Chaotic uncertainty and statistical inference for natural chaotic systems: Choosing predictors for multiple season ahead prediction of precipitation, Extended and Annotated

Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In such systems the chaoticity, amplifying error exponentially fast, is so confounded with the boundary condition fluctuations and the measurement error, that it is impossible to consistently estimate the trajectory of the system much less predict it. Although asymptotic theory exists for estimating the conditional predictive distributions, it is hard to find where this theory has been applied. Here the theory is reviewed, and applied to identifying useful predictive variables for simultaneous multiseason prediction of precipitation with potentially useful updating possible. This is done at two locations, one midocean the other landlocked. The method appears to show promise for fast exploration of variables for multiseason prediction.