Frmal Uncertainty Assessment in Aquarius Salinity Retrieval Algrithm T. Meissner Aquarius Cal/Val Meeting Santa Rsa March 31/April 1, 2015
Outline 1. Backgrund/Philsphy 2. Develping an Algrithm fr Assessing Frmal Uncertainties Level 2 Level 3 3. Physical Errr Mdel 4. Results Descriptin f Majr Cmpnents Frmal Versus Empirical Uncertainties
Aquarius L3 Perfrmance Triple Cllcatin Series V3.0 V3.0 bias adjusted V3.4 (new GMF) RMS 0.220 0.170 0.172 pen cean, very strict Q/C (cld water, high winds, RFI mask, )
Aquarius L3 Perfrmance Triple Cllcatin Map pen cean, very strict Q/C (exclude cld water, high winds, RFI mask, )
Uncertainty Estimates Purpse Any meaningful physical measurement has a value and an uncertainty (errr bar). Required nwadays fr many studies (ROSES calls). Nt easy. Nt straightfrward. Reality is far behind. Imprtant fr cean mdeling wh use Aquarius salinity as input in their mdel. Determines relative weight f bservatin in assimilatin. Creating L3 maps. Apprpriate weighting f L2 bservatins. Identifying degraded cnditins. Uncertainty estimates are needed fr bth L2 and L3. Aquarius has nly few channels and essentially nly ne bservatin (salinity). But it als has lts f errr surces that need t be cnsidered!
Uncertainty Estimates Frmal Methd in a Nutshell Frmal parameter in the physical salinity retrieval algrithm: λ. NEDT, SST auxiliary field, wind speed (rughness crrectin), galaxy, mn, land, RFI, Independent. Physical mdel fr uncertainty λ. Physical retrieval has physical errr. Can be scene dependent. Must be realistic! NOT wrst case! Errr mdel is develped ff-line. Nt always straightfrward and unequivcal. Sme cmpnents are based n SSS input frm grund truth. Run perturbed retrieval fr L2 salinity S Separate fr each parameter λ. Determine derivative: S λ = S λ%ε 'S λ'ε 2ε Depends n scene: SST, wind speed, wind directin,. Uncertainty in S due t errr in λ: ΔS, = -. / Δλ. -, Ttal uncertainty: ΔS 1 = 1, ΔS,. Cmpare with empirical errr: ARGO, HYCOM, PMEL,..
reprted at 6σ cnfidence level (1 : 5 millin chance t ccur randmly)
Randm versus Systematic Errrs Observed Aquarius salinity errrs SSS AQ HYCOM 1.44 sec σ (L2) average # fr mnthly 1 deg average σ L2 N σ (L3) (triple cllcatin analysis) V3.0 0.40 0.05 0.23 V3.4 0.35 70 0.04 0.17 L3 errrs d nt reduce when averaging ver 3 mnths. At L2 randm and systematic errrs are rughly f the same size. Mst f the errr bserved at L3 is nt a randm errr and des nt reduce with 4 6. 5 Physical errr mdel needs t distinguish between randm and (quasi - ) systematic errrs. Need t estimate systematic and randm errrs. Prpagate differently frm L2 t L3. Randm errrs: Get reduced by 4 6. 5 Quasi-systematic errrs: Stay cnstant ver time scales f 1 week 3 mnths and within 100 150 km.
Errr Prpagatin + Crrelatins Independent randm errrs at L2 are added in the rms sense: ΔS 1 = ΔS, 1,. Independent systematic errrs at L2: Cnservative methd: Add abslute values. Standard methd: Can be f either sign. Treat them like randm errrs (add rms). I have adpted this methd. Crrelatins need t be taken int accunt in perturbed retrievals. Fr example: NEDT: V-pl and H-pl independent. When perfrming the perturbed retrieval, they are treated as tw separate parameters λ and perturbed independently. Errr in galaxy: V-pl and H-pl are nt independent. There is nly ne independent parameter, say the V-pl cmpnent TA gal,v-pl. When perfrming the perturbed retrieval, nly the V-pl gets perturbed and the H-pl is calculated frm the perturbed V-pl.
Errr Prpagatin in L3 Averaging Assume we have N bservatins: S :, i = 1, N, which have all the same randm errr (ΔS) CDE and the same systematic errr (ΔS) FGF. Estimatin thery: Best estimate (maximum prbability) is the mean: 5 S = 1 N I S : Standard deviatin f the mean (uncertainty f the average): :J4 ΔS CDE = 5 I S / ΔS S :,CDE : :J4 1 = (ΔS) CDE N Ttal systematic errr: 5 ΔS FGF = 1 N I (ΔS) :,FGF :J4 = (ΔS) FGF This can be straightfrwardly generalized if the errrs f the single bservatins are nt equal r if a weighted average is taken. Cnsider ptimum weighting in L3 averaging: Weight by inverse variance (square errr).
Uncertainty Parameters included λ Type (ran/sys) NEDT (V, H, S3) ran all 3 plarizatins are treated independently calculated in cunt t TA algrithm apply frnt end lsses divide by (# f bs in 1.44 sec) wind speed / rughness crrectin ran + sys see errr mdel wind directin (auxiliary) ran 10 deg randm errr in NCEP SST (auxiliary) sys WindSat Reynlds weekly IU cupling sys see errr mdel galactic reflectin lunar reflectin land cntaminatin sea ice cntaminatin sys sys sys sys see errr mdel V-pl and H-pl are crrelated RFI sys treated n SSS level
λ Uncertainty Parameters neglected/nt cnsidered Type(ran/sys) EIA / pinting ran small. estimated frm difference between nminal (nadir) and actual pinting APC ran + sys nt cnsidered (beside IU cupling) calibratin system ran + sys assumed t be calibrated crrectly t cean RTM RTM: dielectric, O 2,wind emissivity sys assumed that the SST dependent biases are crrected atmsphere: O 2 sys small. estimated sensitivity f SSS t atmspheric temperature errr at mst 0.05 psu/k. atmsphere: water vapr signal itself is already small atmsphere: rain, clud sys sizeable in very heavy rain (0.2 psu t fresh at 10 mm/h) nt accessible as lng as nly NCEP clud water is used in L2 algrithm sun sys signal itself is already small direct galactic sys nt cnsidered
Errr Mdel Wind Speed / Rughness Crrectin Black line: systematic cmpnent (AQ HHH WindSat). Red Line: randm cmpnent (AQ HHH WindSat). Divide by 2. Red dashes: randm errr mdel fr AQ HHH wind speed ( K P value fr σ 0HH, NEDT fr TBH, errr in NCEP backgrund field, wind directin, ).
TA measured expected. Based n grund truth (HYCOM). Errr Mdel Reflected Galaxy
Errr Mdel IU Cupling hrn 1 hrn 2 hrn 3 nn-linear relatin. can NOT be absrbed in APC IU cuplings. TB measured expected. Based n grund truth (HYCOM). Cnsider t crrect in L2 alg. I S3
Errr Mdel Land Cntaminatin hrn 1 hrn 2 hrn 3 subtract "nise flr" TB measured expected. Based n grund truth (HYCOM). Ttal RMS treated as systematic errr. V/H pls crrelated in perturbed retrievals.
Errr Mdel Estimated Undetected RFI 3-year Aquarius SSS ascending - descending
Errr Mdel Estimated Undetected RFI in vicinity f RFI (TF TA peak hld) SSS (asc dsc) < 0: RFI in ascending swath SSS (asc dsc) > 0: RFI in descending swath treated as systematic errr fr retrieved SSS V3.0/V3.4 use this t mask ut undetected RFI.
Frmal Errrs L2 r = randm s = systematic
Frmal Errrs L3 r = randm s = systematic
Estimated L2 Uncertainty stratified with wind speed hrn 1 hrn 2 hrn 3 full lines: SSS AQ HYCOM dashed lines: frmal estimate
Estimated L2 Uncertainty stratified with SST hrn 1 hrn 2 hrn 3 full lines: SSS AQ HYCOM dashed lines: frmal estimate
Estimated L3 Uncertainty
Estimated L3 Uncertainty frmal versus empirical: time series pen cean + strict Q/C triple cllcatin: AQ HYCOM - ARGO frmal estimate RSS ESR
Estimated L3 Uncertainty pen cean + strict Q/C
Empirical L3 Uncertainty triple cllcatin map (AQ HYCOM ARGO)
Estimated L3 Uncertainty frmal versus empirical map Pssible cancellatin r enhancement f systematic errrs in certain regins. Fr example: errrs in wind speed and auxiliary fields. Imprving ne surce fr systematic errrs (e.g. auxiliary SST) des nt necessarily shw as an imprvement everywhere.
Summary and Reflectins We have derived an algrithm fr estimating frmal uncertainties t ur physical Aquarius salinity retrieval algrithm. 2 majr cmpnents: 1. Physical errr mdel fr each cmpnent f the salinity retrieval. 2. Running perturbed retrievals: sensitivity f SSS t the varius parameters. The physical errr mdel is develped ff line. Will be delivered as cllectin f lk-up tables. Sme cmpnents need infrmatin frm grund truth salinity (HYCOM) Tied t physical cmpnents f retrieval algrithm. Keep track f uncertainty in each parameter. Essential t separate randm and systematic uncertainties. Prpagate differently when frming L3 averages frm L2 bservatins. Results fr bth L2 and L3 uncertainty estimate cmpare very well with empirical uncertainty estimates frm grund truth. Triple cllcatin