www.sciencemag.org/cgi/content/full/science.1208897/DC1
Supporting Online Material for The Influence of Nonlinear Mesoscale Eddies on Near-Surface Oceanic Chlorophyll Dudley B. Chelton,* Peter Gaube, Michael G. Schlax, Jeffrey J. Early, Roger M. Samelson *To whom correspondence should be addressed. E-mail:
[email protected] Published 15 September 2011 on Science Express DOI: 10.1126/science.1208897 This PDF file includes: Materials and Methods Figs. S1 to S7 References
Supporting Online Material for “The Influence of Nonlinear Mesoscale Eddies on Near-Surface Oceanic Chlorophyll” by Dudley B. Chelton, Peter Gaube, Michael G. Schlax, Jeffrey J. Early and Roger M. Samelson Materials and Methods Satellite Measurements of Sea-Surface Height Satellite Estimates of Chlorophyll Cross Correlation Between Sea-Surface Height and Chlorophyll Variability Numerical Model Simulations SOM References Figs. S1 to S7 Materials and Methods Satellite Measurements of Sea-Surface Height Sea-surface height (SSH) measured by satellite altimetry (S1) plays a central role in identifying the nonlinear eddies analyzed in this study. The SSH fields analyzed here consist of approximately 16 years (October 1992–December 2008) of the Delayed-Time Reference Series available online from AVISO (Archivage, Validation, Interpretation des donnees des Satellite Oceanographiques) at http://www.aviso.oceanobs.com/es/data/products/ sea-surface-height-products/global/msla/index.html. These SSH fields were constructed from two simultaneously operating altimeters, one in a 10-day exact repeat orbit (TOPEX/ Poseidon, followed by Jason-1 and presently by Jason-2) and the other in a 35-day exact repeat orbit (ERS-1 followed by ERS-2 and presently by ENVISAT) (S2). These anomaly SSH fields are defined to be the residuals of SSH relative to the 7-year 1993-1999 mean. We used the version of these anomaly SSH fields that is provided by AVISO on a globally uniform 1/4◦ latitude by 1/4◦ longitude grid. The AVISO anomaly SSH fields were spatially high-pass filtered for the analysis presented here to attenuate SSH features with wavelength scales larger than 20◦ of longitude by 10◦ of latitude. The zonal wavenumber-frequency spectrum of this filtered SSH along 20◦ S in the southeast Pacific (SEP) region in Fig. 1 is shown in Fig. 5a. Zonal wavenumberfrequency spectra for four other locations are shown in Fig. S1. In all five of these examples, the spectral variance is confined to a band that falls approximately along a straight line of constant (nondispersive) propagation speed, extending to higher frequencies than are allowed by the dispersion relations for Rossby waves, regardless of whether the classical theory is modified to account for effects of mean currents or rough bottom topography. The four examples in Fig. S1 show suggestions of small “spurs” of spectral variance that extend over a a short range of wavenumbers along the Rossby wave dispersion relations. As shown in Figs. 5e and S7a–c, such spurs are expected for nonlinear eddies and are attributable to the small-amplitude SSH variability that occurs outside the nonlinear cores of the eddies. 1
The procedure used to identify and track the eddies analyzed here is described in detail elsewhere (S3). Except for the eddy tracks shown in Fig. 2, we consider only the tracked eddies with lifetimes of 10 weeks and longer in order to alleviate concerns that imperfections of the automated eddy detection and tracking procedure may affect the conclusions of this study; a minimum lifetime cutoff of 4 weeks is used for the eddy tracks in Fig. 2. A radius scale Ls was defined for each eddy at each time along its trajectory to be the radius of a circle with area equal to that enclosed by the SSH contour around which the average rotational speed of the eddy is maximum (S3). The mean radius for the SEP region that is the focus of this study is Ls = 110 km, in good agreement with the value obtained in a previous study (S4). The degree of nonlinearity of the tracked eddies was characterized by the ratio of the rotational speed U of the eddy to its translation speed c, where U is the circum-average speed around the contour of maximum circum-averaged speed that defines the above radius scale Ls and c was estimated from successive locations of the eddy centroid with a small amount of smoothing (S3). The eddy is nonlinear when U/c > 1. Such features maintain a coherent structure of trapped fluid as they propagate (S5, S6). The distributions of U/c are shown for the SEP and two latitude ranges of the global ocean in Fig. S2. Because of the approximate 2◦ zonal by 2◦ meridional wavelength smoothing inherent in the objective analysis procedure used to construct the SSH fields analyzed here (S3), the estimated eddy amplitudes A and radius scales Ls are likely biased low and high, respectively. Since U is proportional to A/Ls , the computed values of U/c are therefore lower-bound estimates of the nonlinearity of the eddies. Their true nonlinearity is likely significantly larger than is suggested from Fig. S2. Satellite Estimates of Chlorophyll The chlorophyll (CHL) fields analyzed for this study consist of 10 years (January 1998– January 2008) of daily, 9-km gridded estimates derived from satellite measurements of ocean color by the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) (S7) using the Garver-Siegel-Maritorena (GSM) semi-analytical ocean color algorithm (S8, S9). These CHL fields are available online at ftp://ftp.oceancolor.ucsb.edu//pub/org/oceancolor/MEaSUREs/Seawifs/. Analysis of the CHL data is much more challenging than analysis of the SSH data. The primary limitation is data gaps from the inability to measure ocean color when clouds are present, which occurs about 75% of the time over the eastern portion of the SEP, decreasing to about 40% of the time over the western portion (S10). Ocean color measurements can also only be made during daylight hours. Another limitation is the noisiness of the CHL fields because the water-leaving radiance from which CHL is estimated accounts for < 10% of the total visible radiance measured by satellites; the measurements must be corrected for atmospheric contamination and other effects in order to estimate CHL concentration. Other complications arise from the fact that the CHL gradient that makes eddy-induced horizontal advection detectable migrates and modulates in intensity seasonally. As is common in analyses of satellite estimates of CHL (S11, S12), and in particular in 2
past studies of Rossby wave and eddy influences on CHL (S13–S19), the SeaWiFS estimates of CHL in mg m−3 were log transformed. This is motivated by the fact that CHL varies globally by several orders of magnitude and tends to be log-normally distributed. Values of log10 (CHL) were then averaged daily into 1/4◦ × 1/4◦ areas centered on the same grid as the SSH fields described above. The availability of 10 years of simultaneous estimates of CHL from SeaWiFS and altimeter measurements of SSH on a common grid facilitates studies of physical-biological interaction on oceanic mesoscales with spatial and temporal coverage that are not feasible from in situ measurements (e.g., S12, S17, S20). The time series of daily values of log10 (CHL) at each grid point was low-pass filtered in time using a 1-dimensional quadratic loess smoother (S21, S22) that attenuated variability with periods shorter than 30 days. This half-power filter cutoff of 30 days is analogous to the filtering properties of 18-day running averages (S23), referred to here as 2–3 weeks. This temporal smoothing also reduces the extensive data gaps from cloud contamination. The temporally low-pass filtered fields of log10 (CHL) were further low-pass filtered spatially to attenuate variability with wavelengths shorter than 2◦ in longitude by 2◦ in latitude, which is the approximate resolution of the SSH fields described above (S3). The relatively small number of remaining gaps were filled by bilinear interpolation. An example map of the resulting log10 (CHL) fields is shown in Figs. 1c,d. To investigate eddy influence on CHL, the log10 (CHL) fields were spatially high-pass filtered to attenuate CHL features with zonal wavelength scales larger than 20◦ of longitude. A 3-year time-longitude section of the resulting filtered log10 (CHL) variability along 20◦ S in the SEP is shown in Fig. 2b. The wavenumber-frequency spectrum computed from all 10 years of data is shown in Fig. 5d. For composite averaging, the eddy-induced small-scale log10 (CHL) variability was isolated by high-pass filtering in time to attenuate variability with periods longer than 500 days and in space to attenuate variability with wavelength scales larger than 6◦ of longitude by 6◦ of latitude. This filtering removes the large-scale and seasonally varying CHL variability (S12) that is unrelated to the mesoscale eddy influence that is of interest in this study. The anomaly CHL values were collocated within the eddy interiors that were identified and defined from the SSH fields as described in detail elsewhere (S3). The locations relative to the eddy centroid of the gridded values of the anomaly log10 (CHL) at points within each eddy interior (defined here to be the region within twice the radius scale Ls defined above) were normalized by Ls in a translating and rotated frame of reference determined by the orientation of the large-scale CHL gradient computed from 200-day smoothing of unfiltered log10 (CHL) fields. When this ambient CHL gradient vector had a nonzero northward component (Figs. 3a,d), the filtered log10 (CHL) was rotated to orient the large-scale CHL gradient vector at a polar angle of 90◦ . When the ambient CHL gradient vector had a nonzero southward component (Fig. 3e), the filtered log10 (CHL) was rotated to orient the large-scale CHL gradient vector at a polar angle of −90◦ . Binned averages of the rotated fields of filtered log10 (CHL) and SSH within a radius of 2Ls from the centroid of each eddy at each point along its trajectory were computed on a fine grid from all available eddies of a given rotational sense. The resulting composite 3
averages are shown for the SEP region in Fig. 3a and for the global ocean in Figs. 3d,e. Composite averages are shown in Fig. S3 for the western and eastern portions of the SEP region to illustrate the geographical variability of the eddy-induced CHL distribution in this region. Profiles of each of the composite averages in Figs. 3 and S3 along lines connecting the extrema of each dipole are shown with estimated 95% confidence intervals in Figs. S4 and S5, respectively. The 95% confidence interval for the sample mean value at each normalized and gridded location x, y within the eddy √ interior was computed using the standard formula ∗ (S24) as ±s(x, y) qt(0.025, N − 1)/ N ∗ , where s(x, y) is the standard deviation of the CHL estimates at that normalized location, N ∗ is the estimated number of independent eddy realizations in the sample mean, and qt (0.025, N ∗ − 1) is the 2.5 percentage point of the Student’s t distribution with N ∗ − 1 degrees of freedom, i.e., the numerical value that a Student’s t random variable with N ∗ − 1 degrees of freedom exceeds with 2.5% probability. It was conservatively assumed that each individual eddy over the 10-year data record contributes only one independent realization along its entire trajectory. Since the minimum number of weekly samples of each eddy considered here is 10, the true confidence intervals are likely significantly smaller than shown in Figs. S4 and S5. As in previous analyses that have investigated Rossby wave influence on CHL (S13–S16, S25–S31), the temporal smoothing of the CHL observations with a 30-day half-power filter cutoff that was used here (analogous to the filtering properties of 18-day running averages, as noted above) attenuates the episodic CHL blooms that sometimes occur in response to transient upwelling of nutrients during eddy formation and intensification (S32–S35, S18, S19) or during eddy-induced Ekman upwelling (S36–S38, S18, S19). Such filtering favors persistent processes that influence CHL, which are shown in this study to be dominated by horizontal advection of CHL by the rotational velocity within the eddy interiors. Cross Correlation Between Sea-Surface Height and Chlorophyll Variability The 95% significance level for the magnitudes of the lagged correlations √ in Fig. 2c ∗ was computed using the standard formula (S24) as qt (0.025, N − 2)/ N ∗ , where qt (0.025,N ∗ −2) is the 2.5 percentage point of the Student’s t distribution with N ∗ − 2 degrees of freedom and N ∗ is the estimated number of independent eddy realizations in the sample cross correlation. As above, it was conservatively assumed that each eddy contributes only one independent realization along its entire trajectory. The estimated number of independent realizations at each longitude along 20◦ S is thus the sum of the numbers of clockwise- and counterclockwise-rotating eddies that propagated across the longitude over the 10-year data record. Since the minimum number of weekly samples of each eddy considered here is 10, the true 95% significance level for the correlation magnitude is likely significantly smaller than the values shown in Fig. 2c. The same method was used to compute the 95% significance level for the magnitudes of the lagged correlations in the right panels of Fig. S6 for the SSH and tracer fields of the model simulations described below. In this case, N ∗ at each longitude was conservatively assumed to be the sum of the numbers of clockwise- and counterclockwise-rotating eddies that propagated across the longitude in the model. 4
Numerical Model Simulations The details of the reduced-gravity quasigeostrophic model with one active layer used here for the simulations of mesoscale eddy influence on SSH are described elsewhere (S6). The model was seeded with random Gaussian eddies that had SSH amplitude and scale distributions and formation rates representative of the statistics of eddies in the altimeter observations in the SEP, but with varying degrees of nonlinearity (see below). As expected for energy- and enstrophy-conserving quasigeostrophic motion, nonlinear spectral interactions result in an upscale energy transfer (S39, S40), and the seeded eddies quickly evolve in the model simulation so that their horizontal scales become larger and their amplitudes become smaller compared with the seeded eddies by the time the model reaches statistical equilibrium. For the present simulations of eddy influence on chlorophyll distributions, the quasigeostrophic model was supplemented with a tracer field C(x, y, t), which was advected by the velocity field. The tracer C was initialized with a field C0 (y) = a + by with uniform northward gradient b. In order to maintain an ambient meridional gradient that would otherwise quickly become unrecognizable from stirring by the energetic eddy field, the tracer field was continuously restored toward the same meridionally varying field C0 (y). In effect, this simulates biological processes that give rise to the persistence of the largescale background CHL field in the real ocean. Following a previous modeling study of the SEP region (S15), a tracer restoring time scale of 30 days was used for our simulations. The analyses of the model SSH and tracer fields in this study are based on days 3000– 15,000 of the 15,000-day model simulations. Four different model runs were performed. The Gaussian eddy seeds had the same times, locations and initial radii in all four model runs. As noted above, the amplitudes, scales and formation rates of these eddy seeds were based on the statistics of observed eddies in the SEP region (S3). The nonlinear dynamics were turned off for the model run for which the wavenumber-frequency spectrum is shown in Fig. 5d. For the other three model runs, the degree of nonlinearity U/c of the eddies was controlled by multiplying the amplitudes A of the seeds obtained from the altimeter data by factors of α = 1, 2 and 3, but leaving the scales Ls unchanged. Since the rotational speed U is proportional to A/Ls , the degree of nonlinearity of the initial eddy seeds increased proportionally for each of the three nonlinear model runs. The high-pass filtering that was used for the composite averages of CHL in Figs. 3a,d,e and S3 was also applied for composite averages of the model tracer field in Figs. 3b,c. Time-longitude sections of the model SSH and tracer fields and their cross correlation analogous to the observational results in Fig. 2 are shown in Fig. S6 for the weakly and strongly nonlinear cases (α = 1 and 3, respectively). Wavenumber-frequency spectra are shown for all three nonlinear cases in Fig. S7. References Cited in the Supporting Online Material S1. D. B. Chelton, J. C. Ries, B. J. Haines, L.-L. Fu, P. S. Callahan, Satellite altimetry. In Satellite Altimetry and the Earth Sciences: A Handbook of Techniques and 5
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S17. B. M. Uz, J. A. Yoder, High frequency and mesoscale variability in SeaWiFS chlorophyll imagery and its relation to other remotely sensed variables. Deep-Sea Res. II, 51, 1001–1017 (2004). S18. D. A. Siegel, D. B. Court, D. W. Menzies, P. Peterson, S. Maritorena, N. B. Nelson, Satellite and in situ observations of the bio-optical signatures of two mesoscale eddies in the Sargasso Sea. Deep-Sea Res. II, 55, 1218–1230 (2008). S19. D. A. Siegel, P. Peterson, D. J. McGillicuddy, S. Maritorena, N. B. Nelson, Bio-optical footprints created by mesoscale eddies in the Sargasso Sea. Geophys. Res. Lett., 38, L13608, doi:10.1029/2011GL047660 (2011). S20. T. S. Moore, R. J. Matear, J. Marra, L. Clementson, Phytoplankton variability off the Western Australian Coast: Mesoscale eddies and their role in cross-shelf exchange. Deep-Sea Res. II, 54, 943–960 (2007). S21. W. S. Cleveland, S. J. Devlin, Locally weighted regression: An approach to regression analysis by local fitting. J. Amer. Stat. Assoc., 83, 596–610 (1988). S22. M. G. Schlax, D. B. Chelton, Frequency domain diagnostics for linear smoothers. J. Amer. Stat. Assoc., 87, 1070–1081 (1992). S23. D. B. Chelton, M. G. Schlax, The accuracies of smoothed sea surface height fields constructed from tandem altimeter datasets. J. Atmos. Oceanic Technol., 20, 1276– 1302 (2003). S24. H. von Storch, F. W. Zwiers, Statistical Analysis in Climate Research. Cambridge University Press, 484 pp. (1999). S25. D. A. Siegel, The Rossby rototiller. Nature, 409, 576–577 (2001). S26. Y. Dandonneau, A. Vega, H. Loisel, Y. du Penhoat, C. Menkes, Oceanic Rossby waves acting as a “hay rake” for ecosystem floating byproducts. Science, 302, 1548–1551 (2003). S27. P. D. Killworth, Comment on “Oceanic Rossby waves acting as a Hay Rake’ for ecosystem floating by-products.” Science, 304, 390b, doi:10.1126/science.1094870 (2004). S28. Y. Dandonneau, C. Menkes, T. Gorgues, G. Madec, Response to Comment on Oceanic Rossby waves acting as a hay rake’ for ecosystem floating by-products. Science, 304, 390 (2004). S29. G. Charria, F. Melin, I. Dadou, M.-H. Radenac, V. Garcon, Rossby wave and ocean color: The cells uplifting hypothesis in the South Atlantic Subtropical Convergence Zone. Geophys. Res. Lett., 30, 1125, doi:10.1029/2002GL016390 (2003). S30. G. Charria, I. Dadou, P. Cipollini, M. Drevillon, P. De Mey, V. Garcon, Understanding the influence of Rossby waves on surface chlorophyll a concentrations in the North Atlantic Ocean. J. Mar. Res., 64, 43–71, doi:10.1357/002224006776412340 (2006). S31. G. Charria, I. Dadou, P. Cipollini, M. Drevillon, V. Garcon, Influence of Rossby waves 7
on primary production from a coupled physical-biogeochemical model in the North Atlantic Ocean. Ocean Sci., 4, 199–213 (2008). S32. D. J. McGillicuddy, A. R. Robinson, Eddy-induced nutrient supply and new production in the Sargasso Sea. Deep-Sea Res. I, 44, 1427–1450 (1997). S33. D. J. McGillicuddy, A. R. Robinson, D. A. Siegel, H. W. Jannasch, R. Johnson, T. D. Dickey, J. McNeil, A. F. Michaels, A. H. Knap, Influence of mesoscale eddies on new production in the Sargasso Sea. Nature, 394, 263–266 (1998). S34. D. J. McGillicuddy, R. Johnson, D. A. Siegel, A. F. Michaels, N. R. Bates, A. H. Knap, Mesoscale variations of biogeochemical properties in the Sargasso Sea. J. Geophys. Res., 104, 13,381–13,394 (1999). S35. D. A. Siegel, D. J. McGillicuddy, E. A. Fields, Mesoscale eddies, satellite altimetry, and new production in the Sargasso Sea. J. Geophys. Res., 104, 13,359–13,379 (1999). S36. A. P. Martin, K. J. Richards, Mechanisms for vertical nutrient transport within a North Atlantic mesoscale eddy. Deep-Sea Res. II, 48, 757–773 (2001). S37. D. J. McGillicuddy, et al., Eddy/wind interactions stimulate extraordinary mid-ocean plankton blooms. Science, 316, 1021–1026 (2007). S38. D. J. McGillicuddy, J. R. Ledwell, L. A. Anderson, Response to comment on “Eddy/ wind interactions stimulate extraordinary mid-ocean plankton blooms.” Science, 320, 448 (2008). S39. R. Fjortoft, On the changes in the spectral distribution of kinetic energy for twodimensional nondivergent flow. Tellus, 5, 225–230 (1953). S40. R. Tulloch, J. Marshall, C. Hill, Scales, growth rates and spectral fluxes of baroclinic instability in the ocean. J. Phys. Oceanogr., 41, 1057–1076 (2011). S41. A. E. Gill, Atmosphere-Ocean Dynamics. Academic Press, 662 pp (1982). S42. P. D. Killworth, D. B. Chelton, R. A. de Szoeke, The speed of observed and theoretical long extra-tropical planetary waves. J. Phys. Oceanogr., 27, 1946–1966 (1997). S43. R. Tailleux, J. C. McWilliams, The effect of bottom pressure decoupling on the speed of extratropical, baroclinic Rossby waves. J. Phys. Oceanogr., 31, 1461–1476 (2001).
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Supporting Figures Figure S1. Zonal (east-west) wavenumber-frequency spectra of filtered SSH (see text of the Supporting Online Material) along four zonal sections from a 16-year data record: a) The North Pacific Ocean, 125◦ E–170◦ W along 24◦ N; b) The South Indian Ocean, 50◦ E– 100◦ E along 24◦ S; c) The South Pacific Ocean, 160◦ E–135◦ W along 24◦ S; and d) The South Atlantic Ocean, 40◦ W–10◦ W along 24◦ S. As in Fig. 5a, the units of SSH are cm and the curved lines correspond to the local dispersion relations for linear Rossby waves from the classical theory for a flat bottom and no mean currents (S41) (solid), a theory that accounts for mean currents (S42) (dashed), and a theory for rough bottom topography and no mean currents (S43) (dotted). These example spectra show suggestions of short spurs of spectral variance along the dispersion relations, similar to the spectra of model SSH in Figs. 5e and S7a–c. Figure S2. The degree of nonlinearity of the observed mesoscale features with lifetimes ≥ 10 weeks as characterized by the parameter U/c (see text of the Supporting Online Material). Histograms (top panel) and upper-tail cumulative histograms (i.e., the percentage of eddies with U/c greater than or equal to any particular value along the abscissa, bottom
Supporting Figures Figure S1. Zonal (east-west) wavenumber-frequency spectra of filtered SSH (see text of the Supporting Online Material) along four zonal sections from a 16-year data record: a) The North Pacific Ocean, 125◦ E–170◦ W along 24◦ N; b) The South Indian Ocean, 50◦ E– 100◦ E along 24◦ S; c) The South Pacific Ocean, 160◦ E–135◦ W along 24◦ S; and d) The South Atlantic Ocean, 40◦ W–10◦ W along 24◦ S. As in Fig. 5a, the units of SSH are cm and the curved lines correspond to the local dispersion relations for linear Rossby waves from the classical theory for a flat bottom and no mean currents (S41) (solid), a theory that accounts for mean currents (S42) (dashed), and a theory for rough bottom topography and no mean currents (S43) (dotted). These example spectra show suggestions of short spurs of spectral variance along the dispersion relations, similar to the spectra of model SSH in Figs. 5e and S7a–c. Figure S2. The degree of nonlinearity of the observed mesoscale features with lifetimes ≥ 10 weeks as characterized by the parameter U/c (see text of the Supporting Online Material). Histograms (top panel) and upper-tail cumulative histograms (i.e., the percentage of eddies with U/c greater than or equal to any particular value along the abscissa, bottom panel) of U/c for the SEP region 15◦ S–25◦ S, 130◦ W–80◦ W (thick line), the global ocean between latitudes 15◦ and 25◦ (medium line thickness), and the global ocean between latitudes 25◦ and 60◦ (thin line). Features with U/c > 1 (shown by the vertical dashed line) are nonlinear. Figure S3. Composite averages of filtered fields in a rotated and normalized coordinate system (see text of the Supporting Online Material) within the interiors of clockwise (top panels) and counterclockwise-rotating eddies (bottom panels) for filtered log10 (CHL) in the western and eastern halves of the SEP region shown in Fig. 1: a) 18◦ S–22◦ S, 130◦ W– 108◦ W; and b) 18◦ S–22◦ S, 108◦ W–80◦ W. As in Fig. 3, the outer perimeter of each circle
Supporting Figures Figure S1. Zonal (east-west) wavenumber-frequency spectra of filtered SSH (see text of the Supporting Online Material) along four zonal sections from a 16-year data record: a) The North Pacific Ocean, 125◦ E–170◦ W along 24◦ N; b) The South Indian Ocean, 50◦ E– 100◦ E along 24◦ S; c) The South Pacific Ocean, 160◦ E–135◦ W along 24◦ S; and d) The South Atlantic Ocean, 40◦ W–10◦ W along 24◦ S. As in Fig. 5a, the units of SSH are cm and the curved lines correspond to the local dispersion relations for linear Rossby waves from the classical theory for a flat bottom and no mean currents (S41) (solid), a theory that accounts for mean currents (S42) (dashed), and a theory for rough bottom topography and no mean currents (S43) (dotted). These example spectra show suggestions of short spurs of spectral variance along the dispersion relations, similar to the spectra of model SSH in Figs. 5e and S7a–c. Figure S2. The degree of nonlinearity of the observed mesoscale features with lifetimes ≥ 10 weeks as characterized by the parameter U/c (see text of the Supporting Online Material). Histograms (top panel) and upper-tail cumulative histograms (i.e., the percentage of eddies with U/c greater than or equal to any particular value along the abscissa, bottom panel) of U/c for the SEP region 15◦ S–25◦ S, 130◦ W–80◦ W (thick line), the global ocean between latitudes 15◦ and 25◦ (medium line thickness), and the global ocean between latitudes 25◦ and 60◦ (thin line). Features with U/c > 1 (shown by the vertical dashed line) are nonlinear. Figure S3. Composite averages of filtered fields in a rotated and normalized coordinate system (see text of the Supporting Online Material) within the interiors of clockwise (top panels) and counterclockwise-rotating eddies (bottom panels) for filtered log10 (CHL) in the western and eastern halves of the SEP region shown in Fig. 1: a) 18◦ S–22◦ S, 130◦ W– 108◦ W; and b) 18◦ S–22◦ S, 108◦ W–80◦ W. As in Fig. 3, the outer perimeter of each circle corresponds to twice the eddy radius scale Ls and the vectors in each panel are the gradient of the composite average SSH, which is proportional to the geostrophic velocity. The number N of eddy realizations in the composite average and the magnitude r of the ratio of the primary pole in the leading (left) half of each composite to the secondary pole in the trailing (right) half are labeled on each panel. The reasons for these geographical variations in the detailed structures of the eddies are a focus of ongoing research.
Figure S4. Profiles of each of the composite averages in Fig. 3 along the line connecting the extrema of each dipole. The blue and red lines correspond to clockwise (CW) and counterclockwise (CCW) rotating eddies, respectively, and the black lines indicate the estimated 95% confidence intervals computed as described in the text of the Supporting Online Material. The confidence intervals are barely discernable in panels b and c because of the large number of eddies in the model simulations and the smaller standard deviation of the tracer values in each sample mean compared with the satellite estimates of CHL. The numbers of degrees of freedom for the 95% confidence intervals estimated conservatively as described in the text of the Supporting Online Material are: a) 280 CW and 282 CCW; b) 2626 CW and 2620 CCW; c) 2788 CW and 2799 CCW; d) 3710 CW and 4085 CCW; and e) 5477 CW and 5399 CCW. Figure S5. The same as Fig. S4, except profiles of the composite averages in Fig. S3 along the line connecting the extrema of each dipole. The estimated numbers of degrees of freedom for the 95% confidence intervals are: a) 138 CW and 135 CCW; and b) 145 CW and 152 CCW. Figure S6. Spatial and temporal variability of filtered SSH and tracer fields along the center latitude of the domain for the quasigeostrophic model described in the text of the Supporting Online Material. Time-longitude sections of westward-only propagation over a 3-year portion of the 15,000-day model run are shown for SSH in cm (left panels), a tracer
Figure S4. Profiles of each of the composite averages in Fig. 3 along the line connecting the extrema of each dipole. The blue and red lines correspond to clockwise (CW) and counterclockwise (CCW) rotating eddies, respectively, and the black lines indicate the estimated 95% confidence intervals computed as described in the text of the Supporting Online Material. The confidence intervals are barely discernable in panels b and c because of the large number of eddies in the model simulations and the smaller standard deviation of the tracer values in each sample mean compared with the satellite estimates of CHL. The numbers of degrees of freedom for the 95% confidence intervals estimated conservatively as described in the text of the Supporting Online Material are: a) 280 CW and 282 CCW; b) 2626 CW and 2620 CCW; c) 2788 CW and 2799 CCW; d) 3710 CW and 4085 CCW; and e) 5477 CW and 5399 CCW. Figure S5. The same as Fig. S4, except profiles of the composite averages in Fig. S3 along the line connecting the extrema of each dipole. The estimated numbers of degrees of freedom for the 95% confidence intervals are: a) 138 CW and 135 CCW; and b) 145 CW and 152 CCW. Figure S6. Spatial and temporal variability of filtered SSH and tracer fields along the center latitude of the domain for the quasigeostrophic model described in the text of the Supporting Online Material. Time-longitude sections of westward-only propagation over a 3-year portion of the 15,000-day model run are shown for SSH in cm (left panels), a tracer field with arbitrary units (middle panels) and the lagged cross correlation between the tracer at time t and SSH at time t+lag (right panels), calculated over 10 years of the model run (the same duration as the overlapping SSH and CHL datasets for which the lagged cross correlations in Fig. 2c were computed); the white areas correspond to correlations smaller than the estimated 95% significance level of 0.027 calculated as described in the text of the Supporting Online Material. Positive lags correspond to the tracer leading SSH and the contour interval is 0.2 with the zero contour omitted for clarity. The structures of these time-longitude sections and lagged cross correlations are very similar to those shown in Fig. 2 for observed anomaly SSH and log10 (CHL). Figure S7. Zonal wavenumber-frequency spectra of filtered SSH in cm (top row) and a tracer field with arbitrary units (bottom row) from days 3000–15,000 of numerical simulations with nonlinear quasigeostrophic dynamics in a model seeded with Gaussian eddies with varying degrees of nonlinearity: a) SSH for eddies with amplitudes, scales and forma-
Figure S4. Profiles of each of the composite averages in Fig. 3 along the line connecting the extrema of each dipole. The blue and red lines correspond to clockwise (CW) and counterclockwise (CCW) rotating eddies, respectively, and the black lines indicate the estimated 95% confidence intervals computed as described in the text of the Supporting Online Material. The confidence intervals are barely discernable in panels b and c because of the large number of eddies in the model simulations and the smaller standard deviation of the tracer values in each sample mean compared with the satellite estimates of CHL. The numbers of degrees of freedom for the 95% confidence intervals estimated conservatively as described in the text of the Supporting Online Material are: a) 280 CW and 282 CCW; b) 2626 CW and 2620 CCW; c) 2788 CW and 2799 CCW; d) 3710 CW and 4085 CCW; and e) 5477 CW and 5399 CCW. Figure S5. The same as Fig. S4, except profiles of the composite averages in Fig. S3 along the line connecting the extrema of each dipole. The estimated numbers of degrees of freedom for the 95% confidence intervals are: a) 138 CW and 135 CCW; and b) 145 CW and 152 CCW. Figure S6. Spatial and temporal variability of filtered SSH and tracer fields along the center latitude of the domain for the quasigeostrophic model described in the text of the Supporting Online Material. Time-longitude sections of westward-only propagation over a 3-year portion of the 15,000-day model run are shown for SSH in cm (left panels), a tracer field with arbitrary units (middle panels) and the lagged cross correlation between the tracer at time t and SSH at time t+lag (right panels), calculated over 10 years of the model run (the same duration as the overlapping SSH and CHL datasets for which the lagged cross correlations in Fig. 2c were computed); the white areas correspond to correlations smaller than the estimated 95% significance level of 0.027 calculated as described in the text of the Supporting Online Material. Positive lags correspond to the tracer leading SSH and the contour interval is 0.2 with the zero contour omitted for clarity. The structures of these time-longitude sections and lagged cross correlations are very similar to those shown in Fig. 2 for observed anomaly SSH and log10 (CHL). Figure S7. Zonal wavenumber-frequency spectra of filtered SSH in cm (top row) and a tracer field with arbitrary units (bottom row) from days 3000–15,000 of numerical simulations with nonlinear quasigeostrophic dynamics in a model seeded with Gaussian eddies with varying degrees of nonlinearity: a) SSH for eddies with amplitudes, scales and formation rates equal to those of SSH observations in the SEP region shown in Fig. 1 (referred
Figure S4. Profiles of each of the composite averages in Fig. 3 along the line connecting the extrema of each dipole. The blue and red lines correspond to clockwise (CW) and counterclockwise (CCW) rotating eddies, respectively, and the black lines indicate the estimated 95% confidence intervals computed as described in the text of the Supporting Online Material. The confidence intervals are barely discernable in panels b and c because of the large number of eddies in the model simulations and the smaller standard deviation of the tracer values in each sample mean compared with the satellite estimates of CHL. The numbers of degrees of freedom for the 95% confidence intervals estimated conservatively as described in the text of the Supporting Online Material are: a) 280 CW and 282 CCW; b) 2626 CW and 2620 CCW; c) 2788 CW and 2799 CCW; d) 3710 CW and 4085 CCW; and e) 5477 CW and 5399 CCW. Figure S5. The same as Fig. S4, except profiles of the composite averages in Fig. S3 along the line connecting the extrema of each dipole. The estimated numbers of degrees of freedom for the 95% confidence intervals are: a) 138 CW and 135 CCW; and b) 145 CW and 152 CCW. Figure S6. Spatial and temporal variability of filtered SSH and tracer fields along the center latitude of the domain for the quasigeostrophic model described in the text of the Supporting Online Material. Time-longitude sections of westward-only propagation over a 3-year portion of the 15,000-day model run are shown for SSH in cm (left panels), a tracer field with arbitrary units (middle panels) and the lagged cross correlation between the tracer at time t and SSH at time t+lag (right panels), calculated over 10 years of the model run (the same duration as the overlapping SSH and CHL datasets for which the lagged cross correlations in Fig. 2c were computed); the white areas correspond to correlations smaller than the estimated 95% significance level of 0.027 calculated as described in the text of the Supporting Online Material. Positive lags correspond to the tracer leading SSH and the contour interval is 0.2 with the zero contour omitted for clarity. The structures of these time-longitude sections and lagged cross correlations are very similar to those shown in Fig. 2 for observed anomaly SSH and log10 (CHL). Figure S7. Zonal wavenumber-frequency spectra of filtered SSH in cm (top row) and a tracer field with arbitrary units (bottom row) from days 3000–15,000 of numerical simulations with nonlinear quasigeostrophic dynamics in a model seeded with Gaussian eddies with varying degrees of nonlinearity: a) SSH for eddies with amplitudes, scales and formation rates equal to those of SSH observations in the SEP region shown in Fig. 1 (referred to as α = 1); b) the same as panel a, except doubling the amplitudes of the seeded eddies (α = 2); c) the same as panel a, except tripling the amplitudes of the seeded eddies (α = 3); d) A tracer field in the same model simulation as panel a; e) A tracer field in the same model simulation as panel b; f) A tracer field in the same model simulation as panel c. Figs. 5e,f correspond to panels b and e in this figure. Analogous to Figs. 5e,f, the straight lines correspond to the mean eddy speeds of 4.1, 4.3 and 4.4 cm s−1 from modeled SSH for the cases of α = 1, 2 and 3, respectively, and the curved line in each panel corresponds to the dispersion relation for linear Rossby waves with zero meridional wavenumber from the classical theory for a flat bottom and zero background mean flow (S41). 10
