Enhancing SMOS brightness temperatures

over the ocean using the nodal sampling

image reconstruction technique

Ver´onica Gonz´alez-Gambau

a,c,∗

, Estrella Olmedo

a,c

,

Antonio Turiel

a,c

, Justino Mart´ınez

a,c

,

Joaquim Ballabrera-Poy

a,c

, Marcos Portabella

a,c

and

Mar´ıa Piles

b,c

a

Department of Physical Oceanography, Institute of Marine Sciences, CSIC

Passeig Maritim de la Barceloneta, 37-49. 08003 Barcelona. Spain

b

Department of Signal Theory and Communications, Universitat Polit`ecnica de

Catalunya, Jordi Girona 1-3, E-08034 Barcelona, Spain

c

SMOS Barcelona Expert Center, Pg. Mar´ıtim 37-49, E-08003, Barcelona, Spain

Abstract

Abrupt changes in the Soil Moisture and Ocean Salinity (SMOS) brightness tem-

peratures, such as those produced by land/sea/ice transitions and Radio-Frequency

Interference (RFI) sources, produce artiﬁcial rippling patterns (i.e. the so-called

Gibbs-like contamination) that propagate through the SMOS-reconstructed image.

A nodal sampling technique focused on the reduction of this kind of contamination

by sampling the signal at the points where the perturbation cancels was introduced

by Gonzalez-Gambau et al. (2015). This work presents an improvement over that

technique by reﬁning the nodal grid determination. A comprehensive assessment of

this new approach over the ocean is presented. The new brightness temperatures are

compared to the ones provided by the current SMOS image reconstruction baseline

and by the original nodal sampling method. The new technique reduces sidelobe lev-

els and ripples in the reconstructed images, being the new brightness temperatures

in better agreement with the theoretically modeled ones. A validation of the salinity

retrievals against near-surface Argo salinity observations shows that the new method

Preprint submitted to Elsevier Science August 3rd, 2015

leads to improved salinity retrievals in open ocean. However, in coastal areas, where

systematic biases due to land-sea contamination are also present, improvements de-

pend on the retrieval algorithm used. This indicates that further research on salinity

retrieval methods is necessary. Research that would beneﬁt from the nodal sampling

technique.

Key words: Soil Moisture and Ocean Salinity (SMOS), interferometry,

radiometry, image reconstruction, nodal sampling, nodal points, sidelobes, Radio

Frequency Interferences (RFI), salinity retrievals

1 Introduction1

The Soil Moisture and Ocean Salinity (SMOS) mission is the ﬁrst Earth Obser-2

vation (EO) mission devoted to the remote sensing of both soil moisture over3

the continental surfaces and sea surface salinity (SSS) over the oceans (Barre4

et al., 2008; Font et al., 2010; Kerr et al., 2010). Its unique payload, MIRAS,5

is a completely new type of instrument: a two-dimensional synthetic aperture6

radiometer with multiple incidence angles and full polarimetric capabilities7

(Martin-Neira and Goutoule, 1997; McMullan et al., 2008).8

The operating principle of MIRAS is based on the measurement of the complex9

cross-correlations of the signals collected by each pair of receivers, providing10

the basic measurements of a two-dimensional interferometer: the samples of11

the visibility function (Corbella et al., 2004). Errors in the visibility samples12

need to be corrected by means of several calibration procedures (Brown et al.,13

2008) before applying an image reconstruction algorithm to obtain the bright-14

ness temperatures (TB) (Anterrieu and Khazaal, 2008; Camps et al., 2008;15

Corbella et al., 2009).16

∗

To whom correspondence should be addressed

Email address: vgonzalez@icm.csic.es (Ver´onica Gonz´alez-Gambau).

2

Due to the ﬁnite extent of the instrument and the ﬁxed locations of the anten-17

nas, visibilities are measured only at selected points in a star-shaped subarray18

over a hexagonal grid. The incomplete sampling at high spatial frequencies19

generates Gibbs-like contamination, i.e., sidelobes and ripples when sharp20

transitions are present in the brightness temperature scenes. In the SMOS21

operational image reconstruction strategy, a Blackman window is applied to22

the Fourier components of the brightness temperatures in order to decrease23

these artifacts. This windowing considerably reduces the amplitude of the rip-24

ples and improves the radiometric sensitivity while meets the spatial resolution25

mission requirement (Anterrieu et al., 2002; Bar´a et al., 1998).26

Radio-Frequency Interferences (RFI) at L-band have been a serious problem27

for SMOS ever since the beginning of the mission. According to international28

regulations, such emissions are illegal, but they are quite frequent. Owing to29

intense eﬀorts conducted by ESA, many RFI sources have been switched oﬀ30

(Oliva et al., 2012). However, there is still signiﬁcant contamination of SMOS31

TB by RFI, which render the retrieval of ocean salinity in some coastal areas32

impossible, and also have a strong impact on the quality of the soil moisture33

retrievals. Hence, many eﬀorts have been dedicated to developing appropriate34

RFI detection and mitigation strategies (Camps et al., 2011; Castro et al.,35

2012; Daganzo-Eusebio et al., 2013; Park et al., 2015; Soldo et al., 2014).36

The presence of any RFI source not only impacts the area directly aﬀected37

by the interference, but also causes strong sidelobe levels and ripples that38

contaminate all over the brightness temperature image. It must be noted,39

however, that Gibbs-like contamination is not restricted to RFI hot spots, but40

it is present wherever any sharp transition in SMOS brightness temperature41

scenes exist, such as land/sea/ice transitions and even the Earth surface/sky42

transition. This means that any image has some small but non-negligible de-43

gree of contamination because, even when no RFI (or land/sea/ice transition)44

3

appears, the Earth horizon is always present.45

This work is being motivated by the fact that, even after applying a Blackman46

window, the sidelobes and ripples caused by strong point sources are still47

signiﬁcant (see as an example the image in Fig. 1). The eﬀect of these ripples48

is not irrelevant in the case of the ocean salinity retrieval: the sensitivity of the49

L-band brightness temperature to salinity is relatively low and therefore, any50

perturbation of few Kelvins may cause large deviations on the retrieved SSS51

(Yueh et al., 2001). As such, the development of speciﬁc methods to reduce52

the impact of these perturbations over ocean scenes is a crucial task.53

Nodal sampling, ﬁrst presented in (Gonz´alez-Gambau et al., 2015), is a novel54

image reconstruction algorithm focused on the reduction of Gibbs-like contam-55

ination. The ﬁrst approach to nodal sampling showed a more than signiﬁcant56

reduction of Gibb-like contamination (mainly ripples and sidelobes). But even57

implying a large gain in quality, there were some remaining issues in the for-58

mulation of nodal sampling, especially regarding the size of the RFI sources59

originating the largest sidelobes. The aim of this paper is twofold: on one60

hand, to discuss the issue of the poor description of the area directly aﬀected61

by the presence of RFI sources, ﬁrst, and then introduce an improvement in62

the nodal sampling algorithm that leads to a general quality enhancement;63

on the other hand, we want to illustrate how the use of nodal sampling will64

contribute to the improvement of salinity retrievals.65

The paper is structurated as follows. The improvements in the nodal grid de-66

termination and the analysis of the system performance using this algorithm67

are presented in section 2. The latest deﬁnition of the nodal sampling algo-68

rithm is compared at brightness temperature level using ocean scenes to the69

initial approach as well as to the currently SMOS operational image recon-70

struction strategy. The comparison of the brightness temperatures to those71

theoretically modeled is also used as a metric to evaluate the performance of72

4

the method (section 3). Section 4 is devoted to the impact assessment of the73

nodal sampling application on the SSS retrievals, using in-situ SSS measure-74

ments as reference.75

2 Nodal sampling image reconstruction tecnique76

2.1 Nodal sampling: conceptual basis and current approach77

The nodal sampling algorithm was recently developed by (Gonz´alez-Gambau78

et al., 2014, 2015). This method is based on sampling TB images at the nodal79

points, i.e., those points at which the oscillating interference causes the min-80

imum distortion of the geophysical signal. The underlying hypothesis of the81

nodal sampling is that the geophysical signal of interest varies relatively slowly,82

at the scale of the spatial resolution of the instrument. At those points where83

there is no perturbation, the subsampled signal will take a value which is the84

result of the interpolation among the points nearby, which introduces some85

error. However, if the geophysical signal present a slow variation this error will86

be rather small. This approximation is especially well suited over the ocean,87

which presents structures of typically tens to hundreds of kilometers.88

The nodal sampling algorithm encompasses three steps: (i) the spatial over-89

sampling of the TB image, (ii) the selection of the nodal grid in the oversam-90

pled TB image and (iii) the reconstruction of a corrected image at the original91

spatial sampling. It is important noting that no apodization window is applied92

to the Fourier coeﬃcients before the image reconstruction. Brightness temper-93

ature images are oversampled in such a way that the Fourier coeﬃcients at94

the known spatial frequencies are kept the same. This oversampling leads to95

a better deﬁnition of the oscillating structures and, as such, the points where96

5

the perturbation cancels can be more accurately determined. Nodal points are97

characterized by the local minima of the Laplacian at the areas deﬁned by the98

pixels at the original spatial sampling. Finally, a new image is constructed by99

taking the values of the oversampled image at the selected nodal points, such100

that each pixel of the new image is given by one speciﬁc pixel of the associated101

oversampled pixels. Hence, the corrected image has the same spatial sampling102

than the original one.103

The key point for the practical application of nodal sampling is to determine104

the set of nodal points, something for which there is no straightforward pro-105

cedure. In (Gonz´alez-Gambau et al., 2015) it was noticed that nodal points106

are referred to the local minima of the Laplacian, but the determination of107

those minima requires a simultaneous change of the sampled points and the108

values of the Laplacian. The iterative procedure for the determination of the109

nodal grid introduced by (Gonz´alez-Gambau et al., 2015) has shown a signif-110

icant improvement of the brightness temperature quality: over ocean scenes,111

previous works yield an average error reduction of approximately 0.7 K. This112

improvement should lead to an error reduction in the SSS estimates of about113

1.4 psu, which is quite signiﬁcant taking into account that the requirements114

of the mission are to fulﬁll an accuracy of 1 psu at Level 2 (see (scientiﬁc115

requirements, 2015)). However, some limitations in the determination of the116

nodal grid were already evident in previous works. As it will be next discussed,117

the observed problems have to do with the particular choice of the nodal grid118

and this choice can be improved with the convenient strategy.119

2.2 Reﬁnement of the nodal grid determination120

The initial nodal sampling approach leads to unexplained changes in the spa-121

tial extent of some RFI sources, that become either wider or signiﬁcantly122

6

reduced than that of the currently operational (i.e., nominal) image recon-123

struction algorithm. We have identiﬁed that part of this increase/decrease of124

the spatial extent of some RFI sources is linked to the condition imposed in the125

spatial locations of the nodal points. In the initial deﬁnition of the algorithm126

in (Gonz´alez-Gambau et al., 2015) (hereafter referred to as NSv1), for each127

pixel of the original image, the associated nodal point is chosen as one of the128

oversampled points corresponding to that pixel, that is, a subpixel belonging129

to the area covered by the pixel at original sampling.130

In this paper, a modiﬁcation of the nodal sampling strategy is proposed to131

better track the nodal lines. In particular, the search condition for nodal points132

has been relaxed by allowing some nodal points to cross the boundaries deﬁned133

by the original pixel. Once a ﬁrst guess of the nodal points has been estimated134

by ﬁnding the local minima of the Laplacian in the oversampled image, an135

iterative reﬁnement of the nodal points selection is performed in order to136

reduce the Laplacian in the original grid (see (Gonz´alez-Gambau et al., 2015)137

for more details). The new algorithm (hereafter referred to as NSv2) proceeds138

as follows (see scheme in Fig. 2):139

(1) The original TB image is spatially oversampled using an oversampling140

factor β = 9. The resulting pixels are referred as subpixels. In a ﬁrst141

step, candidates to nodal points are searched within the subpixels which142

belong to the area of each original pixel. A point will be considered as a143

candidate if the Laplacian of the generated image (obtained by subsam-144

pling the image with the new candidate at the location under study and145

the previous candidates at any other location) is minimum at that loca-146

tion. The process is then repeated at all locations of the original image.147

As all the points are not updated at the same time, it can not be granted148

that any new point verify to be the one leading to the minimum Lapla-149

cian when its surrounding is kept and the point is updated. Therefore,150

7

several iterations are required to attain a close-to-equilibrium state. This151

step is iterated a prestablished number i of times. After the i iterations,152

those candidates which are strictly inside the area belonging to the origi-153

nal pixel are kept ﬁxed. Hence, only those points lying on the boundaries154

of this area can be updated in the successive steps.155

(2) The area where the nodal points are searched for is extended by 1 subpixel156

in all directions (see Fig. 2). The search of the nodal points (step 1) is157

then repeated.158

(3) The algorithm is iterated until all the candidates are ﬁxed. The resulting159

grid is the nodal grid.160

It is worth remarking that the new search condition is more mathematically161

coherent, since the local minimum is now searched in an open set (not in a162

close one as the previous deﬁnition of the algorithm does).163

One of the parameters to be analyzed in the algorithm performance is the164

number of subpixels (in all directions) where the search domain is extended165

beyond the area corresponding to the original pixel. Nodal sampling is a non-166

linear method and thus, it does not produce the same eﬀect in all the points167

over the image. From our experiences, it has been observed that the search168

domain is usually extended beyond the original boundaries to not more than169

3 subpixels in the oversampled image. This ensures that the spatial resolution,170

for those pixels where the search domain is extended, is not degraded more171

than a third (accounting that β = 9) with respect to the NSv1 (nodal points172

are always selected inside the original pixel boundaries). Only in the case173

of very strongly contaminated pixels, the search domain is extended up to 5174

subpixels. In general terms, about half of the candidates lie within the original175

boundaries (and therefore they are ﬁxed from step 1), and a quarter lie exactly176

at the boundaries. The remaining quarter is mainly at 1 subpixel of the pixel177

boundaries, with a very small percentage lying beyond.178

8

Three nodal subgrids are shown in Fig. 3- the regular hexagonal subgrid which179

leads to the same values of brightness temperatures as the original (nominal)180

image, the resulting subgrid from the nodal sampling algorithm proposed in181

(Gonz´alez-Gambau et al., 2015) and that from the new version. White stars182

indicate the points which belong to each subgrid. This image corresponds to183

a zoom-in view of the oversampled TB image in Fig. 4 over the RFI located184

around the position (ξ, η) = (−0.3, 0.2). As it can be seen, the nodal points are185

more concentrated in between the peaks and the valleys (where the Laplacian186

minima are located) in the new version of the NS algorithm (Fig. 3c) than in187

the previous one (Fig. 3b).188

Brightness temperature images have been reconstructed taking the values of189

the oversampled image at the three nodal subgrids (see Fig. 4). As expected,190

the nominal processing shows the RFI-induced ripples everywhere in the im-191

age (Fig. 4a). NSv1 reduces very much the Gibbs contamination, although192

remaining sidelobes are still present (Fig. 4b). In contrast, the NSv2 algo-193

rithm (Fig. 4c) is able to further reduce the remaining sidelobes in the NSv1194

TB image. In addition, some spurious spikes which remain in the NSv1 TB195

image have been also reduced using the new algorithm.196

An example illustrating the diﬀerences on the image reconstruction techniques197

is given in Fig. 5, which shows a scene over the Atlantic Ocean strongly con-198

taminated by a RFI source produced by a ship. A clear reduction in the level199

of sidelobes and ripples is observed using nodal sampling, in its both versions.200

In the case of the NSv2, the spatial extent of the RFI source is signiﬁcantly201

narrower than that using NSv1. This eﬀect can be better appreciated by look-202

ing at the masks of the brightness temperature images in Fig. 6. The mask203

is set for those pixels with negative TB values or values higher than 350 K,204

which correspond to non-natural emissions. This illustrates that NSv2 reduces205

signiﬁcantly the sidelobes and could lead to more localized (narrower) sources.206

9

2.3 Analysis of the radiometric resolution207

One of the parameters used to deﬁne a radiometer system performance is208

the radiometric resolution, deﬁned as the temporal standard deviation of the209

brightness temperatures over a ﬂat and stable scene (Corbella et al., 2000; Tor-210

res et al., 1997). The SMOS radiometric resolution can be estimated using the211

brightness temperature diﬀerence between consecutive snapshots in the same212

polarization in order to reduce the system drift and the scene variation (Wu,213

2014). Using this methodology, the radiometric resolution was empirically es-214

timated during Commissioning Phase (Corbella et al., 2011) and compared215

to the theoretical one, computed using the following formula (Camps et al.,216

1998)217

∆T

B

(ξ, η) =

√

3d

2

2

T

sys

q

Bτ

eff

Ω

a

t(ξ, η)

q

1 − ξ

2

− η

2

α

w

√

N (1)218

where d is the distance between the antennas in wavelengths; T

sys

is the aver-219

age system temperature used for the visibility denormalization; B is the noise220

equivalent bandwidth; τ

eff

is the eﬀective integration time for the one-bit cor-221

relator (Corbella et al., 2000); α

w

is a coeﬃcient that depends on the apodiza-222

tion window used in the TB reconstruction (1 for a rectangular window, 0.45223

for a Blackman window); Ω

a

is the antenna equivalent solid angle and t(ξ, η)224

is the normalized antenna power pattern (both measured on ground); and N225

is the total number of visibilities.226

In this paper, this analysis has been performed both for nominal and NSv2227

processings using ocean scenes over the South Central Paciﬁc in June 2014.228

Figure 7a shows the radiometric resolution estimated from the nominal TBs229

of one descending overpass for dual X-polarization epochs (i.e, epochs with230

all arms in the same polarization status) (Martin-Neira et al., 2002). The cut231

along ξ = 0 in Fig. 7b, shows the agreement between the estimation and the232

10

theoretical computation of the radiometric resolution (with an average 6 %233

error in the EAF-FOV between them). All the overpasses over that zone during234

June 2014 have been analyzed, showing a stable performance over time. The235

radiometric resolution when using NSv2 is presented in Fig. 7c. In this case,236

the standard deviation of the random errors is half the one of the nominal237

processing (on average in the EAF-FOV), as it can be observed in the cuts238

along ξ = 0 (Fig.7b).239

It is worth noting that this improvement in the radiometric resolution could240

as well be obtained by using a spatial low pass ﬁlter, but in this case, the241

geophysical structures in SSS are degraded with respect to the nominal SSS,242

as we show in section 4.3. This reduction in the expected random errors of the243

brightness temperatures is quite signiﬁcant. Note that to achieve an equiva-244

lent reduction from the hardware point of view, the integration time of the245

measurement should be increased by a factor of four.246

In the case of the nodal sampling, the input data are the Fourier components247

of the brightness temperatures without applying any apodization window. The248

α

w

parameter in Eq. (1) is not known for the case of applying the nodal sam-249

pling and has been obtained by least-squares ﬁtting the estimated radiometric250

resolution to the theoretical values. For veriﬁcation purposes, this method has251

been ﬁrst applied to the nominal case. An α

w

value of 0.46 has been obtained,252

as expected for a Blackman window (Camps et al., 1998). The same procedure253

has been then applied to ﬁnd the α

w

value for the nodal sampling technique.254

In this case, α

w

= 0.23, which is consistent with the reduction factor observed255

in the radiometric resolution. This parameter is then used to compute the256

theoretical radiometric resolution in eq. 1 for each snapshot, which is used to257

weight the observational (i.e., TB) term of the Bayesian-based salinity inver-258

sion cost function (Gabarro et al., 2009), as it will be explained later in section259

4.260

11

3 Impact of nodal sampling on brightness temperatures over the261

ocean262

One of the metrics used in this work for the quality assessment of the bright-263

ness temperatures over ocean scenes is the comparison of the SMOS TB mea-264

sured to the theoretically modeled ones, using geophysical priors as input265

variables. The modeled TB have been derived from the forward model or the266

Geophysical Model Function (GMF) presented in (Guimbard et al., 2012), us-267

ing geophysical priors for SSS (climatology), SST and wind speed (data from268

ECMWF) (Zine et al., 2008). The diﬀerence between measured and modelled269

brightness temperatures is computed and the statistics of this new variable are270

assessed. Prior data do not correspond to the actual values of the geophysical271

parameters but they are typically close to them. Comparisons against mod-272

eled brightness temperatures have been widely used as they can help in the273

discrimination of errors larger than those associated to the models.274

The analysis is performed over a very stable zone in the South Central Paciﬁc275

Ocean where the SMOS operational OTT (Ocean Target Transformation) is276

computed (Meirold-Mautner et al., 2009; Tenerelli and Reul, 2010). The OTT277

is used to correct for residual antenna-frame systematic errors and is computed278

as the temporal median of the TB diﬀerence between the measured and the279

modelled TBs as a function of the spatial direction. The OTT is computed for280

each TB dataset (nominal, NSv1 and NSv2) using 10 overpasses. OTTs in Fig.281

8 correspond to the ascending node, dual epoch and Y-polarization measure-282

ments. The statistics computed for all the points in the Alias Free (AF) and283

Extended Alias Free (EAF) FOV are also annotated in the plots. Similar spa-284

tial patterns can be recognized in the three cases, although these are smoother285

for NSv1 and NSv2 than for the nominal processing. The reduction of the spa-286

tial bias in the AF is around 23.4% for NSv2 and 22.5% for NSv1 with respect287

12

to the nominal OTT. Similar results in terms of the spatial bias reduction are288

obtained for X and Y-polarizations and for ascending/descending overpasses289

(see Table 1).290

In order to assess the error reduction on brightness temperatures when using291

NS, the temporal standard deviation of the TB diﬀerence has been computed292

at each point in the EAF-FOV. The distributions of the standard deviation293

values (shown in Fig. 9) reveal that for NSv2 the retrieved brightness tempera-294

tures are in a better agreement to those modelled than for NSv1 and especially295

the nominal processing. The average reduction in the brightness temperature296

errors (w.r.t. the nominal processing) is 1.43 K (0.84 K) in X-polarization and297

1.36 K (0.76 K) in Y-polarization for NSv2 (NSv1). Notice also that the tails298

of the error distributions have been substantially reduced. With this reduc-299

tion, errors are close to the minimum expected when auxiliary information of300

geophysical parameters is used in SSS retrievals. Results conﬁrm that NSv2301

performs better than the previous approach. For this reason, from this point302

onwards, only NSv2 will be analyzed and compared to the nominal processing.303

The analysis discussed above have been carried out over the OTT (clean and304

stable) zone and for only a few orbits. In order to extend this study, in both305

the spatial and temporal domains, a 9-day 0.25

◦

resolution global map of the306

First Stokes brightness temperature diﬀerence (measurements minus model)307

has been generated from both the nominal and NSv2 TBs at Bottom of the308

Atmosphere (BOA). The maps are obtained after averaging all the pixels in the309

AF-FOV. The corresponding OTT has been subtracted to both nominal and310

NSv2 TB datasets, respectively, before the computation of the diﬀerence with311

the modeled brightness temperatures. The residual diﬀerences between the312

OTT-corrected brightness temperatures and the modeled TBs present similar313

structures both for the nominal and the nodal sampling datasets, although314

the latter are smoother (see Fig. 10). These residual patterns are consistent315

13

with those shown in (Corbella et al., 2015) and their origin can be attributed316

to two diﬀerent eﬀects: the ﬂoor error in the image reconstruction (Anterrieu317

et al., 2015; Corbella et al., 2014) and the land-sea contamination (LSC).318

Regarding the standard deviation of the TB diﬀerences, the NSv2 (Fig. 11b)319

clearly shows lower values (1.68 K on average) than the nominal (2.62 K on320

average) reconstruction (Fig. 11a). This reduction can be appreciated not only321

in open ocean (where the average reduction is around 36% at a global scale)322

but also in strongly RFI-contaminated coastal areas such as in the North-East323

Atlantic Ocean, the Arabian Sea, the Bay of Bengal and the China Seas.324

4 Impact of nodal sampling on salinity retrievals325

The impact of improved TB on SSS retrievals will be assessed in this sec-326

tion. Two methods for inverting SSS from TB data have been used: (i) a327

non-Bayesian approach, based on the retrieval of a SSS value per each indi-328

vidual TB measurement and then estimating the most probable value from329

the SSS distributions and (ii) a Bayesian approach similar to that used in the330

operational Level 2 processor (L2OS, 2014) retrieving the SSS consensus of all331

the TB measurements. Salinity maps are generated from both nominal and332

NSv2 TBs using both retrieval methodologies. The geophysical consistency of333

SSS retrievals and the inter-comparison/validation against in-situ data (Argo334

buoys) are also analyzed in this section.335

4.1 Non-Bayesian SSS retrieval336

This inversion scheme is based on retrieving a SSS value for each TB mea-337

surement and accumulate them for each geographical point of the map. Note338

that SMOS has multiple incidence angle capabilities and therefore multiple339

14

TB measurements for each satellite overpass at a certain grid point on the340

ground. All the retrieved SSS values are accumulated for each grid point over341

the selected period, e.g., 9-day average for the 9-day SSS product. To perform342

this simple single-TB retrieval, all the unknown parameters deﬁned in the343

GMF, excepting the SSS, are ﬁxed using auxiliary data (SST, wind speed and344

Total Electron Content). As such, the SSS is retrieved for each point and TB345

measurement at a given incidence angle (θ) by minimizing the diﬀerence be-346

tween the measured (T

meas

B

) and the modeled (T

mod

B

) brightness temperatures347

by means of the Newton’s method348

f(SSS) = (T

meas

B

(θ) − T

mod

B

(θ; SSS))

2

(2)349

This direct approach does not require an error model and is applied without350

previous ﬁltering of the brightness temperatures. Therefore, the analysis of351

the SSS distributions directly provides a quality indicator of the brightness352

temperatures used in the salinity retrievals.353

All the retrievals at diﬀerent incidence angles for the same geographical point354

in a 0.25

◦

spatial grid during 9 days have been accumulated in order to get355

signiﬁcant statistics. SSS values outside the range [0-50] psu have been ﬁltered356

out. Two examples of the a posteriori SSS distributions are shown in Fig. 12357

for two representative grid points: (i) over the South Paciﬁc Ocean (clean358

zone) and (ii) over the Indian Ocean close to the Arabian Sea (very aﬀected359

by land-sea and RFI contaminations). The histograms show the relative fre-360

quency of the retrieved SSS values using bins of 0.5 psu for the nominal (in361

green) and the nodal sampled TBs (in blue). The SSS estimates from Argo362

buoys (cyan vertical line) and climatology from WOA13 (red vertical line) are363

also displayed for reference. The NSv2 SSS distributions evidence a noticeable364

reduction in the standard deviation with respect to the nominal distributions365

(36.7% for the Paciﬁc grid point and 19.7% for the Indian grid point).366

15

At a global scale (Fig. 13), the standard deviations of the a posteriori SSS dis-367

tributions are 7.01 psu for the nominal processing (Fig. 13a) and 5.25 psu on368

average for the NSv2 approach (Fig. 13b). This reduction in the standard devi-369

ation of the distributions (approximately 25%) implies that the nodal sampling370

image reconstruction requires a smaller number of accumulated measurements371

to retrieve a representative SSS value with the same accuracy as that of the372

nominal approach.373

From these SSS distributions, several statistical descriptors (mean, median374

and the mean around the mode) have been explored to ﬁnd which one of375

them provides the most appropriate estimator for the SSS retrievals. The mean376

around the mode of the distribution considering an interval of ±σ is used to377

obtain the retrieved SSS values. The retrieved salinities are presented in Fig.378

14 for both the nominal (Fig. 14a) and the NSv2 (Fig. 14b) TB datasets. Note379

that although the general patterns are similar, regional diﬀerences are quite380

evident, notably in the Southern Ocean. The corresponding anomaly maps381

(w.r.t. the World Ocean Atlas 2013 or WOA13 climatology data) are shown382

in Figs. 14c and 14d. The analysis of these maps reveals that NSv2 SSS are in383

better agreement with the expected mean SSS values than the nominal SSS,384

which show a positive bias (i.e., Fig 14d presents more unbiased SSS areas385

than Fig. 14c). This could be explained by the large standard deviation of386

SSS retrievals in the case of the nominal TB.387

4.2 Bayesian SSS retrieval388

A similar approach to that used in the SMOS operational Level 2 processor389

has been also used to produce SSS maps from the nominal and the NSv2390

TBs. At each grid point all the measurements provided by one overpass of the391

satellite are used for computing a single SSS value. The Bayesian approach392

16

accounts for both TB measurement uncertainties and a priori knowledge on393

the geophysical parameters. The Bayesian-based cost function is deﬁned as:394

f(SSS) =

N

m

−1

X

j=0

(T

meas

B

(θ

j

) − T

mod

B

(θ

j

; SSS))

2

σ

2

T B

(θ

j

)

+

N

p

−1

X

j=0

(P

j

− P

prior

j

)

2

σ

2

P

j

(3)395

where N

m

is the number of measurements available for the current grid point;396

N

p

is the number of geophysical parameters to be retrieved; σ

T B

is the standard397

deviation of the error associated to the measured and modelled brightness398

temperatures (which can be deduced from Eq. (1)); P

j

is the j-th parameter399

to be retrieved; P

prior

j

is its a priori value, and σ

2

P

j

is an estimation of its error400

variance.401

The cost function used in this work is a simpliﬁcation of that deﬁned in402

(Gabarro et al., 2009). As in the non-Bayesian approach, all the auxiliary403

parameters (SST, wind speed and TEC) have been ﬁxed, so the second term404

of the right hand side of equation (3) is zero. The semi-empirical roughness405

model deﬁned in (Guimbard et al., 2012) has been used to model the rough-406

ness component of the GMF. As such, only one geophysical parameter, i.e.,407

the SSS, is retrieved by minimizing the cost function using the Levenberg408

Marquardt’s method. Only dual polarization measurements have been used to409

retrieve SSS maps. Previous to the inversion, several ﬁlters have been applied410

to the TB measurements to disregard any measurement411

(1) that is outside the [0,300] K range,412

(2) that when compared to the modeled TB, the absolute value diﬀers more413

than the minimum between 5 K and 3 times the theoretical radiometric414

resolution.415

Binned maps have been produced by a weighted average of the retrieved salin-416

ities, considering only those values within ±300 km from the center of the417

sub-satellite track (see (SMOS-BEC , 2015) for more details on this product).418

17

No post-ﬁltering has been applied to the retrieved salinities. The SSS retrieved419

from both TB datasets are shown in Fig. 15. From the maps of the anomalies420

in Figs. 15c (nominal) and 15d (NSv2) it can be observed that both maps ex-421

hibit similar large-scale structures and the anomalies are less noisy in the case422

of the nodal sampled SSS. The land-sea contamination eﬀect can be clearly423

observed in both maps, being similar in terms of their spatial extension but the424

bias seems to be higher in the case of the nodal sampling processing. Notice425

that the land-sea transition induces two simultaneous eﬀects. One is a Gibbs426

eﬀect, which is expected from the incomplete sampling of Fourier frequencies;427

nodal sampling is expected to remove this contribution. The other eﬀect is428

still under investigation and seems to be related to correlator eﬃciency errors429

(Corbella et al., 2015). This second eﬀect has long range and is not oscillatory:430

it tends to decrease the average gradient making the transitions smoother and431

much broader than they actually are. As this second eﬀect has a moderate432

gradient nodal sampling cannot remove it, and the removal of the oscillatory433

Gibbs contamination makes it more apparent in nodal sampling images.434

4.3 Geophysical consistency of the SSS retrievals435

One of the questions about the performance of nodal sampling is if this tech-436

nique induces some degradation of the spatial resolution. A visual inspection437

of Figs. 4-5 shows a signiﬁcant widening of some structures, but at the same438

time other structures seem to be better resolved. Note that the nodal sam-439

pling is a non-linear technique and therefore, it acts diﬀerently in the diﬀerent440

parts of the snapshot. Therefore, a simple assessment of its eﬀect on the ﬁnal441

resolution of SSS products is not straightforward.442

In order to assess the impact on the eﬀective spatial resolution of SSS products443

when nodal sampling is used or not, we have applied a standard oceanographic444

18

methodology: a spectral analysis (incluir ref) of the two 9-day SSS maps (3-12445

June 2014), both retrieved with the Bayesian approach, has been performed.446

For this test, we have focused on a zonal box extending from 180

◦

W to 120

◦

447

W in longitude and from 5

◦

S to 5

◦

N in latitude. This choice of zonal box is448

justiﬁed because the region is dominated by the presence of a rich variety of449

mesoscale structures, so leading to well-deﬁned spectral characteristics.450

The power spectra of the nodal sampled (red) and nominal (green) SSS are451

presented in Fig. 16. The approximate slopes of the spectra are also shown452

for providing a rough reference. As shown in the ﬁgure, both NS and nomi-453

nal present peaks and valleys at the same low spatial frequencies (i.e., below454

1

(

◦)

−1

). This means that both have the same resonance spatial frequencies,455

that is, they represent the same large-scale oceanographic structures (e.g.,456

Tropical Instability Waves, Equatorial Current, ﬁlaments, eddies, etc.). Both457

products present a similar cutoﬀ frequency of around 1.5

(

◦)

−1

, from which458

the amplitude of the noise ﬂoor is dominant (that is, the spectrum becomes a459

horizontal line). This cutoﬀ frequency represents the minimum resolved spa-460

tial scale and hence informs us about the eﬀective spatial resolution of the461

products, which in this case is of about 0.75

◦

. Hence, the application of nodal462

sampling is not reducing the eﬀective spatial resolution of SSS products.463

However, it is clear from the ﬁgure that the spectrum of the nominal product464

can be approximately ﬁtted by k

−1.1

, that is, by a power law of slope -1.1.465

A power law behaviour in the spectrum is expected for any ocean scalar at466

mesoscale and larger scales because of the eﬀect of quasi-geostrophic turbu-467

lence (incluir ref). However, the spectral slope is expected to be in the range468

from -5/3 to -3 (incluir ref). A spectral slope close to -1 is an evidence of the469

nominal product being dominated by correlated noise, even at large scales. On470

the contrary, the approximate spectral slope for NS is -1.5, which is more geo-471

physically consistent. This means that the oceanographic structures described472

19

by NS SSS have an energy content closer to reality.473

Spectral analysis also puts into evidence the advantage of applying a non-linear474

method as NS for the removal of Gibbs-like contamination. For instance, when475

a standard spatial ﬁltering is applied to the data, the analysis of its spectrum476

reveals a certain loss of geophysical consistency. To illustrate the diﬀerences477

in the performance, SSS maps applying a spatial ﬁltering to the Fourier coef-478

ﬁcients of the TB have been generated. In this case, we have used a circular479

window in such a way that only the spatial frequencies in the inner circle of480

the star-shape spatial coverage are used in the brightness temperature inver-481

sion (Corbella et al., 2012). In this case, the improvement in the comparison482

with modeled TB is on average 0.2 K with respect to the nominal case. Re-483

garding SSS, when the zonal spectrum is computed (see Fig. 17) we see that484

some spectral peaks and valleys are lost. This implies a signiﬁcant change in485

some geophysical structures, what is clearly an artifact. Besides, as in the case486

of the nominal SSS, the circular SSS are dominated by correlated noise (the487

approximate slope in this case is k

−1.2

). Finally, the cutoﬀ frequency is clearly488

lower than those of nominal and NS products, hence evidencing a worse ef-489

fective resolution in the case of this particular spatial averaging. We conclude490

that nodal sampling is more suitable from a geophysical perspective than a491

linear spatial ﬁltering.492

4.4 Validation with in-situ measurements493

The validation of the SSS maps against in-situ measurements is carried out494

using Argo ﬂoats (see http://www.argo.ucsd.edu). The analysis is split in two495

diﬀerent ocean regions: (i) coastal regions (i.e., wihtin 800 km oﬀ the coast) and496

(ii) open ocean (all the ocean but coastal regions). This is done to diﬀerentiate497

the nodal sampling eﬀect over land-sea contaminated regions and areas where498

20

no signiﬁcant impact from this kind of contamination is expected. All the499

available Argo SSS estimates within the same 9-day period are considered500

in the validation. Each Argo SSS estimate is compared with the SSS value501

provided by its corresponding L3 grid. Therefore, may happen that several502

Argo estimates are compared with the same L3 grid. In this case, all the503

diﬀerences are considered in the full statistics. Since one month of nominal504

and NSv2 data (June 2014) is used for validation purposes, seven 9-day maps505

(generated every 3 days) have been generated. The statistics (the average of506

the statistics for each individual 9-day map) have been computed in the study507

regions indicated in Table 2.508

Figure 18 displays the statistics (mean and standard deviation) of the dif-509

ferences between the 9-day, 0.25

◦

SMOS measurements and the Argo surface510

salinities for the nominal and the NSv2 processings. In open ocean (top row),511

the standard deviation of the SSS diﬀerences for the NSv2 processing is lower512

than that for the nominal processing in all the study regions. For the NSv2513

processing, the standard deviation of the diﬀerences of SSS retrievals and Argo514

are quite similar for both (Bayesian and non-Bayesian) retrieval methods, al-515

though slightly lower for the Bayesian approach. The diﬀerence between the516

NSv2 and the nominal SSS quality is much larger for the non-Bayesian re-517

trieval than for the Bayesian approach. This may be due to the fact that the518

representative SSS for the 9-day accumulated distributions is not well deﬁned519

in the nominal case. Hence, accumulated measurements over a larger period520

would be needed to deﬁne a proper SSS using this retrieval methodology. Glob-521

ally, the biases are very similar for both the NSv2 and the nominal processing.522

Slight diﬀerences appear in North-Paciﬁc (better in nominal) and Southern523

Ocean (better in NSv2), which require further investigation.524

Regarding the matchups located no farther than 800 km from the coast (bot-525

tom row), both the bias and the standard deviation of the SSS diﬀerences526

21

are higher than in open ocean, as expected due to the RFI and land-sea con-527

tamination eﬀects. The standard deviation of the SSS diﬀerences for the non-528

Bayesian approach is lower for NSv2, except in the North Atlantic zone. This529

isolated eﬀect needs to be further investigated. However, this is not the case530

for the Bayesian retrieval, where the standard deviation seems to be generally531

higher for NSv2 than for the nominal processing. This could be due to the pre-532

ﬁltering criteria used in the Bayesian retrieval, which might be masking the533

improvements on the NSv2 TB quality with respect to that of the nominal TB.534

In terms of error biases, the matchups close to the coast display a larger bias535

in the case of NSv2 than the nominal case. We have not at this moment a com-536

plete explanation of this larger deviation close to the coast when the Bayesian537

method is used on NS images, something that does not happen when they are538

processed with the non-Bayesian method. We guess that the removal of the539

oscillatory Gibbs makes brightness temperatures to be systematically biased540

in the NS case whereas in the nominal case the Gibbs contamination makes541

them to get sometimes closer to the right value. Since the TB diﬀerences are542

averaged together in the cost function this would explain a stronger systematic543

bias on SSS retrieved from NSv2 than from nominal TBs. An exception is the544

Southern Ocean, where NSv2 performs better and seems to partially overcome545

the limitations of the SSS retrievals in areas of high winds and low SST values,546

where the low sensitivity of the brightness temperatures to salinity changes547

produce large errors in the SSS retrievals.548

5 Conclusions549

In this paper, a modiﬁcation of the nodal sampling technique has been pro-550

posed to improve the quality of the reconstructed TBs. This improvement con-551

cerns to the ﬁne tuning of the nodal grid determination. This reﬁned technique552

(NSv2) has led to a signiﬁcant quality improvement of the brightness temper-553

22

atures with respect to those of the previous nodal sampling method (NSv1)554

(Gonz´alez-Gambau et al., 2015) and notably those of the current SMOS image555

reconstruction baseline (nominal). At snapshot level, NSv2 improves the TB556

reconstruction in terms of both the sidelobe levels and ripples. In addition to557

that, the spatial extent of the RFI sources, sometimes wider in NSv1 than in558

the nominal images, is clearly reduced using NSv2.559

Since NSv2 leads to a decrease of the expected errors, a new radiometric560

resolution has been empirically estimated over the ocean. The results show561

that NSv2 TB present half the radiometric resolution of the nominal TBs,562

which is an important improvement in terms of the system performance. A key563

point for the general application of the nodal sampling technique is to assess564

the eﬀective spatial resolution of nodal sampling images. As nodal sampling565

is a non-linear method (its eﬀect is not simply applying a convolution kernel566

to the image, as some parts of the image behave in a diﬀerent way than other567

parts) the concept of resolution should be rather considered as an eﬀective568

quantity. The introduction of power spectral analysis has allowed us to show569

that the application of nodal sampling does not degrade the eﬀective spatial570

resolution of SSS products; on the contrary, the spectral slope of NS products571

becomes much closer to what should be geophysically expected.572

The validation of SMOS brightness temperatures over ocean scenes shows that573

NSv2 TBs are in better agreement with the modeled TBs than the nominal574

TBs. Over clean and stable zones, such as the zone in the Paciﬁc Ocean where575

the SMOS OTT is computed, the average error of the NSv2 TBs is about 1.3576

K lower than that of the nominal TBs. At global scale, the error reduction577

is of about 1 K. This improvement in the brightness temperatures is a good578

indicator that the quality of geophysical retrievals could be improved using579

this technique.580

Salinity maps have been produced for both the NSv2 and the nominal process-581

23

ing using two retrieval methods. The non-Bayesian approach allows a more582

direct analysis of the quality of the TB used in the retrieval. It is shown that583

the NSv2 SSS distributions are narrower and therefore better deﬁned than the584

nominal SSS distributions. When compared to the climatology, the NSv2 SSS585

anomalies show similar large-scale structures but less noisy than the nominal586

SSS anomalies.587

From the validation with Argo SSS estimates, it is found that NSv2 improves588

the accuracy of the SSS retrievals in open ocean with respect to the nomi-589

nal SSS product, regardless of the retrieval methodology. The validation has590

been carried out separately for coastal areas (i.e., within the ﬁrst 800 km oﬀ591

the coast), where besides RFI, the eﬀect of the land-sea contamination is also592

present. In these regions, the advantage of the higher quality brightness tem-593

peratures provided by NSv2 is only present in the case of the non-Bayesian594

approach. In this regard, two issues need to be further investigated: (i) the ef-595

fect of the systematic bias induced by the land-sea contamination and (ii) the596

Bayesian-based retrieval which has been used, notably regarding the quality597

control.598

Future improvements at the SMOS image reconstruction level are aimed at599

assessing the capabilities of the nodal sampling to provide valid retrievals600

in strongly RFI-contaminated areas once the land-sea contamination eﬀects601

have been corrected. To do that, the corrections currently proposed by the602

SMOS Level 1 team will be applied prior to the image reconstruction by nodal603

sampling.604

In the context of salinity retrievals, our team is investigating improvements of605

the Bayesian cost function using nodal sampled TB to retrieve, not only SSS,606

but also the wind speed, similarly to the Level2 operational processor. This will607

imply to revisit the main mathematical hypothesis for applying the Bayesian608

approach (unbiased and independent Gaussian errors) to the SMOS case. In609

24

this line, this work allows analyzing the impact that brightness temperature610

biases have on the SSS retrieval when the TB standard deviations are reduced,611

as in the nodal sampling processing.612

Acknowledgments613

This work has been funded by the Spanish Ministry of Economy through the614

National R+D Plan by means of MIDAS-7 project AYA2012-39356-C05-03615

and previous grants. The validation part of this work has been done with the616

support of the FP7-SPACE E-AIMS project (grant agreement 312642). The617

Argo data were collected and made freely available by the International Argo618

Program and the national programs that contribute to it (http://www.argo.ucsd.edu,619

http://argo.jcommops.org). The Argo Program is part of the Global Ocean620

Observing System.621

Authors would like to thank to Francesc Torres Torres and Nuria Duﬀo Ubeda622

from the Universitat Polit´ecnica de Catalunya for their useful insights in the623

system performance assessment.624

References625

Anterrieu, E. and Khazaal, A. (2008). Brightness temperature map recon-626

struction from dual-polarimetric visibilities in synthetic aperture imag-627

ing radiometry. Geoscience and Remote Sensing, IEEE Transactions on,628

46(3):606–612.629

Anterrieu, E., Suess, M., Cabot, F., Spurgeon, P., and Khazaal, A. (2015). An630

additive mask correction approach for reducing the systematic ﬂoor error in631

imaging radiometry by aperture synthesis. Geoscience and Remote Sensing632

Letters, IEEE, 12(7):1441–1445.633

25

Anterrieu, E., Waldteufel, P., and Lannes, A. (2002). Apodization functions634

for 2-D hexagonally sampled synthetic aperture imaging radiometers. Geo-635

science and Remote Sensing, IEEE Transactions on, 40(12):2531–2542.636

Bar´a, J., Camps, A., Torres, F., and Corbella, I. (1998). Angular resolution637

of two-dimensional hexagonally sampled interferometric radiometers. Radio638

Science, vol. 33, no. 5:1459–1473.639

Barre, H., Duesmann, B., and Kerr, Y. (2008). SMOS: The mission and the640

system. Geoscience and Remote Sensing, IEEE Transactions on, 46(3):587–641

593.642

Brown, M., Torres, F., Corbella, I., and Colliander, A. (2008). SMOS calibra-643

tion. Geoscience and Remote Sensing, IEEE Transactions on, 46(3):646–644

658.645

Camps, A., Corbella, I., Bara, J., and Torres, F. (1998). Radiometric sensi-646

tivity computation in aperture synthesis interferometric radiometry. Geo-647

science and Remote Sensing, IEEE Transactions on, 36(2):680–685.648

Camps, A., Gourrion, J., Tarongi, J. M., Vall Llossera, M., Gutierrez, A.,649

Barbosa, J., and Castro, R. (2011). Radio-Frequency Interference detection650

and mitigation algorithms for synthetic aperture radiometers. Algorithms,651

4(3):155–182.652

Camps, A., Vall-llossera, M., Corbella, I., Duﬀo, N., and Torres, F. (2008). Im-653

proved image reconstruction algorithms for aperture synthesis radiometers.654

Geoscience and Remote Sensing, IEEE Transactions on, 46(1):146–158.655

Castro, R., Guti´errez, A., and Barbosa, J. (2012). A ﬁrst set of techniques to656

detect Radio Frequency Interferences and mitigate their impact on SMOS657

data. Geoscience and Remote Sensing, IEEE Transactions on, 50(5):1440–658

1447.659

Corbella, I., Duﬀo, N., Vall-llossera, M., Camps, A., and Torres, F. (2004). The660

visibility function in interferometric aperture synthesis radiometry. Geo-661

science and Remote Sensing, IEEE Transactions on, 42(8):1677–1682.662

Corbella, I., Duran, I., Wu, L., Torres, F., Duﬀo, N., Khazaal, A., and Martin-663

26

Neira, M. (2015). Impact of correlator eﬃciency errors on SMOS land-sea664

contamination. Geoscience and Remote Sensing Letters, IEEE, PP(99):1–5.665

Corbella, I., Martin-Neira, M., Oliva, R., Torres, F., and Duﬀo, N. (2012).666

Reduction of secondary lobes in aperture synthesis radiometry. Geoscience667

and Remote Sensing Letters, IEEE, 9(5):977–979.668

Corbella, I., Torres, F., Camps, A., Bara, J., Duﬀo, N., and Vall-Ilossera,669

M. (2000). L-band aperture synthesis radiometry: hardware requirements670

and system performance. In Geoscience and Remote Sensing Symposium,671

2000. Proceedings. IGARSS 2000. IEEE 2000 International, volume 7, pages672

2975–2977 vol.7.673

Corbella, I., Torres, F., Camps, A., Duﬀo, N., and Vall-llossera, M. (2009).674

Brightness temperature retrieval methods in synthetic aperture radiometers.675

Geoscience and Remote Sensing, IEEE Transactions on, 47(1):285–294.676

Corbella, I., Torres, F., Duﬀo, N., Gonz´alez-Gambau, V., Pablos, M., Duran,677

I., and Mart´ın-Neira, M. (2011). MIRAS calibration and performance: Re-678

sults from the SMOS in-orbit commissioning phase. Geoscience and Remote679

Sensing, IEEE Transactions on, 49(9):3147–3155.680

Corbella, I., Torres, F., Wu, L., Duﬀo, N., Duran, I., and Martin-Neira, M.681

(2014). Smos image reconstruction quality assessment. In Geoscience and682

Remote Sensing Symposium (IGARSS), 2014 IEEE International, pages683

1914–1916.684

Daganzo-Eusebio, E., Oliva, R., Kerr, Y., Nieto, S., Richaume, P., and Meck-685

lenburg, S. (2013). SMOS radiometer in the 1400-1427 MHz passive band:686

Impact of the RFI environment and approach to its mitigation and cancella-687

tion. Geoscience and Remote Sensing, IEEE Transactions on, 51(10):4999–688

5007.689

Font, J., Camps, A., Borges, A., Martin-Neira, M., Boutin, J., Reul, N., Kerr,690

Y., Hahne, A., and Mecklenburg, S. (2010). SMOS: The challenging sea sur-691

face salinity measurement from space. Proceedings of the IEEE, 98(5):649–692

665.693

27

Gabarro, C., Portabella, M., Talone, M., and Font, J. (2009). Toward an694

optimal smos ocean salinity inversion algorithm. Geoscience and Remote695

Sensing Letters, IEEE, 6(3):509–513.696

Gonz´alez-Gambau, V., Turiel, A., Mart´ınez, J., Olmedo, E., and Corbella, I.697

(2014). A novel reconstruction algorithm for the improvement of SMOS698

brightness temperatures. In Microwave Radiometry and Remote Sensing of699

the Environment (MicroRad), 2014 13th Specialist Meeting on, pages 124–700

127.701

Gonz´alez-Gambau, V., Turiel, A., Olmedo, E., Mart´ınez, J., Corbella., I., and702

Camps, A. (2015). Nodal sampling: a new image reconstruction algorithm703

for SMOS. IEEE Transactions on Geoscience and Remote Sensing, in press.704

Guimbard, S., Gourrion, J., Portabella, M., Turiel, A., Gabarr´o, C., and Font,705

J. (2012). SMOS semi-empirical ocean forward model adjustment. IEEE706

Transactions on Geoscience and Remote Sensing, 50:1676–1687.707

Kerr, Y., Waldteufel, P., Wigneron, J., Delwart, S., Cabot, F., Boutin, J.,708

Escorihuela, M., Font, J., Reul, N., Gruhier, C., Juglea, S., Drinkwater,709

M., Hahne, A., Martin-Neira, M., and Mecklenburg, S. (2010). The SMOS710

mission: New tool for monitoring key elements of the global water cycle.711

Proceedings of the IEEE, 98(5):666–687.712

L2OS (2014). SMOS L2 OS Algorithm Theoretical Baseline Document. Tech-713

nical report, Argans.714

Martin-Neira, M. and Goutoule, J. (1997). MIRAS: a two dimensional aper-715

ture synthesis radiometer for soil moisture and ocean salinity observations.716

ESA Bulletin, 92:95–104.717

Martin-Neira, M., Ribo, S., and Martin-Polegre, A. (2002). Polarimetric718

mode of MIRAS. Geoscience and Remote Sensing, IEEE Transactions on,719

40(8):1755–1768.720

McMullan, K. D., Brown, M., Martin-Neira, M., Rits, W., Ekholm, S., Marti,721

J., and Lemanczyk, J. (2008). SMOS: The payload. Geoscience and Remote722

Sensing, IEEE Transactions on, 46(3):594–605.723

28

Meirold-Mautner, I., Mugerin, C., Vergely, J., Spurgeon, P., Rouﬃ, F., and724

Meskini, M. (2009). SMOS ocean salinity performance and TB bias correc-725

tion. In EGU General Assembly.726

Oliva, R., Daganzo, E., Kerr, Y., Mecklenburg, S., Nieto, S., Richaume, P.,727

and Gruhier, C. (2012). SMOS Radio Frequency Interference scenario: Sta-728

tus and actions taken to improve the RFI environment in the 1400-1427729

MHz passive band. Geoscience and Remote Sensing, IEEE Transactions730

on, 50(5):1427–1439.731

Park, H., Gonz´alez-Gambau, V., and Camps, A. (2015). High angular resolu-732

tion RFI localization in synthetic aperture interferometric radiometers using733

Direction-Of-Arrival estimation. Geoscience and Remote Sensing Letters,734

IEEE, 12(1):102–106.735

scientiﬁc requirements, S. (2015).736

SMOS-BEC (2015). SMOS-BEC ocean and land products description, bec-737

smos-0001-pd. Technical report, SMOS Barcelona Expert Centre.738

Soldo, Y., Khazaal, A., Cabot, F., Richaume, P., Anterrieu, E., and Kerr, Y.739

(2014). Mitigation of RFIs for SMOS: A distributed approach. Geoscience740

and Remote Sensing, IEEE Transactions on, 52(11):7470–7479.741

Tenerelli, J. and Reul, N. (2010). Analysis of L1PP calibration approach742

impacts in SMOS TB and 3-days SSS retrievals over the Paciﬁc using an743

alternative Ocean Target Transformation applied to L1OP data. Technical744

report, IFREMER/CLS.745

Torres, F., Camps, A., Bar, J., and Corbella, I. (1997). Impact of receiver746

errors on the radiometric resolution of large two-dimensional aperture syn-747

thesis radiometers. Radio Science, 32(2):629–641.748

Wu, L. (2014). Contribution to spatial bias mitigation in Interferometric rara-749

diometers devoted to Earth observation: Application to the SMOS mission.750

PhD thesis, Universitat Polit´ecnica de Catalunya (UPC).751

Yueh, S., West, R., Wilson, W., K.Li, F., Njoku, E., and Rahmat-Samii, Y.752

(2001). Error sources and feasibility for microwave remote sensing of ocean753

29

surface salinity. Geoscience and Remote Sensing, IEEE Transactions on,754

39(5):1049–1060.755

Zine, S., Boutin, J., Font, J., Reul, N., Waldteufel, P., Gabarr´o, C., Tenerelli,756

J., Petitcolin, F., Vergely, J., Talone, M., and Delwart, S. (2008). Overview757

of the SMOS sea surface salinity prototype processor. Geoscience and Re-758

mote Sensing, IEEE Transactions on, 46(3):621–645.759

30

Table 1

Spatial bias reduction (in percent) of the ascending and descending OTT in the

AF-FOV using both versions of NS with respect to the nominal reconstruction.

NSv1 NSv2

X-pol Y-pol X-pol Y-pol

ASC 19.1 22.5 19.7 23.4

DES 15.3 17.1 16.5 18.5

Table 2

Deﬁnition of the study regions where the statistics of the comparison between SSS

retrievals and Argo estimates are provided.

Zone Description Latitude Longitude

Global Tropics and mid-latitudes [60S-60N] All

Tropics Tropics [30S-30N] All

N. Atlantic North-Atlantic region [15N-37N] [50W,0]

N. Paciﬁc A region of the North Paciﬁc [45N-60N] [170E,140W]

S. Ocean Southern Ocean [60S-40S] All

31

Fig. 1. SMOS brightness temperatures over southern Europe using the nominal

processing (after applying a Blackman window). The sidelobes and ripples caused

by the RFI sources can be appreciated also over the Mediterranean Sea, very far

away from the sources locations.

Fig. 2. Scheme to illustrate how the NSv2 algorithm works.

32

(a) Original (b) NSv1 (c) NSv2

Fig. 3. Zoom-in view of the oversampled brightness temperature image (without

Blackman window) in Fig. 4 over the RFI source located around the position

(ξ, η) = (−0.3, 0.2). Subgrids where sampling the oversampled image are indicated

by the white stars: (a) the original regular hexagonal subgrid (which leads to the

same values of brightness temperatures as the original image), (b) nodal subgrid

from NSv1 and (c) selection of nodal points from NSv2.

(a) Nominal (b) NSv1 (c) NSv2

Fig. 4. Reconstructed brightness temperatures in the fundamental hexagon of a

snapshot over North Africa using the three nodal subgrids in Fig. 3. The reduction

of the sidelobe levels and the ripples can be clearly appreciated when using nodal

sampling.

33

(a) Nominal (b) NSv1 (c) NSv2

Fig. 5. Brightness temperatures in the fundamental hexagon of a scene over the

Atlantic Ocean strongly contaminated by an RFI produced by a ship reconstructed

using the (a) nominal, (b) NSv1 and (c) NSv2 image reconstruction approaches.

(a) Nominal (b) NSv1 (c) NSv2

Fig. 6. Masks of pixels with brightness temperatures corresponding to non-natural

emission (negative TB values and higher than 350 K) for images in Fig. 5. A clear

reduction of the RFI source spatial extension is observed in NSv2 TB with respect

to NSv1 TB.

34

(a) Nominal (b) Cut along ξ = 0 (c) NSv2

Fig. 7. Left: Radiometric resolution [K] estimated using ocean scenes over the South

Central Paciﬁc Ocean for nominal processing. Middle: comparison of estimated ra-

diometric resolution for nominal TBs (dashed blue line) with the theoretically com-

puted ones (dashed red line) along the cut ξ = 0 and estimated radiometric resolu-

tion for NSv2 TBs (solid line). A reduction factor of 2 is achieved on average in the

EAF-FOV using NSv2 with respect to the nominal. Right: Radiometric resolution

[K] estimated for NSv2 processing.

(a) Nominal (b) NSv1 (c) NSv2

Fig. 8. OTT (median of the diﬀerence between TB measurements and the theoreti-

cally modeled TB for the EAF-FOV) for dual epochs in Y-polarization. 10 ascending

passes over the South Central Paciﬁc Ocean have been used to compute the OTT

(Meirold-Mautner et al., 2009; Tenerelli and Reul, 2010). A reduction of the spatial

bias is observed both for NSv1 and NSv2 with respect to the nominal case.

35

(a) X-polarization (b) Y-polarization

Fig. 9. Distributions of the standard deviation of the diﬀerence between the TB

measurements and the model for nominal (red), NSv1 (blue) and NSv2 (black)

approaches. A mean error reduction of approximately 0.8 K is obtained using NSv1

technique and 1.4 K using NSv2 with respect to the SMOS nominal processing. It

also must be pointed out the signiﬁcant reduction in the tails of the distributions

with NSv2 approach.

36

(a) Nominal

(b) Nodal Sampling

Fig. 10. 9-day 0.25

◦

spatial resolution map of the First Stokes TB diﬀerence (OT-

T-corrected SMOS TB minus TB model) for (a) nominal and (b) nodal sampling

image reconstruction approaches.

37

(a) Nominal

(b) Nodal Sampling

Fig. 11. 9-day 0.25

◦

spatial resolution map of the standard deviation of the First

Stokes TB diﬀerence (OTT-corrected SMOS TB minus TB model) for (a) nominal

and (b) nodal sampling image reconstruction approaches.

38

(a)

(b)

Fig. 12. A posteriori SSS distributions per a given grid point over (a) the South

Paciﬁc Ocean (clean zone) and (b) Indian Ocean close to the Arabian Sea (strongly

contaminated by RFI and LSC).

39

(a) Nominal

(b) Nodal Sampling

Fig. 13. Map of the standard deviation of the SSS distributions using (a) nominal

and (b) NSv2 TBs. SSS retrievals have been accumulated during 9 days over a 0.25

◦

spatial grid.

40

(a) SSS nominal (b) SSS nodal sampling

(c) Anomaly nominal (d) Anomaly nodal sampling

Fig. 14. Map of SSS using a non-Bayesian retrieval with (a) nominal and (b) NSv2

brightness temperatures. Map of the anomalies between SSS retrievals and clima-

tology from WOA13 using (c) nominal and (d) NSv2 brightness temperatures. SSS

retrievals have been accumulated during 9 days over a 0.25

◦

spatial grid.

41

(a) SSS nominal (b) SSS nodal sampling

(c) Anomaly nominal (d) Anomaly nodal sampling

Fig. 15. Map of the SSS retrievals using the Bayesian approach from (a) nominal

and (b) NSv2 brightness temperatures. Map of the anomalies between SSS retrievals

using the Bayesian approach and climatology from WOA13 using (c) nominal and

(d) NSv2 brightness temperatures. Binned maps have been generated using SSS

retrievals during 9 days over a 0.25

◦

spatial grid.

42

0.001

0.01

1

psu

2

Degree

-1

Zonal spectra: NS (red) vs nominal (green)

Fig. 16. Zonal spectra for the nominal (green) and nodal sampled (red) SSS maps

obtained by the Bayesian approach. The approximate slope for the nominal spectra

(magenta) corresponds to k

−1.1

and the one for the nodal sampled SSS spectra

(blue) corresponds to k

−1.5

, which is more consistent with the geophysical signal.

43

0.001

0.01

1

psu

2

Degree

-1

Zonal spectra: NS (red) vs circular window (green)

Fig. 17. Zonal spectra for the circular window (green) and nodal sampled (red) SSS

maps obtained by the Bayesian approach. The approximate slope for the circular

SSS spectra (magenta) corresponds to k

−1.2

and the one for the nodal sampled SSS

spectra (blue) corresponds to k

−1.5

.

44

(a) Open ocean, mean (b) Open ocean, standard deviation

(c) Coastal regions, mean (d) Coastal regions, standard deviation

Fig. 18. Statistics of the comparison of SSS retrievals using both Bayesian and

non-Bayesian (indicated in the legend as mode) approaches with Argo SSS esti-

mates. Mean and standard deviation are shown for the 800 km closest to the shore

(top) and from 800 km oﬀshore on (bottom), separately.

45