Area-depth formulas, expressing average precipitation over an area as a function of the area, have been proposed by half a dozen investigators in as many forms, involving the ¼, 0.4, 0.5, 0.6, or other powers of the area, its logarithm, or its exponential. Comparison of these formulas reveals unsuspected similarities as well as restrictions.
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Arnold Court (1961) studied this question.
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