Discussion: Cirrostratus clouds are often wispy and have diffusive boundaries, indicating that the cloud particles are made of ice crystals.

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1 ATSC 201 Fall 2017 Assignment 10 Answer Key Chapter 6: A4g, A12g Chapter 8: A1g, A4g, A7g, A8g Chapter 11: A11g, A22g, A23g Chapter 6 A4g) Given the following descriptions of ordinary clouds: i) First classify as cumuliform or stratiform ii) Then name the cloud iii) Next, draw both the WMO and USA symbols for the cloud. iv) Indicate if the cloud is made mostly of liquid water or ice or both. v) Indicate the likely altitude of its cloud base and top. vi) Finally, sketch the cloud similar to those in Figs. 6.3 or 6.5. g) Thin uniform veil covering most of sky showing some blue sky through it, with possibly a halo around a bright sun, allowing crisp shadows cast on the ground behind trees and people. Solution: i) stratiform ii) cirrostratus iii) WMO symbol= USA symbol= iv) ice crystals v) Likely cloud base = surface to approx. 5km Likely cloud top = approx. 13km vi) Discussion: Cirrostratus clouds are often wispy and have diffusive boundaries, indicating that the cloud particles are made of ice crystals.

2 A12g) Draw the cloud coverage symbol for weather maps for sky cover of the following amount (oktas): g) 6. Solution: From Table 6-7. Discussion: This would be described as broken clouds, with sky cover of 7-8/10. Chapter 8 A1g) Using Fig. 8.4, identify whether the wavelength g) 1.6 (μm) are in a window, dirty window, shoulder, or opaque part of the transmittance spectrum, and identify which sketch in Fig. 8.2 shows how the Earth would look at that wavelength. [Hint: transmittance of 80% indicates a window.] Solution: Wavelength 1.6μm is at a window. It has a transmittance > 80% mostly due to little absorption by water vapor. With a transmittance >80% would look mostly like Fig. 8.2a, maybe partial absorption like Fig. 8.2c. Discussion: A transmittance of more than 80% indicates that the atmosphere absorbs only very little of the upwelling radiation, allowing good observation of clouds and land use. A4g) Find the brightness temperature for the following wavelengths (μm), given a radiance of 10^(-15) W/(m^2 * μm *sr): g) 4.6. Given: λ (μm) = 4.6 Bλ = 1E-15 W/(m^2 * μm * sr) Find: TB =? K

3 Use eqn. 8.2: where: c1b = 1.19E+08 W*m-2*μm4*sr-1 c2 = 1.44E+04 μm*k TB = K C Discussion: The radiance given in this question is very, very small, and the resulting brightness temperature is also small. This isn't that surprising because, for a given radiance, the longer the wavelength, the lower the brightness temperature. This is because waves with shorter wavelengths carry more energy than longwaves. A7g) For the following altitudes (km) above the Earth's surface, find the satellite orbital periods: g) Given: satellite altitude = km m Find: t_orbit =? s Use eqn. 8.8: where: G = 6.67E-11 N*m^2/kg^2 M = 5.97E+24 kg radius of Earth = 6378 km m R = radius of Earth + satellite altitude = m

4 t_orbit = s 8.64 hr Discussion: The calculations here are for circular orbits. A larger orbit is longer orbital time. A8g) What shade of grey would the following clouds appear in visible, IR, and water-vapor satellite images? g) nimbostratus. Given: Find: Cloud type: nimbostratus. Shade of grey nimbostratus clouds would be in visible, IR, and water-vapor satellite images. VIS: White, because it is a cloud. IR: Medium to dark grey because of low-altitude and warm top. Wat - vapor: Invisible because clouds are too low. WV shows moisture aloft. Chapter 11 Discussion: The different shades of grey in different satellite images is indicative of the different wavelengths being picked up by that satellite channel. A11g) Find the magnitude of the thermal wind (m/s) for the following thickness gradients:g) ΔTH(km)/Δx(km) = -0.2/600, ΔTH(km)/Δy(km) = 0.1/400. Given: ΔTH_x = -0.2 km -200 m Δx = 600 km m ΔTH_y = 0.1 km 100 m Δy = 400 km m Find: MTH =? m/s

5 First, use eqns 11.15a and 11.15b: where g = 9.8 m/s^2 fc = 1.10E-04 /s UTH = VTH = m/s m/s Then, use eqn : MTH = m/s Discussion: The thermal wind speed is the difference in the geostrophic wind speeds at the top and bottom of the layer. Thickness (TH) is analagous to the mean temperature of the layer. A22g) For the latitude given below, what is the value of the beta parameter (1/ms): g) 60. Given: φ = 60 Find: β =? 1/(m*s) Use eqn : where : 2*Ω/Rearth = 2.29E-11 1/(m*s) β = 1.15E-11 1/(m*s) Discussion: When we assume that the Coriolis parameter fc changes linearly with latitude (i.e. beta = constant), we are using the "beta plane". This approximation is valid when we are only looking at a small latitude belt.

6 A23g) Suppose the average wind speed is 60 m/s from the west at the tropopause For a barotropic Rossby wave at 50 latitude, find both the intrinsic phase speed (m/s) and the phase speed (m/s) relative to the ground for wavelength (km) of: g) Given: λ = 4000 km m φ = 50 Uo = 60 m/s Find: co =? m/s c =? m/s First, find the beta parameter using eqn : where : 2*Ω/Rearth = 2.29E-11 1/(m*s) β = 1.47E-11 1/(m*s) To find the intrinsic phase speed use eqn : co = m/s To find the phase speed use eqn 11.38: c = m/s Discussion: The intrinsic phase speed tells us how fast the wave is moving relative to the mean flow. A negative intrinsic phase speed means that the waves are actually moving westwards if there is no mean flow in the background. The phase speed is the speed of the wave relative to the ground.

7 What happens if you increase the wavelength (the value for lambda)? Note that this wave travels fairly fast (near mean flow wind speed), which is reasonable as it has a fairly short wavelength for a barotropic wave.