On the multiple time scales of variability in the Northeast Pacific Ocean

The spatial and temporal sea surface height energy distribution of the Northeast Pacific Ocean is described and discussed. Using an altimetric data set covering 15 years (1993-2007), the energy within the 3-9 month band is primarily located within 10o of the coast. In the Gulf of Alaska, this energy signal is on the shelf, while further south, west of the California/Oregon coast, the significant energy in this band is west of the shelf break. In both cases, it is primarily forced by the local wind. Within the 2-3 year band, the signal reflects energy generated by local changes to the wind stress from large atmospheric shifts indicated by the Pacific North American Index and by advective or propagating processes related to El Niño-Southern Oscillation. Over the two 4-6 year periods within this data set, the change is primarily due to the large scale shift in atmospheric systems north of about 30oN which also affect changes in current strengths. Based on the distribution of the energy signal and its variability, a set of three winter-time indices are suggested to characterize the distinct differences in the SSH anomalies in these areas.


Introduction
The ocean's circulation patterns contain variability on a wide range of scales. This paper describes the variability of the circulation patterns of the Northeast Pacific ocean. Using the information from the spectral energy decomposition of the sea surface height (SSH) anomaly signal, a set of SSH based indices is suggested as useful tools to monitor the changes in the flow patterns of the Northeast Pacific that may impact the non-physical aspects of ecosystems of the area.
The motivation and the Northeast Pacific circulation's variability as seen in prior papers is first described briefly in the following sections of the introduction. It is followed by a description of the region of interest and its sub-regions and a description of the analysis methods used for this paper. The third and fourth sections describe the signal in its decomposition and the variability of specific bands of variability, the reasons for the variability, and any relationships between sub-regions. Finally, the last section concludes by providing a set of indices based on the distribution of the SSH spectral energy in time and space over the region that characterize an area's variability.

Motivation
The objective for the research is to understand the spatial and temporal distribution of the variability in the Northeast Pacific and how the information can contribute to an understanding of the predictability of the ocean's circulation. The changes in local energy relate to both local and remotely forced events. Both of these event types will be examined in this paper. Analysis of ocean variability at inter-annual to decadal periods using satellite data is now feasible with the collection of relatively long time series (e.g. SSH and sea surface temperature: SST) of data that are spatially dense. This paper expands on previous research by exploring the multi-scale variability of the SSH signal in the Northeast Pacific over about a decade.

1.Background
The North Pacific Current flows eastward at about 45 • N and then splits into the northward flowing Alaskan Current and the southward flowing California Current. The two currents are out of phase with each other [Chelton andDavis, 1982, Douglass, et al., 2006]. The southward flowing, broad California Coastal Current has been studied extensively including its seasonal variability. On temporal scales longer than seasonal, previous analyses have focused on large-scale atmospheric influences on the circulation. For example, LLuch-Belda, et al. [2003] examined three frequencies of variability in SST and tide-gauge data in the California Current between 45 • N and 22 • N (5-7 year period, a 20-30 year period and a very low frequency signal on the order of 60 years) and concluded that all three are related to the variability of the atmospheric Aleutian Low phenomenon. The area of interest, however, was much smaller than what is being discussed in this paper, primarily the area defined here as sub-regions one and two. In one phase, the flow into the California Current from the North Pacific Current is relatively weak and is also associated with an intensification of the Alaska Current. The California Counter Current, with relatively higher sea level temperatures and heights, may also have more frequent mesoscale eddy formation during this phase. In another study, Tanimoto, et al. [1993] examined 37 years of sea surface temperature data at three periods 24 months, 2-5 years, and greater than 5 years. They found that the SST field at the highest and lowest frequencies had similar spatial patterns of variability, while the 2-5 year band represented El Niño-Southern Oscillation (ENSO) events with a southward shifted spatial pattern. The analysis statistically quantified the data over the North Pacific as a whole, rather than just the Northeast Pacific, the focus of this paper.
Several atmospheric based indices are referenced in this paper. Two of the indices, the Aleutian Low Pressure Index (ALPI) and the Pacific North-America (PNA) index describe the state of the atmosphere and its low frequency variations. The ALPI [Beamish et al., 1997] is the anomalous (referenced to a long-term average) area average sea level pressure over the North Pacific. It is a measure of the area extent of low pressure over the basin. For this paper, the average relative intensity between December and February is used. A positive value indicates a strong Aleutian Low. The PNA index [Barnston and Livezey, 1987] is the average over 3 months (January through March) of the amplitude associated with the loading pattern as defined by a rotated empirical orthogonal function analysis of 500 mb heights for the Northern Hemisphere. While the PNA is similar to the ALPI, it describes a pattern of variability that extends further south to the equator and is primarily influenced by the pressures over North America rather than just changes over the North Pacific. The third index, are winter averages (December-February) of the Multivariate ENSO Index (MEI) [Wolter and Timlin, 1993]. This index is based on the variability of six parameters: sea level pressure, u and v components of the wind, SST, surface air temperatures, and cloudiness. Empirical orthogonal function analysis is used to define the common dominant signal of the set of variables. All these indices can be used to describe some of the variability in the Northeast Pacific but can be enhanced by regional indices based on the ocean's variability as will be discussed in the following sections.

Data set description
The data used in the following analysis is the gridded, joint altimeter data set processed by the AVISO group in France [Ducet, et al., 2000]. The product combines data from several altimeters, TOPEX/Poseidon, Jason-1, ERS-1/2, Envisat, and GFO (Geosat Follow-on) to create an integrated spatial estimate of global SSH anomalies on a weekly basis. The weekly merged gridded SSH anomaly fields (the long-term mean of the 1993-1999 SSH plus geoid has been removed) are then averaged onto a 1-degree uniform grid for easier manipulation. The data covers the period from 1993 through 2007.
For this study, the area of interest is between 15 • and 65 • N and between 200 • and 250 • E in the Northeast Pacific. Figure 1 shows the study area and its bathymetry. Within this larger region are areas referred to as sub-regions. The sub-regions include three coastal regions: 1-south of 42 • N, 2-north of 41 • N (near Cape Mendocino) and 3-south of Alaska, and three other regions: 4-a region to the west of the coastal California region, 5-a "southern gyre" region west of area 4 and south of about 40 • N, and 6-a subpolar area. The areas are numbered in Figure 1 and defined based on the similarity and continuity of the energy levels. The areas are not meant to exact in their size or extent. Rather they are used to help guide the reader through the discussion of the analysis of the signals.
The paper focuses on three bands of variability, a short period band between 3 and 9 months, a middle band of 2-3 years and a long period band of 4 to 6 years. For the purposes of this study, the annual cycle has been removed prior to further analysis using a band-pass filter. Also, the highest frequency signal with a period of less than three months has been removed.
The time period (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007) covered by this study includes a strong El Niño (1997/1998). Figure 2 shows the variance map of SSH for two versions of the data to identify the spatial extent of the spectral influence of this event. Figure 2a shows the variance for a thirteen year period: 1993-2007, minus 1997 and 1998, while the figure on the right (Figure 2b) shows the variance for the full fifteen years -2007 El Niño tends to bias the data in some areas over this relatively short time series. The two averages are similar, but differ in the westward extent of the high variance signal between 30 • and 40 • N seen in Figure 2b. This illustrates how the 1997/1998 El Niño contributes to a more westerly extent of enhanced variability. In addition, the energy in the SSH signal is greatly enhanced in the southeast corner of the region of interest in Figure 2b with the 1997/1998 El Niño . During the fifteen year period, there were several other smaller and but much less significant El Niño events (occurring in 1994/1995, 2002/2003, and 2004/2005) that don't increase the energy levels in a similar manner. Generally, both examples of variance show that there are distinct areas where the energy level related to SSH is quite small. These areas are 1) along the coast, in the boundary region and east of the shelf break, 2) in the mid-gyre area of the North Pacific, both north and south of the location of the North Pacific Current, and 3) in an area centered around 240 • E and 20 • N.

Method for analyzing the temporal signal
The analysis of Tanimoto, et al. [1997] used empirical orthogonal functions (EOF) to examine the variability of sea surface temperatures (SST) within three different frequency bands, while the LLuch-Belda, et al. [2003] paper examined a portion of our area by filtering the area average of several quantities (SST, tide-gauge SSH). This research examines the variability of a signal within three separate and distinct frequency bands and analyses a fifteen year altimetric data set of sea surface height (SSH) anomalies, rather than SST field. And rather than using a broad-band filter which tends to smear out the signal, this analysis uses wavelet methodology to isolate the variability within frequency bands. Unlike SST, SSH reflects more than just changes in the surface fields of the ocean. Because the SSH signal represents some measure of an integrated signal of the ocean's circulation field in the top 500-1000 meters of the ocean, it should reflect a more robust measure of circulation changes.
The wavelet methodology describes the spatial distribution of the SSH variability and its significance in time both within and between frequency bands . Wavelet analysis allows us to look at how the dominant modes vary temporally. An in-depth description of wavelet analysis, the application of it, and an extensive discussion of how to determine the significance of the results are given in Torrence and Compo [1998]. Users are referred to this paper for detailed questions about the method. The method is becoming widely used to analyze a variety of geophysical signals on a wide range of scales. For example, Gu and Philander [1995] used the method to examine the ENSO signal. Meyers et al. [1993] examined ocean wave dispersion, and others have used the method to analyze wave growth [e.g. Liu, 1994]. Tokmakian and McClean, [2003] used wavelets to examine the realism of SSH in high resolution ocean models as compared to satellite 6 data. Similar to windowed Fourier transforms, wavelet analysis allows the localized and dominant frequencies (for which a predetermined scaling can not be defined) to be determined. Given a time series x n , where n = 0 ... N -1 and equal temporal spacing, δt , let W n (s) define the wavelet transform such that where (*) indicates the complex conjugate and ψ defines the "wavelet function" which we are using. The wavelet pattern is constructed by varying the wavelet scale, s and translating it along the time index n. This pattern shows the amplitude of features versus the scales and how the amplitude changes in time. ψ, the wavelet function, can be defined in an infinite number of ways, but it must have zero mean and be localized in time and space [Farge, 1992]. Torrence and Compo [1998] give a detailed discussion on how to choose an appropriate wavelet function. This analysis is done using a Morlet wavelet function, a plane wave modulated by a Gaussian curve where ψ(η) = π −1/4 e iωη e −η 2 /2 . (2) where ω is a non-dimensional frequency, defined in this case as equal to 6. Because the chosen wavelet function is complex, the transform W n (s) is complex. The transform, thus, can reveal information about both the amplitude (= |W n (s)|), and phase (tan −1 [ {W n (s)}/ {W n (s)}]). The wavelet power spectrum is defined as |W n (s)| 2 and for comparisons, different wavelet are normalized by their variance. This gives a sense of the magnitude of the signal relative to white noise.
When determining which portion of the signal is significant (95% level), an assumption can be made regarding the redness of the spectrum. Torrence and Compo [1998] estimate the background "redness" coefficient (α) for modeling the NINO-3 spectrum by calculating the lag-1 and lag-2 autocorrelation coefficients of the data . If describes the time series where α is defined as (R(1) + (R(2))/2 and R(1) is the lat-1 autocorrelation of x, R(1) is the lag-2 autocorrelation of x and z n is a Gaussian white noise addition to the signal, then the mean power spectrum can be defined as where N is the length of the series and k is the spectral point. If a point of the wavelet spectrum is greater than the 95% chi-square distribution curve for this mean spectrum, the signal is significant. A further explanation, with respect to wavelets, is that for a 95% confidence level in a random time series, 5% of the values will be above the significance level by chance. Thus, within a band of interest, we want to find signals that are significant as compared to the background signal. In other words, we are trying to identify signals that are not random. The α term can be used to identify those areas within a specific band that are distinct from the background signal of the band. Torrence and Compo [1998] suggest two things to look for in a wavelet spectrum to subjectively determine if the signal is significant: 1) the power concentrated during certain periods of time and 2) the period of concentration changes with time. Influence of the effects of the boundaries of the time series is reduced by extending the original time series in a cyclic manner and thus, no edge influence is denoted on individual wavelet plots that are shown.

Spatial structure and areal mean temporal evolution
First, before examining the decomposed SSH signal for a specific location, the patterns of variability in specified frequency bands across the entire region are mapped and 8 examined. The three bands examined are: 3-9 months, 2-3 years and 4-6 years. Maps of the average spectral energy are created by decomposing the SSH anomaly time series at each location into its spectral bands, determining the significance of the signal in the resulting field, and then finding the average over time of the spectral energy at a location. In contrast to other analyses that decompose time series into patterns (e.g. empirical orthogonal functions), this methodology allows for the significance of the signal at a location to be quantified. The significance level was determined as described in section 1.4. For computing the significance of a signal within a band, each band used a different background coefficient (α or redness) for the autocorrelation of that part of the spectrum. At high frequencies, α was set to 0.3, for the 2-3 year band, a value of α = 0.7 was used, and for the lowest frequencies, α was set to 0.9 (see previous section for the definition of α. The values are chosen to identify the peaks in the specific portion of the spectrum. The values do not have to be precise, rather are chosen as to how "red" the section of the spectrum appears when examining spectral plots of the filtered time series. Figure 3 shows the maps for each of the three bands; locations with insignificant signal are blank. These maps quantify the importance of a specific temporal scale in a region. Figure 4 shows the associated time series for the maps in Figure 3. The vertical lines denote the approximate times of an El Niño (1994/95, 1997/98, 2002/03, see http://www.cdc.noaa.gov, multivariate ENSO index, Wolter and Timlin, 1993). The different lines on each plot represent averages over different areas as specified in the legend. The time series show the temporal relationships between regions at the three frequencies. The regions are discussed in the following several paragraphs.
The SSH variance in the 3-9 month band ( Figure 3a) is high south of 30 • N in the west and along the eastern boundary south of 40 • N. The eastern boundary area extends westward about 5 • (or 500 km). An area of insignificant signal in this band clearly separates these two regions of high variance. In the north, the area of high variability extends southward about 2 • or 200 km from the coast. The regions closest to the coast have relatively low energy as compared to further offshore. The pattern for the 3-9 month band is reminiscent of the Pacific Decadal Oscillation (PDO, Mantua et al., 1997) and the PNA spatial patterns within the central gyre. However, the temporal variability of this pattern does not reflect the PDO. In this example, the central gyre region has insignificant energy at periods less than a year in contrast to the area along the edges and in the southwestern section of the domain. The corresponding temporal plot of the signal (Figure 4a) shows the similarity temporal pattern for the areas that are east and west of 230 • E. For each area there are several periods in time that have relatively high signal levels (greater than 1) in the 3-9 month band (1993, 1997-1998, 2000, 2004, and 2006) and periods of significantly lower variance, primarily around 1996, 1999 and 2005. The largest differences in the amplitudes of the two time series are during the periods of relatively low overall signal strength (e.g. 1995/1996, 1999). The two time series are correlated such that 28% (the square of the correlation value) of the variance signal is similar between the two areas at a 7 day lag or 1 point in the time-series, suggesting the overall large scale atmospheric pattern is influencing these both these areas as a local change in SSH within the higher frequency band (because of the correlation of around 0.53).  Figure 4b) leads the coastal signal by about 2 years, determined by the maximum correlation value of 0.82 (R1) at 700 days; (correlation between black and gray lines). However, this relationship fails to hold when the amplitude of variability is relatively small as in the years after 2000. This is consistent with other research that has shown the atmospheric pressure signal north of about 20 • N is out of phase with the tropical (and coastal) ENSO signal [Clarke, 2008]. The dashed line in Fig-ure 4b, clearly illustrates how the northern area, north of 45 • N is representing neither the coastal area offshore and south of 45 • N, nor the temporal evolution of the tropical El Niño events. The correlation of this northern area with that of the area north of 20N (R2) and the correlation between the northern region and the coastal area (R3) give values that are not significant (0.66 and 0.61 for 95% probability with 6 degrees of freedom due to the filtering and sampling). Therefore, over the whole of the region of the Northeast Pacific, the signal in the two to three year period is partly a manifestation of ENSO and partly of events unrelated to ENSO. These events may be related to large scale spatial forcing that occur over the whole of the northeast Pacific as indicated by the coincident signal in all three subareas after 2005. Thus, only under some conditions when the signal is large can one area be used to "predict" changes in another area.
The third frequency band examined, the 4-6 year band ( Figure 3c) and its associated temporal evolution (Figure 4c), shows a structure unlike the other two bands. The spatial pattern gives an indication of locations where low frequency changes in the ocean's circulation might be detectable, for example around 47 • N and 210 • E . It is important to note that the central area (200-210 • E and 35-50 • N) shows significant energy in this band with little or no significant energy for the other bands. The high values in the lower right of the spatial domain reflect the dominant 1998 El Niño and are unrelated to the other areas of significant variance as illustrated by the time series for the two regions ( Figure 4c) and the maximum correlation value of 0.74, which is insignificant at 95% for three degrees of freedom.
3.2 Examples of individual area spectra 3.2.1 In coastal regions 1,2, and 3 To better understand the SSH energy distribution in time, examples of the decomposed signals are shown for a set of locations in the coastal regions ( Figure 1). In these areas, the energy close to land is relatively low as compared to further offshore, especially when the 1997/98 period, the extreme El Niño years, is excluded (see Figure 2). Most of the energy for the coastal area is within either the first band (3-9 months) or the 2-3 year band (Figure 3).
A typical wavelet decomposition of the time series for the SSH anomaly at a point in region 1 (238 • E 37 • N), Figure 5a shows a distinct and strong response to the 1997/1998 El Niño in the longer period signals of the spectrum (2 years and greater). There is a noticeable lack of energy towards the end of the time series in these longer period bands. Within the shorter period band of 3-9 months, the significant energy peaks are in the years 1995, 1998, 1999, and late 2004-2007. The energy is unrelated to the ENSO index as denoted by the bars above the spectrum.
The second time series decomposition, at a location further north at 231 • E 51 • N (Figure 5b), shows the El Niño signal, again, dominating the energy decomposition wavelet plot (darkest gray area). There is less energy in this band in the latter half of the record (years 2000-2005) than in the early period (1993)(1994)(1995)(1996)(1997)(1998)(1999) for the 2-3 year period, similar to the signal at 37 • N. The secondary signal is for the 3 to 9 month band that has significant energy across most of the years. This band has a signal that is fairly constant with time in contrast to the variance calculated for the band further south. When the ALPI index (shown by the bars on the figure) is highest in the second half of the record, the longer periods have less energy. A positive ALPI value indicates a strong low pressure pattern and is coincident with the period of time that has increases in energy at the shortest periods (0.125 years) in 1998, 2002 and 2003. At a third location, along the Alaskan coast and within the third region (215 • E, 56 • N), there is no indication of the strong El Niño in the 2-3 year band (Figure 5c). The time evolution is dissimilar to the other two coastal regions at the longer periods. In the 2 to 3 year period band, there is a significant energy in the later half of the record, centered in 2006, coincident with the lower index values of the ALPI (shown by the bars on the graph). However, the energy distribution centered at the semi-annual period (3-9 months) is significant in the years that are consistent with the strong 1997/1998 El Niño, but not inclusive to only that period. The intense 1997/1998 El Niño contributes to the variability at this northerly latitude, but, in general, the ENSO influence is not evident at this northerly location for other years.
3.2.2 In the California Current: Region 4 Figure 6 gives an example of a wavelet spectrum for SSH further offshore and within the California Current, west of Figure 5a at 232 • E, 37 • N. Most of the energy at this location is found at short periods (3-9 months), with much less energy (a much narrower spread across the band) in the 2-3 year band than found in the coastal area. In the shortest period band (3-9 months), there are two distinct periods of significant energy, one between 1993 and 1996 and the second from 2000 through 2006. In the years in between, 1997 through 1999, the energy is much lower or insignificant and similarly insignificant for the same years for the 2-3 year band. Thus, the variance of SSH in this off shore area does not include an enhancement related to any strong ENSO signal (bars on figure) such as seen in the coastal region. Where there is significant energy, the spread of the energy is broad and across the 3-9 month band. In general, for the years with a positive ENSO index, there is relatively low significant energy across the bands, while in years with a negative index, the tendency is for the signal energy to be higher (e.g. 1996, 1999-2002).

Region 5
The wavelet spectrum for a location within region 5 (205 • E, 25 • N) is shown in Figure 7 . At this location there is, again, little indication of an increase in energy that can be clearly related to the 1997/1998 El Niño in the 2-3 year band as indicated by the ENSO index (bars on the figure). The 2-3 year band has a strong signal, but it is unrelated or, perhaps anti-correlated with the El Niño event of 1997/1998 as suggested by the reduction in the energy in 1997/1998 compared to the rest of the time series. The 2-3 year band also has a drop in significant energy in the period 2005-2007. The 3-9 month band indicates relatively high energy in 1995, 2001, and 2004-2005 and a reduction in energy across the band for the period spanning 1998 through 2000. There is also a shift of the higher frequency energy towards lower frequencies during the 1998-2000 period (i.e. a shift in the energy centered at 4 months to a signal centered around 7 months). This is a much different pattern of variability than seen at the more coastal locations, but similar to the signal in region 4.

In the subpolar gyre: Region 6
In the subpolar gyre, the dominant frequency is the lowest band, periods greater than 3 years, as shown in Figure 8. At the location, 215 • E, 47 • N, there is also significant energy, over relatively short periods of approximately a season, found in the 3-9 month band. These energetic signals appear related to a positive ENSO index but not all positive ENSO years show a significant energy increase in this band. The energy in this short period band is somewhat cyclic, with peaks every 3 to 4 years or so. This pattern is consistent with high values of the ALPI index in years 1998 and 2003, but not in 2002, which also has a relatively high index value. The low PNA index for 2002 indicates a relatively high surface pressure over the larger area defined by the index. These two indices suggest that while the variability of the whole of the North Pacific is associated strongly with a weak PNA pattern, the ALPI value reflects another extreme making it difficult to understand the importance of these two indices on the ocean signal. The wavelet decomposition also indicates that there is no significant signal related to the strong 1997/1998 El Niño in the 2-3 year band. Rather than showing intensified energy in 1998 and then relaxing after 1998, the energy in the 2-3 year band is high through the end of the time series. For example, this band shows little energy in the period between 1999 and 2001, but a significant signal in the year 1998 and also in 2003. 14 3.3 Inter-regional connections To understand how regions within the ocean may be related and to further understand how changes within the ocean might be predicted, maps of spectral energy within the bands are plotted in time across a band of latitudes or longitudes.
3.3.1 South to north connections: Relating Region 1 to Regions 2 and 3 As shown in the previous figures, within the 2-3 year band, there is significant indication that the energy is mostly associated with the strong El Niño of 1997/1998. To more fully examine the south to north connections, a latitude/time plot is created from individual spectral decompositions along the coast. Plotting the significant energy, starting from the southern boundary, within the 2-3 year band that occurs within 1 • of the coast, the ENSO influence on the signal is observed to move up the coast (Figure 9a). The energy signal associated with the 1997/1998 El Niño is illustrated by highlighting the points of maximum energy during the winter of 1998 with the gray line on the figure. This distinct signal extends northward to about 40 • N, but beyond this point, the significant energy pattern in this band is weaker and appears to be unrelated to the propagating signal south of 40 • N. The signal found north of 45 • N is a temporally static signal. This portion of the energy signal represents the ocean's local response to a large scale, sustained atmospheric event associated with the large 1997/1998 El Niño, rather than any internal ocean process such as Kelvin wave contributions to the variance of SSH.
The figure also illustrates areas where the signal is modified by smaller areal changes, such as from very local wind stress, as indicated by the increase in the energy levels, for example, around 32 • N and 37 • N. 32 • N is in the area complicated by the islands within the Southern California Bight and 37 • N is about the location of San Francisco, with its complicated topography. 40 • N is the area of Cape Mendocino. There is also an increase in energy at the latitude of Cape Blanco (approximately 43 • N).
In contrast to the longer period band, the shorter 3-9 month time/latitude map (Figure 9b) shows how the energy signal is reflecting locally forced events (e.g. between 35 • N and 41 • N). Only at the southern boundary, does the energy within this band represent any direct relation to the strong El Niño of 1997/1998. There is little if any propagating energy in the signal in this portion of the spectra. It clearly shows the contrast to the 2-3 year band in energy showing how the 3-9 month band dominates the signal at 40 • N.

East to West Connections: Relating Regions 1 and 2 to Regions 4, 5 and 6
To understand the relationships in the energy signals in the coastal band and further offshore, time/longitude plots are shown for the signals in the 3-9 month band at two latitudes, 37 • N and 51 • N. Figure 10a indicates that the energy is primarily localized in space with a few periods in time that show limited and narrow offshore propagation. This is consistent with Kelly et al. [1998] andHaney, et al. [2001]. They suggest the coastal energy signal does not extend offshore in the surface layers, but rather subsurface. For an example at 37 • N, in 1995, the energy is more inshore, while in 1997, in which ENSO dynamics are more energetic, the significant signal extends further offshore. The energy within the coastal and California Current regimes is also distinct from any short period signal generated in the middle of the basin. At 51 • N, the energy in this band is local and significant in the years 1995, 1998, and 2002-2006, both inshore and slightly further offshore and is somewhat coincident with the periods of time with a positive ALPI.
At the southern boundary of the domain (15 • N; Figure 11a), the time evolution of the SSH spectral signal within the 2-3 year band shows the energy moving from the west in 1993 and moving somewhat eastward to about 215 • E (as indicated by the slope of the contour lines at the bottom of the plot) towards 1998, with a strong and stationary signal between 215 • and 230 • E. The eastern most portion of the plot shows another signal that moves from the coast westward, east of 230 • E and centered about late 1996.
At 37 • N, the evolution of the variance in the 2-3 year band (Figure 11b) shows an area of high variance near the coast that is related to the 1997/98 El Niño. At this lat-16 itude, the figure also shows enhancement of the variance centered around 1997/1998 to the west of 225 • E, indicative of a broad area of similar forcing. The 2-3 year band at 37 • N (Figure 11b) does not show any indication of offshore energy propagation, rather the 2-3 year band indicates a temporally consistent pattern of energy along the latitude band that can be identified with the strong 1997/1998 ENSO event. This pattern is consistent with the findings of Strub and James [2002a-c]. They conclude that most of the seasonal change in the upper waters of the California Current is primarily due to advection in the boundary current rather than from the interior of the Pacific. Further north at 47 • N, the east to west connections are quite evident within the 2-3 year band as shown by Figure 11c. The most eastern section (greater than 225 • E) shows the influence of local forcing conditions on the SSH anomaly exhibited by the extended temporally consistent pattern of energy in the band. West of approximately 225 • E, a local enhancement of the forcing centered in 1998 further shows how the energy appears to propagate westward. The reason for the enhancement at this location may be related to the large change in the topography at about 226 • E, 47 • N, the Cobb Seamount (see Figure 1, Codiga and Eriksen[1997] . There is no such distinct pattern at 51 • N (no figure shown).
The 4-6 year band, at 15 • N (Figure 12a), shows the enhanced signal of the 1997/98 El Niño at 230 • E and clearly propagating eastward to the coast. This large scale, low frequency signal dominates the SSH variability showing the 1997/8 signal extending all the way to the coast. This denotes how the strongest ENSO signal dominates the spectrum over the period of the data in this area.
Quite different spectral signals are present for the band at 37 • N and 47 • N (Figure 12b,c). At 37 • N, the signal is chaotic with no clear patterns of variance represented in the band as compared to the 2-3 year band discussed in the previous paragraph. However, further north, at 47 • N, there are two areas that show patterns of related significant energy, one east of 220 • E and the other west of this meridian. Between 230 • E and 220 • E, the energy pattern indicates a westward propagation of coherent SSH change. The signal extends over a broad area for a long period of time, initially driven by a strong shift in forcing related to the ENSO event of 1997/1998. In the western half (west of 220 • E), the plot also shows an extended period of significant variance of the energy in the 4-6 year band (Figure 12c). The signal is strongest in the west around 2001 and shows the pattern of variance moving eastward.
An examination of the wind stress spectral decomposition for this frequency band, (Figure 12d), shows a more zonal pattern of energy distribution indicating that the forcing contribution has a zonal structure in time which is consistent across a band of 20 • of longitude. This is in contrast to the pattern of the SSH energy spectrum which shows the maximum location of variance moving eastward in time. Thus, the differences in the patterns of the energy spectrum in this band between the forcing field of the wind stress and that of the SSH field suggest that the ocean signal represents both a local response to atmospheric forcing and a propagating or advective contribution to the variance.

Quantifying upstream and downstream relationships
It is noted in the first paragraph that the motivation for this work is to explore if there is useful information in the spectral signal relating to the predictability of the ocean's circulation. Capotondi et al. [2005] and Cummins and Lagerloef [2002] explored the influence of Ekman pumping in the Northeast Pacific low frequency changes in circulation, which explains much of the directly forced changes seen in the upper ocean. Both papers, using EOFs to decompose the large scale signal, conclude that at periods longer than 2 years and over large areas, the changes are due to Ekman pumping rather than from changes due to the influence of Rossby waves propagating through field. This paper examines a similar signal through the decomposition of the SSH energy spectrum. The decomposition shows, rather than one dominant large area signal, there are distinct characteristics in different regions and in some of the regions, processes other than the low frequency, local wind forced processes are playing a significant role in the ocean's variability. Examining the SSH anomaly signal in this manner allows spatial as well as temporal similarities within one frequency band to be delineated. Further, by using prior knowledge of a change in the upstream SSH field that this decomposition allows for, a downstream future circulation state may be predictable.
The following is suggested of how this spectral information can be used. In the interior of the region of interest (between 20 • N and 55 • N), the most significant energy is in the 2-3 year band and the 4-5 year band. Using Figure 12c as an example, the maximum of the significant SSH energy west of 220 • E appears to propagate eastward in the latter half of the time series with a less energetic signal in the early part of the record. A similar time/longitude plot of the wind stress curl in the 4-6 year band shows a pattern of energy as observed in the SSH anomaly field for this band west of 220 • N ( Figure 12d) that is stationary across longitudinal space. A covariance analysis shows the highest area of covariance between the wind stress curl and the SSH anomaly 4-6 year spectral energy band is in the area of 210-220 • E and 45-50 • N (not shown), consistent with the previous mentioned papers of direct Ekman pumping, but with a much more limited extent. The difference in the two spectral patterns from SSH and wind, suggests that advective properties within the ocean are also an important contribution to the changes in the spectral characteristics of the SSH signal and thus in circulation patterns.
To examine how advection might be contributing to changes seen in the spectral decomposition, geostrophic velocity anomalies were calculated from the SSH fields. Using the same latitudes as above, 47 • N and 37 • N, several time series were extracted from the fields . The annual cycle and higher frequencies were removed from the fields before calculating the velocities. Figure 13a) shows the zonal velocity anomalies at 47 • N for 205 • E and for 215 • E and also the meridional velocities at 47 • N, 235 • E, each offset between 4 and 6 months. The plot shows the dominant characteristic of the time series as the "event" centered at 2002. The early part of the record, between 1993 and about 2001, shows little variance in the velocities at all locations, however, the general shape of the low frequency after 2001 is similar in all the series. Figure 13a) cannot be compared directly to Figure 11c, as the former contains multiple frequencies over a very broad range of frequencies and the later only shows the very low frequency band. Such changes are the result of advection within the ocean and changes also in the large scale atmospheric conditions. This relational information can be used to inform future changes downstream that may not be obvious. For example: at 37 • N in Figure 13b), the two curves are lagged by about 21 months, with the western series located at 225 • E and the eastern, shifted by plus 21 months, located at 235 • E. While the two series at this location appear to represent a similar signal, defined by either an easterly flow (225 • E) or southerly flow (235 • E) peaking in 1997 and both decaying in time at the very low frequency, there are distinct differences that complicate the use of the series as shown in the wavelet decomposition and add uncertainties to any estimate of using the more western location for predictions at the eastern location.
Quantifying how upstream current changes are reflected in the downstream current shows the similarity between the changes in the current. A time series from the upstream location, x(t), is fit to the data at a downstream location at an offset (o ) in time, y(t+o), determined from an examination of lagged correlation values. A "quality" ratio can then be calculated. A second order polynomial is used for the fitting process, resulting in an estimate of the downstream location's variability, y e (t+o). The difference between the estimate and the actual values, D(t+o) = y e (t+o) -y(t+o), can help to understand the errors in the fit of using upstream information to understand future downstream changes. To understand how different estimates of error relate in importance to one another, given differences in signal magnitudes, each is normalized by the standard deviation of the true downstream signal: y(t+o), resulting in a "quality of fit" estimate (i.e. the standard deviation of the residual of the fit divided by the standard deviation of the signal). In other words, if the error variance is the same or larger than the actual signal variance, then there is a large uncertainty in the estimate, especially when the "quality" values are greater than 1. A low value means that the error is lower than the signal's variance and the upstream information contributes to the downstream variability.
Three examples were examined, using the data shown in Figure  gives a strong indication that the upstream condition is influencing the downstream condition. The other two comparisons indicate that the error in using the upstream condition to predict the downstream condition is less certain, but still the error is less than the variability in the observed record at the downstream location.

Potential ocean based indices
The SSH anomaly signal of the Northeast Pacific was decomposed into 3 spectral bands, 3-9 months, 2-3 years and 4-6 years to show the relationships between the spatial and temporal changes of the signal's spectral energy bands. There is a complicated structure in time and space of the SSH variability and thus of the circulation of the Northeast Pacific Ocean. We also showed the difficulty of using broad atmospheric indices to understand many of the changes in the ocean and whether advection plays a significant role. Based on the information provided above, a set of ocean based in-dices can be defined that allows for the information about the signal's variability to be consolidated and clarified. The spectral decomposition suggests the SSH variability and the associated flow patterns might be represented by several SSH based indices: 1) an index representing the low frequency changes associated of the northern gyre (region 6), 2) an index representing region two north of about 47 • N, along the coast, and 3) an index representing region four centered at 37 • N, 235 • E based on information in Figure 3 (area 4). Data from the winter period is used to develop the indices to be consistent with the atmospheric indices shown.
Correlations between the indices were computed to quantify the similarity between them. Correlations were also computed between the SSH indices and various atmospheric indices. The coastal index at 52 • N is only highly correlated with the ENSO/MEI index (0.8) when 1998/1997 is included. Otherwise, the coastal indices as defined here are not highly significantly correlated to any of the atmospheric indices (maximum R values are approximately 0.3-0.5). The SSH northern gyre index (1) is not significantly correlated with either the PNA or ALPI index. While the correlation of the coastal SSH indices and their connection to ENSO processes is not new, especially when an extreme ENSO event is present in the time series, the SSH based indices can help to identify low frequency changes, other than ENSO, in the ocean that are particular to an area. The lack of significant correlations with the atmospheric indices indicate a need for ocean-only indices.
An example of how these indices can be used is shown by comparing the changes to estimates of fish catch in a particular area. In the previous section, it was shown how the information in the SSH signal upstream and downstream is related and this information may help with understanding changes in fish stock due to changes in circulation patterns and may contribute to projecting potential fish catch. In Figure 14, annual estimates of fish catch (personal communication from the National Marine Fisheries Service) are shown as symbols overlaying the various examples of SSH indices. Similarities in trends can be observed between the various species and with the indices from the regions that may influence their catch size. Figure 14a, the gyre index, shows a strong negative correspondence with two species, salmon and rockfish, a gyre index relating to the more coastal catch of fish with a lag of 1 year. The fish data is based on yearly values, and 1 year is the smallest possible lag other than zero. The salmon catch anomalies show similarities in changes seen in the index with a 1 year lag, while the rockfish catch is similarly negatively related to the SSH index. The same correspondence is not seen with the rockfish catch and the local coastal index with no lag (Figure 14b). In the coastal region, at 37 • N, prior to 2002, there is a similarity in the rockfish catch with the SSH index connected with area 4 (with 1997 being an anomaly), but from 2002 and later, the catch is constant. This most likely due to restrictions placed on the fisheries, rather than fish available to be caught. Understanding the relationships between such SSH based indices and the variability in fish populations will need to be further explored and is only shown here as an example of possible uses of such ocean based indices.

Conclusions
The goal of the analysis was to examine and explore the altimeter data set to understand how decomposing the height signal can help in determining ocean regions where the SSH anomaly signal can be used to monitor significant changes in circulation patterns and if such signals can be used to understand downstream changes. The analysis of a fifteen year time series of altimeter data in the Northeast Pacific through the use, primarily, of wavelets, shows that the SSH variability differs significantly across the larger region, resulting in different frequencies of variability dominating in different regions. The three bands of variability examined were a 3 to 9 month band, a 2 to 3 year band, and a 4 to 5 year band. The analysis identified three distinct indices that can be useful for monitoring changes in the Northeast Pacific: 1) 47 • N, 210-230 • E, 2) a northern coastal area index, near 52 • N (area 2) and 3) an index in the California Current region around 37 • N (area 4).
The final conclusions are: 1. by decomposing the SSH anomaly into its frequency bands in time, the significant signals were determined for various areas and showing their significance in time.
The decomposition showed that there are distinct broad areas of similar spectral energies and areas of dissimilarities. Based on this spectral decomposition, an example of the relationships between upstream and downstream circulation changes was given.
2. From the examination of the spectral characteristics of different regions, a set of three, distinct SSH indices are suggested, one for the northeast coastal area, one for the southeast area and one for the interior of the subpolar gyre area.
3. An SSH based index is not proposed for region 5 (25-45 • N, west of 230 • E) because the area is influenced by locally forced and chaotic events and is generally less energetic with the dominant signal difficult to determine.
The wavelet analysis has allowed for dominant signals in SSH to be identified as a function of time, along with spatially quantifying the regional significance of the signal within each band. In three areas, the indices show promise for monitoring changes in circulation which could be important for understanding connections between the physical and non-physical aspects of the ocean.           10. Contour of significant SSH variance for the 3 to 9 band for zonal points along a given latitude: a) 37 • N (region 1) and b) 51 • N (region 2). The bar graph on the left is the ENSO index and the one on the right is the ALPI index, positive values in black and to the left. Fig. 11. a) Contour of significant SSH variance within 2-3 year band at 15 • N; Contour lines every 2 units starting at 2. b) Same as a), but for 37 • N; Contour lines every 1 units starting at 1. c)Same as a) but for 47 • N; Contours area every 5 units starting at 5. The gray shading represents land.