We thank Peter Bechthold, Roberto Buizza, and Martin Miller for many inspiring discussions and helpful suggestions throughout the duration of this work. Mark Rodwell is acknowledged for his rainfall verification software, which was used for the results in section 4g. Rich Rotunno and Andy Brown are thanked for their insightful comments on earlier versions of this manuscript. We are indebted to Ceçile Penland and an anonymous reviewer for their thoughtful reviews.
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