Biases in radiative transfer models for high resolution sounders Roger Saunders,
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Biases in radiative transfer models for high resolution sounders Roger Saunders, Met Office, Exeter, U.K Acknowledgements Stuart Newman and James Cameron (Met Office, U.K.) Marco Matricardi, Graeme Kelly and Erik Andersson (ECMWF) Phil Watts (EUMETSAT) George Aumann (JPL) Hong Zhang (CIMSS) Louis Garand (MSC) + AIRS RT modellers © Crown copyright 2005 Page 2 Talk overview RT models – the basics Possible sources of bias in RT models Examples of RT model bias Forward model Jacobians How can we reduce biases? © Crown copyright 2005 Page 3 Fast RT models Given an atmospheric state X (T,q,Ts, …) a fast RT model H allows one to compute the top of atmosphere radiance for a radiometer channel within a few msecs. This allows Observed minus Calculated radiance values to be computed “on the fly” in an NWP model In addition for assimilation and retrievals the gradient of the RT model with respect to the atmospheric state variables is also required. This is called the Jacobian. Biases are possible in both the forward model and Jacobian calculations © Crown copyright 2005 Page 4 Fast RT model: Terminology y = H (X ) Where: y is vector of radiance channels ATOVS is 20, AIRS can be 2378, IASI can be 8461 X is state vector: Profile: T(p), q(p), oz(p), etc on 40-100 levels Surface: Ts,qs,Ps, Cloud: LWC(p), IWC(p) Precip: Hydrometeor profile H is observation operator for radiance measurements and comprises: Interpolation of model fields to observations Fast radiative transfer model © Crown copyright 2005 Page 5 Fast model process R1, R2, R3... T(p) q(p) Optical depths O3(p) P(1) P(n) Ts, qs, Ps, εs © Crown copyright 2005 Page 6 Radiative Transfer Equation 0 Rν ≅ ε ν Bν (Θ s )Ts ,ν + ∫ Bν (Θ( p )) ps + (1 − ε ν )Ts ,ν ∂Tν ( p,θ u ) dp ∂p ∂Tν* ( p,θ d ) ∫0 Bν (Θ( p)) ∂p dp + ρν Ts,ν Tν ( p s ,θ sun ) F0,ν cosθ sun ps The first term is the surface emission The second term is the upwelling thermal emssion The third term is the reflected downwelling radiation The last term is the reflected solar radiation © Crown copyright 2005 Page 7 Jacobian/Tangent Linear/Adjoint Operators to compute gradient of model y=H(X) about initial state X. The full Jacobian matrix H is ∂y H≡ ∂X y has dimension of number of channels and X the number of state vector variables H can be a large matrix if more than 1 profile at a time is operated on (hence the TL/AD operators) but for 1 profile it is chans x (levels x ngases + surface) so is used in 1DVar applications. © Crown copyright 2005 Page 8 Infrared channels in 15µm CO2 band IASI channels HIRS channel Spectrum of infrared radiation from atmosphere HIRS 19 channels vs IASI 8461 channels © Crown copyright 2005 Page 9 Fast Model Approaches Linear regression (profile ⇒ optical depth) On fixed pressure levels (RTTOV, PLOD, SARTA) On fixed absorber overburden layers (OPTRAN) Physical method (MSCFAST) Correlated K distribution (Synsatrad) Optimal Spectral Sampling (OSS see Jean-Luc’s talk) Neural nets (LMD) PCA approach for advanced IR sounders (see Xu Liu) © Crown copyright 2005 Page 10 Talk overview RT models – the basics Possible sources of bias in RT models Examples of RT model bias Forward model Jacobians How can we reduce biases © Crown copyright 2005 Page 11 Sources of bias in RT models (1) Underlying spectroscopy: Line parameters (frequency, strength, width, temp dep., line mixing….) Water vapour continuum parameterisation Non-LTE for SWIR channels Zeeman splitting for high peaking channels CFC absorption Assumptions made in Line-by-Line model Quantisation (levels, spectral) Line shape formulation Combination of line and continuum absorption © Crown copyright 2005 Page 12 Bias Overview 650-1600 cm-1 Colour coding>> .20mb....Troposphere....1000mb. © Crown copyright 2005 Page 13 Bias Overview 2180-2670 cm-1 Non-LTE Colour coding>> .20mb....Troposphere....1000mb. © Crown copyright 2005 Page 14 Comparison of AIRS forward models 284 w.v. continuum RFM RTTOV−7 ARTS FLBL Gastropod LBLRTM OPTRAN PCRTM OSS SARTA 4A HARTCODE SIGMA−IASI RTTOV−8 CFCs Br. Temp (degK) 283.5 283 282.5 282 500 © Crown copyright 2005 550 600 AIRS channel number 650 700 Page 15 Water vapour continuum © Crown copyright 2005 Page 16 Non-LTE 2240-2390 cm-1 RTTOV+Non-LTE contribution calculated by the Oxford RFM AIRS daytime-nighttime bias Non-LTE Thanks: Niels Bormann, Anu Dudhia, Phil Watts © Crown copyright 2005 Page 17 O-B difference - Large positive bias in the SW-IR in the day-time due to Non LTE effect in upper sounding chs and sunglint in window 2387cm-1 (4.19micron) Non-LTE © Crown copyright 2005 2392cm-1 (4.18micron) 2618cm-1 (3.82micron) sunglint Page 18 Sources of bias in RT models (2) Fast model parameterisation: Regression or look up table technique Unrepresentative profile training set Level quantisation, plane parallel assumption Omission of reflected solar term Surface emissivity parametrisation Smaller biases over ocean larger over land Incorrect instrument spectral response function Problem for some IR radiometers Not an issue for microwave and HiRes IR Errors in cloud or precipitation radiative properties Water vapour clouds reasonable Ice crystals more difficult © Crown copyright 2005 Page 19 RTTOV fast model errors Fitting errors of RTTOV−7 for AIRS 117 ECMWF independent profiles Mean RTTOV−LbL Br. Temp difference (K) 0.4 Note fairly small compared to spectroscopic biases 0.2 0.0 −0.2 −0.4 600 © Crown copyright 2005 1000 1400 1800 2200 −1 Wavenumber (cm ) 2600 3000 Page 20 Errors in MODIS spectral response functions courtesy of Hong Zhang (CIMSS) MODIS minus AIRS convolved over MODIS SRF MODIS band 35 (13.9 μm) brightness temperature differences using original SRF (black) and using MODIS SRF shifted +0.8 cm -1 (red) unshifted shifted From Tobin et al 2005 SRF shifted for CO2 channels band 36: +1.0 cm -1 band 35: +0.8 cm -1 band 34: +0.8 cm -1 band 33: -0.15 cm -1 show better agreement with AIRS for all temperatures © Crown copyright 2005 Page 21 1.00 Emissivity temperature dependence 0.99 Emissivity 0.98 From Newman et. al. 2005 0.97 o 27.4 C o 17.0 C o 8.4 C o 0.5 C Calculated Fresnel emissivity 0.96 0.95 0.94 Pure water (zero salinity) No need to consider distribution of wave slopes, i.e. use Fresnel equations Calculated emissivity from Downing and Williams refractive indices (1975 paper, measured at 27°C) 0.002 Δε (obs-calc) 0.000 -0.002 -0.004 Trend with decreasing temperature -0.006 -0.008 800 © Crown copyright 2005 900 1000 1100 -1 Wavenumber (cm ) 1200 Page 22 Talk overview RT models – the basics Possible sources of bias in RT models Examples of RT model bias Forward model Jacobians How can we reduce biases © Crown copyright 2005 Page 23 How to validate RT models? Use an independent set of profiles (e.g. ECMWF diverse 117 profile set) but with same LbL model computed transmittances Gives estimate of inherent fast model accuracy of trasmittances and TOA radiances Fast model comparisons (e.g. Garand et al 2001 for HIRS and Saunders et. al. for AIRS) radiances and jacobians Gives performance of model compared to others Line-by-line model comparisons (e.g. LIE) Gives estimate of underlying LbL model accuracy Comparisons with real satellite data using NWP fields Allows validation over wide range of atmospheres Comparison with aircraft data (e.g. NAST-I) Limited sampling but can reduce uncertainties of variables © Crown copyright 2005 Page 24 RTTOV biases in ECMWF model 21 days of O-B in March 2004 Observed-Sim ulated ATOVS 3 RTTOV-7 RTTOV-8 1 0 -1 -2 39 37 35 33 31 29 27 25 23 21 19 17 15 13 11 9 7 5 3 -3 1 Mean bias degK 2 ATOVS channel num ber © Crown copyright 2005 Page 25 Garand fast model intercomparison for HIRS channels Line by line models © Crown copyright 2005 Page 26 Observed - Calculated AIRS spectra CO2 Biases © Crown copyright 2005 Ozone Water CO2 Some biases are from NWP model but some are from RT model Page 27 AIRS Observed-Simulated NIGHT The 4.2 micron CO2 channel bias is +0.15K The bias of the 14 micron CO2 channels is -0.2K below 500 mb and shifts to +0.15K between 500 and 100 mb The bias in the water channels The 4.2 micron channels fit the T(p) within shows a similar pattern 0.1K. Almost equal to the NEDT.The 14 um channels with within 2-3 x NEDT The water channels differ from ECMWF by more than ten time NEDT Courtesy George Aumann/JPL © Crown copyright 2005 Page 28 AIRS RT model comparison Compare AIRS RT models Compute BTs for all 2378 channels for 52 profiles For some models compute jacobians for a selection of 20 channels For some models compute layer to space transmittances of 20 channels © Crown copyright 2005 Page 29 AIRS RT model Comparison Model RTTOV-7 RTTOV-8 Optran OSS LBLRTM RFM Gastropod ARTS SARTA PCRTM 4A FLBL σ-IASI Hartcode © Crown copyright 2005 Participant R. Saunders, METO R. Saunders, METO Y. Han, NESDIS J-L. Moncet, AER J-L. Moncet, AER N. Bormann, ECMWF V. Sherlock, NIWA A. Von Engeln, Bremen S. Hannon, UMBC Xu Liu, NASA S. Heilliette, LMD D.S. Turner, MSC C. Serio, Uni Bas F. Miskolczi, NASA Direct Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Jacobian Yes Yes Yes Yes Yes Yes Yes No No Yes Yes Yes Yes No Page 30 Diverse ERA-40 52 Profile set 0.1 Pressure hPa 1.0 100 10.0 200 300 100.0 190 210 Pressure hPa 1000.0 170 400 500 600 230 250 270 290 Temperature degK700 0 310 330 800 1 1000 0 All 52 profiles dynamically consistent with all 3 variables Pressure hPa 900 0.01 10 0.02 Specific humidity kg/kg 100 1000 © Crown copyright 2005 0.03 0 5e−06 1e−05 1.5e−05 Ozone mass mixing ratio kg/kg 2e−05 Page 31 Mean bias for all 49 diverse profiles 0.10 RTTOV−7 ARTS FLBL Gastropod LBLRTM OPTRAN PCRTM OSS SARTA 4A HARTCODE SIGMA−IASI RTTOV−8 Model−RFM (degK) 0.05 0.00 −0.05 −0.10 0 © Crown copyright 2005 500 1000 1500 AIRS channel number 2000 Page 32 Bias averaged over channels © Crown copyright 2005 Page 33 Model bias for different bands Model-RFM for different spectral regions 0.9 650-770cm-1 chans 2-407 T 0.8 770-980cm-1 chans 408-953 Sfc+Cld 1000-1070cm-1 chans 1001-1133 Ozone 0.7 1250-1350cm-1 chans 1328-1487 Q 2150-2250cm-1 chans 1866-1939 T 2350-2420cm-1 chans 2017-2142 T 0.5 2420-2600cm-1 chans 2143-2318 Sfc 0.4 0.3 0.2 0.1 © Crown copyright 2005 T eD N TT O V8 I R IA S Si gm a- O D E AR TC 4A H SA R TA SS O R TM PC AN PT R O TM LB LR as tro G FL BL TS AR TT O V7 0 R St. dev (degK) 0.6 Page 34 Comparison with observations OSS 1.0 −1.0 −1.0 −3.0 −3.0 500 1000 1500 −5.0 2000 0 500 3.0 1.0 1.0 −1.0 −1.0 −3.0 −3.0 500 1000 1500 −5.0 2000 0 500 RTTOV−8 3.0 1.0 −1.0 −3.0 0 500 1000 1500 −3.0 0 500 1000 2000 AIRS channel number © Crown copyright 2005 −5.0 0 500 1500 2000 1.0 1.0 −1.0 −1.0 −5.0 0 500 1000 1500 2000 0 500 Sigma_IASI 1.0 1.0 −1.0 −1.0 −3.0 −3.0 −5.0 1500 2000 1500 2000 −3.0 −3.0 −5.0 1000 Gastropod 3.0 3.0 1000 −3.0 3.0 3.0 500 2000 −1.0 5.0 5.0 0 1500 1.0 LBLRTM 5.0 −5.0 1000 3.0 5.0 ARTS 5.0 −5.0 −1.0 −5.0 2000 Model − AIRS obs (degK) 3.0 Model − AIRS obs (degK) Model − AIRS obs (degK) 5.0 0 1500 1.0 4A SARTA 5.0 −5.0 1000 3.0 1000 1500 2000 RFM 5.0 Model − AIRS obs (degK) 0 5.0 Model − AIRS obs (degK) Model − AIRS obs (degK) 3.0 1.0 HARTCODE 5.0 5.0 3.0 −5.0 PCRTM OPTRAN 5.0 0 500 1000 1500 2000 3.0 1.0 −1.0 −3.0 −5.0 0 500 1000 1500 2000 AIRS channel number Page 35 Summary of model –AIRS observations Model - AIRS Obs M ean bias all 1.2 RM SD all M ean bias no CO2/O3 1 RM SD no CO2/O3 0.8 0.6 0.4 0.2 0 -0.2 -0.4 © Crown copyright 2005 Page 36 Forward model error correlation matrix for RTIASI © Crown copyright 2005 Page 37 Talk overview RT models – the basics Possible sources of bias in RT models Examples of RT model bias Forward model Jacobians How can we reduce biases © Crown copyright 2005 Page 38 AIRS channels selected 300 290 Br. Temp (degK) 280 270 260 250 240 230 220 210 200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 AIRS channel number © Crown copyright 2005 Page 39 Comparison of Jacobians Temperature jacobian Profile 1 AIRS channel 77 0.1 Pressure (hPa) 1.0 10.0 RFM OSS Gastropod PCRTM OPTRAN LBLRTM 4A FLBL RTTOV−8 RTTOV−7 sigma−iasi 100.0 1000.0 −0.01 0.01 0.03 0.05 0.07 0.09 K/K © Crown copyright 2005 Page 40 Measure of fit For the jacobians the results from each model were differenced with RFM one of the line-by-line models in order to be able to conveniently examine the inter-model differences. For the jacobians the “measure of fit” adopted by Garand et. al., [2001] was used defined as: M = 100 × ∑( X − X ) ∑( X ) i 2 ref 2 ref where Xi is the profile variable at level i and Xref is the reference profile variable which was taken to be the RFM model profile for this study. © Crown copyright 2005 Page 41 Comparison of temperature jacobians © Crown copyright 2005 Page 42 Comparison of water vapour jacobians © Crown copyright 2005 Page 43 Issues for jacobians Temperature jacobian Profile 22 AIRS channel 787 0.10 1.00 Pressure (hPa) This is a weak temperature jacobian but some of the models (e.g. 4A, PCRTM) have very unphysical structures. Does this matter? RFM OSS Gastropod PCRTM OPTRAN LBLRTM 4A FLBL RTTOV−8 RTTOV−7 sigma−iasi 10.00 The measure of fit is not ideal for assessing these features. 100.00 1000.00 −0.001 0 0.001 0.002 K/K © Crown copyright 2005 Page 44 Validation within NWP model RTTOV-5 Model background error as HIRS-12 radiance RTTOV-7 HBHT plotted © Crown copyright 2005 Page 45 Talk overview RT models – the basics Possible sources of bias in RT models Examples of RT model bias Forward model Jacobians How can we reduce biases © Crown copyright 2005 Page 46 Reducing bias in fast RT models For RTTOV a γ factor was developed which scales the channel optical depth and can be useful if the filter response is in error. Another constant offset δ can also be employed which is the mean bias for that channel It was used with some success on AIRS data by Phil Watts at ECMWF and has been used in the past for HIRS. © Crown copyright 2005 Page 47 δ,γ - Estimation 1. Monthly mean ob-fg @ 5 o + Monthly mean NWP(T,Q,O) 2. Effect of γ=1.05 using NWP 3. Best fit x=[δ,γ] : ( [ d m − δ + ε (γ )i , j 1 J= ∑ 2 σo 2 m © Crown copyright 2005 ]) 2 + 1 2σ 2 b ( x − xb ) 2 Page 48 How to reduce RT model bias Improve reference LbL model spectroscopy through new measurements (e.g. ARM, satellite, lab, a/c) and theoretical calculations (line mixing, w.v. continuum) >>Encourage continuing research and measurements Better characterise the channel spectral responses before launch and understand how they will change in orbit. >>Space agencies conduct adequate pre-launch tests. Retain records of instrument characteristics. Improve fast RT model accuracy, include more variable gases, reflected solar, aerosols etc and more levels>>Encourage continuing research in fast RT models >> More powerful computers Better surface emissivity models for ‘window’ channels. Better models of cloud and precip >>Encourage continuing research and measurements As a last resort apply a bias correction. © Crown copyright 2005 Page 49 Thanks Any questions? © Crown copyright 2005 Page 50
