’s in satellite images
Viewing through the
C.
a
Troupin
(
ctroupin@ulg.ac.be), A.
a,b
Barth ,
A.
a,b
Alvera-Azcárate ,
c
Sirjacobs
D.
& J.-M.
a,b
Beckers
a GeoHydrodynamics and Environment Research, MARE, University of Liège, BELGIUM
b F.R.S.-FNRS, BELGIUM
c Algology, Micology and Experimental Systematics, Department of Life Sciences, University of Liège
1. Summary
4.1 Spatial modes
4. Results
st
1
21oW
Corresponding to the SST in Figure 2.
1st mode: meridional temperature gradient.
2nd mode: separation between coastal and open-ocean waters.
example: SST in the Canary Islands region
18oW
15oW
12oW
9oW
21oW
18oW
15oW
12oW
3rd mode: 1% of the total variance, structure similar to
1st mode.
9oW
26
2008−07−27
4th mode: island wakes . . .
34oN
24
32oN
22
30oN
Most of the satellite images are affected by , leaving gaps
in the maps. We present an objective method for filling
incomplete satellite images and called DINEOF.
20
28oN
18
26oN
2. Method
16
DINEOF = Data + INterpolating + Empirical Orthogonal
Functions [Beckers and Rixen, 2003, Alvera-Azcárate et
al., 2005, 2007]
It is an iterative method based on a decomposition into principal modes of variations.
The missing pixels are reconstructed using a truncated Singular Value Decomposition. If X is a matrix containing a
time series of images:
X = USVT
21oW
18oW
15oW
12oW
9oW
21oW
18oW
15oW
12oW
9oW
26
2010−08−21
34oN
24
32oN
22
30oN
20
(1)
28oN
with
18
U , the spatial EOFs,
26oN
V , the temporal EOFs and
16
S , the singular values.
The temporal covariance matrix is filtered in order to enhance the coherence between successive images
[Alvera-Azcárate et al., 2009].
Figure 2: Reconstructions of SST for July 27, 2008 and September 1, 2010.
nd
2
× 106
4
example: TSM in the North Sea
3
2
Original data − 24 Feb 2003
1
(mg/l)
100
(mg/l)
100
100
0
−1
30
500
−2
100
30
500
10
−4
400
3
4.2 Temporal modes
10
1st mode: seasonal cycle of temperature.
3
2nd mode: related to wind curl.
1
EOF 1
−3
400
Figure 4: First four spatial modes for 2008, 2009
and 2010.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1
Figure 1: Time covariance matrix for the SST in
the Canary Island area in 2010.
The optimal number of retained modes is determined by
cross-validation.
300
0.3
0.1
200
200
300
400
500
600
100
Original data − 25 Jun 2003
30
500
0.08
0.06
0.04
0.03
200
300
400
500
600
100
0.01
100
0.02
0
−0.02
(mg/l)
100
30
500
10
−0.04
−0.06
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Aug
Sep
Oct
Nov
Dec
EOF 2
10
0.02
400
3
400
1
300
0.3
• wind, . . .
0.1
200
300
200
0.03
The variables can be used separately (monovariate)
or simultaneously (multivariate).
3
0
1
−0.02
0.3
−0.04
0.1
−0.06
0.03
2008
2009
2010
−0.08
−0.1
200
The outputs are:
2008
2009
2010
−0.08
• total suspended matter (TSM),
The method works on a time series of images.
200
0.01
100
Any kind of satellite measurements can be exploited:
• chlorophyll concentration,
0.1
(mg/l)
100
• sea-surface temperature (SST),
0.3
0.03
The
code
can
be
obtained
at
http://modb.oce.ulg.ac.be/mediawiki/index.php/DINEOF
3. Data
0.1
300
300
400
500
600
100
0.01
200
300
400
500
600
100
0.01
−0.12
Jan
Feb
Mar
Apr
May
Jun
Jul
Figure 3: Reconstructions of TSM for February 24 and for June 25, 2003.
1. The reconstructed fields.
Figure 5: First two temporal EOFs. Thick curves
indicate the 30-day running averages.
2. The temporal and spatial modes.
Summary
DINEOF is an EOF-based method designed to fill in missing data from geophysical fields. It has been successfully applied
to various data sets.
Main references
Alvera-Azcárate, A.; Barth, A.; Sirjacobs, D. & Beckers, J.-M. (2009), Enhancing temporal correlations in EOF expansions for the reconstruction of missing
data using DINEOF, Ocean Sci., 5, 475-485, doi:10.5194/osd-6-1547-2009.
Alvera-Azcárate, A.; Barth, A.; Rixen, M. & Beckers, J.-M. (2005), Recon-
Beckers, J.-M. & Rixen, M. (2003), EOF calculation and data filling from in-
struction of incomplete oceanographic data sets using Empirical Orthogonal Functions. Application to the Adriatic Sea, Ocean Model., 9, 325-346,
doi:10.1016/j.ocemod.2004.08.001.
Sirjacobs, D.; Alvera-Azcárate, A.; Barth, A.; Lacroix, G.; Park, Y.; Nechad,
Alvera-Azcárate, A.; Barth, A.; Beckers, J.-M. & Weisberg, R. (2007),
Multivariate reconstruction of missing data in sea surface temperature,
chlorophyll and wind satellite fields, J. Geophys. Res., 112, C03008,
doi:10.1029/2006JC003660.
complete oceanographic datasets, J. Atmos. Ocean. Tech., 20, 1839-1856,
doi:10.1175/1520-0426(2003)020<1839:ECADFF>2.0.CO;2.
B.; Ruddick, K. & Beckers, J.-M. (2011), Cloud filling of ocean colour and sea
surface temperature remote sensing products over the Southern North Sea by
the Data Interpolating Empirical Orthogonal Functions methodology, J. Sea
Res., 65, 114-130, doi:10.1016/j.seares.2010.08.002.