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First result of ARGO survey - Analysis notes

The region studied extends from 210 ° E to 220 ° E and 20 ° N-25 ° N and the period is from Jan. 1, 2005 to Oct. 14, 2007. The region is small enough that a first estimate of the climatological fields is the average of all ARGO measurements available for this region. This might be OK for most of the water column but not near the surface where there is a still a seasonal cycle.

Temporal and spatial sampling

Fig. 1 shows the sampling of the water column with time for that region given the chosen set of isopycnal surfaces and Fig. 2 shows the sampling of the ARGO float in the horizontal.

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Figure 1: Depths sampled given the chosen set of isopycnal surfaces.

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Figure 2: Sampling of the ARGO float in the horizontal.

Fig. 3 plots the depths obtained for each isopycnal surface together with their mean depth.

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Figure 3: Depths of each isopycnal surfaces (black dots). The red profile shows their mean depth.

Relationship between depth anomalies, sea surface height and Okubo-Weiss parameter

Fig. 4 shows the Okubo-Weiss parameter (W) versus the sea surface height anomaly (SSHA) for the entire region and period (red) and for the space and time sampled by the ARGO float (black) using AVISO product. Regions of negative W are associated with regions dominated by vorticity such as the core of eddies while regions of positive W are associated with regions dominated by strain such as around eddies or along filaments. We see that most large negative values of W are obtained for large SSHA consistent with the idea that these points are located within the core of eddies. For positive W, the larger W the smaller SSHA; this suggests that the larger the strain, the further away from the edge of the eddy (defined as W=0). Fig. 5 shows a typical snapshot of positive W along with SSHA suggesting that high W values are obtained around/between eddies, not necessarily in isolated filaments. Notice, however, that the AVISO SSHA product does to resolve submesoscale features such as filaments. Thus, only negative W values should be interpretated into a relatively precised location, in this case inside the core of eddies and the larger the amplitude of W, the closer to the center of the eddy. Positive W values correspond to outside the core but large positive W values corresponding to isolated filaments are not present so that we cannot interpretate positive W values into a distance from the closest eddies.

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Figure 4: W versus SSHA from AVISO product: entire region and period (red) and space and time sampled by the ARGO float (black).

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Figure 5: Distribution of positive W (colors) and positive and negative SSHA (contours from -15 to -2 and +2 to +15 cm) on Jan. 1, 2005.

Figs. 6 and 7 show the depth of the isopycnal surface σ = 24.5 kg/m^3 that has a mean depth of about 110 m versus SSHA and W respectively. In Fig. 6, about 30% of large depth anomalies are associated with large SSHA such as shallower isopycnal surfaces are associated with a depressed SSHA (barolinic-like). “Large” is defined for each field as larger than one standard deviation. Only about 10% of large depth anomalies occur such as the sense of the deviation of the sea level and of the isopycnal surface is the same (barotropic-like). The majority, about 60%, corresponds to cases where depth anomalies are large but not necessarily the SSHA. Is this an evidence of large depth anomalies due to submesoscale processes (that may or may not have a large SSHA but are for sure filtered out in AVISO SSHA) or just due to the fact that the area of weak SSHA (non-eddy) is much larger than the area with large SSHA (eddies)? More work is needed. By looking at Fig. 6, one can offer another interpretation: It looks that most cases follow the linear relationship between depth anomaly and SSHA suggesting that the spread around that relationship is due to other processes (such as difference in stratification between eddies, error in defining anomalies, etc), not to the presence of submesoscale features.

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Figure 6: Depth anomaly of isopycnal surface σ = 24.5 kg/m^3 versus SSHA. Red lines show plus or minus one standard deviation for each field. Values larger than their corresponding standard deviation are defined as large.

In the relationship between depth anomaly and W (Fig. 7), there are a few points where large depth anomalies might be associated with strong eddies (large negative W), a few points where large depth anomalies are found outside eddies but just around eddies (large positive W) and most of the large depth anomalies are for small values of W –which can be anywhere outside eddies, either close or far away. This large number in the last case might just be because that space (not inside or around eddies) is rather large and will be sampled a lot by ARGO floats. It is nonetheless interesting because it shows that large depth anomalies might more often than not occur outside eddies and not necessarily in region of large mesoscale (AVISO) strain (large positive W).

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Figure 7: Depth anomaly of isopycnal surface σ = 24.5 kg/m^3 versus W. Red lines show plus or minus one standard deviation for each field.

To know what is the expected ratio of sampling eddies versus filaments, we would need to use a numerical simulation from which we would compute the percentage of the area composed of eddies and of the area composed of filaments. Lapeyre and Klein (2006), in their idealized simulation of geostrophic turbulence, found that 17% is filled with eddies, 26% by curved filaments (filaments around eddies) and 57% by isolated filaments, with the caveat that their “elongated” filaments really mean the rest, the background and not necessarily “isolated” filaments.

ARGO floats sample a priori all part of the ocean, inside, around and far away from an eddy. Thus, some large depth anomalies that are not associated with large positive or negative mesoscale (AVISO) W values may be associated with isolated filaments. Using W=0 as the definition of the edge of an eddy, we could calculate the relative position of each ARGO sampling with respect to the closest eddies.

Another interpretation of Fig. 7: among all strong eddies (W smaller than minus one standard deviation), 27% have a correspondingly large depth anomaly, among all strong mesoscale strain regions (W larger than one standard deviation), 18% have a correspondingly large depth anomaly, while among the rest (W smaller in amplitude than one standard deviation), either around or away from eddies, 23% have a correspondingly large depth anomaly. Thus in each case about 20-30% of events have large depth anomalies suggesting that large depth anomalies may not be dependent on the mesoscale structure of the flow? Similarly about 28% of large SSHA anomalies have also large depth anomalies and 20% of weak SSHA anomalies have also large depth anomalies.

Fig. 8 may support the previous interpretation. In the upper panel, it shows the number of large depth anomalies for various ranges of W. There are many more events for weak W than for large W in amplitude but that is because the area covered in the first case is much larger than in the second case. This is confirmed by the lower panel that shows the percentage of large depth anomaly events for each range. Although the percentage is slightly larger (30-40%) for large positive W and moderate positive W, it is about the same (18-25%) for the rest of W values. Notice, also, that for large positive or negative W and for moderately large positive W (W>6e-12 1/s^2), there are slightly more deep than shallow events while for the other ranges of W, it is the contrary. Of course, our statistics are not too sure as there are not too many events, especially for large positive and negative W. We will redo the calculation when we will have a longer time series.

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Figure 8: Analysis for isopycnal surface σ = 24.5 kg/m^3: (a) total number of large depth anomaly events and (b) percentage represented by these events for various ranges of W. In (b) the shallow events are represented in red, the deep events in blue. See ARGO_iso_survey_script.m in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/ARGO/analysis.

At this point, we are offering the interpretation that large depth anomalies appear anywhere, irrespective of the mesoscale flow. This might also explain the interpretation we gave above of Fig. 6 that the majority of large depth anomalies (about 60%) occurs with weak SSHA; the region with weak SSHA is larger and, if the interpretation of occurrence of large depth anomaly is right, we expect that most of the them occurs with weak SSHA. If true, that means that 1) small depth anomalies should also occur 60% of the time with weak SSHA (because large or small, depth anomalies are not dependent on the mesoscale flow) and 2) weak SSHA should represent about 60% of the total SSHA area. About 72% of small depth anomalies occur with small SSHA, 23% with large positive SSHA and 4% with large negative SSHA. 72% is a bit larger than predicted but might be with the statistical error –to check. When taking the SSHA field covering the whole region of interest (not just the SSHA at the positions of ARGO float), we find that weak SSHA represents about 68% of the total area on average in time, as low as 50% during winter-spring where there are a lot of eddies and as high as 72% during the rest of time (note: weak SSHA are defined as SSHA minus the time-mean SSHA (which is not zero) is smaller than the standard deviation of the whole SSHA fields, space and time included; see ARGO_iso_survey_script.m). It looks like I should have removed the time and spatial mean SSHA in the previous figures and calculations.

Some critics of or comments on the present interpretation:

  • Is the interpretation consistent with the asymmetry of Fig. 6 that large depth anomalies inside eddies occur mostly within baroclinic eddies (30%) than barotropic (or large-vertical-scale) ones (10%)? Yes, if we believe that there are more baroclinic eddies than barotropic ones.
  • If the interpretation is correct, that means that large depth anomalies due to eddies occur as often (or a little more often) than large depth anomalies outside eddies. What would that be?
  • In Fig. 6, how can we have large (positive) SSHA but small depth anomalies? This is possible for an eddy with weak stratification. Again, it would be nice to correct but it does not seem to be straightforward. Furthermore, we need to remind ourselves that there are cases where a shallow submesoscale event may be superimposed on a deep mesoscale event, cancelling the net anomaly.
  • Do the depth anomalies and the interpretation change when defined with a mean climatology? with a seasonally-varying climatology?

Interesting, the number of large depth anomalies increase with depths for all ranges of W with the exception of moderately large (12-20e-12 1/s^2) positive W. Because the number of samplings in each W category does not change with depth, the percentage of large depth anomalies behaves the same way (Fig. 9). Both positive and negative anomalies increase in most categories. This increase with depth is illustrated in Fig. 10 where we compare the distribution of depth anomalies with respect to W for σ = 24.5 and 26.5 kg/m^3.

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Figure 9: Percentage of large depth anomalies (red: positive, blue: negative, black: total) for various ranges of W. See ARGO_iso_survey_script.m in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/ARGO/analysis. The range of values above each graph is the range in Wx1e12.

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Figure 10: Depth anomalies versus W for σ = 24.5 and 26.5 kg/m^3. Red lines show plus or minus one standard deviation for the depth anomalies.

I do not have an explanation for this increase. Weaker stratification at depth could explain an increase in the amplitude of the depth anomalies but not in the change in the distribution. On the contrary, if large negative W correspond to eddies and weak and large positive W values correspond to submesoscale features, I would have expected that the percentage of large depth anomalies stay the same in the first case (because eddies have a deep signature) and decrease in the second case (because submesoscale features are believed to be surface trapped). This is not at all what is observed.

Fig. 11 repeats the result of Fig. 9 except that all W categories are plotted together. The increase with depth is again evident. However, the fact, true for σ = 24.5 kg/m^3, that the portion of large depth anomalies is independent of the W category, might not be true at other depths, especially deep in the ocean where some categories appear much more important than other.

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Figure 11: Percentage of large depth anomalies for various ranges of W. The red profile shows the percentage averaged over the W categories and the error bar shows plus and minus one standard deviation of that percentage over the W categories. A small error means that the percentage is relatively constant for all W categories.

Fig. 12 is another version of Figs. 9 and 11. It might be the better version has it shows that at depth, a larger proportion of large negative and positive W values have large depth anomalies.

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Figure 12: Percentage of large depth anomalies for various ranges of W.

Timing of events

Fig. 13 shows the depth anomaly with respect to time for σ = 24.5 and 26.5 kg/m^3. Large depth anomalies occur mostly in winter-spring. Fig. 14 shows the number of large depth anomaly every 30 days for all isopycnal surfaces. Again, one signal is the annual cycle with maximum number of depth anomalies occurring in winter-spring. This may be associated with the increase in eddy kinetic energy that occurs at the period in the region (Fig. 15). Why during the increase of EKE and not during when EKE is high?

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Figure 13: Depth anomalies versus time for σ = 24.5 and 26.5 kg/m^3. Red lines show plus or minus one standard deviation for the depth anomalies.

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Figure 14: Number of large depth anomalies every 30 days.

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Figure 15: Spatial STD of SSHA over the area smoothed by a 30-day running mean.

Some particular cases

On May 4, 2006, one ARGO float is found within a high positive SSHA (12 cm) with a shallower isopycnal surface (32 m shallower) at σ = 24.5 kg/m^3. Fig. 16 shows the SSHA, W and the position of the float on that day. Fig. 17a reveals that the isopycnal surfaces of the upper surface have all shallowed and it is only below 130 m that the isopycnal surfaces deepen as expected from a positive SSHA. The change between shallowing and deepening occurs when the stratification is the weakest (Fig. 17b).

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Figure 16: SSHA, W and depth anomaly (DA) on May 4, 2006. The red dot shows the position of the ARGO float, its color meaning that the DA at σ = 24.5 kg/m^3 is positive.

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Figure 17: (a) DA and (b) an estimate of the stratification for the float and time of Fig. 17.

Another particular case is on March 12, 2007 where all isopycnal surfaces have shallowed, by a lot (Fig. 19a), consistent with the large negative SSHA (about -10 cm; Fig. 18). This is the largest shallowing event recorded here at |sigma| = 24.5 kg/m^3 (see Figs. 6 and 7). What is interesting is 1) the fact that W is weak all across the large negative SSHA structure, suggesting that there are cases where large SSHA is not associated with strong relative vorticity and is not identified as an eddy as defined by W, although from the SSHA in Fig. 18 we would say that the float is inside the eddy 2) the vertical structure of the DA of Fig. 19a (barotropic + first baroclinic mode?).

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Figure 18: SSHA, W and depth anomaly (DA) on March 12, 2007. The red dot shows the position of the ARGO float, its color meaning that the DA at σ = 24.5 kg/m^3 is positive.

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Figure 19: (a) DA and (b) an estimate of the stratification for the float and time of Fig. 18.