What do you sugges? t that I go on roof, which I can reach by way of a second story deck, and put on a tarp? If I do this, how do I make the tarp leak proof while I decide how to fix to the roof itsel?
You're going to have to remove the deck to even see the roof and determine WHY it's leaking. chances are likely the roof was not designed for the deck and the deck was not designed for a roof. I see commonly people throwing on the cheapest roof, especially in new construction, then throwing on the cheapest deck. You can see how that's a recipe for an expensive disaster. Learn more about roof decks: Chicago Roof Decks: What You Need to Know.
You can try tarping it, but not likely that'll help unless you have a large tarp that can cover the whole roof and some how be secured at the walls. Otherwise water will get in around the tarp and will lea anyways. Maybe leak less, but still will leak.
Start removing deck boards in the general area of where you think the leak is. Keep in mind if the roof is multiple leayers the leak can be originating elsewhere on the roof and it'll be a bear to find. Especially examine the seams, penetrations (pipes) and points of contact where the deck makes contact with the roof. These will be the most obvious areas where leaks may occur.
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