Exercise 1 - Longwave radiation in a clear and cloud-topped atmosphere Let us assume an atmosphere whose vertical atmosp

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Exercise 1 Longwave Radiation In A Clear And Cloud Topped Atmosphere Let Us Assume An Atmosphere Whose Vertical Atmosp 1 (239.57 KiB) Viewed 30 times

Exercise 1 - Longwave radiation in a clear and cloud-topped atmosphere Let us assume an atmosphere whose vertical atmospheric temperature profile is given by Ta(z) = To-yz, (1) with To 293 K and y = 6 K/km. We will use simplified clear sky radiative flux profiles that are linear in height. The clear sky upwelling longwave radiative flux is given by LW clr,up = OT-Cuz and the downwelling clear sky longwave radiative flux LW clr,dn = EOT- - Caz, with Cu = 10 W/m²/km, ca = 20 W/m²/km and the near surface emissivity of the clear atmosphere € = 0.8. 1a. (10 points) Compute the temperature tendencies (time rate of change) for a clear sky as a function of height. The vertical density profile reads p = po az, with po = 1.2 and a = 0.8 kg/m³/km. It is generally known that during daytime clouds have a strong effect on solar radiation. Some- times people say that clouds act as a blanket with which they usually mean that clouds tend to temper the minimum temperature during the night. Here we will apply the concepts used in the global energy balance model to clouds and longwave radiation. To this end consider the figure shown below that depicts a cloud layer at an arbitrary height z above the ground surface. If the cloud layer is sufficiently thick it will radiate as a black body (Ecld = acld = 1). We will assume that the temperature in the cloud is equal to the atmospheric temperature at z = Zeld. We will study the radiation that is emitted by the cloud layer if it is present at a height 0 < Zeld < 10 km. Last, we will assume that the clouds are sufficiently thick to radiate as a black body. 1b. (10 points) (i) Plot the downward longwave radiation flux emitted by a cloud layer that is present at a height 0 < Zeld < 10 km. Also plot the vertical profile of the clear sky downward longwave flux in the same figure. What is the effect of the downward longwave flux in case clouds are present? (ii) Redo 1b(i) but now for the upward longwave radiation flux. (iii) Can you explain the so-called 'blanket' function? Can you explain why in satellite infrared images high clouds show up very clearly? 1c. (10 points) Now assume that the clear sky longwave radiation fluxes received at the base and the top of the cloud layer are equal to the clear sky values used in 1a. Compute the change of the net longwave radiation flux across the cloud layer, and plot this result as a function of height of the cloud layer. Discuss whether the cloud layer is being warmed or cooled as a result of the change in the net radiative flux across the cloud layer.