Answer: According to my calculations, you're applying over 20 gallons of water per day. That's excessive, even for an elm tree! I'd suggest you either replace your 5-gallon emitters with 2 or 3 gallon emitters, and either water every 3 days during the summer months leaving the system on for an hour, or water only 15-30 minutes per day. Either schedule will work so choose the one that's the easiest for you to program on your system. Your soil is clay and will hold lots of moisture, especially if you have weed barrier and gravel, or groundcover over the roots of your tree. With a 15' canopy, you probably should move the emitters back a few feet. Most of the roots will be spread out under the canopy so placing the water source 5-6 feet from the trunk should make the roots happier.
I'm sure you'll see an improvement in your tree's health once the soil dries out a bit.
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