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Algorithm Theoretical Baseline Document

Customer: ESA

Ref. ITT: AO/1-9158/18/I-BG

Version: v1r4

Ref. Internal:ARG-003-053_v2r0

Date:14/04/2020

Filename: Arctic+Salinity_D1.3_ATBD_v2r0.tex

Arctic+ salinity

Algorithm Theoretical Baseline Document

Ref: AO/1-9158/18/I-BG

Date:14/04/2020

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Signatures

Name Signature Date

Author Justino Martínez

BEC 14/04/2020

Reviewed by

Carolina Gabarró

BEC 20/04/2020

Antonio Turiel

BEC 20/04/2020

Rafael Catany

ARGANS 20/04/2020

Approved by Justino Martínez

BEC 21/04/2020

Carolina Gabarró

BEC 21/04/2020

Rafael Catany

ARGANS 21/04/2020

Authorized by

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Amendment Record Sheet

Document change record

Date/Issue Description Section/Figure

November 2019 / v1r3 d0computation revised Section 2.1

November 2019 / v1r3 Changed climatology period Section 2.3.1.3, ﬁgures 19,

20 and 21 and table 2

November 2019 / v1r3 Computed distance to the ice

Changed L3 ﬁltering

Sections 2.4.0.1 and 2.5

ﬁgures 34 and 33

November 2019 /v1r3 Deliver to ESA New document

December 2019 / v1r4 Introduction of key tables Added section 4

December 2019 / v1r4 Justiﬁcation of not use NS, Gkj Section 2

December 2019 / v1r4 Use of BEC roughness model Section 2.2

December 2019 / v1r4 Algorithm scheme clariﬁcation Section 2and ﬁgure 1

December 2019 / v1r4 Better explained ﬁgure Section 2.3.1.2 and ﬁgure 14

December 2019 / v1r4 Better explained

temporal correction Section 2.5 and ﬁgure 27

December 2019 / v1r4 Source code moved to appendix Added Appendix A

December 2019 /v1r4 Deliver to ESA New document

April 2020 / v2r0 Added WOA 2018

bibliographic reference and

changes in ﬁgures

Section 2.3.1.4

April 2020 / v2r0 Changed period forSMOS-based

climatology computation Section 2.3.1.3

April 2020 / v2r0 Introduced a spatial

correction in L2B

Sections 2.5 and 4,

new sections 2.6 and 2.7, modiﬁed

ﬁgure 1

May 2020 / v2r0 Deliver to ESA New document

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Table of Content

1 Introduction 15

1.1 Structure of this document ............................... 15

2 Overview and generation of the Arctic+ Salinity product 17

2.1 Generation of the level 1C ............................... 18

2.1.1 The importance of the grid projection ..................... 22

2.1.1.1 Former Arctic Grid Projection: BEC Arctic v2.0 product ..... 22

2.1.1.2 Current Arctic Grid Projection: Arctic+ SSS product ....... 23

2.2 Generation of the level 1D ............................... 24

2.3 Debiasing ........................................ 26

2.3.1 New Debiasing strategy ............................ 28

2.3.1.1 Homogeneous EAF-FOV discretization .............. 28

2.3.1.2 Debiasing brightness temperatures ................ 29

2.3.1.3 SMOS-based climatology computation .............. 32

2.3.1.3.1 Derived statistical quantities ............... 33

2.3.1.4 Annual IF S reference ........................ 36

2.4 Inversion ........................................ 43

2.4.0.1 L2A ﬁltering ............................. 44

2.4.0.2 New L2B generation and its ﬁltering ................ 46

2.4.1 Error propagation ................................ 46

2.4.1.1 L2B computation ........................... 47

2.5 L2B temporal correction ................................ 50

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2.6 L2B spatial correction ................................. 53

2.7 L3 maps creation .................................... 58

3 Dielectric constant study 62

4 Key aspects of processing 66

5 References 68

Appendix Source C code 72

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List of ﬁgures

1 General algorithm SSS retrieval. As part of the algorithm it has been used the

debiased non-Bayesian strategy deﬁned by [Olmedo et al., 2017] but the debias-

ing is performed in TBinstead of in SSS as described in 2.3.1. Note that TBsea

is necessary to compute the reﬂectivity of the sea surface which it is necessary

to perform the TBcorrections and dielectric model must be used in the L1D-BOA

computation. ...................................... 17

2 L1B to L1C TOA algorithm overview ......................... 19

3 (Left) Tessellation of the fundamental hexagon using N hexagons centered on an-

tenna grid points. Example with N = 16 ×16. (Right) Detail of the hexagon cen-

tered in an antenna grid point. Each hexagon is composed by six equilateral trian-

gles with h=dG/2,b=dG/3and dG= 2/(dR√3N)where dR= 0.875 is the dis-

tance between receivers in SMOS wavelength units (from [Martínez et al., 2018])

.............................................. 20

4 64 ×64 SMOS hexagonal ﬁeld of view. Purple line indicate the Earth limit;

beyond this limit the FOV points contain sky TB. Blue and black lines encircle

the AF-FOV and EAF-FOV respectively. Points in the horizontal yellow lines are

known as belt whereas suspenders are the points included in the vertical yellow

lines. Belt ans suspenders are points of transition between free-alias zone and

zones affected by Earth-sky aliases or between zones affected by different Earth-

sky alias, therefore the measures are expected to be somewhat degraded over

there. .......................................... 20

5 FOV projected over the Earth when the SMOS antenna points towards Svalbard

island. SMOS horizon (purple line) extends almost 3000 km beyond the bore-

sight (point 0,0). Green line shows the projection of the hexagonal FOV limits

over the Earth surface. The circles indicate the center of 100×100 km regular

cells in plane coordinates (X-Y) using a Lambert azimuthal equal area projection

centered at 90◦N. The TBcorresponding to each X-Y cell is computed by retro-

projecting its central grid point on the antenna plane and performing a weighted

average in (ξ,η) following and inverse-square law (compare with ﬁgure 4). Only

grid points inside EAF-FOV (black line) will be taken into consideration to retrieve

salinity. ......................................... 21

6 Ascending orbit starting at UTC 2018-08-26 06:35:45 using a Lambert Azimuthal

Equal Area projection with origin (0◦N, 17.18◦W) indicated by a purple circle . . 22

7 Snapshot from orbit shown in ﬁgure 6 corresponding to UTC 2018-08-26 07:28:54. 23

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8 Brightness temperature obtained for UTC 2018-08-26 07:28:54 processed using

a LAEA with origin in the center of the orbit and reprojected to the EASE-Grid

2.0 North (left) and the same snapshot natively processed in the EASE-Grid 2.0

North (right). Black dots indicate the EASE-Grid 2.0 North grid cells center . . . 24

9 Contributions to the measured TB.......................... 25

10 L1C TOA to L1D BOA algorithm overview ...................... 27

11 Non-homogeneous division of the EAF-FOV performed in BEC Arctic v2.0 prod-

uct to compute the SMOS climatology ........................ 28

12 Homogeneous EAF-FOV grid division used. Left: EAF-FOV grid from the 64 ×

64 FOV grid. Right: Sets of 7 elements (denoted by ξη) that will accumulate

measures in order to compute the SMOS-based climatology ............ 29

13 First Stokes value provided by Meissner & Wentz dielectric model for different

values of salinity and temperature. Note how the system moves away from linear

behavior as the salinity and temperature decrease. ................. 30

14 Example of three measures of half ﬁrst Stokes (FS/2) obtained for a grid point

affected by land-sea contamination. The grid point is located at North Sea coastal

waters (53.86◦N, 6.70◦E), approximately at 35 km of the German coast. The

measures (thick lines) have been obtained from successive snapshots (i.e. for

different incidence angles). Thin lines indicate half ﬁrst Stokes value provided by

Meissner & Wentz dielectric model for different values of salinity, FS(SSS)/2. . . 31

15 The SMOS climatological representative for ascending passes at different FOV

positions ......................................... 35

16 The SMOS climatological representative for descending passes at different FOV

positions ......................................... 36

17 Schema of the area weighted average procedure. Orange circles indicate the

center of each dashed cell of 0.25×0.25 degres (source grid). Blue squares are

the center of the 25×25 km cells (destination grid). ................. 38

18 Half ﬁrst Stokes provided by WOA2018 and Meissner & Wentz dielectric model

for different points of the FOV ............................. 39

19 Correction to be applied to measured half ﬁrst Stokes parameter in 4 difference

FOV positions for ascending passes (equation 20) ................. 40

20 Correction to be applied to measured half ﬁrst Stokes parameter in 4 difference

FOV positions for descending passes (equation 20) ................ 41

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21 Mean half ﬁrst Stokes correction in the whole Arctic (half ﬁrst Stokes from WOA

2018 minus SMOS half ﬁrst Stokes representant). Left: ascending case. Right:

descending case. .................................... 42

22 Mean ascending minus descending half ﬁrst Stokes correction in the whole Arctic 42

23 Snapshot from ascending L2A orbit over the Kara Sea on August 2, 2015. Left:

salinity values retrieved using the non-Bayesian procedre described in section

2.4. Right: the corresponding error of each retrieval as has been described in

section 2.4.1 and expressed in equation 26. ..................... 48

24 Ascending L2B orbit over the Kara Sea on August 2, 2015. Left: salinity values

computed from L2A snapshots using expressions 27 and 28. Ob’ and Yenisey

rivers discharge are clear at this level as well as the freshwater accumulation

in the Baydaratskaya bay. Right: the corresponding error of salinity value from

equation 29. ....................................... 49

25 9-day L3 map centered on August 2, 2015 combining ascending and descending

orbits. Left: salinity values computed from L2B orbits using expression 30. Right:

the corresponding error of salinity value from equation 32. ............. 49

26 Argo proﬁlers distribution during the period 2011-2018 (dots). Blue line delimits

the bathymetric curve corresponding to 1000 m. Note the lack of Argo proﬁlers

in the Bering, Beaufort, East Siberian, Laptev, Kara, Barents and North seas and

also in Hudson and Bafﬁn bays. ............................ 50

27 Scheme of the iterative procedure used to correct the temporal salinity bias on

level 2. .......................................... 52

28 Weighted average of all ascending L2B orbits in the period 2013-2019 minus

WOA18-A5B7 ...................................... 54

29 Weighted average of all descending L2B orbits in the period 2013-2019 minus

WOA18-A5B7 ...................................... 55

30 Difference between weighted average of all ascenidng and descending L2B orbits

in the period 2013-2019 ................................ 56

31 Skewness of the half ﬁrst Stokes distribution. Left: ascending. Right: descending.

The corresponding position in the antenna grid is marked with the red dot. . . . . 57

32 Scheme of the procedure used to apply the spatial correction on level 2. Left-

hand side generates the auxiliary ﬁles (one for ascending and one for descend-

ing) that are used to correct all L2B orbits as described in th right-side scheme . 57

33 Salinity error derived from the radiometric error. Arctic+ v3.1 map of the period

August 11-19, 2012. .................................. 58

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34 9-day L3 SSS Arctic+ v3.1 map corresponding to the period August 11-19, 2012.

Note the greater coverage and detail of the gradients to that obtained from the

BEC Arctic v2.0 product (ﬁgure 35). A section of this map containing from the

Barents Sea to the East Siberian Sea together with Sea Ice concentration it is

shown in ﬁgure 36. ................................... 59

35 9-day objectively analized BEC Arctic v2.0 map [Olmedo et al., 2018] correspond-

ing to the period August 11-19, 2012. Compare it with the new Arctic+ v3.1 (ﬁgure

34).A section of this map containing from the Barents Sea to the East Siberian

Sea together with Sea Ice concentration it is shown in ﬁgure 37. ......... 60

36 Detail of the map shown in ﬁgure 34 together with the minimum Sea Ice concen-

tration provided by OSI SAF for the period August 11-19, 2012. The right color

bar indicates Sea Ice concentration whereas the left color bar indicates salinity. . 61

37 Detail of the BEC Arctic v2.0 map shown in ﬁgure 35 together with the minimum

Sea Ice concentration provided by OSI SAF for the period August 11-19, 2012.

The right color bar indicates Sea Ice concentration whereas the left color bar

indicates salinity. .................................... 61

38 Half ﬁrst stokes value obtained for Meissner & Wentz model (blue line), Klein &

Swift model (black line) and George Washington University model (yellow line) fro

different values of SST: SST=0◦C (upper left), SST=5◦C (upper right), SST=10◦C

(bottom left) and SST=15◦C (bottom right). ..................... 62

39 Retrieved SSS minus Argo salinity as a function of SST for MW and KS dielectric

models. Up: mean value. Down standard deviation ................. 63

40 Ascending SMOS-climatology representant (up) and standard deviation (down)

for Greenland Sea as a funtion of incidence angle and cross track distance. Left

column corresponds to KS values. Right column shows difference between MW

and KS cases ...................................... 64

41 Ascending SMOS-climatology excess kurtosis (up) and skewness (down) for Green-

land Sea as a funtion of incidence angle and cross track distance. Left column

corresponds to KS values. Right column shows difference between MW and KS

cases .......................................... 65

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List of tables

1 List of acronyms used in this document ....................... 13

2 Statistics for the ﬁrst Stokes bias correction in the antenna grid .......... 42

3 The relevance takes values from 1 to 5; 1 for the most relevant and 5 for the least

relevant ......................................... 67

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Listings

1 Statistical quantities computation. ........................... 72

2 Area intersection computation. ............................ 77

3 Meissner & Wentz dielectric model. .......................... 78

4 Minimization function. ................................. 80

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Acronyms

AF-FOV Alias free ﬁeld of view

ARF Antena Reference Frame

ATBD Algorithm theoretical basis document

BEC Barcelona Expert Center

BOA Bottom Of the Atmosphere

CCI Climate Change Initiative

CFI Customer Furnished Item

EAF-FOV Extended alias free ﬁeld of view

ECMWF European Centre for Medium-Range Weather Forecasts

ESA European Space Agency

FOV Field of view

L2OS Level 2 Ocean Salinity

LAEA Lambert Azimuthal Equal Area

LSC Land-sea contamination

OSI-SAF Ocean and Sea Ice Satellite Application Facility

PHC Polar science center Hydrographic annual Climatology

RFI Radio frequency interferences

SMOS Soil Moisture and Ocean Salinity

SSS Sea Surface Salinity

SST Sea Surface Temperature

TB Brightness Temperature

TOA Top of the atmosphere

WOA World Ocean Atlas

Table 1: List of acronyms used in this document

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1 Introduction

The main purpose of this Algorithm Theoretical Baseline Document (ATBD) is to provide a

detailed deﬁnition of the processes and algorithms developed to retrieve Arctic sea surface

salinity from the SMOS measures in the context of the Arctic+ salinity project.

This new processing chain that we have implemented and described in this ATBD includes

improvements respect to the previous one [Olmedo et al., 2018] devoted to obtain more de-

ﬁned salinity gradients and improve freshwater ﬂuxes and currents description. Extreme melting

episodes like 2012 and 2019 Greenland melt [Bennartz R. et al., 2013] are indicators of the im-

portance to monitor changes in the Arctic freshwater system. Improving the sea surface salinity

(SSS) Arctic maps is the best option to attain this objective.

1.1 Structure of this document

The document is structured as follows: Next section introduces an overview of the sea surface

salinity (SSS) retrieval algorithm and explains how the processing chain operates, departing

from L1B up to the L3 salinity maps generation. The changes introduced have been important

and the processing chain has been completely recoded affecting to the debiasing, inversion and

salinity products generation.

The new grid implementation is explained in section 2.1.1. The objective of adopting a regional

Arctic grid instead of an orbit-centered grid as in the previous processing chain, is to avoid

spatial interpolations to not to lose information about salinity gradients captured by SMOS.

Debiasing methodology described in [Olmedo et al., 2017] has been changed to be applied to

brightness temperature (TB) instead doing so at salinity level. At least in the regime of low salin-

ity values, the salinity retrieval is a non-linear process. Therefore, freshwater masses should be

better described using this new methodology. Section 2.3.1 contains information about what im-

provements are expected using the new debiasing algorithm implementation together with the

new antenna binning used to perform SMOS-based climatology computation. The new binning

improves the homogeneity of the adquired measures obteining better statistics for the SMOS

representant computation.

The generation of L3 maps has been also deeply changed (section 2.4). This change comes

partially from the fact that, by including the improvements described above, it is unnecessary to

resort to interpolation methods like objective analysis. But this is not the only change in the L3

generation, the new L3 are generated from a new product that has not been created previouly

in the non-bayesian retrieval scheme: the geo-located L2B salinity orbits derived from L1. This

product is corrected to mitigate the known time-dependent biases and it is the basis to create

the level 3 product. In order to account for the error in the retrieved salinity at L2 and L3, a

propagation error of the radiometric uncertainty is introduced in the inversion procedure.

Section 3, is devoted to expose a brief summary of L-band dielectric constant models in SMOS

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mission work (under development). This study supports the choice of Meissner & Wentz model

[Meissner and Wentz, 2004] as dielectric model to perform the salinity retrieval in the Arctic

instead of Klein and Swift model [Klein and Swift, 1977] or the proposed at George Washington

University by Zhou, Lang and collaborators [Zhou et al., 2017].

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2 Overview and generation of the Arctic+ Salinity product

The general SSS retrieval algorithm is summarized in the ﬁgure 1. The processing chain

starts from L1B SMOS product v6.21 distributed by ESA (https://earth.esa.int/web/guest/

missions/esa-operational-eo-missions/smos). This algorithm differs of the nominal SMOS

data processing because it is based in the debiased non-Bayesian (DNB) [Olmedo et al., 2017].

In this work the debiasing is performed in TBinstead in salinity as it is proposed in the referred

paper (see 2.3.1 for detailed information). The general sea surface salinity retrieval algorithm

can be divided in ﬁve blocks:

•Computation of brightness temperature (TB) at the top of the atmosphere (TOA).

•Computation of the measured TBat the bottom of the atmosphere (BOA).

•Correction of TBbiases. This bias is assumed as different for each Earth position and

SMOS antenna grid point but constant in time.

•After the bias correction is applied, proceed with inversion to retrieve Sea Surface Salinity.

The retrieval is perfored using a non-Bayesian approach as described in section 2.4

•Create SSS maps from individual orbits containing retrieved SSS values

Figure 1: General algorithm SSS retrieval. As part of the algorithm it has been used the debiased non-Bayesian strategy deﬁned by

[Olmedo et al., 2017] but the debiasing is performed in TBinstead of in SSS as described in 2.3.1. Note that TBsea is necessary

to compute the reﬂectivity of the sea surface which it is necessary to perform the TBcorrections and dielectric model must be used

in the L1D-BOA computation.

New techniques to improve the quality of SMOS L1 brightness temperatures have not been

considered in the context of this project because i) we had not a proper reference to assess

the cumulative improvement of those improvements, so the ﬁrst step is to have a proper L2

chain adapted for the Arctic region (the main goal of this project) and ii) there is no a precise

assessment of the potential improvement of those techniques in the case of the polar regions,

so the use of those techniques could ﬁnally lead to a degradation of quality while deviating

signiﬁcant effort and resources to a goal that is not deemd prioritary right now. More particularly:

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•The use of nodal sampling (NS) has been reported not only to decrease the impact of the

tails of Radio Frequency Interferences (RFI) but to considerably reduce the radiometric

noise [González-Gambau et al., 2015,González-Gambau et al., 2016]. However, it has

also been reported to produce a contamination close to coastal and ice edges pixels. This

problem can be very disturbing in the case of the Arctic, as the most dynamics areas (and

those of greater oceanographic interest) happen close to the sea ice border; therefore, use

of NS could lead to a degradation of quality precisely at the zones of maximum interest.

While new versions of NS deal with these problems, the assessment of them has not been

completed yet and therefore their use in this project is deemed as speculative and risky,

therefore discarded.

•The use of the modiﬁcation of the correlation eﬁciency by means of a small percentage of

change of the non-zero baseline elements of the Gkj matrix [Corbella et al., 2015] in order

to reduce land-sea and sea ice-sea contamination has also been deemed as potentially

risky: in the last approved ofﬁcial reprocessing of SMOS L1, the adaptation of Gkj matrix

was discarded because they are calibrated using NIR and not ALL-LICEF and the quality

of L2 Soil Moisture data was degraded. Besides, the modiﬁcation of Gkj is known to

slightly increase the range of value of the Ocean Target Transformation (OTT), what is

seen also as a degradation. Therefore, with the evidence available at this time the Gkj

modiﬁcation should be discarded.

2.1 Generation of the level 1C

Computation of TBstarts from the ESA Level 1B (L1B) product. L1B product contains TB

Fourier components arranged in a time-ordered way according to the integration time. The

brightness temperature is computed at TOA level from ESA L1B product in a similar way as

the standard SMOS L1 processor does (https://earth.esa.int/documents/10174/1854456/

SMOS_L1c-Data-Processing-Models). The used processing chain is summarized in ﬁgure 2.

As in the standard SMOS L1 processor, a Blackman window is used to reduce the Gibbs-

like contamination [Anterrieu et al., 2002] and the image is reconstructed by applying an In-

verse Fourier Transformation the resulting TBFourier coefﬁcients. The TBimage is recon-

structed in the Antenna Reference Frame (ARF) and referenced to the antenna coordinates

(ξ,η)=(sin θcos φ,sin θsin φ), where θis the angle from the normal to the instrument plane

(0≤θ≤π/2) and φis the angle in the instrumental plane (0≤φ≤π/2) [McMullan et al., 2008]

The antenna hexagonal grid in which the TBimage is reconstructed (see ﬁgure 3for details),

contains 64 ×64 points instead of 128 ×128 used by standard SMOS L1 processor. This

resolution in the antenna level (4096 grid points) is enough to provide the TBvalues because

the number of visibilities from which snapshots are derived by a linear transformation is 2791.

Therefore, 64 ×64 is the minimum number of points in the antenna grid that provide the best

possible resolution because the hexagonal grid must be constructed as 2n×2ngrid and n≤5

undersamples the image.

After L1B is processed, measured values of TBare expressed in the 64 ×64 hexagonal antenna

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Figure 2: L1B to L1C TOA algorithm overview

grid. However, due to the SMOS orientation with respect to the Earth, the SMOS ﬁeld of view

(FOV) contains TBvalues corresponding to the sky (i.e. points located above the Earth horizon).

In addition, due to the interferometric character of the instrument, some parts of the FOV are

affected by aliases: aliases between different parts of the Earth disc and aliases between the

Earth and the sky. The central part of the hexagonal FOV is free of aliases and it is known as

Alias Free Field Of View (AF-FOV). The called Extended alias free ﬁeld of view (EAF-FOV) is

composed by AF-FOV and the zones containing aliases between Earth and sky TB. The zones

of the FOV containing aliases between different zones of the Earth are discarded (see ﬁgure 4).

Additional information can be found in [Corbella et al., 2005].

The geolocation of antenna grid points is performed during the L1C generation using ESA Earth

Explorer Mission CFI propagation libraries version 3.7.4 [ESA, 2014]. The geographic coordi-

nates (longitude and latitude) are transformed to plane coordinates by means of the Lambert

Azimuthal Equal Area map projection (LAEA) [Snyder, 1987]. This coordinate reference sys-

tem is recommended by the European Environment Agency for spatial and statistical analysis

[European Environment Agency, 2003].

Once all the geolocation magnitudes have been computed and the measured TB(ξi, ηi)are

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Figure 3: (Left) Tessellation of the fundamental hexagon using N hexagons centered on antenna grid points. Example with N =

16 ×16. (Right) Detail of the hexagon centered in an antenna grid point. Each hexagon is composed by six equilateral triangles

with h=dG/2,b=dG/3and dG= 2/(dR√3N)where dR= 0.875 is the distance between receivers in SMOS wavelength units

(from [Martínez et al., 2018])

Figure 4: 64 ×64 SMOS hexagonal ﬁeld of view. Purple line indicate the Earth limit; beyond this limit the FOV points contain sky

TB. Blue and black lines encircle the AF-FOV and EAF-FOV respectively. Points in the horizontal yellow lines are known as belt

whereas suspenders are the points included in the vertical yellow lines. Belt ans suspenders are points of transition between free-

alias zone and zones affected by Earth-sky aliases or between zones affected by different Earth-sky alias, therefore the measures

are expected to be somewhat degraded over there.

known in all 64 ×64 FOV points (i∈ {1..4096}), the Earth grid is generated and the points of

this grid are retroprojected up to SMOS antenna coordinate reference system for each SMOS

snapshot. Next, for any retroprojected Earth point at antenna level (ξk,ηk) the brightness tem-

perature at the corresponding geographical point (xk,yk) is computed performing a weighted

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Figure 5: FOV projected over the Earth when the SMOS antenna points towards Svalbard island. SMOS horizon (purple line)

extends almost 3000 km beyond the boresight (point 0,0). Green line shows the projection of the hexagonal FOV limits over the

Earth surface. The circles indicate the center of 100×100 km regular cells in plane coordinates (X-Y) using a Lambert azimuthal

equal area projection centered at 90◦N. The TBcorresponding to each X-Y cell is computed by retroprojecting its central grid point

on the antenna plane and performing a weighted average in (ξ,η) following and inverse-square law (compare with ﬁgure 4). Only

grid points inside EAF-FOV (black line) will be taken into consideration to retrieve salinity.

average in (ξ,η) following and inverse-square law:

TB(xk, yk) = TB(ξk, ηk) = Pd<d0(TB(ξi, ηi)/d2)

Pd<d0(1/d2)(1)

where the sums extend over all the antenna ξiηigrid points (i∈ {1..4096}) and

d2= (ξk−ξi)2+ (ηk−ηi)2.(2)

In order to ensure a TBvalue in all the grid points, d0must accomplish the inequality d2

0≥

h2+ (b/2)2= (10/36)d2

G→d0.0.011 (see ﬁgure 3for details). The processing chain uses a

value of d0= 0.012 in antenna units.

The effects of the ionosphere on the polarized Tbare computed in this part of the processing

chain. The ionosphere produces a rotation between the TBpolarizations leaving unaltered the

ﬁrst Stokes parameter (Tx

B+Ty

B)

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2.1.1 The importance of the grid projection

Figure 6: Ascending orbit starting

at UTC 2018-08-26 06:35:45 using a

Lambert Azimuthal Equal Area projec-

tion with origin (0◦N, 17.18◦W) indi-

cated by a purple circle

One of the handicaps of the previous SMOS SSS Arctic prod-

uct produced at BEC (BEC Arctic v2.0 hereafter) is the soft-

eness of the salinity gradients. As compared with SMAP

products [Tang et al., 2019], the gradients shown in SMOS TB

seem to be not adequately translated to salinity. We suspect

that this is caused by the objective analysis made to mitigate

the noise in the simple averaging of level 3 products. There-

fore, any spatial interpolation should be avoided as much as

possible. This can be achieved by means of the deﬁnition of a

global grid for the Arctic in the earlier stages of the processing

chain.

2.1.1.1 Former Arctic Grid Projection: BEC Arctic v2.0 prod-

uct

BEC Arctic v2.0 [Olmedo et al., 2018] was created from orbits

processed using a local Lambert Azimuthal Equal Area (LAEA)

projection. The origin of the projection for each orbit was lo-

cated in the equator of the Earth in latitude and in the center

of each orbit in longitude. This means that the brightness tem-

perature (TB) was retrieved in a different grid for each L1C

orbit. A complete orbit projected using LAEA with origin corre-

sponding to its own center (0◦N, 17.18◦W) is shown in ﬁgure

6. A brightness temperature snapshot belonging to this orbit

and located in the north of Greenland is shown in ﬁgure 7. The

selected resolution is 25 km and the center of the orbit (purple

dot in ﬁgure 6) deﬁnes the center of a cell, i.e. it is a bore-

centered grid. The grid used to perform the geolocation and

SSS retrieval processes for each orbit was created departing

from the projection origin by constructing a set of points (the

center of the cells) regularly separated from each other 25 km in x and y directions. Therefore,

the retrieved SSS were obtained in the projection of their own orbit.

The L3 SSS Arctic product v2.0 was distributed in EASE-Grid 1.0 (EPGS:3408) which corre-

sponds to a Lambert Azimuthal Equal Area projection centered at (90◦N, 0◦E) using as ellipsoid

the International 1924 Authalic Sphere (a=b=6371228). The adoption of a regional grid for the

Arctic is essential to generate L3 and L4 products and consequently, in the previous version

of the SSS Arctic product, it was necessary to spatially interpolate every retrieved SSS to this

global grid.

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Figure 7: Snapshot from orbit shown in ﬁgure 6corresponding to UTC 2018-08-26 07:28:54.

2.1.1.2 Current Arctic Grid Projection: Arctic+ SSS product

The EASE-Grid North v1.0 has been superseded by WGS 84 / NSIDC EASE-Grid 2.0 North

(EPGS:6931) [Brodzik et al., 2012,Brodzik et al., 2014,Brodzik et al., 2018] which introduces

important improvements. One of the improvements is to be easier for users to import data from

version 2.0 into standard software packages and it minimizes common reprojection errors that

have been encountered with the original EASE-Grid deﬁnition.

Based on the experience in previous versions of the Arctic SSS products, two points have been

improved concerning the projection used in the processing chain:

1) Use the same projection origin for all orbits in order to avoid spatial interpolations as much

as possible.

2) Introduce the improved version of EASE-Grid North projection

Therefore, in order to tackle these two points the EASE-Grid 2.0 North projection has been

adopted even in the ﬁrst stages of the processing chain. This approach produces L1C orbits

expressed in the same regional grid, avoiding spatial interpolation in later L3 salinity maps

creation. As EASE-Grid 1.0 North, this projection corresponds to a Lambert Azimuthal Equal

Area but it uses as ellipsoid the WGS84 and the projection center (90◦N, 0◦E) does not deﬁne

the center of a cell but the intersection of the central four grid cells. The number of rows and

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Figure 8: Brightness temperature obtained for UTC 2018-08-26 07:28:54 processed using a LAEA with origin in the center of the

orbit and reprojected to the EASE-Grid 2.0 North (left) and the same snapshot natively processed in the EASE-Grid 2.0 North

(right). Black dots indicate the EASE-Grid 2.0 North grid cells center

columns are even (720x720 because the adopted resolution is 25km) and the grid is constructed

from the projection origin establishing the center of four cells at x,y ±12.5 km and every 25 km

from there (black squares in ﬁgure 8).

Despite reprojection can be done without interpolation, previous version of TB(or SSS) values

were obtained using different orbit-centered projections deﬁnition (ﬁgure 7) and could not be

projected over the center of the grid cells of a regional projection (ﬁgure 8left). In this case it

was necessary to resort interpolation methods to create L3 maps. Adopting the EASE-Grid 2.0

North in the early stages of the processing chain, TBand SSS can be obtained in this regional

projection making spatial interpolation unnecessary (ﬁgure 8right).

2.2 Generation of the level 1D

The TBtransformation from TOA to BOA is performed in a similar way as the operational SMOS

level 2 processor chain does (more details are described in [SSS, 2016]). The measured TB

by SMOS is the result of different contributions [Zine et al., 2008] (ﬁgure 9): The galactic and

Sun glitter are attenuated by atmosphere, scattered by sea surface and attenuated again by the

atmosphere before arrive to the top of the atmosphere. The sea emission, composed by the

roughness of the sea surface and the ﬂat sea emission, is also attenuated by the atmosphere.

Even the atmosphere itself contributes to the total L-band emission received by SMOS in two

ways: a direct contribution towards the top of the atmosphere and a contribution that is reﬂected

by the sea and attenuated in its travel up to SMOS.

To retrieve salinity from measured TBit is necessary to quantify all these contributions and

obtain the contribution of the ﬂat sea emission because ﬂat sea emission depends on the

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sea surface temperature (SST) and SSS. The galactic and Sun glitter contributions are com-

puted following [Tenerelli et al., 2008] and [Reul et al., 2007] respectively. The roughness model

used by the ofﬁcial ESA L2 processing chain (known as model 1). Nevertheless the inver-

sion algorithm developed at BEC uses the roughness model (called model 3) described in

[Guimbard et al., 2012]. The BEC roughness model is based on an empirical approach with

SMOS data and, if necessary, it could be adapted to SMOS data adquired in Arctic conditions.

But this is out of scope of this project.

Figure 9: Contributions to the measured TB

The computation of all L-band contributions implies the use of a wide variety of auxiliary in-

formation concerning atmospheric conditions, galactic emission, etc. Additionally, the auxiliary

information must be interpolated to the geographical coordinates and grid used to obtain the

measured TBbefore its use. Therefore, a higher or similar resolution as the used to process the

measured data is desirable for ancillary data. Auxiliary information is also used to ﬁlter data in

zones in which physical conditions are not supported by correction models. The used auxiliary

information is the following:

– Atmospheric correction

−Air temperature 2m over the surface

−Atmospheric pressure at surface

−Total column water vapor content

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– Sun glitter correction

−Wind speed module at 10m of the surface

−Zonal and meridional component of neutral wind speed at 10 m of the surface

– Galactic correction

−Wind speed module at 10m of the surface

−Zonal and meridional component of neutral wind speed at 10 m of the surface

– Surface roughness correction

−Wind speed module at 10m of the surface

– Filtering purposes

−Rain rate

−Sea ice concentration

This information is provided to the ofﬁcial SMOS processing chain by the European Centre

for Medium-Range Weather Forecasts (ECMWF) collocated in time and space for each SMOS

orbit. The grid used to provide this data is the used by the ofﬁcial SMOS processing chain

(Icosahedral Snyder Equal Area or ISEA 4H9, see [Matos et al., 2004]) and is converted to the

plane coordinates using nearest-neighbor interpolation.

The Atmospheric correction is based on the modeling of the absorption coefﬁcient of the oxygen

and the water vapor content following a numerical ﬁtting. Nevertheless, the rest of contributions

are based on lookup tables (LUT) used in ofﬁcial processing chain.

Once all the contributions are computed, the measured TBcorresponding to the ﬂat sea contri-

bution (Tmeas

BF S ) can be obtained.

2.3 Debiasing

Debiasing procedure is an important change with respect to the standard processing used in

the ESA SMOS L2OS chain. This non-Bayesian methodology has been developed at Barcelona

Expert Center (BEC) and introduced in [Olmedo et al., 2017] and used to produce the BEC Arc-

tic v2.0 product [Olmedo et al., 2018]. The minimization of the difference between the measured

ﬁrst Stokes parameter and the modeled one follows a non-Bayesian scheme [Olmedo et al., 2017],

i.e. SSS is retrieved for each incidence angle.

In the SSS retrieval scheme used in [Olmedo et al., 2018] all the SSS retrieved under the same

geographical location, measuring incidence angle, distance to the center of the swath (cross

track distance) and satellite ﬂight direction are accumulated in a SSS distribution. The used

antenna grid consists in a division of the cross track distance in bins of 50 km and a division

of the incidence angles in 5◦bins (ﬁgure 11). The mean around the mode is estimated for

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Figure 10: L1C TOA to L1D BOA algorithm overview

all SSS distributions. These mean values compose the SMOS climatology. This allows to

characterize the systematic errors for each Earth location, measuring antenna position and ﬂight

direction. In this case no Ocean Target Transformation (OTT) is applied since the systematic

errors are already accounted for with the new methodology (see [Tenerelli and Reul, 2010] for

details about OTT). The poor quality measurements are detected by ﬁltering criteria based on

statistical properties of the obtained SSS distributions. By subtracting the corresponding SMOS

climatological value to each SSS value local biases are mitigated, especially those that are

persistent in time as the produced by land sea contamination and permanent Radio Frequency

Interferences (RFI). The computation of absolute SSS from the anomaly is performed by adding

to each level 3 map an annual SSS reference. This annual SSS reference is the same for all

L3 SSS maps and usually World Atlas Ocean 2013 (WOA) climatology [Zweng et al., 2013] is

used but the Polar science center Hydrographic annual Climatology (PHC) [Steele et al., 2001]

has also been used in Arctic region [Olmedo et al., 2018].

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Figure 11: Non-homogeneous division of the EAF-FOV performed in BEC Arctic v2.0 product to compute the SMOS climatology

2.3.1 New Debiasing strategy

In the development of this new version of the SSS Arctic product important changes concern-

ing to debiasing have been implemented as compared to the previous procedure described in

[Olmedo et al., 2017]: improve of the antenna grid division and perform the debiasing not in

SSS but in TB. Why is it advisable to introduce these changes? Statistics improvememnt and

better bias correction at low salinity ranges. Therefore, it is advisable to correct these short-

comings of this part of the processing chain. The approach has been performed by introducing

an homogeneous EAF-FOV discretization and taking into consideration that the salinity retrieval

departing from TBis not a linear process and the debiasing should be addressed at TBlevel

instead of at salinity level.

2.3.1.1 Homogeneous EAF-FOV discretization

As it is shown in ﬁgure 11 the EAF-FOV division formely adopted is not regular, especially

outside of the AF-FOV. This introduces different statistic representativeness for different points

of the antenna when SMOS climatology is computed. Therefore a more homogeneous EAF-

FOV discretization is advisable.

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The hexagonal grid in which FOV is divided is a result of the interferometric nature of SMOS

instrument. This geometry hinderes the division of the FOV in homogeneus sections because

these sections must have hexagonal geometry. On the other hand, each section should include

a large number of measures in order to compute a reliable SMOS-based climatology. This

implies that in order to generate homogeneous distributions of the measures, the 64 ×64

points of the FOV should be also homogeneously grouped to obtain a lower number of antenna

points and increase the statistics of each group. The more effective and simple way to attain this

objective is to group the antenna points contained in EAF-FOV in sets of 7 points (a central point

and their 6 closest neighbors) and accumulate the measures for each 7 points dataset in the

same histogram. This grouping is shown in the right part of ﬁgure 12. By using this EAF-FOV

discretization, we pretend to better describe the statistics of the measured TBthan using the

shown in ﬁgure 11.

Figure 12: Homogeneous EAF-FOV grid division used. Left: EAF-FOV grid from the 64 ×64 FOV grid. Right: Sets of 7 elements

(denoted by ξη) that will accumulate measures in order to compute the SMOS-based climatology

In order to implement this new feature in the processing chain the computation of the closest

neighbors in the antenna FOV has been performed. This information is computationally ex-

pensive, so it has been stored in a new auxiliary ﬁle and it is ingested in the processing chain

developed at BEC.

2.3.1.2 Debiasing brightness temperatures

During the retrieval procedure, the systematic errors in TBare propagated to the SSS. Never-

theless, the SSS retrieval from the measured ﬂat sea TBis not a linear process. Effectively, the

known L-band dielectric models show a non-linear relationship between the measured TBand

the retrieved salinity, especially for low salinity regimes as is shown in ﬁgure 13. Therefore, it is

expected that a debiasing of TBprovide better results than the applied to the SSS.

The melting processes as well as rivers discharges are important in the Arctic. So it is possible

to ﬁnd salinity values as low as to be out from the linear regime (ﬁgure 13). Therefore, at least

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in the Arctic, it seems important to adopt a TBdebiasing procedure instead of SSS debiasing.

Figure 13: First Stokes value provided by Meissner & Wentz dielectric model for different values of salinity and temperature. Note

how the system moves away from linear behavior as the salinity and temperature decrease.

Nevertheless, the presence of geophysical low salinity values is not the only reason to adopt this

new debiasing method. The aim of the debiasing is to mitigate systematic biases as the land-

sea contamination (LSC) or persistent RFI. Coastal zones affected by land-sea contamination

can have biases as much as 20 K in TB. Nevertheless it can easily double this quantity in

coastal zones affected by RFI.

Figure 14 shows three measures of half ﬁrst Stokes parameter (FS/2) obtained at the same grid

point for different incidence angles. Measures are indicated by thick lines (purple and green

affected by LSC) whereas half ﬁrst Stokes value provided by Meissner & Wentz dielectric model

at the same incidence angles are indicated by thin lines (purple, green and black for each

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measure). Performing the minimization of the differences of both quantities (half ﬁrst Stokes

measured and modelled) the solution found for purple and green measures are close to SSS=0

psu (the maximum (TBh+TBv)/2for MW model is around this value for usual SST range) with

a value for the cost function (expression 24) of about 7.33 K2for green measure and 4.25 K2for

purple measure. This collapse of the minimization for different values of TBto the same SSS

value recommends to compute the debiasing in TBinstead of in SSS. The situation is different

in the linear regime (black measure providing a cost funcion close to zero at 24.6 psu). In this

case the debiasing in TBshould provide a similar correction than in the debiasing in SSS. This

similar behavior can be expected for small corrections but not for the larger ones because the

dielectric model can only be considered as linear in SSS for small variations of salinity.

Figure 14: Example of three measures of half ﬁrst Stokes (FS/2) obtained for a grid point affected by land-sea contamination. The

grid point is located at North Sea coastal waters (53.86◦N, 6.70◦E), approximately at 35 km of the German coast. The measures

(thick lines) have been obtained from successive snapshots (i.e. for different incidence angles). Thin lines indicate half ﬁrst

Stokes value provided by Meissner & Wentz dielectric model for different values of salinity, FS(SSS)/2.

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2.3.1.3 SMOS-based climatology computation

The SMOS-based climatology for the Arctic has been computed using the SMOS data from the

2013-2019 period (both included). The year 2011 is discarded because the data corresponding

to this year is too degraded to be considered as typical in the SMOS timeline. This is due

to the large presence of RFI and a payload anomaly (starting at December 30, 2010) which

lead to incorrect temperature readings in one of the segments of the payload antenna arm B.

Canada started to refurbish their equipment in autumn 2011, while Greenland switched off their

transmitters in March 2011. The year 2012 has been also discarded by the abnormal presence

of RFI in Norway and in Ireland and in the United Kingdom.

The SMOS-based climatology computation is performed separately for ascending and descend-

ing orbits and two netCDF ﬁles are generated for each satellite direction; one containing the es-

sential statistical information for all valid points and other storing the histograms corresponding

to the measured ﬂat sea ﬁrst Stokes parameter divided by 2 (Imeas

F S (xy, ξ η)). The histograms

are created accumulating valid measures in bins of 1 K for each 25 km EASE-Grid 2.0 North

grid point (x, y)and FOV division (denoted by ξη, see section 2.3.1.1). Only latitudes beyond

50◦N are considered. The accumulative Imeas

F S values for each 25×25 km cell include the values

obtained in the closest neighbor cells (i.e. an square of 75×75 km around the central grid point)

in order to increase statistical accuracy and to obtain less noisy results.

A measure is considered as valid if it accomplishes

75K< Imeas

F S <165K (3)

On the other hand two outliers detection are performed. The ﬁrst one comes from L1D product

in which a linear regression is performed from all the TB(θ)measures for a given geographical

point obtained for different incidence angles. The outliers are detected from the difference

between this linear regression and each individual measure. The second outlier detection is

carried out for each Imeas

F S (xy, ξ η)distribution. In all cases, a measure classiﬁed as outlier

according Tukey rule [Tukey, 1977]:

∆>Q3+ 1.5×IQR

∆<Q1−1.5×IQR (4)

is discarded. In this expression, ∆stand for the difference between linear regression and each

individual measure in the case of outliers coming fromk L1D product or Imeas

F S (xy, ξ η)in the case

of outliers from histograms. Q1and Q3are the lower and the upper quartile of ∆respectively

and the interquartile range Q3−Q1is denoted as IQR. Also sea ice concentration (SIC) from

ECMWF is taken in to account to discard a valid measure: any measure obtained for SIC>0.3

is not considered in the distribution.

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2.3.1.3.1 Derived statistical quantities

Frequencies

As mentioned above, for a given geographical grid point (x, y)i, the statistical absolute frequency

(histogram) and sum of Imeas

F S (xyi, ξηj)values are obtained by a simple sum of their closer

neighbors for the same FOV point ξηj. The neighbor set includes those contained in a square of

75×75 km from the central grid point (x, y)i. Therefore, for a given grid point iand FOV position

jthe statistical absolute frequency fiin the Imeas

F S interval kis given by the expression

fij

k=X

n

fnj

k(5)

where fij

kis the absolute frequency corresponding to the k Imeas

F S bin (also known as Iclass k)

including nneighbors of the grid point i.

In a similar way, the Isum for a given grid point and Iclass is given by

Iij

k=X

n

Inj

k(6)

Mean

The mean of Imeas

F S for each grid point iand FOV position jis computed by means of the

quantities given by equations 5and 6

< Iij >=PkIij

k

Pkfij

k

(7)

Extending the sum to all Iclases k

Quartiles

The median (second quartile Q2) and interquartile range (IQR=Q3−Q1) are computed by

means of interpolation equation

Qij

n=Iij

LBk+ p

100 PN−1

l=0 fij

l−Pk−1

l=0 fij

l

fij

k!∆Iij

k(8)

where pis the percentile, Iij

LBkis the lower boundary of the class containing the n-th quartile (the

k-th class), ∆Iij

kis its width, Nis the number of classes (bins) and fij

lis the statistical absolute

frequency corresponding to the l-th class. In our study Iij

LB ∈ {65,66,67, ..., 199}and ∆Iij

k=

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1.0Kfor all classes. The class kcontainig the n-th quartile is the ﬁrst one that accomplishes

k

X

l=0

fij

l≥p

100

N−1

X

l=0

fij

l(9)

Second, third and fourth central moments

The second moment (the variance) is expressed here by means of its square root, the standard

deviation σ, which is computed for each grid point iusing the expression

σij =sX

k

ρij

k(< Iij >k−< Iij >)2(10)

where the sum extends over all Irange ((75 : 165) K) in steps of 1K, the relative frequency ρij

k

is given by:

ρij

k=fij

k

Pk0fij

k0

(11)

and

< Iij >k=Iij

k

fij

k

(12)

The third and fourth central moments (skewness γand kurtosis Kurt respectively) are given by

expressions

γij =1

σ3

ij X

k

ρij

k(< Iij >k−< Ii>)3(13)

Kurtij =1

σ4

ij X

k

ρij

k(< Iij >k−< SSSi>)4(14)

Mode and mean around the mode: the climatological representative

The representative value for SMOS ﬂat sea jaf ﬁsrt Stokes at a given grid point, orbit direction

and FOV position (i.e. the SMOS IFS climatological value) is computed as the mean around one

standard deviation from the mode. Although the mode is the value that appears most often and

could be used as the representative value itself, it is not well determined because of the limited

available binning of the IFS histograms (1K in our case). Then, the adoption of our extended

deﬁnition for the representative value is better behaved in terms of accuracy.

In order to estimate the mode a 7-point wide rectangular window is applied 3 times to smooth

each histogram. This results in a 19-points pseudo-Gaussian smoothing window which re-

sulting coefﬁcients are in the ratio 1:3:6:10:15:21:28:33:36:37:36:33:28:21:15:10:6:3:1 reducing

high frequency noise and preserving the peak positions, improving the mode estimation. Never-

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theless the lack of sampling reduces the accuracy of its computation. Hence, the representative

value is estimated from the IF S distribution by averaging the range of one standard deviation

(±σ) around the mode found by applying the described haystack smoothing window. The mean

around the mode (Iij) is computed in a range of one standard deviation around the mode. This

means that for a given grid point i(with given overpass direction and FOV position) we will

consider the classes included totally or partially in the range

Iij

mode −σij ≤Iij

k≤Iij

mode +σij (15)

For those classes, the sums of IFS are added and divided by the sum of the statistical absolute

frequencies

Iij

F S =Pl=M+m

l=M−mIij

l

Pl=M+m

l=M−mfij

l

(16)

where mis the smallest integer greater or equal than the quotient between the standard devia-

tion and the width of the class (1K)

m=pσij

∆Iij k

q(17)

Figure 15: The SMOS climatological representative for ascending passes at different FOV positions

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Figure 16: The SMOS climatological representative for descending passes at different FOV positions

The C code used to compute these statistical quantities is shown in appendix A, listing 1.

2.3.1.4 Annual IFS reference

As has been mentioned the debiasing procedure consists into replace the SMOS-based clima-

tology by an annual reference. The selected one in our case is the WOA 2018 [Zweng et al., 2018].

In particular, the dataset composed by the statistical mean of salinity on 0.25◦grid for 2005-2017

years. This dataset has been used because it is the closest period to the SMOS one (2011-

2019). As far as we know, no brightness temperature exists from World Ocean Atlas, therefore

it is necessary to compute it departing from WOA 2018 SSS and SST.

The emissivity can be computed from SSS and SST by means of the adoption of a dielectric

model. The dielectric model used is the Meissnet & Wentz one [Meissner and Wentz, 2004].

Combining this model with Fresnel equations and the emissivity it is possible to compute the

ﬂat sea brightness temperature for horizontal and vertical polarizations and compute Iij

F Sref for

each geographic point as a funcion of the incidence angle (i.e as a function of the FOV position).

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Details about the procedure are provided in the section 2.4.

Nevertheless, to obtain the correction to be applied at measured half ﬁrst Stokes parameter,

it is necessary to obtain the annual IF S reference in the same projection and grid resolution

as the provided by SMOS-based climatology. The annual WOA 2018 values are provided in

a common longitude latitude projection EPSG:4326 (WGS84 - World Geodetic System 1984,

used in GPS projection see https://epsg.io/4326) with a resolution og 0.25 ×0.25 degrees

whereas SMOS-based climatology is obtained in the projection described in section 2.1.1.2

(WGS 84 / NSIDC EASE-Grid 2.0 North, EPGS:6931) with a resolution of 25×25 km. The

change in the projection is performed using the PROJ coordinate transformation software library

[PROJ contributors, 2019]. Finally, the regridging from the original projected grid to a regular

2525 km is computed by means of the area weighted average. Figure 17 shows an scheme

of superposition of source grid (areas surrounded by dashed lines) and destination grid (areas

surrounded by solid lines). Denoting by Wthe area of a destination grid cell and withe area of

intersection between the original cells and the destination one the following inequality holds:

W≤X

i

wi(18)

The equality only is accomplished if the original cells completely ﬁll the destination one. In this

case any quantity (SSS and SST for WOA 2018) deﬁned in the original grid can be expressed

in the destination one by means of the weighted average

SSSj=PiSSSiwi

Piwi

SSTj=PiSSTiwi

Piwi

(19)

where j stands for the index of the destination grid.

The code of the common area between cells can be easily found from the doOverlap function

available at https://www.geeksforgeeks.org/find-two-rectangles-overlap/ (appendix A,

listing 2)

Note that annual IF S reference has no differences between ascending and descending passes

(ﬁgure 18).

Once both reference IF Sref ﬁelds (SMOS representant from ﬁgures 15 and 16 and WOA refer-

ence from ﬁgure 18) are provided in the same projection and grid (EASE-Grid 2.0 North, see

section 2.1.1.2 for additional information) the debiasing procedure can be applied. The obtained

difference between the WOA IF Sref and the provided by equation 16:

∆Iij =Iij

F Sref −Pl=M+m

l=M−mIij

l

Pl=M+m

l=M−mfij

l

(20)

is computed for both passes (ﬁgures 19 and 20) and it is added to the measured Imeas

F S (xy, ξ η).

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Figure 17: Schema of the area weighted average procedure. Orange circles indicate the center of each dashed cell of 0.25×0.25

degres (source grid). Blue squares are the center of the 25×25 km cells (destination grid).

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Figure 21: Mean half ﬁrst Stokes correction in the whole Arctic (half ﬁrst Stokes from WOA 2018 minus SMOS half ﬁrst Stokes

representant). Left: ascending case. Right: descending case.

Orbit passes Correction range Mean STD

Ascending -24.00:-3.16 -8.75 2.80

Descending -21.42:-4.00 -9.20 2.63

Table 2: Statistics for the ﬁrst Stokes bias correction in the antenna grid

Figure 22: Mean ascending minus descending half ﬁrst Stokes correction in the whole Arctic

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2.4 Inversion

Once the systematic errors of the measured ﬂat sea Tmeas

BF S are corrected, the SSS retrieval can

be performed for a given known dielectric model. The emitted ﬂat sea radiation is characterized

by its TBand for SST. In the L-band regime, the Rayleigh-Jeans law is a good approximation

to describe its spectral radiance. Therefore, the ocean polarized TBand molecular SST are

linearly related by horizontal (h) and vertical (v) emissivity

e[h,v]=TB[h,v]/SST . (21)

The ﬂat sea emissivity, i.e. the effectiveness in emitting energy as thermal radiation, is governed

by Fresnel reﬂection law and is a function of the incidence angle of the radiation θand the

dielectric coefﬁcient ε:

eh= 1 −"cos θ−(ε−sin2θ)1/2

cos θ+ (ε−sin2θ)1/2#2

;ev= 1 −"εcos θ−(ε−sin2θ)1/2

εcos θ+ (ε−sin2θ)1/2#2

(22)

Salinity takes part in the formulation because the dielectric coefﬁcient for the sea water should

be expressed, besides a function of SST and measurement frequency ω, in terms of its con-

ductivity and hence in terms of the salinity. Consequently, a reliable dielectric constant model

ε(SS T, SSS, ω)is necessary to describe with enough accuracy the relation between the mea-

sured brightness temperature and the salinity.

In the L-band regime two constant dielectric models have been adopted to retrieve salinity

from remote sensing measurements: Klein and Swift model (KS) [Klein and Swift, 1977] used

by the operational SMOS L2 Ocean Salinity processor and Meissner and Wentz model (MW)

[Meissner and Wentz, 2004,Meissner et al., 2018] used in Aquarius and SMAP salinity proces-

sors. Nevertheless, these are not the unique dielectric constant models in L-band. Recently a

new model, speciﬁcally designed for 1.413 GHz, has been developed at George Washington

University by Zhou, Lang and collaborators [Zhou et al., 2017] (designated as GW). All these

dielectric models are based on the Debye equation [Debye, 1970] with a conductivity term.

KS model for a frequency of 1.43 GHz was adjusted using a discrete set of measures at 5◦C,

10◦C, 20◦C an 30◦C and should be valid in the range of 4-35 psu. MW model interpolates the

dielectric constant as a function of salinity between 0–40 psu and provides accurate values

for the ocean surface emissivities between −2◦C and 29◦C. GW model has been computed

speciﬁcally for a frequency of 1.413 GHz and adjusts the measures obtained in 30, 33, 35 and

38 psu and a temperature range of 0-35◦C sampled every 5◦C. The temperature range used in

KS model seems to be too short to account of the whole SST range, that is about −2◦C and

35◦C.

Bias between the retrieved SSS and the one provide by Argo proﬁlers for SST values less than

5◦C, are larger for KS model than for the MW model [Zhou et al., 2017,Dinnat et al., 2019].

On the other hand GW model has limitations to retrieve SSS below 20 psu (see section 3).

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Therefore, the MW model is used to retrieve SSS in the Arctic. This model is described in

[Meissner and Wentz, 2004] and is implemented in C as it is shown in appendix A, listing 3.

Equations 21 and 22 together with the dielectric model form a closed system of equations.

In order to avoid possible errors in the evaluation of the quantities involved in the ionospheric

rotation of the measured TB, as well as to reduce the degrees of freedom of the system, the

quantity involved is not the TBF S but the ﬁrst Stokes divided by 2:

IF S =1

2(TBF S h+TBF S v)(23)

since, as has been mentioned, the ﬁrst Stokes parameter is unaltered by the presence of the

ionosphere.

Therefore, for a given value of SSS and providing the value for SST and incidence angle at

which the measure has been taken (θ), it is possible (in virtue of equations 21 and 22) to ﬁnd a

modelled value of the half ﬁrst Stokes for the ﬂat sea (Imod

F S ). Due to the fact that the measured

one (Imeas

F S ) is known, it is possible to obtain the salinity value that minimizes the cost function

F=kImod

F S −Imeas

F S k2.(24)

In order to ﬁnd the SSS value that minimizes Fwe use the well known Newton-Raphson method

[Press et al., 1992]. The implementetation code in C is shown in appendix A, listing 4.

This is a non-Bayesian retrieval scheme because for each measure of brightness temperature a

value of salinity is obtained. This means that the values of SSS recoverred (and their associated

errors ij) depend not only on coordinates over the Earth surface (x,y) but also on the FOV

position (ξ,η) in which the measure was taken. Therefore for each L1C orbit we produce a level

2A orbit (see ﬁgure 1). Hence, in the same way that L1C orbits are composed by snapshots of

brightness temperature, L2A orbits are composed by snapshots of salinity (see ﬁgure 23).

2.4.0.1 L2A ﬁltering

Not all retrieved salinity values can be considered as valid and some ﬁltering should be applied

on them. In fact, previously to the retrieval procedure, the following TBvalues are not included

in the inversion:

•Values of TBobtained too close to the edge of the EAF-FOV or too close to the belts

and suspenders (see ﬁgure 4). Points closer than 0.025 antenna units to these zones are

discarded.

•Points affected by Sun tails or reﬂected Sun circle are also discarded. The width for the

Sun tails when its signal is captured in front or back of the instrument is taken as 0.001

antenna units. The Sun radius is assumed as 0.04 antenna units when it is in front of the

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instrument and 0.02 antenna units if it is captured by backlobes when it is in the back of

the instrument.

•For each Earth surface point (x,y) and FOV position (ξ,η)TBvalues considered as outliers

during SMOS-based climatology computation (section 2.3.1.3) are discarded as well.

Also TB(x, y, ξ, η)values are discarded according to the SMOS-based climatology if this one is

considered as a moderately nonnormal distribution (kurtsis and skewness conditions according

[West et al., 1995]), statistics have been computed with a low number of measures or standard

deviation is too high close to the coast (suspicion of residual land sea contamination):

•Minimum number of measures to create the SMOS-based climatology is taken as 100.

•Maximum kurtosis absolute value accepted is 7.

•Absolute value of skewness must be less than 2.

•For points located less than 100km to the coast, only those having a standard deviation

less than 8 K are accepted.

The TBvalues ﬂaged as good according to above ﬁltering rules are considered as good candi-

dates to proceed with the inversion, therefore they are debiased and introduced in the minimiza-

tion function. It is considered that the minimization has converged if all the following conditions

hold:

•The change in salinity values between two consecutive iterations is less than 0.001.

•The percentage of variation in the cost function between consecutive steps is less than 1.

•The above two conditions are accomplished during 5 consecutive iterations to aboid oscil-

latory solutions.

•The above condition is acomplished in less than 150 iterations.

For each L2A salinity value found SSS(x, y, ξ, η)only those lying in the range 0 < SSS < 55

are considered as acceptable values. This range of acceptable salinity ensures that the salinity

distribution is not cropped increasing the relliability of the next level product (L2B). On the other

hand, mensual WOA 2018 is interpolated to the day of the year of the orbit to be corrected using

Akima periodic interpolation [Akima, 1970]. It is expected that retrieved SSS values can not get

too far from the value found for WOA 2018. With this in mind a limit to the difference between

each retrieved salinity value and the provided by interpolated WOA 2018 is imposed. For salinity

values higher than 25 psu the limit imposed is 7 psu. Conversely, a limit of 21 psu is imposed

for salinities less than 25 psu. We have adopted this strategy to avoid restrictions imposed by

WOA 2018 close to the river discharges or in suddenly and unexpected melting episodes where

WOA 2018 could provide salinities larger than 35 psu.

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Concerning to the sea ice concentration (SIC), some preliminary tests point out that this ﬁltering

and retrieval procedure provides a good agreement with the OSIS-SAF Sea Ice Climate Change

Initiative product OSI-450 and OSI-430-b [Lavergne et al., 2019] (i.e it generally fails for CCI

SIC > 0). Nevertheless, to ensure the minimum ice-sea contamination all points having SIC >

0 according Sea Ice CCI product are discarded and they are not included in the minimization

process. The distance to the ice edge (deﬁned by the line SIC=0) is also stored with the same

purpose: minimize ice-sea contamination by avoiding the points too close to the ice in the L3

generation.

2.4.0.2 New L2B generation and its ﬁltering

The generation of L2B level prior to the generation of L3 maps is an improvement introduced in

the context of the Arctic+ salinity project. The L2B orbits are generated from L2A snapshots by

weighted averaging all the measures obtained for a given grid point (section 2.4.1) producing

salinity values independent of the FOV position. An outlier detection is performed in a similar-

way as it was applied in TB: a linear regression is performed from all the ascending sorted SSS

values of the same orbit obtained for a given geographical point. The outliers are detected,

according Tukey rule [Tukey, 1977] (expression 4), from the difference between this linear re-

gression and each individual measure. L2B SSS values are only computed for those grid points

containing more that 12 unﬁltered L2A retrieved SSS values.

2.4.1 Error propagation

The propagation of the radiometric error from TBup to salinity is made by performing three

minimizations as described in section 2.4:

Imeas−

F S =1

2(TBF S h−σh+TBF S v−σv)−→ SSSij(Imeas−

F S )

Imeas

F S =1

2(TBF S h+TBF S v)−→ SSSij(Imeas

F S )

Imeas+

F S =1

2(TBF S h+σh+TBF S v+σv)−→ SSSij(Imeas+

F S )

(25)

where σ[h,v]is the radiometric accuracy of TB[h,v],istands for the geographical grid point and j

for the FOV position. The salinity error due to the radiometric error is taken as

ij =1

2|SSS(Imeas+

F S )−SSS(Imeas−

F S )|(26)

The next step is to produce level 2B orbits and level 3 maps depending only of the geographical

coordinates departing from L2A values (individual retrievals of SSS) and propagate their error

up to these upper levels.

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2.4.1.1 L2B computation

As has been mentioned, new L2B orbits are generated from L2A snapshots by weighted av-

eraging all the measures obtained for a given grid point. Assuming the weight function as the

inverse of the squared error of each L2A measure, we ensure that the measures comming from

TBhaving a high radiometric error will have a small inﬂuence in the obteined value for SSS at

L2B level.

SSSi=PjSSSij wij

Pjwij

(27)

where the weight function is given by

wij =1

2

ij

(28)

and the jindex stands for all the measures obtained for the grid point i. Therefore, the error of

each L2B salinity value is given by expression

i=1

qPj1/2

ij

.(29)

The error is propagated in the same way from L2B measures to L3 maps:

SSSi=PnSSSinwin

Pnwin

(30)

where the weight function is given by

win =1

2

in

(31)

and the nindex stands for all L2B orbits having salinity value for the grid point iin the L3 period.

The error of each L3 salinity value is given by expression

i=1

qPn1/2

in

.(32)

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Figure 23: Snapshot from ascending L2A orbit over the Kara Sea on August 2, 2015. Left: salinity values retrieved using the

non-Bayesian procedre described in section 2.4. Right: the corresponding error of each retrieval as has been described in section

2.4.1 and expressed in equation 26.

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Figure 24: Ascending L2B orbit over the Kara Sea on August 2, 2015. Left: salinity values computed from L2A snapshots using

expressions 27 and 28. Ob’ and Yenisey rivers discharge are clear at this level as well as the freshwater accumulation in the

Baydaratskaya bay. Right: the corresponding error of salinity value from equation 29.

Figure 25: 9-day L3 map centered on August 2, 2015 combining ascending and descending orbits. Left: salinity values computed

from L2B orbits using expression 30. Right: the corresponding error of salinity value from equation 32.

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2.5 L2B temporal correction

As is pointed out in [Olmedo et al., 2017] the ofﬁcial SMOS L2OS processor correct TBby the

introduction of the Ocean Target Transformation (OTT) [Tenerelli and Reul, 2010]. The OTT is

re-computed daily in version v622. This procedure was implemented to mitigate some global

time-dependent biases cited by [Martín-Neira et al., 2016]. The TBdebiased procedure used

here (section 2.3.1) only accounts for spatial bias. Therefore, a temporal correction should be

implemented.

Previous correction implemented in [Olmedo et al., 2018] operates over L3 maps. The method

uses the Argo proﬁles [Argo, 2018] available the period covered by each 9-day map and com-

putes the median of the differences between the collocated L3 SSS values and the provided by

Argo proﬁlers. This median is substracted to the SSS map.

Unfortunatelly, the Arctic is a zone with scarce salinity measures and Argo proﬁlers are con-

centrated, due to the bathymetry, in the Atlanctic zone providing a biased sample ot the mean

Arctic SSS value as it is shown in ﬁgure 26. Additionally, we need to perform a time-correction

on L2A orbits, not on L3 maps, and the amount of Argo data available for each orbit is clearly

insufﬁcient to perform such correction.

Figure 26: Argo proﬁlers distribution during the period 2011-2018 (dots). Blue line delimits the bathymetric curve corresponding

to 1000 m. Note the lack of Argo proﬁlers in the Bering, Beaufort, East Siberian, Laptev, Kara, Barents and North seas and also in

Hudson and Bafﬁn bays.

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In the absence of SSS in-situ measures, the temporal correction has been performed using

Global Ocean Forecasting System (GOFS) 3.1 (HYCOM + NCODA). In particular the resolution

used corresponds to GLBv0.08 grid having a resolution of 0.08 degrees in longitude and 0.04

degrees in latitude for polar regions [Cummings, 2005,Cummings and Smedstad, 2013]. The

data can be downloaded from https://www.hycom.org/data/glbv0pt08.

After the retrieval of the salinity values (L2A computation) is performed, a ﬁrst assessment of a

correction is introduced (-12 psu) for each L2A measure. This ﬁrst assessment only intends to

reduce the number of the necessary iterations. After applying the ﬁltering process described in

section 2.4.0.1 a new value for all L2B points is obtained and mean difference between each

L2B salinity value and the provided by HYCOM is added to each L2A SSS value of the orbit.

This loop is repeated until difference between two accumulated consecutive corrections is less

than 0.01 psu. The iterative loop is shown in the ﬁgure 27

Only orbits providing at least 50 common grid points with HYCOM are considered. Due to the

fact that HYCOM provides too salty values in the river mouths, only L2B points having a retrieved

salinity value above 25 psu and an error below 2.5 psu are considered to compute the temporal

correction.

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2.6 L2B spatial correction

As it has been described in section 2.3.1.2, the debiasing process is performed at brightness

temperature level before the salinity retrieval. The debiasing method is based on the substitution

of the SMOS-based TBclimatology by the obtained from the WOA 2018 [Zweng et al., 2018].

The WOA dataset used as reference ﬁeld is the one generated from measurements of the 2005-

2017 period (known as A5B7). Therefore, the average salinity obtained for the period used to

compute the SMOS-based climatology (years 2013-2019) should have a spatial distribution very

close to the reference used to carry out the debiasing (A5B7).

However, when all L2B orbits from the years 2013 to 2019 are weighted averaged the result

is not the expected (ﬁgures 28 and 29 should show values close to zero). The average of L2B

orbits is accomplished as it is described in section 2.4.1 using equations 30-32. These averages

have been made separately for ascending and descending passes, ﬁnding differences between

them (ﬁgure 30).

The cause of the differences between ascending and descending passes is mainly linked to

the different performance of the ascending and descending debiasing. Different undesirable

process can affect the same location depending on the orientation of the orbit. So, depending

on the coast orientation a given point can be affected by land-sea contamination differently in

ascending passes or in descending passes. This means a different correction in both passes,

raising the imprecisions between both. A similar matter takes place with ice-sea contamination

and in the presence of RFI.

The cause of the emergence of differences between the used reference (WOA 2018) and the

weighted average of all the L2B orbits of the period is more subtle. The half ﬁrst Stokes dis-

tributions provided by SMOS are generally positive skewned (ﬁgure 31). This means that its

representant at each geographical point (the mean around the mode as is described in sec-

tion 2.3.1.3.1) generally does not coincide with the mean of the distribution. On the other

hand, the WOA 2018 salinity is obtained through an objective analysis scheme using a cor-

rection factor given by a weighted average of the in-situ measurements in a given limited region

[Zweng et al., 2018, sec. 3.2] assuming, therefore, Gaussianity in this region. The substitution

of the SMOS-based climatology by the TBreference obtained from WOA 2018 salinity intro-

duces innaccuracies due to the skewness of the former. The nonlinearity of the inversion pro-

cess leads to unpredictable inexactitudes in the spatial distribution of the salinity. Nevertheless,

the spatial difference can be estimated by means of the ﬁeld described above: the difference

between salinity provided by averaging the L2B salinities and the provided by WOA 2018. In this

way, part of the problem can be corrected by subtracting the dame spatial difference (shown in

ﬁgures 28 and 29) to every L2B orbit. The algorithm describing this process is ahown in ﬁgure

32.

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Figure 31: Skewness of the half ﬁrst Stokes distribution. Left: ascending. Right: descending. The corresponding position in the

antenna grid is marked with the red dot.

Figure 32: Scheme of the procedure used to apply the spatial correction on level 2. Left-hand side generates the auxiliary ﬁles

(one for ascending and one for descending) that are used to correct all L2B orbits as described in th right-side scheme

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2.7 L3 maps creation

L3 maps are generated daily for 3-days periods, 9-days periods and 18-days periods and they

are obtained by temporal averaging of L2B salinity values. Each salinity value provided at a

ﬁxed geographical point has been obtained by a weighted averaging according to the error of

the salinity measure as is described in section 2.4.1 by equations 30-32. Finally, to minimize ice-

sea contamination and land-sea contamination all L2B points closer to 35 km to the ice edge or

to the coastline are not considered in the L3 maps creation. Figures 34 and 33 show an example

of the resulting 9-days L3 salinity maps and the error derived from radiometric uncertainty. It

is wroth noting the greater coverage and detail of the gradients of Arctic+ v3.1 product to that

obtained from the BEC Arctic v2.0 product (ﬁgures 34-37).

Figure 33: Salinity error derived from the radiometric error. Arctic+ v3.1 map of the period August 11-19, 2012.

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Figure 34: 9-day L3 SSS Arctic+ v3.1 map corresponding to the period August 11-19, 2012. Note the greater coverage and detail

of the gradients to that obtained from the BEC Arctic v2.0 product (ﬁgure 35). A section of this map containing from the Barents

Sea to the East Siberian Sea together with Sea Ice concentration it is shown in ﬁgure 36.

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Figure 35: 9-day objectively analized BEC Arctic v2.0 map [Olmedo et al., 2018] corresponding to the period August 11-19, 2012.

Compare it with the new Arctic+ v3.1 (ﬁgure 34).A section of this map containing from the Barents Sea to the East Siberian Sea

together with Sea Ice concentration it is shown in ﬁgure 37.

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Figure 36: Detail of the map shown in ﬁgure 34 together with the minimum Sea Ice concentration provided by OSI SAF for the

period August 11-19, 2012. The right color bar indicates Sea Ice concentration whereas the left color bar indicates salinity.

Figure 37: Detail of the BEC Arctic v2.0 map shown in ﬁgure 35 together with the minimum Sea Ice concentration provided by OSI

SAF for the period August 11-19, 2012. The right color bar indicates Sea Ice concentration whereas the left color bar indicates

salinity.

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3 Dielectric constant study

As has been mentioned in the inversion section (2.4), three dielectric models have been con-

sidered as candidates to be used in the Arctic sea surface salinity retrieval: Klein and Swift

model (KS) [Klein and Swift, 1977] used by the operational SMOS L2 Ocean Salinity proces-

sor, Meissner and Wentz model (MW) [Meissner and Wentz, 2004,Meissner et al., 2018] used

in Aquarius and SMAP salinity processors and the recently developed, and still undergoing im-

provements, by the George Washington University (GW) team by Zhou, Lang and collaborators

[Zhou et al., 2017].

Figure 38: Half ﬁrst stokes value obtained for Meissner & Wentz model (blue line), Klein & Swift model (black line) and George

Washington University model (yellow line) fro different values of SST: SST=0◦C (upper left), SST=5◦C (upper right), SST=10◦C

(bottom left) and SST=15◦C (bottom right).

During the inversion implementation described in this ATBD an important handicap was discover

in GW dielectric model to recover freshwaters. Sea surface salinity values below about 20 psu

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can not be described by this dielectric model. Figure 38 shows the half ﬁrst Stokes parameter

obtained for different SST values. The maximum value obtained around 20-25 psu for GW

model indicates that no solutions below this value could be found using this model. Hence,

where river runoff and melting process are so important. The cause probably is linked with the

limited SSS samples used to develop it (30, 33, 35 and 38 psu) providing a bad extrapolation

for low values of salinity.

Figure 39: Retrieved SSS minus Argo salinity as a function of SST for MW and KS dielectric models. Up: mean value. Down

standard deviation

Shortcomings in KS model against MW at low SST are known [Meissner and Wentz, 2004]

and recently they have been reported in the Aquarius mission context [Zhou et al., 2017] for

individual salinity orbits (level 2). Nevertheless, there is a lack of systematic veriﬁcation at

the space-time resolutions usually used in SMOS L3 salinity maps. To that goal, we have

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generated L3 salinity maps using the MW and KS dielectric constant models mentioned above.

The study has been carried out by comparing with Argo proﬁlers [Argo, 2018] against three

years (2011-2013) of 9-day L3 salinity global maps using the classic non-bayesian debiased

retrieval [Olmedo et al., 2017]. MW model shows a better behaviour as compared with in-situ

measurements providing maps with a lower bias and standard deviation (ﬁgure 39).

Climatologic representantStandard deviation

Figure 40: Ascending SMOS-climatology representant (up) and standard deviation (down) for Greenland Sea as a funtion of

incidence angle and cross track distance. Left column corresponds to KS values. Right column shows difference between MW and

KS cases

The comparison between dielectric models it is also performed at SMOS-based climatology

level. Here the climatology obtained is the classical one ((i.e. salinity representant). The

SMOS-based climatology as a function of incidence angle and cross track distance (the classical

antenna FOV division) it is shown for Greenland Sea (in particfular the area delimited between

68◦N, 75◦N and 15◦W, 7◦E). The mean values of the SMOS climatology (the representant), stan-

dard deviation, kurtosis and skewness are computed for each antenna FOV division for MW and

KS models. The result in ascending passes is shown in ﬁgures 40 and 41. Comparison between

both dielectric models show similar results for descending orbits.

Upper right plot of ﬁgure 40 indicates that MW model systematically retrieves lower salinity val-

ues than KS. On the other hand statistical quantities involving salinity distributions like standard

deviation, excess kurtosis and skewness (ﬁgure 41) are very similar between both models.

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Excess Kurtosis

Skewness

Figure 41: Ascending SMOS-climatology excess kurtosis (up) and skewness (down) for Greenland Sea as a funtion of incidence

angle and cross track distance. Left column corresponds to KS values. Right column shows difference between MW and KS cases

In conclussion, GW model has been discarded to be used in the Arctic due to its inability to

perform a good salinity retrieval at typical salinity ranges that can be found in stuaries and in

zones with strong melting processes. The comparison with in-situ measurements recommend

the use of MW model instead of KS especially in cold waters.

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4 Key aspects of processing

Processing step Level of improvement

Gradients pattern Salinity values

Grid projection High Low

Dielectric model Low Moderate

EAF-FOV discretization Moderate Low

Debiased in TBLow High

Annual IF S reference Moderate Moderate

L2A ﬁltering Low Moderate

L2B ﬁltering Low Moderate

Temporal correction Low High (global value)

Spatial correction Low High

L3 weighted average Low Low

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Processing step Relevance Changes from BEC Arctic 2.0 Computational bur-

den

Grid projection 1Introduced in 3.0 Low

Dielectric model 3Unchanged Low

EAF-FOV discretization 4Changed in 3.0 Moderate

Debiased in TB1Introduced in 3.0 High

Annual IF S reference 4WOA2018 is used in 3.0 Low

L2A ﬁltering 3Changed in 3.0 Low

L2B ﬁltering 3 Introduced in 3.0 Low

Temporal correction 2ARGO proﬁlers are not used in 3.0

Correction in L2A in 3.0 Low

Spatial correction 2Introduced in 3.1 Low

L3 weighted average 5Introduced in 3.0 Low

Table 3: The relevance takes values from 1 to 5; 1 for the most relevant and 5 for the least relevant

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5 References

[SSS, 2016] (2016). SMOS SSS L2 Algorithm Theoretical Baseline Document SO-L2-SSS-

ACR-007. ICM-CSIC LOCEAN/SA/CETP IFREMED. https://smos.argans.co.uk/docs/

deliverables/delivered/ATBD/SO-TN-ARG-GS-0007_L2OS-ATBD_v3.13_160429.pdf.

[Akima, 1970] Akima, H. (1970). A new method of interpolation and smooth curve ﬁtting based

on local procedures. J. ACM, 17(4):589–602.

[Anterrieu et al., 2002] Anterrieu, E., Waldteufel, P., and Lannes, A. (2002). Apodization func-

tions for 2-D hexagonally sampled synthetic aperture imaging radiometers. IEEE Trans.

Geosci. Remote Sens., 40(12):2531–2542.

[Argo, 2018] Argo (2018). Argo ﬂoat data and metadata from Global Data Assembly Centre

(Argo GDAC).

[Bennartz R. et al., 2013] Bennartz R., Shupe M. D., Turner D. D., Walden V. P., Steffen K., Cox

C. J., Kulie M. S., Miller N. B., and Pettersen C. (2013). July 2012 greenland melt extent

enhanced by low-level liquid clouds. Nature, 496:83.

[Brodzik et al., 2012] Brodzik, M. J., Billingsley, B., Haran, T., Raup, B., and Savoie, M. H.

(2012). Ease-grid 2.0: Incremental but signiﬁcant improvements for earth-gridded data sets.

ISPRS International Journal of Geo-Information, 1(1):32–45.

[Brodzik et al., 2014] Brodzik, M. J., Billingsley, B., Haran, T., Raup, B., and Savoie, M. H.

(2014). Correction: Brodzik, m.j., et al. ease-grid 2.0: Incremental but signiﬁcant improve-

ments for earth-gridded data sets. isprs international journal of geo-information 2012, 1,

32–45. ISPRS International Journal of Geo-Information, 3(3):1154–1156.

[Brodzik et al., 2018] Brodzik, M. J., Long, D. G., and Hardman, M. A. (2018). Best practices

in crafting the calibrated, enhanced-resolution passive-microwave ease-grid 2.0 brightness

temperature earth system data record. Remote Sensing, 10(11).

[Corbella et al., 2015] Corbella, I., Durán, I., Wu, L., Torres, F., Duffo, N., Khazâal, A., and

Martín-Neira, M. (2015). Impact of correlator efﬁciency errors on SMOS land?sea contami-

nation. IEEE Geoscience and Remote Sensing Letters, 12(9):1813–1817.

[Corbella et al., 2005] Corbella, I., Torres, F., Camps, A., Colliander, A., Martin-Neira, M., Ribo,

S., Rautiainen, K., Duffo, N., and Vall-llossera, M. (2005). Miras end-to-end calibration: ap-

plication to smos l1 processor. IEEE Transactions on Geoscience and Remote Sensing,

43(5):1126–1134.

[Cummings, 2005] Cummings, J. A. (2005). Operational multivariate ocean data assimilation.

Quarterly Journal of the Royal Meteorological Society, 131(613):3583–3604.

[Cummings and Smedstad, 2013] Cummings, J. A. and Smedstad, O. M. (2013). Variational

Data Assimilation for the Global Ocean, page 303–343. Springer Berlin Heidelberg, Berlin,

Heidelberg.

ARGANS LTD./ICM-CSIC/NERSC. 2020

Arctic+ salinity

Algorithm Theoretical Baseline Document

Ref: AO/1-9158/18/I-BG

Date:14/04/2020

Page: 69 of 82

[Debye, 1970] Debye, P. (1970). Polar molecules. Dover books on chemistry and physical

chemistry. Dover Publ.

[Dinnat et al., 2019] Dinnat, E. P., Le Vine, D. M., Boutin, J., Meissner, T., and Lagerloef, G.

(2019). Remote sensing of sea surface salinity: Comparison of satellite and in situ observa-

tions and impact of retrieval parameters. Remote Sensing, 11(7).

[ESA, 2014] ESA (2014). Earth Observation CFI v3.x branch. http://eop-cfi.esa.int/

index.php/mission-cfi-software/eocfi-software/branch-3-x. [Online; accessed 04-

October-2019].

[European Environment Agency, 2003] European Environment Agency (2003). Short Proceed-

ings of the 1st European Workshop on Reference Grids. In 1st European Workshop on Ref-

erence Grids, Ispra, 27-29 October 2003. JRD-Institute for Environment and Sustainability,

Ispra.

[González-Gambau et al., 2016] González-Gambau, V., Olmedo, E., Turiel, A., Martínez, J.,

Ballabrera-Poy, J., Portabella, M., and Piles, M. (2016). Enhancing SMOS brightness tem-

peratures over the ocean using the nodal sampling image reconstruction technique. Remote

Sensing of Environment, 180:205 – 220. Special Issue: ESA’s Soil Moisture and Ocean

Salinity Mission - Achievements and Applications.

[González-Gambau et al., 2015] González-Gambau, V., Turiel, A., Olmedo, E., Martínez, J.,

Corbella, I., and Camps, A. (2015). Nodal sampling: A new image reconstruction algorithm

for SMOS. IEEE Transactions on Geoscience and Remote Sensing, 54(4):2314–2328.

[Guimbard et al., 2012] Guimbard, S., Gourrion, J., Portabella, P., Turiel, A., Gabarró, C., and

Font, J. (2012). SMOS Semi-Empirical Ocean Forward Model Adjustement. IEEE Trans.

Geosci. Remote Sens., vol. 50, no. 5. pp. 1676-1687.

[Klein and Swift, 1977] Klein, L. and Swift, C. (1977). An improved model for the dielectric con-

stant of sea water at microwave frequencies. IEEE Journal of Oceanic Engineering, 2(1):104–

111.

[Lavergne et al., 2019] Lavergne, T., Sørensen, A. M., Kern, S., Tonboe, R., Notz, D., Aaboe,

S., Bell, L., Dybkjær, G., Eastwood, S., Gabarro, C., Heygster, G., Killie, M. A., Brandt Kreiner,

M., Lavelle, J., Saldo, R., Sandven, S., and Pedersen, L. T. (2019). Version 2 of the eumetsat

osi saf and esa cci sea-ice concentration climate data records. The Cryosphere, 13(1):49–78.

[Martín-Neira et al., 2016] Martín-Neira, M., Oliva, R., Corbella, I., Torres, F., Duffo, N., Durán,

I., Kainulainen, J., Closa, J., Zurita, A., Cabot, F., Khazaal, A., Anterrieu, E., Barbosa, J.,

Lopes, G., Tenerelli, J., Díez-García, R., Fauste, J., Martín-Porqueras, F., González-Gambau,

V., Turiel, A., Delwart, S., Crapolicchio, R., and Suess, M. (2016). Smos instrument perfor-

mance and calibration after six years in orbit. Remote Sensing of Environment, 180:19–39.

Special Issue: ESA’s Soil Moisture and Ocean Salinity Mission - Achievements and Applica-

tions.

[Martínez et al., 2018] Martínez, J., González-Gambau, V., and Turiel, A. (2018). Mitigation of

RFI main lobes in SMOS snapshots by bandpass ﬁltering. IEEE Geoscience and Remote

Sensing Letters, 15(7):1060–1064.

ARGANS LTD./ICM-CSIC/NERSC. 2020

Arctic+ salinity

Algorithm Theoretical Baseline Document

Ref: AO/1-9158/18/I-BG

Date:14/04/2020

Page: 70 of 82

[Matos et al., 2004] Matos, P., Gutiérrez, A., and Moreira, F. (2004). SMOS L1 Processor Dis-

crete Global Grids Document SMOS-DMS-TN-5200. DEIMOS. version 1.4.

[McMullan et al., 2008] McMullan, K. D., Brown, M., Martin-Neira, M., Rits, W., Ekholm, S.,

Marti, J., and Lemanczyk, J. (2008). SMOS: The payload. Geoscience and Remote Sensing,

IEEE Transactions on, 46(3):594–605.

[Meissner and Wentz, 2004] Meissner, T. and Wentz, F. J. (2004). The complex dielectric con-

stant of pure and sea water from microwave satellite observations. IEEE Transactions on

Geoscience and Remote Sensing, 42(9):1836–1849.

[Meissner et al., 2018] Meissner, T., Wentz, F. J., and Le Vine, D. M. (2018). The Salinity Re-

trieval Algorithms for the NASA Aquarius Version 5 and SMAP Version 3 Releases. Remote

Sensing, 10(7).

[Olmedo et al., 2018] Olmedo, E., Gabarró, C., González-Gambau, V., Martínez, J., Ballabrera-

Poy, J., Turiel, A., Portabella, M., Fournier, S., and Lee, T. (2018). Seven Years of SMOS

Sea Surface Salinity at High Latitudes: Variability in Arctic and Sub-Arctic Regions. Remote

Sensing, 10(11).

[Olmedo et al., 2017] Olmedo, E., Martínez, J., Turiel, A., Ballabrera-Poy, J., and Portabella, M.

(2017). Debiased non-Bayesian retrieval: A novel approach to SMOS Sea Surface Salinity.

Remote Sensing of Environment, 193:103–126.

[Press et al., 1992] Press, W. P., Teukolsky, S., Vetterling, W., and Flannery, B. (1992). Numer-

ical Recipes in C. Cambridge Press.

[PROJ contributors, 2019] PROJ contributors (2019). PROJ coordinate transformation software

library. Open Source Geospatial Foundation.

[Reul et al., 2007] Reul, N., Tenerelli, J., Chapron, B., and Waldteufel, P. (2007). Modeling Sun

glitter at L-band for sea surface salinity remote sensing with SMOS. IEEE Trans. Geosci.

Remote Sens., 45:2073–2087.

[Snyder, 1987] Snyder, J. (1987). Map Projections - A Working Manual. U.S. Geological Survey

Professional Paper 1395, U.S. Government Printing Ofﬁce, Washington D.C.

[Steele et al., 2001] Steele, M., Morley, R., and Ermold, W. (2001). Phc: A global ocean hy-

drography with a high-quality arctic ocean. Journal of Climate, 14(9):2079–2087.

[Tang et al., 2019] Tang, W., Yueh, S., Yang, D., Mcleod, E., Fore, A., Hayashi, A., Olmedo, E.,

Martinez, J., and Gabarró, C. (2019). Spacebased sea surface salinity depicts freshwater

changes in the hudson bay. talk: ESA Living Planet Symposium 2019, Milan, Italy; 2019-05-

13 – 2019-05-17.

[Tenerelli and Reul, 2010] Tenerelli, J. and Reul, N. (2010). Analysis of L1PP Calibration Ap-

proach Impacts in SMOS Tbs and 3-Days SSS Retrievals over the Paciﬁc Using an Alternative

Ocean Target Transformation Applied to L1OP Data. Technical report, IFREMER/CLS.

ARGANS LTD./ICM-CSIC/NERSC. 2020

Arctic+ salinity

Algorithm Theoretical Baseline Document

Ref: AO/1-9158/18/I-BG

Date:14/04/2020

Page: 71 of 82

[Tenerelli et al., 2008] Tenerelli, J. E., Reul, N., Mouche, A. A., and Chapron, B. (2008). Earth

Viewing L Band Radiometer Sensing of Sea Surface Scattered Celestial Sky Radiation-

Part I: General Characteristics. Geoscience and Remote Sensing, IEEE Transactions on,

46(3):659–674.

[Tukey, 1977] Tukey, J. (1977). Exploratory data analysis. Addison-Wesley.

[West et al., 1995] West, S., Finch, J., and Curran, P. (1995). Structural equation models with

non-normal variables: Problems and remedies. Structural Equation Modeling: Concepts,

Issues, and Applications.

[Zhou et al., 2017] Zhou, Y., Lang, R. H., Dinnat, E. P., and Vine, D. M. L. (2017). L-band model

function of the dielectric constant of seawater. IEEE Transactions on Geoscience and Remote

Sensing, 55(12):6964–6974.

[Zine et al., 2008] Zine, S., Boutin, J., Font, J., Reul, N., Waldteufel, P., Gabarro, C., Tenerelli,

J., Petitcolin, F., Vergely, J., Talone, M., and Delwart, S. (2008). Overview of the smos sea

surface salinity prototype processor. IEEE Transactions on Geoscience and Remote Sensing,

46(3):621–645.

[Zweng et al., 2013] Zweng, M. M., Reagan, J. R., Antonov, J. I., Locarnini, R. A., Mishonov,

A. V., Boyer, T. P., Garcia, H. E., Baranova, O. K., Johnson, D. R., Seidov, D., and Biddle, M. M.

(2013). World Ocean Atlas 2013, Volume 2: Salinity. Levitus, Ed., A. Mishonov Technical Ed.;

NOAA Atlas NESDIS 74, 39 pp.

[Zweng et al., 2018] Zweng, M. M., Reagan, J. R., Seidov, D., Boyer, T. P., Locarnini, R., Garcia,

H. E., Mishonov, A., Baranova, O. K., Weathers, K., PAver, C., and Smolyar, I. (2018). World

Ocean Atlas 2018, Volume 2: Salinity. A. Mishonov Technical Ed.; NOAA Atlas NESDIS 82,

50 pp.

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Appendix A Source C code

1// ................................................................

2/ / FUNCTION : computeSMOSClima

3/ / DESCRIPTION : C omput es SMOS c l i m a t o l o g y and o t h e r s t a t i s t i c a l q u a n t i t i e s

4/ / :

5/ / DATA OUT :

6/ / th eH is : t he H isto gram d at a acc um ula ted from L1D

7/ / t h eC l im a : s t r u c t u r e t h a t w i l l s t o r e d at a

8/ / :

9/ / RETURN : su cce ss or f a i l e d

10 / / :

11 / / NOTE : The ske wnes s and k u rt o s is s t a t i s t i c s ap pea r t o be v er y d epe nde nt

12 / / : on t h e s amp le si z e

13 / / : Read h t t p s : / / www. s p c f o r e x c e l . com / kn ow le dg e / b a si c −statistics /are−skewness−and−

k u r t o s i s −u s e f u l −statistics

14 / / NOTE a bout z−in dex :

15 / / Gha semi , A . , & Z a he d i as l , S . ( 20 1 2 ) . No r m a l i t y t e s t s f o r s t a t i s t i c a l a n a l y s i s :

16 / / A g ui d e f o r non−s t a t i s t i c i a n s . I n t e r n a ti o n a l Jo u rn al o f E nd o cr in ol og y a nd

17 / / M et abo li sm , 1 0 , 486 −489 . h t t p s : / / www. n c b i . n lm . ni h . gov / pmc / a r t i c l e s / PMC3693611/

18 / /

19 / / A l so n o te th e f o l l o w i n g : M aye rs ( 20 1 3 , p . 5 3) su gg es te d t h a t a c u t o f f o f

20 / / 1 . 9 6 s h o u ld be us ed f o r sam pl es sm a l l e r th a n 5 0 , a c u t o f f o f 2 . 5 8 f o r

21 / / sa mp les f ro m 51 t o 1 00 , and a c u t o f f o f 3 . 29 f o r s amp le s l a r g e r th an 10 0

22 / / when us ed i n c o n j u n c t i o n w i t h th e ex a m in a t io n o f h i s to g r a ms .

23 / /

24 / / Ma yers , A . (2 0 13 ) . I n t r o d u c t i o n t o s t a t i s t i c s a nd SPSS i n ps y ch ol o gy .

25 / / H a rl ow : Pea rs on E d u c at i o n L i m i t e d .

26 / / h t t p s : / / www. n c b i . n lm . ni h . gov / pmc / a r t i c l e s / PMC3591587/

27 / / Ro be rt T reve tha n

28 / / Samp le s i z e S tr a t eg y f o r S & K v al ue s C r i t e r i a

29 / / < 5 0 C o nv er t t o z by d i v i d i n g by st d e r r o r

30 / / I f z > | 1 . 9 6 | , d at a a re n o t n o rm a ll y d i s t r i b u t e d

31 / / 50 t o ~17 5 C on ve rt t o z by d i v i d i n g b y s t d e r r or

32 / / I f z > | 2 . 5 8 | , d at a a re n o t n o rm a ll y d i s t r i b u t e d

33 / / ~17 5 t o 300 C on v er t t o z b y d i v i d i n g by s td e r r o r

34 / / I f z > | 3 . 2 9 | , d at a a re n o t n o rm a ll y d i s t r i b u t e d

35 / / 300+ D o n t c on v e rt t o z v a lue s .

36 / /

37 / / E i t h er an a bs o l ut e s kew ness v a l ue l a r g e r th an 2 o r a n a b s ol u t e k u r t o s i s ( p r op e r )

38 / / l a r g e r t h an 7 may be u sed as v a l u es o f sk ewn ess and k u r t o s i s w i t h o u t f o r

39 / / de t e rm i n in g s u b s t a n t i a l no n−n o r m a l i t y .

40 / / P rop ose d by West e t a l (1 9 95 ) W est SG, Fi nc h J F , Cu rr an PJ . S t r u c t u r a l e qu a ti o n

41 / / m ode ls w i t h n on no rm al v a r i a b l e s : pr ob le ms an d r em ed ie s . In : H oy le RH, e d i t o r .

42 / / S t r u c t u r a l e q ua t i on mo de li ng : Co nce pt s , i s su e s and a p p l i c a t i o n s .

43 / / Newb ery P ark , CA: S age ; 1 99 5. pp . 56 75 .

44 / /

45 // ................................................................

46 int compute SMOSClima ( s_H isMa p ∗myHi s , s _Cl ima ∗myClima ) {

47

48 int i , j , k , l Mode , l , l l ;

49 int lm in , lmax ;

50 int counter ;

51 long MaxFreq ; / / The f r eq u e nc y at wh ic h t h e mode i s a t t a i n e d

52 float MeanModeFreq ;

53 float MeanMode ;

54

55 float MeanSum, Mean Bin ;

56 float moment2 , moment3 , moment4 ;

57 float rh o , d e v i a t i o n , d e v i a t i o n 2 ;

58 float l b , pr eAccF req , Acc Freq , N Freq2 ;

59

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60 int stdbin ;

61

62 / / P seu do ga uss ia n i s f a s t e r t ha t p pa sse s o f a w−window

63 int w= 7; / / w i d t h o f r e c t a n g u l a r wi ndo w

64 int p=3 ; / / nu mber o f pa ss es

65 int p oi n t sG a u ss i a n= 1+p ∗(w−1) ; / / 19

66 int po ints G2 ;

67 un si gn ed l on g i n t in de x ;

68 un s ig n ed s h o r t i n t f r e q ;

69 float t b ;

70

71 float his to_ smo ot h ;

72 float sta nd a rdE rr o rKu rt , st an dar dE rro rS ke w , n f ;

73

74 float pseud oGauss ian [ 19]={1.0 , 3.0 , 6 .0 , 1 0. 0 , 1 5. 0 , 21. 0 , 2 8. 0 , 3 3. 0 , 3 6. 0 , 3 7. 0 , 3 6. 0 , 3 3. 0 ,

2 8 .0 , 21 . 0 , 15 . 0 , 1 0 . 0 , 6 . 0 , 3 . 0 , 1 . 0 } ;

75

76 i f ( p oi n ts G au s si a n %2==0) {

77 po in t sG 2= po i nt sG au s si an / 2 ;

78 }els e {

79 po in ts G2 = ( po in ts G au ss ia n −1) / 2 ;

80 }

81

82

83 f o r ( i =0; i <myHis−>dimL on ; i + +) {

84 f o r ( j =0; j <myHis−>di mLat ; j + +) {

85 f o r ( k = 0 ; k< myH is−>d im A nt ; k + + ) {

86 ind ex = ( u nsi gn ed l on g i n t ) ( myHis−>d imBin ) ∗(un si gn ed l on g i n t ) ( my His−>dim Ant ) ∗(u ns ign ed

l on g i n t ) ( m yHis−>di mLa t ) ∗(un si gn ed l on g i n t ) ( i ) ;

87 ind ex += ( u ns ign ed lo ng i n t ) ( myHis−>di mBi n ) ∗(un si gne d l on g i n t ) ( m yHis−>di mAn t ) ∗(un si gn ed

l on g i n t ) ( j ) ;

88 ind ex += ( u ns ign ed lo ng i n t ) ( myHis−>di mBi n ) ∗(un si gne d l on g i n t ) ( k ) ;

89 / / Number o f m eas ur es

90 myClima−>Nmeas [ i ] [ j ] [ k ] = 0 ;

91 for ( l = 0; l < myHis−>d imB in ; l ++ ) {

92 myClima−>Nmeas[ i ] [ j ] [ k ]+=myHis−>F re qV ec to r [ i nd e x +( u ns ign ed lo ng i n t ) ( l ) ] ;

93 }

94

95 / / Not eno ugh measures

96 i f ( myCli ma−>Nmeas [ i ] [ j ] [ k ]< MIN_MEAS_STAT) {

97 myClima−>Nmeas [ i ] [ j ] [ k ] = 0 ;

98 myClima−>Mean [ i ] [ j ] [ k ] = ( float )NOVALUE ;

99 myClima−>Mode [ i ] [ j ] [ k ] = ( float )NOVALUE ;

100 myClima−>MeanMode[ i ] [ j ] [ k ] = ( float) NOVALUE;

101 myClima−>S td [ i ] [ j ] [ k ] = ( float) NOVALUE;

102 myClima−> K u r t o s i s [ i ] [ j ] [ k ] = ( float )NOVALUE;

103 myClima−>Skew ness [ i ] [ j ] [ k ] = ( float) NOVALUE;

104 myClima−>Me dia n [ i ] [ j ] [ k ] = ( float) NOVALUE;

105 myClima−>Z K u r to s i s [ i ] [ j ] [ k ] = ( float )NOVALUE;

106 myClima−>ZSkew ness [ i ] [ j ] [ k ] = ( float) NOVALUE;

107 continue ;

108 }

109 / / T hi s v a lu es o f s td f o r k u r t o si s and sk ewn ess a re o n ly v a l i d f o r n or mal d i s t r i b u t i o n s

110 / / T he re fo r e , d i s t r i b u t i o n i s ass umed as n orm al and we ch ec k z−s co r e t o kn ow i f

111 / / th e a ss um p ti on i s c o r r e c t .

112 n f = ( float ) m yClim a−>Nmeas[ i ] [ j ] [ k ] ;

113 st a n da r d Er r o rS k e w= s q r t ( 6 . 0 ∗n f ∗( n f −1) / ( ( n f −2.0)∗( nf −1) ∗( n f −3) ) ) ;

114 s t a n d a r d E r r o r K u r t = st a n da r dE r r or S k ew ∗s q r t (4 . 0 ∗( n f ∗n f −1) / ( ( n f −3.0)∗( n f +5 ) ) ) ;

115

116 / / ===============================================================

117 / / S mo ot hi ng o f t h e h i s t o gr a m . . .

118 / / A 7−po i n t s ( w) wi de r e c t a n g u l a r wind ow a p p l i e d 3 t i m es ( p ) . . .

119 / / E q u i v a l e n t t o a pse udo−Gaussian with p∗w−p+1 coefficients

120 // 1:3:6:10:15:21:28:33:36:37:36:33:28:21:15:10:6:3:1

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Date:14/04/2020

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121 / / The pseudo−ga u s si a n can be a p p l i e d fr o m e l em e nt 1+ p o i n ts G a u ss i a n / 2

122 / / t o t h e Hi s −>dimBin−[1+ p o i nt s G au s s i an / 2 ]

123 / / Ex tremes w ei ghte d w it h l e f t o r r i g h t n ei gb or s ( t i p i c a l l y TB < 66 K o r

124 / / l a r g e t h an 1 99 K i f th e r a ng e i s 60 : 20 0 )

125 / / ===============================================================

126

127 for ( l = 0; l < myHis−>dim Bi n ; l + +) {

128 myHis−>h is to Sm oo th [ i nd ex + ( un si gn ed l on g i n t ) ( l ) ] = 0 . 0 ;

129 cou nt er =0 ;

130 f o r ( l l = l −p oi nts G2 ; l l < l + po in ts G2 ; l l ++ ) {

131 i f ( l l > =0 && l l <myH is−>dim Bin ) {

132 myHis−>h is to Sm oo th [ i nd ex + ( un si gn ed l on g i n t ) ( l ) ] + = ps eu do Ga us sia n [ co u n te r ] ∗myHis

−>F r eq Ve ct or [ i nd e x +( u ns ign ed lo ng i n t ) ( l l ) ] ;

133 }

134 c ou nt er + +;

135 }

136 }

137

138 / / ========= Mode (computed usi ng smoothed his tog r am )

139 Max Freq = 0 ;

140 lMo de = 0;

141 MeanSum= 0 ;

142 for ( l = 0; l < myHis−>d imB in ; l ++ ) {

143 f r e q =my His−>Fr e qV ec to r [ i nd e x +( u ns ign ed lo ng i n t ) l ] ;

144 t b =my His−>TB Vec to r [ i n de x +( u ns ig ned lo n g i n t ) l ] ;

145 i f ( f re q > 0) {

146 his to_ smo ot h =myHis−>hi st oS mo ot h [ i nd ex + ( un si gn ed l on g i n t ) ( l ) ] ;

147 i f ( h is to _s mo o th >M axFre q ) {

148 MaxFreq= hi st o_sm oot h ;

149 myClima−>Mode [ i ] [ j ] [ k ] = t b / ( float) f r e q ;

150 lMo de= l ;

151 }

152 MeanSum+= t b ; / / sum o f a l l TB

153 }

154 }

155 i f ( MeanSum= =0 ) {

156 myClima−>Nmeas [ i ] [ j ] [ k ] = 0 ;

157 myClima−>Mean [ i ] [ j ] [ k ] = ( float )NOVALUE ;

158 myClima−>Mode [ i ] [ j ] [ k ] = ( float )NOVALUE ;

159 myClima−>MeanMode[ i ] [ j ] [ k ] = ( float) NOVALUE;

160 myClima−>S td [ i ] [ j ] [ k ] = ( float) NOVALUE;

161 myClima−> K u r t o s i s [ i ] [ j ] [ k ] = ( float )NOVALUE;

162 myClima−>Skew ness [ i ] [ j ] [ k ] = ( float) NOVALUE;

163 myClima−>Me dia n [ i ] [ j ] [ k ] = ( float) NOVALUE;

164 myClima−>Z K u r to s i s [ i ] [ j ] [ k ] = ( float )NOVALUE;

165 myClima−>ZSkew ness [ i ] [ j ] [ k ] = ( float) NOVALUE;

166 continue ;

167 }

168

169 / / ========= Mean

170 / / b y c o n s t r u c t i o n my Clim a−>Nmeas[ i ] [ j ] [ k ] = sum_l (myHis−>Fr eq [ i ] [ j ] [ k ] [ l ] )

171 myClima−>Mean [ i ] [ j ] [ k ]= MeanSum/ myClima−>Nmeas[ i ] [ j ] [ k ] ;

172

173 / / C o mp u ta t io n o f t he mom ents

174 moment2 = 0 . 0 ;

175 moment3 = 0 . 0 ;

176 moment4 = 0 . 0 ;

177 for ( l = 0; l < myHis−>dim Bi n ; l + +) {

178 f r e q =my His−>Fr e qV ec to r [ i nd e x +( u ns ign ed lo ng i n t ) l ] ;

179 t b =my His−>TB Vec to r [ i n de x +( u ns ig ned lo n g i n t ) l ] ;

180 i f ( fr eq >0) {

181 Mea nBin = t b / ( float ) ( f r e q ) ;

182 d e v i a t i o n = ( Mea nBin−myClima−>Mean[ i ] [ j ] [ k ] ) ; / / D e v i a t i o n f o r t h e bi n l

183 d e v i a t i o n 2 = d e v i a t i o n ∗deviation ;

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Date:14/04/2020

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184

185 / / r h o = f r e q o f b i n / Sum o f f r e q u e n c i e s

186 / / to im p ro ve sp eed and a c cu r ac y we d i v i d e by t he sum o f fr e q u e nc i e s o u t f ro m t h i s

loop

187 rh o =( float) f r e q ;

188 moment2+= r ho ∗deviation2 ;

189 moment3+= r ho ∗deviation2∗deviation ;