An observation $($by conventional sounding$)$ of temperature as a function of pressure was made at a

meteorological station. The text file, $$gefd$2024\_$hw$3\_$data.txt$,$ contains the data. A matlab code for

reading the data is given in the Appendix. The code and data will be posted separately. The first record

in the data $($p $=926\mathrm{.}0$ mb$,$ T $=5\mathrm{.}9\backslash$deg C$)$ is the measurement taken at the surface. The elevation of the

station is $650$ m$.($At the surface, the height is already z $=650$ m$.)$

$($a$)$ From the data, calculate and plot the vertical profiles of pressure $($p$),$ temperature $($T$),$ density $(),$

and potential temperature $(\backslash$theta $,$ using ps $=926\mathrm{.}0$ mb as the reference pressure$)$ as a function of height. If

tropopause is defined as the location with the minimum of temperature, what is the height $($in meters$)$

of the tropopause for this observed profile?

$($b$)$ Calculate and plot the vertical profile of the lapse rate of temperature, $\backslash$Gamma $$ dT$/$dz$,$ as a function of

height. Compare it to the dry adiabatic lapse rate, $\backslash$Gamma d $$ g$/$cp$,$ and use this as the basis to discuss the

$($dry$)$ static stability of the atmospheric column. $($Your result here should be consistent with the plot of

$\backslash$theta $($z$)$ from Part $($a$).$ Note that the stability criterion, $\backslash$Gamma $<\backslash$Gamma d$,$ is equivalent to d$\backslash$theta $/$dz $>0.)$

Appendix: How to read the data for Problem $1$

The data file, $$gefd$2024\_$hw$3\_$data.txt$,$ is in plain text and consists of two columns for pressure $($in

mb$)$ and temperature $($in $\backslash$deg C$).$ The following matlab code, also posted separately, can be used to read

the data into two arrays, p and T$,$ each with $143$ elements. The first pair of records, $($p$(1),$ T$(1)),$ are the

pressure and temperature at the lowest elevation $($or highest pressure$),$ which is the surface. As a quick

reference, the matlab code also plots T as a function of p$,$ as shown in the next page.

clear

fid$1=$ fopen$(\text{'}$gefd$2024\_$hw$3\_$data.txt$\text{'},\text{'}$r$\text{'})$;

for n $=1$:$143$

p$($n$)=$ fscanf$($fid$1,\text{'}\%$f$7\mathrm{.}1\text{'})$;

T$($n$)=$ fscanf$($fid$1,\text{'}\%$f$7\mathrm{.}1\text{'})$;

end

fclose$($fid$1)$;

plot$($T$,$p$,\text{'}$r$-\text{'},$'LineWidth',$2)$

axis$([-802001000])$

xlabel$(\text{'}$T$($p$)(\backslash$circC$)\text{'})$; ylabel$(\text{'}$p $($mb$)\text{'})$

set$($gca$,$'YDir','reverse'$)$