E-A = 236 W m-2 Flux = (L↑ E-A) (4πrE2) = (236 W m-2)[(4)(3.14)((6.37 x106m)2)] = (236 W m-2) (5.10 x1014m2) Flux = 1.20 x1017 W c. How any joules (J) does the Earth emit per year? ANSWER: Since a watt (W) is defined as a joule per second (J/s), you can determine this by multiplying the flux by the number of seconds in a year. Flux = (1.20 x1017 W) = (1.20 x1017 J s-1) Joules = (1.20 x1017 J s-1)(365 day yr-1)(24 hr day-1)(60 min hr-1)(60 s min-1) Joules emitted by Earth = (3.78 x 1024 J) d. The flux density of Earth radiation reaching the moon can be viewed as that on a spherical shell concentric about Earth whose radius is the mean distance between Earth and the moon. Calculate the value of this flux density. ANSWER: The flux density of Earth radiation that reaches the moon is determined by the flux emitted by the Earth (determined in b. above) divided by the area of a sphere whose radius is the mean distance between the Earth and moon. This question is analogous to the calculation made to determine the solar constant. 2 Appendix D.1 – Sample Midterm Lab Exam Questions: UNBC ENSC 201 The Earth radiation that reaches the moon is represented by the radiation that reaches the inside of a shell that is the distance from the Earth to the moon. Flux emitted by the Earth = 1.20 x1017 W Distance between Earth and moon = 3.84 x 108 m Flux density from the earth incident on the moon 1.20 1017W 1.20 1017W 4rE2M 4 [(3.84 108 m) 2 ] 1.20 1017W W 0.065 2 18 2 1.85 10 m m e. How does this compare with the solar constant? ANSWER: The solar constant is 1367 W m-2 and the flux density from the Earth incident on the moon is 0.065 W m-2. The solar constant is much, much larger. 4. The Sun is 20 degrees above the horizon. a. What is the zenith angle? (Hint: go back to the diagrams in Lab 2 to see how zenith angle is defined). b. Calculate the flux density of radiation entering the atmosphere. c. If the atmosphere attenuates (absorbs and reflects) 20 % of this value and Earth’s albedo is 0.25, what is K*, the net short wave radiation? ANSWERS: a. Since the Sun is 20 degrees above the horizon, and the zenith angle is defined as the angle between the perpendicular to the horizon and the solar beam, the situation indicates that the zenith angle (Z) must be 900 – 200 = 700. (Also see Figure 2.1 in the lab manual; incident angle also discussed in lecture.) b. Flux density entering the atmosphere: determined by I = I0 cos Z : where I is the flux density entering the atmosphere, I0 = the solar constant, Z = the zenith angle. I = I0 cos Z = (1367 W m-2)(cos 700) = 467 W m-2 c. If the atmosphere attenuates 20% and the αEarth = 0.25 what is K*? To answer this you must remove 20% of the incoming energy to determine K↓ (this is the same as retaining 80%); then use αEarth and K↑ = (αEarth)(K↓) to determine K↑; now you can compute K* from K*= K↓- K↑. So the answer is: I = 467 W m-2 but I is attenuated so K↓ = (0.8)(467 W m-2) = 373.6 W m-2 And K↑ = (αEarth)(K↓) = (0.25)(373.6 W m-2) = 93.4 W m-2 So: K* = K↓- K↑ = (373.6 - 93.4) W m-2 K* = 280.2 W m-2 3 Appendix D.1 – Sample Midterm Lab Exam Questions: UNBC ENSC 201 5. What is the incoming solar radiation (I) on Feb 14 at 8 a.m. at Prince George; assume the latitude of Prince George is 540? [Extension for studying: go back to your Lab 2 answers and compare this value to the one you determined for your lab time January. How are they different? How much radiation are we gaining each day?] ANSWER: Use: I I 0 cos Z where: Io = the max solar flux density = 1367 Wm-2 I = the incident radiation received by the surface cos Z = sin sin + cos cos cos h where: = the latitude of Prince George = 540 N h = the hour angle (150 per hour from solar noon and we assumed that solar noon is the same as local noon). For 8:00 PST h = (4 hours x -150/ hour) = -600 = the solar declination (i.e. the latitude where the sun is directly overhead. A positive value indicates 0North; and a negative value indicates 0South). Determine using: 23.4 0 cos 360TJ 10 365 where TJ = the Julian Day = (31+14) = 45 for Feb 14 23.40 cos 36045 10 13.67 (~140 south of the equator) 365 Determining: cos Z = sin sin + cos cos cos h we get: cos Z = sin(540N) sin(-13.670) + cos(540N) cos(-13.670) cos (-600)= 0.09437 Substituting cosZ into I = Io cosZ we get: -2 I = Io cosZ = 1367 Wm (0.09437) I = 129 Wm-2 6. Earth-Atmosphere Radiation Budget. Using your understanding of the concept of radiation balance complete the missing values in the following table of the annual radiation balance of the Earth (E), the Atmosphere (A) and the Earth-Atmosphere system (E-A). All units are in gigajoules per meter squared per year (GJ m-2 yr-1; G = 109). You are given the average annual solar radiation to the E-A system as 338 Wm-2; the planetary albedo (αE-A) is 0.30; and the following table. System Atmosphere (A) Earth (E) Earth-Atmosphere (E-A) Net solar (K*) GJ m-2 yr-1 2.32 5.14 7.46 Net infra-red (L*) GJ m-2 yr-1 -5.34 -2.12 -7.46 ANSWERS in the table are colour coded below: 4 Net all-wave (Q*) GJ m-2 yr-1 -3.02 3.02 0 Appendix D.1 – Sample Midterm Lab Exam Questions: UNBC ENSC 201 Like the final question in the Radiation Calculation Lab (Lab 2), when answering this question recognize the following relationships exist: o The first two columns add to equal the third column (i.e. net solar + net infra-red = net all-wave radiation or in symbols: K* + L* = Q*). o The first two rows add to equal the last row (Atmosphere + Earth = EarthAtmosphere or in symbols: A + E = E-A). o The net all-wave radiation balance of the Earth-Atmosphere system must equal zero if this system is in radiative balance (i.e. the system isn’t gaining or losing energy on an annual basis). These relationships allow determination of QE* and LE* The value for K*E-A can be derived from understanding that: o the average annual solar radiation to the E-A system of 338 Wm-2 = K↓E-A and o using the planetary albedo of αE-A = 0.30, K↑ can be calculated from K↑ E-A = 338(0.3) = 101.4 Wm-2 o From these K*E-A= K↓- K↑= (338 -101.4) Wm-2 = 236.6 Wm-2 (for those of you who are noticing a short cut to this value it looks like: K*E-A= (338 Wm-2(1-0.30)) = 236.6 Wm-2 o To compare this value to those already in the table, K*E-A= 236.6 Wm-2 must be converted from W m-2 to GJ m-2 yr-1 as follows: 236.6 J K E* A 2 sm 60 s 60 min 24 hr 365 day 1 GJ 9 min hr day yr 10 J GJ 7.46 2 m yr 7. To answer this question, make reference to the figure below. a. Explain the reason(s) for the dip in the QE curve (and the related rise in QH) in July and August. b. How is it possible for the heat used in evapotranspiration (QE) to exceed the available net radiation (Q*) in the September-February period? c. Discuss the behaviour of QG throughout the year (i.e. how does it vary, at what times and why; what is the net QG for the year, why?). d. Discuss and explain the relationship of Q* to the other energy flux density values shown in this graph? ANSWER: a. The QE curve dips in July and August because water for evapotranspiration becomes limited and there is not enough water available to meet the evapotranspiration demand. But, because Q* is still high, the dip in QE causes a rise in QH as the energy goes into heating the air. b. In Sept-Feb heat from the ground (QG) supplements the energy needed for evapotranspiration. The negative value of QG indicates that energy is being conducted from the ground to the surface. (Also, as QH is negative, it is losing 5 UNBC ENSC 201 Appendix D.1 – Sample Midterm Lab Exam Questions: heat to the surface and energy is being made available for evaporation from QH. Often this happens when warmer air masses moves into an area.) c. Throughout the year QG is balanced in terms of negative and positive energy flux densities; this makes intuitive sense if on an annual basis the ground is neither heating or cooling. It is positive during the summer months when Q* is highest and the deeper ground is cooler than the surface so heat flows into the deeper ground. QG is negative during the winter when the deeper ground is warmer than the surface and it releases energy to the surface. d. Q* drives the other fluxes for most of the year. During the summer months, large positive values of Q* result in a surplus of energy at the surface which goes into the air (as convective sensible and latent heat fluxes, QH and QE) and into the ground as the conductive heat flux QG. During the winter, negative values of Q* result in a deficit in radiant energy at the surface causing the ground and the air to cool and provide heat to the surface. 6
© Copyright 2024