A closer look at regime shifts based on coastal observations along the eastern boundary of the North Pacific

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Continental Shelf Research 27 (2007) 2250–2277 www.elsevier.com/locate/csr

A closer look at regime shifts based on coastal observations along the eastern boundary of the North Pacific Laurence C. Breaker Moss Landing Marine Laboratories, 8272 Moss Landing Road, Moss Landing, CA 95039-9647, USA Received 26 October 2006; received in revised form 6 March 2007; accepted 18 May 2007 Available online 3 July 2007

Abstract At least six regime shifts have been reported in the North Pacific since 1920. They occurred in 1925, 1939, 1946, 1976–1977, 1989 and 1999. The major change in 1976–1977 corresponds to a regime shift that is now widely accepted as a canonical event since it had a significant impact on virtually all climatic and ecosystem indicators. We seek to determine if daily sea surface temperature (SST) from Pacific Grove, in central California, and Scripps Pier, in southern California, and coastal observations from several other locations along the west coast of North America can be used to detect and resolve these events. Cumulative sums (CUSUMs) were initially calculated to enhance the detection process. The CUSUM trajectories during the 1976–1977 event at Pacific Grove and Scripps Pier were distinctive, highly correlated, and in phase. The turning point patterns from this event were then used to search for other events that have been reported since 1920. Turning point patterns very similar to the 1976–1977 event were detected in 1946 and 1989. The events in 1925 and 1939 were generally similar, but the CUSUM patterns for the event in 1999 departed significantly from the other events. Further examination of the 1976 and 1989 events revealed inflection points in the CUSUMs near the beginning and end of each transition that correspond to critical values or extrema in the original data. The inflection points and/or critical values provide an improved basis for determining the duration of these events. The robustness of the CUSUM approach for detecting regime shifts was examined by posing the inverse problem to determine if other possible regime changes could be detected that have not been previously reported. The period between 1946 and 1976 was examined, and one match in 1972 was found, which coincided with a large shift in the Aleutian Low Pressure Index. The CUSUM patterns associated with well-defined regime shifts may be essentially unique and thus useful in searching for other events. Whether the temperature ultimately increases or decreases following a regime shift is wellpredicted by the sign of the CUSUM slope during an event. Testing regime shifts for statistical significance may be problematic, but our results suggest that when CUSUMs are employed, the detection problem becomes one that is more closely related to pattern recognition where other tests could be applied. CUSUMs often produce a distinct pattern that appears to be characteristic of regime shifts. During well-defined events such as those that occurred in 1946, 1976, and 1989, the CUSUM trajectories from Pacific Grove and Scripps Pier were highly synchronized and nearly identical in form. The CUSUM transformation allows us to identify, localize and observe how these events evolve. We have only been able to examine these events in such detail because daily observations from single locations were used. Based on the events we have examined, they have time scales that range from about 4–9 months. Salinity and sea level data were also employed in this study and were found to be less sensitive to the changes associated with regime shifts than SST. Regime shifts detected in CUSUMs of SST at two locations off Vancouver Island were found to be weaker in amplitude and less well-defined than those detected at Pacific Grove and Scripps Pier. However, they were Corresponding author. Tel.: +1 831 771 4498.

E-mail address: [email protected] 0278-4343/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.csr.2007.05.018

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in phase with the events observed further south. Establishing the connection between these results, and changes in the ecosystems of the North Pacific, should be given a high priority. Finally, the results of this study are related to decadal climate variability and provide additional insight into the nature of this phenomenon. r 2007 Elsevier Ltd. All rights reserved. Keywords: Regime shifts; Sea surface temperature; Salinity; Sea level; Detecting regime shifts; Cumulative sums (CUSUMs); Pacific Grove; Scripps Pier; Vancouver Island; 1976–1977 regime shift; Change points; Statistical significance; Sustained changes; Pattern recognition

1. Introduction The terms ‘‘regime’’ and regime shift’’ are now used frequently. The term regime is attributed to Issacs (1976), who was the first to use it in reference to different climatic states. Although regime shifts are considered to be a global phenomenon, much of the research in this area has focused on the North Pacific where their occurrence has been documented. Bakun (2004), while recognizing the relation to climatic states, emphasizes the ecological nature of regime shifts and has proposed the following definition. A regime shift implies ‘‘a persistent radical shift in typical levels of abundance or productivity of multiple components of the marine biological community structure, occurring at multiple trophic levels and on a geographical scale that is at least regional in extent’’. Others prefer that the term be reserved only for ecosystem changes that can be shown to be linked to climatic changes (e.g., Alheit and Niquen, 2004; Wooster and Zhang, 2004). Mantua (2004) proposed formal definitions for regime and regime shift that include both ecosystem and climatic changes. According to Mantua, a regime corresponds to ‘‘a period of quasi-stable biotic or abiotic system behavior where temporal variations in key state variables are concentrated near distinct dynamical attractors, or stability wells, within phase space.’’ A regime shift or change corresponds to ‘‘a relatively brief time period in which key state variables of a system are transitioning between different quasi-stable attractors in phase space.’’ Thus, as stated by deYoung et al. (2004), regime shifts are characterized by changes in state where the change between states is much shorter than the time within states. Bakun (2004), however, brings into question the time scales associated with regime shifts, stating that it is not clear whether such changes should be viewed as a sudden system reorganization that may occur within a given year, or as one that continues to evolve over a number of years. In the broader context of

decadal climate variability, changes in the system can take the form of gradual drift, smooth oscillations, or step-like shifts (e.g., Miller and Schneider, 2000). As pointed out by Kerr (1992) and MacCall (1996), since regime shifts tend to be smaller than year-to-year fluctuations and may involve several parts of the climate system, recognizing them is often difficult and may require a decade or longer before a positive identification can be made. Beyond year-to-year fluctuations, changes that signify a regime shift are often far smaller than those associated with events such as the onset of El Nin˜o warming episodes. Thus, detection and identification of regime changes can be a difficult problem. Finally, it should be emphasized that the concept of regime shift as described above has not been universally embraced by the scientific community. Although the major regime change that took place during the mid 1970s is almost universally accepted, other regime shifts that have been reported during the past 50 years or so are less widely accepted. This may be due to the fact that unlike the 1976 event which had a major impact on both the biotic and abiotic systems of the North Pacific, some regime changes have primarily affected only one realm or the other, but not both to the same extent. With respect to the causes of regime shifts, there appears to be a connection with long-term changes in the state of the Aleutian low-pressure system. The intensity and extent of the Aleutian low is described by the Aleutian low pressure index (ALPI). Changes in the sign of the ALPI anomaly, on the order of 15–20 years, often coincide with regime changes in the North Pacific. That the ALPI anomaly changed sign during the 1976–1977 event has been welldocumented (e.g., Mann and Lazier, 2006). Using an indicator similar to the ALPI, Overland et al. (1999) found change points in their index time series of the Aleutian low central pressure in 1925, 1947, and 1976, all times of well-documented regime shifts in the North Pacific. With respect to decadal climate variability, perturbations in the Aleutian

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low generate temperature anomalies in the central and eastern North Pacific through the effects of net surface heat flux, turbulent mixing, and Ekman advection (Miller and Schneider, 2000). Although the state of the Aleutian low may be one factor that is related to regime shifts in the North Pacific, other causal mechanisms have been proposed. Kashiwabara (1987) and Nitta and Yamada (1989), for example, have suggested that warming in the tropical Pacific could have been responsible for the 1976–1977 regime shift. Another parameter that is closely related to regime changes in the North Pacific is the Pacific Decadal Oscillation (PDO), a cyclic pattern of climatic variability that has periods of 15–20 years, on shorter time scales, and 50–70 years, on longer scales (Minobe, 1997). Sea surface temperature (SST) is often used to identify changes in the PDO. The PDO index which describes this phenomenon, is usually defined as the first principal component of the SST anomaly over the North Pacific, north of 201N. Like the ALPI, changes in the sign or phase of the PDO appear to be a good indicator of regime changes in the North Pacific. During the 1976–1977 regime shift, for example, the phase of the PDO changed from negative to positive (e.g., Ebbesmeyer et al., 1991). Although there appears to be a close connection between phase changes in the PDO, and regime shifts, the causes of the PDO are not well-understood (e.g., Mantua and Hare, 2002). Finally, while the region associated with the ALPI tends to lie further north being centered at roughly 501N, the PDO characterizes conditions over a larger portion of the North Pacific that extends further south including the subtropics. Although the two indices are generally similar at decadal time scales and longer, they often differ on shorter time scales. At least six changes since the mid-1920s in the state of the North Pacific have been reported.1 A phase change in the PDO occurred circa 1925 that corresponded to a regime shift in the North Pacific (e.g., Beamish et al., 1999; Overland et al., 1999). A regime shift in 1939 was reported by MacCall (1996), based on SST from Scripps Pier off southern California. According to MacCall, this regime shift represented a change to cooler conditions in the North Pacific. This regime change was also reported 1 Other possible regime shifts in the North Pacific since 1920 have been reported that are not examined in this study (e.g., Rebstock, 2002; Bakun, 2004).

by Ware (1995), who found indications of a similar transition off British Columbia. A change point in 1946–1947 was reported by Peterson and Schwing (2002), Beamish et al. (1999), and Overland et al. (1999) that may be related to the phase change in the PDO that occurred in 1947 (Mantua et al., 1997). A well-documented regime shift occurred in 1976–1977 in the northeastern Pacific (e.g., Ebbesmeyer et al., 1991; Miller et al., 1994; Graham, 1994; McGowan et al., 1998; Hare and Mantua, 2000; Bakun, 2004). This regime shift appears to have been related to the phase change in the PDO that occurred at that time. The 1976 regime shift had a major impact on the marine ecosystems of the North Pacific but was also related to major climatic changes (e.g., Bakun, 2004). Hare and Mantua (2000), Rebstock (2002), and others, have reported a regime shift in 1989. This event, according to Hare and Mantua, was notable in that its primary manifestation was biological and not climatic, since it was apparently limited to certain components of the North Pacific ecosystem. Finally, a regime change in 1999 has been reported following the 1997–1998 El Nin˜o, consistent with a phase change in the PDO that has apparently led to cooler conditions since that time (e.g., Greene, 2002; Peterson and Schwing, 2003; Chavez et al., 2003). However, according to Bond et al. (2003), this event may not have been related to the PDO since the patterns of sea level pressure and SST anomalies show little resemblance to those normally associated with the PDO. Finally, it is important to recognize that these regime changes have occurred on time scales generally consistent with decadal climate variability and so are almost certainly an integral part of this phenomenon. The text is divided into six sections and three appendices. Section 1 is the introduction, followed by Section 2 which discusses the methods used in detecting regime shifts. Section 3 presents the methodology for calculating cumulative sums (CUSUMs). Section 4 applies CUSUMs to the data used in this study and contains nine subsections: 4.1, the observations, 4.2, the 1976–1977 regime shift—a canonical event, 4.3, CUSUMs of coastal SST off central and southern California, 4.4, how transition events appear in the original data, 4.5, tests of significance, 4.6, the inverse problem and robustness, 4.7, sustained changes in temperature between events, 4.8, other variables and other locations, and 4.9, the issue of resolution. Section 5 gives a discussion of several issues that are closely related

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to the central ideas contained in this work, and Section 6 presents a summary and conclusions. Appendix A estimates the signal-to-noise ratio (SNR) improvement in detecting the 1976–1977 regime shift using CUSUMs, Appendix B addresses the effects of serial correlation on estimating the slopes of CUSUMs, and Appendix C addresses the sensitivity to preprocessing the data. 2. Detecting regime shifts Mantua (2004) presented five methods for detecting regime shifts in marine ecosystems that are described in detail. These methods are applied to univaritate and multivariate biotic and abiotic time series. Several other studies have also addressed the problem of detecting climate shifts. Easterling and Perterson (1995) used a regression approach applied to the first differences and then refined the search for discontinuities based on regressions applied to subsets of the record. Lanzante (1996) developed a multiple change point detection (CPD) approach based on the original work of Siegel and Castellan (1988) that does not require a priori information on the timing of the change points. Rebstock (2002) used this method to search for change points that might reflect regime shifts in the North Pacific based on calanoid copepod populations and hydrographic data off southern California. Rodionov (2004) proposed a new method for testing climatic data for regime shifts using a sequential algorithm that also does not require an a priori hypothesis on the timing of the shift. Meteorological time series have also been examined for rapid changes using a method of CPD presented by Hubert (1997). Hubert segmented the original time series into as many subseries as possible producing an optimal partitioning where the difference in the mean between any two adjacent subseries is tested for significance. Most of the methods for detecting regime shifts fall into the category of CPD. Stationarity is a basic assumption that underlies most statistical tests. Change points violate stationarity and so their identification becomes an important issue. Change points occur where the changes are relatively abrupt, often occurring on time scales that approach the sampling period of the observations themselves. Formally, a change point exists at a time t0, if all of the observations up to t0 share a common statistical distribution, and those after t0, share a different statistical distribution (e.g., Basseville and Nikiforov, 1993). Formally, we can test a

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null hypothesis against an alternative hypothesis, where the null hypothesis, H0, is that there has been no change in the process, and the alternative hypothesis, H1, that there has been a change. Given a random sequence, x(t), of length n, a sequential probability ratio test can be performed where p0(t) represents the probability density associated with H0, and p1(t) represents the probability density associated with H1 (e.g., Wald, 1945). Next, we calculate the likelihood ratio, Gn, where Gn ¼

n Y p0 ðtÞ p ðtÞ t¼1 1

(1)

and P represents the product symbol. If Gn is less than, or equal to, a lower threshold, TL, then we accept the null hypothesis, H0. If Gn is greater than an upper threshold, TH, then the alternative hypothesis, H1, is accepted. According to the procedure, if Gn falls between TL and TH, then another observation, x(t+1) is acquired, the likelihood ratio is updated with the new information, and the test is performed again. In practice, the logarithm of the likelihood ratio is normally used to perform these calculations. One of the important points here is that the CPD problem, in its most general form, must be expressed in terms of probability densities since a change could be associated with any of the statistical moments that define the process, although we are usually only concerned with changes in the first moment, or the mean value. One of the most important considerations in CPD is whether a detection algorithm is applied ‘‘on-line’’ or ‘‘off-line’’. In the on-line detection problem, a detection algorithm is applied continuously to incoming data and the object is usually to determine as soon as possible when a change has occurred. In off-line detection, the data have already been acquired and the object is to determine first whether or not a change has occurred, and second, if a change has taken place, when it occurred. With respect to past work in detecting regime shifts, most analyses have been conducted off-line, but as interest in regime shifts grows, it appears that CPD algorithms could be applied on-line because of the benefits that may accrue from more rapid detection of these events. Algorithms for CPD include the Shewhart chart, the geometric moving average (GMA), the geometric moving average (FMA), filtered derivative algorithms, CUSUM and weighted CUSUM

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algorithms, Bayes-type algorithms, and generalized likelihood ratio (GLR) algorithms. Comparisons between many of these algorithms are made and discussed in Basseville and Nikiforov (1993), and elsewhere (e.g., Roberts, 1966; Basseville, 1981; Gibra, 1975). Although the differences in performance between these algorithms are often subtle, one algorithm, in particular, appears to perform as well or better than most under a variety of conditions, the CUmulative SUM or CUSUM algorithm. According to Roberts (1966), when the change magnitude is small, the CUSUM outperforms the Shewhart chart, the GMA, and the FMA. Because the CUSUM approach generally performs well, is well-documented, is relatively easy to implement, and allows us to observe the process as it evolves, we focus on this method of CPD.2 3. The CUSUM A cumulative sum, CS, represents the running total of the deviations of the first n observations from a mean based on the same interval (e.g., Page, 1954; Wetherill and Brown, 1991; Hawkins and Olwell, 1998). This operation can be expressed as CS ¼

n X ðxt  xÞ, ¯

(2)

t¼1

where xt represents the tth observation, x, ¯ the mean of xt from t ¼ 1–n, and CS, the cumulative sum over the same interval. CS is usually plotted versus time to produce the so-called CUSUM chart. Sometimes it is more convenient to standardize the observations first by not only removing the mean but also dividing by the standard deviation. This has the advantage of producing CUSUMs in terms of the underlying standard deviation.3 For on-line applications, the mean is updated as each new observation is acquired. In this sense there is a close connection between the sequential probability ratio test outlined above and the calculation of on-line CUSUMs (Page, 1954). For off-line applications, x¯ represents the global mean for a sequence of 2

The CUSUM approach has its roots in the field of statistical quality control (Woodward and Goldsmith, 1964), but has received little attention in the physical sciences. 3 The units for CUSUMs in this study, with temperature in 1C and time in days, are 1C days. However, it is standard practice to omit the units and simply label the ordinate ‘‘CUSUM’’, and no units are given (e.g., Hawkins and Olwell, 1998). We have followed this practice throughout the text.

observations that has already been acquired. Change points that may not be possible to detect in the original data often become far easier to detect when the CUSUM is plotted. In Appendix A, we calculate the improvement in SNR that is achieved in detecting the 1976–1977 regime shift, using CUSUMs compared to the original data. We express the improvement in SNR in logarithmic notation using Decibels (dB), where an improvement of 3 dB, for example, corresponds closely to a factor of 2 (or 100%), and 10 dB corresponds to a factor of 10, or 10 times as great. We obtain an improvement of 3.4 dB for Pacific Grove, and at Scripps Pier, the improvement is 7.4 dB. Overall, the CUSUM represents a new time series whose statistical properties differ significantly from those of the original data. For detecting change points, CUSUMs have the advantage of greatly reducing high-frequency noise-like variability which might otherwise obscure the changes of interest. Conversely, serial correlation is increased which not only reduces the degrees-of-freedom but can lead to false alarms in the detection process (e.g., Rudnick and Davis, 2003). Changes in the average level of the process are reflected as changes in the slope of the CUSUM plot, where the magnitude of the slope is proportional to the magnitude of the change in mean level. For the case where the slope of the CUSUM is initially zero, the change in the mean is determined by dividing the change in the CUSUM at two successive times by the corresponding time interval between them. Since the slopes are additive, the slope, mE, associated with a particular event, can be calculated according to mE ¼ mO  mAC  mLTD ,

(3)

where mO is the observed slope, mAC is the slope associated with the annual cycle, and mLTD is the slope associated with any long-term drift or trend. At least two factors contribute to long-term drift. First, long-term warming or cooling, which may be of interest, contributes to the drift. Second, and less desirable, is the fact that the times when the CUSUM begins and ends also affect the drift since it is constrained to start and end at zero when the global mean is removed. The problem of estimating the slopes of CUSUMs is examined in greater detail in Appendices B and C. In Appendix B, we illustrate the adverse effects of serial correlation on CUSUMs using simulated time series. As the serial correlation

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is increased, it tends to alter and distort the slopes of CUSUMs, and thus makes it more difficult to determine their true shape and estimate their magnitude. In Appendix C, we first examine CUSUMs for their sensitivity to when the summation begins and ends. This sensitivity is due to the fact that when the global mean is removed prior to calculating the CUSUM, the summation is constrained to start and end at zero. To examine the sensitivity to the start time, the 1976–1977 event at Scripps Pier was examined using four different start times, 1930, 1950, 1970, and 1975. The results show that the slopes during this event are generally similar although slight differences can be detected. Similar results are naturally expected if we vary the CUSUM end times. Serious problems can arise when the events of interest are located close to the beginning or end of a CUSUM where the slopes may be large. Breaker and Flora (2007) apply (3) to CUSUMs in several cases to remove or reduce the background slopes so that the event of interest becomes less distorted and easier to identify. The annual cycle is a major source of variability in all of the records used in this study. At Pacific Grove, for example, it accounts for 44% of the total variance for the period from 1920 to 2002 (Breaker, 2005). In the results presented here we have always removed the mean annual cycle (MAC) prior to calculating CUSUMs. To calculate the MAC, we calculate the mean value for each day of the year, taken over the number of years in the record.4 For a record length of 85 years, 85 copies of the MAC are concatenated and then subtracted from the original observations, producing a residual time series often called the ‘‘anomaly’’. Finally, the global mean is removed from residuals and the CUSUM is calculated. This procedure greatly reduces one source of variability that can affect the slope of CUSUMs during periods of interest. Other methods clearly exist for removing the annual cycle or reducing its influence. In Appendix C, we compare the results of removing the MAC using a low-pass filter to reduce the influence of the annual cycle. Although there is generally closer agreement between the low-pass filter and the data than there is between the MAC and the data, the residuals from 4 In some cases, the mean annual cycle is smoothed slightly before it is removed from the data, but this has not been done here.

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the low-pass filter are smaller and so the CUSUM turning point pattern displays a smaller step change during most events. Our results, to date, suggest that by removing the MAC, CUSUM patterns are produced that are often easy to detect, indicate whether increases or decreases in temperature (or other property changes) have occurred, and that appear to be somewhat unique to regime shifts. However, other methods of preprocessing could produce better results, and so more work is needed to clarify the relationship between the method of preprocessing that is employed, and the CUSUM pattern that is produced. In principle, the sequential probability ratio test described in the previous section can be used to conduct tests of significance for CUSUMs. In practice, however, decision rules that test for significant changes based on CUSUMs have been addressed using a tool called the V-mask (Wetherill and Brown, 1991). The V-mask is essentially a template that is applied to the CUSUM plot whose boundaries form decision lines. When these decision lines are exceeded by the evolving CUSUM plot or trajectory, a change in the process is indicated. As long as the CUSUM trajectory remains within the boundaries formed by the decision lines, no change is indicated. Because several parameters are required to implement the test whose values are chosen by the user, a degree of subjectivity enters the picture, which, in our view, reduces the utility of the V-mask approach. In Section 4.5 we again address the question of statistical significance using the Wilcoxon rank sum test, which is one of several tests that can used to determine the significance of change points. Although the issue of change points and their significance is important, the problem, in our case, is more closely related to pattern uniqueness and recognition, as we will try to demonstrate. Although CUSUMs have been employed in ecological and climatic research before, their use has been limited. Breaker (2005) calculated a CUSUM for the record at Pacific Grove and found change points in 1929 and 1976 that initially alerted him to the possibility that warming in Monterey Bay could be event-like. The work of Beamish et al. (1999), who used CUSUMs to better visualize long-term trends in climatic data, and Rebstock (2002), who used CUSUMS to search for possible regime shifts in biological and hydrographic data off southern California, are two other examples.

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4. CUSUMs and the present study 4.1. The observations Daily observations of SST have been acquired at the Hopkins Marine Station in Pacific Grove, California (36.6201N, 121.9041W) since 1919. Pacific Grove is located at the southern end of Monterey Bay in a partially sheltered location (Fig. 1). Daily observations of SST and salinity have been acquired at Scripps Pier in La Jolla, California (32.8671N, 117.2501W) since 1916. Unlike Pacific Grove, Scripps Pier has an excellent exposure to the coastal ocean. Pacific Grove and Scripps Pier are located approximately 575 km apart. For the purposes of this study we have extracted data for the 85-year period from January 1, 1920 to December 31, 2004. For the record from Pacific Grove an adjustment has been made. An

abrupt increase in SST of approximately 0.92 1C occurred in mid-1929 that has been examined on several occasions and has yet to be adequately explained (e.g., Breaker et al., 2005). We found no corresponding changes in SST at the Farallons or Scripps Pier at this time. Our present view is that it may have been due to a change in measurement location. However, for the purposes of this study, since it does not appear to be related to regime shifts, we have added 0.92 1C to all data prior to mid-1929, effectively removing the discontinuity that occurs in the original record. In most cases we use the daily observations, but in applying tests of significance, we use weekly-averaged data. Twoway layouts of the daily observations at each location are shown in Fig. 2. Day number on the vertical axis is plotted versus year on the horizontal axis. Areas shaded in red are strongly influenced by El Nin˜o warming episodes. El Nin˜o warming often

Fig. 1. Map of the study area. The daily observations of sea surface temperature (SST) used in this study were acquired at Scripps Pier, off southern California, the Hopkins Marine Station at Pacific Grove in Monterey Bay, off central California, Amphitrite Point near the southern end of Vancouver Island, and Kain’s Point at the northern end of Vancouver Island. Sea level data from San Francisco were also used in this study. All measurement locations are shown in the figure, and the distance between the northernmost location at Kain’s Island, and the southernmost location at Scripps Pier, is 2150 km.

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Fig. 2. Two-way layouts show contours of SST with day number plotted along the y-axis, and year along the x-axis for Pacific Grove (a), and Scripps Pier (b). The scales to the right of each figure give the correspondence between color and temperature where temperature is expressed in degrees Centigrade (1C). Areas shaded in red are strongly influenced by El Nin˜o warming episodes.

contributes to large increases in the CUSUM time histories and sometimes makes it more difficult to identify possible regime shifts. Although the daily observations of SST from Pacific Grove and Scripps Pier serve as the primary sources of data for this study, several other coastal records have been drawn upon. Daily observations of surface salinity from Scripps Pier from 1920 to 2004, daily-averaged sea levels from San Francisco from 1901 to 2004, and daily SSTs from Amphitrite Point and Kains Island from 1940 to 2004, are also used in this study.5 Amphitrite Point and Kains 5

The actual record lengths are not important in this study, as long as they encompass the events of interest, if the start and end

Island are both located along the coast of Vancouver Island. The locations of all observing sites are shown in Fig. 1, and span a distance of 2150 km, from Kains Island, to the north, to Scripps Pier, to the south. 4.2. The 1976– 1977 regime shift—a canonical event According to Hare and Mantua (2000), it is now widely accepted that during the winter of 1976–1977, a major regime shift occurred in the (footnote continued) times do not significantly affect the CUSUM signatures during those events.

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Fig. 3. A 17-year time series of the standard deviate averaged by year for 40 environmental variables. The standard deviate along the y-axis is given in terms of the unit less paramater, Vri, which represents the standard deviation of the standard deviates. The step passes through the mean standard deviate for two 8-year intervals (1968–1975 and 1977–1984). The area that falls within the dashed lines represents the standard error of the 40 environmental variables computed for each year. Taken from Ebbesmeyer et al. (1991).

North Pacific. Bakun (2004) refers to the 1976–1977 regime shift as quintessential, since it clearly had a major impact on the marine ecosystems of the North Pacific but also resulted in major climatic changes as well. Ebbesmeyer et al. (1991) examined 40 environmental variables and found that all revealed the impact of this event. Fig. 3 from Ebbesmeyer et al. shows a composite plot of the standard deviate averaged by year for the 40 environmental variables that were included in their study.6 A step function was used to represent the composite change that occurred in response to this event. We consider this a canonical event and proceed to calculate CUSUMs of SST at Pacific Grove and Scripps Pier to examine these cumulative time histories during this period. 4.3. CUSUMs of coastal SST off central and southern California Prior to calculating CUSUMs, the MAC was first removed. By removing the MAC, we greatly reduce one major source of unwanted variance, while at the same time reducing long-range persistence in the data. The global mean was removed after removing the MAC before the CUSUMs were calculated. Fig. 4 shows the CUSUMs for Pacific Grove (red) and Scripps Pier (black), for the period from 1920 to 6

Rudnick and Davis (2003) have shown that changes in the data observed by Ebbesmeyer et al. (1991) similar to the 1976–1977 regime shift, could arise through chance alone in time series with similar statistics.

2005. We refer to the paths taken by the CUSUM time histories as trajectories, and they clearly differ for the two locations. The large-scale drift associated with each trajectory implies nonstationary behavior, which may be due in part to the increase in serial correlation that occurs when the original data are transformed into cumulative sums. The trajectories contain extensive structure with numerous changes in slope. Almost certainly, the changes in the long-term trends following the 1976–1977 regime shift are highly significant, where they become strongly positive for the remainder of the records. The long-term impact of this event sets it apart from most, if not all, of the regime shifts that have occurred during the past century. The impact of major El Nin˜o warming episodes in the early 1930s, 1941, 1957–58, 1982–83, 1992–1993, and 1997–1998 is also clearly evident in both CUSUMs. However, many smaller scale events can also be seen in these trajectories. The times of each of the six regime shifts we examine are identified by vertical arrows in the plot. Even at this scale, we can see in most cases that these events correspond to turning points in the CUSUM trajectories. First, we examine the CUSUM trajectories during the 1976 event. Although the absolute CUSUM amplitudes differ by almost 2000, each trajectory reveals a turning point in 1976 (Fig. 4). In Fig. 5a, we take a closer look at these turning points after correcting for the difference in amplitudes. The region within the dashed window (in green) shows that the two trajectories have essentially the same slope, and follow similar paths from mid-1976 to

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Fig. 4. Cumulative sums (CUSUMs) for the daily sea surface temperatures at Pacific Grove, in southern Monterey Bay (red), and Scripps Pier, just north of San Diego (black), for the period 1920–2005 are shown. The mean annual cycle was first removed and then the global mean was removed from the residuals prior to calculating the CUSUMs. The six regime shifts examined in this study, are indicated by vertical arrows.

early 1977. There is a slight uncertainty as to when these turning points start and end but if the window captures this event in its entirety, we estimate that the transition occurs over a period of approximately 7 months. The similarity of the CUSUMs during this period is almost striking. These turning points also appear to be in phase suggesting that this event occurs at both locations at the same time. Because the slopes of the CUSUMs during the period of interest are positive, they reflect increases in mean temperature. Although warming during this event was observed over a broad band along the Pacific coast of North America, a large portion of the central Pacific was, on average, 0.8 to 1.0 1C cooler, according to Hare and Mantua (2000). According to Miller et al. (1994), the 1976–1977 regime shift occurred during the winter of 1976–1977, and based on their results, the transition period associated with this event appears to have lasted for at least several months. To further demonstrate the similarity between the turning points at the two locations, we have cross-correlated the CUSUM trajectories using a moving window

whose width is approximately 1 year. Fig. 5b shows the maximum running cross-correlation function (CCF) during this event.7 The CCF has a peak value of +0.95 in mid-to-late 1976, reflecting a high degree of similarity in the CUSUM patterns that coincides closely with the time of the 1976–1977 regime shift. The CUSUM turning points are similar in form, highly correlated, and well-synchronized at the time of the 1976–1977 regime shift. We now use this pattern as the basis to search for other regime shifts since 1920 that have been reported. The CUSUM trajectories are shown in detail in Fig. 6 for the reported events in 1925, 1939, 1946, 1976, 1989, and 1999. The exact times of these events were determined by searching the CUSUM time histories for patterns that resembled the pattern for the 1976–1977 event during the periods that have been previously reported. We refer to this as the process of localization, and have been able to identify, in all but two cases, a single unique turning 7

Note that times along the abscissas in (a) and (b) are not quite the same.

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Fig. 5. The top panel shows the CUSUM turning points or trajectories for the 1976–77 regime shift (Fig. 5a). The CUSUM trajectory for Pacific Grove is shown in red and the corresponding trajectory for Scripps Pier, in black. The event is bracketed by a dotted green box. The lower panel (Fig. 5b) shows the corresponding running cross-correlation between the two CUSUM trajectories during the period of the event using a moving window approximately one-year wide. The maximum crosscorrelation is +0.95.

point at or near the reported times that we attribute to the event in question. In each case the trajectories have been corrected for differences in the overall levels between the CUSUMs to facilitate comparisons. The CUSUMs for Pacific Grove are shown in red and those for Scripps Pier, in black. For the event in 1925 (Fig. 6a), the CUSUM turning point amplitude at Scripps Pier is much higher than the amplitude at Pacific Grove, almost four times

higher. The pattern at Scripps Pier clearly resembles the pattern for the 1976–1977 event. Because the slopes at both locations are positive, like the 1976–1977 event, they imply increases in the mean temperature, consistent with the phase change in the PDO that occurred at that time. Although the patterns appear to be in phase, the transition at Pacific Grove ends several months earlier than it does at Scripps Pier. This event actually begins at the end of 1925 and extends well into 1926. At Scripps Pier, we estimate its duration to be at least 9 months. The event in 1939 raises some questions (Fig. 6b). We have found two possible events during the period from 1939 to 1940. They are framed with dotted lines. According to MacCall (1996), the event in 1939 represented a change to cooler conditions. The event in early 1939 is consistent with MacCalls observation since the slopes are negative. However, the second event during late 1939 and 1940 represents a larger positive change. As we will show in Section 4.7, the net effect of these events resulted in an overall increase in mean temperature at Pacific Grove, and a decrease at Scripp’s Pier. The event in 1946 (Fig. 6c) is almost the mirror image of the 1976–1977 event and thus reflects a decrease in mean temperature, consistent with the phase change in the PDO that occurred at this time. This event is well-defined at both locations and the turning point patterns are in phase. In this case, we estimate a transition period of 5 months. The maximum running CCF occurs at the end of 1945 and is +0.89. Next, we examine the 1989 event (Fig. 6e). The similarity and phase-locked nature of the CUSUM trajectories during the period from late 1988 to early 1989 is striking. In this case, the event duration or transition period is estimated to be approximately 5 months. Due to the negative slopes of the CUSUMs, a decrease in temperature is indicated. Although minor cooling was observed off the coast of California during this event, there was a broad region of warming in much of the central North Pacific (Hare and Mantua, 2000). The running CCF between the CUSUMs for the 1989 event has a maximum value of +0.99 in early 1989, occurring where we would expect it to occur, based on the similarity and in-phase nature of the CUSUM trajectories. The last event occurred in 1999 (Fig. 6f). There is little resemblance to the 1976 event at either location. The trajectories are small in amplitude and out of phase, and the duration of this event appears to be only 1–2 months, inconsistent

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Fig. 6. CUSUM trajectories are shown for the events that occurred in 1925 (6a), 1939 (6b), 1946 (6c), 1976 (6d), 1989 (6e), and 1999 (6f). They have been corrected for differences in amplitude to facilitate comparisons (see Fig. 4). The CUSUM trajectories for Pacific Grove are again shown in red and for Scripps Pier, in black. Two boxes are included in Fig. 6b (dotted lines in black) that localize two possible events during 1939 and 1940.

with the other events. One factor that detracts from this comparison is that the leading edge of the trajectory from Pacific Grove corresponds to the trailing edge of the 1997–1998 El Nin˜o (Fig. 4), and, as a result, influences the turning point pattern at this location. Because of the uncertainties associated with these turning point patterns, we have made no attempt to determine whether SST increased or decreased in this case. In summary, our inability to detect and localize this event is due to at least two factors. First, the event itself may not have been well-expressed at these locations, and second, our method is not sufficiently robust to handle cases where departures from the expected patterns and phase relationships are significant. Table 1 lists the estimated start, end time, duration, whether the temperature increased or decreased (i.e., change direction), sustained change in temperature, and statistical significance associated with each event. In all cases, the amplitudes of the regime changes are larger at Scripps Pier than they are at Pacific Grove. According to Breaker (1989), other oceanographic events such as the

spring transition to coastal upwelling are reduced in amplitude at Pacific Grove compared to their amplitude further offshore in the California Current, due primarily to the partially sheltered location of the measurement site.

4.4. How transition events appear in the original data To examine the transition process in more detail, and to help verify previous estimates of event duration, we have taken the CUSUM turning point patterns for the 1976 and 1989 events and first smoothed them in an effort to extract the underlying patterns without the combined effects of noise-like variability that is unrelated to the transition itself (Figs. 7a and c). The smoothing was performed using Loess, a method that is based on robust, locally weighted regression (Cleveland, 1979). Loess fits a linear basis function to the data at the center of regions where the radius of each region contains a specified number of data points. The fraction of data in each region, and thus the smoothness, is

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Table 1 Selected characteristics of the six events examined in this studya Date of event

Date of initiation (month/yr)

Date of termination (month/yr)

Duration (months)

Change direction (+ ¼ m ) and ( ¼ k)

Sustained changes (71C)b

Statistical significance (5% level)

Comments

1925

10/25

5/26

7

+

+0.17

No

1946

10/25 9/39 9/39 12/45

7/26 6/40 6/40 5/46

9 9 9 5

+ + + 

+0.39 +0.29 0.17 0.41

No No No Yes

Coincides with phase change of PDOc Same See footnoted See footnoted Coincides with phase change of PDOc

1976

12/45 8/76

5/46 3/77

5 7

 +

0.25 +0.43

Yes Yes

8/76 10/88 9/88

3/77 3/89 3/89

7 5 6

+  

+0.68 0.22 +0.45

Yes No No

7/99

8/99

–

–

+0.27

No

6/99

7/99

–

–

0.14

No

1939

1989

1999

Coincides with phase change of PDOc Same Almost significant (0.053 vs. 0.05) Event weak and poorly resolved Event weak and poorly resolved

a

For each event, the results for Pacific Grove are shown above, and for Scripps Pier, below. The sign of the CUSUM may determine whether the event results in a sustained increase or decrease in temperature. c Pacific decadal oscillation d There were two possible events during 1939–1940. The values listed correspond to the second (and larger) event during this period. b

determined by a smoothing parameter selected by the user. In our case, the degree of smoothing was chosen with care to retain the underlying pattern but not the short-term variability, whether it is due to actual variations in the data and/or to the effects of serial correlation. Next, first differences of the original and smoothed CUSUMs were calculated (Figs. 7b and d). It was our goal to smooth the CUSUMs sufficiently so that first differences of the smoothed versions might reveal the underlying patterns associated with the event itself as it occurs in the original data. Of particular interest in the CUSUMs are the inflection points that are indicated by the vertical black lines. Inflection points occur where the sign of the second derivative of the function has changed from positive to negative, or vice versa. For the 1976 event at Scripps Pier, there are two welldefined inflection points in the smoothed CUSUM that correspond to well-defined minima in the first differences (Fig. 7b). In both cases, the CUSUM slopes are negative where the inflection points occur. Based on our experience up to this point,

these turning points most likely represent, at least approximately, the beginning and end of this event. If this interpretation is correct, we can estimate its duration rather precisely. In this case, the duration is about 7 months, in close agreement with a similar estimate obtained from the Pacific Grove CUSUM (not shown). This value is also consistent with the estimated duration of this event given earlier in Section 4.3, and listed in Table 1. Turning next to the 1989 event at Pacific Grove (Figs. 7c and d), inflection points again occur near the beginning and end of this event, although the inflection point at the beginning is far less welldefined (and thus more difficult to locate accurately) than the inflection point at the end.8 In this case, the first inflection point, which occurs along a portion of the CUSUM where the slope is slightly positive, corresponds to a relatively small but noticeable maximum in the first differences of the smoothed CUSUM. For the second inflection point, where the 8

See Fig. 6c for the event in 1946 at Scripps Pier for a welldefined inflection point at the beginning of the transition.

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Fig. 7. Smoothed and unsmoothed CUSUMs for the 1976–1977 regime shift at Scripps Pier, and the 1988–1989 regime shift at Pacific Grove are shown in Figs. 7a and c. The vertical lines identify inflection points that may indicate the approximate initiation and termination times for these events. The smoothed CUSUMs were obtained using Loess (see text for details). First differences of the smoothed and unsmoothed CUSUMs are shown in Figs. 7b and d, for each event and location. Since the units for the CUSUMs are in 1C days, the units for the first differences are in 1C, i.e., the units of the original data. See the text for details.

slope is again positive, we observe a second and larger maximum in the first differences of the smoothed CUSUM. For this event, based on the separation of these critical values, we estimate a duration of almost 5 months, in close agreement with our estimate obtained from the record at Scripps Pier (not shown), and close to the value given in Table 1. These results suggest that in classic cases such as the 1976–1977 regime shift, they manifest themselves as smoothly varying, continuous functions of temperature that are preceded and followed by

critical values of the function that signal the approximate onset and termination of the event. If the critical values correspond to minima, then we should expect a sustained increase in temperature to occur, in the absence of other factors. Conversely, if the critical values correspond to maxima, then we may expect a sustained decrease in temperature to occur. That there may be two, rather than one change point associated with these events not only changes our understanding of how the transition process itself occurs, but also has implications for applying tests of significance.

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4.5. Tests of significance Next, we examine the statistical significance of the six events described in the previous section. We have applied the Wilcoxon rank sum test (e.g., Hollander and Wolfe, 1973) to each segment of the records at Pacific Grove and Scripps Pier that contained a potential regime shift and treated it as a single change point. In the application of the test, actually two segments are involved. The first segment corresponds to the section of data from the previous event to the event being tested, and the second segment corresponds to the section of data from the event being tested to the next event. The test allows for segments of different length, which applies in this case. A two-sided rank sum test is performed to determine if two independent samples come from distributions with equal medians. Since we have made the assumption that the locations of possible change points are known then the only question is whether or not the medians from each sample are the same. The test assumes that the observations are independent within, and between, the samples. In this regard, we have weekly averaged the data to reduce short-range persistence, and then removed the MAC to reduce long-range persistence. The data were then subsampled every 10th value to further reduce serial correlation. The results of the test for Pacific Grove indicate that the change points in 1946 and 1976 are statistically significant at the 5% level, whereas the change points in 1925, 1939, 1989, and 1999 are not. The results of the test for Scripps Pier indicate that the change points in 1946 and 1976 are statistically significant, whereas the change points in 1925, 1939, 1989 and 1999 are not. However, the change point at Scripps Pier for the 1989 event was close to the 5% level of significance (0.053). It may also be noteworthy that since the amplitudes of the regime shifts at Scripps Pier were generally larger than the corresponding amplitudes at Pacific Grove, that the tests of significance did not indicate more of the change points at Scripps Pier to be significant than at Pacific Grove. The results of these tests of significance are also included in Table 1. There are several reasons why our application of this test may reduce its power or violate the assumptions upon which it is based. First, the change points in this case correspond more closely to change intervals since the periods of transition for the events we have examined range from about 4–9 months. Second, it appears that some, if not

most, events are composed of two change points, one that indicates the beginning of the transition and a second that indicates the end. Thus, problems may arise in applying tests of significance that assume only a single change point. Third, additional warming or cooling may occur during periods far removed from the change points we examine, but changes in temperature at other times, when and where they occur, are also included in the test even though we are presumably testing only for changes at the locations of interest. Thus, we expect these results to provide only a rough indication of the relative importance of these events. As we stated earlier, however, the primary issues in the present study, since we employ CUSUMs, may be more closely related to pattern uniqueness and pattern recognition, than statistical significance. 4.6. The inverse problem and robustness Now we turn the problem around and use the CUSUM signatures obtained for the well-defined regime shifts and search the record for similar patterns that may not have been reported before. By addressing the inverse problem, we hope to shed some light on the uniqueness of the CUSUM patterns associated with well-defined events and the robustness of the technique in the presence of other sources of variability that could have similar characteristics. In particular, we have selected the interval between 1946 and 1976 to search for possible events since no regime shifts have been reported during this period.9 Initially, sixth-order polynomials were fitted to each CUSUM and then subtracted from the original CUSUMs to reduce the long-term drift, and thus facilitate comparisons (Fig. 8a). Next, the running cross-correlation between the CUSUMs for Pacific Grove and Scripps Pier was examined using a one-year window for possible similarities that could reflect large-scale changes. The drift-corrected CUSUMs were highly correlated in many cases. However, on closer inspection, the patterns, although often similar at the two locations, were not similar to the canonical pattern associated with the 1976–1977 event. Thus, we relied on visual inspection of the two CUSUMs using a magnified moving window to determine whether any matches could be found, based on 9 Actually, a possible regime shift in 1970 was reported by Bakun (2004), but we find no indications of an event in either record at this time.

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Fig. 8. CUSUMs for Pacific Grove (red) and Scripps Pier (black) are shown for the daily observations for the period from 1920 to 2005 (Fig. 8a). The mean annual cycle and the global mean were first removed. After the CUSUMs were calculated, a sixth-order polynominal was fitted to the CUSUMs and then subtracted from the original versions to remove the large-scale drift. Windows identify and localize the events in 1946 and 1976, and a possible event in 1972. Fig. 8b shows an enlarged version of the possible event in 1972.

characteristic slopes, durations, and phase relationships for the CUSUMs at the two locations.10 Only one clear match was found, a step-like decrease in temperature that occurred in 1971–1972, although there were weaker indications of a possible match in 1948–1949. A window has been placed around the period of interest in 1971–1972 as well as the events in 1946 and 1976. An enlarged version of the CUSUMs during the 1971–1972 period is shown in Fig. 8b. The patterns and slopes are similar to the 1976–1977 event, although in this case, the slopes are negative, implying a decrease in temperature. The duration of this possible event is estimated to be 6–7 months, and the patterns appear to be in phase. Although we are not aware of a regime change at this time, the CUSUM turning point closely followed one of the largest negative excursions in the ALPI and the PDO indices since 1900 (Mann and Lazier, 2006, Fig. 9.03). We also note that a major El Nin˜o episode occurred during 1972 and 1973 (Quinn et al., 1978), closely following the event 10 This is a problem that could be addressed using the methods of pattern recognition. In future work, we plan to implement such methods to insure that decisions are made objectively.

shown in Fig. 8b. The event in question occurs in late 1971 and early 1972, whereas the 1972–1973 El Nin˜o episode reached its maximum intensity off central California in October 1972 (Breaker, 2005), at least 6 months later. Based on the timing of these events, we cannot rule out the possibility that there may be overlap, and/or that they are related. Overall, however, we find these results encouraging in that the CUSUM patterns associated with welldefined regime shifts may be rather unique and thus potentially useful in detecting similar events at other times and in other records. 4.7. Sustained changes in temperature between events In principle, we can estimate the instantaneous change in temperature during a given event from the CUSUM, if all of the slopes that contribute to the observed slope, except for the event itself, can be determined since the magnitude of the slope is directly proportional to the change in the mean temperature. Although we have not estimated the slope magnitudes per se, we have indicated from the sign of the turning point slopes, whether increases

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or decreases in temperature occurred. In each case where a well-defined event could be identified, our results agree with previous observations. In order to estimate the changes in temperature that accompany each event, we simply calculate the mean temperatures between each event from the original record, and refer to theses values as ‘‘sustained’’. The procedure we have employed is referred to as bin smoothing, where the data are partitioned into a number of disjoint and exhaustive regions, and then linearly averaged within each region (Hastie and Tibshirani, 1990). It is important to note, however, that mean values, calculated in this manner, represent not only the instantaneous change that may occur during a given event but also longer-term

changes in temperature between events. Thus, the changes we obtain could be largely overestimated since we do not know to what extent warming or cooling between these events contributes to the overall warming process. To better visualize the changes in temperature, we have concatenated the sustained values between each event to form a continuous step-wise function, often referred to as a Manhattan diagram (Fig. 9). The temperature at Pacific Grove and Scripps Pier both show net increases over the period from 1920 to 2005, and in some cases the step changes are similar, such as the increases in 1925 and 1976, and the decreases in 1946. However, a sustained increase of +0.35 1C occurred at Pacific Grove and a

Fig. 9. The mean values of temperature between each change point or event have been concatenated to produce a continuous step-wise plot called a Manhattan diagram. The diagram for Pacific Grove is shown in Fig. 9a, and the diagram for Scripps Pier is shown in Fig. 9b. See text for details.

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decrease of 0.17 1C at Scripps Pier following the events in 1939–1940. The results at Scripps Pier are consistent with MacCall (1996), who indicated that a change to cooler conditions had taken place at this time. For the 1989 event, the slopes of CUSUMs were both negative implying that sustained decreases in temperature would follow (Table 1). However, the temperature increased at Scripps Pier (+0.45 1C), while it decreased (0.22 1C) at Pacific Grove. One explanation for this discrepancy is that sustained warming occurred off southern California during the interval between 1989 and 1999 that was far greater than any cooling associated with the transition itself. It is also possible that another event occurred during this period which led to a positive change that has gone undetected. Because we were not able to clearly identify or localize the event that occurred in 1999, we do not attempt to interpret the changes that occurred at that time. In all other cases, the signs of the changes are the same at both locations, and consistent with previous observations.

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4.8. Other variables and other locations So far, we have considered only one variable, SST, in an effort to detect regime shifts along the eastern boundary of the North Pacific. Now we look at two other variables, sea level and salinity, to see how they respond to several of the events we have already examined. Also, we have only examined events at two locations, Pacific Grove and Scripps Pier. Thus, we look at regime shifts at three other locations along the west coast of North America, San Francisco, in northern California, Amphitrite Point, located near the southern end of Vancouver Island, and Kain’s Island, located at the northern end of Vancouver Island (Fig. 1). In Fig. 10, we show the CUSUM of daily-averaged sea levels at San Francisco during the 1976–1977 event (10a), the CUSUM of daily SSTs at Amphitrite Point during the 1989 event (10b), the CUSUM of daily SSTs at Kain’s Island during the 1976–77 event (10c), and CUSUMs of daily SST, salinity and density (i.e., sigma-t) for the 1976–1977 event at Scripps Pier

Fig. 10. (a) shows a CUSUM for sea level at San Francisco for the 1976–1977 regime shift (10a), (b) shows a CUSUM for SST at Amphitrite Point off Vancouver Island for the 1989 regime shift, (c) shows the CUSUM at Kain’s Island off Vancouver Island for the 1976–1977 regime shift, and (d) shows the standardized CUSUMs of SST, salinity and density at Scripps Pier, for the 1976–1977 regime shift. The mean annual cycle has been removed in each case.

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(10d). Sigma-t in this case is derived from the corresponding observations of SST and salinity at Scripps Pier. Although the CUSUMs, in some cases, have been started at different times, there appears to be, at most, only a small effect on the resulting slopes during the events we examine. The MAC has be removed in each case and the observations from San Francisco, Amphitrite Point, and Kain’s Island have been standardized prior to calculating the CUSUMs, whereas SST, salinity and sigma-t at Scripps Pier have been standardized after the CUSUMs were calculated so that they could be plotted together on the same axis. The turning point pattern associated with the 1976–1977 event in sea level at San Francisco (10a) is in phase with the patterns at Scripps Pier and Pacific Grove. However, the signature in this case is more subject to noise, and the inflection points at the start and end of this event are not clearly defined. We found this to be true for other events as well, and in some cases, the events were not in phase with the events at Scripps Pier and Pacific Grove, and, upon occasion, events that were relatively easy to identify in SST could not be identified in sea level. The CUSUM in SST at Amphitrite Point (10b) during the 1989 event is well defined and in phase with the events at Scripps Pier and Pacific Grove, although this event provided the best agreement we could find at this location. The CUSUMs for other events, including the 1976–1977 event, were more subject to noise-like influences and thus more difficult to identify. The 1976–1977 event in SST at Kain’s Island (10c) is again subject to noise but is essentially in phase with the CUSUMs at Scripps Pier and Pacific Grove. The amplitude of this event at Kain’s Island and Amphitrite Point was also far smaller than it was at Scripps Pier or Pacific Grove, based on CUSUMs that were not standardized (not shown). In addition to SST, salinity data have also been acquired at Scripps Pier, and so it is possible to examine how this variable has responded to selected events. In Fig. 10d, CUSUMs of SST, salinity and sigma-t have been standardized so that they could be plotted together and compared. The inflection points in the CUSUM of salinity are less welldefined than they are for SST, and this was found to be true for other events as well. In this case, both SST and salinity increase, suggesting that density might have been conserved. However, the slope of the CUSUM for sigma-t is negative, at least during

the event itself, consistent with the increase in temperature. In summary, although the CUSUM patterns in SST for the events we have examined are better defined and more distinct at Scripps Pier and Pacific Grove than they are at Amphitrite Point and Kain’s Island, their timing is essentially the same, and the sign of the change, i.e., whether increases or decreases occur, agree, and are consistent with previous reports. Finally, the results indicate that SST is generally a more most sensitive indicator of the changes we have examined, than either sea level or salinity, and so may serve as a better proxy for observing and monitoring the state of the system. 4.9. The issue of resolution Up to this point, we have used daily observations except for the tests of significance conducted in Section 4.5, where weekly averaged data were used. Now we ask the question, how often should the data be acquired to adequately resolve the events we have examined in this study? Once again, we employ the 1976–1977 regime shift to illustrate how well we can resolve this event as the sampling rate is decreased from one sample per day, to one sample per year. In Fig. 11, we show the CUSUM for Pacific Grove for the 1976–1977 event using the daily observations (Fig. 11a), weekly averaged (Fig. 11b), monthly averaged (Fig. 11c), seasonally averaged (Fig. 11d), and yearly averaged data (Fig. 11e). We have employed a window that extends from March 1976 to September 1977, and so includes the event itself plus several months, prior to, and, following it. A comparison of Figs. 11a and b shows that virtually no structure in the pattern is lost in using the weekly averaged data. The pattern produced by the monthly-averaged data also strongly resembles the original daily observations with only a slight loss of detail. When we compare the seasonally averaged and yearly averaged data, however, any correlation with the daily observations is completely lost. We note that since Rebstock (2002) analyzed biological and hydrographic data that were sampled seasonally, regime shift transitions per se, could not be examined. Also, the 1976–1977 event was estimated to have duration of approximately seven months (Table 1) and so monthly averaged data in this case provides at least seven samples to reproduce the original pattern. However, monthly averaged data may not adequate to resolve events that are significantly shorter in duration.

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Fig. 11. This figure shows the CUSUMs for the daily (10a), the weekly averaged data (10b), the monthly averaged (10c), the seasonally averaged (10d), and the yearly averaged (10e) SSTs, for Pacific Grove, for the 1976–1977 regime shift. The period from 1976.2 to 1977.55 is shown which brackets the 1976–1977 event.

In addition to temporal averaging, climatic data are often spatially averaged as well. In our work, we might actually improve the quality of the CUSUM patterns from Pacific Grove and Scripps Pier by averaging, when they are in phase. Averaging in this case would reduce the independent noise-like contributions but preserve the underlying pattern that is common to both records. When the patterns are out of phase, spatial averaging will degrade the results, unless the patterns are first phase aligned. In general, since the underlying phase relationships are usually not known or taken into account, spatial averaging, like temporal averaging, simply reduces our ability to detect or resolve changes that have time scales as short as regime shifts. 5. Discussion Regime shifts are often treated as change points in climatological records. As a result, statistical tests of significance can be applied to determine whether or not the events of interest are significant at least in

a statistical sense. To determine whether or not the change points identified in this study were statistically significant, one test that is often used for this purpose is the Wilcoxon rank sum test. The results of this test for Pacific Grove indicate that the change points in 1946, and 1976 are statistically significant whereas the change points in 1925, 1939, 1989, and 1999 are not. For Scripps Pier, the change points in 1946 and 1976 are statistically significant whereas the change points in 1925, 1939, 1989, and 1999 are not. The significance of the 1989 event at Scripps Pier was border line with a significance level of 5.3% (with our cutoff set at 5%). Although the events in 1925 and 1999 were not statistically significant at either location, it is very likely that they do, in fact, reflect regime shifts, based on information from other sources. In our analysis of the CUSUM time histories, it appears that these events are often characterized by two change points, one that may initiate the transition process, and a second that terminates it. Because there are frequently two change points associated with a

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particular event that are separated by up to 6 months or more, it may be difficult to obtain meaningful results from any conventional test of significance. Hsieh et al. (2005) also question the use of statistical tests to determine whether or not regime shifts have occurred. As they point out, identifying regime changes usually requires a subjective decision at some point, and the transition process itself is usually assumed to involve only two states. As a result we question how useful tests of significance are when CUSUMs are employed and believe that the basic question is more closely related to pattern recognition. Thus, tests based on pattern matching and correlation may be more relevant. One area that needs further attention is in preprocessing the data. Although by removing the MAC prior to calculating CUSUMs, we have been able to produce a turning point signature that appears to characterize these events and is to some degree, unique, it is quite possible that other methods of preprocessing might produce even better results. For some of the weaker and less well-defined events such as the 1999 regime shift, other methods of preprocessing could be more effective in extracting the desired information. Also, the problem of estimating the slopes associated with turning points or events of interest needs to be addressed. We identified several factors that affect the slopes of CUSUMs that should, in practice, be taken into account if the slope associated with the event itself is to be correctly estimated. However, these results are preliminary and more work is needed in this area. Another area where additional work is needed is in estimating the changes that occur during regime shifts. In some cases, they may lead to significant long-term increases or decreases in property values and in other cases they may have little or no longterm impact. Although, in principle, we should be able to estimate the magnitude of these changes directly from the CUSUM, our experience has shown that this is usually not the case. Distortion of the CUSUM patterns from various sources and less-than-accurate slope corrections contribute to the problem. In Section 4.7, we attempted to address this question by simply calculating the mean temperatures between events where we referred to them as sustained values. This raises the basic question of how much warming or cooling actually occurs during the event itself, and how much takes place on longer time scales between events. We are striving to find ways to address this

question. Breaker and Flora (2007) have introduced a procedure called the method of expanding means that allows us to roughly estimate the magnitude of the change during an event, and how well it is sustained. It is based on the original data and not the CUSUMs. Although the procedure appears to be useful, it raises new questions that have yet to be answered. Our goal is to be able to decompose the warming process into a range of time scales so that we can obtain a better understanding of the mechanisms that contribute to it. One of the questions this study raises is how the events that we have identified in SST are related to biological changes in the North Pacific? Previous observations have clearly shown that marine biota from different trophic levels have responded to regime changes in this region. However, with the CUSUM time histories of daily observations off central and southern California, we have been able to observe how regime shifts evolve in far greater detail than has been done before. The only case where CUSUMs have been applied to biological data for the purpose of detecting possible regime shifts, to our knowledge, is based on the work of Rebstock (2002), who applied CUSUMs to nonseasonal anomalies of copepod abundance off southern California. Between 1951 and 1999, Rebstock found numerous step changes in her CUSUM plots, which in some cases corresponded to changes in supporting hydrographic data. She found that many species responded to the events in 1976–1977 and 1989. However, because her data were acquired on a seasonal basis, she was not able to examine the regime transitions themselves, or to ascertain how the hydrographic and biological data were related. To better understand the relationship between the physical forcing and the biological response associated with regime shifts, both high-resolution hydrographic and biological data are required. One of the important questions this study raises is how regime shifts are generated? Although this topic is beyond the scope of the present study, we briefly mention some of the work in this area. As indicated in earlier, there may be a connection between regime shifts and long-term changes in the state of the Aleutian low-pressure system. Also, warming in the tropical Pacific could contribute to regime changes, as Kashiwabara (1987) and Nitta and Yamada (1989) have indicated for the 1976–1977 event. Graham (1994), and Miller et al. (1994) used ocean global circulation models to study decadal and interdecadal variability in the North

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Pacific. Both studies showed that dynamically based models using realistic forcing could reproduce, abrupt step-like changes in various physical properties that were characteristic of the 1976–1977 regime shift. Rudnick and Davis (2003), and Hsieh et al. (2005) indicate that regime shifts could be caused by random environmental fluctuations, i.e., stochastic variability. Rudnick and Davis showed that the major regime shift in 1976–1977 could have been caused by chance alone through stochastic forcing. Hseih et al. indicate that changes in the physical environment may be due to stochastic forcing, but that changes in large-scale marine ecosystems are more likely due to nonlinear mechanisms. Finally, we note that although stochastic forcing is one possible explanation for regime shifts, since they tend to occur on preferred time scales, i.e., decadal, other explanations should be considered. We have been able to examine the events in this study in greater detail than has been done before, because daily observations from single locations were employed. If we had used seasonally averaged, yearly averaged, or in some cases, even monthly averaged data, it would not have been possible to detect these relatively rapid changes, and certainly not to observe their evolution. As a result, many climate-related observations and indices cannot provide the resolution required to detect these changes. Without observations from several locations, in this case, far removed from one another, it would have been more difficult to conduct the foregoing analyses. If we think of the locations where the data were acquired as the elements of an observing array, it is a simple matter using the techniques of array processing to show that the ability to detect signals is directly proportional to the number of elements in the array (e.g., Urick, 1967). Thus, if long-term records from other locations around the Pacific basin can be acquired, it should be possible to improve our ability to exploit the CUSUM technique for CPD, and to help determine how these events evolve spatially. 6. Summary and conclusions Cumulative sums (CUSUMs) of SST time series from Pacific Grove and Scripps Pier for the period from 1920 to 2005, and records of SST from several other locations have been used to detect and localize documented regime shifts in the North Pacific. One of the primary uses of CUSUMs is to detect change

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points that in this case could be related to regime changes that have been reported in the past. Since the regime shift in 1976–1977 is well-documented and generally accepted as a canonical event, we first examined the records from both locations and found that the CUSUM trajectories produced distinctive, highly correlated, and well-synchronized patterns during this event. We then used the turning point pattern from this event as a basis to search for other events in the past that may likewise correspond to regime shifts in the North Pacific. In addition to the event in 1976–1977, unique turning point patterns were found in 1925, 1939, 1946, and 1989, all of which correspond to events or regime shifts that have previously been reported. Turning point patterns, very similar to the patterns detected during the 1976–1977 event, were obtained for the events in 1946 and 1989. The turning point patterns during the other events, although well-correlated between Pacific Grove and Scripps Pier, depart somewhat from the classic pattern associated with the 1976–1977 event. A regime shift in 1999 has also been reported but our results were inconclusive in this case. That these turning points are often highly synchronous at two locations almost 600 km apart suggests that the scale of these events is basin-wide, consistent with spatial scales that are usually associated with regime shifts (Bakun, 2004). Coastal SSTs appear to be a reliable indicator of regime changes, and together with CUSUMs can be used to examine the transition process associated with these events in far greater detail than has been done before. Transition events were further examined by first smoothing the CUSUM patterns and then taking the first differences of the smoothed and the original CUSUMs. By taking first differences of the smoothed CUSUMs we can observe how the transition process actually appears in the original data. It was found that inflection points near the beginning and end of well-defined events correspond to minima in cases where the CUSUM slopes are positive, and maxima in cases where the CUSUM slopes are negative. Thus, inflection points in the CUSUMs, or maxima and minima in the first differences, provide guidance in estimating the duration of an event. The statistical significance of the events examined in this study was determined using the Wilcoxon rank sum test. The events at Pacific Grove in 1946, and 1976 were found to be statistically significant, and the events in 1946 and 1976 were statistically

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significant at Scripps Pier. However, questions arise with regard to tests of significance in detecting regime shifts since the change itself may take at least 6 months, and two, not one, change point may be involved. As a result, tests of significance may not be a reliable indicator of regime shifts. Rather, our results suggest that when CUSUMs are employed, the basic questions are more closely related to pattern recognition, and, as a result, tests based on pattern recognition may be more appropriate. To examine the robustness of the CUSUM approach for detecting regime shifts, the inverse problem of searching the data for unreported regime changes was also addressed. One possible event was detected in 1972 that closely matched the 1976–1977 regime shift. Examination of the ALPI shows that this turning point coincided with a major shift in the ALPI. Overall, since only one match was found, it suggests that CUSUM patterns which characterize well-defined events may be somewhat unique and thus potentially useful in detecting other regime changes that have yet to be identified. In addition to the observations of SST from Pacific Grove and Scripps Pier, salinity from Scripps Pier, sea level from San Francisco, and SSTs from two locations along Vancouver Island were used to extend our results to locations further north along the west coast of North America, and to evaluate how well other variables respond to regime changes. The events examined are better defined and more distinct at Scripps Pier and Pacific Grove than they were further north off Vancouver Island. However, their timing is essentially the same, and whether increases or decreases in temperature occurred generally agree with previous observations, for each location. The results also suggest that SST is a more sensitive, and thus useful, indicator of regime changes, than either sea level or salinity. CUSUMs produce a distinct pattern that may be characteristic of regime shifts. Between events, the CUSUM trajectories often appear to wander independently; however, during well-defined events such as those that occurred in 1946, 1976, and 1989, the trajectories at Pacific Grove and Scripps Pier become highly synchronized and nearly identical in form. The CUSUM transformation allows us to observe the evolution of these events, revealing time scales that range from about 4 months to 9 months. We have been able to examine these events in greater detail because we have used daily observations from single locations, and not data that have been extensively averaged in space and time, where

such events could be completely obscured through the averaging process. In the off-line mode of detection, CUSUMs could be used to search for other regime shifts that may have occurred in the past. In the on-line mode, CUSUMs could be used to detect regime shifts as they occur. Overall, these results emphasize the importance of event-like changes and their contribution to the long-term warming that has occurred at Pacific Grove and Scripps Pier over the past 85 years. Because the time scales associated with the events examined in this study are roughly decadal, the changes we have observed are almost certainly related to decadal climate variability, and they provide additional insight into the nature of this phenomenon. Finally, establishing the connection between these results and changes in the ecosystems of the North Pacific should be given a high priority. Acknowledgments The author thanks David Field for emphasizing the relative importance of the 1976–1977 regime shift, compared to other regime shifts that have been reported during the past century. Thanks are given to Dr. Rick Thomson for providing the SST data off Vancouver Island that was used in this study. Thanks are also given to Steve Gill for providing the sea level data from San Francisco. The author thanks Lynn McMasters for help in reconstructing Figs. 1 and 3, and Stephanie Flora, for assistance in computer programming. The author would especially like to thank two anonymous reviewers for many helpful comments that led to significant improvements in the manuscript. Finally, the author would like to thank the California Sea Grant Program for its continued interest and support of this work. Appendix A. Estimating the Signal-to-Noise Ratio (SNR) improvement in detecting the 1976–1977 regime shift using CUSUMs In Section 3, we indicated that the statistical properties of CUSUMs differ significantly from those associated with the original time series. CUSUMs reduce noise-like variability and consequently make it easier to detect change points in the data. To quantify the ability of CUSUMs to detect abrupt changes we proceed to calculate the improvement in SNR that is achieved in the CUSUM compared to the original record, using the

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1976–1977 regime shift. Although there are several ways to estimate the improvement in SNR, we have chosen one method that is well-suited for the purpose of illustration. We use the daily observations from Pacific Grove and Scripps Pier. Some motivation for the approach is provided by Lanzante (1996), who calculated a SNR which corresponds to the ratio of the variance associated with a discontinuity or change point, to the variance associated with the same set of observations after the discontinuity has been removed. In applying this method to the record at Pacific Grove, we first segment the data in order to isolate the change point in 1976. The change points of interest occur in 1976 and the change point just prior to this event, the change point in 1946. We now extract the period from 1946 to the end of the record in 2004. Next, we take the step increase in temperature that occurred in 1976 (+0.47 1C at Pacific Grove) and add this value to the data for the period between 1946 and 1976, effectively removing the discontinuity that corresponds to the regime shift in 1976. We have now created two records that span the period from 1946 to 2005, one based on the original data (PGw), and a new version that does not contain the discontinuity in 1976 (PGwo ). Thus, we have discarded the data prior to 1946, which is reasonable if we assume that the variance is essentially stationary. Next, we calculate the CUSUMs for PGw and PGwo , having removed the means, obtaincs ing PGcs w and PGwo . Then, we calculate the variances in each case, obtaining s2PGw , s2PGwo , s2PGcs , and w s2PGcs .11 Finally, we use the following expressions wo

to obtain the improvement in SNR in dB, as   SNR1 ¼ 10 Log10 s2PGw =s2PGwo , (A.1)   SNR2 ¼ 10Log10 s2PGcsw =s2PGcsw . o

(A.2)

Thus, the improvement in SNR, SNRI, in dB, is SNRI ¼ SNR2  SNR1 .

(A.3)

The calculations yield a SNRI of 3.4 dB, which corresponds to an improvement of slightly greater than 2, or 100%. Exactly the same calculations were performed for the record at Scripps Pier. The only difference in 11

We could, of course, have used the standard deviations instead of the variances in the above calculations, but then Eqs. (A.1) and (A.2) below would have been expressed as 20 Log10 ( ) instead of 10 Log10 ( ), yielding the same results.

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this case is that the step increase in temperature in 1976 is +0.72 1C. Again, this value was added to the data for the period between 1946 and 1976, to eliminate the step. In the second case, the improvement in SNR was 7.4 dB, a value far greater than the improvement achieved for Pacific Grove. Appendix B. The effects of serial correlation on estimating the slopes of CUSUMs To illustrate the effect of serial correlation on estimating the slopes associated with CUSUMs, we have first taken a normally distributed random sequence of 1000 samples and introduced varying degrees of serial correlation. The serial correlation was introduced using a simple first-order autoregressive model given by xt ¼ a1 xt1 þ t

for t ¼ 1 2 1000,

(B.1)

where xt represents a first-order autoregressive process, a1 represents the autoregressive coefficient, and et is a normally distributed random variable or innovative term. Simulations were performed based on (B.1) using values of a1 equal to 0.50, 0.95, and 0.99. Next, a step was introduced at the mid-point of the sequence to simulate a change point in the process by increasing the mean value at sample number 500. Then CUSUMs were calculated in each case. The results are shown in Fig. B1. At relatively low values, serial correlation has little effect on the slopes of the CUSUM, but as the serial correlation is increased above values of 0.95, the observed slopes of the CUSUM begin to depart from the true slopes. For a1 ¼ 0.99, there can be significant departures from the true slope. The serial correlation for the original time series at Pacific Grove and Scripps Pier was then calculated for a first-order autoregressive process using the algorithm of Burg (Proakis and Manolakis, 1996), yielding values of 0.9992 and 0.9993, respectively. For the corresponding CUSUMs, of course, the serial correlation is even higher, where values of almost 1.0 were obtained. The problem of serial correlation in estimating CUSUMs has been addressed on previous occasions (e.g., Hawkins and Olwell, 1998; Yashchin, 1993). However, the goal in each case was to improve estimates of the average run length (ARL), a CUSUM-related parameter that represents the expected number of observations or times between significant turning points in the CUSUM. In an effort to improve the situation in the present case, we first

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Fig. B1. CUSUMs calculated for simulations based on a first-order autoregressive model for a normally distributed random sequence of 1000 with a step increase at the center of the sequence, are shown. Three increasing levels of serial correlation have been employed as determined by the autoregressive coefficient, a1, used in the model: a1 ¼ 0.50 (red), 0.95 (blue), and 0.99 (green). As the degree of serial correlation is increased, greater distortion occurs in the slope of the CUSUMs. See text for details.

removed the MAC, which is a major source of longrange persistence in the data. However, the most serious problem is short-range persistence. The most obvious approach is to subsample or average the data over suitable periods in an effort to reduce short-term correlation. In any case, we conclude that caution must be used in the application of CUSUMs in cases where serial correlation could affect the results. Appendix C. Sensitivity to preprocessing According to Rebstock (2002), the appearance of a CUSUM may depend on the base period used to perform the calculation. CUSUM time histories can be strongly affected by when the calculation is started and ended, since by removing the mean prior to the summation, we constrain the CUSUM to begin and end at zero. This procedure can clearly affect the CUSUM slopes, particularly when the period of interest is close to the beginning or end of the record. To examine this property of CUSUMs, we have taken the record of SST at Scripps Pier through December 31, 2004, and calculated CUSUMs starting on January 1, 1920, and January 1, 1970, where the MAC has not been removed, but the global mean has been removed (Fig. C1a). Not

only is the presence of the annual cycle apparent but also the slopes of the two CUSUMs are generally different. To further examine the dependence on start time for the 1976–1977 regime shift at Scripps Pier, we have calculated CUSUMs starting in 1930, 1950, 1970 and 1975 (Fig. C1b). In this case, the MAC as well as the global mean have been removed. Although the slopes are generally similar, slight differences can be seen. We expect similar results by varying the end times of the CUSUM. In detecting change points, at least three factors may affect the slopes of CUSUMs in addition to the event itself, removing the global mean, background drift which may be due to long-term warming or cooling and the effects of serial correlation, and any additional preprocessing that is employed. Since the slopes are additive, it is straightforward to estimate the slope of a particular event, if the slopes indicated above can first be determined. We have not attempted to correct the slopes associated with the events of interest for these factors, but recognize that slope corrections should, in principle, be employed. In Section 4.6, we fitted, and then removed, 6th-order polynomials from the CUSUMs at Pacific Grove and Scripps Pier to reduce the influence of long-term drift. This is a method of

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Fig. C1. (a) Shows CUSUMs starting on January 1, 1920 (red) and January 1, 1970 (blue) through December 31, 2004 for the daily SSTs at Scripps Pier. The mean annual cycle has not been removed in either case. (b) Shows CUSUMs of daily SSTs at Scripps Pier during the 1976–1977 regime shift starting in 1930 (green), 1950 (magenta), 1970 (blue), and 1975 (red). The mean annual cycle has been removed in each case.

postprocessing that may be useful in cases where long-term drift is a significant problem. In preprocessing the data, as described earlier, we have removed the MAC in each case. However, there are other methods that can be used to remove the influence of the annual cycle. One approach is to employ a low-pass filter whose half-power point or cut-off frequency is set reasonably close to 1 cycle/ year (cpy). We have applied a low-pass filter with a half-power cutoff of approximately 1 cpy to the data from Scripps Pier, for the period of the 1976–1977 regime shift (Fig. C2a). The MAC has also been removed for comparison. The residuals are shown in Fig. C2b. It is clear that there is closer agreement between the low-pass filter and the data,

than there is between the MAC and the data. Although this might initially suggest that the filtering approach is in some sense better than removing the MAC, inspection of the corresponding CUSUMs in Fig. C2c during this period shows that they differ significantly. This occurs because the residuals from the MAC are larger, contributing to a larger CUSUM during this period, and thus, to a turning point pattern that is easier to detect. Our experience in this area is limited but our results suggest that removal of the MAC produces CUSUM signatures during the events of interest that are often easy to detect, usually indicate correctly whether increases or decreases have occurred, and have turning point patterns that are somewhat

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Fig. C2. (a) Shows the original daily SSTs from Scripps Pier during the 1976–1977 regime shift (black) with two methods of reducing the influence of the annual cycle superimposed, a low-pass filter (red) and the mean annual cycle (blue). (b) Shows the residuals after the lowpass filter (red) and the mean annual cycle (blue) have been removed from the data. (c) Shows CUSUMs of the residuals after applying the low-pass filter (red), and after removing the mean annual cycle (blue). See text for details.

unique. The uniqueness problem was addressed in Section 4.6. However, we conclude that more work is needed in this area.

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