Meteorology 301 - Lab 8

Introduction

This lab extends work done in Lab 7 by using the PW(Ts) relationship in the programs Main.m and prec_wat.m, the latter which you wrote. Here we will use some information relating PW to atmospheric optical depth to couple PW to radiative equilibrium Ts. We will use this information to compute a surface temperature for pure radiative equlibrium.

GOAL: Observe
1. how pure radiative equlibrium surface temperature Ts_rad varies with atmospheric water amount
2. how radiative equillibrium temperatures differ from the actual temperatures.

Instructions

1. As with previous Matlab labs, follow the instructions for accessing meteorology computers to log into your Vincent account. Lab partners should open a window on the host machine and connect to Vincent in the window.

2. Before starting Matlab, copy two codes I wrote:
Optical depth for longwave radiation in the earth's atmosphere from PW
Radiative equilibrium air temperature at the surface and tropospheric lapse rate from optical depth, tau0

Copy the file Tau_PW.m to your home directory
cp /mthome/gutowski/MT301/Tau_PW.m ~
(That last character in the line is the tilde, ~.)
Copy the file Ts_rad.m to your home directory
cp /mthome/gutowski/MT301/Ts_rad.m ~

Use emacs or your editor of choice to look at each file to see what type of input and output variables its function uses.

3. Now start Matlab, from a Vincent prompt. If you forget how, go to Lab 5 , step 4.

4. A mean value for PW is the one we computed last time: PW=20.9 kg/m/m
Let's see how our optical depth varies with precipitable water.

For what value of PW is the optical depth =2.0?
For what value of PW is the optical depth =8.0?
Define a vector of PW values:
>>PW=[4,8,12,16,20,24,28,32,36,40]
Then use these values to compute a vector of optical depths, tau, as a function of the PW values above.
Plot tau vs. PW.
How does tau vary with PW for the function we are using?

5. Use the radiative eqilibrium function file, Ts_rad

Compute the air temperature at the surface, Ts_re, and the tropospheric lapse rate,gamma_re, for pure radiative equilibrium. (In step 2, above you should have determined what are the input and output data fields for Ts_rad.)
Plot Ts_re versus PW.
Questions:
1. What is the radiative equilibrium temperature for the mean PW based on observations (~20 kg/m/m)?
2. How does this compare to the observed mean surface temperature (given in class and previous labs)?
3. Why do you think they differ from each other? What goes on in the real atmosphere that does not in a pure radiative equilibrium atmosphere? (You might find consulting Figure 7.1 of Wallace and Hobbs helpful.)
4. For what values of PW is the radiative equilibrium temperature below freezing?
Print your plot to a file to save it, as in previous labs.
Plot gamma_re versus PW.
Further questions:
1. Recall the lapse rate separating stable from unstable states for dry convective instability. What range of PW has a lapse rate in radiative equilibrium that is unstable?
2. Unstable lapse rates lead to rising and sinking atmospheric motions. How will such motions alter the actual temperature away from the pure radiative equilibrium temperature?
3. The mean lapse rate in the atmosphere is approximately 6.5 K/km, or 6.5*10**(-3) K/m. What value of PW has this lapse rate?
Print a copy of this plot to another file.

6. Hand in your answers to the questions above to complete this lab.

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