Geoscience Reference
In-Depth Information
longer sample periods, there will likely be a progressive and marked decrease in
C
L
with increasing time lags. However, if there is periodicity present in the data series,
the magnitude of the correlation coefficient will increase again for a time lag that
matches the period of one of the fluctuations present. A graph of serial correlation
coefficient versus time lag is called the
correlogram
.
Identification of periodicity in a precipitation time series can also be made using
harmonic (Fourier) analysis. This entails fitting a mathematical function
P
f
of time
t
(in units appropriate to the problem) to a time series with the general form:
kn
=
∑
Pt P P kt
f
()
=+
cos(
−
f
)
(13.9)
k
k
k
=
1
where
P
k
and
f
k
are the amplitude and phase assigned to the
k
th harmonic in the
harmonic series so that it adequately represents
P
f
. The maximum value of
n
is
determined by the requirement that there is at least one full sinusoidal cycle of the
corresponding term in the time period for which data are available. An earlier
autocorrelation analysis might be used to guide the selection of terms in Equation
(13.8) for which fitting is made. The contribution of each harmonic term to the
total variance is subsequently found by expressing the variance for each harmonic
as a proportion of the total variance. Not every harmonic term in the series can
necessarily be associated with an identifiable physical mechanism.
As an alternative to harmonic analysis, numerical filters can be applied to the
precipitation time series to identify and enhance the contributions from influences
with different periodicity. Figure 13.7 shows an example of this approach in which
digital filters are used to identify fluctuating contributions superimposed on the
moving average value, in this figure corresponding to periodicity between 6 and 8
years, between 8 and 13 years and between 13 and 30 years. There is a possible
association with the sunspot cycle when the 8 to 13 year filter is applied to these
data, with the northern hemisphere (as represented by the west coast of the USA)
out of phase with the southern hemisphere (as represented by the east coast of
Australia). There is also some suggestion of association with the 18 year lunar
cycle revealed by applying the 13-30 year filter. Once trends and fluctuations in
observed precipitation records have been clearly established, they might be
extrapolated into the future for forecast purposes.
System signatures
The variation with time of precipitation intensity within a precipitation event is
called the
system signature
of the storm that gave rise to the precipitation. As might
be expected from the discussion given in Chapter 11, there is an important
distinction between convective and synoptic-scale storms. Observations of
precipitation rate during storms indicates that not only do most large-scale
synoptic systems produce longer duration and lower intensity precipitation than
convective storms, but also the distribution of precipitation intensity through the
