Recent methods for Data Interpolation: DINEOF and DIVA

Recent methods for Data interpolation

DINEOF and DIVA

Charles T

ROUPIN

DIVA = Data-Interpolating Variational Analysis

From sparse data points, construct gridded field = analysis

d i

ϕ(xj, yj)

Formulation:minimize cost function that penalizes:

1 _{data–analysis misfit} 2 _{smoothness of the field}

3 _{physical constraint (advection,} sources, . . . )

DIVA = Data-Interpolating Variational Analysis

From sparse data points, construct gridded field = analysis

d i

ϕ(xj, yj)

Formulation:minimize cost function that penalizes:

1 _{data–analysis misfit} 2 _{smoothness of the field}

3 _{physical constraint (advection,} sources, . . . )

DIVA = Data-Interpolating Variational Analysis

From sparse data points, construct gridded field = analysis

d i

ϕ(xj, yj)

Formulation:minimize cost function that penalizes:

1 _{data–analysis misfit} 2 _{smoothness of the field}

3 _{physical constraint (advection,}

sources, . . . )

DIVA = Data-Interpolating Variational Analysis

From sparse data points, construct gridded field = analysis

d i

ϕ(xj, yj)

Formulation:minimize cost function that penalizes:

1 _{data–analysis misfit} 2 _{smoothness of the field}

3 _{physical constraint (advection,}

sources, . . . )

From in situ data to gridded fields

20o W 18o W 16o W 14o W 12o W 10o W 8o W 26o N 28o N 30o N 32oN 34o N T (°C) 15 16 17 18 19 20 21 22 23 24 18o_{W 15}o_{W 12}o_{W 9}o_W 26o_N 28o_N 30o_N 32o_N 34o_N 50 m T (°C) 16 17 18 19 20 21 22

Measurements (left) and analysed field of temperature at 50 m in the Canary Island area.

Why is better than other methods?

Topographic constraints

Optimized computation (finite-elements)

Free software, user-driven developments

0o 9oE 18oE 27oE 36oE 33oN 36o_N 39oN 42oN 45oN −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25

Difference between Optimal interpolation and DIVA for salinity in September at 30 m.

Diva user workshop

Where? STARESO station (2007-2010), Roumaillac (2012)

When? 1/year, Autumn

Public: beginners, intermediate and expert users

More information:

http:// modb.oce.ulg.ac.be/ mediawiki/ index.php/ DIVA

Test and play:

. . . they are limitations:

1

_{Spatial/temporal resolutions}

2

_{Measurements limited to surface}

Examples

21

o

W

18

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W

15

o

W

12

o

W

9

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W

26

o

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28

o

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30

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32

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N

34

o

N

T (

°

C)

19

20

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26

Examples

21

o

W

18

o

W

15

o

W

12

o

W

9

o

W

26

o

N

28

o

N

30

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N

32

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N

34

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N

T (

°

C)

19

20

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26

Examples

48oW 36oW 24oW 12oW 12oN 24oN 36oN 48oN

14−Mar−2009

m/s

0 5 10 15 20 25

DINEOF = Data INterpolating Empirical

Orthogonal Functions

Iterative method

1

_{Start with N = 1 mode}

Compute new values at missing pixels Repeat untilconvergence

Estimate reconstruction error

2

_{Increase number of modes and repeat procedure}

3

_{. . .}

4

_{Final reconstruction: number of modes that minimises}

Results

Results

Results

Spatial modes

Automatic processing

Automatic processing

http:

What’s more?

Multivariate analysis

Merging: polar-orbiting + geostationnary

Forecasts

What’s more?

Multivariate analysis

Merging: polar-orbiting + geostationnary

What’s more?

Multivariate analysis

Merging: polar-orbiting + geostationnary

Forecasts

DINEOF:

remote-sensing

+

model variables

measurements

↓

↓

no explicit

forecasts

What’s more?

Multivariate analysis

Merging: polar-orbiting + geostationnary

Forecasts

"Forecast"

of

Total Suspended

Matter

4oW 2oW 0o 2oE 4oE 49o_N 50o_N 51oN 52o_N 53o_N alpha = 0.03, p = 3 (mg/l) 0.01 0.03 0.1 0.3 1 3 10 30 100

Previous work

Seasonal cycles in the Canary Island region, JMS (2010)

Climatology of the North-East Atlantic, JGR (2010)

Generation of the Cape Ghir filament, OM (2012)

Generation of analysis and error fields using Diva, OM (2012) Depth (m)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 200 180 160 140 120 100 80 60 40 20 0 (°C) 14 15 16 17 18 19 20 21 22 23

Previous work

Seasonal cycles in the Canary Island region, JMS (2010) Climatology of the North-East Atlantic, JGR (2010)

Generation of the Cape Ghir filament, OM (2012)

Generation of analysis and error fields using Diva, OM (2012)

50oW 40oW 30oW 20oW 10oW 0o 0o 12oN 24oN 36o_N 48oN 60oN 600 m S 34.6 34.8 35 35.2 35.4 35.6

Previous work

Seasonal cycles in the Canary Island region, JMS (2010) Climatology of the North-East Atlantic, JGR (2010)

Generation of the Cape Ghir filament, OM (2012)

Generation of analysis and error fields using Diva, OM (2012)

Previous work

Seasonal cycles in the Canary Island region, JMS (2010) Climatology of the North-East Atlantic, JGR (2010)

Generation of the Cape Ghir filament, OM (2012)

Generation of analysis and error fields using Diva, OM (2012)

0o 9oE 18oE 27oE 36oE 33oN 36o_N 39oN 42oN 45oN −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25

In preparation

Structure and evolution of an upwelling filament off Cap Ghir in August 2009

Anomalies in the

tropical/subtropical North Atlantic in 2010

Temporal trends of the Black Sea Cold Intermediate Layer

Depth (m) 1 2 3 4 5 6 7 8 9 10 11 12 13 400 300 200 100 0 T (°C) 12 13 14 15 16 17 18 19 20

In preparation

Structure and evolution of an upwelling filament off Cap Ghir in August 2009 Anomalies in the

tropical/subtropical North Atlantic in 2010

Temporal trends of the Black Sea Cold Intermediate Layer

In preparation

Structure and evolution of an upwelling filament off Cap Ghir in August 2009 Anomalies in the

tropical/subtropical North Atlantic in 2010

Temporal trends of the Black Sea Cold Intermediate Layer

(f)