Marine Geodesy,33(S1):317–335,2010
Copyright©Taylor&Francis Group,LLC
ISSN:0149-0419print/1521-060X online
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DOI:10.1080/01490419.2010.491033
Relative Performance of the MLE3and MLE4 Retracking Algorithms on Jason-2
Altimeter Waveforms
P.THIBAUT,1J.C.POISSON,1E.BRONNER,2AND N.PICOT2
1Collecte Localisation Satellite(CLS),Ramonville Saint-Agne,France
2Centre National d’Etudes Spatiales(CNES),Toulouse Cedex,France
For all altimeter missions,precise estimates of geophysical parameters are obtained
thanks to an algorithm called“retracking”thatfits an analytical model to the measured
waveforms.The Brown model provides a good representation of the return echo over
deep ocean surfaces and is commonly used.Many different chains can be considered
(and have already been tested)for this processing.An unweighted Least Square Estimate
derived from a Maximum Likelihood Estimator(MLE)(Dumont1985;Rodriguez1988)
自制自慰器is implemented in most altimeter ground processing approaches(TOPEX,Jason-1,
同温同压下
Jason-2,and Envisat).
The aim of this paper is to evaluate the performance of two retracking algorithms based on the same least square principle:The MLE3algorithm estimates three param-
eters(range,significant wave height,and power)whereas the MLE4estimates four
parameters(the three previous ones and the slope of the waveform trailing edge).MLE3
镇流器外壳
was used on Jason-1before star tracker problems occurred.The MLE4algorithm has
been used for Jason-1Version B products and onward and for Jason-2products from
the start of the mission.Both algorithms are compared in the paper.Advantages and
drawbacks of both algorithms are pointed out showing notable benefits provided by
MLE4especially for waveforms that do not conform to the Brown model.
Keywords Radar altimetry,retracking,waveforms,sigma bloom event
1.Introduction
Initially,Jason-1retracking specifications assumed an antenna mispointing angle smaller than0.3degrees.The Brown model(Brown1977)(usually developed at thefirst order)used to estimate the ocean parameters is known to be unsuited for higher mispointing angle values (Amarouche2004).Soon after the Jason-1launch,the star tracker system,responsible for maintaining the nominal nadir pointing angle of the platform,showed some occasional abnormal behavior leading to mispointing angles that are higher than specification limits.
Consequently,the echo model was modified to meet the actual platform performance and the retracki
ng algorithm was updated to account for this new model.A complete description of the Brown model formulation has been provided in(Brown1977)and recalled in(Amarouche2004)to develop the new model formulation.The Brown ocean model can be written as a convolution of three terms including the Flat Sea Surface Response Received6January2010;accepted28March2010.
Address correspondence to P.Thibaut,Collecte Localisation Satellite(CLS),8-10,rue Herm`e s, 31526,Ramonville Saint-Agne,France.E-mail:pthibaut@cls.fr
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(FSSR).A Bessel function is used in the FSSR and historically,this function is developed tofirst order(allowing mispointing angles up to0.3degrees).In the new formulation,the Bessel function has been developed to order2to accommodate higher mispointing angles (up to0.8degrees).Nevertheless,with this new model,it became impossible to derive the slope of the trailing edge of the waveform(linked to the mispointing angle of the platform; see later in the paper)with a linear regression as is adopted with thefirst order model.As a consequence,the so-called MLE4retracking algorithm which estimates four parameters (range,significant wave height,po
wer and slope of the trailing edge)was introduced.
Extensive analyses were then performed to compare MLE3and MLE4output.Results from Thibaut(2006,2007)have shown that MLE3and MLE4results were equivalent during satellite well-pointed periods and that the MLE4algorithm was performing very well for mispointing angles up to0.8degrees(during abnormal behavior of the star tracker system).It was also shown that significant improvements in range estimation can be found in geographical areas where altimeter waveforms present atypical trailing edge slopes(over rain cells and sigma0blooms areas notably).
Consequently,the MLE4algorithm was adopted for the reprocessing of Jason-1data (GDR‘B’and GDR‘C’)and was also adopted some years later,for the Jason-2nominal waveform retracking despite the good pointing performance of the Jason-2satellite.
Some drawbacks of this algorithm have however been pointed out(Tournadre2006, 2007;Quartly2008),mainly regarding sigma naught estimation with consequences on rain flagging and wind speed determination.The main parameter of interest being the range (which is improved)and the significant wave height(which is unchanged),the MLE4was retained in spite of these drawbacks.
The aim of this paper is to present the results obtained with both algorithms(MLE3and MLE4)on Jason-2data(Ku band only),to characterize their advantages and drawbacks, and to give some recommendations on the use of their output.
2.Description of the Altimeter Echo Shape
The theoretical shape of a radar echo over an ocean surface is represented in Figure1.The different ocean parameters derived from radar echoes are:
•The epochτ,defined as the position of the signal in the analysis window with respect to the tracking reference point.The precise range estimate is derived from both the tracking range and the epochτestimates.
•The amplitude P u of the waveform which is used to derive the backscatter coefficient σ0.The latter is related to ocean surface wind speed.
•The slope of the leading edge,σc,which is a function of the standard deviation of the sea surface heightsσs and related to the significant wave height(SWH=4σs when assuming a Gaussian distribution of ocean heights).
•The thermal noise level P n.
太阳能
锅炉•The slope of the trailing edge that is typically linked to the antenna off-nadir angle ξ.It is not the aim of this paper to provide the reader with all detailed formulations of the model developed at the second order or with details about the retracking algorithm itself. For such complementary information,interested readers are referred to Dumont(1985), Rodriguez(1988),and Amarouche(2004).In the present paper,we mainly want to focus on results obtained on Jason-2data processed with both MLE3and MLE4algorithms
Estimations from Jason-2Altimeter Waveforms319
Figure1.Altimeter echo shape and corresponding ocean parameters(τ:epoch,σc:sigma composite, Pu:power,ξ:slope of the trailing edge).
(13cycles from cycle10–22,from April14,2002–August21,2002,have been reprocessed to this end).For these cycles,the Jason-2tracking mode was the nominal median tracker mode.
2.1.Look-up Tables
As explained in(Thibaut2004),MLE retracking algorithms developed in the Jason(1/2) ground processing approaches are based on the Hayne model(Hayne1980),which is a refined analytical ocean return model derived from the Brown model and assumes that the instrumental Point Target Response(PTR)can be adjusted with a Gaussian function.The PTR is measured on a regular basis(three times per day)using an internal calibration mode of the altimeter.To account for that Gaussian approximation,Look-up Correction Tables (LUT)are computed from Monte Carlo simulation of altimeter performance(Thibaut 2004).This simulation tool is representative of the hardware and software complexity of the real altimeter.It is a key tool during the whole life of the altimeter from definition and study phases to in-flight acceptance tests phases.In this simulation tool,the real PTR of the altimeter is accounted for to generate realistic echoes,while a Gaussian approximation is consi
dered in the retracking algorithm.LUT are statistically computed from thousands of simulations and are provided for range,significant wave height and sigma0.Of course, specific LUT have to be derived for each retracking algorithm.They have to be updated whenever the PTR ,power,width,and positions of main and side lobes) are significantly modified.Figures2and3show the LUT computed for Jason-2using MLE3and MLE4algorithms.The parameter estimated by the MLE4retracking(epoch, SWH)is corrected by interpolation in the corresponding table.It can be observed that Epoch and SWH parameters are always overestimated by the two MLE algorithms.LUT on sigma naught are not shown here since corrections are quite negligible.Due to the nearly perfect symmetrical shape of the real Jason-2PTR,the parameter most impacted by this approximation is the significant wave height(SWH).
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Figure2.Jason-2Look-Up Tables for Epoch(MLE3and MLE4).
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设计流程
2.2.Slope of the Waveform Trailing EdgeThe aim of this paragraph is to introduce the interest of the MLE4algorithm that cannot be well percei
ved without a good understanding of the geophysical phenomena that sometimes affect the trailing edge of the waveforms.
In the Brown model,potential mispointing angle of the satellite is accounted for. Platform or antenna mispointing angle leads to an increase of the slope of the trailing edge of the waveform.Nevertheless,variations of the trailing edge are observed for many years on all altimeter missions regardless of the pointing stability of these missions.In particular,
Figure3.Jason-2Look-Up Tables for SWH(MLE3and MLE4).
Estimations from Jason-2Altimeter Waveforms321 on Jason-2data,such local and time limited phenomena are sometimes observed though we know that the Jason-2pointing angle is maintained close to zero.This suggests that phenomena independent from real antenna mispointing angles lead to the modification of the slope of the trailing edge.
First,considering“sigma0bloom events,”waveforms are often degraded by the oc-currence of unrealistically high radar return cross sections(sigma0)corresponding most of the time to reflection on specular surfaces in regions of climatologically weak winds and weak waves.This fact has been verified by co-location with scatterometer data,buoy measurements,or model predictions.However,not all the events can be accounted for by very low wind speed,suggesting that other phenomena such as surface slicks could also lead to the same kind of observations.
Sigma0bloom events have been seen by all altimeter systems:Geos3,Seasat,GFO, TOPEX,Poseidon-1,ERS1/2,Jason-1,and Envisat altimeters.Interest readers are referred to(De Biasio1999;Mitchum2004;Garcia2004;Tournadre2006;Thibaut2007)for detailed characterization and analysis of the occurrences of sigma0blooms and their impacts on measurements from various altim
eter missions.All these papers agree that roughly5–6% of altimeter data are impacted by these sigma0bloom effects.
In Synthetic Aperture Radar imagery(SAR),large patches of the ocean surface provide little or no surface reflection back to the radar indicating that cm-scale wavelets are absent on the surface(in this case,measurements are obtained off from nadir).The same process occurs for radar scatterometer,but the low-backscatter case is more difficult to document and study because the satellite scatterometer footprint is much larger than for the m-scale SAR.
Figure4shows an example of Jason-2waveforms during a sigma0bloom event(cycle 22,pass82,descending pass).On this plot(latitudes on the x-axis to be read from right to left),each column represents a waveform of104samples.Colors indicate the power of each sample of the waveform from dark blue(for the noise level observed on thefirst samples of the waveform)to red(observed for the most energetic samples at the end of the leading edge near sample35).
Figure4.Jason-2waveforms observed during a sigma0bloom event(between latitudes−22.85deg and−23.3deg).Colors indicate the power of the waveform samples(waveforms have been corrected for AGC variations to remove jumps of the Automatic Gain Control(AGC)factor).
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