Annual and Intra-annual Sea Level Variability in the Region of the Kuroshio Extension from TOPEX/POSEIDON and Geosat Altimetry

Transcription

1 692 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 Annual and Intra-annual Sea Level Variability in the Region of the Kuroshio Extension from TOPEX/POSEIDON and Geosat Altimetry LIPING WANG NASA UMD JCESS, Department of Meteorology, University of Maryland, College Park, Maryland CHESTER J. KOBLINSKY AND STEPHEN HOWDEN NASA/Goddard Space Flight Center, Greenbelt, Maryland (Manuscript received 11 November 1996, in final form 24 July 1997) ABSTRACT Using 4.2 years of sea surface height data collected by the TOPEX/POSEIDON altimeter and 2.3 years of data collected by the Geosat altimeter, the authors study the annual, intra-annual, and linear-trend sea level height variability in the region of the Kuroshio Extension. Both the annual and intra-annual variabilities are separated spatially into large ( 2000 km), intermediate ( 1500 km), and short scales ( 800 km). The intermediate and short-scale annual and intra-annual sea level height fluctuations in both periods have large components with two-dimensional phase propagation. Close correspondence between the characteristic spatial structure of both the intermediate and short-scale annual and intra-annual sea level height fluctuations and major bottom topographic features suggests that bottom topography plays a critical role in the generation of those low-frequency variabilities. On the other hand, large-scale annual variability is primarily a standing oscillation, and bottom topography does not appear to be involved in its generation. The linear trend of the sea level change in the 4.2- yr TOPEX/POSEIDON period suggests that both the northern and the southern recirculations have been weakening considerably in the last 4.2 years, and that there exists a strong intradecadal to decadal sea level height change. 1. Introduction Prior to the advent of satellite altimetry, observations of low-frequency wave activity in the Kuroshio Extension region were very limited because of a lack of data with sufficient spatial and temporal resolution. Most studies of temporal variability in the Kuroshio Extension region have focused upon the energetic mesoscale variability, for example, Schmitz (1988) and Hall (1991). In the last decade, satellite altimetry data have become increasingly important in studying the temporal variability. However, limited by the record length, most of the studies using altimetry data have also focused mainly upon the mesoscale variability, for example, Fu and Zlotniki (1989), Tai and White (1990), and Qiu (1995). In the atmosphere, characteristics of the spatial structure of low-frequency variability are different from those of synoptic transient variability. Major bottom topographic features, such as the Rocky Mountains and the Tibetan Plateau, are found to play an important role in generating the low-frequency wave activity (Hoskins Corresponding author address: Dr. Liping Wang, NASA/Goddard Space Flight Center, Code 971, Greenbelt, MD lwang@nemo.gsfc.nasa.gov and Pearse 1983). In the Kuroshio Extension region there are three major bottom topographic features, as shown in Fig. 1, which might play similar roles. In the west there is the Isu Ridge; in the middle there is the Shatsky Rise; and in the east there is the Hess Rise. Using expendable bathythermograph (XBT) data, Mizuno and White (1983) and White and He (1986) studied the interannual upper-ocean heat content variability in the Kuroshio Extension region. White and He (1986) found some evidence of a possible influence of the Shatsky Rise on the characteristic spatial structure of the interannual variability, although the temporal evolution was not well resolved because of limitations in the temporal resolution of the XBT data. To determine major characteristics of low-frequency variability (here low-frequency variability includes any variability with frequency lower than the mesoscale variability) and whether major bottom topographic features have any significant influence on this variability, similar to the influence of major bottom topographic features on low-frequency variability in the atmosphere, we need a dataset with sufficient spatial and temporal resolution. Altimetry data from the TOPEX/POSEI- DON (T/P) altimeter are presently the only dataset that offers enough resolution to allow us to identify the nearsurface characteristics of the low-frequency variability American Meteorological Society

2 APRIL 1998 WANG ET AL. 693 FIG. 1. Bottom bathymetry in the region of the Kuroshio Extension. The Izu Ridge, Shatsky Rise, and Hess Rise are indicated in the figure. Land areas are blackened. The contour level is 1 km. Using just the first 1½ years of T/P data, Wang and Koblinsky (1995 hereafter WK95) did a preliminary data analysis on the low-frequency variability in the Kuroshio Extension region. WK95 found that the lowfrequency has two distinctive features. The first one is that the characteristic spatial structure of the low-frequency variability is different from the mesoscale variability. With the mesoscale variability, a close correspondence exists between the eddy kinetic energy and the mean flow, while no such correlation exists in the case with the low-frequency variability. Second, there is a close correlation between the low-frequency variability and the major bottom topographic features, in a way analogous with the low-frequency variability in the atmosphere. Wang and Koblinsky (1996a) also found similar phenomenon in the region of the Aguhlas Retroflection. The present study is a direct continuation of the preliminary study by WK95 on the low-frequency variability in the Kuroshio Extension region. Four years of data from the T/P exact repeat mission (ERM) are used in this study. To supplement the analysis and test the robustness of the signals, 2.3-yr data from the Geosat ERM are also analyzed. In the analysis, we separate the low-frequency variability into intra-annual, annual, and interannual variability through filtering processes, and concentrate our attention on the annual and intra-annual variability. One of the major shortcomings of the WK95 preliminary study is that low-frequency variability with different characteristics (such as propagating versus standing anomalies) were not examined separately, which makes it difficult to discern the various types of low-frequency variabilities. In this study, we will separate low-frequency variability spatially. There are two major objectives for this study. First, we want to identify major characteristics of the intra-annual and annual sea level height fluctuations. Second, we want to determine the correspondence between various types of low-frequency variability and major bottom topographic features in the Kuroshio Extension region. The study is organized in the following way. In section 2, we outline the data processing. In section 3, we discuss the annual sea level height variability. In section 4, we discuss the intra-annual sea level height fluctuation. Discussion about linear sea level height change in the 4.2-yr T/P ERM is presented in appendix B. We summarize the results in section Data processing The sea level height observations (collinear data) collected by the T/P altimeter from cycle 2 to cycle 154 (4.2 years worth of data) are used in this study. The focus region for the study is the region of the Kuroshio Extension, extending from 25 to 45 N and from 130 E to 170 W. There is no significant data dropout in our study region for the 153 cycles. The raw altimetry data are corrected for the solid earth tide, wet and dry tropospheric range delay, ionospheric range delay, atmospheric loading, and electromagnetic bias using the standard output from the Geophysical Data Record (Callahan 1993). The data are also corrected for ocean tides using the Goddard tidal model ( gsfc.nasa.gov/ocean.html). After all the environmental corrections are made, a mean sea level is computed at each grid point for the 153 repeat cycles. If the number of observations at a grid point is less than 75, all data at that point are discarded to avoid undersampled mean sea level. The mean sea level is then removed from each observation, leaving the residual sea level as the database for our present study. The data collected within a cycle are taken as synoptic, considering that our objective in the present study is the low-frequency variability. The residual sea level along ground tracks is then mapped into a 1 latitude/longitude regular grid using an objective mapping technique (Gaussian form) with

3 694 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 a2 (1 ) decorrelation scale and a 4 (2 ) cutoff radius in the longitude (latitude). [Results with a 3 (1.5 ) decorrelation scale and a 5 (3 ) cutoff radius in the longitude (latitude) are essentially the same, except for some minor numerical differences.] The preliminary study of low-frequency variability by WK95 using the first 1½ years of T/P data suggests that there exist strong intra-annual, annual, and interannual variabilities in the Kuroshio Extension region. In light of that preliminary study we separate the sea level height variability into four separate frequency bands as follows: a 1 inter intra r, (2.1) where a, 1, inter, and intra represent the annual (including the semiannual), linear trend, interannual (frequency lower than 1 year), and intra-annual (frequency higher than 1 year) variability, respectively, and r represents the residual signal, which is mostly mesoscale variability with frequency higher than 4 months. The signal is separated in the following way. First, we extract the annual signal by fitting the data with annual and semiannual harmonics, and subtract these signals from the data. Then, we least square fit the residual sea level height data to a linear trend, which crudely represents a 4.2-yr segment of a very low frequency variability. As will be seen, this signal is as strong as the annual signal. After further subtracting the linear trend, we high-pass filter the residual signal with a 45-point Hanning filter to remove the interannual variability. We then low-pass filter the residual signal with a 17-point Hanning filter to extract the intra-annual variability. This filtering process separates the signal in the time domain into annual, linear trend, interannual, and intra-annual variability; 4.2 years are too short for us to discuss characteristics of the interannual variability. In this study we only discuss the annual and intra-annual variability. Because the linear trend in the 4.2-yr T/P is too strong to be ignored, discussion about the linear trend will be presented in appendix B. Part of the reason that the signal of low-frequency phase propagation in the WK95 study is not clearly defined is that the tangling together of variability with different spatial scales blurs the signal. To better describe annual and intra-annual variability, we separate the signal into long, medium, and short wave bands with characteristic zonal scales of over 2000 km, around 1500 km, and around 800 km using 25-point and 13-point Hanning filters. To further remove very short scale variability in the short-scale variability, we low-pass the short-scale variability with a 7-point Hanning filter. This 7-point spatial Hanning filtering and 17-point temporal filtering ensure that very high frequency and very short scale sea level variability is filtered out. The length scale separation can be represented as 1 b h r, (2.2) where represents either a, 1, inter,or intra ; 1, b, and h represent the zonally low-passed, bandpassed, and high-passed low-frequency signals; r represents the residual. (We use lower subscripts to denote temporal filtering and upper subscripts to denote spatial filtering.) As will be seen these low, band, and high pass filterings in both time and space efficiently separate the signals with different characteristic temporal and spatial scales, which are otherwise completely tangled together and difficult to analyze. However, we do not claim that our choice of the spatial and temporal filtering is optimal. Using a parameter model fit to the altimeter range observations, Tsaoussi and Koblinsky (1994) estimated that the measurement error for the raw altimetry data with the mean removed is about 3 cm (rms) in our study region. The Hanning filtering in time and annual fitting not only extracts the low-frequency variability and filters out mesoscale variability, they also can greatly reduce the measurement error. Assuming the measurement errors in different cycles are uncorrelated, the filtered sea level anomaly has an error estimate of 1 cm (WK95). In later sections, the low-frequency signals will be shown to be above this measurement error estimate. Any signals that are below 1 cm will be considered insignificant. The reprocessed Geosat altimetry data from cycle 1 to cycle 50 (2.3 years worth of data) are also used in the present study to test whether the broad basic spatial structure of the annual and intra-annual variability observed by the T/P altimeter is robust over a longer period. The focus region is similar to that of the T/P altimetry data. Major revisions of the Geosat data have been made by NASA s Ocean Altimeter Data Pathfinder Project at Goddard Space Flight Center, including a new orbit, new gravity model, atmospheric correction, ionospheric correction, and tidal correction (more detailed information about environmental corrections can be found at The data processing is similar to that of the T/P data with standard environmental corrections. After all the environmental corrections, a mean sea level is computed at each grid point for the 50 repeat cycles. If the number of observations at a grid point is less than 21, all data at that point are discarded to avoid undersampled mean sea level. The mean sea level is then removed from each observation, leaving the residual sea level as part of the database for our present study. The Geosat data collected within one cycle are taken as synoptic. The data are then gridded into a regular 1 latitude/longitude grid in the same way as the T/P data. As with the T/P data, we first extract the annual variability and then the linear trend. Because of the short duration of the Geosat data, we only low-pass the deannualized and detrended signal with an 11-point Hanning filter to remove the mesoscale variability. The spatial scale separation is different that for the T/P data. In the case with the T/P data, the filtering is carried along zonal lines. In the case with the Geosat data, the filtering axis is rotated from pure zonal lines in order to better extract spatially coherent

4 APRIL 1998 WANG ET AL. 695 structures. In the region roughly west of 158 E, the filtering axis is rotated 14 from due east, while east of 158 E, the filtering axis is rotated 5 from due east. As will be seen, most of the low-frequency variability is strongly coherent with the major bottom topographic features in our study domain. To provide a background for the discussions about the low-frequency variability, bottom bathymetry in the Kuroshio Extension region is shown in Fig. 1. The most notable features of the bottom bathymetry are the Izu Ridge at about 145 E, the Shatsky Rise at about 159 E, and the Emperor Seamount Chain and the Hess Rise between 170 E and The annual variability a. Background annual variability In the study on annual variability of the subtropical recirculation by Wang and Koblinsky (1996b), the background annual variability was shown to be basically a standing oscillation within our study domain, due to seasonal cycle of heating and cooling. However, annual westward propagating Rossby waves are also present, which contaminate the signal of the background seasonal standing oscillation. To separate the standing background annual variability from the westward propagating signals, a low-pass filtering is performed, as outlined in section 2, on the annual component. Furthermore, to determine whether there is a coherent largescale annual variability, we perform an empirical orthogonal functional (EOF) analysis on the spatially lowpass filtered annual sea surface height anomalies. Figure 2b shows the loading pattern of the first EOF mode of the background annual variability along with its amplitude in Fig. 2a in the 4.2-yr T/P ERM. This EOF mode explains most (94%) of the total annual variance. The second EOF mode, not shown here, explains only 6% of the total variance. That the first annual EOF mode explains most of the annual variance indicates that the background annual sea level height variability is predominantly a domainwide standing oscillation. The maximum oscillation, about 17 cm, is located at (34 N, 147 E). The positive maximum occurs in mid-october and negative maximum occurs in mid-april, similar to that computed from the first two years of T/P data (Wang and Koblinsky 1996b). Through spatial filtering, the basic characteristic spatial structure is much more clearly and cleanly identified than that shown by Wang and Koblinsky (1996b). In addition, the percentage of variance explained by this EOF mode is also much higher. The phase structure indicates a stronger surface subtropical recirculation in the late fall and weaker surface subtropical recirculation in the late spring. Shown in Fig. 2c are the loading patterns of the first EOF mode, along with its amplitude in Fig. 2a, of the 1 a in the 2.3-yr Geosat ERM. As with the T/P case, it explains most (97%) of the total annual variance. The broad basic structures estimated from the two datasets FIG. 2. Amplitudes (a) of the first empirical orthogonal functional (EOF) modes of the spatially low-passed annual sea level height fluctuation in the T/P period (solid line) and Geosat period (dashed line), and the corresponding loading patterns of the first annual harmonic EOF modes in the T/P period (b) and Geosat period (c). Shown in the upper left corners of the two loading patterns are the percentages accounted for by the EOF modes of the annual variances in the two periods. are similar, but three significant differences exist between the two. First, the phase of the annual cycle during the Geosat ERM is about 1 month ahead of that during the T/P ERM. Second, the annual cycle during the Geosat ERM is stronger than that during the T/P ERM over most of the study domain. Third, the spatial structures represented by the loading pattern differ substantially. The basic structure during the T/P ERM is much more zonally oriented. Not only is the maximum for the Geosat data much farther west than that for the T/P data (30 N, 133 E versus 34 N, 147 E), but the ridge of maximum variability extends much farther to the east for the Geosat data. All these differences suggest that a strong interannual to decadal variability exists in the Kuroshio Extension region, although part of the difference may be caused by the difference in the sampling schemes of the two datasets and measurement errors in the two datasets. b. Westward propagating annual variability 1) BANDPASSED ANNUAL VARIABILITY Having discussed the spatially low-pass filtered domainwide background annual variability, which is basically a standing background oscillation without no-

5 696 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 FIG. 3. Hovmöller diagrams of the spatially bandpassed, annual sea level height fluctuations estimated from the T/P period at (a) 39 N, (b) 35 N, and (c) 31 N. The contour interval is 0.5 cm. ticeable phase propagation, we now discuss the westward propagating portion of the annual sea level height variability. In the study by WK95 the westward propagating signal, though strongly visible, is contaminated by the presence of the background annual variability discussed above, especially near the western boundary. Longitude time (Hovmöller) plots of the bandpassed annual sea level height fluctuation at 39, 35, and 31 N between 130 E and 170 W are shown in Figs. 3a c. Comparing this figure with Fig. 6 in the study by WK95 would readily demonstrate that the spatial filtering, outlined in section 2, cleanly and efficiently separates annual signals with different characteristics. As Fig. 3 shows, systematic westward phase propagation is present at all three latitudes during the 4.2-yr T/P ERM. The westward phase propagation is much clearer than that discussed by WK95 in their preliminary study of the low-frequency variability. Evident in the 4.2-yr T/P data at 35 N is a systematic westward phase propagation that extends continuously from 170 W to the east coast of Japan. Figure 3b suggests that the zonal wave length is about 15. Thus, the westward phase speed is approximately 4.3 cm s 1. At both 31 and 39 N, the amplitude of the westward propagating signal is much larger to the west of 165 E. East of 165 E, the westward propagating signal is much weaker. This suggests that the Shatsky Rise influences the generation of the westward propagating annual signals. While the Hovmöller diagram gives a good intuitive illustration of the westward phase propagation of the propagating annual signals, it misses the two-dimensional spatial structure of the amplitude and phase of these signals: the amplitude is not spatially uniform and the phase propagation is not exactly zonal. The twodimensional structure of the bandpassed annual propagating signal can be written as 2 b b b A (x, y) sin (x, y) t, (3.1) a a a [ ] b where T yr 1yr, A a (x, y) represents the spatial structure b of the amplitude, and a (x, y) represents the two-di- mensional spatial phase structure of the bandpassed annual variability. The most striking feature of this twodimensional amplitude structure displayed in Fig. 4a is that there are two broad local maxima. The center of the eastern one is located at (35 N, 176 E). The westward propagating annual variability associated with this one is confined roughly within the 5 latitudinal band from 32 to 37 N. The maximum amplitude is 3 cm. Outside this 5 latitudinal band, in the area east of 166 E, the westward propagating annual signal is weak (below 1 cm) as is already shown in the Hovmöller diagrams of Figs. 3a and 3c. The western maximum is much broader than the eastern one and lies basically to the west of the Shatsky Rise in an 8 latitudinal band from 29 to 37 N. The close correspondence between the two local amplitude maxima of the westward propagating annual variability and the two major bottom topographic features (the Shatsky Rise and the Hess Rise) strongly suggests that bottom topography is involved in the generating process of westward propagating annual signals. We will see more similar correspondences between lowfrequency variability and major bottom topographic features later. As already indicated intuitively by the Hovmöller diagram, Fig. 4b shows that throughout most of the domain there is a systematic westward phase propagation. However, in addition to the westward phase propagation, Fig. 4b shows that there is also a southward phase propagating component, notably in the region around the Hess Rise east of 165 E and around the Isu b Ridge. The direction of the phase propagation n a can be written as b b x ai y aj b na. (3.2) b 2 b 2 ( x a) ( y a) Using the phase structure shown in Fig. 4b we can determine the direction of the two-dimensional phase propagation. Propagation is almost due southwestward (about 40 from due west) in the region around the Hess Rise. Because of this southwestward tilting of the phase propagation, the two-dimensional phase speed in the neighborhood of the Hess Rise is smaller than the zonal phase speed estimated from the longitude time plot T yr

6 APRIL 1998 WANG ET AL. 697 FIG. 4. The spatial amplitudes and phase of the spatially bandpassed annual sea level height fluctuation estimated from the T/P data (a) and (b) and Geosat data (c) and (d). The contour interval in (a) and (c) is 1 cm and in (b) and (d) 60. FIG. 5. Hovmöller diagrams of the spatially bandpassed, annual sea level height fluctuations estimated from the Geosat period at (a) 38 N, (b) 35 N, and (c) 32 N. The contour interval is 0.5 cm. shown in Fig. 3b. For the phase propagation west of the Shatsky Rise, there is a weak southwestward tilting (about 20 from due west) in the southern portion (south of 33 N), while there is a weak northwestward tilting (about 20 from due west) in the northern portion (north of 33 N). Discussion about the associated Stokes drift is presented in appendix A. Figure 5 shows the longitude time plots of the annual sea level height fluctuation at 32, 35, and 38 N between 130 E and 170 W during the Geosat ERM. During this period, a systematic annual westward phase propagation is seen at both 32 and 38 N. In both latitudes, the strongest signal lies in the neighborhood of the Shatsky Rise, although the phase propagation extends east to 170 E. On the other hand, at 35 west of 155 E there exists eastward phase propagation. In the longitudinal band from 155 to 170 E there is no systematic zonal phase propagation. Only east of 170 E in the neighborhood of the Hess Rise exists systematic westward phase propagation. This is very different from the phase propagation during the T/P ERM shown in Fig. 3b. In addition, unlike during the T/P ERM, the westward propagating signal at 35 N is weaker than that at 32 N. Shown in Figs. 4c and 4d are the amplitude and phase b of a estimated from the Geosat data. The spatial struc- ture of the amplitude in the Geosat period is different from that in the T/P period. In the T/P period, there are two separated broad local maxima in the neighborhoods of the Shatsky Rise and the Hess Rise. In the Geosat period the local maximum amplitude in the neighbor-

7 698 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 hood of the Shatsky Rise is much larger than the one in the neighborhood of the Hess Rise. Compared to the situation during the T/P ERM, the local maximum in the neighborhood of the Shatsky Rise extend over a larger region and is more clearly defined. In addition, the amplitude during the Geosat ERM is substantially larger than that during the T/P ERM. In the longitudinal band from 140 to 170 E the phase structure in the two periods are similar. The most notable difference is east of 170 E in the neighborhood of the Hess Rise. In the T/P period, the phase is generally oriented from southeast to northwest; it is generally oriented from northeast to southwest in the Geosat period. In spite of the substantial detailed difference in the temporal and spatial structure of bandpassed annual variability between the two periods, the close correspondence between the bandpassed annual variability patterns and the positions of the Shatsky Rise and the Hess Rise remains. This suggests that bottom topography is closely involved in the generation of the bandpassed annual variability. 2) HIGH-PASSED ANNUAL VARIABILITY Apart from the westward propagating annual variability discussed above with a zonal wavelength of about 15 extracted by the bandpass filter, there are other westward propagating signals with shorter zonal scale. Figure 6 is similar to Fig. 3, except that it shows the Hovmöller diagram for the spatially high-pass filtered annual signal. At 35 N, unlike the band-passed annual variability shown in Fig. 3b, the tendency for westward phase propagation is weak within the longitudinal band from 147 to 160 E where the annual variability is mostly a standing oscillation with a characteristic zonal scale of around 7. On the other hand, a systematic westward phase propagation is present east of 160 E in the neighborhood of the Hess Rise, similar to that shown in Fig. 3b for the bandpassed annual signal, though less well organized. But the signal is weaker than the bandpassed annual signal. The most significant difference is that zonal wavelength of the high-passed annual signal is only 10, two-thirds of the bandpassed annual signal. That gives the corresponding zonal westward phase propagation speed at 2.9 cm s 1, only two-thirds of the phase speed of the bandpassed annual signal. Systematic westward phase propagation is also seen at the other two latitudes. At 31 N, westward phase propagation is clearly visible, though much less organized than the bandpassed signal shown in Fig. 3c, and the signal is weaker. At 37 N westward phase propagation is clearly seen like that in the eastern portion at 35 N, but both the wavelength and the phase speed are smaller than at 35 N. As is the case with the bandpassed annual signal, to better illustrate the two-dimensional structure of the high-passed propagating annual signal, we can express FIG. 6. As in Fig. 3 except for the spatially high-passed annual sea level height fluctuations estimated from the T/P data. the high-passed annual signal in the following analytical form: 2 h b h A (x, y) sin (x, y) t, (3.3) a a a [ ] h where A a (x, y) represents the spatial structure of the h amplitude and a (x, y) represents the spatial structure of the two-dimensional phase of the high-passed annual variability. Figures 7a and 7b shows the spatial structure of the amplitude and phase, respectively. Similar to that shown for the bandpassed annual signal (Fig. 4a), there is a local maximum amplitude in the neighborhood of the Hess Rise with a maximum value of 2.5 cm. Though slightly weaker than that shown in Fig. 4a, this maximum is more clearly separated from the rest of the study region, where there is significant annual variability. It is also more localized to the neighborhood of the Hess Rise. In the neighborhood of the Hess Rise, the highpassed westward propagating annual variability is confined roughly within the 4 latitudinal band from 32.5 to 36.5 N. Outside this 4 latitudinal band in the area east of 166 E the westward propagating annual signal is weak, similar to the bandpassed annual signal. In the region west of 166 E (unlike that shown in Fig. 4b), the amplitude breaks into multiple local maxima and minima. As already indicated intuitively by the Hov- T yr

8 APRIL 1998 WANG ET AL. 699 FIG. 7. As in Fig. 4 except for the spatially high-passed annual sea level height fluctuations. FIG. 8. As in Fig. 5 except for the spatially high-passed annual sea level height fluctuations estimated from the Geosat data. möller diagram, Fig. 7b shows that there is a systematic westward phase propagation in the Hess Rise region. In addition to the westward phase propagation, there is also a southward phase propagation, similar to the case of the bandpassed annual variability shown in Fig. 4b. However, the southward tilting of the propagation is weaker than that associated with the bandpassed annual signal. Between 150 and 166 E (unlike that shown in Fig. 4b), the phase structure (Fig. 7b) does not reveal any systematic phase propagation as intuitively shown in Fig. 5b, although the signal can still be written into a generalized wave form (3.4). Shown in Fig. 8 are the Hovmöller diagrams of the high-passed annual sea level height fluctuation at 32, 35, and 38 N between 130 E and 170 W during the Geosat ERM. During the Geosat ERM, systematic annual westward phase propagation is seen at both 32 and 38 N, similar to the case with the bandpassed annual variability shown in Figs. 5a and 5c. In both latitudes, the strongest signal lies in the neighborhood of the Shatsky Rise, although the phase propagation extends east to 170 E. On the other hand, west of 160 E at35 N there is no noticeable phase propagation. However, east of 160 E, in the neighborhood of the Hess Rise, a welldefined systematic westward phase propagation exists. Compared with the case in the T/P period shown in Fig. 6b, the phase propagation extends farther west and is stronger. Figures 7c and 7d show the amplitude and phase of h a estimated from the Geosat data. The spatial structure of the amplitude in the Geosat period is significantly different from that in the T/P period. Unlike in the T/P

9 700 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 period, there are two well-separated and defined local maxima in the neighborhoods of the Shatsky Rise and the Hess Rise. This is also different from bandpassed annual variability shown in Fig. 4c, for which there is only one significant local maximum. The high-passed annual variability in the Geosat period is substantially stronger than that in the T/P period. The phase structure shown in Fig. 7d indicates that two-dimensional phase propagation in the Geosat period is much better defined than that in the T/P period. In the neighborhood of the Hess Rise, the phase generally propagates from east to west from 175 W to 170 E. On other hand, in the neighborhood of the Shatsky Rise from 170 to 155 E phase propagation has a noticeable meridional orientation. Compared to that of the bandpassed annual variability shown in Fig. 4d, the two-dimensional phase propagation of the high-passed annual variability is confined in a much narrower meridional band. The amplitude and phase structures of the bandpassed and high-passed annual variability indicate that in the neighborhood of the Hess Rise, there are two significant wave trains with different wavelengths and different phase speeds in the T/P period. In addition, the propagation directions are also different. On the other hand, in the neighborhood of the Shatsky Rise, there is only one significant wave train. Unlike the situation in the T/P period, there are two significant wave trains in the neighborhoods of both the Shatsky Rise and the Hess Rise in the Geosat period, although the bandpassed annual variability near the Hess Rise is not very strong. This difference might indicate that both or either of the background mean flow and annual wind stress variability in the two periods are different, as will be explained in section The intra-annual variability In the last section we discussed the major characteristics of the annual sea level height fluctuations. In this section we discuss the intra-annual variability. Unlike the discussion with the annual variability, we only discuss the band- and high-passed intra-annual variability (the low-passed intra-annual variability is substantially weaker than the band- and high-passed intra-annual variability and represents a large-scale background standing oscillation). We use the CEOF analysis on the bandpassed and high-passed portion of the intra-annual variability to extract characteristic modes, because this portion of the intra-annual sea level height fluctuation has a strong propagating tendency. To supplement the T/P analysis of the band- and high-passed intra-annual variability we also use the Geosat data. Unlike the situation with the T/P data, the record length of the Geosat data (50 cycles, 835 days) is not long enough to allow us to effectively separate the intra-annual sea level height variability from lower-frequency variability using the Hanning filter. The intra-annual variability is not separated from the interannual variability, as for the T/P FIG. 9. As in Fig. 3 except for the spatially bandpassed intra-annual sea level height fluctuation in the T/P period. The contour interval is 0.5 cm. data, before we perform the complex EOF (CEOF) analysis on the detrended and deannualized Geosat data. However, the CEOF analysis is able to separate the intraannual variability from the interannual variability. a. The spatially bandpassed intra-annual variability As shown in the last section, the bandpassed annual sea level height fluctuations are predominantly propagating oscillations in both the T/P and Geosat periods. As we shall show now, the bandpassed intra-annual sea level height fluctuations are also primarily propagating oscillations. Shown in Fig. 9 are the Hövmoller diagrams of the spatially bandpassed intra-annual sea level height fluctuation along 31, 35, and 39 N. At 31 N, there is no clear westward phase propagation west of 140 E. East of 140 E, a systematic westward phase propagation exists. The strongest signal is confined within the longitudinal band from 145 to 175 E. A large interannual modulation of the intra-annual fluctuation is also evident. In the longitudinal band from 155 to 175 E, the intra-annual variability is very strong from August 1993 to July 1994 and very weak from August 1994 to September In the longitudinal band from

10 APRIL 1998 WANG ET AL to 155 E, the intra-annual variability is much weaker before July 1994 than after July The westward propagating intra-annual variability is much stronger at 35 N as shown in Fig. 9b. The westward phase propagation can be seen in the broad longitudinal band from 145 E to178 W. Similar to that shown in Fig. 9a, the intra-annual variability along 35 N has a large interannual fluctuation. Unlike the situation at both 35 and 31 N, there is no apparent westward phase propagation along 39 N in the T/P period, and the intra-annual variability is much weaker than at both 35 and 31 N. The Hovmöller diagram shows that the spatially bandpassed intra-annual variability weakens away from the Kuroshio axis ( 35 N). This is better depicted by the spatial structure of the corresponding CEOF modes. Characteristics of the two-dimensional phase propagation associated with the bandpassed intra-annual sea level height fluctuation are better illustrated by the corresponding CEOF modes, although the Hovmöller diagrams give a more illustrative view of the zonal phase propagation. CEOF mode analysis has been widely used to extract spatially coherent propagating signals, such as the study by Barnett (1983), in which CEOF mode analysis is used to extract zonally propagating signals associated with the interannual trade wind fluctuation. Shown in Fig. 10a d are the temporal amplitude, temporal phase, spatial amplitude, and spatial phase of the first CEOF mode, respectively. This CEOF mode accounts for 35% of the total variance. According to Preisendorfer s (1988) rule N, this mode is above the level of noise at the 95% confidence level, assuming the degree of freedom is 17 (considering the 17-point temporal Hanning filter operation and contribution to the filtering coming mostly from the middle 9 points). In addition, this mode is statistically separated from the second CEOF mode to be discussed, according to the separation criterion discussed by North et al. (1982). The temporal phase structure suggests that this CEOF mode has an average period of about 9 months during the first 4.2 years of T/P observations. The period is similar to that determined by WK95 in the preliminary study using the first 1½ years of altimetry data. In Tai and White s (1990) analysis of mesoscale variability in the same region using the Geosat data, they also found that the dominant period is around 9 months. Figure 9b together with Fig. 10 demonstrate that the intra-annual variability is a robust signal. The frequency of this CEOF mode ( d /dt) has a large temporal change from one period to the next, as shown in Fig. 11b. Around August 1993, the frequency is 1.6 day 1. It decreases to only 0.8 day 1 around October 1994, suggesting a large interwave variation of this mode in the frequency domain by nonlinearity [Huang et al. (1997), gave a detailed discussion about the interwave and intrawave modulation of oscillations by nonlinearity]. A significant intrawave modulation of the frequency also exists. For example, within the intra-annual cycle from March 1993 to November 1993, the frequency decreases from 1.5 FIG. 10. The temporal amplitude (a), temporal phase (b), spatial amplitude (c), and spatial phase (d) of the first complex EOF (CEOF) mode of the spatially bandpassed intra-annual sea level height fluctuation in the T/P period. This mode accounts for 35% of the total variance. day 1 at the beginning of the cycle to 0.9 day 1. The intrawave variation is weaker than the interwave variation. The Hovmöller diagrams (Fig. 9) already indicate that the intra-annual variability has large interannual fluctuations. The temporal amplitude shown in Fig. 10a shows a further evidence that a large interannual modulation exists. The amplitude grows rapidly in the first 400 days. Around October 1993 the amplitude is three times stronger than it was at the beginning of the record. After October 1993 it decreases rapidly to one-third of its peak value by November It then grows from November 1994 to November Figure 10a suggests that in the first 4.2 years of the T/P observation the amplitude of the CEOF mode went through two cycles of fluctuation with a period of about 2 yr. As shown in Fig. 11b, in the period from November 1992 to November 1995 there is a good positive correlation between the frequency and the amplitude (amplified by 1): the instantaneous frequency of the intra-

11 702 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 FIG. 11. Frequency (a) of the second CEOF modes of the spatially bandpassed (solid line), high-passed (dot dashed line) intra-annual sea level height variability, and temporal amplitude (dashed line) of the second CEOF mode of the spatially bandpassed intra-annual variability in the Geosat period; instantaneous frequency (b) of the first (solid line), second (dot dashed line), and amplitude (dashed line) of the first CEOF modes of the spatially bandpassed intra-annual sea level height variability in the T/P period; instantaneous frequency (c) of the first (solid line), second (thick dot dashed line), third (tri-dot dashed line), and amplitude of the first (thin dot dashed) CEOF modes of the spatially high-passed intra-annual sea level height variability in the T/P period. The CEOF mode amplitudes, the unit of which are cm, are amplified by 1 to better visualize the correlation between the amplitude and the frequency. annual oscillation is small when its amplitude is small, and large when its amplitude is large. In that 3-yr span, the correlation between the two is 0.78, which is above the 95% confidence level. On the other hand, after November 1995, the correlation between the frequency and the amplitude disappears. The spatial phase structure shown in Fig. 10d indicates that in the longitudinal band from 150 to 175 E there is a systematic two-dimensional phase propagation in the latitudinal band from 30 to 38 N. Outside of this band, the signal of phase propagation is weak. The corresponding zonal wavelength is 14. Characteristics of this phase propagation in the regions west and east of 164 E are different. West of 164 E, the phase generally propagates zonally from east to west. On the other hand, FIG. 12. As in Fig. 10 except for the second CEOF mode. This mode accounts for 22% of the total variance. east of 164 E the phase propagates from north northeast to south southwest with a strong southward propagation component. The spatial structure of the amplitude (Fig. 10c) indicates that there exists only one significant local maximum. Most of the signal associated with this CEOF mode is confined within the neighborhood of the Shatsky Rise and generally decreases meridionally away from the Kuroshio axis. Shown in Figs. 12a d are the temporal amplitude, temporal phase, spatial amplitude, and spatial phase of the second CEOF mode, respectively. This mode accounts for 22% of the total variance. [Similar to the first mode, this mode is above the level of noise at the 95% confidence level according to Preisendorfer s (1988) rule N, and this mode is statistically separated from the third CEOF mode according to the separation criterion discussed by North et al. (1982).] Thus, the first and second modes together accounts for a majority (57%) of the total variance of the spatially bandpassed intraannual variability. The temporal phase structure suggests that, similar to the first mode, this mode also has an intra-annual period of about 8.5 months. In addition,

12 APRIL 1998 WANG ET AL. 703 the instantaneous frequency varies both within a period and from one period to the next, as shown in Fig. 11b. The maximum frequency (2.9 day 1 around mid-january 1994) is three times as large as the minimum frequency (0.9 around April 1994). Although the frequencies of the two modes averaged over the 4.2 years are very close, the temporal evolution of the instantaneous frequencies of the two are different. The frequency modulation of the first mode evolves more slowly over a longer timescale. On the other hand, the frequency modulation of the second mode evolves faster over a shorter timescale. In a similar way, the evolution of the amplitudes of the two modes are also different. On average, the first mode is stronger in the first 2 years than in the second 2 years; while the second mode is stronger in the second 2 years than in the first 2 years. The spatial phase structure shown in Fig. 12d indicates that in the region of the southern recirculation south of 35 N in the longitudinal band from 145 E to 180, there is a systematic westward phase propagation, with a zonal wavelength of about 13. The phase structure of the second mode differs from that of the first mode. East of 155 E the phase is generally oriented meridionally; west of 155 E it has a noticeable southwest to northeast orientation. The spatial amplitude of the second mode, shown in Fig. 12c, is also different from that of the first mode (Fig. 10c). For the first mode, the spatial structure is centered around the Shatsky Rise and the Kuroshio axis. For the second mode, most of the spatial structure is in the southern recirculation region south of the Kuroshio axis. Longitudinally, the second mode extends wider than the first mode. There is no gap in the amplitude between the neighborhoods of the Shatsky Rise and the Hess Rise, suggesting that the wave trains generated near the two topographic features are connected zonally. The signal of the second mode is about half as strong as the first mode. The difference in both spatial amplitudes and spatial phases of the two modes suggests that the generating mechanisms of the two modes are probably different. The generation of the first mode might be related to the Kuroshio, while the generation of the second might be related to the southern recirculation gyre, as suggested by the structure of the corresponding spatial amplitudes. In both cases, bottom topography is involved as suggested by the close correspondence between the spatial amplitudes of the two modes and the Shatsky Rise and the Hess Rise. As both the Hovmöller diagram (Fig. 9) and the amplitude (Figs. 10 and 12) suggest, the bandpassed intraannual variability has a large interannual modulation. To test whether a similar kind of intra-annual variability exists in periods other than the T/P period, we analyze the intra-annual CEOF mode estimated from the Geosat data. Shown in Figs. 13a d are the temporal amplitude, temporal phase, spatial amplitude, and spatial phase, respectively, of the second mode computed from the Geosat data. This mode accounts for 23% of the total FIG. 13. As in Fig. 10 except for the second spatially bandpassed CEOF mode in the Geosat period. This mode accounts for 23% of the total variance. variance of the combined intra-annual and interannual variability in the Geosat period. The first mode, not shown here, accounts for 53% of the total variance, and has an interannual frequency. [According to Preisendorfer s (1988) rule N, both modes are statistically different from noise and separated from each other according to North et al. s (1982) criterion, assuming that the degree of freedom is 8.] This figure readily shows that there exists significant intra-annual variability in the Geosat data, as noticed by Tai and White (1990) in their frequency and wavenumber analysis. The averaged period over the Geosat ERM is about 9 months. Similar to the frequency variation of the first bandpassed mode in the T/P period, there exists both intrawave and interwave frequency modulation. In addition to the temporal modulation of the instantaneous frequency, the amplitude also has a significant temporal fluctuation on an intra-annual timescale. There is a good negative correlation between the frequency and amplitude as shown in Fig. 11a. Unlike in the first 3 years of the T/P period, however, the frequency is higher when the amplitude is

13 704 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 lower, such as in periods from June 1987 to December 1987, and lower when the amplitude is higher. The spatial phase structure shown in Fig. 13d indicates that the two-dimensional phase propagation in the Geosat ERM is more complicated than the phase propagation exhibited in both the first and the second modes in the T/P ERM shown in Figs. 10d and 12d. In the region east of 170 E around the Hess Rise, phase generally propagates from northeast to southwest. Between 147 and 170 E, phase generally propagates from southeast to northwest. The spatial amplitude distribution of this mode is similar to the second mode in the T/P mode, except that it lies farther north. In spite of the substantial detailed difference regarding the temporal and spatial structure of the bandpassed intra-annual variability between the two periods, the analysis indicates that strong intra-annual sea level height fluctuation exists during both the Geosat ERM and the T/P ERM. In addition, the characteristics of the spatial phase and amplitude structures in both periods suggests that, like that for the annual variability, the Shatsky Rise and the Hess Rise are closely involved in the generation of the bandpassed intra-annual variability. b. The spatially high-passed intra-annual variability The above discussion indicates that like its annual counterpart, the spatially bandpassed intra-annual sea level height fluctuation is mainly a two-dimensionally propagating signal. Shown in Fig. 14 are the Hovmöller diagrams of the spatially high-passed intra-annual sea level height fluctuation along 31, 35, and 39 N. Compared to the phase propagation of the bandpassed intraannual variability at 31 N, the westward phase propagation of the high-passed intra-annual variability is more organized. In the longitudinal band between 160 and 170 E the westward propagating intra-annual variability is strong in the first 600 days. After that, the whole westward propagating envelop moves eastward. This kind of eastward movement of the westward propagating envelop is also observed east of 170 E in the first 450 days. In the longitudinal band from 145 to 160 E, westward propagating intra-annual variability is weak in the first 13 months. Similar to the bandpassed intraannual variability shown in Fig. 9, the high-passed intraannual variability is stronger at 35 than at 31 N. In the first 20 months, there is a strong westward propagating signal between 170 E and 180. After that, the whole westward propagating packet moves eastward. The intra-annual signal west of 170 E is stronger than that east of 170 E. Similarly, there is an eastward movement of the envelop of the westward propagating intra-annual variability. The intra-annual signal at 39 N, shown in Fig. 14a, is much weaker than that at the other two latitudes. The eastward movement of the envelop of the westward propagating intra-annual variability can also FIG. 14. As in Fig. 9 except for the spatially high-passed intraannual sea level height fluctuation in the T/P period. The contour interval is 0.5 cm. be found between 160 and 175 E in the period from June 1994 to December To further decipher the high-passed intra-annual variability, a CEOF analysis was done. The first mode accounts for 29% of the total variance, the second mode accounts for 21%, and the third mode accounts for 17% of the total variance, respectively. Together they account for 67% of the total variance of the high-pass intraannual variance. According to Preisendorfer s (1988) rule N, all three modes are above the noise level at the 95% confidence level. Unlike the bandpassed CEOF modes discussed above, these three modes are not statistically separated from each other according to the separation criterion discussed by North et al. (1982). However, the third mode is statistically separated from the fourth mode, according to the North et al. criterion. Thus, we will use the first three modes together to represent the characteristics of the high-passed intra-annual variability. Shown in Figs. 15a d are the temporal amplitude, temporal phase, spatial amplitude, and spatial phase of the first mode. Similar to the amplitude variation of the