Harmonic & EOF analysis for North Sea SPM patternsGerben J. de Boer (Deltares, TU Delft)Meinte Blaas (Deltares)Loana Arentz (Deltares)Niels Kinneging (Rijkswaterstaat WaterDienst)Ackowlegdements: Liege GHER group for DINEOF

Contents:1. The context2. Southern North Sea physics3. Harmonic analysis4. DINEOF analysis5. Hybrid analysis

land reclamationsand mining

wind farms

image credit: NASA MODIShttp://www.spaceref.com/news/viewsr.html?pid=23750

1. The context: stability of combined situ + RS signal

• Dutch government (Rijkswaterstaat) is monitoring North Sea SPM and Chl-a > 25 yr• Network of 80 (in 1980s) to 20 (currently) fixed ship-served locations• Visited bi-weekly to bi-monthly with buckets (chemicals)

• Current needs• Impact monitoring for new developments requires more resolution

> wind farms, land reclamation, sand mining• National program for OSPAR, WFD, MSFD requires optimization• Combining and changing observation techniques: ship buckets > buoys + scanfish + EO• RS from different L2 providers and satellites

• Use Remote Sensing data for monitoring too, ensuring consistency and veracity?

# pixe

ls in 1

year

of MERIS data

(binned to cu

rvi-linear

model)

50 to

80 good im

ages

per yea

r

# pixe

ls in 25

years

of in si

tu data

max. 2

6 good sa

mples per

year

1. The approach

Our problem• No in situ match-ups due to low bi-weekly sampling freq.• Gap filling (Nechad et al, 2011) for artificial match-ups won’t help here

Our aimProvide a reduced-order description of the state of the system from EO & in situ• Filtered historic sets to quantify consistency (e.g. cross comparison)• Statistical model to quantify veracity (plausibility) of new samples

Study case• 1 (to do 6) yr Envisat MERIS RR• VU-IVM / Water Insight HYDROPT retrieval

(SPM, Chl-a, CDOM, …)vd Woerd & Pasterkamp, ‘08; Peters et al., ‘05, ‘08

• Binned to curvilinear >1 km grid, focus coastal area

TechniquesHarmonic & DINEOF analysis of SPM• SPM variance quantification• SPM bulk statistic for consistency• SPM patterns for physical insight

Mean SPM

Pietrzak, de Boer, Eleveld, 2011, CSR 31(6). Mechanisms controlling intra-annual mesoscale variability of SST and SPM in the southern North Sea

fine bedsediments

Fortnight + tidalhaline stratifiedRhine ROFI /Coastal riverplume barocliniccoastaltrapping ofwater + SPM

Front: EastAnglia plume+ Frisian front

Seasonally,thermallystratifiedcentral N. Sea

Shallow mixedDogger bank

Central North Sea watersEast Anglia water

Central Channel waterContinental waters

2. Physics Southern North Sea

3. Pure harmonic analysis

Annual cycle:coherent phases: significant

Spatial modePhase annual cycle

Jan.

Oct.

Apr.

1

summer Thides bottom

SPM

winterstormsstirbed

Temporal mode

winterstormsmixS

Spatial modeAmplitude annual cycle

3. Pure harmonic analysis

Semi-annual cycle (6 month cycle):partly coherent phases:

significant?

1

bloom?

Temporal mode

Spatial modePhase semi-annual cycle

Spatial modeAmplitude semi-annual cycle

3. Pure harmonic analysis

Quarter-annual cycle (3 month cycle):incoherent phases: insignificant

1

Temporal mode

Spatial modePhase quarter-annual cycle

Spatial modeAmplitude quarter-annual cycle

4. Pure DINEOF analysis

EOF mode 1• rather steady: equivalent of A0 from harmonic analysis• max. 9 modes are found

1

Temporal modeSpatial mode

4. Pure DINEOF analysis

EOF mode 2• seasonal cycle, but not sinusoidal

• strong jump downward in spring• bumpy trend upwards in autumn

• spatially quite uniform value

1

Temporal mode

Spatial mode

summer Thides bottom

SPM

winterstormsstirbed

winterstormsmixS

4. Pure DINEOF analysis

EOF mode 3• high frequency behavior ~ 2 months• no obvious relation with physical cycles• spatially heterogeneous: continental

water mass stands out with lower response

1

?

Temporal modeSpatial mode

3+4. Explained variances

• East Anglia plume fits well bear UK• Rhine ROFI fits best with harmonic (3 modes)• DINEOF overall has a better fit (all 8 modes)

ExplainedDINEOF variance

Explainedharmonic variance

summer Thides bottom

SPM

winterstormsstirbed

winterstormsmixS

• DINEOF run 5 times• each time with 1 more harmonic component peeled off

• The harmonic annual mean overtakes EOF1• The seasonal cycle does not take over any EOF mode (EOF2)• Seasonal cycle only gets some significance when higher

harmonics are added: to account for steep spring changes?

5. Peeling off harmonics: explained variances

i i

var

mode mode raw raw

rawpixel wise, discarding clouded pixels

5. Temporal EOFS of harmonic residual

(3rd): 3.9 % seasonal sine

(4th): 2.5 % semi-seasonal sine

(2nd): . . . . . . . . . . . . . . . . 6.9 % EOF2

(1st): 44.3 % harmonic mean (EOF1)

(4th): . . . . . . . . . . . . . . . . . . 2.4 % EOF3

5. EOF2 unexplained pattern

no14.8%

- … - harmonic yr9.2%

- … - semi-year7.9%

- … - quarter-year6.9%

- mean13.6%

5. EOF3: unexplained pattern

no3.2%

- mean2.7%

- … - semi-year2.4%

- … - quarter-year2.4%

- … - harmonic yr2.2%

Conclusions: use harmonic + DINEOF

Modes in term of capture variance:• EOF1 ~ temporal (harmonic) mean

• Contains most of variance: close to 50%• Remove harmonic temporal mean before applying DINEOF• Harmonic A0 is least-squares fit: better than geometric mean / median

• EOF2 has 2nd most variance• Captures a little seasonality from raw EO data• Has only 2-month modes left after removal harmonic season from EO• Tele connection: Rhine ROFI & German Bight• Unexplained physical spatial pattern left with ~ 2-month cycle: more research

• Harmonic seasonal has 3rd most variance• mode only captures variance when higher harmonics are added too:• due to steep spring changes seasonality is not sinusoidal

• higher modes not recommended for reduced state

• Harmonic + DINEOF analysis together can yield reduced state with 3 modes• Plan: Match reduced modes with in situ DINEOF (only 1 mode found, data scarcity)

Questions?

image credit: NASA MODIShttp://www.spaceref.com/news/viewsr.html?pid=23750