On the application of CERES SW ADMs Cédric Bertrand

Concern ADMs required to relate radiance to flux: Instantaneous TOA albedo: where  s = solar zenith angle  v = viewing zenith angle  = relative azimuth angle R = ADM anisotropic correction factor where d 2 = Earth-Sun distance S o = solar constant Space-borne radiometers do not measure the instantaneous SW flux directly

CERES-TRMM ADMs vs. CERES-TERRA (AQUA) ADMs Several years of CERES-TERRA data = enough sampling to define ADMs at a higher angular resolution than CERES-TRMM ADMs = extends the CERES-TRMM data (40ºN to 40º S) by adding mid-latitude and polar observations BUT: BUT: polar Sun-Synchronous orbit designed to cross the equator at the same local time each orbit do not provide observations of the angular radiation fields over the full range of  s empty ADMs angular bins TRMM: 350-km circular, precessing orbit with a 35º inclination angle samples each grid box at different local time every day full range of  s acquired every 46 days.

Anisotropy of Earth scenes varies with viewing geometry and cloud/clear sky properties in a continuous manner CERES-TRMM ADMs are defined for discrete angular bins and scene types  s and  v : 9 angular bins from 0º to 90º in 10º step  : 10 angular bins from 0º to 180º with a 10º or 20º step ADMs angular resolution An adjustement to the CERES anisotropic factors is needed to avoid introducing large instantaneous flux error or flux discontinuities between angular bins or scene types.

CERES: linear interpolation of bin-averaged ADM radiance L adm (  s,  v,  ) and fluxes F adm (  s ) to each observation angle (  sa,  va,  a ) and evaluate anisotropic factors from the interpolated quantities R(  sa,  va,  a ) = .L adm (  sa,  va,  a )/F adm (  sa ) RMIB: compute bin-averaged ADM anisotropic factors and use a tri-linear interpolation to estimate R(  sa,  va,  a ). Reduce instantaneous flux errors but no guarantee that ensemble averages of the instantaneous fluxes will remain unbiased R evaluation for specific angles (  s,  v,  ) REDUCE ANGULAR BIN DISCRETIZATION ERRORS:

Bias in the mean flux will occur if: Linear interpolation used when actual radiance varies nonlinearly within an angular bin Theoretical models are used to supplement empirical ADMs. The bias for a specific scene type j in angular bin (  si,  vk,  l ) is given by: Average of all instantaneous flux estimates falling in angular bin [  si ±(  s )/2,  vk ±(  v )/2,  ±(  )/2] ADM mean flux Bias estimation Estimated mean flux

RMIB: CERES: where Correction term to remove the bias When the ensemble average of instantaneous TOA flux from the CERES Eq. is determined, the mean flux is unbiased because CF(  si,  vk,  l ) =  F adm (  si,  vk,  l ) Instantaneous SW flux computation

Clear ocean SW flux Instantaneous flux estimation (clear ocean) CERES: Aerosol correction term where R adm (ws j,  sm,  vm,  m ) = determined from the wind speed-dependent ADMs R th (ws j, L m ) and R th (ws j, L adm ) = anisotropic factors inferred from the measured and ADM interpolated radiances, respectively. determined by comparing L m (  sm,  vm,  m) and L adm (  sm,  vm,  m ) with LUT of theoretical SW radiances stratified by aerosol optical depth

METHODOLOGY (J155, I500) (J416, I500) (J750, I500) MS-7 DATA ALL AVAILABLE 2003/07/02 SLOTS 3 SELECTED ZONES outside sun glint occurrence acquisition geometry SBDART RTM clear sky SW radiance time series RMIB SBDART CERES COMPARISON R2F CONV.

! 18:30’ no MS-7 data ! underestimation

AERO_C + CF

Conclusions Do not account for normalization and aerosol correction when estimating the reflected SW flux at TOA could explain the reported asymmetries in the diurnal variation of the GERB SW fluxes Climatological wind speed values will be considered in order to apply the aerosol correction (LUTs are wind speed dependent) Both correction terms will be implemented in the RGP system as soon as possible …

CERES-TRMM (INT01) = R interpolated according to the CERES scheme CERES-TRMM (INT02) = full CERES scheme Green and Red curves = identical

Joanna Futyan: fit the CERES-TRMM SW ADMs TOA albedo to her derived clear sky fluxes to fill missing clear sky SW data Systematic asymmetries in the diurnal variation of the GERB SW fluxes that are not represented by the CERES models Residual between the fit the observations at local noon ± 2 hours for April 2004 (the fit is constrained to match the data at local noon over the ocean regions)

 adm (  si ) versus  adm/bin (  si,  vi,  i ) CERES-TRMMM SW ADM = 5

Wind speeds and ADMs The wind speed dependence of the ADMs is only an issue near to sun glint: (i) at low wind speeds, the range of angles affected by sunglint is small but intense. (ii) at high wind speeds, the range of angles affected by sunglint is much larger, but not as intense.

MS-7 I500-J