28
occupies only a few percent of the range of frequencies included within the
spectrum, the requirements for establishing the statistical significance of
the peak at a given confidence level will prove to be far more stringent
than in the conventional test. To cite another example, suppose that a
bi-modal probability density function is observed for some prescribed circulation index. If the investigator has explored a number of different ways
of computing the index, and has singled out one variant of the index for
further investigation because it yielded the most convincing evidence of
bi-modality, the significance testing needs to appropriately account for the
manner in which this exploration was conducted, and the sensitivity of
the results to the various permutations of the index that were tried. For
example, if the frequency distributions proved to be highly sensitive to the
exact definition of the index, and "significant" bi-modality, say at the 5%
confidence level in the conventional a priori sense, were found for only one
of five variants of the index that were explored, then the probability that
the reported bi-modality could have occurred by chance would actually
be closer to 25%. Even the most sophisticated formal significance tests
are bound to overestimate the significance of the results unless they are
conducted in the proper context, with due regard for what was, as well as
what was not predicted beforehand, as well as any voluntary choices in the
analysis procedure that might have served to enhance the apparent significance of the results (regardless of how those choices might be justified
after the fact). The assessment of statistical significance of regime shifts
and unprecedented events in a time series of limited duration is particularly
problematical in view of the inherent nonstationarity of most climatic time
series and the a posteriori flavour of any statistic that involves a prescribed
sampling interval, type of event, or specially designed index.
Access to and familiarity with a wide range of climate data sets is essential if an investigator is to have any hope of exploring the multi-dimensional
phase space in which the more important climate signals reside. Among
the most important functions of national and international climate programs is the dissemination of the more fundamental climate datasets in
easily accessible formats.
In this chapter we have managed to avoid the issue of spatial structure
by confining our attention to phenomena that can be represented by just
a few time series or, in the case of Fig. 10, averages over an ensemble of
time series. The next chapter is largely devoted to this topic.
occupies only a few percent of the range of frequencies included within the
spectrum, the requirements for establishing the statistical significance of
the peak at a given confidence level will prove to be far more stringent
than in the conventional test. To cite another example, suppose that a
bi-modal probability density function is observed for some prescribed circulation index. If the investigator has explored a number of different ways
of computing the index, and has singled out one variant of the index for
further investigation because it yielded the most convincing evidence of
bi-modality, the significance testing needs to appropriately account for the
manner in which this exploration was conducted, and the sensitivity of
the results to the various permutations of the index that were tried. For
example, if the frequency distributions proved to be highly sensitive to the
exact definition of the index, and "significant" bi-modality, say at the 5%
confidence level in the conventional a priori sense, were found for only one
of five variants of the index that were explored, then the probability that
the reported bi-modality could have occurred by chance would actually
be closer to 25%. Even the most sophisticated formal significance tests
are bound to overestimate the significance of the results unless they are
conducted in the proper context, with due regard for what was, as well as
what was not predicted beforehand, as well as any voluntary choices in the
analysis procedure that might have served to enhance the apparent significance of the results (regardless of how those choices might be justified
after the fact). The assessment of statistical significance of regime shifts
and unprecedented events in a time series of limited duration is particularly
problematical in view of the inherent nonstationarity of most climatic time
series and the a posteriori flavour of any statistic that involves a prescribed
sampling interval, type of event, or specially designed index.
Access to and familiarity with a wide range of climate data sets is essential if an investigator is to have any hope of exploring the multi-dimensional
phase space in which the more important climate signals reside. Among
the most important functions of national and international climate programs is the dissemination of the more fundamental climate datasets in
easily accessible formats.
In this chapter we have managed to avoid the issue of spatial structure
by confining our attention to phenomena that can be represented by just
a few time series or, in the case of Fig. 10, averages over an ensemble of
time series. The next chapter is largely devoted to this topic.