Rapid dynamic changes at the margins of the Greenland Ice Sheet, synchronous with ocean warming, have raised concern that tidewater glaciers can respond sensitively to ocean forcing. Understanding of the processes encompassing ocean forcing nevertheless remains embryonic. The authors use buoyant plume theory to study the dynamics of proglacial discharge plumes arising from the emergence of subglacial discharge into a fjord at the grounding line of a tidewater glacier, deriving scalings for the induced submarine melting. Focusing on the parameter space relevant for high discharge tidewater glaciers, the authors suggest that in an unstratified fjord the often-quoted relationship between total submarine melt volume and subglacial discharge raised to the ⅓ power is appropriate regardless of plume geometry, provided discharge lies below a critical value. In these cases it is then possible to formulate a simple equation estimating total submarine melt volume as a function of discharge, fjord temperature, and calving front height. However, once linear stratification is introduced—as may be more relevant for fjords in Greenland—the total melt rate discharge exponent may be as large as ¾ (⅔) for a point (line) source plume and display more complexity. The scalings provide a guide for more advanced numerical models, inform understanding of the processes encompassing ocean forcing, and facilitate assessment of the variability in submarine melting both in recent decades and under projected atmospheric and oceanic warming.
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