Computational Modelling Group

Using MEP to determine parameter values of ocean and atmosphere diffusivity

1st June 2011
30th September 2011
Research Team
Maike Sonnewald
Kevin Oliver, James Dyke

The internal entropy production landscape varying kOcean and kAtm. . Note the clearly domed but smooth nature of the landscape. The black dot represents the MEP maxima, while the blue dot represents the empirical value.

Entropy budgets can potentially offer new and valuable insights into the dissipation of energy in the ocean system. Specifically, if one assumes the Earth system maximises the dissipation of energy, one can use this as a guiding principle maximising the internal entropy production. In this study, resultant temperature distributions from a four box ocean-atmosphere-ice model are used to assess to what extent such considerations could ameliorate the need for tuning parameter values associated with oceanic and atmospheric diffusivity. Results from a standard implementation with fixed, empirically determined, parameters were compared to one where the maximum entropy production principle is applied to determine the value of oceanic and atmospheric diffusivity parameters. These methods have been successfully applied to cloud fraction and convection in the atmosphere.

The MEP principle suggested using diffusivity values of 3.3×1014 W K −1 and 3.2×1014 W K −1
for the ocean and atmosphere respectively, where the empirical values were 2.0 × 1014 W K −1
and 1.0 × 1014 W K −1 . The oceanic temperatures of the MEP implementation were 3 and -1oC
away the high and low latitude observed ocean temperatures respectively, while the empirical
implementation was -5 and 3oC away, largely within the observational standard deviation of
8 and 2◦ C respectively. For the atmospheric values, MEP implementation was 3W m−2 away
from the high latitude observed value, while the empirical implementation was 6W m−2 away,
both within the standard deviation of 13.2W m−2 . However, in the low latitudes this reverses,
with the empirical implementation being only -16W m−2 off while the MEP implementation
is -21W m−2 off. However, both figures are outside the range of the standard deviation of
4.2W m−2 . Overall, both methods were found to be very close to oceanic observations. This
confirms that in the model used, the assumption of maximal dissipation of energy is reasonable.

Furthermore, the nature of the landscape of internal entropy production created by the
oceanic and atmospheric diffusivity was found to be fairly smooth, with non-linearities mainly
coming from ice albedo. Assuming the Earth system is in a state of maximal energy dissipa-
tion, applying the MEP principle successfully may depend on such a smooth, easily optimisable
landscape. Thus, the successful application of the MEP principle could be much more difficult
if attempting to aid parametrisation in more detailed ocean models, as these are likely to have
internal entropy production landscapes with local maxima. Nevertheless, results presented
are very promising, and encourage further exploration of to what extent this principle could
be applied to ameliorate the need for tuning parameters in light of lacking information.


Physical Systems and Engineering simulation: Climate, Diffusion, Earth surface dynamics, Energy, Oceanography

Programming languages and libraries: Mathematica

Computational platforms: Linux

Transdisciplinary tags: Complex Systems