Can someone help me answers this question?

Question

Take a parcel of air from the top of Mt. rainier 4,392m (14,410 ft) and follow it to Yakima, WA 325m (1,066ft). Assume the initial conditions of the parcel of air are -10 degree celcius and 100%rh.

What is the initial specific humidity of the parcel?

What will its temp, specific humidity, and relative humidity be in Yakima?

How many degrees warmer is the parcel in Yakima than on top of Mt. Rainier?

Answer 1

There is a formula you use, I believe it's 1 degree increase per 1000ft elevation so in this case it would increase the temp by 13 degrees since your going down instead of up. It's been awhile since I have needed to do this so I'm a bit rusty sorry.

Answer 2

Wow, this is a pretty detailed question and mathematically fairly tricky.  What class is this that you are in???  

There are very specific equations for these answers, especially the humidity questions.  I'm assuming you have them handy in your book or something.  I don't have them handy in front of me but I'm going to try and help.

Specific humidity is in grams/kg of dry air.  It's very close to what is called the mixing ratio which when saturated at -10C = 2.86 hPa (which is proxy for g/kg) (see link).  And mixing ratio is grams of moisture per kg of MOIST air (not dry like specific humidity).  Amount of moisture relative to dry air is tiny, so they are pretty much the same...2.86 g/kg.  I think that should be a good answer, but you could recompute it if you want it out to 3 decimal places:

SH = g_H20/kg dry air

MR = g_H20/(kg dry air+g_H20)

so find equation of MR as a function of SH be recombining.

Then temp decreases 9.8C/1000m.  So it heats up going down the mtn, to approx 4.03*9.8C ~ 40C so -10C goes to +30C.  (9.8C/1000m works out to nearly 5.5F/1000ft)

Now when the parcel goes down the mountain, the specific humidity doesn't change.  It's still the same amount of vapor in the same kilogram of air, even if it's compressed.  The density is higher, but the ratio of vapor to dry air is the same.

But relative humidity has gone down.  Dry air at +30C can hold 42.4 (see link).  The relative humidity is how much moisture in air versus how much moisture the air at 30C can hold.  So it's:

2.86/42.4 (use calculator which I also don't have, but it's around 6%).

And temp in Yakima is about 40C warmer than on top of Mt. Rainier as we found out above.