Evaluation of FASTEM and FASTEM2

Transcription

1 Evaluation of FASTEM and FASTEM2 Godelieve Deblonde Data Assimilation and Satellite Meteorology Division Meteorological Service of Canada 2121 Trans-Canada Highway, 5 th Floor Dorval, PQ Canada H9P 1J3 godelieve.deblonde@ec.gc.ca Nov 16, 2000 FINAL VERSION

2 TABLE OF CONTENTS 1. INTRODUCTION DESCRIPTION OF THE RADIATIVE TRANSFER MODELS GEOMETRIC OPTICS MODELS Isothermal atmoshere aroximation Handling of multile reflections Further differences between GO models FASTEM FASTEM SUMMARY OF MODELS AVAILABLE FOR THE EVALUATION DESCRIPTION OF PROFILE DATA SET USED IN THE EVALUATION RESULTS OF EVALUATION STUDY SSM/I Basic differences between 1DVAR0 and RTM FASTEM, FASTEM2 comared with RTM FASTEM, FASTEM2, RTM comared with 1DVAR Imact of arameter settings on GO models Sensitivity of brightness temerature to surface wind seed Imact of arameter settings on the sensitivity of TB to surface wind seed AMSU Window channels Sounding channels CONCLUSIONS APPENDICES COMPUTATION OF TB ( θ ) AND TB ( θ ) IMPLEMENTATION OF FASTEM2 INTO MICLBL FASTEM2 SIMPLIFIED REFERENCES

3 1. Introduction Over the oceans, the aarent surface temerature for microwaves is modeled with a geometric otics (GO) model (e.g. Phaliou 1996). The surface emissivity is a weighted average of the emissivity over an ensemble of facets that reresent the roughened sea-surface. Similarly, the reflected sky brightness temerature is comuted by summing the down-welling brightness temerature times the reflectivity over the distribution of facets. GO models are fairly comlex and as a result, the models are slow in the context of oerational weather forecasting. A variational assimilation model for DMSP SSM/I brightness temeratures called SSMI1DVAR and initially develoed at ECMWF by L. Phaliou (Phaliou 1996) includes a radiative transfer model (RTM) that simulates microwave brightness temeratures at the to of the atmoshere. The otical deth is comuted with a fast model that uses multile linear regression equations (RTTOV). The surface emissivity model however uses the full GO model. SSMI1DVAR is used oerationally at the UKMO and ECMWF. At MSC (Meteorological Service of Canada), SSMI1DVAR has been used in research mode only. SSMI1DVAR also includes the Jacobians necessary to imlement the variational assimilation of SSM/I brightness temeratures. In order to seed u the surface emissivity model, English and Hewison (1999) develoed a fast model named FASTEM which arameterizes an effective surface emissivity that relaces the secular surface emissivity in RTTOV. However, from an intercomarison study erformed at MSC by the author, it was noticed that the errors of FASTEM were fairly large in some situations and in articular for SSM/I alications. Recently, S. English develoed an imroved version of FASTEM (called FASTEM2) that uses an aroach similar to that of Petty and Katsaros (1994). FASTEM2 comutes the surface emissivity averaged over all facets reresenting the surface of the ocean and an effective ath correction factor for the down-welling brightness temerature. The latter is different for each olarization and therefore the imlementation of FASTEM2 in RTTOV would be quite comlex. In this reort, a simlified FASTEM2 is roosed which gives results with accetable accuracy and which should be easily imlementable in RTTOV. As its redecessor, FASTEM2 is alicable for frequencies between 10 and 220 GHz, for earth incidence angles less than 60 o and for oceanic surface wind seeds less than 20 ms -1. Thus, these models can also be used for other microwave instruments such as NOAA AMSU-A and AMSU-B. 3

4 At MSC, a general microwave line by line radiative transfer model was develoed (called MICLBL). FASTEM and FASTEM2 have been imlemented into this model. Furthermore, three geometric otics (GO) models were also imlemented in MICLBL. As a result, in the intercomarison study resented here, all models used exactly the same transmittances. The secification of the oxygen absortion lines follows that of Liebe et al. (1992) and that of the water vaor lines and continuum follows Liebe (1989). The AMSU channel 14 does not include the Zeeman effect. A descrition of the radiative transfer models embedded in MICLBL is given in Section 2. The notation is largely based on Petty and Katsaros (1994). The atmosheric rofiles used to do the evaluation were taken from the Garand 42 intercomarison data set (Garand et al. 2000) and are described in Section 3. Results of the evaluation study for all the SSM/I channels and a selected subset of AMSU channels are resented in Section 4. This is followed by conclusions in Section Descrition of the radiative transfer models. For microwave frequencies and when the lane arallel aroximation holds, the olarized brightness temerature TB at the to of the atmoshere as a function of the local incidence angle θ is defined as: s TB ( θ) = TB ( θ) + τ [ E ( θ) T + TB ( θ)] s s (1) where TB ( θ ) is the u-welling atmosheric brightness temerature (Section 6.1),τ s is the atmosheric transmittance, E is the olarized surface emissivity, T s is the skin temerature and TB s ( θ) is the reflected sky brightness temerature. is the olarization which is either vertical (V) or horizontal (H). In the case of secular reflection (e.g. we assume that the ocean is an infinite flat surface), the reflected sky brightness temerature becomes: s TB ( θ) = ( 1 E ) TB ( θ) (2) 4

5 where TB ( θ ) is the down-welling atmosheric brightness temerature (Section 6.1) and E is comuted using the Fresnel equations. The olarized aarent surface temerature (TB a ) is defined as the term inside the brackets in Eq. 1. In the case where the atmoshere is assumed to be isothermal with temerature T s Eq. 1 becomes: TB ( θ) = ( 1 τ ) T + τ [ E T + ( 1 E ){( 1 τ ) T + T τ }] (3) s s s s s s C s where T C is the cosmic background temerature GEOMETRIC OPTICS MODELS In the GO models, an effective emissivity is comuted which is a weighted average of the emissivity over an ensemble of facets that reresent the roughened sea surface. The sloes of the facets are samled from a gaussian distribution (Cox and Munk 1954). This effective emissivity will be referred to as E GO. Similarly, the reflected sky brightness temerature TB s GO is comuted by summing the down-welling brightness temerature times the reflectivity over the distribution of facets. The aarent surface temerature of the GO model is defined as: GO GO sgo TB = E T + TB. (4) a s The GO effective emissivity is defined as: E GO = e ρ wds ds s x y ρ wds ds s x y (5a) 5

6 with ρ s Sx + Sy = ex( ) (5b) πvar VAR f f where e is the emissivity of the surface for each facet comuted from the Fresnel equations. ρ s S x S y (, ) is the robability density function (Cox and Munk 1954) of the sloes S x and S y and w(s x,s y ) is a weighting function that is related to the viewing geometry. VAR f is the sloe variance that is adjusted for a frequency deendence. VAR f =VAR*F(ν) and ν is the frequency. The sloe variance VAR is a linear function of surface wind seed and F=0.02ν(GHz)+0.3 if ν < 35 GHz and F=1 for larger frequencies (Wilheit 1979). Thus the sloe variance is reduced for the lower frequencies. Eq. 5a may be rewritten in discretized form as: E GO = ( 1 Rij ) ω ij (6) i j Following the notation in Petty and Katsaros (1994), TB s GO (see Eq. 4) is defined as follows: TB s GO = TB( k )( e ) ρ wds ds GO + ( 1 E ) T τ s, z 1 s x y ρ wds ds s x y C s (7) where k s,z is the z comonent of the unit vector giving the direction of the reflected brightness temerature. The down-welling brightness temerature has to be comuted at the scattering angle of each facet samled in the Gaussian distribution. Eq. 7 may be rewritten in discretized form as follows: s GO TB = RijωijTB ( θij ). (8) i j 6

7 Finally, Eq. 4 can be rewritten in discretized form as: GO TBa = ( 1 Rij ) ωijts + RijωijTB ( θ ij ) (9) i j i j Three GO models were used in this intercomarison study and are referred to as 1DVAR0, 1DVAR2 and RTM. 1DVAR0 is the same radiative transfer model as that obtained from ECMWF (Phaliou 1996) referred to as SSMI1DVAR in the introduction. However, SSMI1DVAR was re-coded at MSC to fit into MICLBL and given the name 1DVAR0. Also, the transmittances in 1DVAR0 are comuted exlicitely and thus do not use regression equations. RTM is based on code obtained from the UKMO in 1998 and was imlemented in MICLBL with several modifications. RTM as obtained assumed the seudo-secular aroximation. For this case, the reflected sky brightness temerature is given by: s GO GO TB = ( 1 E ) TB ( θ ). RTM was modified to include the down-welling brightness temerature contribution reflected from each facet. The difference between 1DVAR2 and 1DVAR0 is that (1) 1DVAR2 does not use the isothermal atmoshere aroximation (See Section below) and (2) the handling of multile reflections can be done as in 1DVAR0 or RTM (See Section below). In summary, MICLBL can be run with either of the 1DVAR0, 1DVAR2 and RTM setus Isothermal atmoshere aroximation 1DVAR0 uses an aroximation to seed u the comutation of the down-welling TB. It is assumed that the atmoshere radiates at a mean temerature T A : 7

8 TB ( θ) = T ( τ ( θ)) + T τ ( θ) 1. (10) A s C s A table of down-welling brightness temeratures is comuted for regularly saced intervals of view angleθ π r between 0 and 2. TB ( θ ) is comuted from TB ( ) which was derived with Eq. 10. r θ using the equation that follows TB s r = TB 1 ( τ ( θ)) ( θ ) ( θ) 1 τs( θ) secθ r secθ (11) TB ( θ ) is then obtained by interolating between TB ( θ r ) values where θ z is the z scattering angle. RTM does not use this aroximation and comutes the down-welling TB contribution exlicitly for each facet Handling of multile reflections When multile reflections occur in 1DVAR0, the reflectivity of the facets is not modified and it is assumed that the down-welling TB is equal to the surface temerature. For the facets whose z-comonent of the scattered vector oints downward with resect to the surface, multile reflections will occur and the scattered brightness temerature of each facet is set to: s GO TBij = Rijω ijts. (12) i j Using Eq. 9 it follows that the aarent brightness temerature of those facets is: 8

9 TB GO aij = ω ij T s (13) The aarent surface temerature of the facet no longer deends on the emissivity of the facet and the aarent surface temerature is not olarized for those facets. When multile reflections occur in RTM, it is assumed that the reflectivity of those facets takes on the square value of the reflectivity. Thus, for each facet, one has a modified emissivity such that: e ij 2 = ( 1 R ) ij (14) where R ij is the reflectivity of the facet. The scattered brightness temerature for each facet is: TB s GO ij 2 = R TB ( θ = 0) ω. (15) ij ij and the aarent surface temerature becomes: GO TB = ( 1 R 2 ) ω T + R 2 ω TB ( θ = 0). (16) aij ij ij s ij ij Thus, both the emissivity and the scattered TB terms are modified. To comute the downwelling TB, we have assumed a ath such that secθ =1.0. The choice of such a ath leads to a s minimum value for TB GO ij. If we make the further assumtion that the atmoshere is isothermal with temerature T s, then TB GO aij will be equal to: GO TB = ω T [ 1 R 2 τ ( θ = 0)] aij ij s ij s. (17) 9

10 Comaring Eqs. 17 and 13 shows that TB GO aij for the first aroach (1DVAR0) will always be larger than that of the latter one (RTM). The number of facets for which multile reflections occur increases with scan angle Further differences between GO models Further differences between 1DVAR0 and RTM are listed in Table 1a. With the aroriate choice of arameters as listed in Table 1a, The selection of arameter settings for RTM was the same as that for FASTEM and FASTEM2. TB a GO was comuted as follows: GO GO s GO TB = { E ( 1 FC) + E FC} T + ( 1 FC) TB (18) a foam s where FC is the foam cover (which is a linear function of surface wind seed (SWS), see Table 1) and to include Bragg scattering, the reflectivity of each facet was multilied by a correction factor defined as follows (English and Hewison 1998): B( SWS, ν, θ) = e ( SWS )(cos θ ) ν 2 2. (19) Thus the Bragg scattering correction factor increases with wind seed. It affects mostly the longest waves and thus the lowest frequencies. This correction term is introduced in the GO model by multilying the term R ij in Eq. 9. The emissivity of foam is set to 1 as the foam is assumed to be a blackbody. The model 1DVAR2 can use any of the arameter choices listed in Table 1a and therefore, these arameters have to be secified each time the model is discussed. The secification of arameters for 1DVAR2 will be defined by an exeriment number and are listed in Table1b. 10

11 Table 1a: Parameter settings for 1DVAR0 and RTM. SWS is the surface wind seed. Basic differences between the models are described in Sections PARAMETER 1DVAR0 RTM Foam Cover (FC) FC=2.95E-6 (SWS) 3.52 FC=1.95E-5 (SWS) 2.55 Dielectric Constant Klein and Swift (1977) (deends on salinity) Lamkaouchi et al. (1997) (does not deend on salinity) Multile Reflections TB = T s E=(1-R 2 ), TB ( θ = 0) Bragg Scattering Not included included, see Eq. 19. Salinity 36 o / oo N/A Table 1b: Parameter secification for 1DVAR2 exeriments. 1DVAR0 and RTM arameters are secified in Table 1a. Exeriment FOAM Dielectric Constant Bragg Scattering Multile Reflections #1 RTM RTM RTM RTM #2 1DVAR0 1DVAR0 1DVAR0 1DVAR0 #3 RTM RTM RTM 1DVAR0 #4 1DVAR0 RTM RTM RTM #5 RTM 1DVAR0 RTM RTM #6 RTM RTM 1DVAR0 RTM 11

12 2.2. FASTEM FASTEM arameterizes the surface emissivity so that the secular reflection formulation can be used (Eq. 2) and E is relaced with E f. E f is defined as follows: f * E = {( 1 R B) + E }( 1 FC) + FC (20) where B is the correction factor to include Bragg scattering, FC is the foam cover which is arameterized by an emirical formula that deends on SWS (Table 1a). R is the secular reflection which is comuted using the Fresnel equations. In the FASTEM code, all terms in Eq. 20 are comuted exlicitly excet for E * which is obtained using a regression equation that deends on the view angle θ and the surface wind seed SWS. E * was obtained as follows. First, comute TB a GO (using the full GO model, i.e. Eq. 4) with arameters selected from Table 1a under the RTM heading. Then, solve for E f which must satisfy the following equation (see Eqs. 1 and 2): f f GO E T + ( 1 E ) TB ( θ ) TB (21) s a It follows that E f GO ( Tba TB ( θ)) = T TB ( θ) s (22) Finally, using Eq. 20, one has: 12

13 f { E ( 1 RB)( 1 FC) FC} * E = { 1 FC} (23) * 2 2 and E C + C sec θ + C (sec θ) + C SWS + C ( SWS) + C (sec θ ) SWS, (24a) with C = C + C ν + C ν (24b) i i0 i1 i2 where SWS is the surface wind seed in ms -1 and ν is the frequency in GHz. E * reresents an increase in emissivity due to the surface roughtness FASTEM2 With FASTEM2, the formulation of the aarent surface temerature is closer to that of the GO model by including an effective down-welling brightness temerature. Moreover, the effective surface emissivity is now an aroximation to E GO ( 1 FC) + FC and is referred to as ~ GO E. Thus, the effective surface emissivity is defined as follows: ~ GO * E = {( 1 R ) B + E }( 1 FC) + FC. (25) ~ GO Since the LHS of the equation is now E and not E f as was the case for FASTEM, it is imortant to note that E * is different in the FASTEM and FASTEM2 models. E * in FASTEM2 uses the same set of redictors as in FASTEM but the regression coefficients are different. With FASTEM2, TB GO a (see Eq. 18) is written as: 13

14 GO * TB = E ( θ) T + ( E ) TB ( θ ) a ~ GO ~ GO s 1. (26) ~ GO GO Note that: 1 E = ( 1 FC)( 1 E ) TB ( * θ ) is the effective down-welling brightness temerature that is comuted as follows: * s GO TB ( θ ) = ( 1 FC) TB ( θ) / ( 1 E ). ~ GO θ * is then obtained from TB * ( ) θ by assuming that the atmoshere can be reresented by a mean radiating temerature T A (See Eq. 10). The down-welling TB is comuted for θ * and not θ as was the case for FASTEM (Eq. 21). It follows that: * ( ) * 1 TB θ T A secθ = ln O TC TA (27) where O is the otical deth of the atmoshere. Furthermore, a ratio P rough is introduced which is a double summation as follows: * secθ i n Prough = = 1+ { Anmi (ln O) }( VARf ) (sec θ) secθ n= 0 m= 0 i = 0 m (28) and the terms for which m+n=3 are ignored. Note that a mean radiative temerature cannot be comuted for sounding frequencies. This is addressed in section Thus, FASTEM2 rovides E method is that TB ( ) * ~ GO ~ GO v, E, P rough (H) and P rough (V). A drawback with this h θ has to be comuted for each olarization (V and H) and the imlementation of FASTEM2 as is, would require major changes to RTTOV-6. However, in section 14

15 6.3 we suggest an aroximation that will allow a straightforward imlementation of FASTEM2 in RTTOV-6. Although FASTEM comutes an effective surface emissivity and FASTEM2 comutes an effective surface emissivity and an effective ath P rough, in this reort, FASTEM and FASTEM2 will refer to the radiative transfer models available in MICLBL that use FASTEM and FASTEM2 resectively Summary of models available for the evaluation Table 2: Summary of radiative transfer models available for the evaluation. All these models are embedded in MICLBL. MICLBL is a general microwave radiative transfer model develoed by the author. Transmittances for all models are comuted exlicitly and in exactly the same way. MODEL NAME 1DVAR0 1DVAR2 RTM FASTEM FASTEM2 DESCRIPTION Same model as SSMI1DVAR (Phaliou 1996) but imlemented in MICLBL. Also referred to as RTSSMI by the RTTOV develoers. This is a GO model. Same model as 1DVAR0 but the down-welling TB is comuted exlicitly for all facets (i.e. the aroximation as described in Section is NOT used). Handling of multile reflections is as in 1DVAR0 or RTM. RTM of UKMO 1998 imlemented in MICLBL with several changes. Downwelling TB is comuted exlicitly for all facets. This is a GO model. FASTEM imlemented in MICLBL. This is a fast model. FASTEM2 imlemented in MICLBL. This is a fast model. 3. Descrition of rofile data set used in the evaluation The atmosheric rofiles that were used in the evaluation were chosen among the 42 rofile Garand intercomarison data set. The total reciitable water (TPW) and skin temeratures are listed in Table 3. Since the surface emissivity model is valid only over the oen oceans, 15

16 rofiles with T s < 275 K were discarded. The remaining number of rofiles is 26. This rofile data set will be referred to as the GARAND26 data set. Table 3: Profiles used in intercomarison study (GARAND26 data set) Profile # (out of 42) TPW (kgm -2 ) Skin Temerature(K)

17 4. Results of evaluation study 4.1. SSM/I Basic differences between 1DVAR0 and RTM The basic differences between the models are listed in Section 2.1. The two to bar lots in Fig. 1 illustrate the imact of using the isothermal atmoshere aroximation (Section 2.1.1). This leads to a bias of < 0.4K and a SD of less than 0.15 K. The small values of these statistics confirm that the aroximation is a reasonable one. The method used to handle multile reflections (Section 2.1.2) leads to a large bias (u to 3.7 K) for the horizontally olarized channels and for large wind seeds (14 and 20 ms -1 ) (Fig. 1, bottom two bar lots). The channel with the largest imact on the bias is the 37 GHz H channel. The largest SD is 0.64 K for the 85 GHz H channel. The fact that the biases are negative is to be exected since the method used to handle multile reflections in 1DVAR2 (#1) will lead to smaller aarent brightness temeratures (Eq. 17) than those of 1DVAR2 (#3) (Eq. 13). 1DVAR2 exeriment numbers are defined in Table 1b. The differences are larger for the horizontal olarization because R v is considerably smaller than R h. In conclusion, the way that multile reflections are taken into account becomes imortant for high wind seeds and horizontally olarized channels. In that resect, it is imortant to remind ourselves that 1DVAR0 and RTM have different ways of imlementing multile reflections. The imact of the isothermal aroximation is small FASTEM, FASTEM2 comared with RTM Bar lots (as a function of surface wind seed) of biases and standard deviations between models of the aarent surface temerature are illustrated in Figs 2a-d for each of the SSM/I frequencies. There are three sets of intercomarisons and hence three sets of bars er wind seed in the lots. The three sets are intercomaring (1) FASTEM with RTM, (2) FASTEM2 with RTM and (3) FASTEM2 simlified (Section 6.3) with RTM. 17

18 Comarison of erformance of FASTEM and FASTEM2 Figure 2a: 19 GHz V: biases for the lower wind seeds (0 and 3 ms -1 ) are smaller for FASTEM2. For the larger wind seeds, the biases of FASTEM2 are larger (u to 1.75 K at 20 ms -1 ). The SD lot shows that FASTEM2 has a SD that is smaller than that of FASTEM for all wind seeds. 19 GHz H: biases at 0 ms -1 are larger for FASTEM2 whereas the FASTEM2 bias ratio of imrovement with resect to FASTEM increases with wind seed and the FASTEM2 biases remain below 2.1 K. The FASTEM2 SD are drastically reduced for wind seeds of 7 ms -1 and u. All SD are now below 0.6 K. With FASTEM, the SD reaches a value as high as 2.35 K at 20 ms -1 with a bias of 9.25 K. In conclusion, at 19 GHz, FASTEM2 is a much imroved fast model for the horizontal olarization excet for a wind seed of 0 ms -1. Figure 2b: 22 GHz V: For the wind seeds different from 0, biases for FASTEM2 are larger than those of FASTEM whereas the SD of FASTEM2 is larger for all wind seeds excet at 20 ms -1. In conclusion, at 22 GHz V, FASTEM2 does not erform better than FASTEM. Figure 2 c: 37 GHz V: The bias and SD for FASTEM2 are smaller for all cases. The bias for FASTEM2 is < 0.23 K and the SD < 0.5 K. 37 GHz H: The bias and SD behavior of this channel is similar to that of the 19 GHz channel. The bias for FASTEM2 is < 2.0 K and SD < 0.75 K. In conclusion, at 37 GHz, FASTEM2 is a much imroved fast model for the horizontal olarization excet at wind seeds of 0 ms -1. The 37 GHz V aarent surface temerature model is better for FASTEM2. Figure 2d: 18

19 85 GHz V: For low wind seeds (0, 3, 7 ms -1 ), the biases are of similar magnitude for FASTEM and FASTEM2. For higher wind seeds, the FASTEM2 bias is much lower. The SD for FASTEM2 is reduced only for seeds 7 ms GHz H: The biases for FASTEM2 are larger for low wind seeds (0 and 3 ms -1 ) and lower for higher wind seeds. The SD are lower for all wind seeds and overwhelmingly so for the largest wind seeds (7, 14 and 20 ms -1 ). In conclusion, at 85 GHz, FASTEM2 is an imroved fast model for the horizontal olarization excet at wind seeds of 0 ms -1. The 85 GHz V aarent surface temerature model FASTEM2 has smaller biases comared with the RTM. Overall, at the SSM/I frequencies, FASTEM2 rovides a more accurate fast substitute to a comlete GO model than FASTEM. The largest imrovements are for the horizontal olarizations and the largest wind seeds. The results are summarized in Table 4. Table 4: Maximum bias (absolute value) and maximum SD between the aarent surface temeratures obtained with the models FASTEM, FASTEM2 and RTM for the SSM/I frequencies and a scan angle with resect to nadir of o. Surface wind seed values range between 0 and 20 ms -1. The biases and SD were comuted at each wind seed (0, 3, 7, 14, and 20 ms -1 ) for the Garand 26 data set and the maximum values are tabulated here for each frequency including both olarizations excet for the 22 GHz channel. FASTEM-RTM FASTEM2-RTM SSM/I Frequencies BIAS (K) SD(K) BIAS(K) SD(K) 19 GHz V and H GHz V GHz V and H GHz V and H

20 Comarison of FASTEM2 and FASTEM2 simlified Difference statistics of FASTEM2 and RTM with FASTEM2 simlified and RTM (Figs. 2ad) show that FASTEM2 simlified (Section 6.3) has a comarable erformance to that of FASTEM2 for all SSM/I frequencies. This aroach should seed u and simlify the imlementation of FASTEM2 in future versions of RTTOV FASTEM, FASTEM2, RTM comared with 1DVAR0 Some of the results resented here are directly comarable to those resented in Fig. 14 of the RTTOV-6 -SCIENCE AND VALIDATION REPORT available from the NWP SAF web site. Fig.14 illustrates the biases between simulated brightness temeratures at the to of the atmoshere for the RTTOV-6 and RTSSMI models. Since the surface emissivity in RTTOV-6 is simulated with FASTEM, RTTOV-6 is similar to the model FASTEM in this reort and RTSSMI is similar to 1DVAR0 (Table 2). The word similar is emloyed here rather than the word same because both RTTOV-6 and RTSSMI use regression coefficients to comute the otical deths and 1DVAR0 comutes the otical deths using a LBL model. The to left bar lot (with the biases) in Fig. 3 (FASTEM -1DVAR0) can therefore be comared with Fig. 14. The biases in Fig. 3 are somewhat higher than those in Fig. 14 but have the same behavior. The to wind seed considered in Fig. 14 was 10 ms -1 whereas here it is 20 ms -1. Fig. 3 also illustrates the SD (to right bar lot) for the same intercomarison case and reaches a maximum of 2.2 K. It is reminded that channel 4 in the figure (or the 22 GHz H channel) is not an SSM/I channel and the results are dislayed here for simlicity in the lotting routines. The bottom bar lots in Fig. 3 illustrate the results for the intercomarison of FASTEM2 with 1DVAR0. Basically, similar biases remain but are often smaller (excet for a surface wind seed of 20 ms -1 ) and the magnitude of the reduction in bias varies with wind seed. The SD are also reduced excet for the 85 GHz and 22 GHz channels Imact of arameter settings on GO models Table 1a lists the differences in arameter choices (foam cover, dielectric constant, Bragg scattering, multile reflections) for the GO models. In this section, difference statistics are 20

21 comuted to find out which arameter choice causes the largest differences between RTM and 1DVAR0. To do this, models 1DVAR2 and 1DVAR0 are used. First, a reference case is setu which comutes the difference statistics between 1DVAR2 (#1 see Table 1b, uses RTM arameters) and 1DVAR0. Subsequently, one arameter at a time is changed in 1DVAR2 and the new value assigned to that arameter is that of the 1DVAR0 setu. Thus, if the difference statistics of any of these exeriments are very close to the reference case, then the arameter that was changed can be identified as the one that causes a large difference in the RTM and 1DVAR0 models. The reason that 1DVAR2 was chosen for this task is because the handling of multile reflections is flexible in 1DVAR2: one can choose either the RTM or 1DVAR0 setu. Figures 4a-d illustrate the difference statistics as a function of wind seed for the 4 SSM/I frequencies. The series of 5 bars in the bar lots for each wind seed corresond to the following setus: (1) 1DVAR2 (#1) - 1DVAR0 (this is the reference case), (2) 1DVAR2 (#1)-1DVAR2 (#4) (foam change), (3) 1DVAR2 (#1)-1DVAR2 (#5) (dielectric constant change), (4) 1DVAR2 (#1)- 1DVAR2 (#6) (Bragg scattering change) and (5) 1DVAR2 (#1)-1DVAR2 (#3) (multile reflection change). For wind seeds of 0, 3 and 7 ms -1, clearly, changing the dielectric constant in 1DVAR2 from the RTM setu to that of 1DVAR0 exlains most of the differences between RTM and 1DVAR0. The choice of the dielectric constant also imacts the largest wind seeds (14 and 20 ms -1 ). For wind seeds different from zero, the imact of the Bragg scattering (Eq. 19) being turned off increases with wind seed and as exected has the largest influence on the lowest frequencies. The effect on horizontally olarized channels is somewhat larger than vertically olarized channels. The choice of foam cover as a function of wind seed affects mostly the highest wind seeds (14 and 20 ms -1 ) and has a higher imact on channels with horizontal olarization. Table 5 lists the values of foam cover as a function of wind seed for 1DVAR0 and RTM. At 7 ms -1, the foam covers are the same. Above 7 ms -1 the foam cover of the 1DVAR0 increases at a much faster rate and therefore also has a larger imact. At 20 ms -1, the foam cover is 3 times larger in 1DVAR0 than in RTM. Finally, the imact of the handling of multile reflections is noticeable only for the largest wind seeds (14 and 20 ms -1 ) and the same conclusions as in Section hold: largest imact for the highest frequencies and horizontal olarizations. 21

22 Table 5: Foam cover as a function of surface wind seed for 1DVAR0 and RTM. Surface Wind Seed (ms -1 ) Foam Cover 1DVAR0 Foam Cover RTM e e e Sensitivity of brightness temerature to surface wind seed wind seed (i.e. The sensitivity of the brightness temerature at the to of the atmoshere with surface dtb ) was comuted using finite differences: dsws 22

23 dtb dsws TB( SWS +.) TB( SWS) 1 where SWS is in ms -1. dtb dsws was also reorted in the RTTOV-6 SCIENCE AND VALIDATION REPORT for the SSM/I frequencies and for models FASTEM and RTSSMI. Thus a direct comarison of results will again be ossible. dtb dsws was comuted here for 4 different models: FASTEM, FASTEM2, RTM and 1DVAR0. If FASTEM and/or FASTEM2 are accurate fast model (and aroximations) to RTM, then dtb of these models should be the same as that of RTM. This is articularly dsws imortant in the context of variational assimilation. Figs. 5a and 5b illustrate the sensitivities for the 4 models. Vertical olarizations: The sensitivity of 1DVAR0 is low for low wind seeds and increases raidly with wind seed with the largest sensitivity > 1.5 K/ms -1 for the 19 and 37 GHz channels and a surface wind seed of 20 ms -1. At 85 GHz, the increase in sensitivity with surface wind seed is considerably lower. The sensitivity of RTM is similar to that of 1DVAR0 for low wind seeds but increases at a much slower rate for higher wind seeds with the maximum sensitivity being less than 1/3 of that of 1DVAR0. It is susected here that the difference in arameterization for foam in the models (larger foam cover in 1DVAR0 model at high wind seeds) is resonsible for this discreancy (See Section 4.1.6). The sensitivities of the brightness temeratures to surface wind seed of FASTEM, FASTEM2 and RTM are quite similar. Horizontal olarizations At 19 GHz, FASTEM sensitivities are too high at low wind seeds. For large wind seeds (14 and 20 ms -1 ), the 1DVAR0 sensitivities become very large: > 3 K/ms -1 at 19 and 37 GHz. At low wind seeds, the sensitivities of FASTEM2, 1DVAR0 and RTM are fairly similar. 23

24 In summary, for vertical olarizations, FASTEM and FASTEM2 behave not too differently. AT 19 GHz H and at low wind seeds, FASTEM exhibits a larger sensitivity to wind seed than that of RTM. 1DVAR0 differs mostly from RTM at higher wind seeds (14 to 20 ms -1 ) with 1DVAR0 being more sensitive by a factor of ~3 at 20 ms -1. The results in Fig. 15 of the RTTOV-6 SCIENCE AND VALIDATION REPORT are in agreement with the results resented here Imact of arameter settings on the sensitivity of TB to surface wind seed In this section, the imact on dtb of changing arameters in 1DVAR2 (with RTM dsws arameters for the reference case) to those in 1DVAR0 is studied. The aroach here is similar to that of Section excet that only biases are comuted. In Fig. 6 a and b, the sensitivity of six models are lotted side by side (as a bar lot) as a function of surface wind seed. The six models are: (1) 1DVAR2 (#1, RTM setu used as a reference) and (2) 1DVAR0 (used as a reference), (3) 1DVAR2(#4) foam change, (4) 1DVAR2(#5) dielectric constant change, (5) 1DVAR2(#6) Bragg scattering, (6) 1DVAR2(#3) multile reflections change. An obvious result from these grahs is that the increased sensitivity of 1DVAR0 for large wind seeds (14 and 20 ms -1 ) is largely due to the different secification of the foam cover. The foam cover for 1DVAR0 increases much more quickly than that of RTM for wind seeds larger than 7 ms -1 (Table 5). The increased foam cover leads to a larger sensitivity of brightness temerature with surface wind seed. At 3 and 7 ms -1 for all horizontal frequencies, all the models give a similar sensitivity and thus the arameter changes have little imact AMSU Unlike the SSM/I which is a conical scanner and has a constant scan angle, AMSU is a cross-track scanner and the scan angle varies with scan osition. Thus, the accuracy of FASTEM and FASTEM2 also has to be evaluated as a function of scan angle Window channels 24

25 The AMSU window channels are listed in Table 6. Sounding channels are identified by S and window channels by W. Fig. 7a illustrates the differences in aarent surface temerature between RTM and FASTEM for a rofile (#18 in Table 3) with a TPW of 33 kgm -2 as a function of satellite view angle from nadir for both olarizations of the AMSU channel #3 (50.3 GHz) and for 5 different wind seeds (0, 3, 7, 10, 14 and 20 ms -1 ). The same lots but differencing RTM and FASTEM2 this time are shown in Fig. 7b. The differences in Fig 7b are the smallest for a scan angle of ~ 25 o. Comaring Figs 7a and b, one may notice that FASTEM2 erforms much better than FASTEM as an aroximator to RTM. In articular, one may note that the bias at 0 o is reduced for FASTEM2 for all wind seeds excet 0 ms -1. Figs. 7c-e illustrate the bias and SD of the aarent surface temerature (both olarizations) over the GARAND26 rofile data set for view angles of 0, 30 and 45 o resectively. The results for only a subset of the window AMSU channels (see Table 6) are resented here. The to bar lots intercomare RTM with FASTEM and the bottom lots RTM with FASTEM2. For a scan angle of 0 o, the SD dros from a maximum of 2.6 K for FASTEM to 0.4 K for FASTEM2, at 30 o from 2.9 K for FASTEM to 0.2 K for FASTEM2 and at 45 o from 2.45 K for FASTEM to 0.9 K for FASTEM2. At 45 o, the maximum biases for FASTEM2 are < 3.0 K whereas it is < 8.5K for FASTEM. The biases of FASTEM2 are < 0.75 K for a scan angle of 30 o and < 1.8 K for a scan angle of 0 o. These statistics are summarized in Table 7. In conclusion, for the AMSU channels, FASTEM2 is a much more accurate model than FASTEM to simulate aarent surface temeratures. 25

26 Table 6: AMSU channels (W=Window channel, S=Sounding channel) Channel # Frequency (GHz) Channel # Frequency (GHz) 1-W (results shown) S W (results shown) S W (results shown) S W (results shown) W S/W W (results shown) S W (results shown) S W/S 183±1 8-S W/S 183±3 9-S W/S 183±7 10-S S Table 7: Maximum biases (absolute values) and maximum SD between the aarent surface temeratures obtained with the FASTEM, FASTEM2 and RTM among the selected AMSU frequencies (i.e. 23.8, 31.4, 50.3, 52.8, 89, 150 GHz ) and both olarizations. Surface wind seed values range between 0 and 20 ms -1. The biases and SD were comuted at each wind seed (0, 3, 7, 14, and 20 ms -1 ) and for each channel and olarization over the Garand 26 data set. The maximum values are tabulated here. FASTEM-RTM FASTEM2-RTM Scan angle with resect to nadir BIAS (K) SD(K) BIAS(K) SD(K) 0 o o o As illustrated in Fig. 7a and b, the magnitude of the biases between the fast models and RTM varies considerably as a function of scan angle and the biases can become quite large for scan angles with resect to nadir > 40 o. The scan angle of the SSM/I is ~ 45 o. To obtain a better erformance of a fast model for large scan angles, it is suggested that the regression coefficients 26

27 be calculated for small variations around a articular scan angle rather than covering all scan angles as is currently done with FASTEM and FASTEM Sounding channels In Table 6, the 183 GHz channels (strong water vaor absortion line) are identified as window or sounding. Whether a 183 GHz channel is a window or sounding channel will deend on the water vaor burden in the rofile. Among channels 18 to 20, channel 18 eaks the highest in the atmoshere and channel 20 the lowest in the atmoshere. For very dry atmosheres, channel 18 can be a window channel since its weighting function will eak low in the atmoshere. The isothermal aroximation (Section 2.1.1) is not valid for sounding channels. This aroximation was used in the develoment of the FASTEM and FASTEM2 models and for the comutation of the reflected sky brightness temerature in 1DVAR0. As a consequence, the aarent surface temeratures generated by FASTEM, FASTEM2 and 1DVAR0 are no longer valid for sounding channels. However, this does not resent a roblem since for those channels the atmosheric transmittance is very low (tends to zero) and multilies the aarent surface temerature and only the term TB in Eq. 1 contributes to TB at the to of the atmoshere. An examle of this is illustrated in Fig. 8 for a rofile with a TPW of 33 kgm -2 (rofile # 18 in Table 3) and for AMSU channel 19. Fig. 8 illustrates the aarent surface temerature as a function of view angles for the 3 models 1DVAR0, FASTEM and FASTEM2. As the view angle increases, the otical deth increases and the isothermal aroximation becomes invalid yielding erroneous aarent surface temeratures. Models 1DVAR2 and RTM do not use the isothermal aroximation and the aarent surface temerature remains valid for all view angles. 5. Conclusions An evaluation of FASTEM and FASTEM2 was erformed by intercomaring them with 3 geometric otics models: 1DVAR0, 1DVAR2 and RTM. FASTEM, FASTEM2 and the three GO models are all embedded in the same general radiative transfer code (called MICLBL) develoed at MSC by the author. The fact that the models share many common subroutines (for examle they all comute transmittances in the same manner) makes the intercomarison straightforward. RTM is a model that has the same arameter settings as FASTEM and FASTEM2 (Table 1a). 27

28 1DVAR0 has the same arameter settings as SSMI1DVAR or RTSSMI (Table 1a). Finally, 1DVAR2 can have arameter settings as those of RTM or SSMI1DVAR. To erform the intercomarisons, a subset of 26 rofiles (with skin temeratures > 275 K) were selected among the 42 rofiles of the GARAND data set. Aart from the fact that RTM and 1DVAR0 have different arameter settings, the 2 models also have differences which are hard-coded into the models. These differences are: (1) the isothermal atmoshere aroximation is used to comute the down-welling brightness temerature in 1DVAR0 and not in RTM, (2) the handling of the multile reflections is done differently in RTM and 1DVAR0. Among these differences (only evaluated for the SSM/I channels in this reort), only the last one significantly affects the comuted aarent surface temerature at the largest wind seeds and for horizontally olarized channels. The aarent surface temerature of the models FASTEM and FASTEM2 were each intercomared with those of RTM. For the SSM/I frequencies, FASTEM2 rovides a more accurate fast substitute to a comlete GO model than FASTEM for the horizontal olarization excet at zero wind seed. A faster version (and much easier to imlement in RTTOV) of FASTEM2 named FASTEM2 simlified is resented in Section 6.3. The intercomarison of FASTEM2 and FASTEM2 simlified shows that FASTEM2 simlified is accurate enough to be considered for imlementation into RTTOV. For the SSM/I frequencies, FASTEM, FASTEM2 and RTM brightness temeratures (at the to of the atmoshere) were intercomared with those of 1DVAR0. Results of the intercomarison of FASTEM and 1DVAR0 are in agreement with those resented in Fig. 14 of the RTTOV-6 - SCIENCE AND VALIDATION REPORT. It was found that for the SSM/I frequencies and for the lowest wind seeds ( 7 ms -1 ), the arameter that most affected the differences in aarent surface temerature between RTM and 1DVAR0 was the secification of the dielectric constant. The choice of foam cover formulation leads to considerably larger foam cover for large wind seeds in the 1DVAR0 model and at high wind seed this arameter contributes to a large ortion of the difference between RTM and 1DVAR0. The sensitivity of the brightness temeratures at the to of the atmoshere to surface wind seed for the SSM/I channels was comuted for FASTEM, FASTEM2, 1DVAR0 and RTM. The intercomarison of results for FASTEM and 1DVAR0 were also reorted for FASTEM and RTSSMI in Fig. 15 of the RTTOV-6 - SCIENCE AND VALIDATION REPORT. Again, the results obtained in the reort are in agreement with those resented here. For the vertical olarizations, the sensitivities of FASTEM, FASTEM2 and RTM are quite similar. For the 19 GHz horizontally 28

29 olarized channel, FASTEM sensitivities are too high at low wind seeds whereas FASTEM2 sensitivities closely follow those of RTM for all horizontally olarized channels. For high wind seeds and both olarizations, the sensitivity of the 1DVAR0 model to wind seed becomes quite large comared to that of RTM and is due mainly to the different secification of the foam cover. In the case of the AMSU channels, the accuracy of FASTEM and FASTEM2 has to be evaluated as a function of scan angle. Results were resented for a selected subset of AMSU window channels and the intercomarisons were also erformed for the GARAND26 data set. In most cases, it was found that FASTEM2 is a much more accurate model than FASTEM and that FASTEM2 is most accurate for scan angles around 25 o. At 30 o, the bias and SD for FASTEM2 comared with RTM were < 0.75 K and < 0.2 K resectively whereas for FASTEM comared with RTM, these were < 4.7 K and 2.9 K. It is not exected that the conclusions would change if all the AMSU channels that are sensitive to the surface had been considered. It should be noted that for sounding channels, the FASTEM, FASTEM2 and 1DVAR0 roduce erroneous aarent surface temerature because they use the isothermal atmoshere aroximation. However for such cases, the atmosheric transmittance tends to zero and therefore the use of this aroximation does not lead to an erroneous comutation of brightness temeratures at the to of the atmoshere. The increase in accuracy obtained by using FASTEM2 rather than FASTEM to comute the aarent surface temerature is significantly larger for the AMSU instrument for scan angles < ~40 o than for the SSM/I instrument. The SSM/I instrument has a large scan angle (45 o ) and the fast models do not erform as well for large scan angles. It may be necessary to develo a fast model that is only alicable for a articular range of scan angles for large angles in order to imrove the accuracy. 6. Aendices 6.1. Comutation of TB ( θ ) and TB ( θ) The u-welling atmosheric brightness temerature is defined as: TB ( θ) = ( 1 / 2) ( T + T 1)( τ 1 τ ) (A.1) j j j j j 29

30 where j is the level, τ j is the transmittance from level j to sace and T j is the atmosheric temerature at level j. The down-welling atmosheric brightness temerature is: TB ( Tj + Tj 1)( τ j 1 τ j ) ( θ) = {( 1/ 2) + Tc } τs τ τ j j j 1 (A.2) where τ s is the transmittance from the surface level to sace or the atmosheric transmittance and T C is the cosmic background temerature. The transmittance at level j is comuted as follows: τ = e j j 1 secθ Ol l= 1 (A.3) where O l is the otical deth of layer l. Level 1 is the to level and the level number increases towards the surface, thus, τ 1 = 10. (A.4) τ 2 = 1 1 θ e O sec * τ 2 θ τ = e O sec * τ * τ etc., 6.2. Imlementation of FASTEM2 into MICLBL 30

31 The imlementation of FASTEM2 in MICLBL (a general microwave radiative transfer code -forward model only, develoed at MSC) was done as follows: Comute otical deths as before (otdeth.f) Comute transmittances as before (transmittance.f) Comute effective ath (need to know transmittance from surface to sace at nadir). (Transmittance.f) Comute TB and TB (using rtint.f) as before. Only intend to use TB. Comute TB ( θ ) * for vertical AND horizontal olarizations (rddnfix.f). This includes recomuting the otical deths and the transmittances to comute the down-welling brightness temerature for vertical and horizontal olarizations. This can be sed u by using the same aroximation as described in section (See section 6.3) Comute E GO using fast_emiss.f. Also use TB ( θ *) comuted for both olarizations and comute scattered brightness temerature for both olarizations. Comute effect of foam as before (addfoam.f) Comute TB at the to of the atmoshere as before (budtoa.f) 6.3. FASTEM2 simlified A simler way to introduce the effective ath correction term ( P rough = sec θ sec * θ ) is described. For the microwave window channels, the following aroximation is done (See also Section 2.1.1): 31

32 TB * secθ s ( ) = TB ( ) ( secθ ) * 1 τ θ θ ( 1 τ s). (A.5) This follows from assuming that the mean radiating temerature of the atmoshere does not change with view angle (or the isothermal aroximation). τ s is the atmosheric transmittance at view angle θ. The aarent surface temerature for FASTEM2 is: GO TB = E T + ( FC) TB a ~ GO s 1 (A.6) s GO where is the olarization index (V or H). Substituting Eq. A.5 in A.6 leads to: GO GO ~ ~ GO s TBa = E Ts + ( FC)( E ) TB ( ) ( 1 τ ( θ 1 1 θ ) 1 τs( θ) * secθ secθ (A.7) GO or TB = E T + R TB a ~ GO ~ GO s ( θ ), (A.8) where sec θ * ~ GO ~ GO s R ( FC)( E ) ( secθ 1 τ = ) 1 1 ( 1 τs). (A.9) Thus, the RTTOV code only has to be modified to comute a reflectivity term as well as an emissivity term for both olarizations. 32

33 7. References Cox, C., and W. Munk, 1954: Measurements of the roughness of the sea surface from hotograhs of the sun s glitter, J. of the Otical Society of America, 44, English, S., and T. Hewison, 1998: A fast generic millimeter-wave emissivity model, Proceedings of SPIE, 3503, Garand, L., D.S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. Deblonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleesies, D.S. McKague, L. McMillin, J.-L. Moncet, J.R. Pardo, P.J. Rayer, E. Salathe, R. Saunders, N.A. Scott, P. Van Delst, and H. Woolf, 2000, Radiance and Jacobian intercomarison of radiative transfer models alied to HIRS and AMSU channels, submitted to the Journal of Geohysical Research. Liebe, H.J. 1989: MPM- An atmosheric millimeter-wave roagation model, Int. J. Infrared and Millimeter waves, 106, Liebe, H.J., P.W. Rosenkranz and G.A. Hufford, 1992: Atmosheric 60GHZ oxygen sectrum: new laboratory measurements and line arameters, J. Quant. Sectrosc. Radiative Transfer, 48, Petty, G.W. and K.B. Katsaros, 1994: The resonse of the SSM/I to the marine environment. Part II: A arameterization of the effect of the sea surface sloe distribution on emission and reflection, J. Atmosheric and Oceanic Technology, 11, Phaliou, L., 1996: Variational retrieval of humidity rofile, wind seed and cloud liquid water ath with the SSM/I: otential for numerical weather rediction, Q. J. Royal Meteorological Society, 122B, RTTOV-6 SCIENCE AND VALIDATION REPORT, Available from the NWP SAF web site. Wilheit, T.T., Jr., 1979: A model for the microwave emissivity of the ocean s surface as a function of wind seed, IEEE Trans. On Geoscience Electronics, GE-17,