1. Level-1A to Level-1B Spacecraft data to Geolocation Data and Antenna Temperature Level-1B to Level-2A Antenna Temperatures Converted to TOA Brightness Temperature Level-2A to Level-2B Sea-surface Salinity found from TOA TB plus Ancillary Data Based on Aquarius Science Pre-CDR Level 1 and 2 Algorithms, Frank J. Wentz 20-21 July, 2006 Algorithm Theoretical Basis Document Aquarius Level-2 Radiometer Algorithm: Revision 1 January 22 2008 Aquarius Data Processing

2. Aquarius Sun sunlat, sunlon sundis Solar Reflection refllat refllon reflinc Gain Angles Direct and Reflected Solar tht_global_sun(2) phi_global_sun(2) Boresight cellat cellon celinc celazm celpra Solar Backscatter suninc sunazm sunglt Galaxy Big Bang glxlat glxlon (J2KM) Moon moonlat, moonlon moondis Earth Surface Radiation Seen by Aquarius Atmosphere

3. Level 1A Data Essentially Organized Version of Level 0  Data organized in orbital files Start near the South Pole where z-velocity=0.  Orbit contain 20% overlap on both ends Accommodate count averaging  Spacecraft Position in MJ2K Coordinates: [x, y, z, t] Coordinates have been verified with CONAE  Spacecraft Attitude [roll, pitch, yaw, t]  Radiometer Counts: Earth and Calibration  Thermistor Counts  Housekeeping Counts

4. Level-1A to Level-1B Processing Geolocation S/C subtrack latitude, longitude altitude, zang. For each horn observation every 1.44 sec: 1. Geodetic latitude and east longitude 2. Boresight incidence angle and azimuth angle 3. Sun incidence and azimuth angle (for backscattering computation) 4. Polarization rotation angles relative to Earth 5. Zenith and azimuth angles for sun and moon 6. Zenith and azimuth angles for reflected ray (MJ2K coordinates) Sun and Moon Contamination Approximate increase in TA due to (requires antenna pattern) 1. Direct and Reflected Sun (assuming nominal flux) 2. Reflected Moon RFI Detection Flags applied to radiometer counts Earth maps of number of occurrences stratified by horn number, pol, and asc/dsc Radiometer Count Averaging Earth Counts averaged 1.44 sec (one complete radiometer cycle) Calibration Counts averaged for longer time periods (TBD) Convert Thermistor Counts to Temperature (K) Level-1A Data All time tagged, MJ2K coordinates S/C Position, Velocity, Attitude Radiometer Counts Thermistor Counts Compute Antenna Temperature TAv, TAh, TAp, TAm (one value for each complete 1.44 s radiometer cycle)

5. Geolocation  Oblate Spheroid Earth Model: WGS-84 RE=6378.137D3, RP=6356.752D3  Sensor Point Geometry for 3 Horns Nadir Angle = [ 25.80 o, 33.77 o, 40.34 o ] Azimuth Angle= [ 9.76 o, -15.33 o, 6.50 o ]  Rotation Matrix for Sensor/Spacecraft Misalignment  Vector formulation in MJ2K coordinates  Plenty of Heritage (SSM/I,TMI,AMSR, etc.)

6. Sun and Moon Contamination  Direct and reflected solar radiation is estimated using antenna pattern measurements  Reflected lunar radiation is also found  Uncertainty in pattern measurements is large  May just be useful as a quality flag

7. RFI Detection  Done before any averaging of Earth counts  Statistical outlier analysis  Earth maps of persistent sources  Suspected Earth counts are flagged and excluded from averaging

8. Count Averaging and Thermistor Temperatures  Earth counts are averaged for 1.44 sec (one complete radiometer cycle)  Calibration counts are averaged over longer intervals  Thermistor counts are converted to physical temperatures using laboratory derived coefficients

9. Antenna Temperature Calculation

10. Direct solar radiation included in T B,Space. Reflected and backscattered solar radiation included in T B (  ) The Antenna Temperature Equation

11. Level-1B to Level-2A Processing Remove Radiation from Far Sidelobes Option: Fixed table computed by running simulator: Tb_land_correction(1440,720,2,12,3,2) Tb_land_correction(nlon,nlat,nasc,nmon,nhorn,npol) Interpolated via. 3-D linear interp. Fixed table computed by running simulator: Ta_space(3,360,360,3); Ta_space(nch,nday,nzang,nhorn) Interpolated via. 2-D linear interp. Option: Dynamic table of solar flux TAsund_actual=TAsund*(flux/flux0) Faraday Rotation Correction Compute TOA TB Remove Radiation from Space Level-1B Data Geolocation Parameters TAsund, TAsunr, TAmoonr TAv, TAh, TAp, TAm Flags (rfi, TBD) Option: TAsunr from L1B Remove Coastline Contamination TB_TOA = a1*TA1 + a2*TA2

12. Removal of Radiation from Space  Cosmic background, TB=2.73 K  Galactic radiation (smoothed by antenna pattern)  Earth limb (very small, TA=0.006)  Pre-computed tables a function of day-of-year and orbit position  Direct solar radiation (expected to be <0.05 K, optional, computed during Level-1)

13. Removal of Reflected Solar and Lunar Radiation  Reflected solar radiation Expected to be <0.05 K, optional, computed during Level-1  Reflected lunar radiation In mainlobe and may be correctable

14. Top of the Atmosphere (TOA) TB (slide 1) Definition of TOA TB: A simple average (no weighting) of the upwelling brightness at the top of the atmosphere The average is just over the 3-dB footprint The incidence angle is constant An effective incidence angle can be used in place of the boresight incidence angle. In other words: TOA TB is independent of antenna characteristics and is just a function of the environment and specified incidence angle. Over the Open Ocean: Very detailed and elaborate simulations show: TB_TOA = a1*TA1 + a2*TA2 to a 1-sigma accuracy of 0.04 K TA1 and TA2 and the first and second TA stokes measurements after removing space contribution and doing Faraday Rotation Correction. See The Estimation of TOA T B from Aquarius Observations, RSS Report 013006, January 30, 2006 Coefficients a1 and a2 determined before launch using scale-model antenna patterns. They may be revised after launch to remove any global, absolute difference between Aquarius TOA TB and TOA TB coming from the RTM.

15. Over Extended Land Areas: The expression: TB_TOA = a1*TA1 + a2*TA2 still works very well, although a1 and a2 are slightly different Areas Containing a Mixture of Land and Water: Very difficult to maintain accuracies required for salinity retrievals Possibly one can extended salinity retrievals towards the coast by 100 km (?). We propose using the simulator to produce correction tables. Tb_land_correction(1440,720,2,12,3,2) {0.5 GB}. 1440 by 720 is a 0.25  latitude, longitude map 2 is ascending/descending orbit 12 is months of year 3 is horns 2 is polarizations Table can be redone at the end of the mission using more realistic L-band land temperatures. Top of the Atmosphere (TOA) TB (slide 2)

16. Coastline Correction Table for Ascending Orbit Segments for 1 st Stokes Coastline Correction Map

17. Level-2A to Level-2B Processing Remove Reflected and Scattered Radiation 1. Galactic reflected 2. Solar backscatter 3. Moon reflected NCEP Profiles of temperature, pressure, vapor Interpolated via. 3-D linear interp. Compute atmospheric upwelling and downwelling radiation (TBup, TBdw) and transmittance t. Salinity Retrieval Algorithm Remove Radiation from the Atmosphere Level-2A Data Geolocation Parameters TBtoav, TBtoah Flags (TBD) NCEP 10-m wind Interpolated via. 3-D linear interp. Fixed table giving galactic maps with varying amounts of smoothing TB_gal(1440,720,21) TB_gal(nlon,nlat,nwind) Interpolated via. 3-D linear interp. Options: solar backscatter=f(tht,thtsun,azm-azmsun,wind) TAmoonr from L1B. !!! Salinity !!! NCEP 10-m wind (TBR) NCEP SST (TBR) Interpolated via. 3-D linear interp.

18. Sea-Surface Emission  Atmospheric parameters come from NCEP 6-hour fields  Spatial averaging of galactic radiation is an important consideration  Option for computing backscattered solar radiation

19. Regression algorithm trained with simulated data (Possibly more terms will be added to account for non-linearities)  SST comes from best available souces (MISST/GHRSST)  Wind from scatterometer and/or ancillary data  Inc. angle knowledge is critical See: Salinity Error due to Surface Roughness Effects RSS Memorandum 121504 Estimation of Sea Surface Salinity

20. Earth Scene Ocean: Salinity, SST, Wind fields Land: Soil moisture, vegetation type, LST Ice: Ice type and temperature Atmosphere (including limb): NCEP profiles TA Integration Full 4-Stokes Integration over Earth and Space Sun Year 2000 actual values Easily scalable Cosmic Background 2.7 K Galaxy To be implemented Faraday Rotation Actual TEC values Earth Magnetic Field Orbiting Antenna CONAE Orbit Parameters Roll/Pitch/Yaw now included Aquarius Scale Model patterns Radiometer Piepmeier Forward Model for TA to counts TBTB TBTB TBTB TBTB T B rotated TATA Radiometer Counts Orbiting Thermal Model Simple harmonic of orbit position Thermistor Response Func. Linear with temperature Temperatures Thermistor Counts Orbit Position End-to-End Aquarius On-Orbit Simulator: Part 1

21. End-to-End Aquarius On-Orbit Simulator: Part 2 Radiometer CountsThermistor Counts Pre-Formatter Format in Group, Block, and Sub-Block Structure Telemetry Formatter Format in Group, Block, and Sub-Block Structure Scatterometer DataPlatform Data Simulated Downlink Telemetry Level-0 to Level-1A Processing Level-1A to Level-1B Processing Level-1B to Level-2 Processing Level-2 to Level-3 Processing Antenna Temperature TOA Brightness Temperature Swath Salinity, SST, wind, etc Time-Averaged Salinity Fields

22. Scale Model Gain Pattern

23. Includes –surface temperature and moisture from NCEP (simultaneous) –Surface type (bare, ice, grass, crop, tree (tropical, deciduous, conifer)) from EUROCLIMAP monthly/annual climatology –Soil roughness effect –Vegetation effect –L-band dielectric model of Dobson et al. 1985 Land Emissivity Model

24. Simulates, based on ATBD (Piepmeier/Pellerano/Wilson/Yueh 2005) –radiometer (Ta  counts) –Ta retrieval (counts  Ta) Used minimum 2 calibration looks for v-/h-pol and 4 calibration looks for 3 rd Stokes Fully used correlated noise diodes Accuracy is better than 0.01K Testing TA  Counts  TA

25. Components of Aquarius On-orbit Simulator 1. Complete integration of the 4-Stokes parameters over the complete 4p steradians 2. Direct and reflected solar radiation for year 2000 3. Cosmic and galactic spillover contribution (galactic TBI) 4. Earth Limb Contribution 5. Faraday rotation in the ionosphere 6. Full slant-path integration through NCEP atmospheres 7. Surface emissivity from NCEP wind fields, Reynolds SST fields, & ECCO salinity model. 8. Intensive numerics with integration error < 0.01 K

26. Error Modeling for Aquarius On-orbit Simulator 1. Year 2000 (maximum of last solar cycle) used for ionosphere electron density 2. Worst case Faraday rotation (Julian day 303 in 2003) 3. NEDT for 6-sec average = 0.08 K 3. Incidence angle knowledge error is 0.03 deg std. dev. error added to incidence angle 4. SST knowledge error is 0.3 C 5. Wind speed knowledge error is 0.5 m/s (also 1.0 m/s) 6. Six-hour variability added to atmospheric model 7. No correction for solar radiation (included in simulation but not retrieval)

27. Atmospheric Absorption at 1.4 GHz

28. Global Results for Salinity Retrievals (7-days) Reference Retrievals

29. Salinity Retrieval Performance (7days) Mean Std. Dev.

30. 313734 701 3830-34 68 2 3 4 248244288289 290Temp 1.01.011.041.031.051.27Loss T ND =500K, T DL =290K, T CND =500K TA to Voltage (count) Forward Simulation

31. 3 rd Stokes Calibration: gain and offset Estimating G pv, G ph, o p, G mv, G mh, o m –3 calibration looks are needed (used 4 looks - overdetermined) Estimating G pU (same for G mU ) –4 th calibration look (v CND ) is used –v p,earth =earth count at 10milisec interval –T CND,v and T CND,h are set to T CND /2

32. 3 rd Stokes Calibration: gain and offset T U produces v p and v m signals Thus v p and v m are used to estimate T U Yet v p and v m are affected also by T v and T h Manipulating the forward equation yields –First, retrieve earth-view T v and T h –Then, estimate G pv, G ph, G mv, G mh, G pU, G mU, o p, o m. –Then, remove contributions of T v and T h to v p and v m –Finally, account for G pU, G mU, o p, o m