For independent first-order sinks acting on the same well-mixed burden, loss frequencies add:
The fraction converted to sulfate before removal by the competing direct-deposition sink is
The individual event fractions are for direct sulfur dioxide deposition, for cloud oxidation and for hydroxyl radical oxidation. These are branching fractions for the sulfur dioxide fate; sulfate formed by oxidation can subsequently be deposited as well. The argument assumes the supplied channel lifetimes are compatible effective first-order rates, not residence times of isolated air masses that never exchange.

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