The Influence of Nonlinear Mesoscale Eddies on Oceanic Chlorophyll. May 23, Submitted to Science

Transcription

1 The Influence of Nonlinear Mesoscale Eddies on Oceanic Chlorophyll Dudley B. Chelton 1, Peter Gaube 1, Michael G. Schlax 1, Jeffrey J. Early 2 and Roger M. Samelson 1 May 23, 2011 Submitted to Science 1 College of Oceanic and Atmospheric Sciences 104 COAS Administration Building Oregon State University Corvallis, OR Northwest Research Associates P.O. Box 3027 Bellevue, WA address for correspondence: chelton@coas.oregonstate.edu Voice phone: ; FAX phone:

2 Abstract Oceanic Rossby waves have been widely invoked as a mechanism for large-scale variability of chlorophyll (CHL) observed from spaceborne sensors. High-resolution satellite altimeter measurements have recently revealed that sea-surface height (SSH) features previously interpreted as linear Rossby waves are nonlinear mesoscale coherent structures (referred to here as eddies). We analyze 10 years of these SSH fields and concurrent satellite measurements of upper-ocean CHL to show that these eddies exert a strong influence on the CHL field, thus requiring reassessment of the mechanism for the observed covariability of SSH and CHL. On time scales longer than 2 3 weeks, the dominant mechanism is shown to be eddy-induced horizontal advection of CHL by the rotational velocities of the eddies. 1

3 Introduction The availability of a decade of overlapping records of satellite measurements of sea surface height (SSH) and upper-ocean chlorophyll (CHL) enables studies of physical-biological interaction that are not feasible from ship-based observations alone. Although satellites provide only near-surface information about oceanic physics and biology, they are the only practical means of obtaining dense, global observations. Of particular importance for the present study is SSH measured by altimetry. Within a few years after the 1992 launch of the first highly accurate altimeter, it was clear that westward propagation of SSH is ubiquitous (1) with characteristics similar to the linear Rossby waves by which the oceans adjust to wind and thermal forcing (2). After the accumulation of a few years of CHL estimated from satellite measurements of ocean color, it became apparent that CHL exhibits westward propagation very similar to that found in SSH. The widespread interpretation of the westward propagating SSH as Rossby waves thus led naturally to interpretations of the CHL variability as being induced by Rossby waves (3-5). The mechanisms for this physical-biological relationship have been debated (4-9), in part because of the inconsistency of the lag between SSH and CHL, which varies geographically as well as temporally. It has been argued that the dominant mechanism for the covariability between SSH and CHL is advection of CHL by the horizontal velocity field associated with Rossby waves (7-9). Prior to the recent focus on Rossby wave influence, the prevailing view was that oceanic CHL is influenced by nonlinear eddies (10-12). Investigations of eddy influence by various mechanisms have continued in parallel with the Rossby wave studies (13-15). Here we show that the co-propagation of CHL and SSH previously interpreted as Rossby waves is actually attributable to eddies. 2

4 The Nonlinearity of the Observed SSH Variability The merging of SSH measurements from two simultaneously operating satellite altimeters (16) has clarified the nature of the westward-propagating SSH variability. The higher resolution of the merged dataset reveals that westward propagating features that were previously believed to be linear Rossby waves are nonlinear rotating coherent structures ( eddies ) with mesoscale radii of ~100 km (17, 18). These eddies are not adequately resolved in SSH fields constructed from a single altimeter, thus explaining why the early altimetric studies were not able to identify their compact structures. It is known theoretically (19) and observationally (17, 18) that nonlinear mesoscale eddies propagate westward with approximately the speed of long Rossby waves. An important distinction is that linear Rossby waves are dispersive (i.e., the propagation speed depends on wavelength) whereas nonlinear eddy variability is not. This key diagnostic is used here to make the case that the observed CHL variability is induced by nonlinear eddies rather than linear Rossby waves. The degree of nonlinearity of a rotating, propagating feature can be characterized by the ratio of the rotational fluid speed U to the translation speed c of the feature. When U/c>1, the feature is nonlinear, which allows it to maintain a coherent structure as it propagates. In a Fourier decomposition, this requires that all of the wavenumber components (inversely proportional to wavelength) of the feature propagate at the same speed, i.e., nondispersively. With linear dynamics, features that are initially spatially compact quickly lose their coherent structure through wave dispersion (20). 3

5 At latitudes higher than 25º, 98% of the mesoscale features tracked for 10 weeks have U/c>1 (Fig. S1). The degree of nonlinearity is slightly less at lower latitudes where the propagation speeds c are faster (17, 18). But even in the latitude range 15 25, 95% of the mesoscale features have U/c>1 (Fig. S1). Westward Co-Propagation of SSH and CHL Past studies that have concluded that CHL is influenced by Rossby waves were based on lagged correlations computed from time-longitude plots of SSH and CHL. The revised interpretation of westward-propagating SSH as nonlinear eddies mandates a reassessment of the hypothesized Rossby wave mechanism for the westward co-propagation of CHL and SSH. The alternative hypothesis that westward-propagating CHL is eddy-induced is examined here from 10 years of concurrent measurements of SSH and CHL in the southeastern Pacific (SEP) region near 20ºS that has been a focus of past studies (6, 7). The trajectories of mesoscale eddies (18) within the SEP are shown in Fig. 1a. There is a preference for clockwise rotating eddies, which outnumbered counterclockwise rotating eddies by 807 to 687. Compared with eddies observed globally in the latitude range 15 25, their mean amplitude is smaller (3.2 cm versus 6.2 cm) but their mean radius is the same (110 km). The eddies in the SEP are therefore less nonlinear (Fig. S1); 87% have U/c>1. The 10-year average CHL distribution in the SEP consists of a generally northward gradient with a northeastward increase toward South America (Fig. 1b). The strong influence of eddies at any particular time is evident from the superposition of CHL on the mesoscale SSH field (Fig. 1c). The sinuous CHL contours are indicative of distortions of what would otherwise be a 4

6 smoothly varying CHL field. These distortions are most apparent where the meridional (northsouth) gradient of CHL is strongest. The manner in which the CHL field is influenced by eddies becomes clearer after filtering to remove the large-scale and seasonally varying CHL and SSH (21). Westward co-propagation of CHL and SSH is apparent from time-longitude plots of the resulting anomaly fields (Figs. 2a,b). The trajectories of the centroids of clockwise- and counterclockwise-rotating eddies in the SEP coincide, respectively, with negative and positive extrema of westward-propagating SSH (Fig. 2a). In contrast, the eddy centroids lag extrema of westward propagating CHL (Fig. 2b). A positive correlation occurs at a lag that decreases from about 1 month in the east to about 0.5 month in the west (Fig. 2c). There is a weaker negative correlation at a negative lag of ~1 month. Eddy Influence on CHL To understand the lagged cross correlation in Fig. 2c, anomaly CHL was composite averaged within the SEP eddy interiors in a translating and rotated coordinate system in which the largescale CHL gradient is oriented at a polar angle of 90 (21). The eddy-induced CHL anomalies consist of dipoles with opposing signs and with different orientations in clockwise and counterclockwise rotating eddies (Fig. 3a). In both cases, the dipoles are asymmetric about the eddy centroid with larger magnitude in the left half of each composite, which corresponds to the leading half of these westward-propagating eddies. The displacements from the eddy centroid are smaller for these primary poles than for the secondary poles of opposite sign in the trailing (right) halves of the eddies. The geographical patterns of anomalous CHL within the eddy interiors are indicative of horizontal advection of CHL within the generally northward gradient of CHL in the SEP by the 5

7 rotational velocities of the eddies (Fig. 4). For clockwise rotating eddies (top panels of Figs. 3a and 4a), the northward velocity in the western half of each eddy advects low CHL from south to north, resulting in anomalously low CHL in the northwest quadrant. The southward velocity in the eastern half of each such eddy advects high CHL from north to south, resulting in anomalously high CHL in the southeast quadrant. The opposite occurs for counterclockwise rotating eddies (bottom panels of Figs. 3a and 4a) in which the southward velocity in the western half of each eddy advects high CHL from north to the south, resulting in anomalously high CHL in the southwest quadrant. The northward velocity in the eastern half of each such eddy advects low CHL from south to north, resulting in anomalously low CHL in the northeast quadrant. The importance of composite averaging the CHL in a rotated coordinate system is clear from Figs. 4a,b, which show the dependence of the geographical distribution of the CHL anomalies on the direction of the CHL gradient. The dipole patterns of anomaly CHL result from a combination of the rotational sense of the eddies (clockwise versus counterclockwise) and the direction of the CHL gradient (generally northward in the SEP). These dipoles of anomaly CHL account for the previously noted sinuous contours of CHL in Fig. 1c. The CHL anomaly within the trailing half of the eddy is generally weaker and noisier than within the leading half because the trailing half encounters a CHL field that has been distorted by the leading half. The noisiness of the secondary poles accounts for the weaker negative correlation at negative lags, as well as their smaller composite average magnitude that results in asymmetry of the magnitudes of the dipoles. Within an individual eddy, the structure of the dipole of anomaly CHL from eddy-driven advection varies, depending on the strength and orientation of the meridional gradient of CHL 6

8 (which vary geographically and temporally), the degree of nonlinearity of the eddy (i.e., the ratio U/c, which varies from eddy to eddy), and the influence of other eddies that have recently perturbed the CHL field. The past confusion about geographical and temporal variations of the lag relationships between SSH and CHL is therefore not surprising. Horizontal advection of CHL by the rotational velocities of the eddies is reproduced in numerical model simulations of random westward-propagating eddies in a tracer field with a northward gradient (21). The dipoles of anomalous tracer variability for weakly nonlinear eddies (Fig. 3b) are very similar to the dipoles of CHL in Fig. 3a. The higher rotational velocities within strongly nonlinear eddies result in tracer dipoles with larger magnitudes and with centers advected farther around the interiors of the eddies (Fig. 3c). Composite averaging separately for the SEP eddies east and west of 108 W (Fig. S2) reveals that the longitudinal variations of the couplet of positive and negative lagged correlations in Fig. 2c are attributable to longitudinal variations of the structures of the CHL dipoles. The westward decrease of the lag of maximum positive correlation is consistent with the westward decrease of the displacements between the eddy centroids and the primary poles of CHL anomaly in the leading halves of the eddies. The near symmetry of the lags of strongest positive and negative correlations in the east is consistent with the near symmetric displacements of the dipole centers from the eddy centroids in the east (Fig. S2). The geographical patterns of eddy-induced CHL anomalies in the SEP are similar to the patterns found in other regions of northward meridional gradient of CHL. Composite averages of anomaly CHL computed globally (21) between latitudes of 15º and 45º are shown in Fig. 3d for the tracked eddies within regions of generally northward CHL gradient. The telltale asymmetric 7

9 dipole patterns from opposing meridional advection in opposite halves of the eddies are readily apparent. The orientations of the axes of the CHL dipoles in composite averages for regions of generally southward CHL gradient (Fig. 3e) are rotated approximately 180º relative to those in regions of northward CHL gradient. These mirrored dipoles still have larger magnitude in the leading (left) half of the westward-propagating eddies. In addition to the asymmetry of the dipoles, another consistent feature of all of the composites in Fig. 3 is the smaller offsets between the eddy centroids and the primary poles in the leading (left) halves of the eddies compared with the offsets between the eddy centroids and the secondary poles in the trailing (right) halves of the eddies. This occurs both in the CHL observations and in the model tracer fields. When U/c > 1, fluid will generally be trapped within the eddy interior and transported long distances along the eddy trajectory (20). This nonlinear signal of sustained interior fluid transport is not the eddy advection signature revealed in the CHL observations described here. Rather, the dipole CHL features are interpreted as transient advection of ambient fluid around the outer edge of the eddy centers, which is induced as the westward translating eddies impinge on pre-existing CHL gradients. Spectral Analysis of SSH and Chlorophyll Variability Wavenumber-frequency spectra of SSH and CHL provide further evidence that the westward propagation of CHL is induced by nonlinear eddies. The nondispersive character of nonlinear eddies noted previously implies that the spectral variance should fall approximately along a 8

10 straight line in wavenumber-frequency space. In contrast, the spectral variance for linear Rossby waves would be constrained to frequencies defined by the dispersion relation for Rossby waves. The zonal (east-west) wavenumber-frequency spectrum of SSH in the SEP (Fig. 5a) is clearly inconsistent with the theoretical Rossby wave dispersion relation, regardless of whether the effects of mean currents or rough bottom topography are taken into consideration. Whereas the dispersion relations from all three linear theories flatten with increasingly negative wavenumber (corresponding to westward propagation), the spectral variance of observed SSH extends to higher frequencies, straddling the straight line of constant (nondispersive) propagation speed. Our hypothesis that the spectral characteristics of SSH in Fig. 5a are attributable to eddies with compact structures was tested by constructing SSH fields consisting only of the interiors of the tracked eddies. Each eddy was approximated as an axisymmetric Gaussian feature with amplitude and scale estimated from the automated tracking procedure. The spectral variance of the resulting eddy-only SSH fields (Fig. 5b) straddles the same straight line as the spectrum of total SSH (22). The discrepancies between the wavenumber-frequency spectra of SSH and the Rossby wave dispersion relations are thus consistent with SSH variability being attributable to a field of propagating eddies. The importance of nonlinearity is clarified from model simulations. The spectral variance of model SSH with purely linear dynamics is restricted to frequencies below the dispersion relation for linear Rossby waves with zero meridional wavenumber (Fig. 5d). The spread of variance to frequencies below this dispersion relation is from Fourier components with finite meridional wavenumbers (2). With nonlinear quasigeostrophic dynamics, the spectral variance of model SSH primarily represents long-lived, coherent eddy features, in which the small-scale spectral components are 9

11 phase-locked to the large-scale components (20). The resulting spectrum (Fig. 5e) consists of a nondispersive band along a straight line that extends to frequencies higher than are allowed by purely linear Rossby wave dynamics, very similar to the spectrum of observed SSH in Fig. 5a. A short spur of spectral variance centered at about cpd extends along the dispersion relation in the model SSH spectrum (Fig. 5e). These spurs arise from small-amplitude SSH variability outside the nonlinear cores of the eddies. The extent of the spur is found to decrease with increasing nonlinearity of the eddies (Fig. S4). Although not apparent in the spectrum of observed SSH in the SEP (Fig. 5a), suggestions of similar spurs exist in SSH spectra in other regions (Fig. S3). Determination of the spectrum of CHL variability is more challenging than for SSH. The primary limitation is data gaps from the inability to measure ocean color when clouds are present, which occurs about 75% of the time at the eastern end of the 20 S section considered here, decreasing to about 40% of the time at the western end (23). Another limitation is the noisiness of the CHL fields owing to the fact that 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 oceanic CHL concentration. Other complications are introduced by the fact that the meridional gradient of CHL that makes eddy-induced horizontal advection detectable migrates latitudinally and modulates in intensity on seasonal and longer time scales. In addition, the CHL within the eddy interiors can evolve along the propagation path of the eddy from a variety of biological processes (10-15). Despite these complications in the interpretation of satellite measurements of CHL, the spectrum of CHL in the SEP (Fig. 5c) is similar to the spectrum of SSH. In particular, the 10

12 spectral variance is concentrated along the same straight line of nondispersive variability to higher frequencies than are allowed by any of the linear Rossby waves theories. Moreover, the spectral variance is restricted to smaller negative wavenumbers than would be the case if the CHL variability were induced by linear Rossby waves. A short spur of spectral variance straddles the dispersion relation at about cpd for the same reason discussed above for the model SSH spectra. Similar spurs are found in spectra of tracer fields in quasigeostrophic model simulations (Figs. 5f and S4d,e,f). Conclusions We have shown that the westward co-propagation of CHL and SSH that has previously been attributed to linear Rossby waves is really caused by nonlinear eddies that were not resolvable in the SSH fields analyzed in past studies. This eddy influence is manifest as sinuous contours of CHL and is most evident in regions of strong meridional gradient of CHL. Eddy influence on CHL becomes clearer after appropriate filtering (21). The distinctly different dipole structures of the resulting anomalous CHL within the interiors of clockwise and counterclockwise rotating eddies (Figs. 3a,d,e) and their similarity to the dipoles of a tracer field in model simulations (Figs. 3b,c and S4d,e,f) are convincing evidence that the dominant mechanism for eddy-induced CHL variability on the time scales longer than 2 3 weeks considered here (21) is the horizontal advection of CHL by the velocity field within the interior of each rotating eddy. The dominance of horizontal advection as the mechanism for the observed westward propagation of filtered CHL variability has been suggested previously (7-9) but these earlier studies attributed the horizontal advection to linear Rossby waves, rather than nonlinear eddies. The role of eddies in defining the dipole structure of CHL anomalies has been suggested 11

13 previously for the central North Atlantic (14, 15). The distinction between linear Rossby waves and eddies is important because the dynamics of nonlinear eddies differ fundamentally from those of linear Rossby waves. In addition to trapping and transporting fluid parcels and their associated water properties, nonlinear eddies can upwell nutrient-rich water by various mechanisms (10-15), thus stimulating the growth of phytoplankton and increasing CHL in the eddy core. However, such eddy-induced enhancements can occur deep in the euphotic zone where they can be undetectable in the near-surface measurements of ocean color by satellites (13). Because of the unique trapping of fluid by nonlinear eddies, it is perhaps surprising that the CHL distribution associated with the eddies consists of dipoles, rather than monopoles of positive or negative CHL anomalies trapped at the eddy centers. Monopole structures do sometimes occur. In contrast to the ubiquitous presence of horizontal advection, however, such monopole structures are episodic, often with time scales shorter than 2 3 weeks that are attenuated by the filtering applied here (21). The physical and biological processes responsible for these transient behaviors are part of our ongoing research. References 1. D. B. Chelton, M. G. Schlax, Science, 272, 234 (1996). 2. A. E. Gill, Atmosphere-Ocean Dynamics (Academic Press, Cambridge, UK, 1982). 3. P. Cipollini, D. Cromwell, P. G. Challenor, S. Raffaglio, Geophys. Res. Lett., 28, 323 (2001). 4. B. M. Uz, J. A. Yoder, V. Osychny, Nature, 409, 597 (2001). 5. D. A. Siegel, D. A., Nature, 409, 576 (2001). 6. Y. Dandonneau, A. Vega, H. Loisel, Y. du Penhoat, C. Menkes, Science, 302, 1548 (2003). 7. P. D. Killworth, P. Cipollini, B. M. Uz, J. R. Blundell, J. Geophys. Res., 109, C07002 (2004). 12

14 8. G. Charria, I. Dadou, P. Cipollini, M. Drévillon, P. De Mey, V. Garçon, J. Mar. Res., 64, 43 (2006). 9. E. Gutknecht, I. Dadou, G. Charria, P. Cipollini, V. Garçon, J. Geophys. Res., 115, C05004 (2010). 10. P. G. Falkowski, D. Ziemann, Z. Kolber, P. K. Bienfang, Nature, 353, 55 (1991). 11. D. J. McGillicuddy, R. Johnson, D. A. Siegel, A. F. Michaels, N. R. Bates, A. H. Knap, J. Geophys. Res., 104, 13,381 (1999). 12. D. A. Siegel, D. J. McGillicuddy, E. A. Fields, J. Geophys. Res., 104, 13,359 (1999). 13. D. J. McGillicuddy and Coauthors, Science, 316, 1021 (2007). 14. D. A. Siegel, D. B. Court, D. W. Menzies, P. Peterson, S. Maritorena, N. B. Nelson, Deep- Sea Res. II, 55, 1218 (2008). 15. D. A. Siegel, P. Peterson, D. J. McGillicuddy, S. Maritorena, N. B. Nelson, Geophys. Res. Lett., submitted. 16. N. Ducet, P.-Y. Le Traon, G. Reverdin, J. Geophys. Res., 105, 19,477 (2000). 17. D. B. Chelton, M. G. Schlax, R. M. Samelson, R. A. de Szoeke, Geophys. Res. Lett., 34, L15606, (2007). 18. D. B. Chelton, M. G. Schlax, R. M. Samelson, Progr. Oceanogr., (2011, in press). 19. J. C. McWilliams, G. R. Flierl, J. Phys. Oceanogr., 9, (1979). 20. J. J. Early, R. M. Samelson, D. B. Chelton, J. Phys. Oceanogr., (2011, in press). 21. Information on methods is available as supplementary material on Science Online. 22. The somewhat smaller variance is because of biases of the amplitudes of compact mesoscale features as estimated by the automated procedure (18). 23. W. B. Rossow, R. A. Schiffer, Bull. Amer. Meteor. Soc., 72, 2 (1991). 13

15 24. P. D. Killworth, D. B. Chelton, R. A. de Szoeke, J. Phys. Oceanogr., 27, 1946 (1997). 25. R. Tailleux, J. C. McWilliams, J. Phys. Oceanogr., 31, 1461 (2001). Acknowledgments: We thank Dennis McGillicuddy and Tom Farrar for discussions throughout the course of this study. This research was supported by NASA grants NNX08AI80G and NNX08AR37G and NSF Award Supporting Online Material Materials and Methods SOM References Figs. S1 to S4 14

16 Figure 1. Geographical characteristics of observed SSH and CHL in the SEP: a) The trajectories from a 16-year data record of eddies that rotate clockwise (blue lines) and counterclockwise (red lines), with the starting locations shown by solid circles; b) The 10-year average log 10 (CHL) for CHL in units of mg m -3, with a contour interval of log 10 (CHL) = 0.1, increasing northward, and with the thick line corresponding to log 10 (CHL) = 1.3; and c) An example map for 7 March 2001 showing anomaly SSH in color with white contours at intervals of 2 cm, excluding the zero contour, and with black contours of log 10 (CHL) at the same interval as in panel b). The horizontal lines in each panel are the section along which the time-longitude plots in Fig. 2 and the spectra in Figs. 5a,b,c were computed. Figure 2. Spatial and temporal variability of filtered SSH and log 10 (CHL) observations (21) along 20ºS between 130ºW and 80ºW. Time-longitude sections of westward-only propagation over a 3-year portion of the 10-year period analyzed here are shown for a) SSH with eddy tracks within ±2 of 20ºS overlaid (dashed and solid lines for clockwise and counterclockwise rotating eddies, respectively); b) log 10 (CHL) with the same eddy tracks overlaid; and c) The lagged cross correlation between log 10 (CHL) at time t and SSH at time t+lag, calculated over the full 10-year data record. Positive lags correspond to log 10 (CHL) leading SSH and the contour interval is 0.2 with the zero contour omitted for clarity. Figure 3. Composite averages of filtered fields in a rotated and normalized coordinate system (21) within the interiors of clockwise (top panels) and counterclockwise-rotating eddies (bottom panels): a) log 10 (CHL) in the region 18ºS-22ºS, 130ºW-80ºW; b) a tracer field in a model 15

17 simulation seeded with weakly nonlinear Gaussian eddies; c) a tracer field in the model seeded with strongly nonlinear Gaussian eddies; d) log 10 (CHL) globally between 15º and 45º latitude in regions of northward CHL gradient; and e) log 10 (CHL) globally between 15º and 45º latitude in regions of southward CHL gradient. The outer perimeter of each circle corresponds to twice the eddy radius (21). 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. Figure 4. Schematic diagram of eddy-driven horizontal advection of CHL for clockwise and counterclockwise rotating eddies (top and bottom, respectively) propagating westward in regions where the CHL gradient is: a) northward; and b) northeastward. An otherwise smooth contour of CHL (dashed lines) is distorted as shown by the solid lines from the rotational velocity field within the eddy. Advection of CHL within the large-scale background CHL gradient results in the positive and negative CHL anomalies shown by the red and purple regions, respectively. The dependence of the locations of these CHL anomalies on the direction of the large-scale background CHL gradient that is evident from comparison of panels a and b was accounted for by composite averaging in a coordinate system rotated for each eddy (21). Figure 5. Zonal wavenumber-frequency spectra: a) Filtered SSH for 130ºW 80ºW along 20ºS; b) SSH for Gaussian approximations of each tracked eddy for 130ºW 80ºW along 20ºS; c) Filtered log 10 (CHL) for 130ºW 80ºW along 20ºS; d) SSH from days of a model simulation with purely linear dynamics; e) SSH from days of a model simulation 16

18 with nonlinear quasigeostrophic dynamics; f) A tracer field in the same model simulation as panel e). The units are cm for SSH, log 10 of mg m -3 for CHL and arbitrary for the tracer field. The straight lines are the mean eddy speeds from observed SSH (-4.9 cm s -1, panels a c) and from SSH in the model (-4.3 cm s -1, panels d f). The curved lines correspond to the dispersion relations for linear Rossby waves from the classical theory for a flat bottom and no mean currents (2) (solid), a theory that accounts for mean currents (24) (dashed), and a theory for rough bottom topography and no mean currents (25) (dotted). The latter two are irrelevant to the SSH fields from the flat-bottom model with no mean currents in panels d f. 17

19 Figure 1. Geographical characteristics of observed SSH and CHL in the SEP: a) The trajectories from a 16-year data record of eddies that rotate clockwise (blue lines) and counterclockwise (red lines), with the starting locations shown by solid circles; b) The 10-year average log 10 (CHL) for CHL in units of mg m -3, with a contour interval of log 10 (CHL) = 0.1, increasing northward, and with the thick line corresponding to log 10 (CHL) = 1.3; and c) An example map for 7 March 2001 showing anomaly SSH in color with white contours at intervals of 2 cm, excluding the zero contour, and with black contours of log 10 (CHL) at the same interval as in panel b). The horizontal lines in each panel are the section along which the time-longitude plots in Fig. 2 and the spectra in Figs. 5a,b,c were computed.

20 Figure 2. Spatial and temporal variability of filtered SSH and log 10 (CHL) observations (21) along 20ºS between 130ºW and 80ºW. Time-longitude sections of westward-only propagation over a 3-year portion of the 10-year period analyzed here are shown for a) SSH with eddy tracks within ±2 of 20ºS overlaid (dashed and solid lines for clockwise and counterclockwise rotating eddies, respectively); b) log 10 (CHL) with the same eddy tracks overlaid; and c) The lagged cross correlation between log 10 (CHL) at time t and SSH at time t+lag, calculated over the full 10-year data record. Positive lags correspond to log 10 (CHL) leading SSH and the contour interval is 0.2 with the zero contour omitted for clarity.

21 Figure 3. Composite averages of filtered fields in a rotated and normalized coordinate system (21) within the interiors of clockwise (top panels) and counterclockwise-rotating eddies (bottom panels): a) log 10 (CHL) in the region 18ºS-22ºS, 130ºW-80ºW; b) a tracer field in a model simulation seeded with weakly nonlinear Gaussian eddies; c) a tracer field in the model seeded with strongly nonlinear Gaussian eddies; d) log 10 (CHL) globally between 15º and 45º latitude in regions of northward CHL gradient; and e) log 10 (CHL) globally between 15º and 45º latitude in regions of southward CHL gradient. The outer perimeter of each circle corresponds to twice the eddy radius (21). 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.

22 Figure 4. Schematic diagram of eddy-driven horizontal advection of CHL for clockwise and counterclockwise rotating eddies (top and bottom, respectively) propagating westward in regions where the CHL gradient is: a) northward; and b) northeastward. An otherwise smooth contour of CHL (dashed lines) is distorted as shown by the solid lines from the rotational velocity field within the eddy. Advection of CHL within the large-scale background CHL gradient results in the positive and negative CHL anomalies shown by the red and purple regions, respectively. The dependence of the locations of these CHL anomalies on the direction of the large-scale background CHL gradient that is evident from comparison of panels a and b was accounted for by composite averaging in a coordinate system rotated for each eddy (21).

23 Figure 5. Zonal wavenumber-frequency spectra: a) Filtered SSH for 130ºW 80ºW along 20ºS; b) SSH for Gaussian approximations of each tracked eddy for 130ºW 80ºW along 20ºS; c) Filtered log 10 (CHL) for 130ºW 80ºW along 20ºS; d) SSH from days of a model simulation with purely linear dynamics; e) SSH from days of a model simulation with nonlinear quasigeostrophic dynamics; f) A tracer field in the same model simulation as panel e). The units are cm for SSH, log 10 of mg m -3 for CHL and arbitrary for the tracer field. The straight lines are the mean eddy speeds from observed SSH (-4.9 cm s -1, panels a c) and from SSH in the model (-4.3 cm s -1, panels d f). The curved lines correspond to the dispersion relations for linear Rossby waves from the classical theory for a flat bottom and no mean currents (2) (solid), a theory that accounts for mean currents (24) (dashed), and a theory for rough bottom topography and no mean currents (25) (dotted). The latter two are irrelevant to the SSH fields from the flat-bottom model with no mean currents in panels d f.

24 Supplementary Online Material for The Influence of Nonlinear Mesoscale Eddies on 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 Numerical Model Simulations SOM References Figs. S1 to S4 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 approximately16 years (October 1992 December 2008) of the Delayed-Time Reference Series available online from AVISO (Archivage, Validation, Interprétation des données des Satellite Océanographiques) that 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 mean. We used the version of these anomaly SSH fields that is provided by AVISO on a globally uniform 1/4 latitude by1/4 longitude grid. These fields were spatially high-pass filtered to attenuate SSH features with wavelength scales larger than 20º of longitude by 10º of latitude. The procedure used to identify and track the eddies analyzed here is described in detail elsewhere (S3). Except for the eddy tracks in Fig. 2, we consider only those eddies with lifetimes of 10 weeks and longer; a minimum lifetime cutoff of 4 weeks is used in Fig. 2. A radius scale L s 18

25 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 southeast Pacific (SEP) region that is the focus of this study is L s =110 km. 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 maximum circumaverage speed around the contour that defines the above radius scale L s and c was estimated from successive locations of the eddy centroid with a small amount of smoothing (S3). Because of the approximate 2 2 smoothing inherent in the objective analysis procedure used to construct the SSH fields analyzed here (S2, S3), the computed values of U/c are lower-bound estimates of the nonlinearity of the eddies. Their true nonlinearity is likely significantly larger than is suggested from Fig. S1. 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) (S4) using the Garver-Siegel- Maritorena (GSM) semi-analytical ocean color algorithm (S5, S6). The CHL fields were log 10 transformed and averaged into 1/4 1/4 areas centered on the same grid as the SSH fields described above. The availability of simultaneous estimates of CHL from SeaWiFS and altimeter measurements of SSH is facilitating studies of physical-biological interaction on oceanic mesoscales with spatial and temporal coverage that are not feasible from in situ measurements (e.g., S7-S9). 19

26 The time series of daily values of log 10 (CHL) at each grid point were low-pass filtered in time using a loess smoother (S10, S11) 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 (referred to here as 2 3 weeks), but the loess smoother has a much better filter transfer function (S12). This temporal smoothing also reduces the extensive data gaps from cloud contamination. The temporally low-pass filtered fields of log 10 (CHL) were further low-pass filtered spatially with a 2-dimensional loess smoother that had half-power filter cutoffs of 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. The maps in Figs. 1b and c display the log 10 (CHL) fields described above. The timelongitude section of log 10 (CHL) in Fig. 2b and its spectrum in Fig. 5d are derived from the log 10 (CHL) fields that were spatially high-pass filtered in the same manner as the SSH fields in order to attenuate CHL features with wavelength scales larger than 20º of longitude by 10º of latitude. For the composite averages in Figs. 3a,d,e and Fig. S2, the filtered log 10 (CHL) fields were further high-pass filtered in time to attenuate variability with periods longer than 500 days and in space to attenuate variability with scales larger than 6º in order to reduce the seasonal modulations of the eddy-induced CHL variations and the large-scale CHL variability attributable to geographical variations of pelagic ecosystems. These CHL anomalies were collocated within the eddy interiors 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 filtered log 10 (CHL) at points within each eddy interior (defined here to be the region within twice the radius L s defined 20

27 above in the summary of SSH data processing) were normalized by L s 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 log 10 (CHL) fields. When the ambient CHL gradient had a nonzero northward component, the filtered log 10 (CHL) was rotated to orient the large-scale CHL gradient vector at a polar angle of 90. When the ambient CHL gradient had a nonzero southward component, the filtered log 10 (CHL) was rotated to orient the large-scale CHL gradient vector at a polar angle of -90. The average value of the rotated field of filtered log 10 (CHL) was computed on a 1/4 1/4 grid from all available eddies of a given rotational sense. The resulting composite averages are shown in Figs. 3a,d,e and Fig. S2. As in previous analyses that have concluded that the CHL field is influenced by Rossby waves (S13-S23), 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 (S24-S29) or eddyinduced Ekman upwelling (S30-S32, S28, S29). 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. Numerical Model Simulations The details of the reduced-gravity quasigeostrophic model with one active layer used for the simulations of mesoscale eddy influence on SSH are described elsewhere (S33). Briefly, 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 21

28 southeastern Pacific, 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 (S34, S35), 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 C 0 (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 C 0 (y). In effect, this simulates the biological processes that give rise to the meridionally varying large-scale background CHL field in the real ocean. As in past studies (S19), the tracer restoring time scale was 30 days. The analyses of the model SSH and tracer fields that are shown in Figs. 3b,c, Figs. 5d f and Fig. S4 are based on days ,000 of the 15,000-day model simulations. Three different model runs were performed. The Gaussian eddy seeds had the same times, locations and initial radii in all three model runs. The degrees of nonlinearity U/c of the eddies were controlled by multiplying the amplitudes of the seeds obtained from the altimeter data by factors of =1, 2 and 3, resulting in the spectra shown in Figs. S4a,b and c, respectively. The high-pass filtering that was used for the composite averages of CHL in Figs. 3a,d,e and Fig. S2 was also applied for composite averaging of the model tracer field in Figs. 3b,c and Figs. S4d,e,f. 22

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31 S19. P. D. Killworth, P. Cipollini, B. M. Uz, J. R. Blundell, Physical and biological mechanisms for planetary waves observed in satellite-derived chlorophyll. J. Geophys. Res., 109, doi: /2003jc (2004). S20. G. Charria, F. Mélin, I. Dadou, M.-H. Radenac, V. Garçon, Rossby wave and ocean color: The cells uplifting hypothesis in the South Atlantic Subtropical Convergence Zone. Geophys. Res. Lett., 30, 1125, doi: /2002gl (2003). S21. G. Charria, I. Dadou, P. Cipollini, M. Drévillon, P. De Mey, V. Garçon, Understanding the influence of Rossby waves on surface chlorophyll a concentrations in the North Atlantic Ocean. J. Mar. Res., 64, 43 71, doi: / (2006). S22. G. Charria, I. Dadou, P. Cipollini, M. Drévillon, V. Garçon, Influence of Rossby waves on primary production from a coupled physical-biogeochemical model in the North Atlantic Ocean. Ocean Sci., 4, (2008). S23. E. Gutknecht, I. Dadou, G. Charria, P. Cipollini, V. Garçon, Spatial and temporal variability of the remotely sensed chlorophyll a signal associated with Rossby waves in the South Atlantic Ocean. J. Geophys. Res., 115, doi: /2009jc (2010). S24. D. J. McGillicuddy, A. R. Robinson, Eddy-induced nutrient supply and new production in the Sargasso Sea. Deep-Sea Res. I, 44, (1997). S25. 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, (1998). S26. D. J. McGillicuddy, Johnson, R., Siegel, D.A., Michaels, A.F., Bates, N.R., Knap, A.H., Mesoscale variations of biogeochemical properties in the Sargasso Sea. J. Geophys. Res., 104, (1999). 25

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34 Supplementary Figures Figure S1. The degree of nonlinearity of the observed mesoscale features with lifetimes 10 weeks as characterized by the parameter U/c (see text). Histograms (top panel) and upper-tail cumulative histograms (i.e., the number 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 15ºS-25ºS, 130ºW-80ºW (thick line), the global ocean between latitudes 15º and 25º (medium line thickness), and the global ocean between latitudes 25º and 60º (thin line). Features with U/c > 1 (shown by the vertical dashed line) are nonlinear. Figure S2. Composite averages of filtered fields in a rotated and normalized coordinate system (see text) within the interiors of clockwise (top panels) and counterclockwise-rotating eddies (bottom panels) for log 10 (CHL) in the western and eastern halves of the SEP region shown in Fig. 1: a) 18ºS-22ºS, 130ºW-108ºW; and b) 18ºS-22ºS, 108ºW-80ºW. As in Fig. 3, the outer perimeter of each circle corresponds to twice the eddy radius 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 part of our ongoing research. Figure S3. Zonal wavenumber-frequency spectra of filtered SSH (see text) along four zonal sections from a 16-year data record: a) The North Pacific Ocean, 125ºE 170ºW along 24ºN; b) 28

35 The South Indian Ocean, 50ºE 100ºE along 24ºS; c) The South Pacific Ocean, 160ºE 135ºW along 24ºS; and d) The South Atlantic Ocean, 40ºW 10ºW along 24ºS. As in Fig. 5a, the units 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 (S36) (solid), a theory that accounts for mean currents (S37) (dashed), and a theory for rough bottom topography and no mean currents (S38) (dotted). These example spectra show suggestions of short spurs of spectral variance along the dispersion relations, as in the spectra of model SSH in Fig. 5d and Fig. S4. Figure S4. Zonal wavenumber-frequency spectra of filtered SSH in cm (top row) and a tracer field with arbitrary units (bottom row) from days 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 =1); b) the same as panel a, except doubling the amplitudes of the seeded eddies ( =2); c) the same as panel a, except tripling the amplitudes of the seeded eddies ( =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 and 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 =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 (S36). 29

36 Figure S1. The degree of nonlinearity of the observed mesoscale features with lifetimes 10 weeks as characterized by the parameter U/c (see text). Histograms (top panel) and upper-tail cumulative histograms (i.e., the number 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 15ºS-25ºS, 130ºW-80ºW (thick line), the global ocean between latitudes 15º and 25º (medium line thickness), and the global ocean between latitudes 25º and 60º (thin line). Features with U/c > 1 (shown by the vertical dashed line) are nonlinear.

37 Figure S2. Composite averages of filtered fields in a rotated and normalized coordinate system (see text) within the interiors of clockwise (top panels) and counterclockwise-rotating eddies (bottom panels) for log 10 (CHL) in the western and eastern halves of the SEP region shown in Fig. 1: a) 18ºS-22ºS, 130ºW-108ºW; and b) 18ºS-22ºS, 108ºW-80ºW. As in Fig. 3, the outer perimeter of each circle corresponds to twice the eddy radius 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 part of our ongoing research.