Mesoscale resolution capability of altimetry: present and future
C.Dufau, M.Orsztynowicz,
Abstract
(CLS)
(LEGOS)
G.Dibarboure ,R.Morrow
,
Jason-2, Cryosat-2 LRM and SARAL/Altika mesoscale resolution capabilities
Wavenumber spectra computed from along-track
Sea Surface Height Anomalies exhibit linear slope
between large and small scales linked to the
geostrophic turbulence and its energy cascades in
the mesoscale band (Le Traon et al., 2008). At small
scales, altimeter measurements are affected by
instrumental noise preventing the observation of
small scales processes. This paper determines the
length scales of ocean dynamics following SQG
theory reachable with along-track 1hz altimeter
data. It relies on a joint analysis of (1) the spectral
slope in the mesoscale band and (2) the noise level
observed for scales lower than 20km. Maps of
mesoscale capability of the on-flight altimeter
missions (Jason-2, SARAL/Altika, Cryosat-2) are
discussed at global scales. Finally, a prediction of the
future 2D mesoscale resolution capability of the
SWOT mission is computed using a simulated SWOT
error level
Given the different error levels of each satellite mission,
estimated from 1hz along-track SSH, and their
geographical distribution (Figure 2),
Given the spatial distribution of spectral slopes values
(Figure 3, very similar for all satellites),
a map of mesoscale resolution capability is proposed for
present satellite altimetry missions (Figure 4).
Very small spectral slopes in the equatorial area
(10°S/10°N) provide unrealistic submesoscale capability.
In this equatorial band, geostrophic turbulence cascade is
no more dominant and this method less pertinent.
SARAL/Altika with its reduced error level compared to J2
and C2 owns a better mesoscale capability.
For all altimeter, the spatial distribution of this capacity
is similar relying on the error level distribution and
spectral slopes distribution.
 Access to sub-mesoscale dynamics with altimeter data
will only be feasible in some oceanic places and may vary
with seasons (due to 1hz error change with time because
partly linked to waves)
Methodology
The mesoscale capability of an along-track altimeter
1hz data depends locally on its small-scales error level
and on the mesoscale spectral slope (geostrophic
turbulence cascade theory).
The geographical description of this mesoscale
capability relies on SSH wavenumber spectral
characteristics of on-flight altimeter missions. SSH is
corrected from all altimeter corrections and from the
Mean Sea surface CNES-CLS-2011.
Wavenumber spectra are calculated following Le
Traon et al. 1990 from March to October 2013 and
averaged over 10°x10°boxes as Xu and Fu 2011,2012.
A SSH wavenumber spectrum obtained in one of
these boxes is illustrated in black in Figure 1.
At high wavenumbers, between 20km and 12km, the
noise level is estimated as the mean value of energy
in this band.
To estimate the spectral slope in the mesoscale band,
between 250km and 90km, by a least squares
regression, we first remove the error (white noise)
effect on the spectrum shape (red curve on Figure 1).
The mesoscale capability is the wavelength of the
crossing point
Figure 1 : Mean
SSH PSD for 7
months of Jason-2
data in a 10°x10°
box located in the
Kuroshio Current
system centered in
[294E, 39N]. The
vertical lines are
90% confidence
intervals.
λ
mesoscale capability
Contact : [email protected]
P.Y. Le
(IFREMER)
Traon
In red: unbiased
spectrum with the
constant noise level
removed
In black :original
spectrum
Figure 2: Altimeter 1Hz noise level (m rms) estimated from mean
SSH wavenumber spectrum over March-October 2013 period.
Values ranging from 1.5 to 3.5 cm rms. a) Jason-2 b) Cryosat-2
LRM and Pseudo-LRM in black contoured areas and c)
SARAL/Altika . Only Boxes with more than 120(J2) and 160 (C2,
AL) samples are plotted
Figure 3: Altimeter spectral slope (*-1) estimated from mean
SSH wavenumber spectrum over March-October 2013 for Jason2 (a), Cryosat-2 LRM (b) and SARAL/Altika (c). Only Boxes with
more than 120 (J2) and 160 (C2 AL) alongtrack samples are
plotted. The slope is estimated after noise level removal in the
PSD (red curve on Figure 1). Units= log(m2/cpkm)/log(cpkm).
Impact of MSS accuracy error on non-repetitive altimeter mission
For non-repetitive altimeter missions such as Cryosat-2, or for new altimeter
orbits with uncharted ground-tracks such as Sentinel-3 or the future SWOT
mission, the SSH anomalies are referenced to a gridded MSS instead of an
along-track precise mean profile.
To date, the error level of the SWOT mission is expected to have a mean value of 2.5 cm RMS for a
1km resolution, with a modulation of the mean across-swath error level by the SWH: ranging from
2.6 cm RMS for SWH less than 2m, it increases up to 5.6 cm RMS for SWH of around 8 m (Peral et
al., 2015).
Using the spatial distribution of SWH estimated from Jason-2 observations from March to October
2013 and the relationship betwen SWH and error in KaRIN, a map of future SWOT error level has
been simulated. Together with the Jason-2 spectral slopes distribution (Figure 3-a), it permits to
estimate the SWOT mesoscale resolution capability (Figure 6).
when Jason-1 is on its interleaved orbit, i.e. a charted ground track (May10June11) = “J1N”- green curve on Figure 5a →
during the Jason-1 end of life phase, when the altimeter is on an uncharted
geodetic ground track (May 12- June13) = “J1G”- black curve on Figure 5a →
The extra energy in the Jason-1 PSD between these two periods infers the MSS
errors along the unchartered groundtracks: the PSDs show a substantial
difference in energy levels from 25-110 km wavelength over these two periods.
In the equatorial band, where the SSH
dynamics are dominated by tropical
waves, and potentially affected by
unresolved internal tides or internal
wave energy, fitting one linear slope
over this wavelength band is not well
adapted, and the proposed
submesoscale capabilities are
considered to be unrealistic.
The ratio of these PSDs over the PSD calculated with Jason-2 (as a reference) for
the two periods confirms that there is up to 17% of additional energy during the
non-repetitive phase (orange curve on Figure 5b →).
In the future, reduced MSS errors are expected over the 25-110 km wavelength
band from the most recent MSS products, such as DTU 2015 (Andersen et al.,
2015) or CNES-CLS 2015 (Schaeffer, personal communication), which include full
cycles of Cryosat-2 and Jason-1 geodetic data
Note: Despite those errors, the technique used to estimate the altimeter noise level below 25km is still relevant
for the Cryosat-2 mission since these wavelengths are barely affected by the MSS errors. In addition, the slope
estimates calculated above 90 km wavelength, are not affected by this additional MSS error
SWOT, future resolution capability to sample mesoscale dynamics
Considering the spectral slopes spatial distribution estimated from current altimetry missions
(Figure 3), the mesoscale resolution capability of the future mission SWOT has been estimated by
taking into account the simulated noise level of its instrument KaRIN .
The overlapping periods of the Jason-1/Jason-2 repeat missions and the
geodetic phase of Jason-1 are used here to infer the gridded MSS error away
from charted ground tracks. We compute the mean global PSD over 2
subsequent 1-year periods:
It means that using the gridded MSS slightly degrades the mesoscale
resolution capability of new altimeter orbits or geodetic orbits.
Figure 4: 1D Mesoscale resolution capability (in
wavelength in km) estimated from mean SSH
wavenumber spectrum over March-October 2013
period for Jason-2 (top), Cryosat-2 LRM (middle) and
SARAL/Altika (bottom).
Figure 5: a) Global (|lat| <60) PSD computed
for one-year of Jason-1 mission for 3 different
orbits (J1= Jason-1 on TOPEX track, J1N
=Jason-1 Interleaved, J1G= Jason-1 Geodetic
Mission). SLA referenced to gridded MSS
along real tracks. b) Ratio of global (|lat| <60)
PSD computed during geodetic period over
PSD computed during repetitive period for J2
and J1 missions. SLA referenced to gridded
MSS over 1 year in 2010-2011 and 2012-2013
along real tracks
Figure 6 : 1D mesoscale
resolution capability (in
wavelength in km) estimated for
the future SWOT mission, taking
into account Jason2 estimated
spectral slopes and mean SWH
from March to October 2013.
It leads to a mesoscale resolution capability strongly improved compared to current missions. Even
compared to SARAL/Altika, SWOT would greatly improve the observability of fine mesoscale and
submesoscale processes, at least in western boundaries current systems (Kuroshio, Gulf Stream,
Agulhas Current) where wavelength lower than 20km seem to be reachable.
Although its mesoscale resolution capability will vary seasonally and geographically, with such
performances this future 2D SSH mission is expected to reveal unprecedented observations of the
small-scale
features of the ocean.
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