  The physics of planetary climate features a variety of complex systems that
are challenging to model as they feature turbulent flows. A key example is the
heat flux from the upper ocean to the underside of sea ice which provides a key
contribution to the evolution of the Arctic sea ice cover. Here, we develop a
model of the turbulent ice-ocean heat flux using coupled ordinary stochastic
differential equations to model fluctuations in the vertical velocity and
temperature in the Arctic mixed layer. All the parameters in the model are
determined from observational data. A detailed comparison between the model
results and measurements made during the Surface Heat Budget of the Arctic
Ocean (SHEBA) project reveals that the model is able to capture the probability
density functions (PDFs) of velocity, temperature and heat flux fluctuations.
Furthermore, we show that the temperature in the upper layer of the Arctic
ocean can be treated as a passive scalar during the whole year of SHEBA
measurements. The stochastic model developed here provides a computationally
inexpensive way to compute an observationally consistent PDF of this heat flux,
and has implications for its parametrization in regional and global climate
models.
