Algorithm Theoretical Based Document (ATBD) - CESBIO

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SO-TN-ESL-SM-GS-0001 Issue 1.a Date: 31/08/2006 SMOS level 2 processor Soil moisture <strong>ATBD</strong> Table 4: Notations Plain notation (no fancy font, subscript, …) has been systematically added even when not used in the document, allowing organizing the table in a strict alphabetic order. Attempts to be systematic are made: C for coefficient, TH for threshold, FL for flags. For some short notations, "local use" means they are used with a definite purpose in a single subsection. CODE values: i (L1 input), d (aux data input), u (user input), v (variable), t (theoretical description), o (output). CODE Plain Notation Nota tion meaning v a a Argument of rotation matrix v A_card Dielectric constant index u a_L , b_L Coefficients for computing Mg_L from estimated SM v a_ST a ST Intermediate function in water dielectric constant v A_t A t Weighting coefficient for T_gc t A1 to A4 Brightness temperatures at antenna level (local use) i AF_FOV, EAF_FOV, BORDER_FOV; SUN_FOV, SUN_POINT, SUN_TAILS, SUN_GLINT_FOV, SUN_GLINT_AREA, RFI L1c flags v ALPHA α Exponent in EPS_s (local use) t ALPHA_sct α sct Coefficient for effective albedo i ASCENDING_FLAG L1c SPH flag i,o AVG_TIME Mean (median time) between first and las t view of a node u B'_F , B''_F Coefficients for computing TAU_0F t B_p Coefficient for computing TAU_p (unused) u B_S , B''_S Coefficients for computing TAU_S_nad u B_t B t Coefficient for computing A_t t BD Bandwidth u BD_S BD S SMOS receiver bandwidth u BERE_1 to 3, BEIM_1 to 3 β e' , β e" Components for exponent BETA v BETA β Exponent complex function in EPS_s u BETA_i_1 to 3 3 coefficients for computing imag(BETA) u BETA_r_1 to 3 3 coefficients for computing real(BETA) v BS_L Dry litter biomass u c Light velocity u C_BORDER,C_ EAF, C_SUN_TAILS, C_SUN_GLINT_AREA Enhancing DTBa factors triggered by L1c flags o C_FM0, C_FM, C_FV DAP numerical information on fractions t C_pol C pol parameter for computing TAU_V (unused) u C_RFI_p, C1_RFI, C2_RFI Enhancing uncertainty factor and coefficients for pol p v C_T C t Function for computing T_g u C_WEF_1 to C_WEF_4 WEF coefficients u CA_TBS1, CB_TBS1 Coefficients for RFI L2 test u CCX, CCXi Sensitivity function and coefficients v CHI ξ Director cosine v CHI', ETA' ξ', η' Differential director cosines v CHI_2 χ 2 Retrieval quality index u CL_P Coefficient for litter optical thickness; v COST Cost function v COV_P Parameter covariance matrices v COV2T, COV4T Surface data aggregated covariance matrices v COV4, COV2 Covariance matrices (indices a or s) v CP Convective precipitation u CPA_1 to 3 Coefficients for EPS_pa . 11
SO-TN-ESL-SM-GS-0001 Issue 1.a Date: 31/08/2006 SMOS level 2 processor Soil moisture <strong>ATBD</strong> CODE u CVAL_2, CVAL_4 Plain Notation Nota tion C val_2 C val_4 meaning Coefficients for computing MVAL_0 u d, f0 Element spacing, central frequency (local use) t D_cp. WI-MAX . ALPHA_I Factors to compute TAU_Ip (unused) t D_tau_G, ZM, D_Z Atmospheric coefficients (local use) u D_TPHYS; D_A_CARD, D_SM, D_TAU, D_TTH, D_(TTV/TTH), D_OMH, D_(OMV- OMH), D_HR, D_SNPAR σ0 TPHYS … ASTD (a priori standard deviations) values v DELTA, ALPHA δ, α Declination, right ascension (local use) u DFFG_STEP STEP of the DFFG u DFG_STEP STEP of the DFG v DIFF (Data-model) difference matrices v DIFF_OM ω V -ω H Vegetation albedo polarisation difference U DLCC DLCC Uncertainty in reference values (cover classes) u DP_SM, DP_A_card, DP_TAU_nad, DP_T_PHYS, DP_TTH, DP_RTT, DP_OMH, DP_DIFF_OM ∆SM etc. Increments for derivatives u DPD Increment vector for derivatives v DRV Derivative matrix v DT_G, DT_O2, DT_H2O Equivalent atmospheric layer temperature to surface differences u DTB_F Scaling coefficient for computing MVAL_0 v DTB4_s, DTB4_a, DTB2_s, DTB2_a Standard deviations vectors (surface, antenna) i DTBa Antenna radiometric uncertainties t EH, EV electric fields v EL, H Elevation, sidereal angle (local use) Dielectric constant real and imaginary part (generic notation) u EPS_0 ε 0 permittivity of free space (=8.854 10 -12 Fm -1 ) u, v EPS', EPS" ε', ε" o EPS_D ε D u EPS_dry-sand ,EPS_sand ε dry-sand , ε sand Dielectric constant inferred from additional MDa retrieval Dielectric constant for dry sand u EPS_frz, EPS_ice ε frz , ε ice Dielectric constants v EPS_fw ε fw dielectric constant of free water u EPS_pa ε pa dielectric content of solid particles u EPS_rock ε rock Dielectric constant for barren areas v EPS_s, EPS_b ε s , ε b complex dielectric constant for whole surface, smooth bare medium (additional subscript for polarisation) u EPS_urban ε urban Dielectric constant still missing v EPS_W ε W Free water dielectric constant (real part) v EPS_wo ε w0 static dielectric constant of water u EPS_woo ε w∞ high frequency limit of the static dielectric constant of water EPS_w0 v ETA η Director cosine u ETA_FS η FS Free space impedance (= 377 Ohms) u f Mean SMOS frequency Hz v f, f0 Frequency, absorption line frequency (local use) t F_VOL F VOL Vegetation volumetric fraction u FCV1, FCV2 Retrieval algorithm convergence criterions v FDE Sum of non nominal fractions (excl water) in FM class v FEB, FEI, FUH, FUL, FFO; FNO, FRZ, FSN, FWL, FWP, FWS,FSI, FTI Aggregated fractions in the FM list v FEB, FEI, FUL, FUH, FFO, FNO, FRZ, FSN, FTS, FTM, FWL, FWO,FS, FTI Aggregated fractions in the FM0 list o FL_CE Flag for computational exceptions (place holder) . 12
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Algorithm Theoretical Based Document (ATBD) - CESBIO

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