I live in Phoenix, AZ and I was able to do a couple things to maintain humidity in a glass tank without the drastic drops you are experiencing.
1) Switch to Eco-Earth as your substrate, does a wonderful job holding humidity.
2) Insulate your tank. I used the stuff below, I only put it on the bottom of the enclosure. With this same material, I also cut out a cardboard box that would fit perfectly on the cool side of the tank, then took two pieces of insulation on each side of the cut out, and tapped it with foil tape.
3) Make sure you have an accurate hydrometer. I recommend the below along with a test kit to calibrate the meter if need be. Don't use the adhesive attachment though that comes with it, use a glue gun to adhere it.
4) Make sure if your using a heat lamp, put it on a dimmer or a thermostat if you can. I ran a Herpstat 2, one probe for my UTH and another probe for my lamp. This will prevent your lamp from running full power 24/7.
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