Viewing through the
’s in satellite images
C. Troupin
a
(
ctroupin@ulg.ac.be
), A. Barth
a,b
, A. Alvera-Azc´arate
a,b
, D. Sirjacobs
c
& J.-M. Beckers
a,b
a GeoHydrodynamics and Environment Research, MARE, University of Li`ege, BELGIUM b F.R.S.-FNRS, BELGIUM c Algology, Micology and Experimental Systematics, Department of Life Sciences, University of Li`ege
1. Summary
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.
2. Method
DINEOF = Data + INterpolating + Empirical Orthogonal Functions [Beckers and Rixen, 2003, Alvera-Azc´arate et al., 2005, 2007]
It is an iterative method based on a decomposition into prin-cipal modes of variations.
The missing pixels are reconstructed using a truncated Sin-gular Value Decomposition. If X is a matrix containing a time series of images:
X = USVT (1) with
U , the spatial EOFs,
V , the temporal EOFs and S , the singular values.
The temporal covariance matrix is filtered in order to en-hance the coherence between successive images
[Alvera-Azc´arate et al., 2009].
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
−4 −3 −2 −1 0 1 2 3 4 × 106
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.
The code can be obtained at
http://modb.oce.ulg.ac.be/mediawiki/index.php/DINEOF
3. Data
Any kind of satellite measurements can be exploited: • sea-surface temperature (SST),
• total suspended matter (TSM), • chlorophyll concentration,
• wind, . . .
The method works on a time series of images.
The variables can be used separately (monovariate) or simultaneously (multivariate).
The outputs are:
1. The reconstructed fields.
2. The temporal and spatial modes.
4. Results
1
st
example: SST in the Canary Islands region
21oW 18oW 15oW 12oW 9oW 26oN 28oN 30oN 32oN 34oN 21oW 18oW 15oW 12oW 9oW
2008−07−27
16 18 20 22 24 26 21oW 18oW 15oW 12oW 9oW 26oN 28oN 30oN 32oN 34oN 21oW 18oW 15oW 12oW 9oW2010−08−21
16 18 20 22 24 26Figure 2: Reconstructions of SST for July 27, 2008 and September 1, 2010.
2
nd
example: TSM in the North Sea
Original data − 24 Feb 2003
200 300 400 500 600 100 200 300 400 500 100 (mg/l) 0.01 0.03 0.1 0.3 1 3 10 30 100 200 300 400 500 600 100 200 300 400 500 100 (mg/l) 0.01 0.03 0.1 0.3 1 3 10 30 100
Original data − 25 Jun 2003
200 300 400 500 600 100 200 300 400 500 100 (mg/l) 0.01 0.03 0.1 0.3 1 3 10 30 100 200 300 400 500 600 100 200 300 400 500 100 (mg/l) 0.01 0.03 0.1 0.3 1 3 10 30 100
Figure 3: Reconstructions of TSM for February 24 and for June 25, 2003.
4.1 Spatial modes
Corresponding to the SST in Figure 2.
1st mode: meridional temperature gradient.
2nd mode: separation between coastal and open-ocean wa-ters.
3rd mode: 1% of the total variance, structure similar to 1st mode.
4th mode: island wakes . . .
Figure 4: First four spatial modes for 2008, 2009 and 2010.
4.2 Temporal modes
1st mode: seasonal cycle of temperature. 2nd mode: related to wind curl.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 EOF 1 2008 2009 2010
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec −0.12 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 EOF 2 2008 2009 2010
Figure 5: First two temporal EOFs. Thick curves indicate the 30-day running averages.
Summary
DINEOF is an EOF-based method de-signed to fill in missing data from geophys-ical fields. It has been successfully applied to various data sets.
Main references
Alvera-Azc´arate, A.; Barth, A.; Rixen, M. & Beckers, J.-M. (2005),
Recon-struction of incomplete oceanographic data sets using Empirical Orthogo-nal Functions. Application to the Adriatic Sea, Ocean Model., 9, 325-346, doi:10.1016/j.ocemod.2004.08.001.
Alvera-Azc´arate, 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.
Alvera-Azc´arate, A.; Barth, A.; Sirjacobs, D. & Beckers, J.-M. (2009),
Enhanc-ing temporal correlations in EOF expansions for the reconstruction of missEnhanc-ing data using DINEOF, Ocean Sci., 5, 475-485, doi:10.5194/osd-6-1547-2009.
Beckers, J.-M. & Rixen, M. (2003), EOF calculation and data filling from
in-complete oceanographic datasets, J. Atmos. Ocean. Tech., 20, 1839-1856, doi:10.1175/1520-0426(2003)020<1839:ECADFF>2.0.CO;2.
Sirjacobs, D.; Alvera-Azc´arate, A.; Barth, A.; Lacroix, G.; Park, Y.; Nechad,
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.
