Emergent patterns of patchiness differ between physical and planktonic properties in the ocean

Domain: earth_science
Published: 2025-02-20
Editorial outcome: major_revision

Abstract
While a rich history of patchiness research has explored spatial structure in the ocean, there is no consensus over the controls on biological patchiness and how physical-ecological-biogeochemical processes and patchiness relate. The prevailing thought is that physics structures biology, but this has not been tested at basin scale with consistent in situ measurements. Here we use the slope of the relationship between variance vs spatial scale to quantify patchiness and ~650,000 nearly continuous (dx ~200 m) measurements - representing the Atlantic, Pacific, and Southern Oceans - and find that patchiness of biological parameters and physical parameters are uncorrelated. We show variance slope is an emergent property with unique patterns in biogeochemical properties distinct from physical tracers, yet correlated with other biological tracers. These results provide context for decades of observations with different interpretations, suggest the use of spatial tests of biogeochemical model parameterizations, and open the way for studies into processes regulating the observed patterns.

Introduction
Most phytoplankton species near the ocean’s surface have a doubling time on the order of a day1. This rapid doubling time means phytoplankton quickly respond to changes in external forcings2. Coupled with the dynamic physical nature of the marine environment and grazing pressures with resulting loss rates similar to growth rates for phytoplankton3,4, the ocean has considerable spatial heterogeneity, or patchiness, at all scales5–8. This spatial heterogeneity supports increased diversity by creating different environmental conditions within close proximity, ecosystem stability through diversity and maintenance of seed populations, and efficient transfer of carbon up trophic levels9. The link between patchiness and the efficient transfer of carbon in the marine ecosystem is largely due to dense aggregations that make it energy efficient for zooplankton to graze, and patches of zooplankton make it feasible for planktivorous fish to meet their own energy requirements10–12. This spatial variability of phytoplankton and zooplankton, and the generally increasing patchiness as one moves up the trophic chain, has important implications for food availability and productivity of the entire ocean food web13–15.

The spatial patterns of the plankton ecosystem and their drivers have long been investigated. An early outline by Hutchinson discusses nutrient and temperature gradients, stochastic events such as storms, intra-species signaling, competition, and predation among processes that likely control these plankton patterns16. An updated synthesis by Levin described pattern and scale as the central problem in ecology, arguing for cross-scale investigations to understand the mechanisms and consequences of marine patchiness5. The scale-dependent spatial heterogeneity exhibited by both biology and physics has been a central focus of studies into pattern and scale in the ocean6, with much of this work attempting to divide spatial scales into domains of scale-independence and then investigating the dominant processes influencing biology in those domains17,18. Power spectral analysis, a Fourier decomposition where variance is partitioned into the contribution of bands of specific frequencies or wavenumbers (see19 for an early review on the implementation of the technique in ecology), is often used to describe phytoplankton patchiness and quantify this scale-dependence. The scaling behavior of a geophysical variable is typically represented as a log-log plot of variance against length scale. If that relationship is approximately linear (in log space) this represents a power law relation between variance and spatial scale where the exponent of that power law relationship is referred to as ‘the spectral slope’20. A flatter spectral slope indicates less of a decrease of variance with scale, i.e. more variability at smaller scales relative to larger scales, when compared to a steeper slope. Spectral slope has often been used synonymously with patchiness, but can also be interpreted as the cascade of variance across scales. While there are a range of issues with this analysis, such as discarding of phase information9,21, it is commonly used as an indicator of the distribution of spatial variance.

There is over a century of inquiry into the spatial heterogeneity of ocean physics. Energy in the ocean generally cascades down spatial scales. Mesoscale eddies spin off of large-scale circulation features. Energy then transfers from these major eddies to smaller turbulent whorls and finally to a small enough scale that energy is dissipated by viscosity into heat22–24. This turbulent cascade generally has a spectral slope of -5/3 in the inertial subrange (3D and a spatial range smaller than the major energy containing eddies, but larger than viscous eddies). While Kolomogrov initially proposed this cascade of variance for fully developed 3D turbulence in the ocean’s inertial subrange, O(10-0.001) meters depending on flow characteristics25, the -5/3 spectral slope has been shown to hold generally true for the inertial subrange of 2D ocean turbulence O(100-1) km as well26. Temperature generally follows the same cascade as turbulent kinetic energy. It has a source of variance at large scales, a dissipation of variance at small scales, and it is typically being mixed by similar turbulent processes27, though could have a variance source at small scales such as spatially heterogenous upwelling of cooler water.

The patchiness of phytoplankton was initially thought to be linked to turbulent stirring simply by physical processes28, with a general conclusion of consistent scaling behavior between physical and biological features18. This conclusion was drawn largely from its spectral slope that appeared similar to the -5/3 of 2D turbulence28,29. Modeling studies indicated that the spectral slope of phytoplankton was also influenced by the phytoplankton reproductive rate, diagnosed by a scaling break at larger spatial scales where the spectral slope became flatter than that of a passive tracer30,31. This led to a substantial amount of work, with many conflicting results, investigating the time and length scales where the contribution of biologically generated spatial variability (growth rates, grazing, etc) to the total planktonic spatial variability is significant vs where physics dominates6,7,9,25,32.

Abraham7 suggested, and others have come to a similar conclusion via modeling33, that the spatial patterns in both plankton and physical tracers are a product of the timescales of their response to physically driven changes. For example, the equilibration of temperature to a heat flux is considerably slower than the response of phytoplankton to a nutrient flux. A small burst of cold nutrient-rich water thus leads to increased spatial heterogeneity in chlorophyll-a (chl-a) vs temperature, but as nutrients are exhausted and the temperature equilibrates over time the patchiness in chl-a and temperature would return to covarying32. Modeling work shows a steeper spectral slope in temperature compared to chl-a, attributing some of the slope variability to low frequency physical variations and the correlation of physical and biological variables to “the dominant role of physics in the spatial variability of plankton distribution“34.

Despite these theoretical advances, interpretations from observational studies remain inconsistent. Some work concludes that at <1 km scales biological processes are important for patch dynamics10,35, while other studies assert that at this scale spatial distributions of phytoplankton are dominated by turbulent diffusion. For example, this latter conclusion is advanced by an investigation that found a strong correlation between chl-a and temperature patchiness at scales below 5 km yet no correlation at scales from 5 km to 80 km19. Instances spring up where phytoplankton are patchier than zooplankton36, conflicting findings that the patchiness of phytoplankton is between that of zooplankton and physical factors7,15,28. Work assessing the spectral slope of chl-a in the same region for multiple years found variable slopes from month to month25,37. After decades of work, it is not clear at which spatiotemporal scales biological processes are important, or even which processes are dominant in controlling patchiness in the ocean.

While biophysical ocean patchiness has been relatively well documented on local scales, its characteristics across the globe have not yet been analyzed. Therefore, there is little data to test new theories, constrain impacts on productivity and diversity, and simply describe the patchiness itself. Importantly, this limits our ability to parameterize global biogeochemical models that are computationally limited from explicitly modeling these scales in our global models of the carbon cycle.

Here we address this gap, and explore the global characteristics of biophysical patchiness using a unique dataset of in situ surface plankton-related optical properties from the S/V Tara program. All data comes from the Tara Pacific38 and Tara Microbiome missions which represent five years of observations spanning the Atlantic, Pacific, and Southern Oceans. This data was collected and processed consistently. After conservative quality control this dataset amounts to N=661,552 (dt=1 minute, dx~200 m) measurements used in this analysis (Fig. 1). As we aim to discern between patterns of physical and biological patchiness, and specifically to test if patchiness in biology is explained by patchiness in physics, the measurements are divided into two corresponding groups of variables, with the physical domain being represented by temperature, salinity and density, and the biological domain by chl-a, particulate attenuation of light at 443 nm (cp(443)), and an optical proxy for mean particle size (γ)39. The latter two, because they represent other living (e.g. bacteria and micro-grazers) and non-living particles in addition to phytoplankton, are referred to as biogeochemical properties.

Results
While the Fourier-based spectral slope is a useful and commonly used tool for characterization of patchiness, it is not suitable for analyzing unevenly sampled datasets. To overcome this limitation here we quantify patchiness via the dependence of the variance, V, on length scale, L following33. As found in previous work, V varies mostly linearly with L in log space (Fig. 2), indicating a power law relationship of the form: (1) V=LΓ, where Γ describes the slope (exponent) of the relationship in log space. In this work we focus on Γ, the “variance slope”. As with a power spectral density slope, a transect with a lower Γ would have relatively more variance retained at smaller length scales relative to larger scales compared to a transect with higher Γ, i.e. a lower Γ is patchier. This metric can be thought of qualitatively as a ratio of large scale to small-scale variance (Figure S1), with Γ increasing as the large-scale variance increasingly dominates the small. This parameter is similar and strongly correlated with the conventional Fourier-based spectral slope exponent (Figures S2 and S3), but our approach (from33) has the advantage of being applicable to data with gaps, as long as they are smaller than 20% of a transect. This parameter is non-parametric and the value is the same for a transect before and after a log-transformation, allowing robust comparison between values like chlorophyll-a, which is often log-distributed40, and values like temperature and salinity. Based on the observed relationship between Γ and the power spectral density slope (Figure S3) the classic -5/3 slope found in previous studies for the inertial subrange would correspond to a Γ value of 0.84.

Specifically in this work, variance was calculated on subsets of 500 samples over a set of 11 log-distributed windows from 3 to 500 samples, spanning ~0.6 km to 100 km. Both variance and window size were log-transformed, and we ran a least-squares fit to find the slope of this line, yielding the Γ of V=LΓ. In our analysis of global patterns of oceanic patchiness, we distinguish between Γ of the biological and biogeochemical variables chl-a, cp(443) and γ (Γchl-a, Γcp(443) and Γγ, respectively), and of the physical variables temperature, salinity and density (Γtemperature, Γsalinity and Γdensity, respectively).

Comparison between the geographic distributions of Γchl-a and Γtemperature reveals distinct differences between global patterns of physical and biological patchiness (Fig. 3). Notably, the geographic distributions of Γtemperature are more random with lower autocorrelation compared to Γchl-a at all spatial lags, while Γchl-a is consistently lower in oligotrophic regions, particularly the subtropical gyres, and higher in physically energetic regions such as western boundary currents, eastern boundary upwelling zones, and equatorial upwelling zones. In agreement with most previous observations, Γchl-a is, on average, lower than Γtemperature, indicating chl-a is patchier than temperature, though there are exceptions, particularly in some coastal regions (Figure S4). Γtemperature is fairly normally distributed around 1, while Γchl-a is slightly right-skewed with a mean around 0.5 (see inserts in Fig. 3). The -5/3 slope found in previous studies for the inertial subrange corresponds to a Γ value of 0.84 which is near, but slightly lower than the mean of our global Γtemperature calculations, 0.97.

Interestingly, running the same analysis on satellite-based chl-a and temperature reveals contradicting results. Although satellite imagery has been successfully used to track individual chl-a patches41,42, and to quantify patchiness at local scales28, in the satellite-based analysis we find Γtemperature is lower than Γchl-a (i.e. the opposite of our in situ results), and the geographic patterns for both chl-a and temperature are different (Figures S5 and S6, respectively). We attribute this discrepancy primarily to issues of measurement sensitivity and atmospheric correction of ocean color remote sensing (from which chl-a is derived) which is applied as a pixel level correction, artificially injecting variance at small scales. This effect is likely to have the strongest impact in oligotrophic regions, where chlorophyll-a levels are particularly low, resulting in minimal absorption and reduced particulate scattering, and thus a low signal to noise ratio in the satellite retrieval. This could cause issues in both spatial and temporal analyzes43. This corroborates results from previous work that used a semivariogram approach to analyze variance in global satellite chl-a patterns from SeaWIFS44 which showed that unresolved variance was negatively correlated with mean chl-a and the authors suggested the high fraction of unresolved variance in the subtropical gyres might stem from atmospheric correction, though they did not differentiate between instrument noise and submesoscale variability. A more recent, but similar study compared the unresolved variance between MODIS-Aqua and SeaWIFS and found it was reduced, but not eliminated with MODIS45.

The global patterns we observe point to a difference between the governing processes underlying the formation of physical and biological ocean patchiness. This is emphasized when plotting the correlation between the different types of patchiness (Fig. 4), which we show both for all individual legs and averaged by Longhurst provinces, a partition of the global ocean into biogeochemical regions46 (shown in Fig. 5). The Γ of biological variables are correlated globally, even between chl-a and γ, the mean particle size (Fig. 4a, b). Similarly, Γ of physical variables are well correlated with each other (Fig. 4c, d). Yet, there is little to no correlation between the Γ of biological variables and physical variables (Fig. 4e, f). This suggests that plankton patchiness is an emergent property due to biological processes that modulate the spatial patterns across scales sufficiently such that it is not correlated to the concurrent physical patchiness. Emergent is defined here as a property that emerges from the ensemble of processes in the ecosystem and environment.

If we decrease the top-end length scale that is used for the calculation of Γ, for example from 100 km to 5 km, Γchl-a and Γtemperature are still uncorrelated (R2=0.04 for 0.6 km to 5 km vs R2=0.02 for 0.6 km to 100 km). This is in contrast with older work which showed that chl-a and temperature patchiness were correlated below 5 km yet not at scales from 5 km to 80 km19.

Similarly to the differences between geographic distributions patterns (Figs. 1 and 3) the correlations between Γ of different physical variables differ substantially from the correlations between absolute values (Figure S7). We show chl-a and γ have minimal correlation in absolute value yet a correlation in Γ (R2 of 0.03 and 0.42 respectively), chl-a and temperature have a strong correlation in absolute value yet minimal in Γ (R2 of 0.36 and 0.02 respectively), and temperature and salinity have minimal correlation in absolute value yet a correlation in Γ (R2 of 0.04 and 0.25 respectively).

Another fundamental difference between patterns of physical and biological ocean patchiness emerges when looking at the data averaged by biogeochemical provinces and plotting the relationship between Γ and the absolute value of each variable (Fig. 6). The biological variables that are concentration dependent (i.e. chl-a and cp(443)) have a positive relationship between their Γ and their absolute value, such that high biomass provinces are less patchy (i.e. associated with higher Γ) than low biomass provinces, (Fig. 6a–c). In contrast, there is no relationship between Γ and the absolute value of the physical variables (Fig. 6d, e). In other words, biomass and biological patchiness are linked (inversely) while heat and salt content does not correlate with their patchiness.

The linkage between biological patchiness and biological productivity is emphasized when taking into account nutrient availability and oxygen saturation averaged by Longhurst Province (Fig. 7). When mapped onto the absolute value of chl-a and Γchl-a, a range of nutrients have a clear increasing relationship with both (Fig. 7), with the highest nutrient values also having high chl-a and Γchl-a. Oxygen saturation has a slight decreasing relationship with more considerable outliers.

The nature of the small-scale variability in biological signals, and the way they differ from the physical signals, is emphasized when zooming in on segments of the transects (Fig. 8). Careful examination reveals that our underway observations of biological variables are characterized by high frequency changes that do not appear in the physical signals. While these high frequency changes may appear to be associated with instrumental noise, the individual measurements are robust, and the changes reflect small scale (<1 km) biological variability patterns (Fig. 8). This robustness can be seen both in the covariation between different sensors (Fig. 8a) and the raw but consistent absorption and attenuation spectra (Fig. 8b, c). This small-scale variability lowers Γ and can make the variance spectra nearly flat in regions without low frequency variation, such as the Sargasso Sea and Subtropical South Pacific.

Our work does not tie the variance slope to any particular process. Possibly Γ represents the integrated impact of physical and biogeochemical characteristics within a region. The lower Γchl-a in oligotrophic regions may be attributed to a sustained injection of variance from ecosystem interactions (e.g. growth, grazing). To investigate this line of thinking we quantified the patchiness of chromophoric dissolved organic matter (CDOM), which can be thought of as a more passive tracer than chl-a and a slow integrator of biological growth products. ΓCDOM appears to be intermediate with a small amount of variance explained by Γchl-a and Γtemperature (R2 of 0.17 and 0.06 respectively) and a statistical distribution closer to that of Γtemperature (Figure S8).

Recent work investigating zooplankton patchiness found coherent small-scale patches across many taxa dominated by length scales of 10-30 m43 and even highly idealized models have been shown to generate patchiness via grazing47 which could help explain aspects of our results. While previous work using this same metric suggested that the response time of phytoplankton (i.e. growth rate) is faster than the response time of temperature (i.e. equilibration time) as the reason chl-a is patchier33, this doesn’t agree with our results, where the regions with higher assumed growth rates are less patchy (e.g. eastern upwelling zones). This may suggest that certain elements of the ecosystem are responding faster in these highly patchy oligotrophic regions, possibly grazers or growth following fine-scale vertical nutrient fluxes. Stratification may play a role with a more stratified water column leading to more intermittent linkages between the surface and the nutrient-rich deep ocean, resulting in turn in a patchier expression in the highly stratified subtropical regions. While the drivers are not clear from our work, previous studies have noted that an increasingly patchy distribution requires finer scale sampling or grid spacing33, and if these processes are important, our work indicates fine-scale grid spacing is in fact still important across broad swaths of the ocean generally considered “homogenous”.

While the focus of this work is on scaling relationships, the fractal-like patchiness of phytoplankton is not infinite. At a fundamental level, patches are formed by individual phytoplankton living and dying48. Currently it is unclear how to connect the scales being investigated here with the individual organisms at the heart of the matter; Franks25 notes that it is not likely we can diagnose the dynamics underlying the observations from spectral slopes alone. Towards mechanistic understanding of the processes underlying the spatial patterns we expect Lagrangian approaches will be key, particularly to parse out spatial and temporal dynamics. Future work should examine joint spatial patterning across trophic levels, combining the methods here, rapid methods for a wide size range of plankton49, and methods for quantifying zooplankton patchiness10. Additionally, it may be that improved atmosphere correction of satellite products could enable a spatial analyzes across the global ocean. Higher signal to noise regions, such as coastal waters or higher latitudes during the spring bloom, may be more amenable to satellite analyzes of spatial patterns under existing atmospheric correction schemes.

We identified two fundamental differences between patterns of physical and biological patchiness: globally plankton patchiness at the scales analyzed here (~0.6 km–100 km) is spatially organized while physical patchiness is less coherent and organized differently, and patchiness of concentration-dependent biological variables is correlated with the absolute values of these variables, while no such correlation is found for physical variables. The statistical distributions of Γchl-a and Γtemperature agree with previous work, where Γchl-a has a generally lower value, i.e. a patchier spatial pattern, compared to Γtemperature. We find global patterns of biological patchiness to coincide with biogeochemical provinces and with nutrients levels. While our analysis shows the patchiness of biological variables are intercorrelated, and patchiness of physical variables are intercorrelated, contrary to common view, we find no correlation between physical and biological patchiness. This suggests that biological processes modulate the physically-driven advective baseline sufficiently to manifest as a different organization of patchiness. We emphasize here that the absolute value of variance itself is correlated at all scales between physical and biological variables (Figure S9). Moreover, while it is well known that there is a relationship between temperature and chl-a, largely attributed to nutrient fluxes50, our findings show this does not extend to variance slope. Our results contradict results from model studies (e.g34.) and from satellite analyzes (e.g51.), including our own (Figure S5 and S6). This discrepancy holds even when comparing to other work on the same range of scales as those examined here, which had concluded that biological patchiness is controlled by mesoscale mixing28. This suggests that these two important tools for understanding ocean ecosystems (models and satellite observations), fail to capture fundamental characteristics of the marine ecosystem. Our results may also help explain the disagreement shown across decades of patchiness research including many in situ studies. It may be that there is no generalizable patchiness relationship between physics and biology in the ocean and no consistent spatiotemporal scale where biological or physical processes dominate the spatial patterns of phytoplankton. Accordingly, basing general theories on the patchiness of a given tracer type from a specific site and over short timescales could be misguided. Instead, the ocean appears to consist of myriad physical and biogeochemical processes manifested as diverse spatial patterns. Thus, while no consistent relationships emerge these observable spatial patterns may provide a window into the processes creating them.

The results presented here support the use of low dimensional spatial encodings such as Γ to study these upper-ocean processes. We speculate these spatial metrics may be sensitive to biogeochemical parameters not represented by the absolute value of chl-a. Importantly, we cannot resolve marine ecosystems at the mesoscale and below in basin-scale biogeochemical models, thus we must increase our ability to observe, invert, and understand what our models are missing52. Spatial patchiness patterns may help drive our models closer to reality and serve as an underutilized source of insight into the underlying processes generating the observed patchiness.

Methods
All in situ measurements are from the S/V Tara underway sampling system which pulls seawater from 2 m depth. Temperature and salinity data is from a Seabird Scientific thermosalinograph (SBE38 and SBE 45) and all optical data is derived from particulate absorption and attenuation measured with a Seabird Scientific ACs.

We quantify patchiness using variance slope, Γ, following33 which is similar to spectral analysis, but able to ingest vectors (i.e. transects) with small gaps within them. Γ is calculated on groups of 500 samples using a set of 11 log-distributed windows from 3 to 500. The median distance traveled between individual samples is 0.21 km (Figure S10) thus patchiness is calculated for scales from ~0.6 km to 100 km. Variance and window size were log-transformed, and we ran a least-squares fit to find the slope of this line, yielding the Γ of V=LΓ. It is worth noting a few characteristics of Γ to gain some intuition into the metric. The variance slope of a randomly distributed variable is centered around 0. The calculation is not sensitive to whether a variable is log-normally distributed (such as chl-a). For example, Γchl-a is identical whether raw chl-a values are input or log-transformed chl-a values. The S/V Tara is a sailing vessel and thus does not always travel in a straight line or with the same speed so here we have used time (minute bins of data) instead of distance to calculate the window, but filtered out legs that have a maximum distance traveled under 30 km or over 150 km. We have required at least 80% of the transect to contain data and filtered out transects where the maximum time elapsed is greater than 16 hours leading to a total of 820 transects used in this analysis.

Hyperspectral absorption and attenuation (400 to 735 nm at ~4 nm spectral resolution, AC-s, Seabird Sci.) were measured continuously. A 0.2 μm filter cartridge was connected to the system and we automatically redirected the flow to measure the properties of filtered seawater for 10 minutes every hour. Total (“normal”) seawater was flowing the rest of the time. Absorption and attenuation measurements recorded during the filtered periods were interpolated across the transect and subtracted from the total seawater measurements to obtain an estimate of the particulate absorption (ap), attenuation (cp) spectra. During the Tara Microbiome transect, the filtered periods were interpolated using the variation in CDOM fluorescence (fCDOM) also measured continuously with a SeaPoint ultraviolet fluorometer (SUVF). fCDOM data was recorded with a Seabird Scientific WSCD CDOM fluorometer during the Tara Pacific transect. The signal to noise ratio of the WSCD is lower than the SUVF’s which introduced noise in the fCDOM interpolation and the product derivation. Therefore, the filtered periods were interpolated linearly across the Tara Pacific transect. This approach permits retrieval of particulate optical properties independently from the instrument drift and biofouling53. For each minute of total seawater measurements (sampled at 4 Hz) the signal between the 2.5th and 97.5th percentiles were averaged, and their standard deviation was used to quantify uncertainty. Dropping the 2.5th to 97.5th percentiles filters out noisy spikes from bubbles which can be a major problem in optical measurements. All spectra were manually checked and quality controlled for obviously bad measurements (e.g. bubbles, bad filtered seawater measurements). These inherent optical properties were used as proxies for a range of particulate properties, primarily chl-a line height, a chl-a estimate derived from the absorption peak at 676 nm54,55, and γ, a proxy for mean particle size39.

Underway data was collected using Inlinino56 an open-source logging and visualization program, and processed using InlineAnalysis (https://github.com/OceanOptics/InLineAnalysis) following best practices57. Longhurst provinces46 (downloaded from https://www.marineregions.org/sources.php#longhurst) were used as approximate delineations of the global ocean into biogeochemical regions. Nutrient data was from the World Ocean Atlas 2018 (downloaded from https://www.ncei.noaa.gov/data/oceans/woa/WOA18).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Summary: The authors perform a global analysis to show that some biological and physical parameters are decorrelated across spatial scales. Although this analysis is fairly comprehensive and relies on extensive data, I have several concerns with the data interpretation and the robustness of the results. With some extensive modification, I could see this manuscript being a useful and timely contribution.\nMajor concerns:\n1. The terms ‘ocean biology’ and ‘ocean physics’ are far too broad for the data that are actually being studied. There are many components of ocean biology, such as phytoplankton diversity, physiological traits, etc. that are not directly captured in this study. Similarly, the influence of ocean physics goes beyond temperature and salinity (wind speed, ocean currents etc.). I would suggest that the authors limit their title, abstract and major conclusions to prevent over-interpretation of the data actually being studied. In the best-case scenario, this study is arguing for a decorrelation (not decoupling) between phytoplankton biomass and seawater density, not ocean physics and biology.\n2. Although I understand the reasons for using linear regression to identify the strength of the relationship, the distribution of points for many of the plots shows that the fit is not optimal. The effect sizes are also low. In Fig. 4, the greatest R2 value is 0.46 (between Γ_density and Γ_temp), which makes sense, given the known relationship between seawater density and temperature. Otherwise, there are no additional analyses to support the arguments throughout the paper. In its current form, I am not entirely convinced that the data support the authors' conclusions (Ln 226-235). Here are some suggestions:\n- It might be interesting to highlight where Γ_chl and Γ_temp are equal, where Γ_chl exceeds Γ_temp and where Γ_chl is less than Γ_temp on a map. This could add nuance to your arguments and provide more context for the results.\n- Consider reinforcing the correlation plots with supplementary figures showing what the residuals look like.\n- Density plots could indicate where the points are concentrated when comparing any 2 variables. The Longhurst provinces all seem to cluster around the middle, with some interesting exceptions.\n3. Ln 261-270: All of Fig.6 just seems to show clouds of points with no obvious correlation. The regression lines also seem weird (6a-c) compared to the reported equations.\n- Why are the intercepts so different in the equations (~0.7)? The lines on the plots show an intercept less than 0.6.\n- In 6a, why does Γ_chl only go up to 0.9?\n- In 6c, why does the line on the actual plot appear to show positive slope when it is -0.21?\nThese are some major irregularities.\n4. Ln 279-283: O2 saturation is not a nutrient. In this case as well, I am not sure why Γ_chl only goes up to 0.9 when Fig. 2 shows the histogram going up to 1.5.\n5. Some additional thoughts and questions:\n- From what I understand, the data presented here were all measured right at the surface. It might be useful to discuss whether vertical mixing rates, phytoplankton mobility, buoyancy (species composition) could alter observed patchiness on short time scales.\n- I am surprised there was no mention of local wind patterns on observed chlorophyll patchiness, especially given that the sampling was conducted on a sailing vessel (Ln 413). Instead of temperature and salinity, my understanding was that wind, currents and mixed layer depth tend to be important in determining patchiness.\nGeorge, D. G., & Edwards, R. W. (1976). The Effect of Wind on the Distribution of Chlorophyll A and Crustacean Plankton in a Shallow Eutrophic Reservoir. Journal of Applied Ecology, 13(3), 667–690. https://doi.org/10.2307/2402246\nKahru, M., S. T. Gille, R. Murtugudde, P. G. Strutton, M. Manzano‐Sarabia, H. Wang, and B. G. Mitchell (2010),Global correlations between winds and ocean chlorophyll, J. Geophys. Res., 115, C12040, doi:10.1029/2010JC006500.\nOverall, by generalizing over the entire dataset and not really looking into the actual spatial patterns, the conclusion that there is “a decoupling between ocean physics and biology” seems overstated.\nAdditional comments:\nFig. 2 (right panel): Might be useful to indicate the Γ values more explicitly for readers. Showing the entire equation is fine, but I expected some discussion on the intercept values (the fourth panel looks different). It is also interesting to me where the red and green lines cross (at what length scale). Also, consider using a color-blind friendly combination.\nFig. 3: Why is the range of the distribution greater than the legend on the right? It seems the values for Γ_chl go up to 1.5 and Γ_temp go up to 1.9, but the legend ends at 1 and 1.5.\nLn 239: “Marginally more correlated” is quite the bold claim. When comparing an R2 of 0.04 vs 0.03, I think it is safe to say that Γ_chl and Γ_temp are not correlated in both cases.\nFig. S6: Please check the equations for the last 2 panels.", "reviewer_2": "Review Gray et al.\nThis paper examines a large data set of underway, near-surface, bio-optical, temperature and salinity data from the S/V Tara. The data set and the information it holds is impressive, as the ship’s track covers the Atlantic and Pacific, with multiple basin crossings, as well as tracks along the basin margins. The authors examine the patchiness of physical (temperature and salinity) and biogeochemical (chlorophyll-a, beam attenuation cp(443) and gamma. ) variables using the exponent of the variance vs length-scale (V-L) relationship for each of the variables. The exponent can be used as a patchiness measure, as shown previously in ref. 31.\nConsistent with previous literature, the authors find that the patchiness (exponent of the V-L relationship) differs between physical and biogeochemical variables. They also find that the patchiness of physical variables is not correlated with the patchiness of biological variables across different regions of the oceans. This leads them to conclude that “patchiness of physics and biology are decoupled at the global scale.” This conclusion is misleading. On first reading, it would be easily mis-understood that the authors conclude that patchiness of biological variables is not related to the patchiness of physical variables. This would be wrong. The physics does indeed affect the patchiness of biology. I think that the authors’ conclusions are either incorrect or mis-stated.\nAssuming that the conclusions (interpretation) is mis-stated — it would be worth understanding why the authors expect the exponent of physical and biological variables to be correlated. Even if the distribution of biological variables were shaped by the physics, the difference in the exponent of the V-L relationship could vary depending on the time scales of the biological processes as compared to the physical processes. Their ratio could differ regionally and hence the findings should not lead to the conclusion that the authors have drawn.\nThere are several other issues (inaccuracies) in this paper. The term “global scale” is used incorrectly. The authors mean to convey that the relationship between the regional-scale patchiness of temperature and chlorophyll-a differs from one region to another. This result is not surprising nor does it challenge any of the previous literature that states that the patchiness of biogeochemical and physical variables is related. The result does not pertain to the global scale (largest scales).\nPlease see: Campbell, J.W., Lognormal distribution as a model for bio-optical variability in the sea, JGR 1995, which addresses some of the questions raised in the manuscript.\nWhat exactly is “gamma”? The paper refers to this only once and explains it as an optical proxy for mean particle size.\nMethods: In the text, the authors say the spacing between measurements is about 150m. But since the measurements are at certain time intervals, the lateral spacing between 2 measurements could differ considerably. The authors do the analysis using windows defined by time (lines 414-415). This could affect the results significantly. It is just like calculating spectra for unevenly spaced data, assuming equal spacing. At the least, the authors need to show the spacing - and the variability in the spacing of measurements.\nSupplementary materials was not very helpful because the figure captions were inadequate and there was no supporting text.\nLine 23: slope of Variance vs. Spatial scale (rather than spatial scale vs. variance)\nLine 27: Incorrect to state that the patchiness of physical and biological parameters are uncorrelated.\nLine 28 What is meant by “variance slope is an emergent property”?\nLine 30 No, this does not “provide context for decades of discrepancy”\nLine 31 New tests? What is meant by this?\nLine 32 insight instead of “new insight”\nLine 40 that result in\nLine 43 “with close proximity” What does this mean?\nLine 49 Is there a reference to substantiate this statement? “generally increasing patchiness as one moves ups the trophic chain”\nLine 72 “this parameter” — Spectral slope?\nLine 73 replace “thought of as quantifying” by “interpreted”\nLine 75 It is not a decomposition\nLines 78-90 —There are many incorrect or inaccurate statements in this section.\nLine 79 Energy cascades, not turbulence\nLine 79 Replace “turbulent mesoscale” by “mesoscale” as the large scale turbulence is different from 3D turbulence\nLine 81 No, this is not how it works. Energy is transferred up scale at small Rossby number (the downscale cascade is facilitated by submesoscale processes)\nLines 84-87 This is confusing and misleading. The inertial subrange of Kolmogorov is different from the large-scale dynamics of the ocean - which is affected by rotation and stratification.\nLine 88-90 Temperature could have a variance source at smaller scales too — for example, due to upwelling on small scales.\nLine 92 Previous literature did not attribute phytoplankton patchiness simply to turbulent stirring\nLine 103 These references (7,30,31) did not all corroborate each other — on the contrary, they gave different reasons for the observed patterns in patchiness of temperature and chlorophyll.\nLine 105 What is the “new” heat flux?\nLine 108 The SST equilibrates with the atmosphere largely due to air-sea heat exchanger and the statement “heat is mixed over time” is not correct.\nLine 109 “return to covarying” - not correct\nLines 103-113 The references are inaccurate\nLine 115 What is meant by “actual observations remain inconsistent” ?\nLines 116-119 - could use a better word than “work” which appears repeatedly\nLine 120 “yet not so above 5 km to 80 km” what does this mean?\nLine 142 Measurements of what?\nLine 173 (fig 2 caption) What are “absolute” values\nLine 194 — related to the reference by Campbell (see above)\nLine 206-208 - previous papers have not reported contradictory results — not sure why the authors find contradictory results when using satellite data\nLine 214-216 Could this be because chlorophyll is log normally distributed\nLine 234-235 - No. This conclusion is not substantiated by the findings.\nLine 273\nFig 7. Same as Fig 6a except for the color of dots?\nFig 8. Could this figure go in the supplementary material?\nLine 315 scale\nLine 320 - seems that Reference 31 is for oligotrophic regions, whereas the results presented here are for productive regions\nLine 353 - “physical patchiness is more random” - this does not seem correct\nLine 361-2 why should there be an interdependence?\nLine 365 - this is not a conclusion that can be drawn from the results presented - and seems incorrect\nDue to the incorrect interpretation of findings, several inaccuracies, and understanding gaps of previous literature, I do not recommend publication of this article.", "reviewer_3": "This article examines the scales of variability in both optical and physical variables from in-situ ocean surface observations.\nResults demonstrate that basin-scale variance slope does not correlate between the biological/biogeochemical and physical variables. A shorter analysis of similar variables from satellite data (mainly in the supplement) demonstrates one reason why previous studies have found correlations in spectral slopes or variance slopes, as those do occur in the satellite record.\nThese results are critical for understanding decades of disagreements in the field, as it seems there will not be a simple relationship to be found between the variance slope for physical and biological variables, but rather only an underlying set of relationships between the physical environment and biological concentrations, and then from concentrations to variance slope. This is an important step toward improving biogeochemical and climate models and satellite data analysis in the future.\nThis is a well-written article with clear methods and results. The analysis supports the conclusions drawn. There are no major flaws. I recommend this article be returned for minor revisions to address comments below.\nMinor Revisions\n1. Line 120, citation 17. Is the correlation below 5km and maybe above 80km, or is the correlation occurring at small scales with an uncertain upper limit between 5 and 80 km? Please rewrite for clarity.\n2. At the beginning of the results, please repeat or move (from line 198) the equivalent value for Gamma (variance slope) to -5/3 for spectral slope. I really wanted to know at that time when reading.\n3. In Figures 1 and 3, the dots on the map are quite small. Is it possible to increase their size while still allowing the gaps to be visible? Maybe they can be drawn as ellipses or rectangles so that there are larger colored areas without excessive overlap.\n4. Line 230: please add a brief description of Longhurst provinces and note that Figure 5 shows their location-- I read this as the averages would be in Figure 5 separately from the full data in Figure 4.\n5. Figure 6c: Please add a note as to why the x-axis is reversed or remake this with an increasing x-axis. It is quite jarring to see a negative slope in the labeled equation with the visually 'positive' slope. Also please explain why R2=0.02 is considered correlated and R2=0.00 is not. Even though p is small, it is hard to understand why this is convincing. Would showing the log be better?\n6. Figure 7d: The Longhurst province averages for O2 do not appear to be correlated to chl-a or Gamma_chla here. Please confirm that this is the case, as you assert (line 282) that this is a clear increasing relationship and by eye it is not.\nTypos Etc.\n1. Line 290: add 'in' after 'zooming'\n2. Figure 8: please label the location this data is from in more detail-- can you give a latitude/longitude for the middle, perhaps?\n3. The end of the results section includes author names for references, which is not the case elsewhere. Please double check these choices.\n4. In the references, sometimes 'Boss' does not have initials for first/middle name.\n5. Please check references to make a consistent format. The number of authors included, for example, before going to et al., is variable."}, "author_response": "We thank all three reviewers for a thorough and very constructive review. Their review helped\nus significantly improve and clarify the manuscript. All comments have been addressed below.\nPlease also note that we found and corrected a small error in the calculation of variance slope.\nSpecifically, we were calculating from ~3km to ~75km instead of ~0.5 to ~75km as stated in the\ntext. We have corrected this to calculate from 0.5 to 75km which has changed some of the\nslopes slightly and this has been updated in all figures and text.\nReviewer #1 (Remarks to the Author):\nSummary: The authors perform a global analysis to show that some biological and physical\nparameters are decorrelated across spatial scales. Although this analysis is fairly\ncomprehensive and relies on extensive data, I have several concerns with the data\ninterpretation and the robustness of the results. With some extensive modification, I could see\nthis manuscript being a useful and timely contribution.\nMajor concerns:\n1. The terms ‘ocean biology’ and ‘ocean physics’ are far too broad for the data that are actually\nbeing studied. There are many components of ocean biology, such as phytoplankton diversity,\nphysiological traits, etc. that are not directly captured in this study. Similarly, the influence of\nocean physics goes beyond temperature and salinity (wind speed, ocean currents etc.). I would\nsuggest that the authors limit their title, abstract and major conclusions to prevent over-\ninterpretation of the data actually being studied. In the best-case scenario, this study is arguing\nfor a decorrelation (not decoupling) between phytoplankton biomass and seawater density, not\nocean physics and biology.\nWe have limited the scope of the title and terminology. It is a good point that this isn’t\nnecessarily a decoupling but rather a lack of correlation. We have clarified further that we aren’t\narguing for a decorrelation of biomass and density, but rather their cascades of variance.\nWe have changed the title to now say plankton instead of biology and physical properties instead of\nphysics to be more precise and in line with previous studies which have used these same\nparameters.\n2. Although I understand the reasons for using linear regression to identify the strength of the\nrelationship, the distribution of points for many of the plots shows that the fit is not optimal. The\neffect sizes are also low. In Fig. 4, the greatest R2 value is 0.46 (between Γ_density and\nΓ_temp), which makes sense, given the known relationship between seawater density and\ntemperature. Otherwise, there are no additional analyses to support the arguments throughout\nthe paper. In its current form, I am not entirely convinced that the data support the authors'\nconclusions (Ln 226-235).\nWe have clarified that we are testing if patchiness in one field is explained by the other,\nfollowing on previous work examining these relationships. We have also noted that the\ncalculation of Γ is non-parametric and that much of what drives these relationships in the\npresence of noise is their dynamic range relative to subpixel variability. Note that despite Γ\nhaving a very small dynamic range (the range of Γ is from 0 to 1.5), it shows robust relationships\nconsistent within the physical or biogeochemical parameters. This dynamic range is significantly\nsmaller than for any of the variables themselves.\nHere are some suggestions:\n- It might be interesting to highlight where Γ_chl and Γ_temp are equal, where Γ_chl exceeds\nΓ_temp and where Γ_chl is less than Γ_temp on a map. This could add nuance to your\narguments and provide more context for the results.\nFollowing this comment, we have added a plot as suggested into the supplemental (Figure S4)\nand discuss it in the results.\n- Consider reinforcing the correlation plots with supplementary figures showing what the\nresiduals look like.\nWe have generated these plots, but they all generally cluster around zero, with no structure\nsuggesting the linear relationship is appropriate.\n- Density plots could indicate where the points are concentrated when comparing any 2\nvariables. The Longhurst provinces all seem to cluster around the middle, with some interesting\nexceptions.\nThank you for this suggestion, we have tried a number of options to better show the density of\nthe points and have now added contour lines to show the density of points which does indeed\nmake these plots more interpretable.\n3. Ln 261-270: All of Fig.6 just seems to show clouds of points with no obvious correlation. The\nregression lines also seem weird (6a-c) compared to the reported equations.\nWe have confirmed that the regression lines are all correct as written. The density contours\ndescribed above also help clarify the relationships.\n- Why are the intercepts so different in the equations (~0.7)? The lines on the plots show an\nintercept less than 0.6.\nWe have re-confirmed in analysis and in the figures and these intercepts are all ~0.7 and in\neach plot at x=0 the intercept matches the reported value. Because the plots all go into the\nnegative on the x-axis (because it is a log plot) we understand this may be confusing.\n- In 6a, why does Γ_chl only go up to 0.9?\nBecause nearly all the Γ_chl values fall from 0 to 1 we limited it to better show the data. We\nhave changed this upper limit to 1 instead of 0.9 to span nearly all the data.\n- In 6c, why does the line on the actual plot appear to show positive slope when it is -0.21?\nThis parameter is inversely related to size so we had initially flipped the x-axis to better show\nthe same pattern across variables, but we understand this may be not clear to readers so we\nhave flipped it so they are all consistent.\nThese are some major irregularities.\n4. Ln 279-283: O2 saturation is not a nutrient. In this case as well, I am not sure why Γ_chl only\ngoes up to 0.9 when Fig. 2 shows the histogram going up to 1.5.\nThank you for the catch on not clarifying O2 saturation specifically in the caption. This has been\ncorrected. Γ_chl was limited to 0.9 to focus on the Longhurst province data distribution and the\nbulk of the data. We have changed this plot to a max of 1.0 which spans nearly all the Γ_chl\ndata.\n5. Some additional thoughts and questions:\n- From what I understand, the data presented here were all measured right at the surface. It\nmight be useful to discuss whether vertical mixing rates, phytoplankton mobility, buoyancy\n(species composition) could alter observed patchiness on short time scales.\n- I am surprised there was no mention of local wind patterns on observed chlorophyll\npatchiness, especially given that the sampling was conducted on a sailing vessel (Ln 413).\nInstead of temperature and salinity, my understanding was that wind, currents and mixed layer\ndepth tend to be important in determining patchiness.\nGeorge, D. G., & Edwards, R. W. (1976). The Effect of Wind on the Distribution of Chlorophyll A\nand Crustacean Plankton in a Shallow Eutrophic Reservoir. Journal of Applied Ecology, 13(3),\n667–690. https://doi.org/10.2307/2402246\nKahru, M., S. T. Gille, R. Murtugudde, P. G. Strutton, M. Manzano‐ Sarabia, H. Wang, and B. G.\nMitchell (2010),Global correlations between winds and ocean chlorophyll, J. Geophys. Res.,\n115, C12040, doi:10.1029/2010JC006500.\nThank you for these helpful references. We have clarified that we are revisiting previous work\nwith the same variables (which did not include wind and other physical variables). Additionally,\nwe are not looking at correlations between biological and physical parameters here, or even at\ncorrelations in their variance, but in their spatial patchiness. Atmospheric parameters like wind\nhave different mesoscale bands (5 days, 100km) vs those of the ocean (1mo, 30km) and thus,\na-priori, are not expected to have similar patchiness as the much more viscous and denser\nocean. MLD variance is expected to be reflected in temperature (e.g. deepening mixed layers\nhave anomalous low temperature and higher densities).\nOverall, by generalizing over the entire dataset and not really looking into the actual spatial\npatterns, the conclusion that there is “a decoupling between ocean physics and biology” seems\noverstated.\nWhile there are likely many interesting investigations into the specific details and patterns in\neach transect, here we were investigating statistical patterns in spatial organization over a large\ndataset. Towards clarifying this goal we have substantially toned down the language stating now\nin the abstract that “Here we show that the patchiness of physical parameters and plankton are\nuncorrelated across the globe” and further in the results that our observations “suggest that\nbiological processes may modulate the initial physically-driven spatial pattern baseline\nsufficiently to manifest as uncorrelated levels of patchiness”.\nAdditional comments:\nFig. 2 (right panel): Might be useful to indicate the Γ values more explicitly for readers. Showing\nthe entire equation is fine, but I expected some discussion on the intercept values (the fourth\npanel looks different). It is also interesting to me where the red and green lines cross (at what\nlength scale). Also, consider using a color-blind friendly combination.\nWe have added a note that the variance slope can be seen in the legend for each panel and\nthat the intercept value corresponds both to the magnitude of the variance and the slope. For\ncolorblind friendliness we have used a dashed line and one of our authors who is colorblind has\nnoted it is clear for him.\nFig. 3: Why is the range of the distribution greater than the legend on the right? It seems the\nvalues for Γ_chl go up to 1.5 and Γ_temp go up to 1.9, but the legend ends at 1 and 1.5.\nThis was to emphasize the bulk of the distribution of the data, which for Γ_temp falls within 0.5\nto 1.5 and for Γ_chl falls within 0 to 1. This allowed us to show them both with the same span\nand more clearly show the bulk of the data.\nLn 239: “Marginally more correlated” is quite the bold claim. When comparing an R2 of 0.04 vs\n0.03, I think it is safe to say that Γ_chl and Γ_temp are not correlated in both cases.\nThis is a good point, we have removed this statement and stated that “the variables are still\neffectively uncorrelated”.\nFig. S6: Please check the equations for the last 2 panels.\nChecked. These equations are correct as written.\nReviewer #2 (Remarks to the Author):\nReview Gray et al.\nThis paper examines a large data set of underway, near-surface, bio-optical, temperature and\nsalinity data from the S/V Tara. The data set and the information it holds is impressive, as the\nship’s track covers the Atlantic and Pacific, with multiple basin crossings, as well as tracks along\nthe basin margins. The authors examine the patchiness of physical (temperature and salinity)\nand biogeochemical (chlorophyll-a, beam attenuation cp(443) and gamma. ) variables using the\nexponent of the variance vs length-scale (V-L) relationship for each of the variables. The\nexponent can be used as a patchiness measure, as shown previously in ref. 31.\nConsistent with previous literature, the authors find that the patchiness (exponent of the V-L\nrelationship) differs between physical and biogeochemical variables. They also find that the\npatchiness of physical variables is not correlated with the patchiness of biological variables\nacross different regions of the oceans. This leads them to conclude that “patchiness of physics\nand biology are decoupled at the global scale.” This conclusion is misleading. On first reading, it\nwould be easily mis-understood that the authors conclude that patchiness of biological variables\nis not related to the patchiness of physical variables. This would be wrong. The physics does\nindeed affect the patchiness of biology. I think that the authors’ conclusions are either incorrect\nor mis-stated.\nThis is a helpful point and clarification. We do not mean to say that they are unrelated, but\nrather biological patchiness is not statistically correlated to physical patchiness in our dataset.\nSo not necessarily decoupled, but that the variance biological patchiness cannot be explained\nby the physical patchiness. Our observations suggest plankton are active tracers in the sense\nthey have an impact on their spatial organization, physics creates the baseline and our results\nsuggest biology modulates the patchiness sufficiently to decorrelate. We have changed the title,\nlanguage, and added more details to clarify this point. We have also added a Figure (S4) which\ndescribes locations where the chlorophyll-a is patchier than temperature, less patchy, and equal\nto show further nuances of this across the globe. Based on this suggestion we have also\nconducted a new analysis of patchiness for CDOM, which we collected for the second half of\nthe cruises used in this paper, and this indeed seems to fall somewhere in between the\npatchiness of physical and biological variables. CDOM can be thought of as a somewhat more\npassive tracer, following physical mixing more closely but also slowly responding to biological\nprocesses. This is shown in Figure S8.\nAssuming that the conclusions (interpretation) is mis-stated — it would be worth understanding\nwhy the authors expect the exponent of physical and biological variables to be correlated. Even\nif the distribution of biological variables were shaped by the physics, the difference in the\nexponent of the V-L relationship could vary depending on the time scales of the biological\nprocesses as compared to the physical processes. Their ratio could differ regionally and hence\nthe findings should not lead to the conclusion that the authors have drawn.\nOur work here is the result of a data-driven exploration, given that the fields are strongly\ncorrelated, and so are their variances, we might expect their patchiness to be correlated, but our\nfindings are that their patchiness values are uncorrelated. Beyond this baseline if we think of\nplankton as a quasi-passive tracer in an environment where advection dominates, we might\nexpect the patchiness of physical parameters and plankton to be similar. We are investigating\ninstantaneous patchiness, but as pointed out there could be a lagged correlation in patchiness\nand we have noted that this could account for some of the lack of statistical explanation.\nThere are several other issues (inaccuracies) in this paper. The term “global scale” is used\nincorrectly. The authors mean to convey that the relationship between the regional-scale\npatchiness of temperature and chlorophyll-a differs from one region to another. This result is not\nsurprising nor does it challenge any of the previous literature that states that the patchiness of\nbiogeochemical and physical variables is related. The result does not pertain to the global scale\n(largest scales).\nThank you for this helpful point. We no longer write ‘global scale’ in the paper, and instead\nwe’ve clarified that across all the studied environments, given our analysis window is 0.6 -\n100km, we find that patchiness of physical parameters and plankton is uncorrelated.\nPlease see: Campbell, J.W., Lognormal distribution as a model for bio-optical variability in the\nsea, JGR 1995, which addresses some of the questions raised in the manuscript.\nThank you for this helpful reference that indeed has an interesting discussion on many points\nraised in the manuscript. We have added a reference to this and included some points in the\ndiscussion.\nWhat exactly is “gamma”? The paper refers to this only once and explains it as an optical proxy\nfor mean particle size.\nGamma (γ) is an optical size parameter that is inversely related to the mean size of particles\nfrom approx 0.2μm to 20μm. It is called gamma in optical oceanography but we have removed\nthis from the manuscript to avoid confusion with Γ and instead refer to it as mean particle size\nparameter (γ). It is derived from the beam attenuation coefficient of particles and has been\nshown to correlate well with the slope of the particle size distribution, e.g. Boss et al., 2001,\nApplied Optics.\nMethods: In the text, the authors say the spacing between measurements is about 150m. But\nsince the measurements are at certain time intervals, the lateral spacing between 2\nmeasurements could differ considerably. The authors do the analysis using windows defined by\ntime (lines 414-415). This could affect the results significantly. It is just like calculating spectra\nfor unevenly spaced data, assuming equal spacing. At the least, the authors need to show the\nspacing - and the variability in the spacing of measurements.\nWe have shown that random perturbations in spacing don’t materially influence the slope which\nis quite robust to these small differences. We also did an extended analysis to determine the\nideal minimum spacing between two measurements and we found the results were not sensitive\nto the minimum lateral distance range used in this analysis (100m to 300m). We have added a\nhistogram of the median spacing between each sample per transect as a supplemental figure\n(Figure S10). These attributes are a primary benefit and motivator for using this specific method\nover the classical Fourier based power spectra calculation and why we have used it here for this\ndataset.\nSupplementary materials was not very helpful because the figure captions were inadequate and\nthere was no supporting text.\nWe have extended the discussion in the captions of the supplemental materials and added\nfurther supporting text.\nLine 23: slope of Variance vs. Spatial scale (rather than spatial scale vs. variance)\nCorrected.\nLine 27: Incorrect to state that the patchiness of physical and biological parameters are\nuncorrelated.\nWe have clarified that physical properties and plankton patchiness are uncorrelated based on\nour analysis, though they may be correlated across subsets of the data. We have also further\nexplained that their absolute values and their variance may be strongly correlated. We have\nemphasized that this does not mean that physical processes don’t impact biological spatial\npatterns.\nLine 28 What is meant by “variance slope is an emergent property”?\nBy emergent property we mean a property that comes from behavior of the ecosystem (such as\nprey-predator interactions and reproduction) and the impacts of physics - a property that\nemerges from the ensemble of processes in the ecosystem and environment. We have now\ndefined this in the manuscript.\nLine 30 No, this does not “provide context for decades of discrepancy”\nWe have changed this to now state our results provide context for decades of observations with\ndifferent interpretations.\nLine 31 New tests? What is meant by this?\nHere we mean using spatial patchiness as an assessment for models, to see if their spatial\npatchiness distributions and relationships are similar to those found at the same scales in\nobservations. We have clarified this further in the discussion.\nLine 32 insight instead of “new insight”\nCorrected.\nLine 40 that result in\nCorrected.\nLine 43 “with close proximity” What does this mean?\nHere we mean that the ocean can contain different patches near each other that can have very\ndifferent physical and biogeochemical properties and that this supports biodiversity.\nLine 49 Is there a reference to substantiate this statement? “generally increasing patchiness as\none moves ups the trophic chain”\nThis is addressed in both of our cited examples, for example section 4.4 in Estapa et al. We\nhave added an additional citation to one of the original papers discussing this:\nMackas, D. L., and C. M. Boyd (1979), Spectral analysis of zooplankton spatial heterogeneity,\nScience\nLine 72 “this parameter” — Spectral slope?\nCorrect, this has been clarified.\nLine 73 replace “thought of as quantifying” by “interpreted”\nChanged.\nLine 75 It is not a decomposition\nWe have changed decomposition to analysis.\nLines 78-90 —There are many incorrect or inaccurate statements in this section.\nWe have corrected each noted point below, thank you for these suggestions.\nLine 79 Energy cascades, not turbulence\nCorrected\nLine 79 Replace “turbulent mesoscale” by “mesoscale” as the large scale turbulence is different\nfrom 3D turbulence\nCorrected\nLine 81 No, this is not how it works. Energy is transferred up scale at small Rossby number (the\ndownscale cascade is facilitated by submesoscale processes)\nHere we have summarized and updated the description in the text based on the overview of\nturbulence in Atmospheric and Oceanic Fluid Dynamics, Vallis, 2017 2nd edition.\nLines 84-87 This is confusing and misleading. The inertial subrange of Kolmogorov is different\nfrom the large-scale dynamics of the ocean - which is affected by rotation and stratification.\nHere clarify the 2D - large scale from 3D inertial subrange turbulence.\nLine 88-90 Temperature could have a variance source at smaller scales too — for example, due\nto upwelling on small scales.\nThis is a good point and we have added this in this paragraph.\nLine 92 Previous literature did not attribute phytoplankton patchiness simply to turbulent stirring\nWe have changed this to say that phytoplankton patchiness was initially thought to be primarily\ncontrolled by turbulent stirring.\nLine 103 These references (7,30,31) did not all corroborate each other — on the contrary, they\ngave different reasons for the observed patterns in patchiness of temperature and chlorophyll.\nCorroborate was an imprecise word, thank you for catching this. We have changed this to\n“come to a similar conclusion”. While these three studies have different specific conclusions\nAbrahams states:\n● “The characteristic spatial patterns of the phytoplankton and zooplankton are a\nconsequence of the timescales of their response to changes in their environment caused\nby turbulent advection.”\nAnd Mahadevan notes:\n● “This suggests that sea surface Chl is more patchy (has smaller p) than SST at\nmesoscales because the characteristic time scale of phytoplankton growth in response\nto the availability of nutrients is less than that for the equilibration of temperature in\nresponse to heat fluxes.”\nSince Levy and Klein is not directly commenting on this same aspect, we have removed this\ncitation in this line and discuss it later in this paragraph in relation to their discussion of physics\nplaying a dominant role in the spatial variability of plankton.\nLine 105 What is the “new” heat flux?\nThis was imprecise language and “new” has been removed.\nLine 108 The SST equilibrates with the atmosphere largely due to air-sea heat exchanger and\nthe statement “heat is mixed over time” is not correct.\nThis has been corrected.\nLine 109 “return to covarying” - not correct\nThis has been corrected to say that the patchiness in these variables returns to co-varying.\nLines 103-113 The references are inaccurate\nAs noted above we have changed these citations, moving the reference to Levy and Klein and\nconfirmed the others apply directly where noted.\nLine 115 What is meant by “actual observations remain inconsistent” ?\nThis has been re-written to say that the interpretations from observational studies remain\ninconsistent.\nLines 116-119 - could use a better word than “work” which appears repeatedly\nChanged to “studies” and “investigation”.\nLine 120 “yet not so above 5 km to 80 km” what does this mean?\nThis has been re-worded to clarify the scales being discussed.\nLine 142 Measurements of what?\nThese are outlined in the following sentence, we have clarified the text here to connect these\nsentences.\nLine 173 (fig 2 caption) What are “absolute” values\nThis was to differentiate between measured values and variance but we see it could be\nconfusing and have removed “absolute”.\nLine 194 — related to the reference by Campbell (see above)\nWe have shown that the metric used is not sensitive to the log distribution of chla or the\nattenuation coefficient, and that the calculated 𝛤chla is identical whether chla is log transformed\nbefore being input into the calculation.\nLine 206-208 - previous papers have not reported contradictory results — not sure why the\nauthors find contradictory results when using satellite data\nYes precisely, this contradictory result is a key finding of this paper and a major issue if satellite\ndata is being used for a similar method. We have not found other papers that reported this\ncontradiction.\nLine 214-216 Could this be because chlorophyll is log normally distributed\nWe have tested the algorithm before and after a log transformation and it is insensitive, i.e. non-\nparametric, to the distribution of the data, and have added a sentence to that effect in the text\nLine 234-235 - No. This conclusion is not substantiated by the findings.\nWe have re-worked this conclusion and defined emergent. This section now states that plankton\npatchiness is modulated by biological processes sufficiently that the variance in patchiness\ncannot be statistically explained by the concurrent physical patchiness field. By emergent\nproperty we refer to a possibly unexpected outcome from the fields, a property that comes from\nbehavior of the ecosystem (e.g. prey-predator interactions, reproduction, viruses). We have\nclarified this in the manuscript at the first mention of ‘emergent’.\nFig 7. Same as Fig 6a except for the color of dots?\nCorrect, this is showing the same data but colored by nutrient concentration in the provinces.\nFig 8. Could this figure go in the supplementary material?\nWe consider Figure 8 critical to the conceptual understanding of the patchiness we observe and\nfor showing that this fine scale variability stems from high quality measurements not from noise\nin the instrument or measurement process.\nLine 315 scale\nCorrected\nLine 320 - seems that Reference 31 is for oligotrophic regions, whereas the results presented\nhere are for productive regions\nOur study area includes many oligotrophic regions (e.g. subtropical gyres in the Pacific) in\naddition to more productive waters.\nLine 353 - “physical patchiness is more random” - this does not seem correct\nWe have changed this to state that physical patchiness is less coherent spatially and organized\ndifferently. We have quantified this via the autocorrelation of patchiness at multiple lags, where\nthe autocorrelation of 𝛤 is higher than 𝛤 at all lags. We have also added this to the\nchla temp\nresults.\nLine 361-2 why should there be an interdependence?\nIf plankton were simply a passive tracer we could expect a strong relationship between the\npatchiness of plankton and temperature.\nLine 365 - this is not a conclusion that can be drawn from the results presented - and seems\nincorrect\nWe have removed the word \"independently\" and reworked this whole section.\nDue to the incorrect interpretation of findings, several inaccuracies, and understanding gaps of\nprevious literature, I do not recommend publication of this article.\nWe have addressed each point provided, all of which we believe have considerably clarified and\nstrengthened the paper. We thank you for your thorough review and time spent on this work.\nReviewer #3 (Remarks to the Author):\nThis article examines the scales of variability in both optical and physical variables from in-situ\nocean surface observations. Results demonstrate that basin-scale variance slope does not\ncorrelate between the biological/biogeochemical and physical variables. A shorter analysis of\nsimilar variables from satellite data (mainly in the supplement) demonstrates one reason why\nprevious studies have found correlations in spectral slopes or variance slopes, as those do\noccur in the satellite record. These results are critical for understanding decades of\ndisagreements in the field, as it seems there will not be a simple relationship to be found\nbetween the variance slope for physical and biological variables, but rather only an underlying\nset of relationships between the physical environment and biological concentrations, and then\nfrom concentrations to variance slope. This is an important step toward improving\nbiogeochemical and climate models and satellite data analysis in the future.\nThis is a well-written article with clear methods and results. The analysis supports the\nconclusions drawn. There are no major flaws. I recommend this article be returned for minor\nrevisions to address comments below.\nMinor Revisions\n1. Line 120, citation 17. Is the correlation below 5km and maybe above 80km, or is the\ncorrelation occurring at small scales with an uncertain upper limit between 5 and 80 km? Please\nrewrite for clarity.\nWe have re-written this to be clearer in both instances where this reference occurs in the\nmanuscript.\n2. At the beginning of the results, please repeat or move (from line 198) the equivalent value for\nGamma (variance slope) to -5/3 for spectral slope. I really wanted to know at that time when\nreading.\nWe have repeated the variance slope value that corresponds to -5/3 in this first results\nparagraph for easier reader interpretation.\n3. In Figures 1 and 3, the dots on the map are quite small. Is it possible to increase their size\nwhile still allowing the gaps to be visible? Maybe they can be drawn as ellipses or rectangles so\nthat there are larger colored areas without excessive overlap.\nWe agree the dots are small. But given the legs in close proximity it is challenging to make them\nlarger without covering other data. These maps are very high resolution and we will ensure if\npublished that the highest resolution possible is shared so that readers can zoom in and\nexamine the data clearly.\n4. Line 230: please add a brief description of Longhurst provinces and note that Figure 5 shows\ntheir location-- I read this as the averages would be in Figure 5 separately from the full data in\nFigure 4.\nBrief description added as well as a note that Fig 5 shows their location.\n5. Figure 6c: Please add a note as to why the x-axis is reversed or remake this with an\nincreasing x-axis. It is quite jarring to see a negative slope in the labeled equation with the\nvisually 'positive' slope. Also please explain why R2=0.02 is considered correlated and R2=0.00\nis not. Even though p is small, it is hard to understand why this is convincing. Would showing\nthe log be better?\nWe have changed this back to not be flipped on the x-axis for consistency. This is a good point\nabout the R2 value. In the text we specify that only the concentration dependent variables (chla\nand cp) have a correlation between patchiness and absolute value.\n6. Figure 7d: The Longhurst province averages for O2 do not appear to be correlated to chl-a or\nGamma_chla here. Please confirm that this is the case, as you assert (line 282) that this is a\nclear increasing relationship and by eye it is not.\nWe have corrected this to say “Oxygen saturation has a slight decreasing relationship with more\nconsiderable outliers.”\nTypos Etc.\n1. Line 290: add 'in' after 'zooming'\nCorrected\n2. Figure 8: please label the location this data is from in more detail-- can you give a\nlatitude/longitude for the middle, perhaps?\nWe have now noted the centroid for this transect which is centered on 20.23 S, 152.90 E.\n3. The end of the results section includes author names for references, which is not the case\nelsewhere. Please double check these choices.\nCorrected\n4. In the references, sometimes 'Boss' does not have initials for first/middle name.\nThank you for this detailed check, we have corrected author initials.\n5. Please check references to make a consistent format. The number of authors included, for\nexample, before going to et al., is variable.\nWe have corrected references to a consistent format."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I think the revised text and figures more closely align with the stated claims in the manuscript. My only suggestion would be to perform a careful proofreading, as I noticed some minor grammatical errors and miscitations.", "reviewer_3": "This is a well-written article with clear methods and results. The analysis supports the conclusions drawn. There are no major flaws. The revised manuscript has addressed all my previous minor concerns. I recommend this article be published in this journal."}, "author_response": "Thank you for your follow on review, we have gone through the manuscript more\nthoroughly and corrected typos and errors in grammar as well as cleaned up the figure\ncaptions for clarity, proper format, and language consistency.\nThank you for this review, we appreciate your prompt second round of comments."}]

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