SMOS Ocean Salinity Retrieval Level 2 Marco Talone, Jérôme Gourrion, Fernando Martin Porqueras, Nicolas Reul, Joe Tenerelli, Marcos Portabella, and the SMOS Barcelona Expert Centre (SMOS-BEC) Team Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, 2010

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Motivation

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Ocean salinity monitoring: motivation/overview SSS variations governed by: E-P balance freezing/melting ice freshwater run-off Key oceanographic parameter (density) Thermohaline circulation and heat redistribution

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Ocean salinity monitoring: motivation/overview Surface salinity distribution is closely tied to E-P patterns 10-m depth salinity field reconstructed from Argo floats data. There are still “holes” and spatial resolution is low SSS time-series Historical lack of SSS observations

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Ocean salinity monitoring: motivation/overview Oceanographic models already assimilate SST and SSH from satellite data, while SSS is still climatologic The absence of any specific treatment of salinity in ocean models can lead to significant errors: Near-surface currents errors [Acero-Schetzer et al., 1997] Tropical dynamics [Murtugudde and Busalacchi, 1998] Dynamic height difference [Maes et al., 1999; Ji et al., 2000] Spurious convection [Troccoli et al., 2000] ENSO predictions [Ballabrera-Poy et al., 2002]

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS, general features

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS satellite – general features 1.4 GHz, L-band (unique payload) Optimum SSS sensitivity Reasonable pixel dimension Atmosphere almost transparent Full scene acquired every 2.4 s Variable number of observations according to the satellite sub-track distance Different measurements of T B corresponding to a single SSS under different incidence angles Synthetic Aperture Radiometer (MIRAS) Sun-synchronous LEO orbit, 3 days revisit time 69 elements array, Y-array: arms 120º apart Field Of View (EAF FOV) about 1000 km Dual-pol / Full-pol Multi-angular capabilities Spatial Resolution: 32 (boresight) km

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS satellite – Field Of View Radiometric Accuracy and Radiometric Sensitivity (quality of the measurement) [calculated using SEPS] Incidence Angle and Spatial Resolution [calculated using SEPS] boresight nadir

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS satellite – Field Of View Due to MIRAS geometry Nyquist criterion is not satisfied 3 FOV can be defined: Hexagon resolved by MIRAS Alias-Free FOV Extended Alias-Free FOV

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS processing chain

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS processing chain Level 1Level 0Level 2Level 3 Level 4 Data Assimilation MeasurementsObservationsGlobal mapData fusionRaw data

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS processing chain Level 0 Raw data Level 1A Calibrated Visibilities Level 1B T B Fourier components Level 1C T B geocoded (ISEA4H9) Level 2 Salinity Maps (single-overpass) Level 3 Spatio-temporal averaged SSS Level 4 Merged product Scientific requirements for salinity retrieval Global Ocean Data Assimilation Experiment (GODAE, 1997) 0.1 psu, 200 km, 10 days Salinity and Sea Ice Working Group (SSIWG, 2000) 0.1 psu, 100 km, 30 days SMOS (Mission Requirements Document v5, 2002) 0.1 psu, 200 km, 30 days lower accuracy, higher resolution products (e.g. 100 km, 10 days or single passes) are useful for applications other than climate and large scale studies ISEA DGGs (Discrete Global Grids)

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 From Level 1C to Level 3 Level 1CLevel 2Level 3 pre- processing post- processing quality control & filtering SSS inversion Level 1C

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C What does a radiometer measure? G accounts for the receiver’s gain and the antenna pattern receiver temperature Boltzmann constant is the only term dependent on the observed scene it is also referred as Apparent Temperature because sum of various contributions

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C - Forward Models surface atmosphere ionosphere

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C - Forward Models flat sea contribution roughness contribution Klein & Swift (1977) dielectric model at microwave frequencies TB sensitivity to SSS increases with SST The total dynamic of TB is 2-4 K 3 MODELS Two-scale model IFREMER Brest, France Small Slope Approximation (SSA) model LOCEAN, Paris, France Empirical Model ICM, Barcelona, Spain

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C - Forward Models Brightness temperature as measured by SMOS TXTX TYTY

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 From Level 1C to Level 3 Level 1CLevel 2Level 3 pre- processing post- processing quality control & filtering SSS inversion Level 1C pre- processing Level 2 pre-processing

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C – Errors and inaccuracies Several different phenomena contribute to the final The main error sources for the SSS retrieval are: The forward Tb models The estimation of the antenna pattern The estimation of the galactic noise Radio Frequency Interference Land contamination Some of them are solved by pre- and post-processing techniques

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing Ocean Target Transformation spatial pattern Average instrumental spatial pattern against ocean target, to be subtracted from measurements prior to SSS retrieval. [J. Tenerelli, Tech Note, 2010] land RFIAn accurate filtering of the snapshots must be applied to discard land and/or Radio Frequency Interferences (RFI) contaminations. Ascending descendingAscending and descending passes must be considered separately. many orbitsFinally, many orbits are used to increase the robustness of the estimation. INCLUDED IN THE CURRENT PROCESSING

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing Strong systematic patterns are found in SMOS TB measurements Features are clearly associated to brightness temperature transition: Sky/Land Alias Free/Extended Alias Free Field of View

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing forward modelinaccuracies The use of a forward model can introduce error due to inaccuracies in its definition Unhomogeneitiesgeophysical parameter Unhomogeneities in the geophysical parameter statistical distribution in the FOV affect the estimation of the OTT Model-free OTT – X polModel-free OTT – Y pol INCLUDED IN THE NEXT REPROCESSING (july)

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing Histograms are calculated for all the pixel of the reconstructed brightness temperature image (black lines). A selection of the grid point used in the averaging is performed to homogenize all the histograms the most internal one (red line) Sea Surface Temperature [°C] Wind Speed [m/s]

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing The average sea surface salinity, sea surface temperature, and wind speed inside the FOV are shown for the standard OTT and the “homogenized” OTT. STANDARDSTANDARD HOMOGENIZEDHOMOGENIZED

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing STANDARDSTANDARD MODEL-FREEMODEL-FREE Model-free OTT – X pol Model-free OTT – Y pol Standard OTT – X pol Standard OTT – Y pol The difference between the “homogenized” and “no-homogenized” OTT °C for sea surface temperature and m/s for wind speed up to K (peak to peak) in the estimation of the bias spatial pattern.

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing External Brightness Temperature Calibration temporal pattern Average instrumental temporal pattern (scene-dependent bias) against ocean target, to be subtracted from measurements prior to SSS retrieval. [Camps et al., Radio Science 2005] IN TESTING PHASE

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing Radio Frequency Interference (RFI) Spurious stable or intermittent man-made interferences. Receiver Co-Channel Interference + Receiver Adjacent Signal Interference - the signal itself or its tails can fall within the receiver’s RF passband. Receiver Out of Band Interference - the signal is outside the receiver’s RF passband, nevertheless spurious signals due to the mixer stage. Transmitter Fundamental and Harmonic Emissions - the Transmitter Transfer Function. Transmitter Noise - thermal noise generated in the various stages of the processing. Transmitter Intermodulation - local mixing of a transmitter’s output emission with that of another transmitter or any other component of the instrument. Concerning SMOS the strongest interference come from WiFi networks and Radar As expressed in the Technical Note on “L-band RFI detected in SMOS data over the world oceans” by Nicolas Reul of IFREMER.

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 pre-processing By estimating the impulsional response of the RFI, this can be eliminated from the scene, as done for the Sun effects. [Camps, 2010] INCLUDED IN THE NEXT REPROCESSING (july)

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 From Level 1C to Level 3 Level 1CLevel 2Level 3 pre- processing post- processing quality control & filtering SSS inversion Level 1C pre- processing Level 2 quality control & filtering SSS inversion Level 2

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Quality control and filtering Quality control is performed on both measurement and gridpoint basis Distance from the coast: Ice Suspect ice Heavy rain Sea condition Number of valid measurements Sunglint Moonglint Galactic noise position in the FOV: RFI Land < 40 km 40 km km > 200 km AF EAF Border FOV Aliased FOV OK Retrieved but Flagged Discarded

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SSS Inversion The problem observations state variables forward model The solution exact algebraic solution, relaxation, least squares estimation, truncated Eigenvalue expansion, Bayes’ theorem, etc … – maximum likelihood, – maximum posteriori probability, – minimum variance, – minimum measurement error – etc …

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SSS Inversion - theoretical background Bayesian approach knowledge about the state variables uncertainty of observations and forward model ASSUMING AND INDEPENDENT (ERRORS UNCORRELATED) posterior probability

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SSS Inversion - theoretical background Maximum Likelihood Estimation Errors are generally assumed Gaussian 1.Forward Model (GMF, Geophysical Model Function) is assumed perfect 2.Errors are assumed uncorrelated is diagonal

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS SSS Inversion part observables part Background term SMOS Sea Surface Salinity Retrieval Cost Function is minimized iteratively min NO YES INITIALIZATION

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 From Level 1C to Level 3 Level 1CLevel 2Level 3 pre- processing post- processing quality control & filtering SSS inversion Level 1C pre- processing Level 2 quality control & filtering SSS inversion post- processing Level 3 Level 2 post-processing

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 post-processing External Sea Surface Salinity Calibration Correcting for the mean uncertainty introduced by the forward model inaccuracies as done for rain radar calibration (Seo and Breidenbach, 2002) using as ancillary in-situ database the ARGO array of buoys. [Talone et al., IEEE TGARS 2008] IN TESTING PHASE

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C RFI Galactic Noise Land contamination

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C - RFI North Pole case: Radar climatological SSS Average SSS in April – ASCENDING PASSESAverage SSS in April – DESCENDING PASSES SOURCE anti-missile radar protection array from Alaska all along the Northern Canada pointing to the horizon

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C - RFI First Stokes’ parameter in brightness temperature (I=TX+TY). One-month averaging, only descending passes. Retrieved SSS 60-degrees spaced tails star Due to the signal processing in SMOS, a point strong source generates 60-degrees spaced tails, like a star.

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C - RFI 60-degrees spaced tailsstar Due to the signal processing in SMOS, a punctual strong source generates 60-degrees spaced tails, like a star. First Stokes’ parameter in brightness temperature, both the ascending and descending passes of the month of May

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C - RFI RFI has effects several kilometers from the source. Sources on land frequently affects SSS retrieval. First Stokes’ parameter in brightness temperature, both the ascending and descending passes of the month of May

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Galactic Noise Very geographic, pass-type & incidence angle dependent Scattering model for ocean surface reflection of downwelling celestial radiations [Nicolas Reul, IFREMER, 2010]

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 1C – Land cont. The image reconstruction algorithm in SMOS is almost a FFT. Any sharp transition introduce singularities and its inversion introduce errors. Land’s brightness temperature is 300 K, while the average sea surface brightness temperature is 120 K.

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 Products

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 Products SMOS Level 2 User Data Product – UDP is available, one file per semi-orbit, on: (a data request form must be filled first) SM_OPER_MIR_OSUDP2_ T140558_ T145957_316_001_1.zip SM_OPER_MIR_OSUDP2_ T140558_ T145957_316_001_1.HDR header in XML SM_OPER_MIR_OSUDP2_ T140558_ T145957_316_001_1.DBL binary data file start YYYYMMDDThhmmss end YYYYMMDDThhmmss proc version

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 Products Different programs are available to open, display, partially process, and export SMOS Level 2 data, among them: BEAM software, including SMOS-box plug-in can be downloaded from Binary.DBL files can be read by using ad-hoc programs (C, Matlab, Fortran…), exported data can feed any program you are most used to (IDL, Matlab, ODV…) Details on DBL file structure can be found in the L2 Product Specification Document, on:

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 Product

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 Product 3 retrieved SSS 3 theoretical uncertainties associated to the 3 retrievals Acard theoretical uncertainty associated to the retrieval of Acard Wind Speed theoretical uncertainty associated to the retrieval of WS Sea Surface Temperature theoretical uncertainty associated to the retrieval of SST Modeled Brightness Temperature at 42.5° pol H (surface) theoretical uncertainty associated to TB H Modeled Brightness Temperature at 42.5° pol V (surface) theoretical uncertainty associated to TB V Modeled Brightness Temperature at 42.5° pol X (antenna) theoretical uncertainty associated to TB X Modeled Brightness Temperature at 42.5° pol Y (antenna) theoretical uncertainty associated to TB Y Control Flag: Several quality flags one for retrieval (4) Dg_chi2: Retrieval fit quality index, one for retrieval (4)

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 Product Dg_chi2_P: chi2 high value acceptability probability, one for retrieval (4) Dg_quality: Descriptor of SSS uncertainty, one for retrieval (4) Dg_num_iter: number of iterations until convergence, one for retrieval (4) Dg_num_meas_L1c: number of measurements at L1c Dg_num_meas_valid: number of valid measurements after discrimination Dg_border_fov: number of grid-points at the border of the FOV Dg_eaf_fov: number of grid-points in the Extended Alias-Free FOV Dg_af_fov: number of grid-points in the Alias-Free FOV Dg_sun_tails: number of grid-points affected by sun reflection tails Dg_sunglint_area: number of grid-points affected by sun reflection Dg_sunglint_fov: number of grid-points with reflected sun in the FOV

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 Product Dg_sunglint_L2: number of grid-points with reflected sun in the FOV, as computed at L2 Dg_suspect_ice: number of grid-points with suspected ice Dg_galactic_Noise_Error: number of grid-points affected by galactic noise Dg_galactic_Noise_Pol: number of grid-points affected by polarized galactic noise Dg_moonlight: number of grid-points with reflected moonlight in the FOV Science_Flags: several geophysical flags Dg_sky: number of gridpoints with specular direction toward a strong galactic source Land_Sea_Mask: Land/Sea descriptor

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 SMOS Land Cover Tool Tool from GMV to display and export SMOS product to Google Earth files

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Level 2 Product Exercise

Thank you! Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, 2010 Marco Talone, Jérôme Gourrion, Fernando Martin Porqueras, Nicolas Reul, Joe Tenerelli, Marcos Portabella, and the SMOS Barcelona Expert Centre (SMOS-BEC) Team

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 Interferometric Radiometer The idea at the basis of interferometric radiometry is to synthesize a large antenna with a number of small ones. Output voltages of a pair of antennas (e.g. located at and ) is cross-correlated to obtain the so- called “visibility sample”: The result is a potential degradation of the radiometric sensitivity in terms of a higher rms noise, on the other hand a complete image is acquired in one snapshot, permitting to increase the integration time and improve the measurement quality. Nevertheless, the major advantage of interferometric radiometry is the multi-angular measurement: the output of an IR is, in fact, an image; this permits having several views under dierent incidence angles of the same point on the Earth before it exits from the Field of View where, B 1 and B 2 are the receivers' noise bandwidths, G 1 and G 2 the available power gains, and b 1 (t) and b 2 (t) the signals measured by elements 1 and 2. The complete set of the visibility samples is called a visibility map, and it is approximately the Fourier transform of the brightness temperature distribution of the scene. To invert this process the inverse Fourier transform can be applied as a first approximation (Camps et al., 1997) or a more sophisticated G-matrix inversion (Anterrieu and Camps (2008); Camps et al. (2008a))

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 RFI FROM Receiver Co-Channel Interference This is defined as undesired signals with frequency components that fall within the receiver’s RF passband and are translated into the Intermediate Frequency (IF) passband via the mixer stage. The interfering signal frequency is equal to the sum of the receiver’s tuned frequency and one half of the narrowest IF bandwidth. These signals are amplified and detected through the same process as the desired signals; therefore, a receiver is very susceptible to these emissions even at lower levels. Results: Receiver desensitization, signal masking, distortion. 2.0 Receiver Adjacent Signal Interference This is defined as undesired signals with frequency components which fall within or near the receiver’s RF passband and are translated outside of the IF passband via the mixer stage. These signals must be of sufficient amplitude to produce non-linear effects within the receiver’s RF amplifier or mixer stages. Some of the resulting non-linear response signals may be converted to the IF passband frequency via the mixer stage where they are amplified and detected through the same process as the desired signals. These become similar to co-channel interference signals at this point. The undesired emissions which are translated outside of the IF passband may still pass through the remaining receiver stages, if at high enough levels to survive the out-of-passband attenuation. They may then be processed by the detector. The predominant response for this case is desensitization. Results: Non linear effects in the RF or mixer stages producing receiver desensitization, intermodulation and cross modulation.

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 RFI FROM Receiver Out of Band Interference This is defined as undesired signals with frequency components that are significantly removed from the receiver’s RF passband. High level signals may produce spurious responses in the receiver if mixed with local oscillator (LO) harmonics to produce a signal falling within the IF passband. The spurious responses result from the mixing of an undesired signal with the receiver’s LO. The amplitude of these responses is directly proportional to the level of the undesired signals prior to mixing with the LO. The spurious responses in a receiver usually occur at specific frequencies. Any other out of band signals are attenuated by the IF selectivity. Results: An undesired response created by the mixing of an undesired signal with the LO. The undesired signals which mix with the LO and are capable of being translated to the IF stages are the spurious response frequencies. These frequencies and their interference power levels are a function of the receiver’s susceptibility to these responses. 4.0 Transmitter Fundamental Emissions The transmitter’s fundamental output signal includes characteristics of the power distribution over a range of frequencies around the fundamental frequency. These are determined by the base-band modulation characteristics and are represented by a modulation envelope function. The primary parameter associated with the modulation envelope is the transmitter’s nominal bandwidth (3dB). This may be derived from the transmitter modulation characteristics (by Fourier analysis), measured, or from the manufacturer’s specifications. The power distribution in the modulation sidebands may be represented by a modulation envelope function showing the variation of power with frequency.

Course on Earth Observation Understanding of the Water Cycle Fortaleza, Brasil, November 1-12, /46 RFI FROM Transmitter Harmonic Emissions The main concern with a transmitter’s harmonic emissions is the undesired signal outputs which are harmonically related to the fundamental signal rather than to other oscillator circuits. The relative power associated with the harmonic emissions may be modeled using data for the particular transmitter type. However, since harmonic output power can vary considerably from one transmitter to another for the same type and model, it should be represented statistically. Harmonic emission models may be derived from statistical summaries of measured data or from manufacturer’s equipment specifications. Transmitter spurious emission models for prediction of frequencies above the fundamental are based on harmonic emission levels. The modulation envelope must be represented for harmonics as was done for the fundamental. 6.0 Transmitter Noise Transmitter noise includes the output spectrum that is a result of the thermal noise generated in the driver and final amplifier stages as well as the synthesizer noise from lower level stages. This is a broad-band noise; however, it usually does not cover the immediate modulation sidebands. The level may be specified as the power per bandwidth as a function of frequency (dBm/Hz). 7.0 Transmitter Intermodulation These are the undesired signals that result from the local mixing of a transmitter’s output emission with that of another transmitter. The mixing usually occurs in the non-linear circuits of a transmitter whose antenna receives a high level of RF from another transmitter antenna in close proximity. The mixing products are radiated by the transmitter’s antenna as possible co-channel or adjacent signal interference signals