A practical approach for the assimilation of cloudy infrared radiances and its. evaluation using AIRS simulated observations.

Transcription

1 A practical approach for the assimilation of cloudy infrared radiances and its evaluation using AIRS simulated observations. Sylvain Heilliette and Louis Garand Environment Canada 2121 TransCanada Highway Dorval QC H9P 1J3 Corresponding author coordinates: Phone: (514) Fax: (514)

2 1 Abstract A variational estimation procedure for the simultaneous retrieval of cloud parameters and thermodynamic profiles from infrared radiances is proposed. The method is based on a cloud emissivity model which accounts for the frequency dependence of cloud absorption and scattering, and possible mixed phased situations. An effective cloud top height and emissivity are assumed. Monte Carlo experiments performed in a 1D-var assimilation context using simulated Atmospheric Infrared Radiance Sounder (AIRS) observations from 100 channels demonstrate the substantial added value, in theory, of cloudy radiance assimilation as opposed to clear-channel assimilation. Improved temperature and humidity retrievals are obtained for a broad layer above the cloud as well as below cloud level under partial cloud cover conditions. The impact is most pronounced in broken to overcast situations involving mid level clouds. In these situations, the effective cloud top height and emissivity are retrieved with estimated rms errors typically lower than 30 hpa and 3 %, respectively. Expected relative errors on the retrieved effective particle size are of the order of %. The methodology is directly applicable to real hyperspectral infrared data upon inclusion, for local estimation, of the cloud parameters in the Canadian 4D-var assimilation system.

3 2 1 Introduction Numerical Weather Prediction (NWP, see Appendix A for acronyms) centers routinely assimilate infrared radiances identified as free from cloud contamination. This condition represents an important limitation. Indeed, the field of view (FOV) of a typical infrared sounder (~14-17 km diameter) is cloudy approximately 75% of the time (Wylie and Menzel 1999). Some centres, like the UKMET (at the time of this writing), only assimilate clear sky observations from hyperspectral sounders, while other centers, like the ECMWF (McNally et al. 2006), allow the assimilation of channels which are insensitive to low or mid level clouds. To limit the probability of cloud contamination, the selection criteria have to be restrictive. Consequently, there is a substantial loss of available information in regions thought to be of highest meteorological interest (McNally 2002). The assimilation of cloudy infrared radiances represents a major scientific challenge, and even a partial solution, i.e. applicable to specific cloud conditions, could yield important benefits in terms of impact on forecasts. In this paper, the feasibility of directly assimilating cloudy infrared radiances is investigated. A variational method for the simultaneous estimation of temperature profiles, water vapour profiles and cloud parameters is proposed. This method

4 3 includes a modelling of the spectral variation of cloud emissivity and consideration of the mixed phase. It is well suited for the new generation of hyperspectral infrared sounders such as the Atmospheric Infrared Radiance Sounder (AIRS) and the Infrared Atmospheric Sounding Interferometer (IASI). To evaluate the potential impact, Monte Carlo experiments within a 1D-variational assimilation context are carried out for the AIRS instrument. The approach is simple in the sense that no attempt is made to assimilate cloud layering information or to retrieve cloud water profiles. Rather, the definition of the cloud field is simplified to four effective parameters: cloud height, 15 µm effective emissivity, and effective particle size pertaining to water and ice phases. Similar approaches using a less sophisticated cloud modelling are currently studied at other operational centers (Dahoui 2006, Pavelin and English 2006). Chevallier et al. (2004) proposed a more complex approach which includes cloud parameterisation in the retrieval process. Here the goal is to explore the strengths and limitations of the simpler approach just defined. To that effect, controlled experiments involving various cloudy situations are very useful. Indeed, it is the most convenient way to estimate retrieval errors associated with both atmospheric profiles and cloud parameters. The proposed methodology is a natural extension, to first order, of the current clear pixel assimilation system. Therefore, it has the advantage that it could be implemented with relatively minor changes to that system and minimal additional computational costs. An important part of the

5 4 problem is the determination of situations where this simplified treatment of clouds allows reliable atmospheric soundings down to the cloud top and, in scattered or broken sky conditions, below the cloud. Again, simulations provide specific suggestions on quality control procedures which will be needed in an eventual operational implementation. Another approach to cloudy radiance assimilation is that of cloud cleared radiances (Chahine et al. 2006, Suskind et al. 2003, Li et al. 2005). As the name indicates, a procedure transforms cloudy radiances into equivalent clear radiances which can then be used to derive temperature and humidity profiles. Such retrievals are provided by the AIRS science team in near real time (see An obvious advantage of using retrieved profiles is that the assimilation process in NWP is greatly facilitated. One limitation is that such products are available later than radiances, resulting in a data loss of the order of 20 % for operational applications (ECMWF 2005, private communication). The direct assimilation of radiances is currently the preferred approach at NWP centers, providing among other advantages the control on each individual channel (bias correction, error assignment) and the assimilation of radiances from all sensors together in a coherent manner. While the present work is anchored to that methodology, all options are open to best take advantage in operational NWP of the meteorological information present in cloudy hyperspectral radiances.

6 5 This article is organized as follows. Section 2 defines the cloud emissivity model. Section 3 describes the Monte-Carlo experiments designed to evaluate the added value of assimilating cloudy radiances. Section 4 presents the results of the experiments for several effective cloud height and emissivity conditions. The capability to retrieve the effective particle sizes is evaluated in Section 5. Section 6 concludes the article. 2 Cloud emissivity model One of the simplest ways to model the impact of clouds on outgoing infrared radiation is given by the following equation: I cld I ovc 1 I clr (1) where ν is the channel frequency, I cld is the cloudy radiance, I ovc is the overcast radiance corresponding to an opaque cloud, I clr is the clear sky radiance, and Nε is the effective cloud emissivity. This last parameter represents the product of the geometrical fractional cloud cover, N, with the frequency-dependent cloud emissivity, ε(ν). In the following, all radiative transfer calculations are performed

7 6 using the fast RTTOV-8 code (see Matricardi et al for a detailed description) based on the radiative transfer equation given by: I clr ( ν ) = ε ( ν ) τ ( ν ) B( T, ν ) + + s 1 ( ν ) 1 B ( ν ) ( T ( τ ), ν ) ( 1 ε ( ν )) τ ( ν ) B( T ( τ ), ν ) dτ s s s s τ s τ s dτ (2) and I ovc 1 ( ν ) = τ c ( ν ) B( Tc, ν ) + B( T ( τ ), ν ) dτ. (3) τ ( ν ) c In these two equations, T(τ) is the temperature profile, τ is the transmission function between the top of the atmosphere and the current atmospheric level, τ' is the transmission function between the surface and the current atmospheric level, B(T,ν) is the usual Planck function, T s is the skin surface temperature, ε s (ν) is the surface emissivity, τ s (ν) is the transmission function between the surface and the top of the atmosphere, T c is the cloud temperature and τ c (ν) is the transmission function between the top of the cloud and the top of the atmosphere. Equation (1) is based on the hypothesis that the geometrical depth of the cloud is negligible. This equation, together with the assumption of a frequency independent cloud emissivity, forms the basis of many cloud parameter retrieval

8 7 methods such as the minimal residual method (see e.g. Eyre and Menzel 1989), or the widely used CO 2 slicing method (Smith and Platt 1978, Menzel et al. 1983). The CO 2 slicing technique is based on Eq. (1) using two spectrally close channels to eliminate Νε(ν) and solve for the cloud top pressure P c. In our implementation for the AIRS instrument (Garand and Beaulne 2004), several estimates are obtained for up to 12 pairs of channels and the mean is retained. In the context of cloud parameter retrievals, the assumption of a constant cloud emissivity is valid only if spectrally adjacent channels are used, which is not optimal for such a multi-spectral instrument. The MLEV technique, a cloud emissivity and cloud top pressure retrieval method (Huang et al. 2003), may seem more appropriate because it allows for a frequency dependent emissivity. However, this method works best with very high spectral resolution. This requirement is often not satisfied at NWP centres. In the case of AIRS, only a subset of 281 channels out of 2378 is available at MSC in real time. Instead of retrieving the cloud emissivity directly from the cloudy radiance spectra as in the MLEV method, this study takes advantage of a cloud emissivity model. In the context of the absorption approximation often used in the thermal infrared spectral range, the cloud effective emissivity is given by: 1 [ k ()secpg CWC ] N( ν ) = 1 exp (4) abs *

9 8 where k abs (ν) is the specific absorption coefficient, θ is the viewing angle, P is the pressure difference between the bottom and the top of the cloud, g * is the gravitational constant, and CWC is the cloud water content expressed in kg.kg -1. For convenience, the following cloud parameter is defined: δ, which represents the effective cloud water path (units kg.m -2 ): = secpg 1 * CWC (5) Radiative transfer calculations, performed with the widely used DISORT code (Stamnes et al. 1988), have shown that the effects of scattering usually cannot be neglected, especially for the shortwave channels. A rigorous treatment of multiple scattering effects is out of reach at the present time in the context of data assimilation for NWP. A simple and efficient way to account for scattering is therefore required. In this study, scattering is considered by replacing the absorption coefficient k abs (ν) in Eq. 4 by the modified cloud absorption coefficient k cld (ν) following Chou et al. 1999: [( 1 ( ) ) +b( ) ( )] kcld () = kext() (6) In Eq. 6, k ext (ν) is the extinction (scattering and absorption) absorption coefficient, ω is the single scattering albedo and b is the backscattered fraction defined as :

10 b = (, ). 2 dµ µ µ µ 0 P d (7) 1 where P ' is the azimuthally averaged phase function and µ and µ are the cosines of the directions of incident and scattered radiation. As noted by Matricardi (2004), this simple approximation gives better results for cirrus clouds than for low level liquid water clouds. Following the common assumption of a Henyey-Greenstein phase function, an analytical expression for b in terms of the asymmetry factor g can be used (Wiscombe and Grams 1976) or the polynomial approximation proposed by Chou et al The former solution was used in this study. The optical properties necessary for k cld calculations (i.e. k ext, ω and g) depend on wavelength and on the size distribution of water droplets or ice particles via a size parameter, namely the effective radius r e for liquid water clouds, and the effective diameter D e, as defined in Baran (2004), for ice water clouds. Many parameterisations for these optical properties are available in the scientific literature. For pure liquid water clouds, the parameterisation of Hu and Stamnes (1993) is one of the most widely used. However, their parameterisation uses three distinct expressions depending on the effective radius value. A more recent parameterisation using only one analytical expression was preferred for this study, that of Lindner and Li (2000). For pure ice clouds, the situation is more complex

11 10 because the shape of ice crystals has to be taken into account. Parameterisations for various ice crystal habits such as hexagonal columns or plates, aggregates and droxtal, are available. Although these parameterisations lead to different results, their qualitative spectral behaviour is generally very similar. This is the most important point for our purposes. The parameterisation of Baran et al. (2004, 2002 and 2005 private communication) for hexagonal column ice crystals was retained in this study. For mixed phase clouds, an estimation of the liquid water fraction f w is necessary. In this study, the simple parameterisation proposed by Rockel et al. (1991), giving f w in terms of the cloud temperature T c, was retained: 2 [ ( T ) ] exp c ; Tc < f w = (9) 1.0 ; Tc > Optical properties of pure ice and water are then combined in the following way (see Cess 1985): k w i ext = f wkext +( f w )kext 1 (10)

12 11 = f k w w w ext w f wkext +( 1 f +( 1 f w w )k )k i ext i ext i (11) g = f k g w w w ext w f wkext w w +( 1 f +( 1 f w w )k )k i i i ext g i i ext (12) In these three equations, the superscript i refers to ice phase and the superscript w to liquid water. Examples of cloud emissivity spectra given by this model for a pure liquid water cloud and a pure ice cloud are plotted in Fig. 1 and 2. In these figures, 15 µm effective cloud emissivity is fixed at 0.3 and 0.7 and the impact of the size parameters r e and D e is illustrated. It can be seen that for both liquid water and ice, the spectral variation is more pronounced as the particle size decreases. It is worth noting that AIRS does not provide observations in the range cm -1 so that the main region of sensitivity to the particle size is cm -1. Using this simple model, cloudy radiance spectra can be obtained using only four cloud parameters which are independent of wavelength: the cloud top pressure P c, the effective cloud water content δ,the effective radius r e and the effective diameter D e. A variational scheme is proposed in the next section for the retrieval of these four parameters. In order to perform the assimilation experiments presented in the next section,

13 12 it is necessary to evaluate the partial derivatives of cloudy radiances with respect to the four cloud parameters. The RTTOV-8 code was modified to allow the effective cloud fraction to be frequency dependent. The partial derivatives that are needed are then obtained from RTTOV's outputs as follows: I cld ( ) I cld ( ) = P c P c RTTOV I + cld RTTOV f w f T w c Tc P c (13) and I cld ( ) I = cld RTTOV ( ). (14) In (13) and (14), the partial derivative indexed by RTTOV correspond to RTTOV's outputs and the other partial derivatives are obtained from equations 6 to 12 except T c P c which is calculated by assuming that the variation of the temperature profile is linear with respect to the logarithm of pressure. Partial derivatives with respect to the size parameters r e and D e are obtained using an equation similar to (14) since the optical parameters k ext, ω and g are simple functions of the size parameters. 3 Description of the Monte-Carlo experiments

14 13 a Variational procedure In order to evaluate the possible benefits resulting from cloudy radiance assimilation using this cloud emissivity model in comparison to the classical assimilation of clear radiances, Monte-Carlo experiments within a 1D variational context were performed. In 1D-var assimilation experiments, the following cost function is minimized: J( x) = 1 2 t 1 t 1 {( x x ) B ( x x ) + ( H(x) y) O ( H(x) y) } b b (15) In Eq. (15), x is a vector containing temperature and water vapour profiles discretized on 35 levels (the 28 eta levels of CMC s GEM model, see Côté et al. 1998, plus 7 additional levels corresponding to the 7 highest RTTOV-8 pressure levels), surface parameters (T s and P s ) and cloud parameters (δ, P c, r e and D e ). Thus, the dimension of x is 76. The y s represent the observations, here the AIRS brightness temperatures (BT) of the selected channels. H(x) is the radiative transfer model. B is the background-error covariance matrix used at the CMC (Gauthier et al. 1998) augmented to account for error statistics of the four cloud parameters and x b stands for the first guess or background state. O is the observation-error covariance matrix for the AIRS instrument

15 14 The background cloud parameter errors are considered as independent of the background temperature errors. It was verified that the error correlation between these variables is low (< 0.1) and could therefore be neglected. On the other hand, the error correlation between cloud top pressure and cloud effective emissivity is rather high, of the order of 0.8. The impact of this error correlation was also evaluated and found to be insignificant on the retrieved thermodynamic profiles. Thus, for this study, the cloudy part of the B matrix is considered as diagonal. In addition, for this study, a diagonal O matrix was used as it is customary in most operational centers (the current MSC operational assimilation code assumes a diagonal O matrix). Also, a clear-sky estimate for this matrix (Garand et al. 2007) was used as its possible dependence on cloud conditions through radiative transfer could not be inferred. Possible under-estimation of the observation error resulting from the above approximations could result in an over-estimation of the impact of the assimilation of cloudy infrared radiances. b Clear sky assimilation The current setup of AIRS clear FOV radiances assimilation was chosen as a reference. A short description of this setup here follows. 100 AIRS channels were selected from the 281 available channels in order to obtain information about temperature and water vapour. The selection was based on various criteria: shape of the Jacobian function, low sensitivity to ozone, low observation error, lack of

16 15 sensitivity above the model top at 10 hpa. These channels are defined in Fig. 3. As a first step, the CO 2 slicing implementation described in Garand and Beaulne (2004) is applied to get an estimate of the cloud top pressure P c and the 15 µm effective cloud emissivity. More precisely, the CO 2 slicing algorithm is applied to 12 pairs of channels located between cm -1 (14.13 µm) and cm -1 (12.18 µm); the mean and standard deviation of the successful retrievals are calculated. The CO 2 slicing algorithm is usually relatively accurate but it is well known that, in some situations, especially for boundary layer clouds, it fails to give a meaningful result. In such situations, where all the 12 estimations fail, an effective cloud height is estimated by matching a window channel BT with the background temperature profile, assuming an overcast cloud cover. The resulting cloud height is generally underestimated in that situation. Next, the local response function (derivative of total transmittance with pressure) of each channel is calculated. Channels are selected for assimilation if the cloud top is below the level where the response function becomes significant. A precautionary measure consists in rejecting channels for which the observed minus background equivalent brightness temperature exceeds 3 times the standard deviation of that quantity (this is referred to as the background check). In the following, these assimilation experiments will be designated as clear mode and labelled CLR. The average number of channels used in these experiments is summarized in Table 1. Very few channels are used when the cloud pressure height is lower than

17 hpa. c Monte Carlo experiments The Monte-Carlo experiment process is sketched in Fig. 4. A true atmospheric state x t is defined. In these experiments, the US standard atmosphere was chosen to provide the temperature and water vapour profiles and 9 cloudy configurations were obtained by combining 3 values of P c {500 ; 700 ; 850 hpa} with 3 values of Nε (15 µm) {0.3 ; 0.7 ; 1.0} following an approach similar to that used by Li et al Climatological values are assumed for the size parameters: r e =13 µm and D e =25 µm. This true state is used to generate synthetic brightness temperatures using RTTOV and the cloud emissivity model. These brightness temperatures are then perturbed by a Gaussian random number generator of zero mean and covariance matrix O to get pseudo-observations. The O matrix is diagonal with stddev in the typical range 0.4 to 1.1 K, with highest values associated with µm ( cm -1 ) water vapour channels (see Garand et al., 2007). The atmospheric and surface part of x t (i.e. the temperature and water profiles, the surface skin temperature and the surface pressure) are also perturbed with a Gaussian random number generator of zero mean and covariance matrix B to get the atmospheric and surface part of x b. The cloudy part of x b is obtained by application of the above-mentioned CO 2 slicing implementation to the synthetic brightness temperatures to get P c and δ, keeping the size parameters to their

18 17 climatological values. The impact of an incorrect specification of the size parameters is evaluated further in Section 5. The cost function (15) is minimized using a procedure very similar to the one described in Garand (2002) to obtain the analyzed state x a. Three inversion experiments were designed to evaluate the impact of the errors assigned to cloud parameters on the retrievals. As indicated earlier, possible error correlations between cloud parameters were ignored. In a first set of experiments called fixed cloud parameters the errors statistics on cloud parameters were set to very low values so that the initial cloud parameters remained essentially unchanged. In a second set of experiments called controlled cloud parameters labelled CTRLD, the errors associated with P c and δ were set to the standard deviations resulting from the CO 2 slicing retrievals. The error associated with r e was set to 3 µm and that with D e to 5 µm. In a last set of experiments called free cloud parameters labelled FREE, the errors were set to large values so that the cloud parameters were essentially unbound. In order to prevent the assimilation of potentially bad data or extreme values, a background check, similar to the one used for clear channels assimilation, was also tested for each cloud configuration. The threshold used was again 3 times the standard deviation of the difference between the observed brightness temperature and the brightness temperature calculated with x a. Interestingly, that standard deviation turns out to be very close to the estimated observation error established

19 18 from clear radiances which indicates that our assimilation system gives consistent results. These experiments, labelled BT3SIG, are the only ones involving a reduced number of channels. For validation purposes, the Monte-Carlo experiments were first performed with clear sky situations. In that case, assuming that the radiative transfer response to moderate temperature and water vapour perturbations is nearly linear and that observation and background error statistics are exactly specified, the theory predicts that the analyzed state is unbiased with respect to the true state and the associated error is lower than the background error. The error covariance matrix of the analyzed state A is obtained from: 1 1 t ( B HO H ) 1 A = + (16) In equation (16) H represents the Jacobian matrix of the radiative transfer model. This predicted covariance matrix A, labelled linear theory, was compared with the covariance directly calculated from the Monte-Carlo experiments as <(x t -x a ) i (x t -x a ) j >. Results were very close, thus confirming the correct statistical behaviour of the simulations using 1000 realizations. The quality of the random number generator used was also checked from comparison of the B matrix with <(x t -x b ) i (x t -x b ) j >. That comparison also gave satisfactory results. In the cloudy case, Eq. (16) is expected to yield an unrealistic analysis error (underestimated) because the assumption of linearity between input cloud

20 19 parameters and output radiances is no longer valid. The Monte-Carlo approach is therefore the only rigorous way to evaluate the expected impact from the assimilation of cloudy variances. As will be seen in the next section, in our case, Monte Carlo experiments typically lead to significantly higher analysis errors than those predicted from Eq. (16). 4 Results In the following, statistics resulting from the Monte-Carlo experiments are presented. As stated before, the CO 2 slicing technique provides a first estimate of the effective cloud height and emissivity. Because of the nonlinearity of the problem, that first estimate represents an important asset versus a start with arbitrary values. Yet, the CO 2 slicing estimates are in general not precise enough to keep these fixed in the retrieval process. Fixed cloud parameter experiments gave a clear indication to that effect and are therefore not shown a atmospheric variables Fig. (5) provides an example of retrieval error statistics (bias and stddev) associated with temperature and humidity statistics for various retrieval options in the case of an opaque cloud located at 500 hpa (horizontal green line). The guess profile bias (black curve) with respect to the truth is small by construction. The

21 20 biases of the various analyses with respect to the truth remain relatively small except for water vapour in the upper troposphere (0.12 for CTRLTD and FREE). This is possibly linked with the non-linear behaviour of radiative transfer with respect to water vapour. The experiments labelled BT3SIG, which by definition reject extreme departures between observed and calculated BTs, display a significantly smaller bias. It is also noted that the two CTRLD experiments result in a bias of ~0.25 K near the cloud level, a feature not seen in the FREE experiments. In Figs. 5-c and 5-d, the standard deviation associated with the guess is plotted for reference. The linear theory result (orange curve) represents standard deviation of the analysis according to Eq. (14) assuming that there is no error in the determination of the cloud parameters. It can be interpreted as a lower limit of the error which can be expected from the cloudy radiance assimilation. As expected, the other curves normally lie between the guess and linear theory curves. A very significant reduction (dln(q) = ~0.15) of the error for the humidity variable is noted in a broad layer ( hpa) above cloud level. The corresponding temperature error reduction is about 0.25 K, which is also significant given a background error of the order of 1.25 K. A perhaps more convenient way to appreciate the relative impact of the various experiments is to plot the error variance reduction V r defined as the diagonal of the matrix R (times 100 to express it in percentage):

22 21 R 1 = I AB (15) When there is no improvement, Α = Β and V r is zero whereas when Α = 0 (perfect analysis) V r is 100 %. V r should be positive if, as expected, the analysed state is closer to the true state than the background state. The added information content of the retrieval can also be expressed by a single number: the degrees of freedom for signal (DFS, Rodgers, 2000), defined as the trace of the R matrix. It is possible to split this DFS into a temperature and a specific humidity part because the two variables are not directly coupled through B. There is only a very low coupling via P s which is only significant for the lower pressure level located below the cloud. Figures 6 and 7 provide the error variance reduction for temperature and water vapour for the nine cloud configuration studied. As expected, the assimilation of cloudy radiances always gives a larger error variance reduction than the CLR reference experiment (red curve) especially for high clouds where the number of CLR channels is very limited. Generally, the FREE experiments seem to give slightly better results than the CTRLD experiments. The experiments performed with a background check (BT3SIG) lead to a lower V r than the others, notably for the humidity variable. This is expected as fewer channels are used, but the effect is not dramatic. Also lower humidity biases are noted in Fig. 5 for these experiments. Overall, the added value of cloudy radiance assimilation over CLR

23 22 assimilation is substantial for both atmospheric variables. Even when the 15 µm effective emissivity is as high as 0.7, there is a significant gain of information recovered below cloud level, often down to the surface. In practice, the error variance reduction may not be as large as expected due to factors not considered in this study such as the presence of multilayered clouds in the field of view. The best conditions for added information relative to the clear cases are expected in the presence of mid or high level clouds when the effective cloud amount is of the order of 0.5 or more. Tables 2 and 3 synthesize the information from Figs. 6 and 7 in terms of DFS. For a cloud at 500 hpa or 700 hpa, the temperature DFS for FREE experiments is typically a factor of 2 higher than that of CLR experiments. The humidity DFS on the other hand increases by a factor of about 3. The DFS for BT3SIG experiments is about % lower. The DFS of course lowers substantially with cloud height in CLR experiments. In contrast the DFS values related to cloudy assimilation are remarkably similar for all cloud conditions. b cloud parameters The quality of the retrievals can also be evaluated in terms of the cloud parameters. Tables 4 to 7 present the retrieval statistics pertaining to the four cloud parameters before and after assimilation for the FREE experiments. Except for the low cloud and low emissivity configuration (P c = 850 hpa; emissivity =

24 23 0.3), there is a significant decrease in bias and standard deviation associated with P c and δ (in Tables 6-7, δ statistics are translated into 15 µm effective emissivity to ease interpretation). The problems with the low cloud/emissivity configuration are to be expected due to the inherent difficulty of separating cloud and surface contributions to top-of-the-atmosphere radiances. In real applications, some quality control measures will likely be needed beyond the background check. For example, based on Tables 4-7, it appears safer not to assimilate cloudy radiances when the cloud is pre-identified as below 700 hpa with a 15 µm effective emissivity below 0.5 or when the CO 2 slicing technique fails (P c error in excess of 50 hpa and emissivity error in excess of 10 %). Clearly, the positive P c biases (cloud too low) in excess of 5 hpa noted in Table 4 are compensated by positive emissivity biases. It is not obvious how to establish the most appropriate rejection criteria. However, assimilating only when the best conditions for the determination of the cloud parameters are met makes sense, and such situations already represent an enormous increase in data volume compared to clear assimilation. For most cloudy conditions where P c > 700 hpa and where the cloud cover is above 50 %, it appears possible to retrieve P c with an error of the order of 30 hpa or less. Corresponding 15 µm emissivity errors are typically below For completeness, error statistics pertaining to the effective particle size are presented in Tables 8 and 9. Biases are generally low. Depending on the cloud emissivity category, errors associated with D e are in the range 4-9 µm (16-36 %)

25 24 and those associated with r e are in the range 3.0 to 4.5 µm (23-35 %). The role of the size parameters in the assimilation is further studied in the next section. 5 Sensitivity to size parameters Additional Monte Carlo experiments were performed in order to evaluate the possible impact of an incorrect specification of the size parameters D e and r e as well as the capability of the assimilation to retrieve these parameters. According to ISCCP ( the typical range for r e is 5 to 20 µm while it is 10 to 50 µm for D e. The 13 µm value used in this study for r e is quite typical of areas over the sea whereas r e tends to be lower over continents (near 10 µm). For the experiments presented here, the 15 µm effective cloud emissivity is set to 0.7. High (500 hpa) and low (850 hpa) P c were considered in order to evaluate the impact for both ice and liquid water clouds. In a first set of experiments, the 1D-var retrievals were performed by assuming size parameters widely different from those used to generate the synthetic data. By assigning a small error to these parameters, they remain essentially fixed to their assigned incorrect value. The simulated brightness temperatures were calculated with true values D e =50 µm and r e =8 µm whereas in the retrieval process D e =25 µm and r e =13.0 µm was assumed. In a second set of experiments, the parameters

26 25 were allowed to vary. Statistics for the two situations are presented in terms of bias in Fig. (8) and variance reduction in Fig. (9). Figure 8 shows that the bias pertaining to the FIXED size parameter experiments is significantly greater than that pertaining to the FREE size parameter experiments. Figure 9 on the other hand shows that the variance reduction is very similar for both experiments. Retrieval statistics for the size parameters are presented in Tables 10 and 11. For the water cloud at 850 hpa, the initial bias of 5 µm is reduced to 0.9 µm and the rms error of 3.7 µm represents a relative error of 46 %. In part, this result is facilitated by the low value of the true radius at 8 µm, which maximizes the sensitivity to particle size (Fig. 1). For the ice cloud at 500 hpa, the initial bias of - 25 mm is reduced to -8.5 µm and the rms error of 12.9 µm represents a relative error of 26 %. These results indicate that the assimilation has some skill in retrieving the effective particle size. More importantly, inclusion of the size parameters in the assimilation process results in reduced temperature and humidity retrieval biases. 6 Conclusion

27 26 A relatively simple infrared cloud emissivity model and a procedure for the simultaneous estimation of cloud parameters and atmospheric profiles are proposed. Mixed phase cloud situations are considered. By providing a realistic description of the frequency dependent cloud emissivity, only four cloud parameters, independent of frequency, are required in the retrieval process: P c, δ, r e and D e. Monte Carlo simulations demonstrate the substantial added value of cloudy radiance assimilation over clear channel radiance assimilation. This holds true for a broad atmospheric layer above cloud level. Significant information is also retrieved below cloud level in non-overcast conditions. Cloud parameters are best retrieved in broken to overcast situations involving mid level clouds. In these situations, cloud top and emissivity errors are typically below 30 hpa and 3 %, respectively. The capability to retrieve the effective particle size is limited, but nevertheless non negligible, with expected errors of the order %. The simplicity of the approach allows its application with real data in 3D and 4D data assimilation cycles. There are two basic possible avenues: 1) The simplest approach is to pre-determine the cloud parameters in a 1Dvar retrieval and then keep these fixed in 4D-var assimilation. In light of results obtained in this study, this approach is not ideal. Degraded results were often noted in fixed parameter experiments along with significant biases compared to free experiments. In principle, the approach would work if cloud parameters

28 27 could be pre-determined to excellent precision. However, due to the high sensitivity of the radiances to cloud parameters, the latter will be best evaluated using all available information, which can only be achieved in a 3D or 4D assimilation system. 2) The second approach is to let the cloud parameters vary in 3D/4D assimilation. This requires a modification to the operational code to include in Eq. (15) a background term for the local estimation of the four cloud parameters. There is no intent to produce global maps of cloud parameters at this time. The size of the minimization process which yields the NWP analysis is augmented by the number of cloudy radiance sites times the four cloud parameters. This represents a modest increase to the dimension of the assimilation problem and therefore the extra cost should be small. The first guess for the effective cloud top and emissivity will again come from the CO 2 slicing technique. At the present time, assimilation tests have begun following that methodology. A more costly option, hopefully not necessary, is to provide improved estimates from 1D retrievals as in the first option. In conclusion, the potential impact associated with the assimilation of cloudy infrared radiances is substantial, even in the context of the simple modeling and assimilation framework proposed here. It remains to be seen to what extent this impact will be measurable with real data. A good part of the problem will be to

29 28 identify those situations where cloudy radiance assimilation is likely to succeed and to discard situations where this is not the case. Some quality control measures were suggested from this study. Collocated high resolution imagery could be used for a better characterization of the clouds within the FOV of the assimilated channels. This includes measures to detect multilayered clouds. The problem of radiance bias correction in a cloudy context will also have to be addressed. Because the method proposed here is a first-order extension to the clear pixel assimilation system, it will be possible to evaluate its impact on NWP analyses and forecasts in the near future. Acknowledgements The authors are grateful to Antony Baran and Peter Francis for providing their ice cloud optical property data. The authors would like also to thank Dr. Hershell Mitchell and Dr. Godelieve Deblonde for their careful reading of the manuscript and the anonymous reviewers for their constructive comments. Sylvain Heilliette was funded by a NSERC grant. The development of the AIRS processing system was funded by the Canadian Space Agency within the context of the Government Related Initiative Program.

30 29 Appendix List of acronyms 1D-var AIRS BT CMC One Dimensional variational Atmospheric Infrared Radiance Sounder Brightness Temperature Canadian Meteorological Centre ECMWF European Centre for Medium-range Weather Forecasts FOV GEM GOES IASI MLEV Field Of View Global Environmental Multiscale Geostationary Operational Environmental Satellite Infrared Atmospheric Sounding Interferometer Minimum Local Emissivity Variance NESDIS National Environmental Satellite Data and Information Service NOAA NWP National Oceanic and Atmospheric Administration Numerical Weather Prediction RTTOV Radiative Transfer for TIROS Operational Vertical Sounder UKMET United Kingdom's METeorology office

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37 36 P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= ε(15µm)= ε(15µm)= Table 1. Average number of AIRS channels used in the CLR experiments. P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= / 2.39 / / 2.15 / / 1.55 / 1.40 ε(15µm)= / 2.39 / / 2.21 / / 1.86 / 1.52 ε(15µm)= / 2.29 / / 2.24 / / 1.78 / 1.71 Table 2. Temperature DFS for the CLR / FREE / FREE BT3SIG experiments, respectively.

38 37 P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= / 3.51 / / 2.81 / / 1.85 / 1.36 ε(15µm)= / 3.38 / / 3.12 / / 3.09 / 2.36 ε(15µm)= / 3.12 / / 3.15 / / 3.33 / 2.57 Table 3. Natural logarithm of specific humidity DFS for the CLR / FREE / FREE BT3SIG experiments, respectively. P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= / / / ε(15µm)= / / / ε(15µm)= / / / 5.41 Table 4. Cloud top pressure biases (hpa) before/after 1D-var assimilation.

39 38 P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= / / / 9.33 ε(15µm)= / / / ε(15µm)= / / / Table 5. Cloud top pressure stddev (hpa) before/after 1D-var assimilation. P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= / / / ε(15µm)= / / / ε(15µm)= / / / Table µm emissivity bias before/after 1D-var data assimilation.

40 39 P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= / / / ε(15µm)= / / / ε(15µm)= / / / Table µm emissivity standard deviation before/after 1D-var data assimilation. P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= / / / 3.41 ε(15µm)= / / / 6.44 ε(15µm)= / / / 8.58 Table 8. Effective diameter (D e, µm) bias/stddev after 1D-var data assimilation. The ice fraction f i is 0.0/0.35/0.83 at 850/700/500 hpa, respectively.

41 40 P c =850 hpa P c =700 hpa P c =500 hpa ε(15µm)= / / / 0.78 ε(15µm)= / / / 4.21 ε(15µm)= / / / 4.31 Table 9. Effective radius (r e, µm) bias/stddev after 1D-var data assimilation. The water fraction f w is 1.00/0.65/0.17 at 850/700/500 hpa, respectively. P c =850 hpa P c =500 hpa ε(15µm)= / / 2.81 Table 10. Effective radius (r e ) bias/stddev after 1D-var data assimilation. The water fraction f w is 1.0 at 850 hpa and the ice fraction f i is 0.84 at 500 hpa. P c =850 hpa P c =500 hpa ε(15µm)= / / 9.72 Table 11. Same as Table 10, but for the effective diameter (D e ).

42 41 Figure 1. Spectral variation of liquid water cloud effective emissivity for various values of the effective radius r e. The 15 µm emissivity is set to either 0.7 or 0.3.

43 42 Figure 2. Same as Fig.1 but for the variation of the effective ice particle diameter D e.

44 43 Figure 3. Wavenumber (cm -1 ) versus AIRS channel number (1-2378) for the subset of AIRS channels

45 Figure 4. Schematic description of the Monte-Carlo experiments performed. 44

46 45 Figure 5. Error bias (top panels) and standard deviation (bottom panels) of temperature and water vapour retrievals for an opaque cloud at 500 hpa.

47 46 Figure 6. Temperature error variance reduction for the 9 cloudy configurations studied.

48 47 Figure 7. Natural logarithm of specific humidity error variance reduction for the 9 cloudy configurations studied.

49 48 Figure 8. Temperature (upper panels) and natural logarithm of specific humidity (lower panels) biases resulting from a mis-specification of the size parameters. Results shown for free or fixed size parameters in the assimilation. Initial bias also shown.

50 49 Figure 9. Variance reduction for temperature (upper panels) and water vapour (lower panels) retrievals associated with a mis-specification of the size parameters. Results shown for free or fixed size parameters in the assimilation. Linear theory result also shown.