A. Montuori1, M. Portabella2, S. Guimbard2, C. Gabarrò2, M. Migliaccio1

1Dipartimento per le Tecnologie (DiT), University of Naples Parthenope, Italy2SMOS Barcelona Expert Centre (SMOS-BEC), Institute of Marine Sciences, Barcelona, Spain

Operational SMOS Bayesian-based inversion scheme

for the optimal retrieval of salinity and wind speed at sea

VII Riunione Annuale CeTeM-AIT sul  telerilevamento a Microonde: sviluppi scientifici ed implicazioni tecnologiche

Villa Larocca, via Celso Ulpiani, 27 - Bari, 4-5 Dicembre 2012

OUTLINESMOS Mission Overview

SMOS Bayesian-based Cost Function:

General Formulation Sensitivity AnalysisMultiple-minima AssessmentEffects of constraints

SMOS Bayesian-based minimization procedure Assessment:

Levenberg-Marquardt (LM) procedure (Monte-Carlo simulations)Optimization for both SSS and wind speed (U10) retrieval purposes

Ideal Optimum Lower Bound Accuracy Sea surface contribution onlyNo Effects of other source contributions (e.g. T.E.C., Galaxy, Sun, R.F.I.)Realistically-simulated marine scenarios (reference values from DPGS)

SMOS MISSION OVERVIEWSMOS makes global observations of soil moisture

over Earth's landmasses and salinity over the oceans.L-band full-polarized Microwave Imaging Radiometer using Aperture Synthesis (MIRAS).

Data Product Generation System (DPGS) provides consistent SSS, SST and SSR (e.g. U10) retrievals through the SMOS Level 2 Salinity Prototype Processor (L2PP) by processing geolocated TBs provided at the SMOS Level 1C (L1C) after the image reconstruction step.

Assessment of the Operational SMOS Bayesian-based inversion procedure to develope a parallel simplified version of the SMOS DPGS inversion scheme for the optimal retrieval of SSS and wind speed at sea (U10).

General Complete Formulation

SMOS Bayesian-based Cost Function

Forward Model for sea surface contribution only

Klein and Swift, 1997 Guimbard et al., 2012

Zine et. al, 2008

p = polarization q = incidence angleSSS = Sea Surface SalinitySST = Sea Surface TemperatureU10 = Wind Speed at 10mNobs = Number of observables

SMOS Bayesian-based Cost Function

Sensitivity Analysis Ideal case

Low sensitivity of noise-free and un-biased SMOS TB observables with respect to SSS, SST and U10

When only one parameter is restricted with an auxiliary a priori information, both the cost function minimum and the corresponding

SSS, SST and U10 solution values are better defined.

When all the constraints are used, both the cost function minimum and the corresponding SSS, SST and U10 solution

values are the best defined.

SSS=35psu, SST=20°C, U10=5m/sσSSS=2psu, σSST=2°C, σu10=2.5m/s

SMOS Bayesian-based Cost Function

Multiple Minima Assessment (Real noisy TB measurements)

Contour Plot of Cost FunctionTrue ValueEstimated Value

Contour Plot of Cost FunctionTrue ValueEstimated Value

A unique absolute minimum numerical value is retrieved when only the observational term is considered.

SSS=35psu, SST=20°C, U10=5m/sσSSS=2psu, σSST=2°C, σu10=2.5m/s

A unique absolute minimum numerical value is retrieved when the SSS-U10 constraint is considered.

A unique absolute minimum numerical value is retrieved when the SSS-U10 constrained cost function configuration is considered.

Contour Plot of Cost FunctionTrue ValueEstimated Value

SMOS Bayesian-based Cost Function

Effect of SST constraint

Very low sensitivities of realistically simulated TB measurements with respect to SST variations.

The retrieved SST values tend to be at extremes of the forward model look-up table (LUT).

This large SST retrieval error does impact the SSS and U10 retrievals.

Fixing or constraining the SST in the SMOS cost function is clearly required to optimize SMOS SSS and U10 retrievals.

Un-constrained cost function (OBS term) SST constrained cost function (OBS + SST Background)SSTEstim- SSTTrue

SMOS Bayesian-based Cost FunctionEffect of constraints

Retrieved - True Retrieved - PriorSSS-U10-SST constrained cost function configuration

SST fixed or constrained To derive SSS from SMOS data, SSS (U10) constraints can be used.

SSS=35psu, SST=20°C, U10=5m/sσSSS=0.3psu, σSST=1°C, σu10=2m/s

SMOS Bayesian-based Cost FunctionEffect of constraints

Retrieved - True Retrieved - PriorSSS-U10-SST constrained cost function configuration

SSS=33psu, SST=0°C, U10=14m/sσSSS=0.3psu, σSST=1°C, σu10=2m/s

Exept for SSS retrieval in cold water.

Cost Function Configuration Assessment

Levenber-Marquardt (Monte-Carlo Simulations approach)

Optimization for SSS and U10 retrieval:

SST constrained of fixed to an auxiliary a priori value SSS un-constrained for SSS retrieval

SMOS Bayesian-based inversion AssessmentSSS retrieval optimization

(σSSS=100psu) (σSSS=100psu) (σSSS=100psu)

(σSSS=100psu) (σSSS=100psu) (σSSS=100psu)

(σSSS=100psu) (σSSS=100psu) (σSSS=100psu)

(σSSS=100psu) (σSSS=100psu) (σSSS=100psu)

DPGS (SST-SSS (σSSS=100psu) -U10) cost function configuration is optimal for SSS retrieval

SMOS Bayesian-based inversion AssessmentU10 retrieval optimization

(σSSS=100psu) (σSSS=0.3psu) (σSSS=0.3psu)

(σSSS=100psu) (σSSS=0.3psu) (σSSS=0.3psu) (σSSS=100psu) (σSSS=0.3psu) (σSSS=0.3psu)

(σSSS=100psu) (σSSS=0.3psu) (σSSS=0.3psu)

Fully constrained (SST-SSS-U10) cost function configuration is optimal for U10 retrieval

SMOS Bayesian-based inversion AssessmentAF & EAF-FOV Nadir

SSS (psu) retrieval – DPGS Configurationμ (DPGS / Prior) RMSE (DPGS / Prior) STD (DPGS / Prior)AF EAF AF EAF AF EAF

Warm & Low 0.01 / -0.01 0.01 / 0.02 0.37 / 0.36 0.34 / 0.36 0.37 / 0.36 0.34 / 0.36Warm & High 0.02 / 0.04 0.01 / -0.01 0.57 / 0.56 0.59 / 0.55 0.57 / 0.56 0.59 / 0.55Cold & Low -0.07 / 0.06 -0.04 /-0.04 1.24 / 1.22 1.11 / 1.07 1.24 / 1.21 1.11 / 1.07Cold & High 0.05 / 0.01 0.15 / -0.11 1.86 / 1.83 1.78 / 1.83 1.86 / 1.83 1.77 / 1.83

U10 (m/s) retrieval – Fully constrained Configuration

μ (DPGS / Prior) RMSE (DPGS / Prior) STD (DPGS / Prior)AF EAF AF EAF AF EAF

Warm & Low 0.04 / -0.02 -0.04 / 0.01 0.82 / 0.91 0.87 / 0.91 0.82 / 0.91 0.87 / 0.91Warm & High 0.03 /-0.01 -0.03 /-0.04 0.67 / 0.74 0.63 / 0.64 0.67 / 0.74 0.63 / 0.64Cold & Low -0.05 / 0.02 -0.02 / 0.00 0.8 / 0.78 0.79 / 0.72 0.8 / 0.78 0.79 / 0.72Cold & High -0.06/ 0.04 0.01 /-0.02 0.54 / 0.56 0.5 / 0.49 0.54 / 0.56 0.5 / 0.49

SMOS Bayesian-based inversion AssessmentAF & EAF-FOV Edge (300km)

SSS (psu) retrieval – DPGS Configurationμ (DPGS / Prior) RMSE (DPGS / Prior) STD (DPGS / Prior)AF EAF AF EAF AF EAF

Warm & Low -0.01 / 0.02 -0.01 / 0.01 0.4 / 0.4 0.38 / 0.41 0.4 / 0.4 0.38 / 0.41Warm & High 0.03 / 0.0 0.03 / 0.02 0.57 / 0.56 0.56 / 0.54 0.57 / 0.56 0.56 / 0.54Cold & Low 0.01 / 0.01 0.01 / 0.0 1.35 / 1.29 1.25 / 1.21 1.35 / 1.29 1.25 / 1.21Cold & High 0.05 / -0.09 0.06 / 0.03 1.85 / 1.89 1.80 / 1.79 1.85 / 1.89 1.80 / 1.79

U10 (m/s) retrieval – Fully constrained Configuration

μ (DPGS / Prior) RMSE (DPGS / Prior) STD (DPGS / Prior)AF EAF AF EAF AF EAF

Warm & Low 0.04 / 0.06 -0.03/ -0.01 0.92 / 0.87 0.88 / 0.88 0.92 / 0.86 0.88 / 0.88Warm & High -0.04 /-0.01 -0.01 /0.07 0.72 / 0.69 0.67 / 0.69 0.72 / 0.69 0.67 / 0.69Cold & Low 0.08 /-0.04 0.04 /0.07 0.84 / 0.79 0.82 / 0.83 0.84 / 0.79 0.82 / 0.83Cold & High 0.01 /-0.07 -0.01 /-0.01 0.62 / 0.65 0.53 / 0.55 0.62 / 0.64 0.53 / 0.55

ConclusionsInternal SMOS Bayesian-based processing chain for SSS and U10 retrieval purposes has been

developed.

Low sensitivities of SMOS TB measurements with respect to geophysical parameter changes, especially for SST.

Unique absolute minimum value for all the cost function configurations Unique triplet solution of SSS-U10-SST.

Fixing or constraining SST to an auxiliary value improves the retrieval of SSS and U10.

Successful assessment of LM minimization procedure for the retrieval of SSS and U10 by means of realistically simulated SMOS TB measurements.

SSS optimal retrieval DPGS [SST-U10] configuration.

U10 optimal retrieval Fully [SST-SSS-U10] constrained configuration.

Future test with both real SMOS TB data.