Sensors 2009, 9, 1306-1329; doi:10.3390/s90301306
OPEN ACCESS
sensors
ISSN 1424-8220
www.mdpi.com/journal/sensors
Article
Observing and Studying Extreme Low Pressure Events with
Altimetry
Loren Carrère 1,*, Françoise Mertz 1, Joel Dorandeu 1, Yves Quilfen 2 and Jerome Patoux 3
1
2
3
CLS, 8-10 rue Hermès, 31520 Ramonville St Agne, France; E-mails : fmertz@cls.fr (F.M.);
jdorandeu@cls.fr (J.D.)
IFREMER, Z.I. Pointe du Diable B.P. 70, 29280 Plouzané, France ; E-mail: yves.quilfen@ifremer.fr
(Y.Q.)
University of Washington, Box 351640 Seattle WA 98195-1640, USA; E-mail:
jerome@atmos.washington.edu (J.P.)
* Author to whom correspondence should be addressed; E-Mail: lcarrere@cls.fr;
Tel.: (+33) 5 61 39 37 96; Fax: (+33) 5 61 39 37 82
Received: 29 December 2008; in revised version: 9 February 2009 / Accepted: 24 February 2009 /
Published: 26 February 2009
Abstract: The ability of altimetry to detect extreme low pressure events and the
relationship between sea level pressure and sea level anomalies during extra-tropical
depressions have been investigated. Specific altimeter treatments have been developed for
tropical cyclones and applied to obtain a relevant along-track sea surface height (SSH)
signal: the case of tropical cyclone Isabel is presented here. The S- and C-band
measurements are used because they are less impacted by rain than the Ku-band, and new
sea state bias (SSB) and wet troposphere corrections are proposed. More accurate strong
altimeter wind speeds are computed thanks to the Young algorithm. Ocean signals not
related to atmospheric pressure can be removed with accuracy, even within a Near Real
Time context, by removing the maps of sea level anomaly (SLA) provided by
SSALTO/Duacs. In the case of Extra-Tropical Depressions, the classical altimeter
processing can be used. Ocean signal not related to atmospheric pressure is along-track
filtered. The sea level pressure (SLP)-SLA relationship is investigated for the North
Atlantic, North Pacific and Indian oceans; three regression models are proposed allowing
restoring an altimeter SLP with a mean error of 5 hPa if compared to ECMWF or buoys
SLP. The analysis of barotropic simulation outputs points out the regional variability of the
SLP/Model Sea Level relationship and the wind effects.
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Keywords: Altimetry, Detection, Tropical cyclones, Extra-tropical depressions, sea level
pressure, barotropic model
1. Introduction
At present, the observation of extreme events such as tropical cyclones (TCs) and extra-tropical
depressions (ETDs) through satellite measurements is mainly performed either through visualization of
large cyclonic cloudy areas and infrared temperature data (METEOSAT; POES, GOES and DMSP
satellites), or via wind field measurements by the Special Sensor Microwave/Imager (SSM/I) or
scatterometers (SeaWinds on QuikSCAT [1]; ERS, ADEOS and METOP satellites, [2]). Most
altimeter-based studies usually focus on ocean dynamics: by locating warm ocean patterns (such as the
Loop Current in the Gulf of Mexico), altimeter measurements allow the detection of ocean heat
content anomalies which can be associated with the sudden intensification of tropical cyclones [3,4].
The direct observation of very low pressure systems by radar altimeters has not been investigated yet.
Altimeters (ERS-2, ENVISAT, TOPEX/Poseidon, Jason-1, GFO) provide global sea surface height
(SSH) measurements of the ocean under nearly all weather conditions, with the exception of periods of
extremely heavy rain, which sometimes occur in hurricanes. The global SSH error for Jason-1 (J1) is
estimated to 3.9 cm in normal meteorological conditions [5]. Radar altimeters thus have some potential
for determining storm surge heights when flying over the storms. Now, three satellites (J1, ENVISAT,
ERS-2) fly together, thus deeply improving the global temporal and spatial altimeter coverage.
The Inverse Barometer (IB) response has been extensively studied for normal meteorological
conditions [6-10]; but it remains uncertain that there exists a significant Sea Level Pressure/Sea Level
Anomaly (SLP/SLA) correlation during storms and hurricanes, which are generally characterized by
heavy rains, high sea states and strong winds.
Indeed, the ocean response to tropical cyclone surface forcing is a complex interaction between
baroclinic and barotropic motions that re-distribute energy in the ocean during and after these strong
forcing events. This response has been characterized as a predominately baroclinic phenomenon
associated with the isopycnal displacements in the thermocline and the excitation of near-inertial three
dimensional oscillations. A secondary component is the barotropic response associated with the sea
surface depression of several tenths of a cm in geostrophic balance with a cyclonically rotating current
field [11,12].
The inverse barometer effect is balanced by the surface Ekman divergence in the eye of the storm
(pressure+wind induced surge on Figure 1). Most (> 85 %) of the storm surge is caused by winds
pushing the ocean surface ahead of the storm on the right side of the track in the Northern hemisphere
and left side in the Southern hemisphere [11,12].
In general, the strongest winds in a hurricane are found on the right side of the storm (Northern
hemisphere) because the motion of the hurricane adds to its swirling winds. Since the surface pressure
gradient (from the tropical cyclone centre to the environmental conditions) determines the wind
strength, the central pressure indirectly does indicate the height of the storm surges, but not directly.
The aim of this paper is to improve the observation of extreme low pressure events with altimetry
and to investigate the relationship between atmospheric SLP and the SLA measurements during such
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extreme conditions. Issues raised are the problem of the lack of altimeter data due to measurement
corruption by rain and to the low accuracy of the different geophysical/instrumental altimetric
corrections during TCs; the filtering of the SLA variability not related to atmospheric pressure; and the
availability of accurate SLP fields.
Figure 1. Localization of the storm surge (http://www.aoml.noaa.gov/phod/cyclone).
The paper is organised as follows: after the introduction, the second part describes the database and
the methodology; the third one is dedicated to the detection of tropical cyclones and describes the
specific treatments developed for altimeter data; the fourth part gives results about the analysis of
ETDs cases and more precisely on the possibility of retrieving a SLP signal from altimeter
measurements during ETDs. The last part gives a complementary analysis of the SLP-SLA
relationship in the case of ETDs from barotropic model outputs (MOG2D, [1]).
2. Database and Methodology
2.1. Database
The 2003/2004 time period has been chosen for the analysis because it is covered by several
independent databases:
- the ENVISAT, Topex/Poseidon and Jason-1 altimeter missions;
- an extensive observing network deployed in the Atlantic ocean by the National Oceanic and
Atmospheric Administration (NOAA). The NOAA hosts the National Hurricane Center (NHC) and
the Hurricane Research Division (HRD), which has defined an experimental wind analysis tool to
provide
regular
high-resolution
wind
fields
for
tropical
cyclones
([13];
http://www.solar.ifa.hawaii.edu/Tropical/tropical.html). This database gives an extensive list of
tropical storms which have occurred on all ocean basins, with information on the track of the storm
and estimates of the maximum sustain winds, wind gusts and the minimum central pressure.
However these estimates give a measure of the storm’s intensity but not of the wind or SLP field
which can be easily compared with the altimeter ground track measurements;
- a collocated JASON/buoy database: buoy data include the NDBC network, data available via
Météo-France, and the TAO array;
- the ECMWF pressure analyses at 0.5 degree-6 hour resolution;
- the QuikSCAT scatterometer wind measurements; QuikSCAT winds have been assimilated into
the ECMWF Numerical Weather Prediction (NWP) model since 2002.
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The ECWMF global pressure fields are used to provide long time series of surface pressure with
global space/time coverage. However, in this study, we are mostly interested in low and very low
pressure systems. In such conditions, NWP models such as ECMWF suffer from limitations related to
their coarse space and time resolution, to very few assimilated SLP measurements (aside from those of
ships of opportunity limited to the ships’main tracks), and the fact that the dense scatterometer winds
are severely under-sampled when assimilated in the NWP. However, we can derive SLP fields from
scatterometer wind measurements using an atmospheric planetary boundary layer (PBL) model
[14,15]. These QuikSCAT-derived SLP fields have the advantage of retaining the fine scale structures
present in the QuikSCAT wind fields. These SLP fields, although accurate for ETD cases, are less
accurate for TC situations because the QuikSCAT measurements are often contaminated by rain [16].
This last database has been constituted within this study and will help validating the altimeter-based
pressure signal during ETDs (section 4.2).
The SLA derived from altimetry has the following formulation:
SLA = Orbit – Range – Σ Corrections – MSS_CLS
(1a)
where Σ Corrections = Sea State Bias + Radiometer wet tropospheric correction + Ionospheric
correction + GOT2000 ocean tide + Solid earth tide + Polar tide [17,18]. The IB and dry tropospheric
corrections are not applied because they are correlated to SLP:
IB 0.9948 * (SLP SLP) in cm
(1b)
DryTropo 2.227 * SLP * (1 0.0026 * cos(2 )) in mm [18]
(1c)
where SLP is the atmospheric pressure (in hPa), SLP is the instantaneous mean of SLP over global
ocean, and φ is the latitude. The scale factor 0.9948 is based on the empirical value [19] of the IB at
mid latitudes. Several studies have shown the zonal dependence of this coefficient, from about 0.9
cm/hPa at high latitudes to -0.5 cm/hPa at the Equator [9], with a strong space variability due to wind
effects and also to some dynamic response to pressure forcing. For the present study, the SLA fields
have been computed by subtracting a Mean Sea Surface field MSS_CLS, [20]), to reduce the crosstrack geoid’s errors [7,9,21].
Altimeter data are usually selected using thresholds on the most relevant parameters characterizing
the altimeter and radiometer measurement quality. This editing procedure thus allows the selection of
useful altimeter datasets for most applications and ocean studies (altimeter Validated Database or VD).
However, in the present study, the phenomena of interest can be outside the validity domain
conventionally defined, because of extreme conditions such as heavy rain, high sea state and strong
wind. Figure 2 shows the location of Jason-1 cycle 062 measurements edited by conventional editing
procedures [17]. It shows that, except for rejected measurements over sea ice, altimeter measurements
are mainly edited in the warm pool and wet areas because of waveform contamination by rain. Other
areas of strong sea state (high waves) are also present. One issue of the study was thus to
modify/remove the selection procedure in order to keep enough altimeter data in very low pressure
condition.
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Figure 2. Edited measurements on Jason-1 cycle 062, for ocean applications.
2.2. Global Methodology
The methodology consists in first computing specific SLP and SLA storm databases, respectively
for TCs and ETDs. Tropical cyclones and extra tropical storms are treated separately: ETDs are
frequent large scale systems, while TCs are more occasional phenomena occurring over very short
distances, with great evolution speeds and particularly severe wind and rain conditions. In the TC
cases, altimetry measurements are found to be severely corrupted.
Extreme events are localized on the NHC or ECMWF databases (resp. for TCs and ETDs) based on
the following criteria:
Wind speed > 17 m s-1 for TCs, which is the official threshold for detecting tropical storms
DP = SLP- SLP < -10 hPa for ETDs
(2)
where SLP is the instantaneous mean global ECMWF SLP.
The low pressure events are placed with the altimeter measurements while screening the pressure or
wind speed values within the along-track altimeter databases. With the selection criterion of DP lower
that -10 hPa, the typical length of the ETDs detected is greater than ~1,000–1,500 km. If considering
SLP from ECMWF data, as well as from a PBL model applied to QuikScat data, the typical scale of
variability of such atmospheric events is between several hundreds of km and about 2,500 km.
To compute the corresponding along-track SLA from altimeters, the conventional validated
altimeter databases and corrections are used for ETDs [17], while specific dedicated processing and
corrections (described in section 3) are defined for TCs.
In order to study the impact of the pressure forcing on the sea level during extreme events and to
improve the SLP-SLA correlation, it is crucial to remove from the SLA signal the ocean variability not
related to atmospheric pressure; these other oceanic signals are the mesoscale variability (scales of
~50–200 km with periods of one to a few months) and the steric variations (seasonal time scale and
basin scales; [22]).To that end, several filtering methods have been tested:
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Along-track low-pass spatial filtering with different cutoffs for ETDs and for TCs;
Removing SLA maps: because the oceanic variability is mainly at low frequencies, one possible
filtering method is to remove the low frequency signals by using existing SLA maps (MSLA).
These MSLA are routinely produced by SSALTO/Duacs ([18]) with an objective analysis method
that combines altimeter missions in both near real time (NRT) and delayed mode (OI, [23]). They
are thus optimal observations of the ocean variability by altimeters. In this study, along-track SLA
can be corrected with a map of SLA derived from past SLA data (e.g., a map representing the sea
level one week before the low pressure event), or using a map recomputed without taking into
account the cyclone area.
The quantitative impact of the different filtering methods has been evaluated via the computation of
along-track ECMWF DP-filtered SLA correlations: for each storm case, we consider 215 altimeter
measurements at 1Hz frequency for ETDs (~1,500 km), and 100 measurements for TCs (~700 km).
For ETDs, several filtering with wavelengths between 700 km and 1,500 km have been
investigated: a short 700 km cutoff generally does not allow removing the mesoscale variability of the
SLA, while on the other hand, the 1,500 km filter can smooth out some pressure induced signal when
the scale of the phenomenon is shorter. The best choice should be to adapt the filter wavelength to the
scale of the event; however this is not feasible for a systematic analysis and within a real time
processing context. The 1,500 km cutoff wavelength has been applied here because it gives the better
SLP/filtered SLA correlations on the wide panels of ETDs studied.
For TCs, the MSLA filtering gives better results due to the small scale of the phenomena and to
their rapid evolution; this filtering method is very robust even in a real-time processing context. Note
that the MSLA filtering is not adapted to ETDs due to their larger spatial scale and to their higher
frequency of occurrence.
To study the relationship between the SLP and SLA signals, statistical correlation and regression
analyses have been performed on a wide number of storms (during year 2003; cf. Sections 4 and 5).
Following the IB approximation used for normal meteorological conditions, a linear regression model
between SLP and SLA has been investigated for extreme weather conditions:
DP (hPa) = A*SLA (cm) + B
(3)
SLA is the along-track filtered Sea Level Anomaly, and DP is the pressure difference.
As this relation can vary spatially (due to wind effects or pressure enhanced effects in the eye of the
storm …), we focused the analysis on the fiercest area of the storm, which is defined as the 16
consecutive along track points with the highest pressure drop (16 altimeter points along the track
correspond to ~100 km, for each storm); all the storms detected on a given basin are considered in a
same database. The results are thus mean correlation/regression coefficients for each ocean basin
studied (Atlantic, Pacific and Indian): in this case, there is no regional variability taken into account at
scales lower than the basin scale.
To investigate the regional variability of the SLP/MOG2D sea level relation (cf. Section 5),
correlations and regressions have been performed on the 6-hours ECMWF and model maps,
considering for each one degree box all cases with DP < -10hPa in the 2003 period.
Note that as the dry tropospheric correction has not been applied to SLA, this correction is
implicitly included in the resulting regression model of equation (3). Following equation (1c) and since
the variability of the dry tropospheric correction is about five times smaller than the standard IB, this
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would lead to IB-like coefficient of about -1.12 cm/hPa at high latitudes (or A = -0.89 hPa/cm for
equation (3)).
The regression models will be validated using independent datasets in section 0.2: ECMWF
pressure during different time periods from the analysis period, QuikSCAT-derived SLP, and in situ
data.
3. Detection of Tropical Cyclones
Altimeter dual-frequency measurements can provide valuable information for tropical cyclones
analysis and forecasting. Indeed, although limited by their dimensional sampling for operational use,
the dual-frequency capability makes altimeters a unique satellite-borne sensor performing
measurements of key surface parameters in a consistent way, i.e. surface winds, sea state, and rainfall
rate. It is especially true where and when no aircraft measurements are available and when the classical
Dvorak intensity analysis may be less accurate (at night, or when the cyclone eye is partially or totally
obscured by clouds). This is illustrated in Figure 3, which displays the infrared GOES images the
closest in time to the Jason altimeter track intersecting TC Isabel. These altimeter data were unique at
that night time. Careful analysis of the altimeter retrieved wind speed and associated sea state could
certainly help the intensity analysis performed from the GOES image.
Figure 3. GOES infrared brightness temperatures measured in TC Isabel and the Jason
altimeter ground track in black. The arrow indicates the direction of the cyclone motion.
For studying tropical cyclones, the first issue is the lack of reference surface pressure data and wind
fields. The NWP surface fields are less accurate for TCs because of the model resolution, the
limitations in the physics and parameterizations, and the lack of observations to assimilate into the
model. The HRD wind analysis benefit from various sources of observations (buoys, aircraft, satellite)
but, although useful, it is a limited data-set which accuracy is strongly affected by the scarcity of
surface data [13]. Finally, the ECMWF/QuikSCAT merged SLP fields presented in the previous
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section are hardly usable in TCs situations because the QuikSCAT measurements are heavily
contaminated by rain [16].
The second issue is the lack of validated altimeter data during TCs. Due to their short scale and very
high propagation speed compared to satellite inter-track distances and delay, frequent satellite flying
over the eye of a hurricane is unlikely, unless a constellation of altimeters is operated. Moreover, when
it does happen, altimeter measurements are severely affected: the measurements are corrupted by rain
(Ku-band is very sensitive to rain) and the different geophysical/instrumental altimetric corrections
used are not accurate enough for extreme weather.
Specific altimeter data processing is thus needed in order to improve the capability of altimetry to
observe TCs and to allow extreme sea state conditions in the database. The points with the ice flag, the
land flag and the S-band anomaly set on are still eliminated. The problem of rain contamination is
partly fixed using C- or S-band measurements on Jason 1 and Envisat respectively; these bands are less
affected by rain than the Ku band, but they are also noisier. SSB and wet Troposphere correction need
to be recalculated in this specific extreme weather context.
Note that due to the lack of accurate SLP data and to the heavy altimeter data treatments needed,
this part focuses on the SLA signal restitution during TCs and on the detection of such systems from
altimetry.
3.1. Rain Effects and Computation of New 0 and Wind Speed
Even though the Ku band is corrupted in tropical cyclone cases [2] due to strong attenuation by
rain, an expected-Ku band backscatter coefficient (0) can be recomputed from the 0 at the lower
frequency (C-band for Topex and Jason, S-band for Envisat) along with the mean rain-free relationship
between the two frequencies (Ku/C and Ku/S) [24]. An iterative algorithm is used to account for the
fact that C or S-band are also affected by rain, although the attenuation is small at these frequencies.
The Young algorithm [25] and the expected Ku 0 allow the computation of a new wind speed for
values over 20 m s-1.
Figure 4. Comparison of different wind speeds for Jason-1 during tropical cyclone Isabel.
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This new altimeter wind speed is shown in Figure 4 for TC Isabel: it is stronger than the ECMWF
value and closer to the HRD measurements in the fiercest area of the storm. All details about the
methodology are given in Quilfen et al. [26].
3.2. Wet Troposphere Radiometer Correction
For J1 data, the GDR wet tropospheric correction is used. In this case, the algorithm is parametric
and uses three channels of the radiometer, including the 18.6 GHz channel which gives information
about the sea surface; it can retrieve consistent values of the wet tropospheric correction during
extreme events. These values will be used to validate the new wet tropospheric formula developed for
Envisat and described hereafter.
The neural wet troposphere correction used for the Envisat data is very noisy and is not formulated
for high sea state conditions [27], as shown in Figure 5 for TC Isabel. The ECMWF correction is
underestimated in such extreme conditions and cannot be used either.
Figure 5. values of the neural radiometer and ECMWF wet troposphere corrections (in m)
for Envisat during TC Isabel, in function of latitude (degrees).
3.2.1. The Parametric Algorithm for Envisat
The radiometer correction can be deduced from the brightness temperatures and the wind speed or
backscatter coefficient in Ku band; this last parameter, wind speed or σ0, gives information about the
sea surface. The parametric formula used in the beginning of the distribution of the Envisat GDRs is
based on the radiometer brightness temperatures (two channels onboard Envisat: 23.8 and 36.5 GHz)
and on the backscatter coefficient (σ0 in Ku-band). It is a multilinear algorithm fitted on the basis of
normal surface conditions [28]: the drawback of this initial computation is the overestimation of the
correction in extreme conditions where it can reach 1.5 m (black curve on Figure 6).
A new parametric formula has thus been computed, including in the learning database the altimeter
winds greater than 25 m.s-1 as defined in the previous section (from S-band σ0 and Young algorithm).
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Wet _ tropo Extreme 62.1360
58.1935 * LOG(280 TB
48.1591 * LOG( 280 TB
23.8
36.5
0.236073( WindSpeed 7)
)
(4)
)
where the wind speed is in m.s-1, the brightness temperatures (TB) are in K, and the resulting
correction is in cm. This new parametric algorithm has a minimum adjustment error of 4cm.
Figure 6. Wet troposphere correction computed for Envisat for TC Isabel (cycle 19-track
792).
The new correction (red curve) has weaker values during TCs but is not adapted for lower wind
speeds around the area of the TCs (around 17°N and 18°N). In order to obtain a more realistic wet
tropospheric correction all along the track, the two parametric corrections have been combined into a
composite correction (blue curve): if the initial correction is greater than 0.5 m (which is the threshold
for normal sea state conditions), the recomputed wet tropospheric correction is taken. A final
smoothing avoids any discontinuities between the two corrections.
3.2.2. Validation of the New Parametric Correction
For validation, the new parametric formula obtained for Envisat (Equation 4) has been applied with
the Jason-1 TBs and the wind speed recomputed for J1, on J1 track 50/cycle 62 over flying TC Isabel.
The first channel is the same for Envisat and J1 (23.8 GHz) but the second one is slightly different
(36.5 GHZ for Envisat and 34 GHz for J1). This can lead to a difference in the two algorithms for
normal conditions, but the result for TC Isabel (red curve on Figure 7) shows that the formula is
appropriate for the higher values of winds and TBs, where the correction reaches 0.7m as for the
correction given by J1’s algorithm. Again we notice that the values around the event are not consistent,
which points out that this model is not adapted to normal conditions.
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Figure 7. Envisat parametric formula calculated with Jason-1 TBs (red) compared to the
radiometric correction (black) for Jason for TC Isabel (J1 track 50/cycle 62). Wet
troposphere correction unit is m.
3.2.3. The Neural Algorithm
Quartly [29] applied the neural algorithm using the “expected” Ku Sigma0 defined in section 3.1 as
input to compute the wet tropospheric radiometer correction. In the case of TC Juan [30], this approach
gives a continuously increasing water vapor curve until 90 kg/m2 (which corresponds to a 56 cm
decrease in the wet tropospheric path delay) in the fiercest area of the storm. But in the case of TC
Isabel, the results are not realistic (Figure 8, left): the recomputed correction (red) gives estimations
that are within the usual editing criteria (0 and 50 cm), but its along track variability is not
continuously decreasing as expected during an extreme event. The inconsistency of the correction is
likely due to the stronger conditions in TC Isabel: higher rain and stronger brightness temperatures
(Figure 8, right).
Figure 8. Values of the wet tropospheric corrections computed with Neural Network
algorithm with SIG0-Ku from GDR (black) and “expected” SIG0-Ku (red) (left) and values
of TBs (right).
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3.3. SSB Estimation
A new SSB estimation has been computed in S-band for Envisat and for extreme low pressure
cases. For normal sea states, the S-band SSB is computed with the non parametric algorithm using the
Ku-band SSB [30].
In extreme conditions, the Ku-band is unusable. Moreover, if considering only extreme events (one
year of crossover data with altimeter wind speeds over 15 m s-1), the number of points is reduced and
the NP SSB algorithm is very close to fitting a simple linear model (SSB=A*SWH):
New SSB (Envisat) = -6% * SWH
(5)
where SWH is the significant wave height in m. The error of this algorithm is below 1% of SWH for
normal meteorological conditions.
This new SSB is very close to the NP SSB for SWH values of 6 m and 20 m s-1 wind speed, which
shows the continuity between the SSB values in normal and extreme meteorological conditions.
In the same way, a computation of SSB has been made for Jason-1, based on C-band data:
New SSB (J1) = -4.6% * SWH
(6)
3.4. SLA Noise Reduction for TCs Applications
The C and S bands are less affected by rain than the Ku band, but they are noisier. Table 1 gives the
standard deviation of each 1-Hz measurement of the SWH (m), SIGMA-0 (dB) and Range (m) in the
two bands for Jason-1 and Envisat. These values are derived from the standard deviation of 20-Hz
altimeter measurements used to compute 1-Hz estimations. High noise tends to reduce the correlation
between SLA (derived from C- or S-band measurements) and sea level pressure. The along-track
filtering of S- and C-band measurements for Envisat and Jason-1 respectively has been tested for
several wavelengths. A simple Lanczos filtering ([31]) of 85 km significantly reduces the noise in the
SLA computation, as shown on Figure 9 (black curve).
Table 1. Standard deviation (m for SWH and Range, dB for Sigma0) of the 1-Hz
measurements for Envisat and Jason-1 for the Ku and C or S bands for standard conditions
(2-m SWH and 11-dB backscatter coefficient or sigma0).
SWH
Range
SIGMA-0
Envisat
Ku band
0.11
0.02
0.03
Jason-1
S band
0.42
0.07
0.06
Ku band
0.12
0.016
0.02
C band
0.3
0.04
0.03
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Figure 9. Comparison of initial SLA (blue), recomputed SLA with wet tropospheric and
SSB corrections (red) and recomputed SLA with the noise reduction applied (black) in m
for Envisat during Tropical Cyclone Isabel.
3.5. SLA Filtering for TCs Applications
The MSLA filtering removes the ocean signal not related to atmospheric pressure with good
accuracy during TCs. Several SLA maps have been computed in order to improve the filtered signal:
optimal interpolations (OI, [23]) have been performed using the complete data set with a window of 40
days or removing spatial and temporal areas corresponding to the cyclone. A correlation analysis
between SLA-MSLA and SLP has shown close results for the different mapping, confirming the
robustness of this filtering method.
Note that the MSLA filtering has been tested in a Near Real Time (NRT) context, using in the OI
only the measurements before the day of the cyclone with a decentred window: results are very similar
to the off-line MSLAs and show the efficiency of the method and the ability of NRT altimetry to detect
such extreme events.
Figure 10. Initial and final SLA computed for Envisat (cycle 19, track 792) and Jason-1
(cycle 62, track 50) during Tropical Cyclone Isabel.
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Figure 10 shows the reconstructed signal (SLA-MSLA) using all new dedicated processing (SSB
for Jason-1 and Envisat, Wet troposphere for Envisat) for TC Isabel. One gets a very interesting alongtrack SLA signal within the fiercest area of the storm, showing a storm surge greater than 50 cm: it is
consistent with an IB response to a strong low pressure forcing. Notice that, at the present time, no in
situ measurement is available to validate quantitatively this new SLA during TCs.
4. Retrieving SLP during Extra Tropical Depressions
The relationship between SLP and SLA during extra-tropical storms has been investigated in order
to retrieve the surface pressure from altimeter measurements. The ECMWF pressure fields and the
altimeter validated database are used. For ETDs, the main issue is to filter out ocean variability not
related to atmospheric pressure forcing: an along track low-pass filter has been applied systematically
with a wavelength of 1,500 km. A variable wavelength adapted to the size of each depression allowed
a better filtering but is hardly usable for a systematic analysis.
4.1. SLP-SLA Regression Analysis
The analysis covers all ETDs occurring during year 2003. The altimeter filtered SLA and the
ECMWF pressure fields are used to fit the A and B regression coefficients (from Equation 3) through a
least-squares method focusing on the fiercest area of the storms. The analysis has been performed
separately for three different ocean basins: North Atlantic, North Pacific and Indian Oceans. The best
correlations between SLP and filtered SLA have been obtained when excluding coastal areas and
strong mesoscale variability areas from the analysis (cf. Table 2). Note that the correlations are strong
in the three zones, and the regression coefficients are very stable within a 95 percent confidence level.
A is smaller than the 1hpa/1cm value, because the dry tropospheric correction has not been applied
to the SLA (cf. 2.2). Thus the values of A are not very different from the standard IB in the three
oceans. During extreme events one would expect that strong winds will impact the sea level, which is
not appearing on these regression values: this might be due to the global approach (means on wide
basins, unique along-track SLA filtering). A regional analysis will better point out the wind effects
(see sections 5.2, 5.3).
Table 2. SLP-SLA regression models for 2003 extra-tropical depressions.
Ocean
North
Atlantic
North
Pacific
Indian
A (hPa/cm) with
95% confidence
level
B
(hPa)
Correlation
Nb of
samples
Error on
2004
rms/mean
(hPa)
-0.796 ± -0.00011
-172.89
-0.83
6962
5.25/-0.4
-0.77 ± -0.00011
-173
-0.84
6654
5.2/-0.3
-0.817 ± -0.00008
-175.35
-0.88
6810
5.16/-1.2
The rms error of the regression model (Table 2), if compared to ECMWF SLP in 2004, is 5.2 hPa
for the three oceans. As the Saffir-Simpson scale used to classify hurricanes/depressions, defines each
Sensors 2009, 9
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category within a pressure increment of 15/25 hPa [32], such observations with an accuracy of 5 hPa
or less are valuable. However during ETDs, one can still expect reducing this error while improving
the SLA and/or the filtered SLA signals and the regression model (cf. section 5).
4.2. Validation of the Altimeter SLP during ETD
Comparisons of the altimeter restored SLP have been performed with different datasets:
QuikSCAT-derived SLP, ECMWF SLP and the collocated Jason/buoy product. Buoy data include the
NDBC network operated by NOAA and available via internet, data acquired in Europe available
through Météo-France, and data from the TAO array operated by PMEL. The criteria for collocation
between buoy and altimeter measurements are: maximum time separation of 60 min, maximum spatial
separation of 50 km. These databases are available at IFREMER. Only off shore buoys with an
estimated local pressure difference greater than 10 hPa have been used for the validation, which
reduces the dataset to 162 collocated measurements.
Table 3 presents some Jason-QuikSCAT and Jason-ECMWF statistical comparisons: the mean
correlation is close to 0.95 for all ocean basins. The percentage of collocations with a correlation lower
than 0.8 is close to 10, with significantly lower values in the northern hemisphere. This difference
between the northern and southern hemispheres is likely due to the strong variability associated with
the ACC, which may pollute the pressure-induced SLA signal in the southern hemisphere. Figure 11
illustrates the problem of the along-track filtering process within strong mesoscale areas (ACC
variability): the method cannot properly extract the pressure-induced signal.
Table 3. Mean correlation coefficient between the SLP, and percentage of cases for which
this correlation is lower than 0.8, for each ocean basin. The upper value is for the
Jason/QSCAT correlation, the lower one for Jason/ECMWF.
Mean correlation
coefficient
% of correlation
coefficient < 0.8
N.Atlantic
0.96
0.96
6.7
8.1
N.Pacific
0.95
0.94
8.5
6.4
Indian
0.96
0.96
11.8
10.8
Figure 11. Comparison of the along-track SLP for the ETD of 11/01/2004 2:50 UTC
QuikSCAT time. The abscissa shows the along-track distance in km (one stick every 100
km).
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When the ETDs are strong and large-scale when compared to the background variability, an
accurate pressure signal can be retrieved from altimetric measurements (Figure 12). But the error can
be greater for smaller-scale ETDs that might be smoothed out by the large-scale along-track filtering,
and due to strong and localised wind effects that are not taken into account within the basin-wide mean
regressions (Figure 13).
Figure 12. Comparison of the along-track SLP for the ETD of 23/04/2004 21:08 UTC
QuikSCAT time. The abscissa shows the along-track distance in km (one stick every 100
km).
Figure 13. Comparison of the along-track SLP for the ETD of 21/03/2004 5:12 UTC
QuikSCAT time. The abscissa shows the along-track distance in km (one stick every 100
km).
Figure 14. Comparison of the Jason SLP with buoys measurements (abscissa). The colored
bar gives the SLA in m.
Sensors 2009, 9
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Figure 14 shows the comparison of the Jason SLP with buoys measurements. The Jason SLP is
overestimated by about 3 hPa, which reflects the mean overestimation of the ECMWF SLP used to
calibrate the SLP/SLA relationship in low pressure systems. The rms error between Jason and buoys
SLP is only 5 hPa. There is a small residual dependency of the error (Jason – buoy SLP) on the sea
level anomaly, which means that the regression models could still be improved. It should be noted that
a multivariate regression analyses between SLP, filtered SLA and the altimeter wind speed, did not
significantly improve the rms error.
5. Comparisons with a Dynamical Modeling Approach for ETD
Barotropic simulations are used to further investigate the SLP-SSH relation during mid-latitude
storms. MOG2D is a finite elements non-linear gravity wave model using shallow water equations.
This global barotropic model allows simulating the high-frequency response of the ocean to
atmospheric pressure and wind forcing [6,33]. The model is forced by ECMWF pressure and wind
fields. MOG2D outputs only contain, in essence, atmospherically forced signals; if neglecting model
errors, the model sea level thus represents the ideal along track filtering and the ideal altimeter
measurement of the SLA signal.
5.1. SLP/MOG2D Sea Level Regression Analysis
The mean regression between MOG2D sea level and the ECMWF SLP has been performed on all
2003 ETDs (Table 4). Note that the MOG2D sea level does not need to be along-track filtered as it is,
in essence, only representative of the ocean response to atmospheric wind and pressure forcing.
Table 4. SLP-MOG2D Sea level regression models for 2003 extra-tropical depressions.
Ocean
North Atlantic
North Pacific
Indian
A (hPa/cm) with
95% confidence level
-1.13 ± -0.00005
-1.07 ± -0.00003
-1.2 ± -0.00007
B (hPa)
Correlation
-2.7
-0.95
-4.66
-0.91
-0.94
-0.87
Nb of
samples
7447
7407
8109
Error on
2004 (hPa)
3.57/-0.34
3.45/0.15
4.77/-0.81
As expected, the linear regression coefficient A is greater than 1 hPa/cm in absolute value,
reflecting the anticorrelation between the pressure and the wind effects. The global error on the
restituted pressure is significantly weaker when considering the MOG2D signal instead of altimeter
measurements (Table 2): the improvement reaches more than 30 % for the North Atlantic and North
Pacific oceans and represents the minimum gain we could get on the altimeter-based regression
models, while improving the filtering of altimeter data from all signals not related to atmospheric
forcing. The residual error is due to model errors (physics approximations, grid size, bathymetric
errors, atmospheric forcing errors [34,35]), and to the limitation of the global linear regression model.
Note that a multivariate and linear regression analysis between SLP, MOG2D sea level and altimeter
wind speed, did not significantly improve the performance of the regression model to restore
atmospheric pressure.
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5.2. Regional Variability of the SLP-SLA Relation
The spatial variability of the SLP-MOG2D sea-level relation has been investigated: the regression
coefficient A is plotted on Figure 15 for the Indian and the north Pacific oceans. As expected, it has a
strong spatial variability [9]: A is smaller in absolute value, in coastal areas, due to non-linearities,
dissipation, and coastal wind effects [36]. A is greater in absolute value, in deep ocean regions where
the ocean has a strong dynamic response to wind forcing [6,37], due to the anticorrelation between the
wind and pressure effects; these results are consistent with prior studies on the regional IB effects
during normal meteorological conditions [8,9]. Note that north of 45°S in the Austral Indian ocean, the
analysis is not significant because of too few extreme cases.
Figure 15. Upper panel is Indian ocean, lower panel is north Pacific ocean. Left:
regression coefficient A between SLP and MOG2D sea level (hPa/cm). Right: number of
cases with DP < -10hPa.
-1.6
-1.2
-1.6
-1.3
-1
-0.6
-1
2
-0.6
600
3
221
5.3. Focus on the ETD of 03/21/2004 5:12 UTC QuikSCAT
We focus on the ETD of 03/21/2004 in the north-east Pacific Ocean. We compare the restored
pressure signals from the SLA based regression analysis on one hand (cf. 4.1) and from the MOG2D
sea level regression models on the other hand. In this last case, MOG2D model is forced with ECMWF
wind and pressure and then the pressure is estimated from the model sea level (as described in sections
5.1 and 5.2). Figure 16 shows the collocated Jason-1 track on the ECMWF IB signal (a), the ECMWF
wind speed map (b), and the IB deviation (IBD) map computed with the MOG2D model (c). Figure 17
1400
487
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shows the along-track unfiltered and the 1500-km low-pass filtered Jason-1 SLA (a), the along-track
ECMWF and altimeter wind speed profiles (b), and the along-track SLP profiles (c, and d for regional
regression model in green).
Figure 16. Case of 21/03/2004 over the North Pacific Ocean – J1 cycle 81 – track 71. (a)
map of the IB signal at the time of the event, in cm (top panel). (b) map of the ECMWF
wind speed in m.s-1 (center panel). (c) map of the IBD signal in cm (lower panel).
Sensors 2009, 9
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This ETD has a small spatial scale (about 500 km) if considering the pressure gradient DP > 10 hPa,
with a sharper pattern about 48°-49° North (Figures 16a and 17a). The altimeter and the model wind
profiles are in good agreement: the minimum in wind speed is well localized around 48°-49° North,
but the ECMWF wind speed gradient is too sharp (Figure 17b).
Figure 17. Case of 21/03/2004 over the North Pacific Ocean – J1 cycle 81 – track 71.
Along-track plots, abscissa is latitude. (a) SLA in black and filtered SLA in red (cm, upper
left panel); (b) ECMWF wind speed in red and altimeter wind speed in black (m.s-1, upper
right panel); (c) ECMWF DP in black, altimeter-restored DP from global model in red and
from barotropic model global analysis in green (Pascals, lower left panel); (d) same as (c)
with green line showing DP from the regional regression model (Pascals, lower right
panel).
The local response of the SLA to this forcing is not clear in Figure 17a, because it is of the same
order of magnitude as the surrounding mesoscale variability; the 1,500-km along-track filtering
applied on SLA for the systematic analysis (cf. 2.2 and 4.1) smoothes out most of this small scale ETD
signal (examples Figure 11, Figure 13).
MOG2D simulation clearly shows a local response of the ocean to these forcings (cf. Figure 16c): a
small cell of strong IBD signal (IBD = sea level – IB), reaching -12 cm, is localised under the satellite
Sensors 2009, 9
1326
track. This small spatial scale dynamic response is clearly due to a local enhanced response of the
ocean to the sharp wind forcing.
The restored DP based on altimeter SLA (from model defined in section 4.1) is widely
underestimated and too smoothed likely due to the too large scale filtering applied (red line in Figures
17c-d).
The restored DP based on the MOG2D model (from the model defined in Section 5.1) has a better
spatial variability, but its absolute value is still lower than the ECMWF pressure field (cf. green line in
Figure 17c). This lower restored pressure could be due to a too weak regression coefficient; indeed, the
basin-wide regression coefficient used is smaller in absolute value than the regional coefficient
inferred from section 5.2.
If using the regional regression model (A = -1.3 hPa/cm from Section 5.2), the restored SLP is
closer to the QuikSCAT pressure field shown in Figure 13 (blue line), although it is still a bit
underestimated within the fiercest area of the storm (SLP is plotted in green in Figure 17d).
This local underestimation of the MOG2D-based restored pressure can be explained by the smallscale signal (due to sharp wind forcing) which cannot be well modelled by the too large finite element
mesh in this area (grid cells of about 200 km).
This analysis shows the importance of the regional variability of the relationship between sea level
and atmospheric pressure as previously shown for normal meteorological conditions ([9]). The alongtrack filtering of SLA is also a challenge as the filter wavelength should be adapted to the scale of the
event but should also be able to deal with the mesoscale signal. Using model outputs gives interesting
results although it is still limited by resolution issues and, forcing and model errors.
6. Conclusions
Many SLA altimeter measurements during TCs have been restored with a new dedicated altimeter
processing using S or C band; specific SSB and wet tropospheric corrections have been computed for
extreme events. A quantitative validation of this SLA signal was not possible due to the lack of in situ
data during TCs. However these new SLA data are now available for the scientific community for use
and validation. A more accurate altimeter wind speed has been computed for extreme winds [26]. For
TCs, the MSLA filtering has proven to be very efficient at extracting the atmospherically forced
signal, even in a NRT context, showing the ability of altimetry to detect such extreme events.
This study showed that a pressure signal can be retrieved from altimetric measurements during
extra-tropical storms with a good correlation between SLP and SLA (>0.8). The regression model error
is about 5hPa; mesoscale variability areas as well as intense and localised wind effects are a strong
error source. The along-track filtering of SLA is still a challenge as the filter wavelength should be
adapted to the scale of the event but should also be able to remove properly the mesoscale signal.
The mean regression models based on MOG2D outputs have a lower error (3hPa error), which is
explained by the intrinsic definition of the model which only contains the ocean response to wind and
pressure forcing. The residual error is likely due to ECMWF forcing errors and to the barotropic model
errors. The MOG2D dynamical approach has also pointed out the importance of the spatial variability
of the regression models during extreme events, similarly to previous studies for normal
meteorological conditions.
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Is should be noted that following the Saffir-Simpson scale, each hurricane/depression category is
defined within a pressure increment of 15/25hPa, thus observations with accuracy of 5hPa (3hPa for
model) or less are valuable particularly when few other sources of data are available, ie. during highly
extreme conditions. During ETDs an increase accuracy could be achieved either by tuning the alongtrack filtering process of the altimeter SLA, or by improving model sea level simulation using better
mesh, forcing or model physic.
For TCs’ cases, some statistical regression analysis between the new SLA and the pressure signal
could be done in a future work, while considering any accurate SLP from a regional atmospheric
model if available, and perform the analysis over several years in order to increase the number of
samples.
Acknowledgements
Thanks to Dr. Chung-Chi Lin (ESA) for proposing this very interesting RELPA study, under
European Space Agency Contract 18132/04/NL/FF, to Dr. R.M. Ponte (AER) for his constructive
collaboration, and to C. Boone.
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