1. Long-term variability of eddy activities in the South China Sea
张萌1 ,Hans von Storch12, 陈学恩2 and 王东晓3
1Institute of Coastal Research, Helmholtz Zentrum Geesthacht, Germany
2中国海洋大学
3中国科学院南海海洋研究所
中国科学院海洋研究所, Qingdao, 21. November 2018

2. Introduction / Purpose
This is a PhD work by 张萌, who studies with me in Geesthacht (in Germany, near Hamburg) with a stipend by CSC.
The issue of the work is
Determination of the statistics of eddies in the South China Sea as simulated by a state-of-the-art ocean model forced by daily NCEP atmospheric state. Its grid resolution in the SCS is about 0.1o.
Examining the resulting statistics if they may be used in empirical downscaling schemes, which skillfully estimate certain parameters representative for the seasonal eddy activity in the SCS from seasonal mean large-scale oceanic features.
(An empirical downscaling model makes use of paired data sets, one providing the predictors, and the other the predictands. Both data sets must be homogenous (of uniform quality across time). When using atmospheric states as predictors, then re-analysis data are in most cases suitable. Long term data sets of the state of marginal seas in the past decades based on observations hardly exist. Available ocean re-analyses cover only a few decades. Therefore it makes sense to use a multi-decadal hindcast with a high-resolution OGCM subject to atmospheric re-analysis as forcing.)

3. STORM simulation
We use the “STORM” simulation of the Max Planck Institute of Meteorology, designed and supervised by Jin-Song von Storch (徐劲松)
MPI-OM model
Atmospheric forcing by NCEP1
Covering
Time step: 600 seconds
Tripolar curvilinear Arakawa-C grid
Number of vertical levels: 80
Number of horizontal grid points: 3602 x 2394
Horizontal grid point distance: approx. 10km in the region of the SCS
The figure from

4. 1. Verification of STORM
Data sets
Data type
Time period
Gri
variables
STORM
Ocean Simulation
0.1o
sea surface height anomaly (SSHA), sea surface temperature (SST), currents etc.
AVISO
Satallite observations
0.25o
SSHA
C-GLORS
Data of moorings, ARGO floats, AVISO satellite data and so on assimilated
Ocean re-analysis data
SSHA, SST, currents and so on
We first compare STORM with AVISO and C-GLORS, and find sufficient similarity; from that we conclude that we may continue the verification of STORM by comparing with the derived C-GLORS data, which cover more variables that AVISO.
张萌 (Zhang M.), and H. von Storch, 2017: Towards downscaling oceanic hydrodynamics - Suitability of a high-resolution OGCM for describing regional ocean variability in the South China Sea. Oceanologia, DOI /j.oceano
C-GLORS also assimilates SST observations from the NOAA high-resolution daily analyses, which
uses AVHRR and (from 2002) AMSR-E radiances
temperature, salinity (from moorings and ARGO floats) and sea surface height (from AVISO satellite data
The global STORM/NCEP simulation: about 0.1° resolution; covering ; forced by the NCEP1 (“observed” atmosphere).
The AVISO sea surface height anomaly (SSHA) altimeter observations: 0.25° resolution; covering ; merge TOPEX-POSEIDON, ERS, JASON and ENVISAT products.
The C-GLORS re-analysis dataset: 0.25° resolution; covering ; forced by ERA_Interim; assimilated AVISO satellite data, moorings, ARGO floats.

5. SSHA in AVISO, C-GLORS and STORM
Good agreement with AVISO:
In winter (DJF), basin-wide cyclonic currents control most part of the SCS. In summer (JJA), anti-cyclonic currents dominate the SCS region.
The value in the center of the gyres is similar.
Seasonal mean of detrended SSHA

6. EOFs monthly SSHA fields
The coefficients of the first two EOFs
The main feature of EOF1 in the three dataset are similar.
The explained variance of the dominate mode in STORM is closer to AVISO.
The coefficient time series of STORM and C-GLORS are highly correlated with the “true” AVISO.
The first two EOFs (units: m) of monthly detrended SSHA (removing mean annual cycle)
correlations
1st
2nd
C-GLORS
0.936
0.795
STORM
0.911
0.773 6

7. Surface current fields in C-GLORS and STORM
The seasonal mean surface current fields of STORM and C-GLORS show similar variability: the strong current along the western boundary and the gyre in the south SCS with opposite directions in winter and summer.
The speeds in STORM are generally higher than in C-GLORS, which may be result of the much higher resolution of STORM and its ability to present more small-scale variability.
sea surface currents (at 6m depth). Units: m/s

8. Statistical analysis demonstrates that C-GLORS and STORM capture the main variability features of the SCS dynamic in terms of SSHA and currents
We conclude that the much longer STORM data set, extending form may be suitable for deriving indicators for small scale oceanic features, such as eddies.

9. 2. Eddies
In our research, eddy is defined as an extreme of SSHA moving in space and time.
An eddy detection and tracking algorithm based on gridded sea surface height anomaly (SSHA) fields was developed.
Most of those methods get the eddy size by using differential or integral computation to derive the streamline or geostrophic velocity.

10. Eddy detection and tracking
Eddies are detected, tracked and characterized in several steps
In the SSHA field, local minima or maxima of SSH are determined, which are at least ζ smaller (larger) than the nearest 24 surrounding grid points.
These minima, or maxima are connected to tracks of eddies. Only tracks longer than a minimum length L and a peak minimum (maximum) ζ of P are considered. Further criteria may apply.
The area of each eddy at each time is determined as the largest number of grid-points around the earlier determined minimum (maximum), so that all inner points are smaller (larger) than the grid-points along the outer border of the region. The difference between inner minimum (maximum) and the maximum value along the outer border is considered the intensity I of the eddy. If the number of inner points is n, then the diameter d of the eddy is defined to be d2 = 2n /π (dx)2. km.
SSHA contour lines, with an eddy in the center
Location and extension of the cyclonic eddy shown above

11. Eddy tracks in the South China Sea in 2001
The mean eddy travel length in our tests from the STORM daily data ranges from 150 to 280 km in 2001.
Anti-cyclonic eddy tracks
Cyclonic eddy tracks
Detected anti-cyclonic eddy tracks (left) and the cyclonic eddy tracks (right) for a given set of parameters: ζ = 3mm, and P = 6mm

12. When comparing the number of eddies, if ζ = 3mm/P = 6mm or ζ = 6 mm/P = 10 mm is employed in the detection algorithms, we find
a correlation of the annual number of anti-cyclones of 0.82,
and in the number of cyclones of 0.80.
Thus, the inter-annual variability of the annual eddy number is similar.
The correlation coefficient between the annual numbers of  anti-cyclones and cyclones eddy is
if ζ = 3 mm/P = 6 mm, and
if ζ = 6 mm/P = 10 mm.
which are comparable numbers
Even if the absolute numbers depend strongly on the choice to the parameters, the estimates about correlations among statistics and variability and trends is hardly affected.

13. Eddy statistics
On average, 28 anticyclonic eddies (AEs) and 54 cyclonic (CEs) eddy tracks per year are detected during
all AE CE
The area with high eddy frequency corresponds to the strong currents in the northern SCS well.
The frequency of eddy tracks passing by in each grid box during
Eddies are concentrated in the Luzon Strait and near the western coast.
Anticyclonic eddies are rare in the southern SCS.

14. Climatological characteristics
PDF of eddy travel length
The longest length: km for AEs; km for CEs.
The mean length: km (AEs); km (CEs).
The range of lifespans: days (AEs); days (Ces).
The mean lifespan: days (AEs); days (CEs).
PDF of eddy lifespan
Probability Density Function
The shorter travel length is, the more eddy track occurs.
The shorter lifespan is, the more eddy track occurs.

15. The intensities (EI) of peak points range from 0. 55 cm to 37
The intensities (EI) of peak points range from 0.55 cm to 37.3 cm, with peaks of 3-4 cm for AEs and 2-3 cm for CEs .
The diameters (EDs) of peak points have a range of 43 km-631 km, with most frequent interval of km.
Binned frequency distributions and scatter diagrams of the intensities and diameters of detected cyclonic and anti-cyclonic eddies in the South China Sea,
Anticyclonic eddies tend to be a bit stronger and larger than cyclonic eddies.
Intensities: sorted into bins of 1 cm length (start at 0.0 cm),%
Diameters: sorted into bins of 10 km (start from 25km), %

16. Seasonal variability
Seasonal cycle of eddy genesis number in Note, the numbers represent accumulated numbers.
The axis for AEs is on the left, and for CEs on the right. .
Much more CEs are generated in winter than in summer.
The genesis number of AEs reaches peak in spring and falls to bottom in autumn.
More CEs are generated than AEs in every month (note different axes!).
Most CEs are generated in winter, with a peak of cyclonic eddies in March.
More AEs are formed in spring than in autumn.

17. Diameter D
The monthly mean I and D of peak points reveal annual cycle, peaking in July with I = 9.14 cm and D = 205 km for AEs, while peaking in October with I = 7.93 cm and D = 192 km for CEs.
From July to October, the D and I values of peak AEs decline sharply, from the maxima hitting the minima
Rapid growth occur in both the D and I variability of CEs and increase to the maxima during these four months.
Intensity I
Different from eddy number

18. Strong inter-annual variability but weak decadal variability.
intensity [cm] of peak points
Number of eddy tracks
Strong inter-annual variability but weak decadal variability.
The annual mean D and I are correlated, with correlation coefficients of 0.76 and 0.68 for AEs and CEs.
Data problems prior 1958 – known from NCEP
diameter [km] of peak points
The amplitudes of AEs are stronger than CEs in terms of both diameter and EI.
Annual means of diameters and intensities

19. Summary of findings about eddy statistics
Statistics since 1958 seemingly stationary.
In general, CEs are much more active than AEs, but the proportion of AEs with high intensity, or large diameter, is higher than similar CEs.
I, D and eddy number exhibit distinct annual cycles.
The annual D, I and eddy number vary in a stationary manner, dominated by substantial inter-annual variability.
There are no noteworthy long-term trends in any of the studied annual statistics of eddy performance.
I and D exhibit high correlations on both seasonal and interannual time scales
The annual cycle between the two types of eddy is quite different, which may result from different genesis mechanism.

20. Earlier studies
Already earlier, Xiu et al. (2010) simulated the eddy activity in the South China Sea in ; in this study the separation into traveling and non-travelling eddies was not done; the time window was too short to assess the interdecadal variability and trends, and the correlation with the AVISO data set resulted in correlations smaller than in our case.
Xiu, P., F. Chai, L. Shi, H. Xue, and Y. Chao (2010), A census of eddy activities in the South China Sea during 1993–2007, J. Geophys. Res., 115, C03012, doi: /2009JC005657
correlations
STORM
ROMS/Xiu et al
AVISO satellite
0.21
0.03
-0.14
Chen et al (2011) examined the full AVISO data set. The issue of the limited accuracy of the SSH estimates from the satellite retrievals was not considered. Again the data set was too short for assessing interdecadal variability and trends.

21. Added value of present study over earlier studies
Progress over Xiu et al.’s work (2010):
[Xiu, P., F. Chai, L. Shi, H. Xue, and Y. Chao (2010), A census of eddy activities in the South China Sea during 1993–2007, J. Geophys. Res. Oceans, 115(C3), doi: /2009JC ]
Longer time period ( vs )
Better reproduction of AVISO-based statistics
Full range of travelling eddies (D≥30km vs. D≥90km)
over Chen et al.’s work (2011):
[Chen, G., Y. Hou, and X. Chu (2011), Mesoscale eddies in the South China Sea: Mean properties, spatiotemporal variability, and impact on thermohaline structure, J. Geophys. Res. Oceans, 116(C6), doi: /2010JC ]
Longer time period ( vs )
Finer resolution (0.1° vs 0.25°)
Full range of travelling eddies (D≥30km I≥0.11cm vs. D≥35km I≥3cm)
STORM produce more accurate sea surface height anomaly (SSHA), however, SSHA from AVISO is not that accurate.
Decadal variability and trend added.
Strong seasonal and annual co-variability between ED and EI

22. Lack of spatial structure
An astounding result is that – very different to most cases – the first EOFs of the spatial distribution of eddy parameters (seasonal number, mean seasonal intensity and mean seasonal diameter) do not really sum up a significant percentage of the variability.
Seasonal mean of cyclonic eddies
diameter (3.0%) intensity (4.0%) number of cases (2.9%)

23. Lack of spatial structure
Very likely, the EOFs are degenerate, i.e. represent random combinations reflecting spatial white noise variability, which hardly can be related to large-scale (i.e., organized) driving features. When the data are binned into larger spatial blocks, then some structures seem to form, but it is unclear if these would pass the test of “non-whiteness”.
The explained variance of the corresponding EOF1s
0.1° 1° 2° D
3.0%
7.8%
13.5% I
4.0%
8.8%
12.5% N
2.9%
12.4%
24.4%
Eigenvalue spectra of EOFs of number of eddies in different gridding
0.1° 1° 2°

24. Eddies as manifestation of intrinsic noise
In a separate study, we found that eddies are formed in a numerical model of the ocean hydrodynamics , even if no atmospheric variability is employed (apart of the annual cycle.) The higher the grid resolution, the more eddies are formed.
Thus, eddies are to large extent expression of intrinsic (unforced) variability.
[唐声全 , H. von Storch, 陈学恩, and 张萌: “Noise” in climatologically driven ocean models with different grid resolution. Oceanologia (submitted)]
Eddy occurrence for the 21 model years in the 0.2o model (a; left) and in the 0.04o model (b; right). The units are the numbers of the eddy. The blue lines indicate the 200m isobaths.

25. However, when vectors of aggregated statistics for the entire SCS are formed, some systematic structures emerge - which may indicate that large-scale drivers have an impact.

26. A canonical correlation analysis of aggregated eddy statistics and barotropic stream function point to a “conditioning” of eddy activity by the barotropic state
Summer season
I intensity, D diameter, N number, L track length, T life time; #I number of itense events

27. Large scale conditioning of eddy statistics in the SCS
At this time, all statements made here are tentative.
Using the barotropic stream function does not lead to a link of spatial distributions.
However, aggregated eddy statistics may be related to large-scale states.
The annual cycle of eddy statistics also points to a conditioning by large-scale states.
These large-scale states may be thermodynamic, and the barotropic stream function may not be a good predictor.
Tentative, speculative

28. Short Summary
We have derived long-term statistics of eddy formation and lifecycle in the South China Sea using a multidecadal simulations with an OGCM. There are no trends, but a clear annual cycle and inter-annual variability. The spatial variability is hardly organized, and a robust link to the large-scale current state has not yet been determined. 基于多年代际的全球环流模式模拟结果，我们提取了南海涡旋形成及其成长衰减的长期统计特性。我们发现南海涡旋没有年代际趋势变化，但是有显著的年循环和年际变率。其空间变化没有显著模态，与大尺度环流状态没有显著关联