The Fundamental Theorems of Atmospheric Science (Invited Presentation)

The goal of atmospheric science is to understand and predict the evolution of atmospheric flow and phenomena by taking advantage of empirical knowledge derived from observation and by deducing theorems from axioms. If we accept some form of the atmospheric equations of motion as the basic axioms describing atmospheric thermodynamics and flow, then we can deduce theorems mathematically and generate empirical information with computer simulations that are representing the actual phenomena with gradually improving verisimilitude. The fundamental theorems include assertions that temperature gradients are the basic cause of atmospheric motion, that total energy is bounded for all time, that entropy is decreased when temperature gradients are amplified by differential heating, and that nonlinear flows are required to transfer heat poleward. In quasi-geostrophic flow, mean square vorticity is also conserved, thereby creating constraints on the direction that energy can flow from one wavelength to another and ordaining that the phase-space trajectories of spectral representations of atmospheric flow will eventually be trapped in a specific ball in phase space, with all initial sets converging asymptotically to phase-space sets of zero volume. Chaos today is a child of the computer age, rediscovered by the late Prof E. N. Lorenz (now a half-century ago!), with profound implications for predictability. But we find that its consequences can be mitigated with three strategies. First, we link atmospheric flow with the ocean and land surface that have greater thermal mass and slower variations. Second, we compute many simultaneous forecasts to produce probability distributions that indicate confidence. And third, we achieve predictive skill (with appropriate definitions) by using temporal averages commensurate with length of lead: averages over weeks for leads of weeks, over months for months, over seasons for seasons … . Attempting to formulate a theorem corresponding to this empirical result might suggest definitions and strategies that would improve understanding and prediction even if a proof remained elusive.