Coherence in Statistical and Physical Processes

  We all know how variable the weather from time to time and from place to place and the global means reflect this to a smaller extent. Thermodynamics and Statistical Mechanics tell us that a large physical system can experience fluctuations from its equilibrium state. The Earth's weather also has seasonal variations due to the inclination of the Earth relative to its orbit and annual changes in its distance from the Sun. Cloudy weather can block the amount of sunlight that a location can receive throughout the year. The Earth's rotation produces a daily cycle of heating and cooling. Consequentially the Earth's weather is in a constant state of flux. There may be some coherence between one location and another nearby but there is no guarantee that this is so for large separations of time and space. There are statistical and physical processes for which the mean and variation of a distribution vary with time and there is no long term pattern to observations. We can check to see if there is a "coherence time" for the global anomalies and the test that we designed for predictions might be useful for this. I have put together a list of readings that might help to give another view on global warming along with two references on statistics.

Cyclostationary process

Stationary process

Thermal fluctuations

Gaussian noise

Ornstein-Uhlenbeck process

An Introduction to Scientific Research - Wilson

The Statistical Analysis of Experimental Data - Mandel