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Summer sea surface temperature variability off Vancouver Island from satellite data, 1984-1991 Fang, Wendong 1993

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SUMMER SEA SURFACE TEMPERATURE VARIABILITY OFFVANCOUVER ISLAND FROM SATELLITE DATA, 1984-1991byWENDONG FANGB.Sc., Ocean University of Qingdao, 1986A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of OceanographyWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOctober 1993© Wendong Fang, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of 0 C ettm T P hAj The University of British ColumbiaVancouver, CanadaDate^OcA e4- 14, lqfjDE-6 (2/88)AbstractSatellite-sensed Advanced Very High Resolution Radiometer (AVHRR) SeaSurface Temperature (SST) data over eight summers (1984-1991) were used to analyze thesummer SST patterns of variability off the west coast of Vancouver Island. EmpiricalOrthogonal Function (EOF) analysis of the spatial variance for 133 nearly cloud-freesummer images was performed. The first EOF mode, which resembled the mean of allimages, showed a strong cool water band located at the northwest corner of VancouverIsland, a cool tongue extending seaward from the Strait of Juan de Fuca and a warm patchoff Barkley Sound. The second mode revealed topographically controlled upwelling-- coolwater over the shelf region with its seaward boundary roughly following the 200-m depthcontour, plus a cold eddy located just north of the Juan de Fuca Canyon. The third modedisplayed cool water extending southwestward off Brooks Peninsula, while the fourthmode showed a cool water plume extending off Cape Scott at the northern tip of VancouverIsland. These 4 modes accounted for respectively, 33, 12, 10 and 5% of the SST variance.With the first 4 modes accounting for 60% of the total variance, the EOF method is highlyeffective in condensing the huge amount of satellite data. The temporal amplitude of theEOF modes revealed how the SST features changed as summer progressed. From theseimages, we also constructed an overall seasonal coolness index, which revealed thesummers of 1986 and 1991 to have the coolest coastal water, with both summersimmediately preceding an El Nifio.IIiiiTable of ContentsAbstract ^  iiTable of Contents ^  iiiList of Tables  ivList of Figures ^  vAcknowledgments  Vii1. Introduction ^  12. Data collection and processing ^  83. The EOF method ^  144. The EOF analysis of the SST patterns off Vancouver Island ^ 17S. Reconstructing individual SST patterns from EOF modes ^ 346. A coolness index ^  457. Correlation between E0Fs and various indices ^ 508. Summary and conclusions ^  53Bibliography ^  55Appendix A Temporal Variance Pattern and Covariance EOF modes ^ 59Appendix B Time Series of First Four Gradient EOF Modes ^ 68List of Tables2.1 List of summer satellite images (1984-1991) over the study area. ^ 114.1 The percentage of total variance explained by first six EOF modes. ^ 184.2 Summer SST indices off Vancouver Island from 1984 to 1991. ^ 227.1 The cross correlations between time series of the gradient EOFmodes and various indices. ^  50B1 Time series index of first four gradient EOF modes. ^ 68ivList of Figures1.1 Summer prevailing circulation over the Vancouver Island continental regionfrom Thomson et al. [1989].^1.2 Summer SST patterns off Vancouver Island from NOAA satellite images.2.1 Study area off the west coast of Vancouver Island.2.2 The re-sampled grids. The solid grid indicates the centre of re-sampled pixels,whereas the dashed grid shows the centre of the original pixels. ^ 104.1 Spatial amplitude patterns for the SST gradient EOF modes 1 to 4, respectively.The spatial domain extends 150 km offshore and 350 km alongshore. In thealongshore direction, the mouth of the Juan de Fuca Strait stretches from 0 to30 km, Barkley sound from 70-90 km, and Brooks peninsula protrudes fromthe coast at 250 km alongshore.   234.2 Temporal amplitude for the SST gradient EOF modes 1 to 4, respectively. ^ 294.3 The mean SST field from 133 images over eight summers (1984-1991). ^ 324.4 The monthly averaged temporal amplitudes of the gradient EOF modes 1 to 4over all years, revealing the monthly progression of the SST patterns assummer advances. ^  335.1 The fraction of total spatial variance explained by first K gradient EOF modes. ^ 355.2 Satellite SST pattern on July 25,1984 and its reconstructed patterns from EOFmodes.^  37V4795.3 Satellite SST patern on September 19, 1986 and its reconstructed patterns fromEOF modes. ^  41vi6.1 Cool and warm regions used for calculating the coolness index C as discussedin the text. ^  466.2 Summer coolness index C off Vancouver Island derived from satellite-sensedSST data (using images from June to September). The index C defined byequation (6.1) indicates on average how much the SST in the coastal region iscooler relative to the offshore SST.  6.3 Fluctuations in the summer coolness index C as data from various two-weekintervals are omitted in the computation of C to simulate missing data fromclouds. The C values computed with data omitted are marked by the symbols 1to 7 corresponding to the seven possible two-week intervals omitted, and the Cvalues with no missing data are marked by the + symbol (linked by the dashedcurve).  Al Pattern of Temporal Variance from 133 images over eight summers (1984-1991). ^A2 Spatial amplitude patterns for the SST covariance EOF modes 1 to 4.A3 Temporal amplitude for the SST covariance EOF modes 1 to 4.4849616266VIIAcknowledgmentI sincerely thank my research supervisor, Dr. William W. Hsieh, for his guidance,support and encouragement. I would also like to thank the members of my thesissupervisory committee, Professor Gordon A. McBean and Professor Paul H. LeBlond, fortheir helpful suggestions and comments.Thanks go to Gordon Staples for his kindly help with collecting and processing thesatellite images, and to Denis Laplante and Liusen Xie for their assistance in computerprogramming.Thanks are also extended to Professor Guo Zhongxin and Professor Gan Zijun ofSouth China Sea Institute of Oceanology, Academia Sinica, for their support during mystudies in University of British Columbia.1Chapter 1IntroductionSea surface temperature (SST) from satellites has many uses in oceanography[Robinson, 1985; Stewart, 1985; and Abbot and Chelton, 1991]. An important applicationis to use satellite SST to study the dynamical processes in the upper ocean, includingcoastal phenomena such as fronts, eddies, meanders of coastal currents and upwelling Forinstance, cloud-free satellite SST images were used to extract dynamical information ofeddies in the Atlantic Ocean [Spence and Legeckis, 1981], by showing evolution of theeddies by tracking their horizontal elliptical shapes. Satellite SST imagery were also used toshow a spatial and a temporal view of upwelling fronts along coastal boundaries [e.g.Legeckis, 1988]. Thus satellite SST data are capable of providing a two-dimensional viewof coastal features at a given time and information about their time-space variability.Early studies involving satellite SST imagery usually used the images to describespatial patterns of short-term events, due to the limited amount of data. However, withincreasing amounts of cloud-free satellite SST data available over longer periods of time,statistical analysis of coastal features in these SST data has been developed to explore theirgeneration mechanisms [e.g. Kelly, 1985; Seaver, 1987; and Lagerloef and Bernstein,1988]. SST variability could be analyzed by calculating the standard deviation (or thevariance). A map of the standard deviation values indicates the amount of variability at eachgrid point but does not indicate how the variability progresses with time. To analysize thedominant pattern of SST variability (or anomaly) and to track the temporal behavior forlarge SST data sets, the Empirical Orthogonal Function (EOF) method has been a verypowerful tool. The primary advantage of the EOF method is its ability to compress the2complicated variability of the original data set into a relatively few uncorrelated (ororthogonal) modes. These modes can usually explain the major physical features of theoriginal data sets by presenting a spatial pattern and a time series and can be used toreconstruct the original data sets to a given accuracy by summing over enough modes.How much of the total variance of the original data set is explained in a given mode isindicated by the corresponding normalized eigenvalue. Application of the EOF method tolarge-scale SST variability dates back to Davis [1976] and Weare et al., [1976]. Theprincipal advantages of the EOF decomposition are summarized as follow: (i) it providesthe most efficient method for compressing data; (ii) the EOF modes can be regarded asuncorrelated modes of variability of the data field; and (iii) the method simplifiesunderstanding the procedures of minimum mean square error estimation.Therefore, Empirical Orthogonal Function (EOF) analysis (also known as PrincipalComponent Analysis) is generally regarded as the most efficient way to extract informationfrom large data sets. For the past few years, EOF analysis has been used to extractdominant satellite SST patterns [Kelly, 1985; Lagerloef and Bernstein, 1988; and Padeneta!., 19911. There are several ways to calculate the E0Fs, but no matter which method isused, the solution is unique for the non-missing data [Kelly, 19881. While the analysismethods are the same whether a temporally-averaged mean or a spatially-averaged mean isfirst removed from the data set, different E0Fs are obtained [Paden eta!., 1991]. Lagerloefand Bernstein [1988] suggested that for satellite images where spatial features tended to bepersistent or only weakly time varying, spatial E0Fs (i.e., E0Fs performed on data withtheir spatial means removed) were more appropriate than temporal E0Fs, which mainlyexplained structures with strong temporal variability. This property was also found byPaden et al. [1991] while using E0Fs to analyze the patterns of SST variability in the Gulfof California in relation to tidal and wind forcing.3Since 1984, the Satellite Oceanography and Meteorology Laboratory at Universityof British Columbia has received coastal SST images off the west coast of North Americavia the US National Oceanic and Atmospheric Administration (NOAA) satellite series.These SST images, which were derived from the Advance Very High ResolutionRadiometer (AVHRR), were converted into brightness temperature and registered to Earthcoordinates. Satellite SST images provided by the laboratory have been applied to view themajor surface circulation patterns of the coastal area. For instance, in a recent study byHickey [1992], satellite-sensed SST images in the Southern California Bight, combinedwith the hydrographic surveys and moored arrays of current meters, were used to analyzethe dynamics of circulation over the Santa Monica Pedro basin and shelf off California.With the increasing availability of satellite SST data, it has become possible to usesatellite data to monitor SST variability in both space and time, improving vastly on thevery limited spatial coverage offered by ship observations. Off the west coast of VancouverIsland, SST images of the summer coastal upwelling were used to study baroclinicinstability [Emery and Mysak, 1980], eddies, upwelling events and coastal currents [Ikedaand Emery, 1984; Thomson eta!., 1985; Burgert and Hsieh, 1989; and Jardine, 1991] andto compare with numerical modeling results [Ikeda et al., 1984]. Thomson et al. [1989]gave a general description of the circulations off Vancouver Island, showing the spatial andtemporal variability of the coastal current and its effects on the coastal fishery. Theseformer studies related to the SST variability off Vancouver Island, used satellite data mainlyfor descriptive purposes by examining individual images for a short period. In this study,the nearly cloud-free SST data extending over eight summers are used to study the longerterm SST variability.Prevailing summer circulation (Figure 1.1) over the Vancouver Island continentalmargin is affected by the upwelling-favorable northwesterly wind over the continentalregion, the buoyancy fluxes and the tidal currents. The oceanography is further modified4by the dynamical interaction with the local bottom topography, by friction effects and byoffshore oceanographic processes [Thomson et cd., 1989]. During summer, the NorthPacific Aleutian Low weakens and shifts to the west as high pressure builds up to thesoutheast. Thus summer geostrophic surface winds off Vancouver Island are affected bythe high pressure system and are often from the northwest. The northwesterly surfacewind drives the equatorward surface current over the Vancouver Island continental margin.A filament or plume often occurs to the southwest of Brooks Peninsula, crossing the shelf-break region and extending seaward to as far south as 48°N (Figure 1.1). A polewardcoastal current, driven by buoyancy fluxes from the Strait of Juan de Fuca, flows along thecoast to the south of Brook Peninsula, then turns seaward, partly merging into theequatorward shelf-break current.Fig. 1.1 Summer prevailing circulation over the Vancouver Island continental region.[From Thomson et al., 1989]5Summer upwelling is one of major physical features over the Vancouver Islandcontinental region. Upwelled surface cold water off Vancouver Island can be seen insatellite SST imagery. Figure 1.2a shows one of the summer SST features off VancouverIsland. A cold water band, where a filament had previously been observed [Ikeda andEmery, 1984, see Figure 1.2a], started off Brook Peninsula at the northwestern coast ofVancouver Island and extended southwestward along the shelf-break region. The width ofthis upwelling plume is about 20 km, consistent with the baroclinic Rossby radius ofdeformation in the region. This cold surface water plume has been investigated as a surfacefeature of shelf-breaking upwelling whose cause may be associated with the alongshoregradient of local northwesterly wind [Staples, 1993].Another feature from summer SST imagery (Figure 1.2b) shows a larger cool waterarea covering the entire shelf and continental region with a seaward boundary aligned withthe shelf-break region. An apparent feature in the image is the presence of meanders alongthe seaward boundary of the cool area. Theoretical studies of baroclinic instability of thecurrent system over the continental region [e.g., Ikeda et al., 1984] have helped to explainthe existence and evolution of the observed meanders.Therefore, we will ask, do these features represent the dominant summer SSTpatterns of the continental region? What is the variability of these patterns in space andtime, and what affects the variability?In this thesis, the objectives are to identify the dominant patterns of summer SSTvariability off Vancouver Island using E0Fs, to study the seasonal and interannualvariability in coastal upwelling, and to set up a method for compressing the large satelliteSST data set. The hypotheses of this study are:(1) Major larger scale physical features (e.g. upwelling, major eddies, meanders) andtheir variability off Vancouver Island can be represented by a few dominant EOFpatterns.6(2) Summer upwelling either shoreward or seaward of the shelf break region is one ofthe major features from the satellite SST data.(3) Individual SST patterns off Vancouver Island could be reconstructed from severaldominant EOF modes.(4) The interannual variability of summer SST off Vancouver may be associated withthe El Nirio Southern Oscillation phenomenon.This thesis is organized as follows: Chapter 2 introduces the collection andprocessing of the AVHRR SST data. After briefly describing the EOF method in Chapter3, we show the dominant EOF modes and relate them to oceanographic structures inChapter 4. Chapter 5 shows the individual SST images reconstructed from severaldominant EOF modes. Chapter 6 presents the coolness index derived from the SSTimages, while Chapter 7 performs correlation analysis between the time series of EOFtemporal amplitudes and various indices which affect the SST in the study region. Asummary and conclusion is given in Chapter 8.(a)(b)Fig. 1.2. Summer SST patterns off Vancouver Island from NOAA satellitedata, showing a cool water plume on July 25, 1984 (top); a larger-scalecoastal cool surface water on September 7, 1987 (bottom).78Chapter 2Data Collection and ProcessingIn this study, the primary data source was satellite imagery from polar-orbitingNOAA satellites. The UBC Satellite Oceanography and Meteorology Laboratory hasreceived and processed 133 nearly cloud-free AVHRR images off Vancouver Island duringeight summers (1984-1991) via these NOAA satellite series. The data and orbit number ofthe images are listed are listed in Table 2.1. All satellite images were navigated (i.e.corrected for distortion and registered to a map), and were nudged (i.e., entire imageshifted to fit map overlap) to correct for receiving system timing errors or satellite attitudeerrors. The accuracy of the navigation was about 1 pixel (1.1 km). The navigation andcloud detection techniques used in this study were described in Emery eta!. [1986]. Onlyinfrared images from band 4 (10.3-11.3 1.tm) were converted to brightness SST [Lauritsonet al., 1979]. Since SST variability rather than absolute SST is important in this study, nocorrection was made for the atmospheric water vapor effect on the infrared temperature.The nearly cloud-free condition causes the irregular temporal coverage of thecollected satellite data set. The irregular temporal coverage of the images might causeserious aliasing as some short-term events might be missing in the satellite data. However,there is little doubt that the main variability features can be covered by the satellite data, asdiscussed in Kelly [1985]. In our study, we focus on the larger scale and longer term SSTvariability, so the effects from the irregularity of time series may not be too serious. Alimited test on the seriousness of missing temporal coverage will be shown in Section 5.9Fig.2.1 Study area off the west coast of Vancouver Island.The study area (Figure 2.1) is about 350 km alongshore by 150 km offshore,covering the entire continental shelf and slope region off Vancouver Island. For theconvenience of computation and analysis, we re-sampled the spatial grids (Figure 2.2), sothat the SST spatial resolution changed from the original 1.1 km by 1.1 km pixel to 1.5 kmby 1.5 km. A spatial weighted moving filter matrix121F = 1—[2. 4 216121was used to smooth the SST data and to reduce small scale image noise [Wang et al. 1983].Each selected image was at least 85% cloud-free over the study region. There were 105 by253 spatial data points over the study area. The data were arranged into a 2-dimensionalarray T(x,t) where x and t were the spatial and temporal indices, respectively.Fig. 2.2 The re-sampled grids. The solid grid indicates the centre of re-sampled pixels,whereas the dashed grid shows the centre of the original pixels.10(2.1)11Table 2.1 List of Summer Satellite Images (1984-1991) off Vancouver IslandSatellite Orbit Date(M-D-Y) Satellite OrbitDate(M-D-Y)NOAA6 26231 07-14-84 NOAA8 12304 08-10-85NOAA7 15779 07-14-84 NOAA8 12318 08-11-85NOAA7 15793 07-15-84 NOAA9 3435 08-12-85NOAA7 15807 07-16-84 NOAA8 12346 08-13-85NOAA7 15821 07-17-84 NOAA8 12403 08-17-85NOAA6 26302 07-19-84 NOAA8 12417 08-18-85NOAA7 15863 07-20-84 NOAA9 3576 08-22-85NOAA6 26367 07-23-84 NOAA9 3618 08-25-85NOAA7 15906 07-23-84 NOAA9 8033 07-04-86NOAA7 15920 07-24-84 NOAA9 8245 07-19-86NOAA6 26388 07-25-84 NOAA9 8485 08-05-86NOAA7 15976 07-28-84 NOAA9 8499 08-06-86NOAA7 15990 07-29-84 NOAA9 8507 08-07-86NOAA7 16019 07-31-84 NOAA9 8521 08-08-86NOAA6 26487 08-01-84 NOAA9 8527 08-08-86NOAA7 16033 08-01-84 NOAA9 8612 08-14-86NOAA6 26501 08-02-84 NOAA9 8620 08-15-86NOAA7 16400 08-27-84 NOAA9 8697 08-20-86NOAA9 3011 07-13-85 NOAA9 8704 08-21-86NOAA8 11920 07-14-85 NOAA9 8781 08-26-86NOAA8 11962 07-17-85 NOAA9 8894 09-03-86NOAA9 3138 07-21-85 NOAA9 8908 09-04-86NOAA8 12048 07-23-85 NOAA9 8993 09-10-86NOAA9 3181 07-25-85 NOAA9 9120 09-19-86NOAA9 3195 07-26-85 NOAA9 9275 09-30-86NOAA8 12105 07-27-85 NOAA9 13042 06-24-87NOAA9 3223 07-28-85 NOAA9 13070 06-26-87NOAA8 12133 07-29-8512(Table 2.1 Continued)Satellite Orbit Date Satellite(M-D-Y) OrbitDate(M-D-Y)NOAA9 13126 06-30-87 NOAA10 10172 09-01-88NOAA9 13310 07-13-87 NOAA9 19193 09-02-88NOAA9 13324 07-14-87 NOAA9 19306 09-10-88NOAA9 13352 07-16-87 NOAA9 19320 09-11-88NOAA9 13564 07-31-87 NOAAll 3828 06-22-89NOAA9 13578 08-01-87 NOAAll 3842 06-23-89NOAA9 13592 08-02-87 NOAAll 3856 06-24-89NOAA9 13676 08-08-87 NOAAll 4025 07-06-89NOAA9 13860 08-21-87 NOAAll 4251 07-22-89NOAA9 13874 08-22-87 NOAAll 4293 07-25-89NOAA9 14072 09-05-87 NOAAll 4477 08-07-89NOAA9 14100 09-07-87 NOAAll 4872 09-04-89NOAA9 14128 09-09-87 NOAAll 4900 09-06-89NOAA9 14311 09-22-87 NOAAll 4914 09-07-89NOAA9 14396 09-28-87 NOAAll 4928 09-08-89NOAA9 14424 09-30-87 NOAAll 4956 09-10-89NOAA9 18262 06-28-88^NOAAll 5013 09-14-89NOAA9 18389 07-07-88^NOAAll 5041 09-16-89NOAA9 18530 07-17-88 NOAAll 5126 09-22-89NOAA9 18756 08-02-88 NOAAll 5140 09-23-89NOAA9 18770 08-03-88^NOAAll 5154 09-24-89NOAA9 18869 08-11-88^NOAAll 5210 09-28-89NOAA9 18897 08-12-88^NOAAll 5224 09-29-89NOAA9 19024 08-21-88 NOAAll 9188 07-07-90NOAA9 19038 08-22-88 NOAAll 9202 07-08-90NOAA9 19052 08-23-88 NOAAll 9245 07-11-90NOAA9 19151 08-30-88 NOAAll 9315 07-16-90NOAA9 19165 08-31-88 NOAAll 9344 07-18-9013(Table 2.1 Continued)Satellite Orbit Date(M-D-Y) Satellite OrbitDate(M-D-Y)NOAAll 9358 07-19-90 NOAAll 14283 07-03-91NOAAll 9372 07-20-90 NOAAll 14650 07-29-91NOAAll 9471 07-27-90 NOAAll 14749 08-05-91NOAA10 20100 08-01-90 NOAAll 14974 08-21-91NOAAll 9569 08-03-90 NOAAll 15003 08-23-91NOAAll 9626 08-03-90 NOAAll 15017 08-24-91NOAAll 9894 08-07-90 NOAAll 15384 09-19-91NOAAll 9908 08-26-90 NOAAll 15398 09-20-91NOAAll 9993 08-27-90NOAAll 10007 09-02-90NOAAll 10021 09-04-90NOAAll 10162 09-14-90NOAAll 10247 09-20-90NOAA1 1 10261 09-21-9014Chapter 3The EOF MethodThe application of EOF analysis to satellite infrared data has previously beenpresented by Kelly [1985], Lagerloef and Bernstein [1988] and Paden et al. [1991]. E0Fsare the principal axes of a data covariance matrix, with the E0Fs usually ordereddecreasingly by eigenvalue. The first few E0Fs denote the dominant patterns of thevariance with the corresponding eigenvalues representing the percentages of total varianceaccounted for.In order to explicitly decompose just the spatial or just the temporal variability ofSSTs, one of two different means must be removed from T(x,t) before calculating the datacovariance matrix. To study the strongly temporal patterns associated with warming orcooling of some study area, the temporally-averaged mean at each point is removed fromthe data, i.e.1 x--.NT'(x,t)= T(x,t)– -T(x,t)N t=i(3.1)where t represents a particular image in the data set and N the total number of images.In contrast, for the study area where structures vary very strongly in space butweakly in time (e.g., fronts, upwelling or topographic eddies), spatially-averaged mean ineach image is removed from the data, i.e.x--,mT'(x,t)= T(x,t)– —1 LT(x,t)M x=i(3.2)15where M is the total number of pixels in an image.Lagerloef and Bernstein [1988] called the resulting E0Fs from removing temporalmeans, "temporal E0Fs", and those from subtracting spatial means, "spatial E0Fs". Forconvenience of discussion and to avoid confusing terminology, Paden et aL [1991] calledthe former "covariance E0Fs" , and the latter "gradient E0Fs". Lagerloef and Bernstein[1988] and Paden et al. [1991] used both approaches to analyze the SST patterns ofvariability. They suggested that the approach with spatial means removed was moresuitable for AVHRR SST patterns where oceanographic features tended to persist overtime. This hypothesis was tested with our satellite SST data and similar results wereobtained. Hence, we will concentrate mainly on the gradient E0Fs in the following section.The EOF decomposition of the data set T'(x,t) to form the covariance matrix is alinear combination of eigenfunctions,Nr(x,t)=Ian(t)F„(x)^(3.3)n=1with the coefficient a„(t) obtained by projecting the data set onto each function F„(x),ma„(t)=IT'(x,t)F„(x)x.i(3.4)With this presentation, F„(x) is called the spatial amplitude, which presents the spatialcovariance pattern of an EOF mode, while the coefficient an (t) is called the temporalamplitude, which describes the time variations of an EOF mode.The E0Fs are calculated by solving the eigenvalue problem of the data covariancematrix (formed by multiplying the data matrix T' by its transpose). Instead of solving forthe eigenvectors of the covariance matrix (the "covariance method"), one can also calculate16singular vectors by using singular-value decomposition (SVD) . Hence, there are at leasttwo different ways to calculate E0Fs, but the solution is unique when there are no datamissing [Kelly, 1988]. With SVD, missing data must be estimated [Kelly, 1985; Paden etal. 1991], but fewer computations are required. In contrast, the use of the covariancemethod allows one to simply skip over missing data. The latter method is used in thisstudy. For the details of the covariance method and the processing technique for calculatingthe data covariance matrix from the data set T'(x,t) where rows outnumber columns, seeLagerloef and Bernstein [1988].17Chapter 4EOF Analysis of the SST Patterns off Vancouver IslandThe spatial patterns of the first six gradient EOF modes are presented in Figure 4.1,and their corresponding temporal amplitudes in Figure 4.2. The percentage of total varianceaccounted by each mode, is given in Table 4.1. The first gradient EOF (Figure 4.1a),accounting for 33% of the total variance, shows positive spatial amplitudes in thesouthwest corner of the study area and in a small region off Barkley Sound. The negativespatial amplitudes cover the northeast area offshore from the northwest coast of VancouverIsland and the region offshore from the Strait of Juan de Fuca. As the temporal amplitudeof this mode was almost always positive (Figure 4.2a), the negative spatial amplitudesrepresent the cooler water. For the area more than 75 km offshore, the spatial amplitudesdecrease from south to north, revealing a northward cooling trend. The spatial pattern ofthe first mode is very similar to the mean temperature field from averaging over all 133images (Figure 4.3). The mean SST field shows that strong temperature gradients in theshelf regions off the southern and northern coast of Vancouver Island where the coldesttemperature are 11.2 °C and 11 °C, respectively. A patch of warm water off Barkley Soundseparates the two cool water masses. Both the first EOF mode and the SST mean fieldindicate that the two cool water features are temporally persistent. But mode 1 providesmore information than the mean pattern by revealing the temporal behavior (Figure 4.2a) ofthis pattern.18Table 4.1. The Percentage of Total Variance Explained by the EOF ModesGradient E0Fs Covariance E0FsMode Percentage Percentage1 33.3 59.92 12.2 7.23 10.0 6.04 5.0 4.05 3.0 2.06 2.4 1.6In Figure 4.1a, the cool water band along the northwest coast of Vancouver Islandappears to originate from the northern tip of Vancouver Island and then flow southwardpast Brooks Peninsula. This cool water band can often be observed from individual imagesduring summer and its somewhat uncertain source (from northern tip of Vancouver Islandor from Brooks Peninsula) has been argued by Ikeda and Emery [1984] and Emery et al.[1986]. Another cool water core originates from the mouth of Juan de Fuca Strait. Theflow of this cool water must be affected strongly by the discharge from the strait, and byupwelling induced by the complex local topography, e.g. the Juan de Fuca canyon[Freeland and Denman, 1982]. From numerical simulations [Weaver and Hsieh, 1987], thedischarge should flow northward along the coast. However, with shallow banks to itsnorth forming a northern "barrier", the cool surface water appears to deflect seawardsduring its northward flow [Thomson et al., 1989]. The persistence of this feature impliesthat despite upwelling favorable wind, which opposes the flow, this cool water still flowsnorthward because of peak discharge from the strait during summer. The small patch ofwarm surface water off Barkley Sound separates the Juan de Fuca cold tongue and the coolwater off the northwest coast of Vancouver Island. This warm feature has also been19observed from the summertime individual images by Emery et al. [1986], who suggestedthat this warm water over the shallow banks off Barkley Sound was related to solarheating in this region, especially in Barkley Sound. Thomson et al. [1989] systematicallydescribed the circulation mechanism over the shallow topographically complex banks,pointing out that the summer circulation over the region was weak, and tidal rectificationand outflow of the water in Barkley Sound played an important role in the region. Thevelocity EOF analysis in this region by Hickey et al. [1991], showed the first EOF ofvelocity at 30 m depth off Barkley Sound to be directed weakly offshore, confirming theseaward-flowing feature of this warm water band.Gradient EOF mode 2, accounting for 12% of the total variance, shows a zero-crossing along the continental slope (Figure 4.1b). Except for being further offshore, thezero crossing is closely aligned with the 200m-depth contour which is about 65 kmoffshore in the southern portion and less than 5 km offshore off Brooks Peninsula. This200m-depth contour indicates the shelf-break region where upwelling is a common featurein summer [Freeland and Denman, 1982; Ikeda and Emery, 1984; Denman and Freeland,1985]. The seaward extension of the cool water beyond the shelf break may be caused bythe offshore Elcman transport in wind-induced upwelling. Ikeda and Emery [1984] noticedthat the cool water boundary propagated offshore at 10 km/day, extending eventuallybeyond the shelf break. The largest negative spatial amplitude occurred just north of theJuan de Fuca canyon, where a topographically controlled cyclonic eddy is often found[Freeland and Denman, 1982; Denman and Freeland, 1985; Weaver and Hsieh, 1987].When the temporal amplitude of this mode (Figure 4.2b) is positive, this pattern describesthe topographically controlled, wind-induced upwelling over the entire shelf-slope regionwith the coolest surface water located in the southeast region. Freeland and Denman [1982]also found summertime upwelling to be especially pronounced at the edges of the southernbanks owing to the presence of major canyons. During upwelling, the temporal variability20of this mode may also be related to the remotely wind-driven coastally trapped waves. Thistype of upwelling structure may be present during summer despite weak or downwelling-favorable local winds [Thomson eta!. 1989].Explaining 10% of the total variance, the third gradient EOF mode shows a largetongue of negative amplitude extending southwestward from Brooks peninsula. A similarcold water band has been observed in 1980 summertime images [Ikeda and Emery, 1984].They argued that this band appeared to be advected by the southward flow from the coolernorthern district, but could also be the expression of upwelling at the local shelf break.When the temporal amplitude is positive, this mode represents the presence of a "squirt" orseaward jet of cool water. The temporal amplitude of this mode changes sign frequently,thus the cold squirt is not permanent but instead may suggest the trapping of temporalupwelling events in the region off southwestern Brooks peninsula. In the southern region,the amplitude values are positive, implying an out-of-phase relation with the squirt region.The fourth mode explains 5% of the total variance. When the temporal amplitude ispositive, this mode represents a cold plume originating off Cape Scott at the northern tip ofVancouver Island and extending seaward. The fifth mode explains 3% of the total variance.One major feature in this mode is that the spatial amplitude pattern presents an eddy-likestructure to the southwest of Brooks peninsula, where a wind-induced cyclonic eddy hasbeen observed and investigated [Thomson and Gower, 1985]. The spatial scale of theeddy-like feature is about 50 km. The sixth mode explains 2.4% of the total variance,showing two out-of-phase eddies off the Brooks peninsula.For these higher modes, we need to determine if they are statistically significant. Asignificance test introduced by Overland and Preisendorfer [1982] uses the Monte Carlotechnique for selecting E0Fs. However, when the data set is very large, the cost of MonteCarlo simulations becomes excessive. Instead, the asymptotic theory for large data sets canbe used [Preisendorfer, 1988, p. 204 - 205]. As the data set in this study is large, we used21the asymptotic method to test the significance of the E0Fs. From Preisendorfer (1988,eq.5.18, but with the incorrect minus sign preceding (ab)1/2 replaced by a plus sign), wefound that the first 13 EOF modes were above the 99% significance level.In summary, the first four gradient EOF modes, altogether accounting for 60.5% ofthe SST variance, represented some of the well-known features in the region. The fifth andsixth modes, though explaining smaller percentage of total variance (5.4%), showed somemesoscale eddy-like structures which may represent some physical eddy features over theVancouver Island continental margin. The first mode closely resembled the mean summerupwelling pattern, the second, the topographically-controlled upwelling, the third, thesquirt off Brooks Peninsula, and the fourth, the northern plume off Cape Scott. Figure 4.4shows the temporal amplitude averaged over the particular summer months during 1984-1991. The temporal amplitude for mode 1 increases monotonically from June toSeptember, revealing the intensification of the mode 1 pattern (Figure 4.1a) as the summerprogresses. Mode 2 also intensifies from June, peaking in August. Mode 3 shows a declinein the temporal amplitude in August and especially in September, implying a decrease in thelikelihood of a strong squirt off Brooks Peninsula as summer progresses.The temporal amplitudes for the first four E0Fs were also averaged over eachsummer (Table 4.2), revealing that the mode 1 type of SST pattern was strongest in 1990.The mode 2 type of upwelling was strongest in 1991 and 1986.In order to compare with the gradient E0Fs, covariance E0Fs (i.e. with thetemporal mean removed from the data as in equation (2.2)) were also calculated. The firstthree covariance EOF modes accounted for 59.9, 7.2 and 6.0% of the total variance (Table4.1), respectively. The covariance EOF spatial patterns for modes 1, 2 and 3 somewhatresembled gradient EOF modes 1, 2 and 3, respectively, though the covariance EOFpatterns were much noisier than the corresponding gradient EOF patterns when plotted inhigher resolution. The spatial and temporal amplitudes of the first four modes from22covariance E0Fs are presented in Appendix A. In general, the gradient EOF modes explaina higher percentage of the total variance than the corresponding covariance EOF modesexcept for mode 1 (Table 4.1). Mode 1 is a much more dominant mode among thecovariance E0Fs than among the gradient E0Fs.Table 4.2. Summer SST Indices off Vancouver Island from 1984 to 1991Summer a, a2 a3 a4 d C1984 7.5 1.0 1.0 -4.1 70 0.591985 6.3 1.9 5.2 4.5 73 0.641986 8.1 4.7 -1.4 3.1 71 0.921987 5.9 1.2 -1.3 -0.3 65 0.541988 9.0 -2.2 -3.0 -0.3 65 0.511989 7.8 -5.5 -7.7 7.8 72 0.421990 9.4 0.5 0.4 -1.6 65 0.811991 8.0 4.9 0.4 -4.0 80 0.86Monthly averages of the indices were first calculated from the images for the months Juneto September, then averaged to form the summer index. The a. (timed by 100) are thesummer values of the temporal amplitudes of the gradient EOF modes 1 to 4. The d are theoffshore locations of the front in kilometers, and C are the coolness indices in degreesCelsius (see Chapter 6).(A) SPATIAL AMPLITUDE FOR EOF MODE ONE50^100^150^200ALONGSHORE DISTANCE (1W)Fig.4.1 Spatial amplitude patterns for the SST gradient EOF modes 1 to 6 ,respectively.The spatial domain extends 150 km offshore and 350 km alongshore. In the alongshoredirection, the mouth of the Juan de Fuca Strait stretches from 0 to 30 km, Barkley soundfrom 70-90 km, and Brooks peninsula protrudes from the coast at 250 km alongshore.250^300^350(B) SPATIAL AMPLITUDE FOR EOF MODE TWO0^50^100^150^200ALONGSHORE DISTANCE (KM)Fig.4.1. (Continued)250^300^3500•••I100^150^200ALONGSHORE DISTANCE (KM)0\ 'I )) 250^300^3500(C) SPATIAL AMPLITUDE FOR EOF MODE THREEFig.4.1. (Continued)50^100^150^200ALONGSHORE DISTANCE (KM)300 350(D) SPATIAL AMPLITUDE FOR EOF MODE FOURFig.4.1. (Continued)(E) SPATIAL AMPLITUDE FOR EOF MODE FIVE50^100^150^200^250^300^350ALONGSHORE DISTANCE (KM)Fig.4.1. (Continued)(F) SPATIAL AMPLITUDE FOR EOF MODE SIX0^50^100^150^200ALONGSHORE DISTANCE (KM)Fig.4.1. (Continued)250^300^35019861985fit1984 1991E<0id)90491990 19911984 198711985 19891988(a) Mode 11987jiff1988 19901989iftJAS JAS^JAS JJAS^JJAS JJAS .JAS JAS(b) Mode 2AS JAS JAS JJAS JJAS JJAS JAS JASFig. 4.2. Temporal amplitude for the SST gradient EOF modes 1 to 6, respectively.1986 1988 1989 1990 19914.19871984 19661991198419901985 1988 19891986 1987(49(c) Mode 3JAS^JAS^JAS^JJAS^JJAS^JJAS^JAS^JAS(d) Mode 4JAS^JAS^JAS^JJAS^JJAS^JJAS^JAS^JASFig. 4.2. (Continued)19871986 1988(e) Mode 519911 I1985ih19901984■1984 1045 1986 1987 1988 1989 1990 19911IIIIIIIIIIIIIIIIIvIIIIIIIIIIIIIII,,,JAS^JAS^JAS^JJAS^JJAS^JJAS^JAS^JAS(f) Mode 6JAS^JAS^JAS^JJAS^JJAS^JJAS^JAS^JASFig. 4.2. (Continued)300250 3500^50^100^150^200ALONGSHORE DISTANCE (KM)MEAN SURFACE TEMPERATURE FIELDFig. 4.3. The mean SST field from 133 images over eight summers (1984-1991).33JUN^JUL^AUG^SEPFig. 4.4. The monthly averaged temporal amplitudes of the gradient EOF modes 1 to 4over all years, revealing the monthly progression of the SST patterns as summer advances.34Chapter 5Reconstructing Individual SST Patterns from EOF ModesThe empirical orthogonal function method provides the optimal decomposition of adata field into its several principal modes, which helps to interpret the data field bypresenting the smallest number of degrees of freedom. These dominant EOF modes presenta concise description of the distribution of variance between various spatial patterns. Thishas been illustrated in Chapter 4 by using a few dominant EOF modes to present the majorfeatures of the SST off Vancouver Island. For instance, the first six EOF modes from thelarge satellite data set could describe the major features of SST variability from the datafield by accounting for 66% of the total variance, i.e., the major features of SST variabilitycan be described only by several principal EOF modes instead of by the large original dataset. EOF modes could also provide a most efficient method to reconstruct the approximateoriginal data field, i.e., using the statistically significant EOF modes to recompose thesatellite SST data set within a given accuracy. The advantage is that this method of datareconstruction could compress large data set which will be used for other proposes. Forexample, Davis [1976] used EOF representation as a natural way to reduce the number ofdata variables used in examining predictability of Pacific SST and sea level pressure.The reconstruction technique of individual SST patterns can be briefly described asfollows: The data set T'(x,t) (spatial mean subtracted) can be approximated as a linearcombination of the first K EOF modes from the total number of EOF modes in equation(3.3),Ktt (X ,t) =la„(t)F(x)^(5.1)n=135The first K EOF modes lead to the smallest sample mean square errorI I( T'(x, t) — f'(x,^ (5.2)where { denotes the temporal mean.As two simple examples, the reconstruction of two specified SST individual imagesfrom the dominated EOF modes were examined. Instead of determining the K fromequation (5.2), we just chose several different K (e.g. 4, 8, etc.), then compared theseapproximate SST patterns ( t'(x,t) added to the spatial mean) to the original one. Thechoice of K can be referred to the accumulated variance of the first K modes (Figure 5.1).Beyond K = 4, the accumulated variance increases at an slow rate. This indicates that thefirst four EOF modes are very dominant in describing the major varying features of satelliteSST over the study region as presented in Chapter 4. The first 13 modes which aresignificant over the 95% level explained almost 80% of the total spatial variance. Weconstructed l''(x,t) for K = 4, 8 and 12.0.50 0 0 0 0 00 0^ 0 0 00000.90.70.30.10^5^10^15Figure 5.1 The fraction of total spatial variance explained by the first K gradient EOFmodes.36The tested results from two specified SST images are presented in Figure 5.2 and inFigure 5.3, respectively. The SST pattern on July 25, 1984 shows a cold plume tosoutheast of Brooks Peninsula with the lowest temperature in its core (Figure 5.2a). Thereconstructed approximate pattern from first four EOF modes (K =4) shows the larger scalefeature of the original pattern. With increasing number of EOF modes used for thereconstruction, the smaller scale features could be included in the approximate patterns (K= 8 in Figure 5.2c, and K = 12 in Figure 5.2d ). The reconstructed pattern with K=12shows the largest similarity with the original one. The SST pattern on September 19, 1986shows the coldest surface water located at the southeast corner of the study region (Figure5.3a). This pattern showed more complex spatial variation of SST over the study regionthan that one in the image of July 25, 1984. The reconstructed approximate patterns alsoreflected the basic features of the SST pattern without the smaller-scale variations or noise.These two examples of SST pattern reconstruction indicated that the reconstructedindividual SST patterns from the first four spatial EOF modes in general represented thelarger scale variation features in the corresponding original SST patterns. With increasingK, more small-scale features are included. The patterns from first 12 EOF modes generallyagree well with the original patterns. If only larger scale features are of concern, the firstfour or five EOF modes are generally adequate for reproducing the SST patterns offVancouver Island.The data set of 133 images used in the EOF analysis required 15 Mbytes of storage.The first 4 EOF modes used 0.5 Mbytes, i.e., only 3% of the original storage. The first 12EOF modes used 1.4 Mbytes, only 9.3% the original storage. These numbers illustrate thepowerful data compression possible with the EOF method. A useful SST data distributionsystem could have the first 12 EOF spatial amplitude Fn(x) stored on the user computerand the transmission of the 12 an (t) from the most recent image to the user by fax. Hence,only 12 numbers had to be transmitted instead of an entire satellite images.250^300^35010 .0^1 0 .4150^200ALONGSHORE DISTANCE (KM)(a) Satellite SST pattern on July 25, 1984.Fig. 5.2 Satellite SST pattern on July 25, 1984.and its reconstructed patterns from EOFmodes.250 3000^■111111111IM11111111,^I..0 50^100^150^200ALONGSHORE DISTANCE (1cm)(b) SST pattern reconstructed from first 4 gradient EOF modes (K = 4).Fig. 5.2. (Continued)00.-4o0.oU)3501 2 . 50--.'r 1 2 . 25■ \ ■^11.5g,^50^100^150 200^250ALONGSHORE DISTANCE OM0 350300(c) SST pattern reconstructed from rust 8 gradient EOF modes (K = 8).Fig. 5.2. (Continued)1 2 . 4■ _50^100^150^200ALONGSHORE DISTANCE (1cii)(d) SST Pattern reconstructed from first 12 gradient EOF modes (K = 12).Fig. 5.2. (Continued)350250 300ALONGSHORE DISTANCE (KM)(a) Satellite SST pattern on September 19, 1986.Fig. 5.3. Satellite SST pattern on September 19, 1986 and its reconstructed patterns fromEOF modes.13.5—C—14. 03501 . 5\ .___ 1 2 . 050^100^150^200^250^300ALONGSHORE DISTANCE (KM)C13.1 3 . 0 /^\\\5\-----------\,-12.0(b) SST Pattern reconstructed from first 4 gradient EOF modes (K = 4).Fig. 5.3. (Continued)50^100^150^200^250^300^350ALONGSHORE DISTANCE (10.)(c) SST Pattern reconstructed from rust 8 gradient EOF modes (K = 8).Fig. 5.3. (Continued)0to1-4c1 4 . 012.5\K_^112.0/ /ioo(----9 . 550300 350150 200ALONGSHORE DISTANCE (KM)250(d) SST Pattern reconstructed from first 8 gradient EOF modes (K = 12).Fig. 5.3. (Continued) t45Chapter 6A Coolness IndexIt would be useful to defme a simple index that characterizes the relative strength ofthe coastal cool water. By calculating the difference between adjacent pixel values, welocated the maximum temperature gradient in the offshore direction, thereby defining anoffshore SST front a distance d from the coast (Figure 6.1). We then chose a line, 7.5 kmseaward from the SST front, as a boundary to divide the study area into two-- theshoreward part representing the cool, upwelling region, and the seaward part, the warmeropen ocean. The overall coolness index C, which represents a regional average of therelative mass of cold water, is defined as253 105 _^ 253 105C = [E E(Tocean(J) — T(I,J))S(I,J)]1[E Esu,.01^(6.1)J=1 1=1(1)^ 1=1 I= f (J)where I, J denote the onshore and alongshore indices of each pixel, 5(I,J) the pixel areaand T(I,J) the temperature at that pixel. Toce.(J) denotes the temperature averaged alongrow J over the region seaward of the partitioning line I= f(J) (shown as the dashedcontour in Figure 6.1). The summations in equation (6.1) are over the shoreward regionfrom the partitioning line I = f(J).The mean coolness index C for each summer, estimated by averaging the individualC values from each image over each summer, indicated that coolest coastal water occurredin 1986 and 1991 (Figure 6.2). As the C index measures the average temperature anomalyin the coastal upwelling region with respect to the temperature in the offshore region, theseVancouverIsland46strong anomalies in the C index indicated that the shelf water was relatively cool in thesummers of 1986 and 1991. The mean offshore location of the front (Table 4.2) was alsogreatest in 1991 (80 km offshore). The years 1987, 1988 and 1990 had the front closest tothe shore (at 65 km offshore).Fig. 6 A schematic diagram of cool and warm regions used for calculating the coolnessindex C as discussed in the text.As the satellite data are available only during cloud-free periods, we have toquestion the reliability of our summer upwelling index. To test the interference of clouds,we deliberately computed C with data missing at a two-week period during different timesin each summer. Figure 6.3 shows that the fluctuations of these C values computed withmissing data were in general smaller than the interannual variability in C, therefore givingIs confidence that the interannual variability in C observed was above the noise generated47by missing data from cloudy periods. Figure 6.3 also shows that missing data in June(when upwelling was still immature) tended to result in C being shifted higher, whereasmissing data in September (when upwelling was mature) tended to result in C being shiftedlower.The coolness index C covers two El Nirio events (1986-1987 and 1991-1992). Asthe strongest C occured in the summers of 1986 and 1991, this suggests that the C indexleads the El Nilio events. This result was tested by calculating the lagged correlationbetween the C index and the seasonal Southern Oscillation Indices (SOT) (i.e. the spring,summer, autumn and winter means of the monthly SOT as defined by Chelliah [1990]). Thehighest correlation of -0.92 was attained when the summer C was correlated with the SOTfrom the following spring, which means that cool summer coastal SST (high C index) offVancouver Island preceded the El Niiio warm events (low SOT), which peaked at aroundthe following spring. From assuming one degree of freedom for each year, a correlation of-0.92 is significant at the 99% level, though for such short interannual time series, thesignificance level cannot be determined reliably. Clearly a much longer time series for C isneeded before one can confirm this relationship between the two indices.0.480.o1984 1985 1986 1987 1988 1989 1990 1991Fig. 6.2 Summer coolness index C off Vancouver Island derived from satellite-sensedSST data (using images from June to September). The index C defined by equation(6.1) indicates on average how much the SST in the coastal region is cooler relative tothe offshore SST.5e"4730:1cN2 24.3^ I"35 1494Data omitted1 --- 16-30/Jun2 -- 01-15/Jul3 --- 16-31/Jul4 --- 01-15/Aug5 --- 16-31/Aug6 01-15/Sept7 --- 16-30/Sept1 1984 1985 1986 1987 1988 1989 1990 1991Fig. 6.3 Fluctuations in the summer coolness index C as data from various two-weekintervals are omitted in the computation of C to simulate missing data from clouds. The Cvalues computed with data omitted are marked by the symbols 1 to 7 corresponding to theseven possible two-week intervals omitted, and the C values with no missing data aremarked by the + symbol (linked by the dashed curve).50Chapter 7Correlations between E0Fs and various indicesTo examine the relationship of the dominant gradient EOF modes with variousindices, we calculated the correlations between the weekly-averaged time series of the firstfour gradient EOF temporal amplitudes with various related time series. From the dailyBakun upwelling indices (kindly provided by NOAA/NMFS Pacific FisheriesEnvironmental Group, Monterey, CA, at two offshore sites (48°N, 125°W and 51°N,131°W), we computed the weekly Bakun indices by averaging the daily data over the dayswhen satellite images were available. The Bakun coastal upwelling indices were based oncalculations of offshore Ekman surface wind transport from surface atmospheric pressuredata [Bakun, 19731. Weekly time series for the coolness index C and for the Fraser Riverdischarge measured at Hope, British Columbia, were prepared in a similar way.Table 7.1. The Cross Correlations Between Time Series of the Gradient EOF Modesand Various IndicesC Mode 1 Mode 2 Mode 3 Mode 4C 0.59/99% 0.70/99% 0.07/30% 0.01/6%B akun.S -0.13/50% -0.10/48% -0.05/21% 0.24/88% -0.10/54%Bakun.N -0.06/39% -0.30/96 % 0.20/80% 0.30/96 % 0.34/98 %Discharge -0.43/98 % -0.23/84% -030/92% 0.24/91 % -0.26/91 %The levels of significance given after the correlation coefficients, were calculated withthe number of degrees of freedom estimated by the method of Davis [1976]. Correlationsabove the 90% significance level were printed in bold, and they all have at least 30 degreesof freedom. C denotes the coolness index, while Bakun.S and Bakun.N represent theBakun upwelling index at (48°N, 125°W) and at (51°N, 131°W), respectively.51The correlation coefficients between the time series of the EOF modes and variousindices are listed in Table 7.1. Correlations of the coolness index C with the first four EOFtemporal amplitudes showed the highest correlation of 0.70 with mode 2, the next highestcorrelation of 0.59 with mode 1, and insignificant correlations with modes 3 and 4. Thissuggests that the first two EOF modes strongly influenced the overall coolness index C.The satellite data tend to suffer from fair-weather bias, i.e. satellite images areavailable only during cloud-free days with high pressure over the northeast Pacific, whichcorrespond to days with upwelling favorable winds. Thus, despite the bias in the satellitecollection, the occurrence of strong upwelling should coincide with days of high pressureand clear weather, and hence would have been included in our data collection andincorporated into our indices. Table 7.1 also shows the correlation between our indiceswith the Bakun upwelling indices. The Bakun index at 48°N,125°W (Bakun.S), lying justsouth of our study region, showed generally low correlations with the EOF amplitudes.The Bakun index at 51°N,131°w (Bakun.N), lying just to the northwest of our domainshowed higher correlations with the EOF amplitudes. Except with the first EOF amplitude,the positive correlations between Bakun.N and the other EOF amplitudes meant that anupwelling favorable Bakun index tended to concur with cool coastal SST in these modes.Since modes 3 and 4 involved, respectively, plumes off Brooks Peninsula and Cape Scott,both in the northern part of our study region, it is not surprising that they were correlatedwith the Bakun index to the north (Bakun.N) than with Bakun.S. The highest correlation,which occurred between mode 4 and Bakun.N, is expected since of the four modes, mode4 with the Cape Scott plume must have its upwelling most strongly affected by windsaround the northern part of our domain. The negative correlation between the first EOFamplitude and Bakun.N seemed to suggest that an upwelling favorable Bakun index tendedto concur with the weakening of the mode 1 coastal upwelling pattern, in contradiction to52our expectations. To explain this paradox, we note that the mode 1 amplitude time series(Figure 4.4) has a notable seasonal trend, indicating an intensification of the pattern ofFigure 4.1a from June to September. The corresponding seasonal trend for the Bakun.Nindex showed a decrease from June to September (not shown). Hence the negativecorrelation between the two could simply be due to opposite seasonal trends.While the coolness index C was not correlated with either Bakun.N or Bakun.S, Cand the Fraser River discharge had a significant negative correlation of -0.43 (Table 7.1).In summer, Fraser River water and thus surface water in the Strait of Georgia are normallywarmer than that in the Strait of Juan de Fuca, where there is much tidal mixing. Hickey etal. [1991] reviewed the transport process of the monthly pulse of warm, fresh water exitingthe Strait of Georgia from satellite SST images. They pointed out that the outflow of thisanomalously warm fresh water was one of the causes for warmer water appearing at themouth of the Juan de Fuca Strait. A large outflow event from Fraser River implies thatmore warm water flows through the Strait of Juan de Fuca, which diminishes the overallcoolness index of our study region, hence the observed negative correlation betweendischarge and C. Discharge was also negatively correlated with the EOF amplitudes inTable 7.1 except with mode 3, where the marginally significant positive correlationsuggests that strong discharges tended to concur with the appearance of the cold squirt offBrooks Peninsula.53Chapter 8Summary and ConclusionEOF analysis of the spatial variances for 133 nearly cloud-free SST imagesprovided us the first systematic classification of the summer SST patterns off VancouverIsland, and a way to follow their evolution as summer progresses. The first EOF mode ofspatial variance resembled the mean SST pattern obtained from averaging all images, whilethe second mode revealed upwelling controlled by the bottom topography. The third modecorresponded to cool water extending southwestward off Brooks Peninsula, while thefourth mode showed a cool water plume extending off Cape Scott at the northern tip ofVancouver Island. These 4 modes accounted for 33, 12, 10 and 5% of the SST variance,respectively. As 60% of the total variance can be accounted for with only 4 modes, weconclude that the EOF method is highly effective in condensing the huge amount of satelliteSST data off Vancouver Island and that if only large scale features are of interest, summingthe first four modes is generally adequate for approximating the SST images off VancouverIsland.Correlations between Bakun upwelling indices and our EOF temporal amplitudesshowed that SST in our study region was significantly influenced by the Bakun index tothe northwest of our domain but insignificantly by the Bakun index immediately to thesouth of our domain. That the wind (as represented by the Bakun index) to the north had agreater influence than the wind to the south of our region could be explained by the fact thatmodes 3 and 4 had plumes extending southwestward from Brooks Peninsula and CapeScott, both in the northern part of our domain. These SST EOF time series can potentiallybe used as new upwelling indices, providing a measure of the fine features of coastal54upwelling, which the Bakun index, based on large-scale geostrophic wind, cannot.From these images, we also constructed an overall coolness index C, measuring thecoolness of the coastal upwelling region relative to the offshore region. The negativecorrelation between C and the Fraser River discharge tends to suggest that high dischargeconcurs with warmer SST in our study region. Interannual variability in the average valueof C over each upwelling season revealed the summers of 1986 and 1991 to have thecoolest coastal water. These two cool anomalies slightly preceded the last two ENSOevents (1986-1987 and 1991-1992).This study shows that the continental region off Brook Peninsula is a physicallyactive region. The wind-induced shelf-break upwelling, mesoscale eddies, and the coldwater advection from the northern tip of Vancouver Island could be observed in the EOFspatial patterns. From this study and Staples [1993], the summer cool water plume over theshelf break region off southwestern Brooks Peninsula seems to be an indicator of wind-driven shelf-break upwelling though the advection from northern tip of Vancouver Islandmay affect this upwelling plume. A simple two-dimension numerical model was successfulin reproducing the time scales during two upwelling events, which observed from satelliteAVHRR images, but could not reproduce the results of AVHRR images [Jardine, 1991].To further understand the dynamics of the summer SST patterns off VancouverIsland, future investigations may involve:(1) analysis of the surface wind field and its effect on the SST patterns;(2) detailed numerical models of the wind-driven shelf breaking upwelling plume.55BibliographyAbbot, M. R., and D. B. Chelton, 1991, Advances in passive remote sensing of the ocean,in U.S. National Report 1987-90, International Union of Geodesy and Geophysics,American Geophysical Union, 571-587.Bakun, A., 1973, Daily and weekly upwelling indices, west coast of North America,1946-71, NOAA Tech. Rep., NMFS-SSRF-671, U.S. Dept. of Commer..Burgert, R., and W. W. Hsieh, 1989, Spectral analysis of the AVHRR sea surfacetemperature variability off the west coast of Vancouver Island, Atmosphere-Ocean,27, 577-587.Chelliah, M., 1990, The global climate for June-August, 1989: A season of near normalconditions in the tropical Pacific. J. Climate ,3, 138-162.Davis, R. E., 1976, Predictability of sea surface temperature and sea level pressureanomalies over the north Pacific Ocean. J. Phys. Oceanogr., 6, 249-266.Denman, K. L., and H. J. Freeland, 1985, Correlation scales, objective mapping, andstatistical test of geostrophy over the continental shelf, J. Mar. Res., 43, 517-539.Emery, W. J. and L. A. Mysak, 1980, Dynamical interpretation of satellite-sensed thermalfeatures off Vancouver Island, J. Phys. Oceanogr. 10, 961-970.Emery, W. J., A. C. Thomas, M. J. Collins W. R. Crawford, and D. L. Mackas, 1986,An objective method for computing advective surface velocities from sequentialInfrared satellite images, J. Geophys. Res., 91(C11), 12,865-12,878.Freeland, H. J., and K. L. Denman, 1982, A topographically controlled upwelling centeroff southern Vancouver Island. J. Mar. Res. 40, 1068-1093.Hickey, B. M., 1992, Circulation over the Santa Monica-San Pedro base and shelf, Prog.Oceanog., 30, 37-115.56Hickey, B. M., R. E. Thomson, H. Yih, and P. H. LeBlond, 1991, Velocity andTemperature Fluctuations in a Buoyancy-Driven Current Off Vancouver Island, J.Geophys. Res., 96(C6), 10,507-10,538.Ikeda, M. and W. J. Emery, 1984, A continental shelf upwelling event off VancouverIsland as revealed by satellite infrared imagery, J. Mar. Res., 42, 303-317.Ikeda, M., L. A. Mysak, and W. J. Emery, 1984, Observation and modeling of satellite-sensed meaders and eddies off Vancouver Island, J. Phys. Oceanogr., 14, 3-21.Jardine, I., 1991, Upwelling off Vancouver Island, M.Sc. Thesis, The University ofBritish Columbia, 87pp.Kelly, K. A., 1985, The influence of winds and topography on the sea surface temperaturepatterns over the northern California slope, J. Geophys. Res., 90(C6), 11,783-11,798.Kelly, K. A., 1988, Comment on "Empirical orthogonal function analysis of advancedvery high resolution radiometer surface temperature patterns in Santa BarbaraChannel" by G. S. E. Lagerloef and R. L. Bernstein, J. Geophys. Res., 93(C12),15,753-15,754.Lagerloef, G. S. E., and R. L. Bernstein, 1988, Empirical orthogonal function analysis ofadvanced very high resolution radiometer surface sea temperature patterns in SamtaBarbara Channel, J. Geophys. Res., 93(C6), 6863-6873.Lauritson, L., G. Nelson, and R. W. Porto, 1979, Data Extraction and calibration ofTIROS-N/NOAA A-G radiometers, NOAA Tech. Memo NESS 107, pp. 44-46, U.S. Dept. of Commerce, Washington, D. C..Legeckis, R, 1988, Upwelling off the gulfs of Panama and Papagayo in the tropical Pacificduring march 1986, J. Geophys. Res., 93(C12), 15,485-15,489.57Overland, J. E., and R. W. Preisendorfer, 1982, A significance test for principalcomponents applied to a cyclone climatology, Monthly weather Review, 110, 1-4.Paden, C. A., M. R. Abbott, and C. D. Winant, 1991, Tidal and atmospheric forcing ofthe upper ocean in the Gulf of California. Part I: Sea surface temperature variability,J. Geophys. Res., 96(C10), 18,337-18,359.Preisendorfer, R. W., 1988, Principal Component Analysis in Meteorology andOceanography, Elsevier, New York, 425pp.Robinson, I. S., 1985, Satellite Oceanography: An introduction for oceanographers andremote-sensing scientists, Ellis Horwood, England, 445 pp..Seaver, G., 1987, Geographic and temporal eddy variability in the western North Atlanticas sensed by satellite: an eddy generation mechanism, J. Phys. Oceanogr., 17, 1602-1618.Spence, T. W. and R. Legeckis, 1981, Satellite and hydrographic observations of low-frequency wave motions associated with a cold core gulf stream ring, J. Geophys.Res., 86 (C3), 1945-1953.Staples, 1993, Satellite AVHRR observation of the intensification of the shelf break currentduring an upwelling event off Vancouver Island, M.Sc. Thesis, The University ofBritish Columbia, 120pp.Stewart, R. H., 1985, Methods of Satellite Oceanography, University of California Press,Berkeley, 360 pp..Thomson, R. E. and J. F. R. Gower, 1985, A wind-induced mesoscale eddy over theVancouver Island continental slope, J. Geophys. Res., 90(C5), 8981-8993.Thomson, R. E., B. M. Hickey, and P. H. LeBlond, 1989, The Vancouver Island coastalcurrent: fisheries barrier and conduit. In Effects of Ocean Variability on Recruitmentand an Evaluation of Parameters Used in Stock Assessment Models, edited by R. J.58Beamish and G.A. McFarlane, Can. Spec. PubL Fish. Aquat. Sci., 108, 265-296.Wang, D. C. C., A. H. Vagnucci and C. C. Li, 1983, Digital image enhancement: Asurvey, Computer Vision, Graphics & Image Processing ,24 , 363-381.Weare, B. C., A. R. Navato and R. E. Newell, 1976, Empirical orthogonal functionanalysis of Pacific sea surface temperature, J. Phys. Oceanogr., 6, 671-678.Weaver, A. J. and W. W. Hsieh, 1987, The influence of buoyancy flux from estuaries oncontinental shelf circulation, J. Phys. Oceanogr., 17, 2127-2140.59Appendix ATemporal Variance Pattern and Covariance EOF modesA.1 Temporal Variance PatternFigure Al shows the temporal variance computed at each resampled pixel from 133SST images. The larger values are distributed in the seaward part (100-150 km offshore) ofthe study region with a maximum of 2.7 ° C2. Contrast to the seaward part, the shelf andinshore region shows smaller variance values except for the region off Barkley Sound. Thelowest values are near the northern tip of Vancouver Island, where cold water advectionfrom the north is a common feature in summer, and just off the Juan de Fuca Strait,indicating that the cold water plumes off the strait and from the northern tip of the island arerelatively persistent. These features are also seen in the mean SST field from 133 images(Figure 4.3) and in the spatial pattern of the first gradient EOF mode (Figure 4.1a).A.2 Covariance EOF modesThe covariance EOF modes were computed by using similar method fromcalculating the gradient EOF modes but with the temporal means subtracted from the datasets replacing the spatial means subtracted (see equation (2.1)). The spatial amplitudepatterns of the first four EOF modes are showed in Figure A2. Their corresponding time-series are presented in Figure A3.The spatial amplitude pattern of mode 1 explains 60% of total variance. Comparedwith the higher modes, this first mode is very dominant, thus showing a resemblance to thetemporal variance distribution (Figure Al). The spatial amplitude patterns of mode two and60three somewhat resemble those of mode two and three of gradient EOF but with a lessvariance (Table 4.1). Mode 4, which is not similar to any of first few gradient EOFmodes, explains 4% of the total variance. This mode shows that the zero crossingapproximately overlays the shelf-breaking region and turns seaward at Brooks Peninsula.Our covariance EOF analysis shows that the decomposition of the temporal variance maynot be suitable for presenting the useful spatial temperature structures which is theconcerned in this thesis.50^100^150^200^250^300^350ALONGSHORE DISTANCE (KM)Fig.A1 Pattern of Temporal Variance from 133 images over eight summers (1984-1991).F.:t"---\^r-100^150^200^250ALONGSHORE DISTANCE (KM)50 300 350(a) Mode 1Fig.A2 Spatial amplitude patterns for the SST covariance EOF modes 1 to 4.100^150^200ALONGSHORE DISTANCE (KM)250 300 350(b) Mode 2Fig.A2 (Continued)0^50^100^150^200ALONGSHORE DISTANCE (KM)(c) Mode 3Fig.A2 (Continued)250 300 350(d) Mode 4Fig.A2 (Continued)1989 19911986 198719859c•I9 •1988_0)03:r3.0(NI919911984 19871985 1986 1988(a) Mode 1JAS JAS JAS JJAS JJAS JJAS JAS JAS(b) Mode 2JAS JAS JAS JJAS JJAS JJAS JAS JASFig.A3 Temporal amplitude for the SST covariance EOF modes 1 to 4.Fig. A3 (Continued)i I'JASJAS(c) Mode 31984 198619t19911990198919881987(d) Mode 41990 1991IT 1^II^I^1^I^I1988r.1984 1985 1986-JAS JJAS JJAS JJAS JAS JASJAS JAS JAS JJAS JJAS JJAS JAS JASqo9(49Csioroqo;(49-1-_68Appendix BTable B.1 The temporal amplitude an(t) of the First Four Gradient EOF ModesDate(M-D-Y) ai a2 a3 a407-14-84 0.028 0.016 -0.084 0.02707-14-84 0.100 -0.078 -0.012 0.02907-15-84 0.103 -0.008 -0.024 0.00307-16-84 0.120 -0.137 -0.014 0.00107-17-84 0.149 0.014 0.051 -0.11007-19-84 0.125 0.063 0.048 -0.12307-20-84 0.060 0.080 0.027 -0.12607-23-84 0.088 0.080 0.096 -0.04607-23-84 0.070 -0.020 0.159 0.04807-24-84 0.064 0.009 0.104 0.02507-25-84 0.064 0.058 0.144 0.04607-28-84 0.010 -0.010 -0.029 -0.00207-29-84 0.081 -0.054 -0.051 -0.08507-31-84 0.056 0.065 -0.086 -0.10008-01-84 0.072 0.007 -0.077 -0.08308-01-84 0.039 0.096 -0.004 -0.08308-02-84 0.043 -0.018 0.017 -0.05008-27-84 0.079 0.018 -0.091 -0.10807-13-85 -0.011 -0.056 -0.096 0.10807-14-85 0.056 -0.045 -0.109 -0.05807-17-85 0.048 -0.062 -0.064 -0.05707-21-85 0.029 -0.047 -0.057 -0.04607-23-85 0.054 -0.084 0.051 0.03707-25-85 0.125 0.094 0.004 0.04407-26-85 0.101 0.052 0.081 0.15507-27-85 0.092 0.126 0.087 0.15907-28-85 0.091 0.036 0.155 0.15207-29-85 0.101 0.043 0.134 0.12608-10-85 0.043 0.109 -0.078 -0.07869Table B.1 (Continued)Date(M-D-Y) ai a2 a3 a408-11-85 0.033 0.127 0.055 -0.06408-12-85 0.015 0.137 0.054 0.10508-13-85 0.034 0.048 0.126 0.06508-17-85 0.100 -0.036 0.077 0.07008-18-85 0.057 -0.116 0.092 -0.02808-22-85 0.080 0.004 0.215 0.05608-25-85 0.080 0.004 0.215 0.05607-04-86 0.034 -0.072 0.033 0.04207-19-86 0.089 0.086 -0.034 -0.00308-05-86 0.003 -0.056 -0.122 0.07208-06-86 0.095 0.038 0.043 0.03108-07-86 0.117 0.044 0.059 -0.01908-08-86 0.104 0.054 0.065 -0.02108-08-86 0.112 -0.095 0.102 0.00908-14-86 0.139 0.042 0.087 0.07408-15-86 0.097 0.155 -0.024 -0.00208-20-86 0.084 0.068 0.028 0.15908-21-86 0.135 0.101 0.013 0.07408-26-86 0.050 0.016 -0.063 0.12009-03-86 0.071 -0.028 -0.099 -0.05809-04-86 0.085 0.069 -0.013 0.03509-10-86 0.076 0.137 -0.077 -0.07809-19-86 0.044 0.236 -0.193 0.09609-30-86 0.048 0.009 -0.046 0.00306-24-87 0.000 0.042 -0.009 0.09506-26-87 0.074 -0.062 -0.038 -0.01606-30-87 -0.046 0.031 -0.004 -0.00907-13-87 0.031 -0.160 0.067 0.07907-14-87 0.108 0.010 -0.052 -0.09670Table B.1 (Continued)Date(m-D-Y) ai az a3 a407-16-87 0.084 0.085 -0.025 -0.04007-31-87 0.027 0.005 -0.059 0.00408-01-87 0.050 0.015 -0.029 -0.02608-02-87 0.056 0.037 -0.031 0.00608-08-87 0.075 -0.076 0.107 0.10508-21-87 0.050 -0.016 -0.020 0.01308-22-87 0.060 0.029 -0.171 0.06609-05-87 0.085 0.041 0.041 0.01409-07-87 0.053 0.253 0.044 -0.03109-09-87 0.028 0.133 0.002 0.00409-22-87 0.090 -0.129 -0.109 -0.09209-28-87 0.119 0.022 -0.016 -0.14409-30-87 0.123 -0.047 0.071 0.00706-28-88 0.048 -0.092 -0.013 0.01207-07-88 0.081 -0.110 0.117 -0.05207-17-88 0.068 0.033 -0.003 -0.03308-02-88 0.118 0.113 0.018 0.03408-03-88 0.147 -0.067 0.054 -0.03908-11-88 0.060 0.026 -0.074 0.08408-12-88 0.094 -0.063 0.111 0.01008-21-88 0.068 0.054 -0.025 -0.01608-22-88 0.092 -0.079 -0.054 0.05008-23-88 0.098 -0.032 0.052 0.16808-30-88 0.026 -0.078 -0.098 0.04108-31-88 0.106 0.002 -0.107 -0.12209-01-88 0.124 -0.127 -0.113 -0.08109-02-88 0.120 -0.147 -0.035 0.03509-10-88 0.107 0.137 -0.120 -0.08409-11-88 0.077 0.072 -0.184 -0.05671Table B.1 (Continued)Date(M-D-Y) ai a2 a3 a406-22-89 -0.003 -0.152 -0.049 0.03306-23-89 0.088 -0.130 0.092 0.04206-24-89 0.087 -0.213 0.127 0.01107-06-89 0.021 -0.137 -0.040 0.05207-22-89 0.082 -0.104 -0.033 -0.00307-25-89 0.036 -0.028 -0.126 0.06408-07-89 0.094 0.028 -0.140 -0.01509-04-89 0.092 0.076 -0.154 0.00409-06-89 0.111 -0.041 -0.183 -0.08609-07-89 -0.015 -0.038 -0.153 0.19209-08-89 0.089 0.043 -0.175 0.13409-10-89 0.061 0.011 -0.184 0.15909-14-89 0.189 -0.068 -0.024 0.09909-16-89 0.081 0.091 -0.052 0.13009-22-89 0.084 -0.069 -0.099 0.27909-23-89 0.135 -0.022 -0.041 0.09409-24-89 0.041 -0.131 -0.126 0.30009-28-89 0.127 -0.045 -0.069 0.02209-29-89 0.086 -0.108 -0.041 -0.02807-07-90 0.080 -0.014 0.098 -0.11407-08-90 0.051 -0.152 -0.034 -0.04507-11-90 0.087 -0.132 -0.072 0.03407-16-90 0.118 0.051 0.043 -0.15707-18-90 0.083 0.149 0.081 -0.07807-19-90 0.082 0.086 0.114 -0.00607-20-90 0.087 0.041 0.116 0.05707-27-90 0.097 0.074 -0.024 0.03608-01-90 0.066 0.112 0.051 0.10308-03-90 0.129 -0.107 -0.010 -0.15772Table B.1 (Continued)Date(M-D-Y) ai az a3 a408-03-90 0.173 -0.152 -0.095 -0.20908-07-90 0.032 0.101 -0.078 -0.01008-26-90 0.040 0.068 -0.097 0.12208-27-90 0.047 0.087 -0.043 -0.04809-02-90 0.094 0.054 0.049 -0.00209-04-90 0.148 -0.118 0.043 -0.02409-14-90 0.058 0.038 -0.137 0.16109-20-90 0.126 -0.054 0.020 -0.01209-21-90 0.179 -0.045 0.052 0.04707-03-91 0.080 -0.032 -0.016 -0.04307-29-91 0.070 0.078 -0.075 -0.04408-05-91 0.032 0.111 0.005 0.09108-21-91 0.112 -0.069 0.071 -0.12408-23-91 0.060 0.105 0.010 -0.05208-24-91 0.059 0.073 -0.012 0.00609-19-91 0.110 0.048 0.039 -0.05409-20-91 0.115 0.080 0.009 -0.100

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