Meteorology 301 - Lab 7

Introduction

GOAL: Understand how PW varies with surface temperature and surface relative humidity.

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

3. First re-verify that the script prec_wat.m you created in Lab 6 works. If you know already that it is not working, see me. Otherwise, enter:

• Set up the input variables. For our lapse rate, we again use the standard atmosphere; for our surface temperature, we again use the global average values.
  >>N=51
  >>Dz=200
  >>Ts=288
  >>gamma=6.5e-3
  

• We again use representative values of surface relative humidity and its rate of change withh height
  >>RHs=0.80
  >>dRHdz=-0.4/10000
  (Note the minus sign and that the denominator in the last line is ten thousand. This tells us that RH decreases by 40 percentage points in 10,000 meters, or 10 km.)

• Compute temperature (TEM), pressure (PR), relative humidity (RH), and specific humidity (q) as functions of height, using the Main.m function:
  >>[z,TEM,PR,RH,q]=Main(N,Dz,Ts,RHs,gamma,dRHdz)
  Note that the output quantities are all contained within the square brackets, [ ].

• Compute precipitable water (PW) from the specific humidity distribution in height, using the script you wrote for Lab 6:
  >>PW=prec_wat(N,PR,q)
  You should again get an answer back of 20.8936, or something very close to that.

4. Now let's see how PW varies with surface temperature.

• Assign an array of values to a surface temperature variable:
  >>Tsdat=[200,220,240,260,280,300]
  
  
• Compute PW for several choices of surface temperature.
  • For what (approximate) Ts is PW=2?
  • For what (approximate) Ts is PW=200?

• Use them to obtain an array of PW values by invoking Main and prec_wat 6 times in sequence:
  >>[z,TEM,PR,RH,q]=Main(N,Dz,Tsdat(1),RHs,gamma,dRHdz)
  >>PWdat(1)=prec_wat(N,PR,q)
  >>[z,TEM,PR,RH,q]=Main(N,Dz,Tsdat(2),RHs,gamma,dRHdz)
  >>PWdat(2)=prec_wat(N,PR,q)
  .
  .
  .
  >>[z,TEM,PR,RH,q]=Main(N,Dz,Tsdat(6),RHs,gamma,dRHdz)
  >>PWdat(6)=prec_wat(N,PR,q)
  

EXTRA CREDIT - Write a program (".m" file) to do this (Step 4) for you and email it to me and the TA (Eric)

• Plot PWdat vs. Tsdat and answer this question:
  Why does PW increase so rapidly with Ts? (Hint: Think about how saturation specific humidity changes with temperature.)

• Print a copy of your plot to turn in with your lab answers.

5. Now let's see how PW varies with surface relative humidity.

• Compute PW for several choices of RH.
  
  • For what (approximate) RH is PW=2?
  
  
• Assign an array of values to a surface relative humidity variable:
  >>RHsdat=[0.0,0.2,0.4,0.6,0.8,1.0]

• Use them to obtain an array of PW values by invoking Main and prec_wat in sequence 6 times:
  >>[z,TEM,PR,RH,q]=Main(N,Dz,Ts,RHsdat(1),gamma,dRHdz)
  >>PWdat(1)=prec_wat(N,PR,q)
  >>[z,TEM,PR,RH,q]=Main(N,Dz,Ts,RHsdat(2),gamma,dRHdz)
  >>PWdat(2)=prec_wat(N,PR,q)
  .
  .
  .
  >>[z,TEM,PR,RH,q]=Main(N,Dz,Ts,RHsdat(6),gamma,dRHdz)
  >>PWdat(6)=prec_wat(N,PR,q)
  

EXTRA CREDIT - Write a program (".m" file) to do this (Step 5) for you and email it to me and the TA (Eric).

• Plot PWdat vs. RHsdat and answer these questions:
  How does PW change with RHs? Why is this reasonable? (Hint: Think about how specific humidity changes with relative humidity.)

• Print a copy of your plot to turn in with your lab answers.

6. You should turn in to me the answers to your questions along with a printed copy of your plots.

If you do the extra credit, you should email me a copy of the ".m" files you create. Doing both extra credits correctly will double your score on this lab!

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