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Last autumn I was fortunate enough to visit Jordan - a last minute decision, but I'd never seen the flight prices so low to coincide with my school's October Half Term (I'm a teacher) so jumped on it when I had the chance.
About an hours drive north of Petra is a stunning gorge called Wadi Ghuweir. It begins in what feels very arid, but the further into it you get, the more water there is and bit by bit, it becomes that bit more green until you find yourself in a full blown desert oasis.
We decided to do the hike as a there and back, but you can keep hiking and arrange for transport to take you back to where you parked the car, or do it with a guide as an organised tour. The prices we were being quoted were very expensive, which is why we turned back before the waterfall (which if you jump down, you can't get back up).
There are a small handful of 'tricky' spots within the wadi, requiring a bit of scrambling or climbing, but I expect that if you enjoy hiking, these shouldn't pose too much of a problem.
I've put together a video of our hike - if you choose to watch it, I hope you enjoy it.