Using the semivariogram approach from geostatistics, we characterize for the first time the global patterns of mesoscale (approximately 10–200 km and days to a few weeks) ocean biological variability. The magnitude of the variability and spatial length scale fields are reported for a full year of Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean color data. The analysis shows a number of coherent geographical patterns across a wide range of biological and physical environments. Submonthly, small spatial scale variance dominates ocean color variability in oligotrophic regimes and is about a third of the total variance even in regions with strong seasonality. When normalized to the mean chlorophyll as a coefficient of variation, the resolved mesoscale variance (relative sill) is approximately uniform in the open-ocean tropics and subtropics (0.1–0.2), increasing to 0.3–1.0 in western boundary current, upwelling (Equatorial Pacific, coastal) and subpolar/polar regions, approximately scaling with the mean chlorophyll concentration. The unresolved variance (nugget), which includes submesoscale geophysical variability as well as instrument/algorithm noise, is inversely correlated with mean chlorophyll concentration in the oligotrophic subtropical gyres, reducing to a low background value (0.1) elsewhere. The high fraction of unresolved variance in the subtropics is consistent with other studies showing substantial speckling due to noise in the atmospheric correction methods. The mesoscale spatial scale (range) is approximately zonal, with values of 200–350 km near the Equator to less than 50 km close to the poles similar to the physical scales estimated from altimeter sea surface height variability data and the first baroclinic Rossby deformation radius. Our results demonstrate the global generality of previous local and regional findings that small-scale variability in ocean biology and physics occurs on comparable spatial length scales. Regional deviations from these large-scale variance and spatial length scales trends, for example, lower range and higher resolved variance in coastal upwelling regimes, are explicable by the characteristics of the biological-physical interaction in those environments.
 Routine measurements of ocean color from space provide for the first time a globally coherent, synoptic picture of the patterns and variability of upper ocean biology [McClain et al., 1998]. The large-scale ocean color field, a measure of surface layer phytoplankton chlorophyll concentration, is governed by the seasonal distributions of light, nutrients, upwelling and upper ocean mixing [Yoder et al., 1993a]. Significant ocean color variability occurs also on the ocean submesoscale (0.5–10 km) and mesoscale (10–200 km), and theories about the physical and biological controls on such patchiness have a rich history [e.g., Steele, 1978; Okubo, 1980; Denman and Gargett, 1995]. In this regime, biological variability is a dynamic balance between local and regional generation processes and downscale turbulent eddy transfer of variability from large to small scale, where it is eventually dissipated [Mackas et al., 1985]. The biological signal can be modulated by physical processes either directly by turbulent advection and stirring [Abraham, 1998] or indirectly via impacts on phytoplankton growth rates and trophic interactions [Haury et al., 1978; Garçon et al., 2001]. However, the mesoscale biological and physical fields do not always map on to each other in a straightforward manner, the relationship differing from biological variable to variable [Yoder et al., 1993b; Mahadevan and Archer, 2000].
 From a global perspective, satellites provide the only feasible approach for mapping ocean surface chlorophyll at the required time and space scales to characterize mesoscale variability (see Yoder  for a recent review). Based on spectral analysis of LANDSAT surface reflectance images for example, Gower et al.  suggested that mesoscale phytoplankton patchiness is governed by physical advection. Denman and Abbott  and Denman and Abbott  used auto-spectra and cross-spectra analysis of CZCS and AVHRR sea surface temperature data off coastal California to demonstrate strong similarity in the characteristic biological and physical timescales. Qualitative and quantitative analysis of satellite ocean color and 1-D surface transects shows a similar correspondence for spatial variability [Yoder et al., 1987; Smith et al., 1988; Yoder et al., 1993b; Washburn et al., 1998; McGillicuddy et al., 2001]. These and other studies, however, have been conducted for small regions of the ocean and, for CZCS data in particular, restricted mostly to coastal environments.
 Using the semivariogram approach from geostatistics [Journel and Huijbregts, 1978], we calculate the mesoscale variance, the combination of subgrid scale noise and measurement error, and spatial decorrelation length scales globally for a full year of SeaWiFS ocean color data [McClain et al., 1998]. The spatial semivariogram, also-called the structure function in statistics [Yaglom, 1957] or meteorology [Gandin, 1963], provides a useful measure for quantifying biological-physical interactions and discriminating among theoretical models. It is also a necessary component of future work to objectively analyze ocean color images using methods such as kriging [e.g., Davis, 1986; Chelton and Schlax, 1991]. Spectral analysis is another common method for computing spatial scales from oceanographic data, but while quite powerful, spectral approaches have a number of drawbacks including problems with missing data (most of the spectral analyses discussed above were conducted on carefully chosen, cloud free images) and potential ambiguities over the interpretation of spectral slopes [e.g., Fasham, 1978]. Geostatistical techniques (or as discussed below closely related correlation analysis) provide less detailed information but should be more robust for typical geophysical data [Chelton and Schlax, 1991; Fuentes et al., 2000].
 A detailed description of the statistical techniques and preliminary results for a single month for the North Atlantic can be found in the work of Fuentes et al. . Here we present the more extensive full annual and global analysis, focusing on relating the observed patterns to underlying physical and biological processes. The SeaWiFS ocean color satellite data set used in this study and the necessary geostatistical tools are presented in section 2, covering the robust empirical semivariogram and semivariogram models. In section 3.1, we discuss in detail an example calculation of the semivariogram approach for a single 5° × 5° area. We then present the global patterns of ocean color mesoscale variability and spatial scales over an annual cycle (section 3.2) followed by a summary and discussion (section 4).
2. Data and Methods
2.1. SeaWiFS Ocean Color
 The Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean color instrument [Hooker and Esaias, 1993; McClain et al., 1998] provides near-global coverage every 2 days of upwelled radiance for eight spectral bands in the visible and near-infrared. Surface ocean chlorophyll concentrations (Chl mg m−3) are calculated from the ratios of different water-leaving visible bands using ground-truthed empirical algorithms [O'Reilly et al., 1998]. In addition to the required atmospheric corrections, pixels with land, clouds or heavy aerosol loading are removed prior to the calculation of surface chlorophyll. Continuous Global Area Coverage (GAC) data with a nominal resolution of 4 km × 4 km is subsampled from the raw 1 km × 1 km data and is stored aboard the spacecraft for later transmission to ground stations.
 Here we use Level 3 daily standard mapped images (reprocessing 2), which are projections of the GAC data onto a global, equal-angle grid (2π/2048) with a nominal 9 km × 9 km resolution. The most recent SeaWiFS data reprocessing (reprocessing 3, May 2000), completed after the bulk of our data analysis, incorporates a number of algorithmic and data processing changes that impact the large-scale SeaWiFS ocean color fields (e.g., revised vicarious calibration and atmospheric correction scheme, reduced number of pixels with negative water leaving radiances, downward adjustment of abnormally high chlorophyll concentrations in coastal environments, allowance of very low chlorophyll concentrations <0.01 mg m−3) [Robinson et al., 2000]. The third reprocessing, however, did not significantly affect the two most important issues with respect to small-scale variability, namely pixelization (or speckling) and cloud detection and masking [Robinson et al., 2000; Hu et al., 2000a, 2000b]. These problems, which are discussed at more length below with regards to the interpretation of our findings, will likely be addressed more directly in future SeaWiFS reprocessings.
 The natural log transformation is applied to the chlorophyll data:
following the arguments of Campbell  that oceanic bio-optical variability is distributed approximately lognormally. Monthly and annual geometric means of surface chlorophyll are computed as the arithmetic mean of the log-transformed data C(x, t). To avoid spurious effects in the semivariogram [Clark, 1979; Cressie, 1993], large-scale spatial trends are removed by subtracting monthly mean fields mon(x) smoothed with a moving two-dimensional 24 × 24 pixel spatial filter (equivalent to about 200 × 200 km scale at the equator or roughly 2° × 2°). The resulting lognormalized and detrended data:
are referred to as the daily anomalies. We also investigate the impact of using running time averages (still with a one month window) rather than monthly block time averages.
2.2. Semivariogram Analysis
 The semivariogram or structure function γ(v) measures the local spatial variation of geophysical data Z(x), describing how samples are related with vector distance v [Journel and Huijbregts, 1978]:
The semivariogram is closely related to the covariance function. In general, two neighboring points are more likely to have similar values than sample pairs farther apart. Thus the semivariogram (covariance) function will have low (high) values at small spatial lags, increasing (decreasing) with distance. Beyond some distance, the data points can often be assumed to be uncorrelated or independent, in which case the semivariogram approaches a uniform variance while the covariance function goes to zero.
 Because of clouds and other problems leading to incomplete spatial sampling, the ocean color semivariogram must be computed empirically [Matheron, 1971]. We use a robust (to contamination by outliers) semivariogram estimator proposed by Cressie and Hawkins :
where N(v) is the number of data points separated by vector distance v. In the robust estimator, the spatial difference is transformed into an approximate Gaussian form prior to computing the semivariances [see also Cressie, 1993; Fuentes et al., 2000].
 Semivariograms are computed numerically for each month of 1998 for 5° × 5° areas over the globe, the size chosen after some experimentation to minimize the spatial heterogeneity of the ocean color data while retaining sufficient spatial extent to resolve the full span of the mesoscale (10 km–200 km). For each day, the surface chlorophyll pixels (daily anomalies) within the box are sorted to find all possible combinations of valid data pairs in the zonal (E-W) and meridional (N-S) directions. Separate semivariograms versus distance (in km) are then calculated using equation (4) in the two directions to highlight anisotropy. A discretized version of equation (4) is used, with the approximate spatial bin size (nominally 9 km) differing with direction and latitude because of the equal angle grid. The daily semivariance estimates at each distance lag are then averaged over the month, weighted by the number of valid data pairs, to create the monthly semivariograms.
 Semivariograms are rarely used in their original form but rather are fit with simple statistical models to extract the desired information [Journel and Huijbregts, 1978], and we have chosen to use the spherical model: (v) =
because of its common use and simple interpretation [Clark, 1979]. An example is shown in Figure 1. The idealized spherical model has a (typically) small value near the origin set by the nugget c0, the unresolved, subscale variance and/or measurement error at zero lag. The semivariance then increases with distance out to the range r, at which point samples are essentially uncorrelated and the model curve plateaus at the value of the total sill σ2. A fourth parameter, the relative sill σrel2, can be defined as that part of the total variance resolved by the observations
and which is attributable to geophysical processes.
 For each 5° × 5° area, the spherical model is fit to the monthly semivariograms using a modified version of the Levenberg-Marquardt nonlinear least squaress regression [Press et al., 1992], and the model parameters (nugget, range, total and relative sill), estimated errors, and correlation coefficients are stored as final output. Before and during the nonlinear fit the semivariances are passed through a series of tests to remove the results from those 5° × 5° cells that appear either nongeostatistical and/or overly contaminated by noise. A minimum of 30 valid data pairs are required at each spatial lag, and at least 4 spatial lags must be represented in order to fit the model. The spherical model parameters are retained only if the Levenberg-Marquardt method converges, the correlation coefficient has a statistical significance level greater than 95%, and the fit parameters do not imply any nongeostatistical results (total sill less than nugget, negative range, negative nugget). As a final test, the relative standard deviations of each model parameter must be less than 200% and the range not exceed the size of the 5° cell. In certain cases the above fit is performed while forcing the nugget to be zero; this is done when all other tests were positive except the negative nugget restriction.
 The variance, empirical semivariogram, and model values in Figure 1 and throughout the remainder of the paper are translated back into coefficients of variation in geophysical (rather than lognormalized) space (mg Chl m−3), i.e., the standard deviations divided by the means. The coefficient of variation has several desirable qualities for ocean color. In particular if the variability scales with the mean, as might be expected at least roughly on theoretical and empirical grounds [Campbell, 1995], then the coefficient of variation will be approximately uniform even over large variations in the mean surface ocean chlorophyll concentration. For a log-transformed variable this is equivalent to a constant standard deviation. Deviations from this general relationship due to either oceanographic or instrumental sources can then be examined unobscured by the large dynamic range of ocean color.
3.1. Example Calculation
 To better illustrate the semivariogram structure function approach, we first discuss in detail the results for an example 5° × 5° area. Figure 2a displays the smoothed, monthly geometric mean SeaWiFS chlorophyll composite for June 1998 over a region of the South Pacific with relatively low mean chlorophyll concentrations. The coverage from a single day for the region is shown in Figure 2b. The 5° × 5° area bounded by 105–110°W by 30–35°S used in the analysis is outlined in the figure. The monthly composite data show large-scale trends associated with the edge of the subtropical gyre. As demonstrated by the individual daily image, cloud contamination and orbital sampling constraints would complicate traditional spatial structural analysis techniques such as spectral analysis. Mesoscale features are evident in the daily image but with considerable background noise, much of it associated with cloud-ocean transitions. In fact, this 5° × 5° box is chosen because of its high noise level to highlight the ability of the robust semivariogram technique to extract information under poor data collection conditions. The distribution of the daily chlorophyll values over the month is approximately Gaussian once the log-transform is applied (not shown), consistent with previous findings [Campbell, 1995] and supporting our normalization procedure.
 The monthly east-west semivariogram for the 5° × 5° area is shown in Figure 1. Although there is considerable scatter in the individual daily semivariance estimates at any particular distance (not shown) [Fuentes et al., 2000], the monthly semivariogram follows a well-defined curve that is closely approximated by the spherical model (r2 = 0.957). The estimated values for the model parameters are range 150 km, nugget 0.22, total sill 0.31, and relative sill 0.09. The nonlinear regression routine provides estimates of the error in these parameters, but since the semivariances themselves are not statistically independent these error estimates are likely overestimates and not reported here. The high nugget relative to the partial sill suggests that the unresolved variance at this location is quite large, and as discussed below is associated with subgrid scale processes, instrument noise, and algorithmic uncertainties. The behavior of the semivariogram at short spatial lags (roughly <20 km in Figure 1) is not as well characterized as one perhaps would wish from the global Level 3 data (nominal resolution of 9 km), and the estimated nugget is sensitive to the fit through one or two data points near the origin.
 The mesoscale variability for the 5° × 5° area shows a directional anisotropy, with the estimated range in the north-south direction being 230 km (versus 150 km E-W). The total sill parameter (partial sill plus nugget) is approximately the same in each direction (E-W 0.31 versus N-S: 0.35) as is the nugget (0.22 in both directions). Directional anisotropy in the mesoscale variability can arise because of spatial orientation in the physical flow and turbulence fields and/or biological gradients associated with, for example, the equatorial waveguide, western boundary currents, coastal currents and upwelling. Alternatively, it could arise because of methodological issues. For example, the gradient in the large-scale chlorophyll field for this region is also oriented approximately north-south, and the larger range calculated in that direction may reflect a partial aliasing of the nonstationarity in the mean, despite the removal of the smoothed monthly field.
3.2. Variance, Relative Sill, and Nugget
 Turning to the global distributions, one of the goals of our research is to see whether we can relate the spatial structure function of ocean chlorophyll mesoscale variability to patterns of physical and biological variables. The global annual geometric mean SeaWiFS ocean color distribution for 1998 (Figure 3a) shows quite clearly the large-scale patterns of ocean biomass: low levels in the convergent subtropical gyres; higher concentrations in the coastal upwelling regions and subpolar latitudes of the North Atlantic and western North Pacific; and intermediate levels in the high nitrate-low chlorophyll regions of the Equatorial Pacific and Southern Ocean. Note also the large variations in open-ocean surface chlorophyll concentration spanned by the standard logarithmic color bar, covering almost two orders of magnitude in the open ocean.
 The second panel in Figure 3 shows the total coefficient of variation (or relative standard deviation) of the daily level 3 SeaWiFS ocean color data C(x, t) about the geometric mean in Figure 3a. The total coefficient of variation varies over a wide range, from a minimum of 0.3–0.5 (30–50%) in some oligotrophic areas to greater than 1.0 (100%) in coastal upwelling and high latitude bloom regions. Elevated relative variability (>0.6) is also observed along frontal boundaries (e.g., Equatorial Pacific, subpolar/subtropical transitions) and in regions of large ocean color seasonality (e.g., Arabian Sea, subpolar North Atlantic) [Yoder et al., 1993a].
 The coefficient of variation of the daily anomalies Canom(x, t) (Figure 3c), by contrast, is generally more uniform over the open ocean, with values of about 0.3–0.5 (30–50%) except for coastal, localized high latitude, and (as discussed below) some very oligotrophic (e.g., eastern South Pacific) regions. Since the large-scale seasonal cycle is removed in the creation of the daily anomalies by subtracting the smoothed monthly means (equation (2)), Figure 3c quantifies only the contribution of variability occurring on timescales of less than one month and spatial scales of less than 2°, which we attribute to mesoscale processes (plus unresolved noise and submesoscale effects). The approximate uniformity of the coefficient of variation of the daily anomalies over much of the ocean demonstrates that submonthly, mesoscale ocean color variability is approximately (but not linearly as shown below) proportional to the total amount chlorophyll present.
 The annual surface chlorophyll variance (power) is simply equal to the square of the annual standard deviations of the daily data. The fraction associated with submonthly (mesoscale) variability can be found as the ratio of the daily anomaly standard deviations squared divided by the total variance. The remainder is the fraction due to processes on timescales greater than a month, which would include the seasonal cycle and aliased inter-annual variability such as the 1997–1998 El Niño. The submonthly signal displayed in Figure 4b dominates in the oligotrophic gyres but is a much smaller fraction (30–40%) of the overall variance in the subpolar gyres, Arabian Sea, Equatorial Pacific and subtropical/subpolar transition regions noted above.
 In regions of strong seasonality, the computation of the daily anomalies using smoothed, block monthly means could potentially introduce problems with the temporal scale separation in Figures 3 and 4. For example if the mean chlorophyll concentration changed rapidly over the month, the daily anomalies from the block monthly means would be too large or small at the beginning and end of the month leading to an overestimate of the submonthly variance. To explore this effect, we have recomputed the daily anomalies using smoothed, sliding (one month window) time averages. The coefficients of variation of the daily anomalies are almost identical except for high latitudes in the summer season, where the block average is biased somewhat higher (not shown). However, the general spatial patterns for the two techniques are nearly identical, with elevated high latitude variability in the sliding mean case as well. Further, the semivariance estimator (equation (4)) is applied only to differences within daily images and is thus insensitive to mean offsets in the daily anomaly fields (which would, however, get aliased into the block time mean variance estimate), as would occur as the chlorophyll over the whole 5° × 5° block rose and fell with the seasonal cycle.
 The results of the semivariogram analysis for the 1998 SeaWiFS data are presented as annual mean maps of the monthly range, relative sill, and nugget parameter values for the east-west (Figure 5) and north-south (Figure 6) directions. The semivariogram technique further partitions the submonthly variability in the daily anomalies (Figure 3c) into resolved mesoscale (relative sill) and unresolved/noise (nugget) components. The relative sill values (Figures 5b and 6b) in the subtropics and tropics are approximately uniform and relatively low (about 0.1–0.2). Moderately larger values are observed in a band across the Equatorial Pacific and in the subpolar gyres while high values are observed along the coasts (particularly in coastal upwelling regimes) and at high latitudes. Little directional anisotropy is found in the relative sill between the east-west and north-south semivariograms except at high latitudes where the east-west relative sill is somewhat larger with a corresponding decrease in the unresolved nugget component.
 The patterns of submonthly biological variability [total (Figure 3c) and resolved mesoscale (Figures 5b and 6b)] can be compared with the satellite altimeter derived eddy kinetic energy estimates of Stammer  (Figure 7). The major signals in the eddy kinetic energy maps are in the western boundary currents and Antarctic Circumpolar Current. Note that the equatorial signal in eddy kinetic energy is strongly damped due to a weighting by the sin2(latitude) to avoid the equatorial singularity in the geostrophic kinetic energy. The striking east-west asymmetries in eddy kinetic energy are much less evident in the ocean color fields. Elevated daily anomaly coefficients of variation and relative sill values are associated with the tracks of the Gulf Stream, Kuroshio, Aghulus, Brazil-Malvinas convergence, North Brazil Current, and Antarctic Circumpolar Current, but the maximum biological signal is more concentrated near the coasts compared with eddy kinetic energy. Note also that the 5° × 5° boxes used in the semivariogram analysis tends to spread the narrow, coastal variability maxima, clearly observed in the daily anomaly coefficients of variation (Figure 3c), into the interior.
 A scatterplot of the coefficient of variation of the east-west relative sill versus the mean chlorophyll concentration (Figure 8a) shows essentially similar findings: low and uniform relative sills for annual mean chlorophyll concentrations less than 0.1 mg Chl m−3 growing in an approximate linear fashion with ln(Chl) above that value. High latitude cells (poleward of 60°) are separated out in Figure 8a because of potential sampling and SeaWiFS data processing issues (e.g., low Sun angle, sea-ice, cloud cover, seasonal bias, Level 3 bin aspect ratio). Although the polar relative sill values are generally high, likely due to summer season bias and more coastal values, they show generally the same relationship to mean chlorophyll data. Our current conclusion is that the large relative sills at high latitude are likely real, though the same cannot be said as definitively for the directional anisotropy implied by the different sill values in the east-west and north-south directions.
 The spatial patterns of the annual mean nugget or unresolved variance (Figure 5c and 6c) are opposite to that of the relative sill, high in the subtropics and low at mid- to high latitude. As demonstrated by a scatterplot against annual mean chlorophyll (Figure 8b), the nugget coefficient of variation is inversely correlated with ln(Chl) at low chlorophyll levels, and in fact, for mean chlorophyll values less than 0.1 mg m−3 the nugget generally exceeds the relative sill. At higher mean chlorophyll levels, the nugget coefficient of variation does not show a trend with the chlorophyll concentration and is typically less than 0.15. Based on Figure 8b, a very simple model for the absolute value of the spatially unresolved variability in the SeaWiFS data then could be expressed as a background variability source together with an additional component proportional to the mean chlorophyll concentration. The background process becomes more dominant at very low chlorophyll values leading to the observed inverse correlation.
 The nugget quantifies the point variability in the derived SeaWiFS chlorophyll product, and at least three sources of small-scale variability need to be considered: real geophysical variability in the water leaving radiances, instrument noise, and noise due to atmospheric corrections and other algorithmic issues. The effective cut-off between the resolved and unresolved oceanographic signal with the semivariogram technique is roughly one spatial lag or nominally 9 km for the level 3 standard mapped images. A significant fraction of submesoscale variability, therefore, will be partitioned into the nugget. Pixelization or speckling of SeaWiFS chlorophyll images is also known to arise from the atmospheric aerosol model due to digitization and other noise sources in the near-infrared bands [Hu et al., 2000a, 2000b]. Based on the spatial resolution of the Level 3 data alone, we can not distinguish between instrument/algorithmic noise and submesoscale processes. But the nugget-chlorophyll relationship in oligotrophic waters (Figure 8b) is consistent with a significant algorithmic noise contribution as found by other studies and with visual inspection of individual images, which show for example satellite memory effects at open ocean/cloud transitions (Figure 2b).
3.3. Spatial Length Scale
 The east-west spatial range field (Figure 5a) exhibits a strong, banded latitudinal pattern with maximal values of 250–300 km along the Equator, decreasing poleward to less than 50 km near the poles. The equatorial north-south ranges are somewhat lower than the east-west values and tend to be more uniform from the equator to midlatitudes before again decreasing toward the poles (Figure 6a). The zonal averages of the east-west and north-south ranges are summarized in Figure 9. Regionally, somewhat larger zonal spatial ranges are found in the western North Atlantic than in the east (Figure 5a), the opposite to the trend reported by Fuentes et al.  from a single latitude band and single month. The asymmetry could reflect longer zonal spatial scales of Gulf Stream meanders but is not as clearly defined for the other western boundary currents. The coastal upwelling regions (e.g., Benguela current, California Current, Peru), which show large mesoscale variability, are notable exceptions to the overall latitudinal range patterns, with markedly smaller ranges in both the east-west and north-south directions. The time/space space scales in these upwelling regions are shorter, often associated with sharp offshore gradients and episodic upwelling jets and filaments [Abbott and Zion, 1987].
 Some directional anisotropy in the ranges is expected especially in the tropical upwelling regions. A particularly striking example is the zonally elongated, wave-like structures in ocean color associated with the phytoplankton bloom that occurred in June 1998 following the transition to La Niña conditions in the equatorial Pacific [Murtugudde et al., 1999]. The differences between the two directional range estimates also could be in part methodological. For example, the SeaWiFS equal angle L3m data grid size decreases with the cosine of latitude in the east-west direction while the north-south resolution remains constant with latitude. If the spatial scales of ocean color variability also decrease toward the poles, as argued below, the north-south range estimates may under resolve the mesoscale variability and thus overestimate the actual oceanographic scale lengths. The original binned data product, while using equal area grid cells, offers other computational difficulties. Further problems may arise because away from the coasts the main spatial gradients in chlorophyll are approximately north-south, and errors in removal of the large-scale spatial trends can be aliased into the semivariogram range estimate, also tending to produce range estimates that are too large [Fuentes et al., 2000]. Therefore we assign more confidence to the east-west range estimates at higher latitudes.
Figure 9 presents zonally averaged, spatial-scale estimates for mesoscale physical variability from Stammer  based on along-track, autocorrelation analysis of the TOPEX/Poseidon satellite altimetry. The altimeter results are comparable to a number of other physical estimates including analyses of high-resolution, eddy-resolving numerical simulations [Smith et al., 2000] and spatial length scales computed from Advanced Very High Resolution Radiometer (AVHRR) sea-surface temperature imagery [e.g., Krauss et al., 1990]. All of these studies show that physical eddy spatial scales outside the tropics vary roughly proportional (though not identical) to the Rossby deformation radius, the horizontal scale where rotation becomes important relative to buoyancy and a key parameter governing turbulent ocean flow [Chelton et al., 1998]. This finding has been argued as support for the hypothesis that the baroclinic instability of the density field is the primary process driving mesoscale eddy formation. The similarity of the spatial scales derived from ocean color (particularly in the east-west direction) and altimetry in both magnitude and meridional trends in Figure 9 suggests that baroclinic instability may also be a dominant factor in structuring the biological fields.
4. Summary and Discussion
 Our analysis of the mesoscale variability of global SeaWiFS ocean color data shows a number of coherent geographical patterns across a wide range of biological and physical environments. Submonthly, small spatial-scale variance dominates ocean color variability in oligotrophic regimes and is about a third of the total variance even in regions with strong seasonality. When normalized to the mean chlorophyll as a coefficient of variation, the resolved mesoscale variance (relative sill) is approximately uniform in the open-ocean tropics and subtropics (0.1–0.2), increasing to 0.3–1.0 in western boundary current, upwelling (Equatorial Pacific, coastal) and subpolar/polar regions, approximately scaling with the mean chlorophyll concentration. The strong west-east asymmetry found in physical eddy kinetic energy estimates is less apparent in ocean color mesoscale variability estimates. The unresolved variance (nugget), which includes submesoscale geophysical variability as well as instrument/algorithm noise, is inversely correlated with mean chlorophyll concentration in the oligotrophic subtropics reducing to a low background value (0.1) elsewhere. The large contribution of unresolved “noise” in the oligotrophic gyres is consistent with speckling or pixelization due algorithmic noise [Hu et al., 2000a, 2000b]. The mesoscale spatial scale (range) is approximately zonal, with values of 200–350 km near the Equator to less than 50 km close to the poles similar to the physical scales estimated from altimeter sea surface height variability data and the first baroclinic Rossby deformation radius. Regional deviations from these large-scale variance and spatial length scales trends, for example lower range and higher resolved variance in coastal upwelling regimes, are explicable by the characteristics of the biological-physical interaction in those environments.
 Quantifying the ocean color mesoscale structure function has a number of practical applications. First, quantifying the structure function is fundamental for any time/space objective analysis of the ocean color data set, a serious issue given the amount of missing data due to cloud cover etc. As demonstrated by Chelton and Schlax , optimal (unbiased) time averages of a series of satellite images could only be accomplished by using a priori knowledge of the variance and correlation (structure) functions of the satellite signal. Second and related, the information inherent in a structure function is required in order to create the cost function (weighting of model data misfit) for data assimilation [U.S. Joint Global Ocean Flux Study (JGOFS), 1992]. Third, the variance and spatial range estimates provide key constraints for the emerging field of basin (and soon global) eddy resolving ecosystem simulations [e.g., Oschlies and Garçon, 1998]. Much as satellite altimeter sea surface height variability has done for physical models [Smith et al., 2000], maps of mesoscale ocean color statistics will highlight the deficiencies of current generation models and spur improvements (either in biological parameterizations and/or spatial resolution). Validated physical fields and eddy statistics likely may be a necessary but not sufficient condition for accurate biological dynamics (e.g., if significant nutrient input is occurring at the submesoscale).
 Further work is needed in a number of areas to clarify some of the questions raised here. Our results demonstrate the global generality of previous local and regional findings that small-scale variability in ocean biology and physics occurs on comparable spatial length scales. The semivariogram technique does not address directly, however, the causality of how physical mesoscale turbulence may govern biological spatial scales. Two avenues to explore are cross-correlation studies of high spatial resolution sea surface height, sea surface temperature, and ocean color data and eddy resolving coupled biological-physical models.
 The behavior of the ocean color semivariogram at short spatial lags (<15 km) is not well characterized using the GAC Level-3 standard mapped images product, and thus we cannot clearly separate the effects of submesoscale variability from instrumental and algorithm noise. For that, we will have to turn to the higher resolution Local Area Coverage (LAC) data at the full SeaWiFS nominal resolution of 1 km × 1 km or alternatively the high resolution MODIS data. The SeaWiFS LAC data is available only regionally, and the objective would be to extrapolate to global scale by examining the higher resolution data for a number of specific environments. Plans are also underway in future SeaWiFS data reprocessings to reduce speckling in the chlorophyll data by, for example, spatially smoothing the near-infrared data and/or aerosol model output and modifying the cloud masking scheme.
 The response of mesoscale signal in ocean color to the seasonal cycle and interannual variability needs to be explored in more detail. Analysis of individual months shows to first order the same large-scale patterns as the annual mean figures, though with increased noise in the monthly semivariogram parameter fields. The longer, multiyear record now available would allow for separate estimates to be made for each season. Also, a transition from strong El Niño to La Ninã conditions occurred in 1998, and it would be useful to examine how the magnitude and distribution of small-scale variability changes from year to year.
 Finally, our treatment here neglects any discussion of the temporal correlation scales. The Eulerian temporal decorrelation timescale has as much to do with the rates of physical circulation as biological processes [Denman and Abbott, 1994]. But combined with Lagrangian decorrelation timescales computed from drifters [e.g., Abbott et al., 1995; Abbott and Letelier, 1998], the satellite timescale data will certainly be useful.
 A number of colleagues have contributed to this paper through comments and discussions over the last several years. In particular, we would like to thank T. Hoar, I. Lima, D. McGillicuddy, J. K. Moore, D. Nychka, and D. Siegel. We also extend especially thanks to D. Stammer for providing results from his analysis of the TOPEX/Poseidon satellite altimeter data set. M. Fuentes acknowledges the support of the NCAR Geophysical Statistics Project, and S. Doney and D. Glover are supported in part by NASA SeaWiFS Grants W-19,223 and NAG-5-6456. This work would not be possible without the dedicated efforts of the NASA SeaWiFS project team (http://seawifs.gsfc.nasa.gov/SEAWIFS.html). Ocean color data used in this study were produced by the SeaWiFS Project at Goddard Space Flight Center. The data were obtained from the Goddard Distributed Active Archive Center. Use of this data is in accord with the SeaWiFS Research Data Use Terms and Conditions Agreement. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This is WHOI contribution no. 10861.