Lakegeezer has the general formula. That's under normal conditions, a typical fair weather day with warmest air near the ground and cooler as you go up.
Apart from that, this is New England which means there is no formula! I say this with laughter but it's true. We get those days when the "Basic Physics" textbook is right (usually when nothing is happening,) but it seems every time a storm comes, its prediction requires breaking out the "Advanced Physics" textbook. A certain percentage of those storms require changing the textbook for a blank notebook + pen. Those are the days when God looks at the wee professors and says "Ok listen up people!!!"
Every time I travel far away I see more "Basic Physics" days than anything else. Then as I get close to New England on the way home I can often hear a certain heavenly voice ahead in the distance saying, "okay listen up people!"
To get an idea of how varied our vertical temp profile can be in New England, go to the
Mount Washington Observatory site (look for the Auto Road temp profile) or the
AIRMAP site on a regular basis just to see what the temps are, at different altitudes.
On at least a couple of occasions I've climbed Mt. Washington in winter, starting off in the cold, finding above-freezing temps at mid-mountain, and arriving at the summit to find the same temperature as at the base. One time, as a blizzard was clearing, we went
above the clouds at 4,000 feet and arrived at the summit to find warmer temps than at the base. Most winter storms DON'T do that... but that one did. The models had a good handle on it, so we were actually expecting it (but ready to turn back, just in case.) Weather around here can be so outside-the-box!
One thing the forecasters at the NWS said in their discussion yesterday was that the situation coming up this weekend (I'll spare you the technical terms) has a long track record of confusing the living daylights out of computer models and human forecasters. It doesn't have to mean the storm will be powerful, just complicated from a forecaster's perspective (or as a surgeon would say sometimes the smallest operations end up causing them the biggest headaches... same thing.) Whenever that happens it means it's time to consult your great-grandfather's farm journal for advice on predicting it. And all the while, those poor TV guys still have to smile like flight attendants and act like they have it all figured out.
Here's the storm as depicted on the Thursday night watch & warning map. Look at how many different types of weather there are! And a few of them aren't even supposed to be where they are in mid-April. The blue and red boxes are severe thunderstorm and tornado watch boxes. Everything else is in the map legend.
Keeper, are you with the DES dam operations?