Except for the fact that he apparently relies on Jewell triggers,
(I hate 'em) Timber338 offers some very good insight and obviously has experience shooting over canyons. It's called a hunt, and not a "shoot", for the very good reason that we don't venture out into the wilderness and just shoot something. The two tools that may help you most in setting up a shot across and canyon are a VERY GOOD range finder and VERY GOOD binoculars. IMO, accurately judging wind speed is secondary to judging wind direction when your faced with a shot across a canyon.
Compare the leaf movement (or whatever active vegetation you have) on your side of the void with the movements of similar vegetation on the other side. How do they compare? Sometimes their speed and direction essentially cancel each other. Also understand that, as the wind passes along the edges of the canyon it can develop eddies that raise havoc with an otherwise well placed shot.
With a shot across a canyon you probably have quite a lot of time to weigh the variables, check your dope sheet(s), and come up with a good solution. The wind currents most often neglected in my experience are the eddies and those that move upward. Even over relatively flat terrain (Wyoming prairies) the wind gains speed as it rolls over the raised portions of the gently rolling terrain.
One last thought - before you take the shot, remember that you will have to find a way to get to the other side of that canyon, field dress and pack out the game, and arrive home safely. It's OK to pass up a shot that isn't right for the circumstances.
No offense Timber338. Just couldn't pass up the opportunity. I likewise wish you good hunting and safe passage.
I have a great woman, fantastic kids, a warm place to sleep and an accurate rifle. Life is good ..............
Hunter Safety Instructor - California Hunter Safety Meritorious Service 1971 - 1972. Rifle/Pistol Marksmanship Instructor - NRA Life Member
American rifleman's triad - God, guts and guns. It built America and it'll preserve America. Abandon one and you lose them all.