mean values of each calendar day, 2) fit a probability
distribution (such as the three-parameter gamma distri-
bution) to the daily anomalies for each Julian day, and
3) compute the thresholds from the fitted probability
distributions. Folland et al. (1999) also recommended
that data from additional proximate calendar days be
added to improve the stability of the probability distri-
bution parameter estimates but that those days should
be far enough apart such that data from different days
are effectively independent. This method was imple-
mented in Jones et al. (1999), who used five observa-
tions with 5-day intervals between them (referred to as
the 5SD window hereafter). In many other applications
(e.g., Frich et al. 2002; Klein Tank and Können 2003;
Kiktev et al. 2003), thresholds have been estimated us-
ing data from five consecutive days centered on the day
of interest (referred to as 5CD). In either case, the daily
thresholds are, in effect, percentiles estimated from
samples of no more than 5 ⫻ 30 ⫽ 150 days of data
when a standard 30-yr base period is used.
Despite the importance of these indicators in the de-
tection and monitoring of climate change, their statis-
tical properties have not been well documented. For
example, what differences would result in the index
time series when 5CD and 5SD windows are used?
Does the fact that the thresholds are “adapted” to (cal-
culated from) the base period cause any systematic dif-
ferences between the statistical properties of the index
time series during the base period (in base) and before
or after the base period (out of base)? Such differences
need to be understood before the indices can be used
with confidence for the purpose of climate change de-
tection and monitoring.
The main objective of this paper is to examine,
through Monte Carlo simulations, the characteristics of
the index time series that are obtained when threshold
functions are estimated with existing methods. We
show that these threshold estimation methods produce
substantial inhomogeneities in the index time series at
the beginning and end of the base period in the sense
that inhomogeneities become clearly apparent when a
large number of station series are averaged (Fig. 1) as
might be done in a climate change detection study. We
propose an approach that corrects the problem. The
remainder of this paper is organized as follows. We
describe existing methods for calculating thresholds
and index time series in section 2. The Monte Carlo
experiment that is used to study the performance of
these methods is also described in this section. Results
are presented in section 3. An improved method for
calculating the index time series is described and evalu-
ated in section 4. Conclusions and discussion follow in
section 5.
2. Methods
a. Threshold function estimation
There are three aspects to consider in constructing an
estimate of the threshold function. The first consider-
ation is the choice of base period. To ensure that index
time series can be easily extended into the future, the
base period is usually chosen to be consistent with a
recent World Meteorological Organisation (WMO) op-
erational climatology base period (e.g., 1961–90 or
1971–2000). Most studies have used the 1961–90 base
period because most indices of climate extremes were
developed in the late 1990s (Karl et al. 1999) and be-
cause there is greater availability of data during this
period than during other operational climatology base
periods.
The second consideration is the type of subsampling
that is used to select the data within the base period
that will be used for threshold estimation. In this study,
we use both the 5CD and 5SD windows. For example,
to estimate the threshold for 13 January, the 5CD win-
dow selects data for all days in the base period dated
11–15 January. In contrast, all base period observations
FIG. 1. Average of exceedance rate of daily values greater than
the 90th percentile in 1000 simulations in which the lag 1-day
autocorrelation has been set to 0.8. Thresholds are estimated us-
ing data from a 5-consecutive-day moving window and the em-
pirical quantile as defined in the text. The first 30 yr are used as
the base period. A jump (increase) in the exceedance rate is ap-
parent at the boundary between the in-base and out-of-base pe-
riods, as indicated by 30-yr averages (thin dashed lines). Because
of this jump, a highly significant trend (thick dashed line) can be
identified if a linear trend is fitted to the exceedance time series,
even though there is no trend in the simulated data.
1642 JOURNAL OF CLIMATE VOLUME 18
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