An Introduction to the JCSDA Community Radiative Transfer Model (CRTM) Yong Han NOAA/NESDIS JCSDA

Transcription

1 An Introduction to the JCSDA Community Radiative Transfer Mode CRTM Yong Han NOAA/NESDIS JCSDA

2 Outine The roe of a fast radiative transfer mode in sateite data assimiation CRTM main modues Radiative transfer RT equation appied CRTM surface emissivity/refectivity modes RT soution in cear sky environment CRTM fast transmittance mode RT soution in coudy/aeroso environment CRTM Forward, Tangent-inear, Adjoint and K-Matrix modes CRTM user interface

3 Why need a fast RT mode? ] [ ] [ 2 2 m F m T m b T b y x y E E y x y x x B x x x J + + Background mode state x b and its covariance B Measurement y m and its error covariance E m Radiative transfer RT mode yx and its error E F Variationa Anaysis: the cost function 0 } { x y y E x H x x B x J m T b Minimization: } { j i j i x y h x H, Jacobian matrix with respect to state variabes x An RT mode maps state variabes to radiances and it can be used to retrieve information about the state variabes from the radiance measurements. CRTM is a fast RT mode, which empoys many computationa efficient agorithms to meet the requirements of the operationa data assimiation system.

4 Community Contributions Community Research: Radiative transfer science UWisc Successive Order of Iteration University of Coorado DOTLRT UCLA Deta 4 stream vector radiative transfer mode Princeton Univ snow emissivity mode improvement NESDIS Advanced doubing and adding scheme, surface emissivity modes, LUT for aerosos, couds, precip AER Optima Spectra Samping OSS Method UMBC SARTA Core team ORA/EMC: Smooth transition from research to operation Maintenance of CRTM CRTM interface Benchmark tests for mode seection Integration of new science into CRTM

5 What CRTM does? Compute sateite radiances Forward mode Compute radiance responses to the perturbations of the state variabes Tangent-inear mode Compute Adjoint Adjoint mode Compute Jacobians K-matrix mode

6 CRTM Major Modues pubic interfaces CRTM Initiaization Forward mode Tangent-inear mode Adjoint mode K-matrix mode CRTM Destruction SfcOptics Surface Emissivity Refectivity Modes AerosoScatter Aeroso Absorption Scattering Mode CoudScatter Coud Absorption Scattering Mode AtmAbsorption Gaseous Absorption Mode RTSoution RT Sover Source Functions Supported Instruments IR & MW TIROS-N to NOAA-8 AVHRR TIROS-N to NOAA-8 HIRS GOES-8 to 3 Imager channes GOES-8 to 3 sounder channe 08-3 GOES-R ABI Terra/Aqua MODIS Channe -0 METEOSAT-SG SEVIRI Aqua AIRS Aqua AMSR-E Aqua AMSU-A Aqua HSB NOAA-5 to 8 AMSU-A NOAA-5 to 7 AMSU-B NOAA-8 MHS TIROS-N to NOAA-4 MSU DMSP F3,5 SSM/T DMSP F4,5 SSM/T2 DMSP F6 SSMIS NPP ATMS Coriois Windsat METOP-A AMSUA, MHS, HIRS, AVHRR

7 Radiance: Two of the fundamenta variabes in CRTM Specific intensity: I ν mw/m 2.sr.cm - the fux of energy in a given direction per second per unit frequency range per unit soid ange per unit area perpendicuar to the given direction Brightness Temperature: BT ν Kevin which is the Inverse of the Panck function BT ν B ν I ν B ν 3 2hν T 2 hν / kt c e Atmospheric transmittance: p 0 p e σ p' dp' e.g. if I s is a upward radiance emitted from the surface, then I s τ ν p s is the amount of energy contribution from the surface received by a sateite sensor. τ ν p τ ν p p s { TOA

8 Radiative Transfer Equation Stokes vector: { I, Q, U, V} where I I v + I h, Q T describes the intensity, phase and poarization of the radiation fied. The current operationa CRTM does not mode the Stokes vector; instead CRTM soves the foowing equation for a scaar intensity: di τ, Ω ω τ --- optica path μ dτ The current operationa CRTM assumes: I τ, Ω + P τ, Ω, Ω' I τ, Ω' dω' 4π τ / μ + ωp τ, Ω, Ω F / 4π e + ω B T τ p0 p Layer Soar radiation & Cosmic background the atmospheric radiation is unpoarized exception: O2 eeman absorption and emission in the mesosphere 2 Poarization is negected for IR sensors. Coud Absorbing gases pn- pn Layer n Surface aeroso

9 CRTM surface emissivity/refectivity modes

10 Bidirectiona refectance distribution function BRDF: BRDF θ, ϕ, θ, ϕ Refectance: i i Specuar surface: i i r r dir θr, ϕr I θ, ϕ cos θ dω Lambertian perfect rough surface: i i i i i r r i i θ, ϕ ρ θ, ϕ BRDF θ, ϕ, θ, ϕ cos θ dω Emissivity by Kirchhoff s aw: ε θ, ϕ ρ θ, ϕ i i i i i i Ii x i i r r i i θ, ϕ dω i BRDF θ, ϕ, θ, ϕ ρ θ δ θ θ δ ϕ ϕ /cos θ sin θ i i r r i r i r i r r r ϕ i y BRDF θ, ϕ, θ, ϕ ρ π θ i ϕ r θ r di r θ, ϕ r r dω r CRTM assumes a specuar refection for MW sensors and Lambertian refection for IR sensors, and uses reationship: ρ θ ε θ but ε θ is not imited to the two specia cases r P i θ θ Pr-εP i P i θ Specuar surface Air Rough surface Air

11 Poarization in surface emission and scattering MW Emission and scattering by a surface is usuay poarization-dependent. A radiometer with a ineary poarized antenna woud measure the same amount of atmospheric emission randomy poarized regardess of the direction of the antenna poarization vector p a ; but woud receive a different amount of radiation from the surface when the p a vector changes orientation Since the atmospheric radiation is assumed unpoarized, we may sti use a scaar RT equation to compute a radiance with a poarization p a by using a surface emissivity/refectivity that is a combination of poarization components. Exampe: the AMSU sensor has channes with inear poarized antennas. For v poarized antennas when viewing nadir direction, p a is in the scanning pane: 2 ε p nadir V po. εv cos φ + ε h sin a 2 φ and for h poarization p a is perpendicuar to the scanning pane: 2 ε p nadir h po. εv sin φ + ε h cos a 2 φ Verticay po. E vector O k φ Antenna z Scan O k Verticay po. E vector O Refector P a varies its orientation Surface The circes represent the horizonta poariztion perpendicuar to the k,z pane Mode cacuations: soid ine for wind speed 3.5 m/s; dashed ine for 3.5 m/s. Measured: crosses for wind speed 3.5 m/s; circes for 0.5 m/s Over ocean surface

12 CRTM surface emissivity/refectivity modue The CRTM surface emissivity modue is spit into 8 sub-modues to accommodate new mode impementations and mode improvement.

13 ε IR Sea Surface Emission Mode IRSSE ν ν θ ν ν ν ˆc2 w, 4,,,,, θ, ν ˆc w w c w + c w + c w θ 0 3 c 0 c 4 are regression coefficients, obtained through regression against Wu-Smith mode. The IRSSE mode is a parameterized Wu-Smith mode for rough sea surface emissivity

14 IR emissivity ookup tabe for and surfaces Surface types incuded in the IR emissivity database Carter et a., 2002: Surface Type Compacted soi Tied soi Sand Rock Irrigated ow vegetation Meadow grass Scrub Broadeaf forest Pine forest Tundra Grass soi Broadeaf/Pine forest Grass scrub Oi grass Urban concrete Pine brush Broadeaf brush Wet soi Scrub soi Broadeaf70/Pine30 Water Od snow Fresh snow New ice

15 Microwave Ocean Emissivity Mode FASTEM- Engish and Hewison, 998: Mode inputs: sateite zenith ange, water temperature, surface wind speed, and frequency Mode outputs: emissivity Vertica poarization and emissivity horizonta poarization

16 NESDIS Microwave Land Emission Mode LandEM Three ayer medium: I 0 I I τ 0, μ R2 0 R 2 Layer, ε τ 0 I0 R2 I τ, μ I τ R, μ 23 Layer2, ε 2, B T desert, canopy, τ I e3b T Layer3, ε 3 2 Emissivity derived from a two-stream radiative transfer soution and modified Fresne equations for refection and transmission at ayer interfaces: ε β [ + γe ] + α R [ β γe 2k ττ 0 2 αr2 + R2 2k ττ 0 βr2 β R2 γe 2k τ τ Conditions using LandEM: over and: f < 80 GHz, use LandEM; f > 80 GHz, e_v e_h 0.95 over snow: f < 80 GHz, use LandEM; f > 80 GHz, e_v e_h ] Weng, et a, 200

17 Microwave empirica snow and ice surface emissivity mode Emissivity Database: 2 Snow type discriminators are used to pick up snow type and emissivity: DI N N 2 i a0 + a jtbj + a2 jtbj + a j j + a3ts 3 cosϑ 3 Supported sensors: AMSU, AMSRE, SSMI, MSU, SSMIS T b,j e.g. AMSU window channe measurements

18 Radiative transfer soution under cear sky conditions sun sun s s n n s n k k k k F p I T B T B I θ π θ τ ρ τ ε τ ε τ τ ν ν ν ν ν ν ν ν ν ν ν ν ν cos /,, 0,,,, k j j e k cos / θ σ τ Transmittance at the kth eve: σ k optica depth of the kth ayer 2 3 Contribution from the atmospheric absorbing gases; 2 Contribution from surface emission attenuated by the atmosphere 3 Surface refected downweing radiation from the atmosphere and space cosmic background attenuated by the atmosphere. 4 Surface refected soar radiation attenuated by the atmosphere c d n n k k d k d k d s I T B I,,,, θ τ θ τ θ τ θ ν ν ν ν ν + MW: θ d sateite zenith ange specuar surface refection IR : θ d diffuse ange Lambersian surface refection

19 Weighting function: or wk w Weight function and radiance Jacobian τ ν, k τν, k / zk zk k τ ν, k τν, k/n pk n pk Jacobian radiance derivative with respect to state variabes: I x k TOA } Emission decreases x k - air temperature, water vapor mixing ratio, etc Layer contribution When the ayer moves up Attenuation decreases The atmosphere contribution the first term of the RT soution in the previous side can be express as I atm ν n k Δz w k k, νbν Tk a The atmospheric contribution is the weighted sum of the source functions; b The weighting function tes the reative importance of the contribution from each atmospheric ayer. c Weighting function does not depend on the ayer thickness. 2 The Jacobian is the radiance response to a unit perturbation of the state variabe; it depends on the ayer thickness.

20 Weighting function and Jacobian profies Weighting function Jacobian with respect to temperature Jacobian with respect to H2O mixing ratio times ayer mixing ratio ch4 AMSUA ch3 ch2 ch ch0 ch9 ch8 ch7 ch6 ch5 ch4 MHS ch3 ch ch2 ch4 ch5 Computed with CRTM for US standard atmosphere over ocean surface

21 CRTM fast transmittance mode Microwave and infrared spectra Why we need fast agorithm Transmittance parameterization There are other we known transmittance modes: RTTOV UK, OSS AER, Inc and SARTA UMBC. The JCSDA RT team is integrating them into CRTM.

22 Microwave transmittance spectrum

23 MW O 2 transmittance near 60 GHz eeman-spitting effect 9+, eft-circuar poarization B e Earth s magnetic fied strength. θ B ange between the observation direction and the Earth s magnetic fied. Be 60 µt

24 IR tota transmittance spectrum

25 IR tota transmittance spectrum 2

26 HIRS/3 spectra response functions SRFs

27 Why need fast agorithm: I ch Fast transmittance modue In the atmosphere, the absorption ine width α L is about 0.05 cm - at 000mb and cm - at 250 mb. So, e.g., for a sensor with cm - passband, a arge number of monochromatic radiance cacuations are needed for channe radiance simuation: N i I ν i φ v i From Goody The channe s spectra response function SRF Current operationa systems can not hande such computation wavenumber offset from ine center, cm- w idth0.025cm- p250mb w idth0.025cm- p500mb w idth0.05cm- p000mb Soution: parameterize the optica depth σ ch,k, defined as σ n τ ch, k / τ ch, ch, k k Parameterization: σ and τ n ch, k c 0, k + ci, kxi, k i N ch, k τ νi, kφv i i Predictors, such as T and water vapor The radiance is then computed with the reguar RT equation without the need for spectra integration. CRTM currenty is impemented with the OPTRAN transmittance agorithm

28 Radiance errors due to transmittance mode uncertainty RMS fitting error Tota Dry Water Vapor RMS fitting error K Tota Dry Water vapor Ozone AMSU channe number HIRS channe number Radiance Jacobians with respect to water vapor, compared with LBLRTM

29 Comparison between SSMIS observations and simuations with/without eeman-effect Without incuding eeman-effect in the mode. Channes 23 & 24 are not affected by eeman-spitting Coocated temperature profies for mode input are retrievas form the SABER experiment. Sampe size: 097 sampes

30 CRTM coud absorption/scattering, aeroso absorption/scattering and RT soution modues

31 Coud absorption/scattering modue provide coud optica parameters for RT soution modue Six coud types: water, ice, rain, snow, graupe and hai NESDIS/ORA ookup tabe Liu et a., 2005: mass extinction coefficient, singe scattering abedo, asymmetric factor and Legendre phase coefficients. Sources: IR: spherica water coud dropets Simmer, 994; non-spherica ice coud partices Liou and Yang, 995; Macke, Mishenko et a.; Baum et a., 200. MW: spherica coud, rain and ice partices Simmer, 994.

32 Aeroso absorption/scattering modue provide aeroso optica parameters for RT soution modue GOCART aeroso profies: Dust, Sea Sat, Organic carbon, Back carbon, Sufate. Optica parameter ookup tabe. Dust abedo Size μm waveength Dust Dust mass extinction asymmetry facto waveength waveength

33 RT soution for coud/aeroso scattering environment: Advanced Doubing-Adding Method ADA AtmOptics Optica depth, singe scattering Abedo, asymmetry factor, Legendre coefficients for phase matrix Panck functions Panck_Atmosphere Panck_Surface SfcOptics Surface emissivity refectivity Compute the emitted radiance and refectance at the surface without atmosphere Compute ayer transmittance, refectance matrices by doubing method. New agorithm compute ayer sources from above ayer transmittance and Refectance anayticay. Loop from bottom to top ayers Output radiance Combine transmittance, refectance, upweing source current eve and added ayers to new eve.7 times faster then VDISORT; 6 times faster than DA Maximum differences between ADA,VDISORT and DA are ess than 0.0 K. Liu and Weng, 2006

34 Time series of AMSU-A, MHS observations versus CRTM simuations using CoudSat data non-precipitating weather Rain rate near surface Coud cassification Mode simuations with coud component on back and off yeow; AMSU-A and MHS observations red, 07/27/2006 Mode input: coud iquid/ice content and partice size profies from CoudSat Large differences between Observations and simuations near 3. are due to CoudSat data that excude precipitation. Upper two panes: Red AMSUA+MHS retrievas Back derived from CoudSat Radar

35 Time series of AVHRR observations versus CRTM simuations using CoudSat data Coud cassification Coud cassification Mode simuations with coud component on back and off bue AVHRR observations red Mode input: coud iquid/ice content and partice size profies from CoudSat

36 Mean & RMS difference between AMSU-A, MHS & AVHRR observations and simuations under coudy conditions The differences between the observations and simuations are significanty reduced with the incusion of modeing coud absorption and scattering AMSU-A Mean & RMS Diff. obs. simuation w. coud on Mean & RMS Diff. obs. simuation w. coud off 23.8GHz 3.4GHz 50.3GHz Sampe size GHz Mean difference obs simuation with coud component on Mean difference obs simuation with coud component off RMS difference obs simuation with coud component on Mean difference obs simuation with coud component off Sampe size 3396 AVHRR cm cm- Mean difference obs simuation with coud component on Mean difference obs simuation with coud component off RMS difference obs simuation with coud component on Mean difference obs simuation with coud component off MHS 89.0GHz 50.0GHz Mean difference obs simuation with coud component on Mean difference obs simuation with coud component off RMS difference obs simuation with coud component on Mean difference obs simuation with coud component off Sampe size 0692

37 CRTM Tangent-inear, Adjoint and K-Matrix Jacobian modes Order of deveoping these modes: FW TL AD K _ Matrix

38 Forward mode: Y FX X x, x,..., } { 2 { 2 x n Y y, y,..., } y m T T State vector n state variabes Radiance vector m channes FW mode may be considered as a composition of a set of K functions: F X F K... F 2 [ F 0 X ] or expressed with the hep of the intermediate variabes as F 0 X,..., F,..., k F k k Y 2 In CRTM, many of the functions F are coded expicity with subroutines or functions: - input variabe vector output variabe vector

39 Tangent-inear TL mode: X X H Y δ δ δy δx perturbation of Y perturbation of X }, ;,, {, n j m i x y H j i j i HX, a matrix with eements: Jacobians derivatives of the radiance with respect to a state variabe H H H H Y K K K K δ δ Appying the chain rue to : } { } {, j i j i F H H 0 0,,..., k k k k H H X H δ δ δ δ δ δ In CRTM, is deveoped by differentiating the FW counterpart. H δ δ, δ δ or expressed as Inputs where F Naming convention: If is a FW variabe name, then δ is named is _TL; 2 if Sub is the FW subroutine or function name, then the corresponding Tangent-inear subroutine or function is named as Sub_TL. Output

40 Adjoint AD mode: Let the function J. transforms the radiance vector Y FX into a scaar: J JY Note, CRTM does not incude this function The gradient of J with respect to X: X J X where Y Y X J --- AD mode J J J [,..., ] x x n T yi Y {, j, n; i, m} x X j Y J J J [,..., ] y y m T both vectors transpose of the Jacobian matrix Since F,..., 0 X and Y F X F k F [ F... F k k ] we have J k k k 2 J F F F... F So J is aso a function Define Adjoint variabes: δ J, δ X J, δ Y X Y J

41 J Y J Y X X Y H H H Y X H X T K T T T 2 δ δ δ Into the form: So we can write 2 2 2,,,, H X H H Y H T T K T K K T K K δ δ δ δ δ δ δ δ or T H δ δ In CRTM, is deveoped by reversing the order of the operations in the TL counterpart, foowing a set of rues Giering and Kaminski, 998 δ δ Input Output H δ δ Naming convention: if is the FW variabe, the corresponding AD variabe is named as _AD; if Sub is the FW routine, then Sub_AD is named as the AD routine. Adjoint AD mode Cont.:

42 The outputs of the TL and AD modes: TL mode provides: or δy i yi yi yi δx + δx δx x x x i, m δ Y H X δx 2 n n A summation over the state variabe dimension AD mode provides: δ X or δ x j j, n T H X δ Y y y2 ym δ y + δ y δ y x x x j j j m A summation over the channe dimension { δ y i, i, m} are the AD mode input variabes. If they hod the vaues Y J { J / yi, i, m}, then the output δ x j hod the vaues X J --- the gradient of the J function. 2 The TL and AD modes do not provide Jacobians uness you set one of the inputs δx j for the TL mode and δy i for the AD mode and set the reset of the deta inputs to zero and oop over the range of i or j --- a sow process.

43 K-matrix mode compute the Jacobian matrix H: K-matrix mode is a sighty modified version of the AD mode; The modification is to separate the terms yi / x j δ yi in the summation expression see previous side. The K-matrix mode may be expressed as X where _ X _ K K [ h δ y, h δ y,..., h m δ y 2 2 m y y y h [,,..., ] i i i T i x x2 xn yi x i, j; i, m; j, n} { yi, i, m; j x j { δ δ ] n} δy,, δy m are part of the K-matrix mode input variabes To obtain Jacobians, set a the inputs δy,, δy m to one. Naming convention: in CRTM K-Matrix mode, δx i,j is named as x_k and δy i as y_k.

44 CRTM user interface CRTM software characteristic: A set of Fortran subroutines and functions; users ca CRTM from their appication programs. Structure variabes derived types are used as input and output variabes in the routine interfaces. Benefits: cean, 2 adding variabes does not change the interfaces Disadvantages: variabes are hidden under the structure variabe name e.g. X.x and X.x2 are hidden in the interface where ony X appears; 2 it is easy to forget initiaize those variabes that are not interested to the users. There is a set of coefficient data that are oaded during CRTM initiaization stage. These data are incuded in severa fies, some of which are sensor/channe independent and some are sensor/channe dependent.

45 CRTM Caing procedure an exampe: CRTM User Interface 2 CRTM Initiaization oad coefficient data In this process, the set of sensors supported in the foowing cas are determined. Memory aocation using CRTM routines for structure pointer array members { May be repeated CRTM FW mode Sensor seection among the sensors specified during CRTM initiaization or Set CRTM input variabes or or CRTM TL mode CRTM AD mode CRTM KM mode or Ending { process Memory deaocation using CRTM routines for aocated structure pointer array members CRTM destruction deaocate memory for interna variabes

46 CRTM initiaization: CRTM User Interface 3 Error_status CRTM_Init ChanneInfo, &! Output SensorID, &! input CoudCoeff_Fie, &! input AerosoCoeff_Fie, &! input EmisCoeff_Fie! Input SensorID : string array containing a ist of the sensor IDs e.g. hirs3_n7, amsua_n8, etc; array size n_sensors specified by the user. The sensor IDs are used to construct the fies for the SpcCoeff and TauCoeff fie names: e.g. hirs3_n7 wi be used for hirs3_n7.spccoeff.bin and hirs3_n7.taucoeff.bin CoudCoeff_Fie, ArosoCoeff, EmisCoeff: fie names for coefficient data fie used for coud, aeroso, surface emission and scattering cacuations; the data are currenty not sensor specific. ChanneInfo : structure array type ChanneInfor_type containing sensor/channe information when returned from this function, array size n_sensors. CRTM destruction: Error_status CRTM_Destroy ChanneInfo The memory for ChanneInfo is reeased, 2 a dynamicay aocated memory for interna variabes is reeased.

47 CRTM User Interface 4 Caing CRTM FW mode exampe: Error_Status CRTM_Forward Atmosphere, &! Input Surface, &! Input GeometryInfo, &! Input ChanneInfo2:2, &! Input RTSoution! Output Atmosphere: structure array type Atmosphere_type containing data describing atmospheric state; array size n_profies specified by user. e.g. Atmospere%temperature is an array of size n_ayers specified by user containing the temperature profie for the first atmospheric profie. Surface: structure array type Surface_type of size n_profies containing data describing surface state. e.g. Surface%water_temperature is a scaar variabe for the water surface temperature. GeometryInfo: structure array type GeometryInfo_type of size n_profies containing sateite/sensor geometry information. e.g. the scaar GeometryInfo%Sensor_enith_Ange describes the sensor s zenith ange. ChanneInfo: expained in the previous side; ChanneInfo2:2 is a one-eement array containing sensor/channe information for the second sensor, which the user specified with the SensorID array during CRTM initiaization. RTSoution: structure array type RTSoution_type of size ChanneInfo2:2 %n_channes x n_profies. e.g. the scaar variabe RTSoution,%brightness_temeprature is the BT for the first channe and first profie.

48 CRTM User Interface 5 Caing CRTM TL mode exampe: Error_Status CRTM_Tangent_Linear & Atmosphere, Surface &! Input Atmosphere_TL Surface_TL, &! Input GeometryInfo, &! Input ChanneInfo2:2, &! Input RTSoution, RTSoution_TL! Output Atmosphere_TL: structure array of the same type and dimension as Atmosphere containing TL variabes corresponding to those in Atmosphere. Surface_TL: structure array of the same type and dimension as Surface containing TL variabes corresponding to those in Surface. RTSoution_TL: structure array of the same type and dimension as RTSoution containing the resuting TL variabes corresponding to those in RTSoution. e.g. Atmosphere_TL%temperature0 is the temperature perturbation at ayer 0 of the first profie and RTSoution_TL,%brightness_temperature is the response to the perturbations of those variabes in Atmosphere_TL and Surface_TL for the first channe and first profie. Note, when caing this routine, make sure a the perturbations are correcty set. E.g. Surface%wind_speed has a defaut vaue of 5 m/s. Since Surface_TL has the same type Surface_type as Surface, Surface_TL%wind_speed perturbation is automaticay set to 5 m/s. So it must be set to zero or the intended vaue.

49 CRTM User Interface 6 Caing CRTM AD mode exampe: Error_status CRTM_Adjoint Atmosphere, Surface, &! Input RTSoution_AD, &! Input GeometryInfo, ChanneInfo2:2, &! Input Atmosphere_AD, Surface_AD, &! Output RTSoution! Output RTSoution_AD: structure array of the same type and dimension as RTSoution containing the AD variabes corresponding to those in RTSoution. Atmosphere_AD: structure array of the same type and dimension as Atmosphere containing AD variabes corresponding to those in Atmosphere. Surface_AD: structure array of the same type and dimension as Surface containing AD variabes corresponding to those in Surface.

50 CRTM User Interface 7 Caing CRTM K-Matirx mode exampe: Error_Status CRTM_K_Matrix Atmosphere, Surface, &! Input RTSoution_K, &! Input GeometryInfo, ChanneInfo2:2, &! Input Atmosphere_K, Surface_K, &! Output RTSoution! Output RTSoution_K: structure array of the same type and dimension as RTSoution containing the K variabes corresponding to those in RTSoution. Atmosphere_K: structure array of the type Atmosphere_type with dimension n_channes x n_profies, containing K variabes corresponding to those in Atmosphere. Surface_K: structure array of the type Surface_type with dimension n_channes x n_profies, containing K variabes corresponding to those in Surface. Note: compared with Atmosphere_AD and Surface_AD in the AD mode, Atmosphere_K and Surface_K have an additiona dimension n_channes as y i δ yi x j BT i / x j mentioned earier, this dimension separates term from the other terms. 2 To request a brightness temperature Jacobians, in this exampe, set RTSoution_Ki,%brightness_temperature.0 and RTSoution_K%radiance 0.0, i,n_channes.

51 Expain why need setting one of Radiance_K & BT_K to one and the other to zero In the FW routine Compute_FWX, Rad, BT: CALL Compute_RadianceX, Rad CALL Compute_BrightnessTmperature, Rad, BT In TL routine Compute_TLX, X_TL, Rad_TL, BT_TL: CALL Compute_Radiance_TL, X_TL, Rad_TL CALL Compute_BrightnessTemperature_TL, Rad_TL, BT_TL In AD routine Compute_ADX, Rad_AD, BT_AD, X_AD: CALL Compute_BrightnessTemperature_AD, BT_AD, Rad_AD CALL Compute_Radiance_ADRad_AD, X_AD In Compute_BrightnessTemperature_AD, BT_AD, Rad_AD:. Rad_AD Rad_AD + abt_ad BT_AD 0. In Compute_Radiance_ADRad_AD, X_AD:. X_AD X_AD + brad_ad Rad_AD 0 Red coor input variabes Back coor output variabes