Statistical Field Significance and its Determination by Monte Carlo Techniques

The effects of number and interdependence in evaluating the collective significance of finite sets of statistics are frequently non-trivial, especially for spatial networks of time-averaged meteorological data. These effects can be taken into account in two steps: By first prescreening for significance assuming data independence and then, if necessary, by taking into consideration dependence through the use of estimated effective degrees of freedom and the binomial distribution or, failing that, Monte Carlo simulation. Seasonal averages of 700 mb height data are used to illustrate the problem and to demonstrate how the data set properties are taken into account. Papers by Hancock and Yarger (1979), Nastrom and Belmont (1980) and Williams (1980) are critically examined in light of these considerations and Monte Carlo strategies for clarification of ambiguities suggested.