Use seawater specific heat capacity , which is an additional standard material approximation: the paper supplies the ice heat capacity, not the seawater heat capacity. Relative to freezing, the assumed uniform column has . Its ocean heat content per horizontal area isThis is heat above the reference freezing state, not the absolute internal energy of seawater.
If all this heat reaches ice already at its fusion temperature, divide by the supplied latent heat:For a chosen ice mass density , this corresponds to about of ice. Density was not specified for this conversion, so the mass per area is the result that needs no further ice-density assumption.
Cold ice must first be warmed. If its initial temperature is , the corresponding ideal melt mass is , using the supplied ice specific heat capacity . No initial ice temperature or salinity-dependent fusion temperature is supplied. The latent-only result is therefore an upper bound; actual melting is smaller when sensible warming, ocean or atmospheric losses and incomplete heat transfer matter.
Solar geometry must be included before multiplying by the summer duration. Let , solar declination , and hour angle , measured from local noon. The cosine of solar zenith angle isOnly positive values receive sunlight. Integrating through a day gives the daily mean solar irradiance at the top of the atmosphere:with clipped to for polar day and to zero for polar night. At the solstice, for example, polar-day averaging gives . It would be wrong to apply continuously to a horizontal surface.
A simple seasonal approximation , with calendar day , gives a June–August daily-mean average of about . There are 92 days. With surface albedo , the no-atmosphere absorbed-solar ceiling isThis calculation neglects the small seasonal change in Earth-Sun distance. The ceiling is larger than the required in part (i), so geometry alone does not make a uniform column impossible.
A reasonable conditional estimate includes an effective atmospheric short-wave transmission and net non-solar loss :before adding advection or subtracting ice melting. The parameters are scenario assumptions, not measurements supplied by the question. For example, gives before other losses, barely enough; with a modest mean loss of , the retained amount is only . That would raise a uniform 50 m column from freezing by about , reaching roughly . With no other losses the transmission required for is ; with that illustrative loss it rises to about . Clouds, emitted thermal radiation, evaporation, transfer to colder water and melting all affect the balance.
The satellite surface temperature is insufficient evidence for a seabed. A warm, shallow ocean mixed layer can overlie colder water because meltwater and salinity maintain stable density stratification. Heating only the upper 10 m through costs , much less than heating all 50 m. Warm Pacific-water advection can also raise surface temperature or supply additional heat. If measured net solar input were too small for full-depth warming, shallow surface heating would be the natural alternative; if mixing and additional heat supply were strong enough, full-depth warming remains possible. The missing transmission, loss, mixing and inflow information prevents a unique yes-or-no conclusion from the supplied surface observation.
Articles by others on the same topic
There are currently no matching articles.