Weather and Climate Forecasting as Problems in Hydrodynamics

Abstract

Prediction equations for complicated hydrodynamic flows are examined in a critical and didactic manner. The conventions adopted in the derivation of the Navier-Stokes equation from kinetic theory are shown to imply progressive error in prediction. Time averages, space averages (including spectral decompositions) and ensemble averages of the Navier-Stokes equation me discussed in turn and it is shown in each case that the open set of equations which is usually quoted as the result of the averaging process is valid only in the meteorologically trival circumstance of statistically stationary and homogeneous flow. It is further shown that procedures, other than those purely empirical, for approximate closure of these sets of equations also Presume stationary homogeneous flow. The only logically valid prediction with the types of equation now used in meteorological practice is one of no change. Prediction equations ostensibly based on dynamics are empirical and must be validated empirically. If climatic predictions cannot be validated against the historical record (which, in general, is insufficiently long or Insufficiently detailed), they must be validated as they am applied. There is no reason to expect performance superior to that of statistical or other empirical techniques.