NONLINEARITY, WEATHER PREDICTION, AND CLIMATE DEDUCTION.
Final rept. Mar 63-Feb 66,
MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF METEOROLOGY AND PHYSICAL OCEANOG RAPHY
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The equations governing the atmosphere are nonlinear. Weather prediction is identified with determining particular solutions of these equations, while climate deduction is identified with determining statistics of the general solution. The nonperiodicity gives rise to small-scale motions and nonperiodicity. The nonperiodicity makes analytic solution of the equations unfeasible. Particular solutions must therefore be determined numerically, and the small-scale motions cannot be properly included. The range at which accurate detailed forecasts can be produced is thus limited. The nonlinearity also prevents the derivation of closed systems of equations with statistics as unknowns. The statistics must therefore be estimated from particular numerical solutions, which are merely samples. Numerical methods are not required when only upper and lower bounds of the statistics are sought. The need for numerical methods when precise valves are desited is illustrated with a simple quadratic difference equation, while the process of establishing upper and lower bounds is illustrated with a simple partial differential equation. Author
- Numerical Mathematics