27
statistical significance of the more specialized "signal" in relation to the
background space-time variability. With certain notable exceptions such
as the annual march, the more specialized the conceptual model (e.g., the
more periodic or the more step-like), the smaller the fraction of the variance of the climate record that it is likely to be able to account for and
the more difficult the task of establishing the statistical significance of the
products of the analysis. For example, it is easier to determine the variance
or skewness of a time series than to determine whether its PDF is unimodal
or multi-modal; it is easier to determine the degree of redness of a time
series than to determine in detail the shape of its power spectrum. Unless
the period of record can be made arbitrarily long, the investigator is bound
to be faced with a tradeoff between quantity (or degree of refinement) and
quality (i.e., statistical significance) of the statistical information that can
be derived from the analysis.
Regardless of the phenomenon under investigation, the simpler and more
straightforward the analysis scheme used in presenting the results, the more
convincing the presentation and the broader the audience it can reach. I
am convinced that the climate 'signals' of primary importance for prediction, detection of global climate change, and elucidation of how the
climate system works should be visible to the naked eye in time series,
time sections, and/or animations of data that have been subjected to only
a minimal amount of processing. The more sophisticated analysis tools
can sometimes provide useful guidance as to what parameters or combinations of parameters reveal a particular climate signal most clearly, but
once that determination has been made, it should be possible to revert to
simpler and more widely used tools to communicate the new results to the
scientific public.
In exploratory climate diagnostics, the assessment of statistical significance is often a more formidable task than it might appear, because of the
a posteriori character of the results (i.e., the fact that the form of whatever
space-time structures emerge from the analysis was not predicted beforehand). For example, suppose that a single narrow spectral peak is identified
in an exploratory POP's or singular spectrum analysis, whose frequency
was not predicted beforehand. In this case it is necessary to assess the
probability that a peak of the observed amplitude could have occurred by
chance, not at some specified frequency, as in the conventional 'cookbook'
formula, but in any frequency band of comparable width within the entire
spectrum (e.g., see Madden and Julian 1972). If the newly discovered peak
statistical significance of the more specialized "signal" in relation to the
background space-time variability. With certain notable exceptions such
as the annual march, the more specialized the conceptual model (e.g., the
more periodic or the more step-like), the smaller the fraction of the variance of the climate record that it is likely to be able to account for and
the more difficult the task of establishing the statistical significance of the
products of the analysis. For example, it is easier to determine the variance
or skewness of a time series than to determine whether its PDF is unimodal
or multi-modal; it is easier to determine the degree of redness of a time
series than to determine in detail the shape of its power spectrum. Unless
the period of record can be made arbitrarily long, the investigator is bound
to be faced with a tradeoff between quantity (or degree of refinement) and
quality (i.e., statistical significance) of the statistical information that can
be derived from the analysis.
Regardless of the phenomenon under investigation, the simpler and more
straightforward the analysis scheme used in presenting the results, the more
convincing the presentation and the broader the audience it can reach. I
am convinced that the climate 'signals' of primary importance for prediction, detection of global climate change, and elucidation of how the
climate system works should be visible to the naked eye in time series,
time sections, and/or animations of data that have been subjected to only
a minimal amount of processing. The more sophisticated analysis tools
can sometimes provide useful guidance as to what parameters or combinations of parameters reveal a particular climate signal most clearly, but
once that determination has been made, it should be possible to revert to
simpler and more widely used tools to communicate the new results to the
scientific public.
In exploratory climate diagnostics, the assessment of statistical significance is often a more formidable task than it might appear, because of the
a posteriori character of the results (i.e., the fact that the form of whatever
space-time structures emerge from the analysis was not predicted beforehand). For example, suppose that a single narrow spectral peak is identified
in an exploratory POP's or singular spectrum analysis, whose frequency
was not predicted beforehand. In this case it is necessary to assess the
probability that a peak of the observed amplitude could have occurred by
chance, not at some specified frequency, as in the conventional 'cookbook'
formula, but in any frequency band of comparable width within the entire
spectrum (e.g., see Madden and Julian 1972). If the newly discovered peak