The barometers used in flight controllers for multicopters and other hobby grade UAVs can be (AFAIK) precise to about ten centimeters variation in height. They are probably using more modern (and less tested) technology than ones used in airliners… besides I don’t think you’d need precision to the tenth of a meter to fly a big bird.
Survey equipment is available for rent.
(I hope the rest of my post isn’t against forum rules. If it is, please remove following and accept my apology in advance.)
Surveying Equipment Rentals from Duncan-Parnell
http://www.duncan-parnell.com/surveying-mapping/Rentals.html
Trimble S6 Total Station Series
http://www.duncan-parnell.com/surveying-mapping/Trimble-S6-Total-Station-Series-plu23882.html
GeoExplorer 6000 Series
http://www.duncan-parnell.com/surveying-mapping/GeoExplorer-6000-Series-pluTrimble_89000-01.html
The usual way is with a level and Philadelphia rod- they’ll actually give you the actual elevation difference, while a transit or a theodolite will just measure an angle for you, and you’ll have to do other distance measurements and trigonometry to figure out your elevation.
Home depot has a Lufkin 1/2" x 200 ft Hi-Viz Orange Fiberglass Tape Measure for $27 and a CST/Berger Pro-Series Zip-Line 200 ft. PVC Coated Fiberglass Tape, also for $27.
You could also use a 3 in. Aluminum Line Level ($4) and a low stretch cord or a Empire True Blue Digital Laser Level ($160) to find the horizontal.
You could buy or make a hypsometer, which is basically a long stick, or pipe, which is alternately colored every inch (white, red, white, red).
Measure the distance from the deck top to the low point in your yard. Measure the distance from the deck to the horizontal point directly above the low point or the distance from the low point to the horizontal point on the hypsometer.
Then it just a matter of a(square) + b(square) = c(square).
That’s correct. One that I have direct experience with is the Bosch BMP085. Although the absolute pressure accuracy is not that great (~1 hPa, which corresponds to ~7 m), it has much greater resolution than that. At its highest resolution setting, it has about 0.03 hPa RMS noise, which is about 20 cm. The noise is well distributed, so that you can average together even more samples for greater accuracy. At 10 Hz sample rate you get ~10 cm precision.
Interesting - what do they cost?
Really cheap. Mine was a part of a 10 degree-of-freedom integrated sensor kit, very much like this one. That unit has 3-axis accelerometer, gyro, and magnetometer as well as barometer (it uses the BMP180, which AFAIK is just a slightly newer model of the BMP085). All for $10 and using a simple I2C interface.
The iPhone 6 uses a Bosch BMP282, reportedly an Apple-specific variant of the BMP280, itself the successor to the BMP180.
http://www.bosch-sensortec.com/en/homepage/products_3/environmental_sensors_1/bmp280/bmp280