An empirical orthogonal function analysis of remotely sensed sea surface temperature variability and its relation to interior oceanic processes off Baja California

REMOTE SENS. ENVIRON. 47:375-389 (1994)

An Empirical Orthogonal Function Analysis of Remotely Sensed Sea Surface Temperature Variability and Its Relation to Interior Oceanic Processes off Baja California Timothy C. Gallaudet* and James J. Simpson* E m p i r i c a l orthogonal function (EOF) analysis was applied to a 4.6-year sequence of AVHRR images off Baja California centered near Punta Eugenia to examine largeand mesoscale processes in this region of the California Current System (CCS). The mean structure found in the image sequence describes the seasonal cycle in sea surface temperature (SST) and the large-scale, north-south, oceanic SST gradient of the region. The first EOF-amplitude pair also describes the seasonal cycle in SST. Both results are consistent with long-term, large-scale, mean shipboard data for the region. The second EOF-amplitude pair defines two distinct regions paralleling the coast. The inshore region coincides with the coastal zone of Lynn and Simpson (1987), and the adjacent region farther offshore is identical to their transition zone. The third through fifth EOF-amplitude pairs primarily represent meandering of the California Current and anticyclonic mesoscale eddy occurrences in the region; these results also are consonant with a large number of shipboard observations. The EOF results provide independent satellitederived evidence for the existence of a transition zone off Baja California which is similar to that found off central and southern California. Moreover, the agreement between the satellite-based results and the shipboard observations indicates that satellite data can be used successfully to study other current systems (e.g., Peru Current), where in situ observations (ships, buoys) are less abundant.

* Digital Image Analysis Laboratory, La Jolla, California. Address correspondence to James J. Simpson, Scripps Satellite Oceanography Ctr., Scripps Institution of Oceanography, Digital Image Analysis Lab., La Jolla, CA 92093. Received 13 July 1992; revised 8 June 1993. 0034-4257/94/$7.00 ©Elsevier Science Inc., 1994 655 Avenue of the Americas, New York, NY 10010

INTRODUCTION The California Current System (CCS) is one of the world's most studied eastern boundary currents; especially its large-scale structure and variability (Sverdrup and Fleming, 1941; Reid et al., 1958; Pavlova, 1966; Hickey, 1979; Chelton, 1984; Lynn and Simpson, 1987). Generally, these studies have emphasized the southern and central regions of the CCS because the California Cooperative Oceanic Fisheries Investigations (Calcofi) program (Lynn et al., 1982), upon which many of these studies are based, has taken comparatively little shipboard data off Baja California. Harmonic analysis of the Calcofi data supports the existence of a transition zone between the inshore coastal and offshore oceanic flows of the CCS (Lynn and Simpson, 1987). Located approximately 200-300 km offshore and parallel to the coast, this transition zone is characterized by a relative minimum in the seasonal range and a relative maximum in the standard deviation of dynamic height. This zone coincides with the core flow of the California Current and mesoscale eddies and energetic meanders consistently recur at preferred locations within this transition zone (Koblinsky et al., 1984; Simpson et al., 1984; 1986; Simpson and Lynn, 1990). Bathymetrically induced instability of the California Undercurrent may be a generation mechanism for some of these mesocale features (Simpson and Lynn, 1990). A similar instability mechanism also may explain the recurrent nature of the Sitka eddy found off Sitka, Alaska (Swaters and Mysak, 1985). The existence of the transition zone in the Baja California region of the CCS, however, is more difficult to determine compared with that off central and southern California because detailed in situ observations in

375

376 Gallaudet and Simpson

this region of the CCS are especially sparse and very nonuniformly distributed spatially compared to the other more intensely sampled regions of the CCS (Lynn et al., 1982; Koblinsky et al., 1984). Nonetheless, the CCS off Baja California is another region where recurrent mesoscale eddies, which characterize the transition zone of central and southern California, have been found (Hickey, 1979; Burkov and Pavlova, 1980; Simpson et al., 1986; Lynn and Simpson, 1987). In this study, satellite data were used to determine the large- and mesoscale sea surface temperature (SST) structure of the CCS off Baja California and to compare this structure with that found off central and southern California. These data were used because they are most abundant and more uniformly distributed than shipboard data and, in many cases, satellite-derived SST provides a surface signature consistent with subsurface dynamical processes (Voorhis and Schroeder, 1976; Nelepo et al., 1978; Simpson et al., 1984; Fiedler, 1988). Empirical orthogonal function (EOF) analysis was used to analyze the satellite data because this technique can concisely represent the dominant patterns of residual variance found in large and complex data sets. When and where available, in situ shipboard data also were used to confirm results obtained from analysis of the satellite data. DATA Satellite

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analysis, less than 0.5% of the data used in this study resulted from either image compositing or spatial interpolation. Moreover, the length of the image sequence and the sampling interval between images ( - 5 0 days) is adequate to resolve the temporal scales of interest in this study.

Data

Satellite data (11 lxm band) from the NOAA Advanced Very High Resolution Radiometer (AVHRR) were collected for a region centered off Punta Eugenia, Baja California from 24 October 1984 to 29 June 1989. This period was chosen for study because careful examination of 11 years of satellite data showed that it contained a relatively large number of cloudfree images of the region, and this period was approximately uniformly sampled in time. Channel 4 data were chosen for this study because combined satellite-in situ analyses show that these data correspond well to near surface oceanic thermal structure in the CCS (Koblinsky et al., 1984). Each of the 35 satellite images, selected on the basis of the above criteria [see Gallaudet (1991) for satellite, date, and time of each image], covers an identical geographic area which is approximately 500 km x 500 km in size (Fig. 1). They form the image sequence analyzed in this study. Preprocessing steps included: a) geophysical calibration of counts to brightness temperature in °C (e.g., Lauritson et al., 1979 and updates); b) geographic registration (e.g., Legeckis and Pritchard, 1976); c) landmasking (Simpson, 1992); d) cloud screening (Simpson and Humphrey, 1990; Gallaudet, 1991); and e) final correction for the cloud contaminated data by image compositing (Gallaudet, 1991) and spatial interpolation (Jain, 1989). Because of the time period chosen for

CALCOFI

Data

In situ near-surface temperature data, taken with an approximate station separation of 75 km over a 28-year period by Calcofi, were used to construct harmonic curves of surface temperature (Lynn, 1967; Godfrey and Ridgway, 1985; Lynn and Simpson, 1987) for each of the stations in Figure 1. Near-surface temperature maps, constructed as image data, were generated from these curves [see Gallandet (1991) for details of the procedure]. Each provides an in situ map of the long-term, mean, near-surface temperature off Baja California for its respective julian day in the corresponding AVHRR image sequence. Hereinafter, the sequence of images derived from the Calofi data is referred to as the ISD sequence. Methods

Empirical orthogonal function (EOF) analysis was used to determine the dominant patterns of residual variance in the AVHRR and ISD image sequences. EOF analysis is a statistical method used to decompose a multivariate data set into an uncorrelated linear combination of separate functions of the original variables. In most oceanographic and meteorologic applications, a time-space data set T(t,x) (in which t and x refer to generalized temporal,

Sea Surface Temperature and Oceanic Processes 377

[t~l, and spatial, [x~}, coordinates) is decomposed into separable functions of time and of space, ranked by variance (Holmstrom, 1970; Hardy, 1978; Barnett and Patzert, 1980; Kelly, 1985; Eslinger et al., 1989). The essentials of the method are given below. Let T(t, x) be a sequence of satellite images. Specifically, T(t, x) is a set of N T images, or time-steps, represented as T(t, x) = [T~], i = 1, 2 . . . . . NT,

(1)

where Ti denotes the ith image in T(t, x). For simplicity, let T~ be a single-band image (e.g., AVHRR Channel 4 calibrated to °C). Thus, T~ contains NL lines and NS samples in an array consisting of N= NLxNS spatial points, or pixels. The set [T~I consists of N T distinct realizations of N spatial points. Each pixel in Ti is coregistered with the corresponding ( N T - 1) other pixels in the set ITil. A data array X' (t, x) first is formed with T(t, x), where X' is a NT x N matrix in which each row, [x~q,is a time-step T~ with its NL lines concatenated one after another. Because the objective of EOF analysis is to describe the variability in T, a mean vector is computed and removed from X' to form a restructured and demeaned data array, X. The selection of which mean to remove depends on the objectives of the specific EOF analysis. For example, the 1 x N temporal mean row vector, which represents the average value over the NT time steps for each of the N spatial locations, is computed as 1 Nr [mt] = - - ~ [x~] (2) NTi

=1

where [xf] is the ith row of X'. In this application, (2) can be interpreted as the long-term, temporal mean of the image sequence. Alternatively, the N T x 1 spatial mean column vector, m,, which represents the average value over the N spatial points for each of the N T time steps, is computed as m, =

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where x~ is the jth column of X'. This vector contains an image-specific spatial mean (single value) for each image in the image sequence. In order to mathematically define the demeaning process in a convenient and clear manner, the N T x N temporal mean matrix Mt and the N T x N spatial mean matrix M, are formed as [[mt] 1

n,=/tm,] /

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Llm,lJ i.e., N T replicates of [mt], and

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i.e., N replicates of m~. For a given analysis, the appropriate mean is removed from X' to reduce the demeaned data array X= [X'- M],

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where M represents either Mt for the temporally demeaned EOF analysis (i.e., remove the same long-term mean from each image in the sequence) or M, for the spatial-demeaned EOF analysis (i.e., remove an image specific spatial mean from each image in the sequence). For most earth science applications, the number of time steps N T in the sequence T(t, x) is much less than the number of spatial points N. This is particularly true for image data (in this study, NT-- 35 and N = 4502). For this reason, the EOFs were formulated in terms of the N T × NT covariance matrix, Cx, defined by C x , = ~ _ 1 [ X ' - M ] [X'- MIT= N _1 1XXT.

(7)

In C~,, each diagonal element (Cx,), represents the variance in the ith row (i.e., time step) of X', and each off-diagonal element (Cx,)ij(i*3~ represents the covariance between the ith andjth rows of X'. The EOF decomposition is formed from the eigenvectors of the covariance matrix of X': Cx,C ~-- G~A,

(8)

where the rows of the N T x NT matrix G are the transposed eigenvectors of Cx,, [gi]. The N T x N T matrix A is diagonal, with each diagonal element 2i equal to an eigenvalue of Cx,. By convention, the eigenvalues in A are ordered to contain decreasing amounts of variance. The EOF decomposition of X is GTY=X.

(9)

Each row [y,] is an EOF and represents a spatial pattern of residual variance in the restructured and demeaned data, X, and hence T; each transposed eigenvector [gi] in G is a corresponding time-varying amplitude vector. The method of EOF construction used in the present study is the singular value decomposition (SVD) of X (Golub and Reinsch, 1970; Wilkinson and Reinsch, 1971; Forsythe et al., 1977; Gill et al., 1991). The SVD method does not require the construction or storage of the covariance matrix; therefore, it is computationally more efficient than the formal covariance method presented above. The time-varying amplitude method of normalization causes the time-varying amplitudes to be unitless; consequently, the EOFs are expressed in °C. It was used in this study because the EOFs have the same units as the image sequence. Hence, geophysical interpretation of the EOFs is more straightforward. Spectra of the time series of temporal amplitudes were computed to determine the dominant periods associated with specific EOF patterns of residual variance. Prior

378 GaUaudet and Simpson

TEM RAL MEAN IMAGES

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RESULTS Temporal

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to performing the spectral analysis, each time series of temporal amplitudes was multiplied with the Parzen window. The Parzen window is used when the frequency response function (and/or the corresponding coherence function) is the main goal of the spectral analysis (Bendat and Piersol, 1971). There is no practical way to smooth the spectral estimates given the limited length of the times series. Both temporally demeaned and spatially demeaned EOFs were computed. Because the patterns of residual variability were the same for both EOF analyses [apart from patterns removed in the pre-processing (demeaning) and random sign shifts in the EOFs which are compensated for by sign changes in the corresponding temporal amplitudes], only results from the temporally demeaned analyses are given below.

and Spatial Means

The temporal mean images of the original (i.e., nonfiltered) 4.6-year image sequence (NF, Fig. 2a), and the Calcofi in situ data (ISD, Fig. 2b), show a strong northsouth SST gradient, which is consistent with the largescale, north-south thermal gradient of the CCS reported in the literature (Robinson, 1976). These images correspond to [nat] in eq. (2) computed from their respective data sets, where the 1 × N temporal mean row vector has been deconcatenated into a NL x NS image for visualization. The time series of image specific spatial means of the NF image sequence (Fig. 3a), and the ISD data (Fig. 3b), show a strong seasonal cycle in SST. The spatial means of the ISD, however, are higher (~1.02.0°C) than those of the image data because the Calcofi data were sampled at a depth of about I m and extrapolated to the surface, whereas the satellite-derived SST is a surface skin temperature (Liu et al., 1979; Simpson and Paulson, 1980; 1981). These time series plots correspond to the N T × 1 spatial mean column vector, m,, in Eq. (3) computed from their respective data sets. EOFs o f t h e 4 . 6 - Y e a r N F I m a g e S e q u e n c e The first five temporally demeaned EOFs of the 4.6-year NF image sequence, their associated time-varying am-

Sea Surface Temperature and Oceanic Processes 3 79

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plitudes, and the power spectrum for each of the amplitudes are given in Figures 4, 5, and 6, respectively. For optimal geophysical interpretation, it is essential that the EOFs and their associated time-varying amplitudes (and hence power spectra of the amplitudes) be interpreted together (see next section). The first temporally demeaned EOF (Fig. 4a) contains 38.7% of the variance in the NF sequence and is composed of two distinct regions. The east-west boundary between the two regions is roughly parallel to the coast and occurs about 200 km offshore. Highest values are found in the coastal region; lowest values occur offshore. The corresponding time-varying amplitude plot (Fig. 5a) is very similar in shape to the spatial mean plot of the image sequence (Fig. 3a); it represents the strong interannual/seasonal SST cycle observed in the California Current System (Lynn et al., 1982; Lynn and Simpson, 1987). The power spectrum of the time series of time-varying amplitudes (Fig. 6a) contains a dominant period of approximately 420 days. The second temporally demeaned EOF (Fig. 4b) contains 6.8% of the residual variance in the NF sequence and describes a pattern opposite to that of the first EOF. A distinct boundary, which occurs about 150 km from the shore, separates a coastal region with lowest values from an offshore region with highest values. The corresponding amplitude plot (Fig. 5b) is complex, and its power spectrum (Fig. 6b) contains three peaks at periods of approximately 150 days, 280 days, and 420 days. The third temporally demeaned EOF (Fig. 4c) contains 3.9% of the residual variance in the NF sequence and is dominated by a diagonally oriented feature which extends across the entire region. This feature contains relatively high values, and separates two regions with relatively low values. The power spectrum (Fig. 6c) of the associated time-varying amplitude plot (Fig. 5c) contains multiple peaks, but the strongest peak has a period of approximately 168 days. This spectrum also contains energy at periods of about 280 days and 420 days. The fourth (Fig. 4d) and fifth (Fig. 4e) temporally demeaned EOFs (which contain 3.5% and 3.2% of the residual variance in the NF image sequence, respectively) exhibit a number of similarities. Both contain a large eddylike structure offshore and a separate feature

Figure 4. The first five temporally demeaned EOFs of the 4.6-year NF image sequence. The EOF number and percent variance in each EOF are given below each panel. For this and the remaining grey scale figures in this paper, darkest grey shades correspond to highest values (i.e., black, highest SST), and lightest grey shades correspond to lowest values (i.e., white, lowest SST). The land is masked and mapped to the color white.

380

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near the southwest tip of Punta Eugenia. The geographic locations of these features, however, are not identical in each of these EOFs. Moreover, the power spectra of their respective time-varying amplitudes also differ. The power spectrum associated with the fourth EOF contains pronounced peaks at periods of approximately 140 days, 187 days, and 336 days, whereas that associated with the fith EOF has its two strongest peaks at periods of about 153 days and 280 days. EOFs

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The first two EOFs (temporally demeaned) of the ISD set (Fig. 7) are well correlated with the corresponding EOFs (Fig. 4) of the NF image sequence (Table 1). The first two EOFs of the ISD set, however, contain a much higher percentage of the variance than the corresponding EOFs of the NF sequence. The third through fifth EOFs of the ISD data appear more irregular than the first two, and correlations with the corresponding EOFs of the NF sequence are relatively low.

Sea Surface Temperature and Oceanic Processes 381

Table 1. Correlations between the First Five EOFs Generated from the In-Situ Data (ISD) and the Nonfiltered (NF) SST Image Sequence EOF Number 1 2 3 4 5

Correlation Coefficient + 0.880 + 0.828 + 0.265 +0.156 -0.165

DISCUSSION

4,2%

Interpretation of the EOF Results The approach. Although numerous EOF studies appear in the literature, no percise method of interpreting the results has been developed, and many investigators neglect to clearly define their own interpretative approach. To avoid ambiguity, the approach used in this study is: Interpret each EOF-amplitude pair as a unit of information, that is, a given EOF describes a spatial pattern of residual variance in the demeaned image sequence that is modulated by its corresponding timevarying amplitude. Spectra of the time varying amplitudes are used to determine the dominant time scales associated with a given EOF spatial pattern of residual variability. This intuitive approach necessarily follows from the mathematical formulation of the EOF decomposition [Eq. (9)]. The significance of EOF topography. Detailed investigations (Buell, 1975; 1979; Richman, 1986) have shown that EOF topography is determined by the shape of the grid on which the data are sampled. In almost every EOF investigation of data sampled on a rectangular grid (including this study), the first EOF is entirely positive; the second contains one zero crossing; and the third contains mixed regions of positive and negative values (Richman, 1986). Therefore, interpretation of the zero crossings in a given EOF or amplitude is avoided in this study, and only the relative patterns in each (i.e., higher vs. lower values) are emphasized. Although the unrotated EOFs did exhibit the domain shape dependence described above, their geophysical significance was clear, especially in light of available in situ data. The possible effects of subdomain instability (Richman and Lamb, 1985) were investigated; subdomain instability was not a problem for the Punta Eugenia data. For these reasons, and because there exists a lack of complete objectivity in defining rotated EOFs, only unrotated EOFs were used in this study.

Figure 7. The first five temporally demeaned EOFs for the ISD set. The EOF number and percent variance in each EOF are given below each panel.

382 Gallaudet and Simpson

Statistical significance of the EOFs. Statistically significant EOF-amplitude pairs may be determined using various selection rules (Preisendorfer and Barnett, 1977; Overland and Preisendorfer, 1982; Preisendorfer, 1988). For example, the Rule N (Overland and Preisendorfer, 1982) defines the Nth EOF-amplitude pair as statistically significant if it represents a larger percentage of variance than 95% of the Nth EOF-amplitude pairs computed from a random data set. This rule was used because it selects those patterns of residual variance that are of interest to this study. All EOFs discussed below satisfy this criterion. Interpretability also was improved by computing correlations between various EOF-amplitude pairs. Moreover, power spectra of their time-varying amplitudes were used to determine the dominant temporal scales of variability.

Large-scale Structure Mean Structure. The temporal mean images (Figs. 2a and 2b) show a strong north-south SST gradient consistent with the large-scale, north-south, mean thermal gradient of the CCS based on extensive shipboard observations (Robinson, 1976; Lynn et al., 1982). The time series of spatial means (Figs. 3a and 3b) show a strong interannual / seasonal cycle in SST which again is consistent with reported ship-based observations (Hickey, 1979; Chelton, 1984; Lynn and Simpson, 1987). Patterns of Residual Variability in the NF Sequence. The large-scale seasonal and interannual cycles in SST dominate the time-varying amplitudes (Fig. 5a) corresponding to the first EOF of the NF image sequence (Fig. 4a), while the spatial pattern in the first EOF defines two distinct dynamical regions. The nearshore region is approximately 150-200 km wide; the other region extends from the end of the nearshore region to the western boundary of the study area (approximately 500 km from the coast). Collectively, these figures show that the dominant pattern of variability off Baja California is described by a near-shore region where the seasonal cycle in SST is relatively strong (dark shades in Fig. 4 represent high values) and an adjacent region farther offshore where the seasonal cycle in SST is relatively weak. These results are consistent with the known seasonal variability of the California Current System based on available shipboard observations for the region (Reid et al., 1958; Hickey, 1979; Chelton, 1984; Lynn and Simpson, 1987). The pattern in satellite-derived sea surface temperature (SST) described above is similar to that obtained from the Calcofi-derived seasonal differences in the steric height of the sea surface relative to 500 db (Fig. 8). Steric, or dynamic, height is a measure of the geopotential distance between two pressure levels in the ocean; its horizontal gradient is proportional to the speed of the large-scale geostrophic flow (Pond and

Pickard, 1983). Theoretical studies (Nelepo et al., 1978), in situ observations (Voorhis and Schroeder, 1986; Simpson et al., 1984; Simpson and Lynn, 1990), and satellite data (Koblinsky et al., 1984; Simpson and Lynn, 1990) have shown that SST patterns observed by satellite often reflect the quasigeostrophic adjustment of the near-surface thermal layer to large-scale and mesoscale subsurface pressure-induced flows. The Calcofi steric heights (Fig. 8) show that there is a cross-shelf change in the slope of the baroclinic field of pressure, which occurs about 150-200 km offshore, and that the normal spring and summer low pressure in the upper ocean baroclinic pressure field at the coast is replaced by a higher inshore pressure during the fall and winter (Reid and Mantyla, 1975; Simpson 1984). This change in baroclinic pressure is geostrophically balanced by a poleward surface inshore flow, the California Countercurrent, during the fall and winter. Farther offshore, the California Current flows southward throughout the year (Hickey, 1979; Chelton, 1984; Lynn and Simpson, 1987). The first and second EOF-amplitude pairs for the 4.6 year SST image sequence appear to reflect this seasonal variation in the circulation of the region. Moreover, the corresponding power spectra of the time varying amplitudes for these EOFs (Figs. 6a and 6b) contain peaks at seasonal and interannual time scales. This result is consonant with the interpetation that ENSO-related warming events in the California Current (a major source of interannual variability in the CCS) are associated with intensified seasonal cycles (Simpson, 1984a,b; 1992). The pattern in the second EOF (Fig. 4b) also defines two distinct regions, each located in approximately the same locations as those defined by the first temporal EOF. Peaks in the power spectra (Fig. 6b) of the timevarying amplitudes (Fig. 5b) associated with this EOF occur at periods of 150 days, 280 days, and 420 days; these are consistent with periods observed for both interannual/seasonal (as discussed above) and mesoscale processes in the CCS (Simpson et al., 1984; 1986). Thus, the low values in the nearshore region of this EOF suggest that mesoscale SST variability on these time scales is relatively weak nearshore, while the high values farther offshore suggest that mesoscale SST variability is relatively stronger in that region of the CCS. Together, these patterns define two distinct regions paralleling the coast that are almost identical to those identified by Lynn and Simpson (1987) from long-term statistics of Calcofi dynamic heights (Fig. 9). The boundary between the nearshore region and adjacent offshore region in the first and second EOFs marks the limit of the coastal zone in Lynn and Simpson (1987). The domain shoreward of this boundary is characterized by a relative maximum in the mean seasonal range of dynamic height (Fig. 9b), a relative minimum in the standard deviation of dynamic height (Fig. 9d), and it is primarily influenced by coastal circulation (e.g., Califor-

Sea Surface Temperature and Oceanic Processes 383

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nia Undercurrent). The offshore region in these EOFs coincides with Lynn and Simpson's transition zone, which is defined by a relative minimum in the mean seasonal range of dynamic height (Fig. 9b) and a relative maximum in the standard deviation of dynamic height (Fig. 9d). The offshore region observed in the first and

second EOFs also coincides with a narrow zone where the occurrence of minimum seasonal range and maximum standard deviation in dynamic height is erratic and nonseasonal (Fig. 9c). In Situ Data Variability. The high correlation between the first and second EOF-amplitude pairs of

384 Gallaudet and Simpson

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Figure 9. Long-term statistics of the dynamic height field derived from the CalCOFI data (from Lynn and Simpson, 1987): a) The difference between the mean fields of dynamic height for January 15 and July 15 (in dynamic centimeters). The zero line is shown dashed. (The characteristics depicted in Figs. 9a-9d refer to the dynamic height of the sea surface relative to 500 dbar), b) The range of dynamic height derived from harmonic analysis (in dynamic centimeters)• Range less than 5 dyn cm is hatched, c) The months of occurrences of the seasonal minimum in dynamic height. Most months fall into two periods that are geographically separated. Those months that fell in neither period are separated by contours and hatched, d) The standard deviation of dynamic height for the entire record of each station (i.e., seasonal variation removed). Standard deviation greater than 4 is hatched; standard deviation greater than 5 is densely hatched. The heavy circles give location of mesoscale eddies confirmed by independent shipboard studies.

the in situ data (ISD) and the corresponding E O F amplitude pairs of the NF image sequence (Table 1) indicates that the ISD pair also represent the same large-scale pattern: A coastal region with a cross-shelf

length scale of approximately 150-200 km, where the interannual/seasonal cycle in SST is relatively strong; and an adjacent region farther offshore where the seasonal cycle in SST is relatively weak [i.e., the transition

Sea Surface Temperature and Oceanic Processes 3 8 5

zone (Lynn and Simpson, 1987)]. This result, and the

corresponding mean analyses (Figs. 2 and 3), imply that large-scale variability in oceanic current systems can be studied reliably with long-term sequences of AVHRR data; a result relevant to investigating the dynamics of important but less well-sampled (e.g., with either ships or buoys) oceanic current systems (the Peru Current).

Mesoscale Structure The third EOF-amplitude pair (Figs. 4c and 5c) describes both interannual/seasonal and mesoscale SST variability, as evidenced by the three prominent peaks in power spectra (Fig. 6c) of the associated time-varying amplitude (Fig. 5c). Features of the EOFs 4 and 5 (Figs. 4d and 4e) are associated with two anticyclonic eddylike patterns that are centered in the region described by the diagonal feature in the third EOF. Individual SST realizations (Figs. 10g and 10h) contained in the NF image sequence confirm at least five anticyclonic eddy occurrences, mostly in the fall and winter in the region described by the diagonal feature in the third temporal EOF. These figures indicate that the diagonal feature in the third EOF may represent a region where eddies recur frequently in the CCS. This interpretation is consistent with theoretical models (Swaters and Mysak, 1985) and observations (Simpson and Lynn, 1990), which suggest that bathymetrically induced instability of the seasonally intensifying California Undercurrent could be a generation mechanism for recurrent mesoscale eddies found in the offshore California Current (e.g., off Point Conception and Punta Eugenia) and for the Sitka eddy near Sitka, Alaska. The anticyclonic eddylike patterns that appear in the fourth and fifth EOFs (Figs. 4d and 4e) occur in different locations, and are defined by different time scales (Figs. 6d and 6e). Most of the energy in these spectra occurs at mesoscale time scales, and they suggest that the features in these two EOFs primarily represent anticyclonic eddy variability off Punta Eugenia. These patterns indicate that either eddies occur at two distinct locations near Punta Eugenia, or that they advect with some small translation speed. This interpretation is consonant with shipboard data, which indicate frequent anticyclonic eddy occurrences off Punta Eugenia (Hickey, 1979; Burkov and Pavlova, 1980; Simpson et al., 1986; Lynn and Simpson, 1987). The low correlations between the higher-order EOFs of the ISD set and those of the NF (SST) image sequence (Table 1) result from the coarser spatial sampling of the Calcofi data (75 km resolution) compared with that of the NF image sequence (1.1 km for AVHRR at nadir), as demonstrated in Figure 10. The latter EOFamplitude pairs of the NF sequence describe mostly mesoscale processes (Fig. 6). The corresponding EOFamplitude pairs of the ISD set, however, contain large

seasonal components, evidenced in the power spectra of the correspoinding amplitudes (not shown). The coarser spatial resolution of the Calcofi data undersamples mesoscale processes (Simpson et al., 1986) and hence aliases the spectra associated with the higher-order EOFs of the ISD set. These results demonstrate the utility of satellite data in studies that require high spatial resolution data.

Baja California-Comparison with the Central and Southern California Regions in the CCS The transition zone described by the first and second EOF amplitude pairs of the NF image sequence off Baja California is consonant with the Calcofi-derived transition zone defined by Lynn and Simpson (1987). This latter zone is apparent throughout the CCS from San Francisco to Caho San Lucas (Fig. 9). Shipboard observations have verified the recurrent presence of numerous mesoscale eddies and meanders in this zone (Reid et al., 1963; Hickey, 1979; Burkov and Pavlova, 1980; Simpson et al., 1984; 1986; Simpson and Lynn, 1990). Historically, the transition zone off Baja California has been less well defined than that off southern and central California because 1) the region is relatively undersampled (i.e., with shipboard and buoy observations) compared with the central and southern California regions of the CCS and 2) the coarse spatial resolution of most shipboard data for the region (Figs. 1; 10a-d) precludes proper resolution of the relevant mesoscale signals (Simpson et al., 1986). The EOF analysis (Figs. 4, 5, and 6) provides independent evidence that many of the thermodynamical and dynamical processes in the CCS off Baja California are similar to those in the CCS off central and southern California. Data Set Dimensionality The first five EOFs contain approximately 56% of the total variance in the NF image sequence. Thus, five of the possible 35 EOFs for this study encapsulate over half the residual variance in the image sequence. In many previous EOF investigations, however, the first five EOFs contain over 90% of the residual variance in the data (Kelly, 1985; Lagerloef and Bernstein, 1988; Paden, 1990). This difference occurs because the geometric dimensionality (i.e., temporal and spatial extent) and geophysical dimensionality (i.e., number of significant physical processes represented) of the NF image sequence are relatively large in the present study compared with those in these other studies. The Punta Eugenia region (Fig. 1) is approximately 500 x 500 km 2, and the image sequence spanned 4.6 years. By comparison, the AVHRR data for the Santa Barbara Channel studied by Lagerloef and Bernstein (1988) covered only 100 km x 50 km and spanned only I year. Likewise, the image data off northern California used by Kelly (1985)

CALCOF! IN SITU DATAVS. AVHRR SST IMAGE DATA {7.9

°C 10,8

(e) MAY 3

MAY 3, 1988

AUGUST 23

AUGUST 23, 1985

(c 1988

NOVEMBER 21 !9,9

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DECEMBER 28 Image representation of CalCOFI tered (NF) AVHRR image examples.

Figure 10.

DECEMBER 28, 1987 in situ

data (ISD) and corresponding nonfil-

Sea Surface Temperature and Oceanic Processes

had a maximum width and length of 200 km and spanned only three consecutive months, and Paden's (1990) image sequence for the Gulf of California had average spatial dimensions of 600 km × 100 km and spanned only 2 years. The more restricted geometric and temporal dimensionalities of these other image dat sets also limit their respective geophysical dimensionalities. For example, the Santa Barbara Channel (Lagerloef and Bernstein, 1988) is a relatively enclosed region in the northern half of the southern California Bight, which is primarily characterized by the seasonal variability in the "Southern California Eddy" (Reid et al., 1958; Hickey, 1979; Lynn and Simpson, 1987). Hence, the seasonal cycle in SST heavily dominated the first EOF of their results (91% of the residual variance). Similarly, persistent coastal upwelling off northern California in April to July (Hickey, 1979) dominated the EOFs in Kelly's (1985) study, and tidal mixing and seasonal heating/cooling which dominate the circulation in the Gulf of California strongly feature in Paden's (1990) results. Compared with these data sets, the NF image sequence of the Punta Eugenia region has a greater geometric and temporal dimensionality. Moreover, historical Calcofi data (Figs. 8 and 10) for the Punta Eugenia region reveal relatively complex thermal structure and intermittent incoherence in the subsurface and surface flow (Reid et al., 1963; Wyllie, 1966; Wooster and Jones, 1970; Lynn and Simpson, 1987). These factors, along with complex bathymetry, contribute to a relatively high geophysical dimensionality compared with that in the aforementioned studies. Data with a relatively high degree of geometric, temporal, and/or geophysical dimensionality (i.e., the NF image sequence) require a higher number of EOFs to describe a majority of their residual variance than do less complex data. The EOF Method: Further Considerations The EOF method is a powerful analysis technique for compressing the dimensionality of a large, complex data set. The method, however, is not without its limitations. For example, the first EOF in this study is dominated by seasonal and interannual SST cycles (Figs. 5a and 6a). This result was expected because seasonal heating / cooling in the midlatitudes is well documented (Robinson, 1976). In both the annual and seasonal EOF analyses (computed but not shown), there were relatively few temporal realizations because of cloud cover (seven images per annual analysis, and five images per seasonal analysis). Therefore, the first few EOF-amplitude pairs generated from both of these analyses were dominated by individual events (Figs. 10g and 10h), which contained a relatively high percent variance compared with other elements in the image sequence. Hence, the EOFs from

387

these analyses failed to describe patterns of residual variability common to all realizations and were not used in this study. CONCLUSIONS

EOF analysis was applied to a 4.6-year sequence of AVHRR images centered off Punta Eugenia, Baja California. The spatial and temporal mean structures contained in this sequence describe the interannual/seasonal cycle in SST and the large-scale, north-south, oceanic thermal gradient found in the region. The first EOF-amplitude pair also describes the interannual/ seasonal cycle in SST. Both results are consistent with the large-scale, long-term, mean structure of the region as determined from shipboard observations. The second EOF-amplitude pair defines two distinct regions paralleling the coast. The coastal region coincides with the coastal zone of Lynn and Simpson (1987) and the adjacent region farther offshore is identical to their transition zone. The third through fifth EOF-amplitude pairs primarily represent meandering of the California Current and anticyclonic mesoscale eddy occurrences in the region. Collectively, the EOF results provide independent, satellite-derived evidence for the existence of the transition zone off Punta Eugenia. Moreover, the results provide independent evidence that long sequences of satellite images can be used to study the thermodynamic and dynamic processes associated with major oceanic current systems. This latter result is especially important given the size of the world's oceans and the limited ship and buoy resources available for in situ measurements. Finally, this report also shows the usefulness of interpreting each EOF-amplitude pair as a unit of information, that is, a given EOF describes a spatial pattern which is modulated by the temporal pattern in its corresponding time-varying amplitude. Power spectra of the time-varying amplitudes generally provide evidence of the dominant physical processes associated with a given EOF.

This work was sponsored by the Marine Life Research Group (MLRG) of the Scripps Institution of Oceanography and by grants from NASA and the O~ce of Naval Research. This paper also was funded in part by the National Sea Grant College Program, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, under grant number NOAA NA 89AA-D-SG/38, project number R/0E-25, through the California Sea Grant College, and in part by the California State Resources Agency. The views expressed herein are those of the authors and do not necessarily reflect the views of NOAA or any of its subagencies. The U.S. Government is authorized to reproduce and distribute for governmental purposes. L. A1-Rawi, D. Atkinson, J. Gobat, and S. Yhann assisted with the computer analysis, P. Misiowiec and M. Wilke typed the manuscript. G. Tapper and the staff of the SIO photolab prepared the final figures.

388

Gallaudet and Simpson

REFERENCES Anderson, T. W. (1963), Asymptotic theory for principal component analysis. Ann. Math. Stat. 34:122-148. Barnett, T. P., and Patzert, W. C. (1980), Scales of thermal variability in the tropical Pacific. J. Geophys. Res. 10:529540. Bendat, J. S., and Pierso, A. G. (1971), Random Data: Analysis of Measurement Procedures, Wiley-Interscience, New York, 407 pp. Buell, C. E. (1975), The topography of empirical orthogonal functions, in Preprints Fourth Conf. on Prob. and Stat. in Atmos. Sci., Tallahassee, FL, American Meteorological Society, p. 188. Buell, C. E. (1979), On the physical interpretation of empirical orthogonal functions, in Preprints Sixth Conf. on Prob and Stat. in Atmos. Sci., Banff, Alta, American Meteorological Society, p. 112. Burkov, B. A., and Pavlova, Y. V. (1980), Description of the eddy field of the California Current, Oceanologia (Eng. Transl.) 20:272-278. Chelton, D. B. (1984), Seasonal variability of alongshore geostrophic velocity off central California, J. Geophys. Res 89: 3473-3486. Eslinger, D. L., O'Brien, J. J., and Iverson, R. L. (1989), Empirical orthogonal function analysis of cloud containing coastal zone color scanner images of the northeastern North American coastal waters, J. Geophys. Res. 94:10,88410,896. Fiedler, P. C. (1988), Surface manifestations of the subsurface thermal structure of the California Current, J. Geophys. Res. 93:4975-4983. Forsythe, G. E., Malcolmm M. A., and Moler, C. B. (1977), Computer Solution of Linear Algebraic Systems, PrenticeHall, Englewood Cliffs, NJ. Gallaudet, T. C. (1991), The Application of Satellite Imagery to the Analysis of Mesoscale Sea Surface Temperature Variability and Near Surface Acoustic Structure in the California Current System. M.S. Thesis, Scripps Institution of Oceanography, pp. 301. J. J. Simpson, Thesis Advisor. Gallaudet, T. C., and Simpson, J. J. (1991), Automated cloud screening of AVHRR imagery using split and merge clustering, Remote Sens. Environ. 38:77-121. Gill, P. E., Murray, W., and Wright, M. H. (1991), Numerical Linear Algebra and Optimization, Addison-Wesley, New York. Godfrey, J. D., and Ridgway, K. R. (1985), The large-scale environment of the poleward-flowing Leeuwin Current, Western Australia: longshore steric height gradients, wind stresses, and geostrophic flow, J. Phys. Oceanogr. 15:481495. Golub, G. H., and Reinsch, C. (1970), Singular value decomposition and least squares solutions, Numer. Math 14:403420. Hardy, D. M. (1978), Empirical eigenvector analysis of vector wind measurements, J. Appl. Meteorol. 17:1153-1162. Hickey, B. M. (1979), The California Current System-hypotheses and facts, Prog. Oceanogr. 8:191-279. Holstrom, I. (1970), Analysis of time series by means of empirical orthogonal functions, TeUus 15:127-149.

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ment of features observed in satellite data, Remote Sens. Environ. 33:17-33. Simpson, J. J. (1992a), Image masking using polygon fills and morphological transformations, Remote Sens. Environ. 40: 161-183. Simpson, J. J. (1992b), Response of the southern California Current System to the mid-latitude North Pacific coastal warming events of 1982-93 and 1940-1941, Fisheries Oceanogr. 1:57-79. Simpson, J. J., and Humphrey, C. (1990), An automated cloud screening algorithm for daytime AVHRR imagery, J. Geophys. Res. 95:13,459-13,481. Simpson, J. J., and Lynn, R. J. (1990), A mesoscale eddy dipole in the offshore California Current, J. Geophys. Res. 95: 13,009-13,022. Simpson, J. J., and Paulson, C. A. (1980), Small scale sea surface temperature structure, J. Phys. Oceanogr. 10:399410. Simpson, J. J., Dickey, T. D., and Koblinsky, C. J. (1984), An offshore eddy in the California Current System: Part I: Interior dynamics, Prog. Oceanogr. 13:5-49. Simpson, J. J., Koblinsky, C. J., Pelaez, J., Haury, L. R., and Weisenhahn, D. (1986), Temperature-plant pigment-optical relations in a recurrent offshore mesoscale eddy near point conception, California, J. Geophys. Res. 91:12,919-12,936. Sverdrup, H. U., and Fleming, R. H. (1941), The waters off the coast of Southern California, March to July 1937, Scripps Inst. Oceanogr. Bull. 4:261-387. Swaters, G. E., and Mysak, (1985), Topographically-induced baroclinic eddies near a coastline with application to the northeast Pacific, J. Phys. Oceanogr. 15:1470-1485. Voorhis, A. D., and Schroeder, E. H. (1976), The influence of deep mesoscale eddies on sea surface temperature in the north Atlantic subtropical convergence, J. Phys. Oceanogr. 6:953-961. Wilkinson, J. H., and Reinsch, C. (1971), Handbook for Automatic Computation, Springer-Verlag, Heidelberg. Wooster, W. S., and Jones, J. H. (1970), California Undercurrent off northern Baja California, J. Mar. Res. 28:235-250. Wyllie, J. G. (1966), Geostrophic flow of the California Current at the surface and at 200 meters, in California Cooperative Fisheries Investigation Atlas, No. 4.