Maurice J McHugh Douglas G Goodin

Interdecadal-scale climate variability must be considered when interpreting climatic trends at local, regional, or global scales. Significant amounts of variance are found at interdecadal timescales in many climate parameters of both "direct" data (e.g., precipitation and sea surface temperatures at specific locations) and "indirect" data through which the climate system operates (e.g., circulation indices such as the Pacific North American index [PNA] or the North Atlantic Oscillation index [NAO]). The aim of this study is to evaluate LTER climate data for evidence of interdecadal-scale variability, which may in turn be associated with interdecadal-scale fluctuations evident in ecological or biophysical data measured throughout the LTER site network.

In their conceptualization of climatic variability, Marcus and Brazel (1984) describe four types of interannual climate variations: (1) Periodic variations around a stationary mean are well known to occur at short timescales, such as diurnal temperature changes or the annual cycle, but are difficult to resolve at decadal or longer timescales. (2) Discontinuities generated by sudden changes in the overall state of the climate system can reveal nonstationarity in the mean about which data vary in a periodic or quasi-periodic manner. These sudden alterations can result in periods perhaps characterized by prolonged drought or colder than normal temperatures. (3) The climate system may undergo trends such as periods of slowly increasing or decreasing precipitation or of warming or cooling until some new mean "steady" state is reached. (4) Climate data may exhibit increasing or decreasing variability about a specific mean value or steady state. Interdecadal contributions to climate variability can be described in terms of types 2 and 3 of Marcus and Brazel's conceptual classification—discontinuities in the mean and trends in the data. Records of the Northern Hemisphere's average land surface temperature show dis continuities in the mean state of the hemispheric temperature record in conjunction with obvious trends. Conceptually, it is hard to distinguish between these aspects of climate variability. Trends are an essential component of an alteration in the mean state of the temperature series, as they serve as a temporal linkage between the different mean states.

Climate Variability: Complexity and Chaos

Evaluating the causes of climatic variability tends to be difficult for a variety of reasons. Data, even when accurately measured during a lengthy period, tend to be significantly affected by local factors such as topography, urbanization, or location relative to large water bodies. Additionally, significant amounts of variability can often be attributed to larger scale associations with climate variability in distant locations. Climatologists, therefore, evaluate climate data in terms of in situ trends and variations but also in terms of the processes causing or associated with those variations, such as ocean-atmosphere circulation anomalies in far-distant locations, which are referred to as "teleconnections"—literally meaning "remote connection." Therefore, climate data must be understood to be influenced by both local-and large-scale climatic forcing. One of the inherent problems in evaluating tele-connections is that the apparent association between measures of atmospheric circulation or climate variability and far-flung locations may result from indirect causal pathways. For example, forcing by variable C may produce the apparently significant correlation between variables A and B.

The NAO, for example, is a measure of the sea level pressure gradient between Iceland and the Azores, and indirectly of the westerly wind speed across the North Atlantic Ocean, and it is long known to have statistically significant associations with rainfall over portions of India or China. Whether the NAO actually causes rainfall variability in India or China or whether those phenomena are correlated because they are both being driven by some external phenomenon remains to be determined.

Further complicating the matter, the climate system is inherently nonlinear in nature because of the large number of feedback mechanisms of which we are aware. Dynamic and thermodynamic thresholds within the climate system ensure that analysis and evaluation of climate variability and change is complicated. A myriad of small changes can result in the atmosphere changing from a stable state to an unstable state, from a laminar to a turbulent flow regime, and from ice melting to remaining solid. For example, alterations in atmospheric circulation can affect surface temperatures and increase snowmelt. Reduced snowcover results in decreased albedo, with energies that otherwise would be reflected now available to cascade through various climate system components. Each of these components may further enhance those energies, producing a positive feedback or eliminating the energy from the climate system altogether in a negative feedback. The often large and important differences in atmospheric state produced by subtle changes in climatic variables attest to the existence and power of these thresholds and feedback mechanisms. These thresholds and feedbacks can produce, or magnify, the apparently chaotic nature of the climate system.

Traditionally, statistical analysis of climate data relies heavily on linear methods, such as linear regression or simple correlations. Nonlinear statistical methods using techniques based on Bayesian analysis and neural networks are beginning to slowly permeate the atmospheric sciences. In some circumstances, neural networks are merely being used to produce results comparable to those of a linear regression, but in other circumstances the method is being used in truly nonlinear applications such as nonlinear principal components analysis (Hsieh and Tang 1998; Hsieh 2001).

Analysis and evaluation of the causal nature of the interrelations among climate trends, periodicities, and remote linkages is therefore extremely complex, with atmospheric scientists, including climatologists, well aware of the analytical problems they face. Given these issues, many atmospheric scientists believe that the only correct and appropriate manner in which causal analysis can be performed is through the use of sophisticated numerical models of the entire climate system, including coupling between the atmosphere and components such as the oceans, cryosphere, and, importantly, the biosphere.

Recurrent Variability in the Climate System

Recurrent or quasi-periodic variability intrinsic in the climate system can be found at timescales of 1 day, 365 days, several years, and possibly several decades. Our records of the climate system have been gathered on a near-global scale only since the end of the 1940s, but they have been truly global only since the advent of the modern satellite in the 1970s (Kalnay et al. 1996). This relatively short timescale prevents truly global analyses of intermediate and long-term timescales of variability. However, individual stations have been recording data since the 1600s in Europe (Vose et al. 1992). Climatologists have used various records of climate change and variability from before the 1600s, such as records of French grape harvest dates (e.g., Lamb 1977), documentary evidence of historical climate changes (e.g., Lamb 1977; van Loon and Rogers 1978; Mantua et al. 1997), dendrochronology (e.g., Minobe 1997), ice core data (e.g., Thompson et al. 1998), and sedimentary records from the ocean bottoms (e.g., Hays et al. 1976).

Causes of interdecadal-scale variability in the climate system are not very well understood and are thought to include solar variability, air-sea interaction, and certain coupled modes of atmospheric variability that exhibit quasi-periodic behavior. Sunspot numbers have a pronounced periodicity at 11 years (Labitzke and van Loon 1988; Mitra et al. 1991; Currie and O'Brien 1992) and a lesser known periodicity at 22 years (Vines 1986). Some well-known modes of atmospheric variability are also associated with interdecadal-scale variability. In particular, the Pacific Decadal Oscillation (PDO) in sea level pressure over the northern Pacific Ocean (Trenberth and Hurrell 1994) is known to play an important role in modulating sea surface temperatures (SSTs) across the North Pacific, which in turn affect the Pacific Salmon catch (e.g., Mantua et al. 1997; chapter 13 of this volume). This is only one example of the well-documented and extensive changes in the climate over the North Pacific that occurred in the late 1970s (e.g., Namias 1978; Trenberth 1990;

Graham 1994; Trenberth and Hurrell 1994)—changes that appear strongly coupled to concurrent ecological changes (e.g., Venrick et al. 1987; Ebbesmeyer et al. 1991; Francis and Sibley 1991; Brodeur and Ware 1992; Hollowed and Wooster 1992; Beamish and Boullion 1993; Francis and Hare 1994; Mantua et al. 1997).

Given the varied nature of these interdecadal-scale signals in the climate system, their detection in instrumental climate data proves to be quite difficult for a variety of reasons. Quasi-periodic signals at a variety of timescales can be envisaged reverberating throughout the climate system simultaneously with a multitude of other nonperiodic signals. Because signals tend to oscillate at certain periodicities, occasionally the combined amplitude of the signals may overlap and reinforce each other, or cancel each other out. Climate signals may have direct effects on climate data (e.g., through modulation of precipitation or temperature), and thus indirectly on ecological data, whereas other climatic signals may have direct effects on ecological data (e.g., solar variability). In addition to quasi-periodic signals in the climate system, nonoscillatory factors such as humankind's alteration of Earth's surface and atmospheric chemistry, as well as changes in the energy and carbon content of oceanic bottom waters, may induce additional degrees of variance into the system, making it more difficult to isolate and describe one specific periodic signal.

Data and Methodology

Additional problems arise in the statistical description and evaluation of the existence and significance of these quasi-periodic signals. One technique commonly used to evaluate periodic components of data variance is spectrum analysis, which relies on its ability to estimate proportions of variance at specific frequencies (periods/year). It is known that some proportion of the variance at one frequency can "leak" into adjacent frequencies and contaminate the spectral estimates by spreading the information too widely across several frequencies. This is referred to as spectral leakage (Mitchell et al. 1966). Other biases may occur if trends in the data are not removed (e.g., Warner 1998).

LTER climate data used include monthly mean, maximum, and minimum temperatures and precipitation where available at LTER stations. Data at Palmer Station in Antarctica were analyzed in addition to North American data. Data were obtained from the LTER CLIMDES database, available on the internet (http:// intranet.lternet.edu/archives/documents/Publications/climdes/index.html) (figure 11.1). To relate significant findings to ecologically relevant research, only average growing-season (March to September) data are used.

There are two potential approaches to the efficient and accurate identification of interdecadal-scale variability in the LTER climate data. One approach is to examine the relationship between LTER data and indexes of climatic phenomena known to have a substantial portion of their variance occurring at interdecadal timescales, for example, sunspot numbers or the PDO. The second approach is to use power spectrum analysis to evaluate the proportions of variance in the climate data occurring at interdecadal timescales. Both of these methods were used in this study,

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Figure 11.1 Locations of LTER stations recording (a) mean temperature, (b) maximum temperature, (c) minimum temperature, and (d) precipitation data used in this study. Palmer Station, Antarctica, is included in the mean temperature data set but is not plotted here.

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Figure 11.1 Locations of LTER stations recording (a) mean temperature, (b) maximum temperature, (c) minimum temperature, and (d) precipitation data used in this study. Palmer Station, Antarctica, is included in the mean temperature data set but is not plotted here.

but only the latter approach is described in detail. This is because most of the well-known climate phenomena exhibiting significant interdecadal-scale variability are most readily apparent and are at their strongest during winter. This may be due to the nature and origin of the climate phenomena and/or to the relatively low variance found in winter climate data that allows easier signal detection.

For example, interdecadal-scale variability is dominant in Trenberth and Hur-rell's (1994) index of North Pacific sea level pressure between November and March. Other times of the year show little, if any, interdecadal-scale variability over the North Pacific. This merely represents a shift from polar domination of midlatitude climate variability during the winter months to a regime increasingly influenced by tropical variability during the nonwinter months. Correlations performed between Trenberth and Hurrell's (1994) North Pacific sea level pressure index and LTER growing-season data do produce statistically significant relationships, but it is possible that large portions of the covariance between the series do not occur at interdecadal timescales, but at interannual timescales during the growing season. The timescales at which the covariance occurs may be assessed by cross-spectrum analysis (Warner 1998). However, Goodin et al. (chapter 20 in this volume) show that some interdecadal-scale climate signals are found to correlate significantly with growing-season (April-September) temperature, precipitation, and annual net primary productivity at the Konza Prairie LTER site near Manhattan, Kansas.

To allow efficient analysis of LTER climate data, principal component analysis (PCA) is used to decompose time series of the mean growing season climate data into their principal modes of variability, principal components (PCs). The first four PCs are retained for varimax rotation. Spectral analysis is then used to evaluate the variance spectra of the rotated PCs (e.g., Mitchell et al. 1966). PCs are detrended, and deviations from the mean are calculated prior to spectral analysis; all missing data are ignored. The relatively large proportion of missing data prior to the mid-1950s ensures that results from the LTER climate data set for the first half of the century is biased in favor of those few stations with data. It is possible that the results may reflect the interdecadal components of variability relevant to those sites, rather than across the data set as a whole. However, elimination of those stations without long time series precludes meaningful analysis of interdecadal-scale variability at most LTER sites. Additionally, use of LTER climate data over more limited periods (e.g., Greenland 1999) does not allow for evaluation of interdecadal-scale variability in a meaningful manner.

Results and Discussion Mean Temperature

The first four rotated PCs of growing-season mean temperature account for almost 62% of its variance. Spectral analysis performed on each of the rotated PCs (figure 11.2) depicts statistically significant periodicities in PCs 1, 2, and 4. Although mean temperature data are dominated by low-frequency variability, statistically significant peaks are found between 3.0 and 3.5 years in the first two components, and a significant peak occurs at 2.88 years in PC 4, indicating the importance of quasi-triennial periodicities in the LTER growing season mean temperature data. These quasi-triennial periods appear similar to those found in the El Nino-Southern Oscillation (ENSO) signal that has variance concentrated between 2 and 3 years and also between 4 and 6 years (Rogers 1984; Keppene and Ghil 1992; Mann and Park 1994; McHugh 1999; Greenland 1999). Significant quasi-quintennial periodicities are observed in PC 4, and a prominent but insignificant peak in PC 1 occurs in this latter band of ENSO variance.

Statistically significant low-frequency variability between 50 and 100 years is evident in the spectra of each PC, except PC 3. A similar 50- to 70-year spectral peak was found in North American tree ring data (Minobe 1997), whereas the 100-year periodicity may be related to solar forcing (Friis-Christensen and Laasen 1991) and/or anthropogenic factors (IPCC 1995). However, PC 3 exhibits a significant concentration of spectral variance at interdecadal periodicities, but the relatively small amount of variance explained by PC 3 indicates that this interdecadal signal is of fairly small importance to the overall data set. More prominent, but statistically insignificant, signals at and near this periodicity are also evident in the spectrum of PC 1. The spatial distribution of PC loadings is rendered relatively meaningless because of the minuscule number of sites across North America, the lack of any coherent trend or distribution, and the juxtaposition of nearby sites with strong positive and negative loadings. Loading maps are therefore not displayed.

Figure 11.2 Spectral analysis of the principal components of mean temperature (a) PC 1, (b) PC 2, (c) PC 3, and (d) PC 4. The percentage of the data set's variance accounted for by each PC is measured along the y-axis. The thick solid line depicts the spectral estimates, which are unitless; period lengths are indicated along the x-axis in years/cycle. The red noise spectral power estimates represented by the uppermost dashed line represent the 95% confidence limit; the lower dashed line represents the red noise spectral power estimates at the 5% confidence limit. The middle (solid) line represents the 50% confidence level.

Figure 11.2 Spectral analysis of the principal components of mean temperature (a) PC 1, (b) PC 2, (c) PC 3, and (d) PC 4. The percentage of the data set's variance accounted for by each PC is measured along the y-axis. The thick solid line depicts the spectral estimates, which are unitless; period lengths are indicated along the x-axis in years/cycle. The red noise spectral power estimates represented by the uppermost dashed line represent the 95% confidence limit; the lower dashed line represents the red noise spectral power estimates at the 5% confidence limit. The middle (solid) line represents the 50% confidence level.

Maximum Temperature

In comparison to the mean temperature spectra, low-frequency variability dominates the spectra of PC 1, PC 3, and PC 4 (figure 11.3); significant periodicities at about 50 years are evident in all three spectra. Significant interdecadal-scale variability is evident in PC 3, with smaller and insignificant peaks also observed at this periodicity in PC 1. The spectrum of PC 1 closely resembles that of the first PC of mean temperature, depicting a significant quasi-triennial periodicity in addition to a smaller nonsignificant periodicity between 5 and 6 years. These periodicities are similar to those associated with ENSO, and suggest an interrelationship such as the one described by Greenland (1999). Statistically significant quasi-biennial variability is evident in PC 3 and PC 4, in addition to the aforementioned low-frequency signals.

Figure 11.3 Spectral analysis of the principal components of maximum temperature (a) PC 1, (b) PC 2, (c) PC 3, and (d) PC 4. The percentage of the data set's variance accounted for by each PC is measured along the y-axis. The thick solid line depicts the spectral estimates, which are unitless; period lengths are indicated along the x-axis in years/cycle. The red noise spectral power estimates represented by the uppermost dashed line represent the 95% confidence limit; the lower dashed line represents the red noise spectral power estimates at the 5% confidence limit. The middle (solid) line represents the 50% confidence level.

Figure 11.3 Spectral analysis of the principal components of maximum temperature (a) PC 1, (b) PC 2, (c) PC 3, and (d) PC 4. The percentage of the data set's variance accounted for by each PC is measured along the y-axis. The thick solid line depicts the spectral estimates, which are unitless; period lengths are indicated along the x-axis in years/cycle. The red noise spectral power estimates represented by the uppermost dashed line represent the 95% confidence limit; the lower dashed line represents the red noise spectral power estimates at the 5% confidence limit. The middle (solid) line represents the 50% confidence level.

Minimum Temperature

Spectral characteristics of growing-season minimum temperatures (figure 11.4) exhibit significant variability at low frequencies, but more high-frequency signals are observed in comparison to the spectra of mean or maximum temperatures. PC 1, PC 3, and PC 4 all have large proportions of their variance at low frequencies, but they also have statistically significant signals at quasi-quintennial periodicities. All PCs depict significant or prominent spikes at quasi-biennial or shorter periodicities. None of the PCs exhibit much power at interdecadal periodicities.

Precipitation

Precipitation spectra for the four retained PCs are depicted in figure 11.5. These spectra show little quasi-periodic variability across the LTER sites, and few significant periodicities are found. Prominent signals at quasi-biennial periods are observed in PC 2, PC 3, and PC 4, with marginally significant variance observed at

Figure 11.4 Spectral analysis of the principal components of minimum temperature (a) PC 1, (b) PC 2, (c) PC 3, and (d) PC 4. The percentage of the data set's variance accounted for by each PC is measured along the y-axis. The thick solid line depicts the spectral estimates, which are unitless; period lengths are indicated along the x-axis in years/cycle. The red noise spectral power estimates represented by the uppermost dashed line represent the 95% confidence limit; the lower dashed line represents the red noise spectral power estimates at the 5% confidence limit. The middle (solid) line represents the 50% confidence level.

Figure 11.4 Spectral analysis of the principal components of minimum temperature (a) PC 1, (b) PC 2, (c) PC 3, and (d) PC 4. The percentage of the data set's variance accounted for by each PC is measured along the y-axis. The thick solid line depicts the spectral estimates, which are unitless; period lengths are indicated along the x-axis in years/cycle. The red noise spectral power estimates represented by the uppermost dashed line represent the 95% confidence limit; the lower dashed line represents the red noise spectral power estimates at the 5% confidence limit. The middle (solid) line represents the 50% confidence level.

low frequencies in PC 2 and PC 3. There is little, if any, spectral variance observed in any of the PCs at interdecadal timescales.

Discussion and Conclusions

Prominent or significant spectral powers at interdecadal timescales appear uncommon in the LTER climate data on mean growing season (March-September) used in this study. High-frequency variability, especially that observed at quasi-biennial and quasi-quintennial periodicities, appear as important as the variability occurring at the interdecadal timescale. Although some significant quasi-periodic components of variability are observed, few, if any, are consistently observed across the four variables examined. Significant periodicities appear relatively consistently between the temperature variables at timescales associated with ENSO, but some subtle differences are noted, in particular in the high-frequency spectral domain. Much of

Figure 11.5 Spectral analysis of the principal components of precipitation (a) PC 1, (b) PC 2, (c) PC 3, and (d) PC 4. The percentage of the data set's variance accounted for by each PC is measured along the y-axis. The thick solid line depicts the spectral estimates, which are unitless; period lengths are indicated along the x-axis in years/cycle. The red noise spectral power estimates represented by the uppermost dashed line represent the 95% confidence limit; the lower dashed line represents the red noise spectral power estimates at the 5% confidence limit. The middle (solid) line represents the 50% confidence level.

Figure 11.5 Spectral analysis of the principal components of precipitation (a) PC 1, (b) PC 2, (c) PC 3, and (d) PC 4. The percentage of the data set's variance accounted for by each PC is measured along the y-axis. The thick solid line depicts the spectral estimates, which are unitless; period lengths are indicated along the x-axis in years/cycle. The red noise spectral power estimates represented by the uppermost dashed line represent the 95% confidence limit; the lower dashed line represents the red noise spectral power estimates at the 5% confidence limit. The middle (solid) line represents the 50% confidence level.

the variance in temperature data is found to contain significant, or prominent, spectral powers at periodicities at 50 years or longer.

However, the interpretation of these oscillations that have such extremely long periodicities must be questioned in a data set containing, at best, 104 years of data. Given such a short time period, only two complete 50-year cycles could possibly occur. Statistically, these signals may be significant according to the chi-square test or other criteria, but it is doubtful that their significance can be accurately assessed given that there are potentially only two complete cycles. Realistically, this oscillation would be unlikely to have completed these two cycles during the past century. Even if this were so, it is not likely that the oscillation would take exactly 50 years to complete: some variance around an approximate 50-year period would likely have occurred because of probable interactions between this phenomenon and other climate system components. Such signal variability would result in decreased spectral power and observed significance at the 50-year periodicity, making accurate estimates of this cycle's statistical significance unlikely.

We must also remember that these results do not necessarily reflect the individual power spectra of the climate data at each LTER site. Rather, they reflect the spectral characteristics of the whole LTER network as a result of the decomposition of data into principal modes of variability across the whole data set. Actual periodicities at individual sites may be somewhat stronger or weaker relative to those found across the entire network.

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