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BIAS TRENDS IN THE 1-SLOPE (REPROCESSING) AND CALIBRATED L1 BRIGHTNESS TEMPERATURES

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## BIAS TRENDS IN THE 1-SLOPE (REPROCESSING) AND CALIBRATED L1 BRIGHTNESS TEMPERATURES

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**BIAS TRENDS IN THE 1-SLOPE (REPROCESSING) AND CALIBRATED L1**BRIGHTNESS TEMPERATURES Joe Tenerelli SMOS Payload Calibration Meeting 11 20-21 September 2012**PLAN**Brieflydescribeprocedure for calculating the biasesbetween the reconstructed and modeledbrightnesstemperatures; Summarize the latitudinallyaveragedbias trends observed in SMOS brightnesstemperatures over the last twoyears. Examine the possile impact of geopysicalparameters on the descending-ascendingbiasdifferences; Examine the correlationbetween the alias-free field of viewbias, the antenna patch physicaltemperature and the most important geophysicalparameters; Examine the time-latitude structure of the biases.**HOW BIASES ARE COMPUTED**STEP 1: For eachscene of eachhalf-orbit, compute the domainaverage of the difference (or bias) betweenreconstructed and modeled Stokes vectorelements in the instrument polarization basis (Tx, Ty, Uxy, and Vxy). Averages are computed over both the alias-free (AF) and extended alias-free (EAF) portions of the field of view (FOV). We do not includegridpointswithin 0.044 directorcosineunits of the domainboundaries.**HOW BIASES ARE COMPUTED**STEP 2: Filtering of scenes/snapshots. Scenes are thenexamined for possible contamination by direct sunaliases, land, ice, or radio frequencyinterferencewhichcould impact the statistics. Severalfilters are applied as outlined in the next few slides:**HOW BIASES ARE COMPUTED**FILTER 1: Anygridpointwithin 0.1 directorcosineunits of any direct sun alias are alsoexcludedfrom the averagingprocedure.**HOW BIASES ARE COMPUTED**FILTER 2: Anyscene for which the maximum value of |Tx| or |Ty| over the fundamentalhexagonexceeds 500 K, or for which the maximum value of |Uxy| exceeds 230 K isexcludedfrom the averaging. This filterisappliedafter correction by an OTT.**HOW BIASES ARE COMPUTED**FILTER 3: A land and icefilterisapplied. Anyscene for which the fraction of land in the earth portion of the entirefundamentalhexagonexceeds 0.02 isremoved. Likewise, anyscene for which the ice fraction exceeds 0.05 isremoved. Finally, gridpointscloserthan 80 km from land are removed.**HOW BIASES ARE COMPUTED**STEP 3: After the scenefiltering, the filtered per-sceneaverages for all half-orbits for a givenpass direction (ascending or descending) are collectedinto a set of global dailyregular latitude-longitude grids, eachwith a gridspacing of 0.25o in latitude and 1o in longitude. Thesegridscontaining the per-scenefiltered AF and EAF averagebiases. The plots below show, for both the reprocessing data (left) and the calibrated L1 test data(right) the number of ascendingpassscenescollected in eachgridbox over the entireperiodconsideredhere (over twoyears). Reprocessing Data (1-Slope model) Calibrated L1 Test Orbits**HOW BIASES ARE COMPUTED**STEP 4: Creation of time-latitude profiles of bias (Hovmoller plots). For eachday, eachpass direction and each latitude, the (filtered) AF and EAF biases (as well as domainaveragedgeophysicalparameters and model brightnesstemperatures) are averaged over all longitudes: Time-latitude (Hovmoller) maps Filtereddailybiasmaps averaging over longitudes**HOW BIASES ARE COMPUTED**STEP 5: Creation of latitudinallyaveragedbiascurves: The time-latitude filtered and griddeddomain (AF and EAF) averagedbiases, geophysicalparameters, and model solutions are averaged over a latitude band rangingfrom 60oS to 5oN. This isdone for ascending and descending passes separately. The yellow box on the time-latitude Hovmoller plot (lower-left) shows the latitude band used for averaging. Time-latitude (Hovmoller) maps AF and EAF bias trend curves for asc/desc passes averaging over latitude**HOW BIASES ARE COMPUTED**NOTE: We have far fewerorbits for the calibrated L1 test than for the 1-slope Reprocessing data. But the biasresultswith the twomethods are, nevertheless, are similar. The yellow boxes highlight latitude band used to compute the bias trend curves (rangingfrom 60oS to 5oN). Reprocessing Data (1-Slope model): The complete set of half-orbitsobtainedfrom ESA reprocessingcampaign Calibrated L1 Test Orbits: A smallsubset of half-orbitsprocessed by ESA on GPOD**TEMPORAL FILTERING OF BIAS TRENDS**STEP 6: Temporal filtering. Afterobtaining the domain and latitudinallyaveragedbiasesbetweenbrightnesstemperaturesobtainedfrom MIRAS and the forwardocean model (MIRAS-model), a running 10-day smootherisapplied to smooth out the small-scaleripplesin the time series. The impact of thisfilterisshownbelow for both the calibrated L1 test orbits (left) and the complete set of orbitsfrom the first reprocessing. The resultsalsoillustrate the impact of the reduced set of orbitsused to test the calibrated L1 method.**TEMPORAL FILTERING OF BIAS TRENDS**Note that the unfilteredbiascurve for reprocessing 1-slope data (redcurve, right panel) issmootherthanthat for the calibrated L1 data (redcurve, left panel) becausethesecurves are averages over both longitude and latitude, and as wesaw on the previousslideswe have much more coverage in the reprocessing 1-slope data. Impact of smoothingmuchgreater for Cal L1 than for the 1-Slope model owing to far fewerhalf-orbits in the average for Cal L1.**A LOOK AT THE BIAS TRENDS**Havingestablished the methodused to evaluate the biasbetween the reconstructed and model brightnesstemperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), wenow move on to present the biases for both the mostrecent ESA reprocessingcampaign, whichemployed the ‘1-slope’ loss model, and the ‘calibrated L1’ methodrecentlyproposed. Belowis an outline of whichfollows: Examination of biasesaveraged over longitude and latitude, including a look atcoherencewith variations in the correspondingaverage Tp7; Examination of the potential impact of geophysicalparameters on descending-ascendingbiasdifferences; Examinationof the correlationbetweenbias variations and variations in Tp7 and severalgeophysicalparameters; Examination of time-latitude structure of the bias, whichhighlights the strong high-latitude bias variations late in eachyear.**A LOOK AT THE BIAS TRENDS**Havingestablished the methodused to evaluate the biasbetween the reconstructed and model brightnesstemperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), wenow move on to present the biases for both the mostrecent ESA reprocessingcampaign, whichemployed the ‘1-slope’ loss model, and the ‘calibrated L1’ methodrecentlyproposed. Belowis an outline of whichfollows: Examination of biasesaveraged over longitude and latitude, including a look atcoherencewith variations in the correspondingaverage Tp7; Examination of the potential impact of geophysicalparameters on descending-ascendingbiasdifferences; Examinationof the correlationbetweenbias variations and variations in Tp7 and severalgeophysicalparameters; Examination of time-latitude structure of the bias, whichhighlights the strong high-latitude bias variations late in eachyear.**The sensitivity of L-band brightnesstemperature**(Tx+Ty)/2=(Th+Tv)/2 to sea surface salinitydependsupon the sea surface temperature (SST), but ranges from about -0.4 K/psu in cold water to about -0.7 K/psu in warm water. These are important numbers to keep in mindwhenweconsiderbrightnesstemperaturebiases in whatfollows. (Tx+Ty)/2 bias +1 K SSS bias -2 psu (independent of incidence angle)**BIAS TRENDS AVERAGED OVER LONGITUDE AND LATITUDE**Webegin by comparing AF and EAF descending and ascendingpassbias trends for the calibrated L1 test (left) and the 1-slope reprocessing data (right).The trends are similar but thereis an offset between the twomethods. Most noticeableis the descendingpass 0.7-1 K dropoffaround Sep-Nov, equivalent to a SSS increase of around 2 psu! Note that the dropoffislargerwith Cal L1 thanwith the 1-slope model (yellowcircles). This maybe a result of differences in the set of half-orbitsused for the two calibration methods.**BIAS TRENDS AVERAGED OVER THE SOUTHERN HEMISPHERE**Wenowconsideronly the AF FOV and overlay Tp7 in green (adjusted to zero time mean). For descending passes variations in Tp7 and the biasesseem to exhibit a clear phase relationship. For ascending passes the relationshipbetween Tp7 and the biasesislessclear. Ascendingpass Tp7 adjusted to zero time mean Descendingpass Tp7 adjusted to zero time mean**BIAS TRENDS AVERAGED OVER THE SOUTHERN HEMISPHERE**Wenowconsider the differencebetweendescending and ascendingpassbiases for both calibration methods. A clearannual cycle is apparent withsimilar trends in the AF and EAF fields of view. Also, betweenNovember and March the AF and EAF biasesseparate (circled in yellow). This separation in more pronounced in Cal L1 than in the 1-slope results. Possiblyrelated to error in galacticscattering model Separationbetween EAF and AF biasesgreater for Cal L1 than for 1-slope model. Possiblyrelated to differences in the sets orbitsused.**BIAS TRENDS AVERAGED OVER THE SOUTHERN HEMISPHERE**Wenow overlay the (zeromean) differencebetweendescending and ascending Tp7. There issome apparent correspondencebetween variations in Tp7 and the annual cycle in the biases:**CONCLUSION #1**The latitudinallyaveraged AF and EAF bias trends for the 1-Slope and Calibrated L1 methods are verysimilar. Differencesmayberelated to differences in the orbit sets used for analysis. Bothmethodsyielda strongseasonal cycle in (Tx+Ty)/2 bias of about 1 kelvin in peak-to-peak amplitude with a distinct minimum in the reconstructedbrightnesstemperaturestoward the end of eachyear. This cycle isassociatedwith a seasonal cycle in the meanretrievedsea surface salinity (SSS) bias of nearly2 psu in peak-to-peak amplitude (withoutperiodic OTT correction).**A LOOK AT THE BIAS TRENDS**Havingestablished the methodused to evaluate the biasbetween the reconstructed and model brightnesstemperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), wenow move on to present the biases for both the mostrecent ESA reprocessingcampaign, whichemployed the ‘1-slope’ loss model, and the ‘calibrated L1’ methodrecentlyproposed. Belowis an outline of whichfollows: Examination of biasesaveraged over longitude and latitude, including a look atcoherencewith variations in the correspondingaverage Tp7; Examination of the potential impact of geophysicalparameters on descending-ascendingbiasdifferences; Examinationof the correlationbetweenbias variations and variations in Tp7 and severalgeophysicalparameters; Examination of time-latitude structure of the bias, whichhighlights the strong high-latitude bias variations late in eachyear.**IMPACT OF GEOPHYSICAL PARAMETERS ON THE BIAS TRENDS**Wenowbriefly examine the extent to which the scenebright model maycontribute to the descending-ascendingdifference in (Tx+Ty)/2. This shouldprovide an indication of the possible influence of variability in the scenesampling. The resultisthatonlyscatteredgalacitc radiation contributessignificantly to the descending-ascendingdifferences. Green curves = modeled contributions to desc-asc (Tx+Ty)/2 fromvarious radiation sources Specularemission atmemission Rough emission reflgalactic scat galactic Only the scattered/reflectedgalactic radiation contributessignificantly to descending-ascendingdifferences in (Tx+Ty)/2**CONCLUSION #2**Of all main geophysical contributions to the descending-ascendingdifferences in (Tx+Ty)/2, scatteredgalactic radiation is the onlysignificant one, and thisistakenintoaccount in the biascalculations. Somepotential for errorremains in this model, but the impact shouldbelessthan a few tenths of a kelvin and limited to descending passes in September-October.**A LOOK AT THE BIAS TRENDS**Havingestablished the methodused to evaluate the biasbetween the reconstructed and model brightnesstemperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), wenow move on to present the biases for both the mostrecent ESA reprocessingcampaign, whichemployed the ‘1-slope’ loss model, and the ‘calibrated L1’ methodrecentlyproposed. Belowis an outline of whichfollows: Examination of biasesaveraged over longitude and latitude, including a look atcoherencewith variations in the correspondingaverage Tp7; Examination of the potential impact of geophysicalparameters on descending-ascendingbiasdifferences; Examinationof the correlationbetweenbias variations and variations in Tp7 and severalgeophysicalparameters; Examination of time-latitude structure of the bias, whichhighlights the strong high-latitude bias variations late in eachyear.**CROSS CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2,**GEOPHYSICAL PARAMETERS, AND TP7 In the slidesthatfollowwepresent the cross correlationsbetween a number of variables averaged over the alias-free field of view and expressed as functions of latitude and time. The correlations are computed over variations in both time and latitude.**CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL**PARAMETERS, AND TP7 Webeginthis section by notingthatthereis a very large cross correlationbetween Tp7 and the bias in (Tx+Ty)/ in descending passes. The correlationexceeds 0.9 in magnitude between 60oS and 5oN latitude!**CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL**PARAMETERS, AND TP7 We have computed the correlation coefficient between (Tx+Ty)/2 and various AF-FOV averagedparameters, including Tp7 (lower right panel). SLP SSS SST CWV WS Tp7**CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL**PARAMETERS, AND TP7 For descending passes the large correlationbetween the bias in (Tx+Ty)/2 and the parametersshowninvolves Tp7! SLP SSS SST CWV WS Tp7**CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL**PARAMETERS, AND TP7 For ascending passes the situation islessclear: SLP SSS SST CWV WS Tp7**CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL**PARAMETERS, AND TP7 Wenext arrange the cross correlationsbetween all combinations of variables into a matrix. Note the strongcorrelationbetweenwind speed and (Tx+Ty)/2 (st1) thatappears to berelated to the correlationbetweenwind speed and Tp7 (owing to latitude dependence of thesetwo variables): DESCENDING PASSES St1=(Tx+Ty)/2 Correlationsbetweenwind speed, tp7 and first stokes! Correlationsbetween sst and sss; sst and columnar water vapor; sss and slp.**CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL**PARAMETERS, AND TP7 The correlation matrix for ascending passes does not exhibit the same dominant correlationbetween Tp7 and the first Stokes parameter. ASCENDING PASSES St1=(Tx+Ty)/2 Much smallercorrelationsbetweenwind speed, tp7 and first stokes for ascending passes than for descending passes!**CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, FORWARD MODEL**COMPONENTS, AND TP7 Wenextformedsimilar matrices for various components of the scenebrightness model, includingroughnessemission (rgh), atmosphericemission (atm), specularemission (flt), and galacticreflection (gal): Correlationsbetweenroughnessemission, tp7 and first stokes! DESCENDING PASSES**CONCLUSION #3**Descending passes exhibitstrongcorrelationbetween (Tx+Ty)/2 bias and Tp7 (correlation coefficient around -0.9). Ascending passes do not exhibitthisstrongcorrelation.**A LOOK AT THE BIAS TRENDS**Havingestablished the methodused to evaluate the biasbetween the reconstructed and model brightnesstemperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), wenow move on to present the biases for both the mostrecent ESA reprocessingcampaign, whichemployed the ‘1-slope’ loss model, and the ‘calibrated L1’ methodrecentlyproposed. Belowis an outline of whichfollows: Examination of biasesaveraged over longitude and latitude, including a look atcoherencewith variations in the correspondingaverage Tp7; Examination of the potential impact of geophysicalparameters on descending-ascendingbiasdifferences; Examinationof the correlationbetweenbias variations and variations in Tp7 and severalgeophysicalparameters; Examination of time-latitude structure of the bias, whichhighlights the strong high-latitude bias variations late in eachyear.**DESCENDING PASSES, REPROCESSING DATA**The bias trends presentedearlierinvolvedaverages over latitude from 60oS to 5oN. But thereis a seasonalevolution of the latitudinal (orbital time scale) variation of bias, especially in descending passes.**DESCENDING PASSES, CAL L1 TEST DATA**The same plot but for the calibrated L1 data shows trends similar to those for the reprocessing data except for a slightlyhigher amplitude in the seasonal oscillation. High latitude positive bias in (Tx+Ty)/2 justafter the suneclipse**DESCENDING PASSES, REPROCESSING DATA**The seasonalevolution of the latitudinal (orbital time scale) variation of biasissmaller in amplitude in ascendingthan in descending passes, but thereis a strongseasonal cycle in the latitudinallyaveragedbias:**DESCENDING PASSES, TP7**The biasnorth of 30oN late in the year corresponds to a negativedeviation in Tp7: High latitude negativedeviation in Tp7 in the same area.**DESCENDING PASSES, TP6**Tp6 alsoexhibits a (muchsmaller) negativedeviation in the same area: High latitude negaitvedeviation in Tp6 in the same area.**DESCENDING PASSES, RMS ERROR**The spatial AF-FOV RMS errorbetween model and the data exhibits a clearincreasefrom 2010 to 2011, but onlytoward the end of the year. RMS errorincreasessignificantlyfrom end of 2010 to end of 2011.**DESCENDING PASSES, SUN ALIAS BRIGHTNESS**The sun angle fromboresightexhibits a pattern quitecoherentwith the evolution of the spatial RMS error. In particular the RMS erroris large where the sun angle fromboresightissmall: Sun angle fromboresightisat a minimum in this high-latitude regionat the end of the year.**DESCENDING PASSES, SUN ALIAS BRIGHTNESS**The portion of the time-latitude plots where the suniseclipsedisverysmall but isnear the strong RMS error and biasfeatures: Sun iseclipsed by the earth over a verysmall portion of the hovmoller plots.**DESCENDING PASSES, SUN ALIAS BRIGHTNESS**Coincidentally, the averagebias in a disc of radius 0.1 in dc coordinatescentered on the lowerleft direct sun alias exhibits maximum in the same high-latitude area towards the end of 2010 and 2011: Lower-leftsun alias bias in (Tx+Ty)/2 alsoslightlyincreasesfrom 2010 to 2011.**EVOLUTION OF SUN BRIGHTNESS TEMPERATURE AT L-BAND**For reference, the sunbrightnesstemperatureat L-band increasedsignificantlybetween the end of 2010 and the end of 2011: Time period of high latitude biases Big jump in sun L-band Tb from end of 2010 to end of 2011!**CONCLUSION #4**Time-latitude plots of the AF-FOV meanbiasbetweenreconstructed and modeled (Tx+Ty)/2 revealsignificant latitudinal structure thatis not revealed in the latitudinallyaveragedbiascurves. This structure isespeciallystrong in descending passes north of about 30oN toward the end of eachyear. Moreover, thisregion of high latitudinaly gradient in the biascoincideswith a region of high spatial RMS error, a minimum in the sun angle fromboresight, stronglyvarying Tp7 and Tp6, and stronglyvarying(Tx+Ty)/2 biasaveragedwithin a disc of radius 0.1 dc unitscentered on the lower-leftsun alias. The spatial RMS error in this high-latitude regionismuchstronger in 2011 than in 2010. Coincidentally, the sunbrightnesstemperatureat L-band increasessignificantlybetween the end of 2010 and the end of 2011.**SUMMARY OF CONCLUSIONS**Both the ‘1-Slope’ and ‘Calibrated L1’ calibration methodsyield a strongseasonal cycle in (Tx+Ty)/2 bias of about 1 kelvin in peak-to-peak amplitude with a distinct minimum in the reconstructedbrightnesstemperaturestoward the end of eachyear. This cycle isassociatedwith a seasonal cycle in the meanretrievedsea surface salinity (SSS) bias of nearly2 psu in peak-to-peak amplitude (withoutperiodic OTT correction). Of all main geophysical contributions to the descending-ascendingdifferences in (Tx+Ty)/2, scatteredgalactic radiation is the onlysignificant one, and thisistakenintoaccount in the biascalculations. Descending passes exhibitstrongcorrelationbetween (Tx+Ty)/2 bias and Tp7 (correlation coefficient around -0.9). Time-latitude plots of the AF-FOV meanbiasbetweenreconstructed and modeled (Tx+Ty)/2 revealsignificant latitudinal structure thatis not revealed in the latitudinallyaveragedbiascurves. This structure isespeciallystrong in descending passes north of about 30oN toward the end of eachyear. A number of otherparametersalsoexhibit patterns coherentwith the pattern of bias.

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