1. Eddy statistics in the South China Sea
Towards statistical downscaling ocean hydrodynamics
Eddy statistics in the South China Sea
Hans von Storch and Zhang Meng(张萌)
Institute of Coastal Research, Helmholtz Center Geesthacht, Germany
11 October  青岛 (Qingdao)

2. Outline Framework: empirical downscaling in marginal seas.
High-resolution, homogenous and temporally extended data needed: the STORM simulation
Eddy detecting and tracking
Eddy statistics in the South China Sea.

3. The downscaling problem
Climate models, and in general environmental models resolve only scales larger than a certain threshold, given by the employed grid-size.
The summary effect of smaller scales is described by parameterizations, which are considered to provide the correct feedback on the resolved dynamics of the unresolved dynamics (parameterizations are conditional empirical models, which are motivated by physical concepts).
Therefore, even if the effect of unresolved small scale features is implicitly taken into account, a detailed description of the changing unresolved scales is not available in such models.
In this case, downscaling is applied – when physical arguments indicate that the smaller scales are conditioned, or even determined by the larger scales. The same method can be applied, when local or regional impacts, which are also conditioned (but not caused) by the large-sale state, are considered.
In both cases, empirical models are fitted to samples of predictors, represented large-sale states, and of predictands, representing the local or regional statistics. These models are then used to estimate the unknown change related to a projected large-scale state.

4. First example in oceanography, done with visiting scientist 崔茂常 of IOCAS to MPI-Met in Hamburg in about 1993.
Predictor: Monthly SST and monthly SLP in the North Pacific
Predictand: Monthly sea level at a number of stations along the Japanese coasts
崔茂常 (Cui M.), H. von Storch and E. Zorita, 1995: Coastal sea level and the large-scale climate state: A downscaling exercise for the Japanese Islands, Tellus 47 A, also in 1996: 沿海水位和大尺度气候状态-降尺度技术在日本列岛的应用, Studia Marina Sinica 36, 13-32

5. 2. Data to construct empirical downscaling methods 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.

6. STORM simulation
We use the “STORM” simulation of the Max Planck Institute of Metyeorology, designed and supervised by Jin-Song von Storch (徐劲松)
MPI-OM model
Forced 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

7. 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
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.
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

8. 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

9. 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 9

10. 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

11. 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 data set, extending form may be suitable for deriving indicators for small scale oceanic features, such as eddies.

12. 3. Eddy detection and tracking
SSHA contour lines, with an eddy in the center
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 minimum life time τ and a peak minimum (maximum) 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 of the eddy is defined to be d2 = 2n /π (dx)2. km.
Location and extension of the cyclonic eddy shown above

13. Sensitivity to parameters minimum ζ and intensity P
The number of eddy tracks in 2001 in the SCS detected in the STORM simulation
ζ=1mm
ζ=3mm
ζ=5mm
ζ=7mm
Anti
Cyc
P=2mm 64
122 -
P=4 mm 43
103 36 87
P=6 mm 22 76 19 73 13 52
P = 8 mm 14 54 53 11 44 7 26
P = 10 mm 31 6 29 4
Results depend sensitively on the ζ threshold and on the maximum minimum maximum P along the eddy track (and further parameters not discussed here)
More cyclonic than anti-cyclonic eddy tracks are detected.
If a distance for connecting daily eddies is increased from 20km to 25km, more tracks are detected.
It is worthy noting that when the minimum maximum intensity is up to 10mm, the number of anti-cyclonic eddies tracks is getting very small.
张萌 (Zhang M.), H. von Storch, and 李德磊 (Li D.), 2017: The effect of different criteria on tracking eddy in the South China Sea , Research Activities in Atmospheric and Oceanic Modelling (WGNE Blue Book) , 2.25

14. (blue: cyclonic eddies; red: anti-cyclonic eddies)

15. 4. Eddy statistics in the South China Sea
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 = 4mm

16. correlations STORM ROMS/Xiu et al
AVISO satellite
0.31
0.03 1
-0.11
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

17. The number of cyclonic and anticyclonic eddies in each year when set the minimum local minimum ζ= 6mm and the minimum P = 10mm (strongest local minimum along one track). The correlation amounts to 0.38.

18. Sensibility to the choice of local minimum depth ζ maximum depth P along the eddy tracks
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 0.72,
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

19. Intensities: sorted into bins of 1 cm length (start at 0.0 cm),%
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.
Diameters: sorted into bins of 12 km (start from 10km), %

20. Present status of work and outlook
PhD work by CSC-student Zhang Meng (张萌), designed and supervised by Hans von Storch, with advice from SCSIO-CAS in Guangzhou and OUC in Qingdao.
Basic idea: testing the concept of empirical downscaling of statistics of small-scale features in marginal and coastal seas.
Three steps envisaged for doing so: a) identifying a suitable data set, which allows to determine samples of annual statistics of small-scale features – needed for training statistical downscaling models – here: STORM-simulation done at MPI-Met; done; publication available b) determining the frequency and intensity of eddies in the South China Sea, as described by STORM. Almost done, publication in preparation. c) Building empirical links between annual (seasonal) eddy statistics in the SCS and large-scale predictors, both atmospheric and oceanic – in order to estimate changes of eddy statistics as a response to global change and inter-annual/decadal variability. Will be begin soon.
Outlook – develop models, which allow for dynamical downscaling (by constraining large-scale state in marginal and coastal seas); apply to climate change simulations.