hm8 Posted January 30, 2013 Share Posted January 30, 2013 So I'm having trouble with this homework problem... Calculate the 1000- to 850-hPa thickness for an atmosphere with the constant lapse of Γ = 6.5 K km-1. The temperature and pressure at the surface (z0 = 0 m) are T0 = 273 K and ps = 1000 hPa. I did a couple problems with an isothermal atmosphere fine...but I can't seem to figure out how to incorporate a lapse rate into the equation correctly. Thickness = (Rd/g)* ∫(T/P)*dPSo when I plug in the lapse rate (Γ) I getThickness = (Rd/g)* ∫[(T0 - Γz)/P]*dPBut then I have that z variable in there, and I'm not sure how to change it to P so I can integrate Link to comment Share on other sites More sharing options...
ohleary Posted January 31, 2013 Share Posted January 31, 2013 So I'm having trouble with this homework problem... Calculate the 1000- to 850-hPa thickness for an atmosphere with the constant lapse of Γ = 6.5 K km-1. The temperature and pressure at the surface (z0 = 0 m) are T0 = 273 K and ps = 1000 hPa. I did a couple problems with an isothermal atmosphere fine...but I can't seem to figure out how to incorporate a lapse rate into the equation correctly. Thickness = (Rd/g)* ∫(T/P)*dP So when I plug in the lapse rate (Γ) I get Thickness = (Rd/g)* ∫[(T0 - Γz)/P]*dP But then I have that z variable in there, and I'm not sure how to change it to P so I can integrate Slide 10 may help: web.missouri.edu/~lupoa/atms4310lab5.ppt Link to comment Share on other sites More sharing options...
H2Otown_WX Posted February 1, 2013 Share Posted February 1, 2013 So I'm having trouble with this homework problem... Calculate the 1000- to 850-hPa thickness for an atmosphere with the constant lapse of Γ = 6.5 K km-1. The temperature and pressure at the surface (z0 = 0 m) are T0 = 273 K and ps = 1000 hPa. I did a couple problems with an isothermal atmosphere fine...but I can't seem to figure out how to incorporate a lapse rate into the equation correctly. Thickness = (Rd/g)* ∫(T/P)*dP So when I plug in the lapse rate (Γ) I get Thickness = (Rd/g)* ∫[(T0 - Γz)/P]*dP But then I have that z variable in there, and I'm not sure how to change it to P so I can integrate This might not be the most realistic way of doing this, but you could plot your temperature profile on a skew-T and then use the method of equal areas to find a mean temperature of the layer. Then that way temperature isn't a variable anymore. You would make T - the lapse rate a constant that you can therefore pull out of the integral. Then you just have to integrate (1/P)dP. Link to comment Share on other sites More sharing options...
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