Trying a metric on atmospheric flows

摘要

The definition of a "distance" as given by eq. (5) was obtained by considerations about fluids in local thermal equilibrium and in uniform motion. In spite of this, we have found that it gives reasonable results also in the atmosphere. More specifically: 1) Even in the jet regions, the kinetic-energy term is, at most (remember that some density fluctuations have been neglected by taking isobaric coordinates),10 times larger than the other contributions. 2) The magnitude of the wind and temperature terms are of the same order on the 850 hPa level over the whole globe. The level on which the wind contribution is more dominant is the 250 hPa surface. 3) Extra-tropical regions contribute, per unit area, approximately 5 times the contribution of tropical ones. If one uses the geopotential-height measure then this difference grows to become a factor of approximately 25, i.e., the geopotential measure gives an overwhelming weight to the extrotropical regions. We have extended the distance definition by including humidity. It turned out that this variable gives a contribution comparable to the temperature terms only in the lower tropical atmosphere; this agrees with one's expectations. We performed other checks, like searching best analogues in the record available to us. For more details, please refer to [[10]]. As already mentioned, we are developing the metric generated by non-uniform flows, i.e., with gradients in the density, temperature and velocity.