Assimilation of overcast cloudy infrared radiances of the geostationary MTSAT-1R imager

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1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 139: , April 2013 A Assimilation of overcast cloudy infrared radiances of the geostationary MTSAT-1R imager Kozo Okamoto* Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Japan *Correspondence to: K. Okamoto, MRI, JMA, 1-1 Nagamine, Tsukuba, Ibaraki , Japan. kokamoto@mri-jma.go.jp Infrared radiances from the Multi-functional Transport Satellite (MTSAT)-1R satellite were assimilated in cloudy conditions where effective cloud fractions were greater than 0.8. These cloudy radiances provide new information that currently assimilatedclear-skyradiancesfromgeostationarysatellitesandmicrowavesounders do not have. The radiance data to be assimilated were created by averaging pixels from the original radiances. We investigated how the characteristics of spatially averaged observations (super-observations or super-obs) vary with the super-ob size. The cloudy super-ob radiances were simulated by using a simple radiative transfer model with cloud-top pressure (P c ) and effective cloud fraction (N e ). The model assumed a single-layer cloud and that cloud emissivity does not depend on spectral wavelength. These two parameters were estimated by a minimum residual method with the infrared channel 1 (10.8 µm) and channel 2 (12.0 µm). To further ensure the validity of these assumptions, we limited use of super-ob radiances to almost completely overcast (N e 0.8) conditions with homogeneous, middle to relatively high clouds (160 P c 650 hpa). These overcast super-ob radiances (OSRs) from geostationary satellites have the advantages of (i) providing temperature information that is highly vertically resolved at the cloud top, (ii) providing frequent measurements, and (iii) being available in cloudy areas where clear radiances are often rejected by cloud quality-control procedures. Data assimilation experiments revealed that OSRs generally had a small impact on analyses and forecasts but provided a slightly improved forecast of temperatures in the upper troposphere and winds in the low troposphere. Copyright c 2012 Royal Meteorological Society Key Words: cloudy radiance; satellite observation; data assimilation; MTSAT Received 20 February 2012; Revised 9 May 2012; Accepted 18 May 2012; Published online in Wiley Online Library 23 July 2012 Citation: Okamoto K Assimilation of overcast cloudy infrared radiances of the geostationary MTSAT- 1R imager. Q. J. R. Meteorol. Soc. 139: DOI: /qj Introduction Assimilation of satellite data in cloudy and precipitating areas is crucial to improving the accuracy of analyses and forecasts in numerical weather prediction (NWP). Challenges to assimilating cloud- and precipitation-affected satellite data include the nonlinearity of physical processes in clouds and precipitation, complex and non-gaussian error statistics, and a mismatch in the spatial resolution of observations and models (Errico et al., 2007; Bauer et al., 2011a). Nevertheless, many investigators have recently made progress in developing and operationally implementing the assimilation of cloud- and precipitation-affected infrared radiances (Greenwald et al., 2002; Heilliette and Garand, Copyright c 2012 Royal Meteorological Society

2 716 K. Okamoto 2007; Pavelin et al., 2008; McNally, 2009; Pangaud et al., 2009; Lupu and McNally, 2012) and microwave radiances (Bauer et al., 2010; Geer et al., 2010; Aonashi and Eito, 2011). These authors assimilated infrared radiances by assuming a single-layer cloud, in which radiative transfer is calculated simply by using the cloud-top pressure and an effective fraction of cloud, rather than a cloud profile. Even with this simple treatment, appropriately selected data offer valuable information not available from other measurements. For example, McNally (2009) showed that overcast radiances of hyperspectral infrared sounders generated analysis increment of warming at 700 hpa and cooling at 850 hpa due to a sharp Jacobian of radiances with respect to temperature above the tops of stratocumulus clouds. While this approach has been used mostly for infrared sounders on board polar orbiting satellites, we focused on applying it to infrared imagers on geostationary satellites. Assimilating cloudy radiances from geostationary imagers offers the advantage of using information that is frequently measured, despite having many fewer available channels than are used by hyperspectral sounders on polar orbiting satellites. It also addresses the underuse of data from geostationary satellites in operational data assimilation systems. Although space agencies disseminate various data including atmospheric motion vectors (AMVs), clear-sky radiances (CSRs), all-sky radiances (ASRs) and visible channel products, NWP centres currently assimilate only AMVs and CSRs. We expect even more benefit from applying this approach to advanced imagers on board the next generation of geostationary satellites, including the Himawari-8, Geostationary Operational Environmental Satellites (GOES)-R, Meteosat Third Generation (MTG) and FengYun (FY)-4. Another goal of this study was to address the problem of inconsistent spatial scales between models and observations. For example, the spatial resolution of the global model of the Japan Meteorological Agency (JMA) is 20 km, while that of the infrared imager on the geostationary MTSAT- 1R satellite is 4 km. Many NWP centres deal with the problem by assimilating CSRs that are spatially averaged clear-sky pixels (e.g pixels for MTSAT) in clear conditions. In cloudy conditions the spatial inconsistency becomes more serious because of the large variability of clouds and the strong sensitivity of infrared radiances to clouds. To address the spatial mismatch, we also adopted an up-scaling approach of averaging original pixels to the model resolution, rather than a down-scaling approach, such as a sub-grid cloud scheme (Jakob and Klein, 1999), because the former is both simpler and widely used in satellite data processing. A synthetic up-scaled observation is called a super-observation or super-ob. Geer and Bauer (2010) have recently improved the all-weather assimilation of microwave imager radiances by replacing the assimilation of radiance at the pixel closest to a model grid with assimilation of super-ob radiances averaged over the resolution of their assimilation system, after investigating the model s representation of precipitation. Super-ob radiances have two additional advantages: first, statistics estimated from original pixel radiances may be used as an indicator of quality. Second, their error distribution can be more Gaussian than that of the original pixels, according to the central limit theorem that states the mean of sufficiently large number of samples randomly distributed is approximately normally distributed. In fact, assimilation of CSRs, which are super-ob radiances consisting of only clear-sky pixels, uses clear-sky rate (fraction of all pixels which are clear-sky) and the standard deviation (SD) of the clear pixel radiances in order to ensure the identification of clear radiances (Köpken et al., 2004). The goal of this study was to characterize super-obs of infrared radiances from the MTSAT-1R imager, and to assimilate them under cloudy conditions into the global data assimilation system. Section 2 describes the MTSAT- 1R imager and the characteristics of super-ob data. Section 3 presents a simplified radiative transfer model (RTM) and estimation of the cloud parameters. Section 4 explains the pre-processing and main analysis for assimilating overcast super-ob radiances. Section 5 presents their impact on analyses and forecasts, as shown by assimilation experiments. The article concludes with a summary, discussion and future plans in section Super-ob of the MTSAT imager 2.1. MTSAT-1R imager The geostationary satellite MTSAT-1R was launched by Japan on 26 February 2005 and began routine operation at 140 E on 28 June It carries a visible and infrared imager called the Japanese Advanced Meteorological Imager (JAMI). The imager has one visible and four infrared channels (specifications in Table 1). The four infrared channels are called IR1, IR2, IR3 and IR4 in this study. The imager scans the full Earth disk for about 24 minutes once every hour. We processed the raw High Rate Information Transmission (HRIT) data of JAMI, which has pixels in a full Earth image (JMA, 2003). Puschell et al. (2006) provide more details about JAMI. Table 1. Channel characteristics of the MTSAT-1R imager. Spectral channels IR1 IR2 IR3 IR4 VIS Wavelength (µm) Central wavelength (µm) Ground resolution at nadir 4 km 1 km Radiometric sensitivity Scene K 0.11 K 0.09 K 1.59 K 55 Scene K 0.05 K 0.01 K 0.03 K 1110 Pixels in a full disk (line column) Radiometric sensitivity shows the in-flight Noise Equivalent Differential Temperature (NEDT) measured in scene 1 at 220 K and in scene 2 at 300 K for infrared (IR) channels; for visible (VIS) channels, it shows the Signal-to-Noise Ratio (SNR) in scene 1 at 2.5% albedo and in scene 2 at 100% albedo.

3 Assimilation of Cloudy Radiances from MTSAT-1R Super-ob The super-ob of the MTSAT-1R imager is a weighted average of original pixels. The shape of a super-ob was assumed to be a circle with radius r s. The weight of pixel p (w p )was calculated with a Gaussian function of distance d p from the centre of the super-ob: ( ) w p = W 0 exp d2 p 2rs 2, (1) where W 0 is a normalization factor. This Gaussian function gives 60% smaller weight to pixels at the edge (d p = r s ) than those at the centre (d p = 0) of the super-ob. The centre of a super-ob was placed at a model grid point so that observation operators in the data assimilation process did not need to spatially interpolate model variables to the observation point. This can be crucial for variables that are spatially inhomogeneous, such as clouds, because a simple interpolation might damage the balance of the model. Pixels were eliminated when departures from the mean radiance were three times greater than the SD of pixel radiances in the corresponding super-ob. Pixels in each super-ob also provided useful information for quality control (QC) in data assimilation: the SD of pixel brightness temperatures (BTs), the number of pixels that form the super-ob, the clear-sky rate and the sea rate (fraction of all pixels which are over the sea). Clear pixels were identified with a threshold approach based on the MTSAT CSR algorithm (Uesawa, 2009), which used differences between IR1 channel BT and IR2 channel BT and between IR1 BT and the sea-surface temperature (SST). The characteristics of super-obs vary with their radius r s. The number of pixels used to construct a super-ob, shown in the columns (a) and (b) of Table 2, reaches a maximum at satellite nadir and a minimum at the edge of Earth s disk. As satellite nadir angle increases, there are fewer pixels in a super-ob because the size of a pixel increases with this angle. Figure 1(a) shows that the SD of pixel BTs varies with the super-ob BT. The pixel SD increases with the super-ob r s because a larger super-ob includes more diverse types of clouds (therefore, the pixel BTs are more diverse as well). The average number of super-obs in a full Earth disk image per hour (that is per image) is shown in columns (c) to (f) of Table 2. The super-obs were calculated from MTSAT-1R imagery at every two model grid points (approximately 120 km), every two hours on 25 July Column (d) of Table 2 shows that, as the super-obs become larger, their numbers over the sea decrease because the larger super-obs are more likely to include land pixels. Figure 2 shows that the relative frequency of channel IR1 super-ob BTs over the sea decreases with increasing super-ob radius r s at very high (BT 290 K) and low temperatures (BT 240 K), whereas it increases with increasing r s at medium to high temperature (250 BT 286 K). Consequently, as r s increases the variance of super-obs decreases. This result suggests that with increasing super-ob size, low BT (high, opaque cloud) pixels and high BT (clear-sky) pixels tend to be mixed, and thus averaged, in the same super-ob, which reduces the number of super-obs at extreme BTs. This explains the apparent contradiction between the increasing pixel SD, shown in Figure 1(a), and the decreasing super-ob SD as r s increases. In addition, since super-ob populations with medium and higher temperatures increase in frequency with increasing r s, low clouds are more likely to be identified in larger super-obs. This behaviour is consistent with the increase of low clouds as spatial resolution increase from 1 km to 20 km for the Moderate-resolution Imaging Spectroradiometer (MODIS) instrument, as Menzel et al. (2008) reported. The variation in the frequency distribution of superob BTs with the super-ob scale suggests that the use of super-obs with an inappropriate scale may cause systematic differences between the representation of clouds by models and the super-obs data. For example, if the super-ob scale is smaller than the scale of the model representation, even a perfect model might fail to simulate very high or low BTs of the super-obs. In contrast, for super-obs that are larger than the model scale, the model might predict excessively low temperatures in high clouds or excessively high temperatures in low clouds. Thus, one must carefully select the scale of super-obs to simulate cloudy radiances when model cloud variables are used. Ideally, this should be done after accounting for the situation-dependent representativeness of model and observation, and spatial correlation of observation error (Berger, 2004; Lopez et al., 2011). In this study, however, the inconsistency between the model and the super-obs was small because we did not extract cloud variables from the model but rather from the super-obs, as we will show in the next section. Thus, r s was simply set to 30 km to fit the resolution of the model used in this study (60 km, see section 4). 3. Simulation of cloudy radiances and quality control This study focused on cloudy radiances that a simple RTM can simulate well, under the assumption of a single-layer cloud. The simple RTM calculates a radiance at channel i (R i )as R i = R c i (1 N e) + R o i N e (2) Table 2. (a) (b) Numbers of pixels used to construct a single super-ob, and (c) (f) numbers of super-obs in a full Earth disk image, for each super-ob radius r s on 25 July Number of pixels in a super-ob Number of super-obs in a full Earth disk (a) (b) (c) (d) (e) (f) r s (km) min max mode all over sea N e 0.8 over sea OSR over sea Super-obs were generated at every two model grids. N e is effective cloud fraction and Overcast Super-ob Radiances (OSRs) are homogeneous super-obs with N e 0.8, which are defined in section 3. Super-obs over sea contains more than 95% pixels with land ratio below 0.01%.

4 718 K. Okamoto Figure 1. (a) Mean of the standard deviations (SDs) of pixel brightness temperatures (BTs) at each super-ob BT bin (upper curves, for super-ob radii of 100, 60, 30 and 10 km, as indicated in legend at upper right). The number of super-obs at each bin is also plotted for radii r s = 10 and 100 km with black and grey bars, respectively; the number values are on the right axis. (b) As (a) but for bins of cloud-top pressure (hpa) estimated from super-ob BT over the sea, for effective cloud fraction N e greater than 0.8. wherer c i is a clear-sky radiance and R o i is a completely overcast radiance from a blackbody cloud at cloud-top pressure P c,andn e is the effective cloud fraction, defined as the cloud fraction multiplied by the cloud emissivity. In this study, we calculated R c i with the Radiative Transfer model for the TIROS Operational Vertical sounder (RTTOV) version 9 (Saunders et al., 1999; Matricardi et al., 2004) and R o i was provided as a part of the calculation of R c i. Note that Eq. (2) also assumes that N e is independent of wavelength or channels. Thus, the channels to be used must be carefully selected to avoid encountering quite different optical properties. We estimated the two cloud parameters P c and N e using the minimum residual method (Eyre and Menzel, 1989), which employs no model cloud variables. The minimum residual method determines P c and N e so as to minimize the radiance residual J: J = i = i J i = i (R m i R i ) 2 {R m i R c i N e(r o i R c i )}2, (3) where R m i is a measured radiance. By setting dj/dn e = 0, we obtain (R c i Rm i )(R c i Ro i ) i N e = (R c i. (4) Ro i )2 i Since Eq. (4) relates N e to P c,bothp c and N e that minimize the residual J in Eq. (3) are easily determined. The channels

5 Assimilation of Cloudy Radiances from MTSAT-1R 719 Figure 3. Scatter plot of cloud-top height (km) from CloudSat and MTSAT super-obs: CloudSat on the left axis, and MTSAT on the bottom. The grey shading of each symbol represents effective cloud fraction N e from the super-obs (legend at right); circles indicate N e 0.8 and squares, N e < 0.8. The data were observed over the sea from 25 July to 9 September Points were considered collocated if within 15 km of location and 5 minutes of time difference. Figure 2. Relative frequency (i.e. frequency normalized by total number of super-obs over the sea) of super-ob BTs of MTSAT-1R channel IR1 over the sea for (a) the whole BT range between 200 and 300 K and (b) a zoomed-in range from 270 to 295 K. These plots use the same data as in Figure 1(a). This figure is available in colour online at wileyonlinelibrary.com/journal/qj IR1 and IR2 were chosen in the method to avoid as much wavelength dependence of N e as possible. We removed unphysical cases, where N e > 1.0, N e < 0.0 or cloud-top height was higher than tropopause level estimated from the model. P c was determined at a discrete model level where R o i was calculated. To improve the P c estimate, we attempted to calculate P c by interpolating P ci, which minimized the residual of each channel J i, with weights of the inverse of J i, instead of a simple approach that just adopted the model level that minimized J. However, because J i of channels IR1 and IR2 were close, this attempt made almost no difference and we decided to employ the simpler approach. We validated the cloud-top pressure derived from the minimum residual method with that from the Cloud Profiling Radar (CPR) on board the CloudSat satellite (Stephens et al., 2002). We obtained CloudSat cloud information from cloud mask profiles in the 2B-GEOPROF dataset from 25 July through to 9 September Collocation was made where the difference between the CloudSat CPR footprint and the centre of the MTSAT super-obs was less than 15 km in distance and 5 minutes in time. We averaged the collocated cloud-top heights of CloudSat and compared them with the corresponding super-ob of MTSAT-1R (Figure 3). The MTSAT super-ob cloud-top height agreed with the CloudSat value when N e 0.8 (correlation coefficient of 0.972; root mean square error (RMSE) of km), although the mean MTSAT-1R height was km higher than the mean CloudSat value. This result confirmed that the minimum residual method provided a reliable cloud-top height when N e 0.8. To further confirm the validity of the assumption of a single-layer cloud, we removed spatially inhomogeneous super-obs where clear-sky rates exceeded 5% or pixel SDs exceeded 4.5 K, a criterion that was experimentally determined. The pixel SD tended to increase for larger super-obs and higher cloud-top pressures (Figure 1(b)). If an excessively small criterion was adopted, it would remove most of the super-obs containing high clouds, especially when r s was large. The clear-sky rate also depended modestly on r s as small super-obs were more likely to have the minimum (0) or maximum clear-sky rate (100). For example, with an r s = 100 km, more than half (539 of 962) of the super-obs with N e 0.8 would be removed under this quality-control criterion, shown in the columns (e) and (f) of Table 2. However, for r s = 30 km, as adopted in this study, the rejection rate was reduced to less than 40% (446 of 1169). The super-ob radiances that met the above criteria (N e 0.8, pixel SD 4.5 K and clear-sky rate 5%) are hereafter called overcast super-ob radiances (OSRs). The first-guess departures, that is, observed BT minus the background BT (denominated O B, mean ± SD) are shown in Figure 4, for OSRs in channels IR1 and IR2 as a function of P c. The background BT was calculated with Eq. (2) from a short-range forecast and the estimated cloud parameters. The variability of O B was small: for instance, the SD was 0.16 K for channel IR1 and 0.15 K for channel IR2 over the whole range of P c. This result demonstrates that Eq. (2) simulated the measured BT well in overcast conditions, as we expected from the principle of the minimum residual method. However, the channel IR1 departure was shifted slightly towards the negative, and the channel IR2 departure towards the positive, especially when cloud top was low or very high. This channel-dependent bias may be attributed to the effect of N e on wavelength because underestimation or overestimation of either cloud height or the geometric cloud fraction would cause biases in the same direction for both IR1 and IR2.

6 720 K. Okamoto Figure 4. (a) Mean value of observed BT minus the background BT (O B) of overcast super-ob radiances (OSRs) over the sea (upper curve), and the number of OSRs (bars at the bottom), for channel IR1, against cloud-top pressure (hpa, horizontal axis). Error bars indicate ±1SD.(b)Asin(a)butfor channel IR2. (c) As in (a) but for assimilated OSRs that passed all QCs.

7 Assimilation of Cloudy Radiances from MTSAT-1R 721 It is important to remove or correct these biased data, as the assumption of Eq. (2) is violated. We did not apply a bias correction because we prioritized less complex approaches in this study; bias correction may cause a complex interaction with estimation of cloud parameters and QCs (Auligné and McNally, 2007). Therefore, we removed OSRs when the cloud top was above 160 hpa or lower than 650 hpa. These two thresholds were determined so that the opposite sign of O B virtually disappeared in channels IR1 and IR2. After this cloud-height-related QC, OSRs from clouds at levels between 170 and 400 hpa were dominant (Figure 4(c)). A slight bias still remained in the middle troposphere that may require bias correction, which we will investigate in the future. 4. Assimilation set-up for OSRs We used a low-resolution version of the operational global data assimilation system of JMA in this study. The system is composed of a forecast model with a resolution of TL319L60 (approximately 60 km horizontally and 60 vertical layers) and the model top at 0.1 hpa, and a 4D-Var analysis system with an inner loop of T106L60 (approximately 120 km). We performed assimilations every 6 h. The assimilation window of each analysis is six hours long and is divided into six time slots: the first is 0.5 h, the second to fifth are 1 h, and the sixth is 1.5 h long (for the 1200 UTC analysis, for example, the slots are , , , , and ). The irregular time slots are adopted to reduce computational burden by shortening forecast integration range in 4D-Var, compared to equally divided windows (JMA, 2007). Assimilated satellite data included AMVs from five geostationary satellites and two polar-orbiting satellites; radiances of the Advanced Microwave Sounding Unit (AMSU-A, AMSU-B), Microwave Humidity Sounder (MHS), Special Sensor Microwave/Imager (SSM/I), Advanced Microwave Scanning Radiometer (AMSR-E), TRMM Microwave Imager (TMI) and Special Sensor Microwave Imager/Sounder (SSMIS) instruments on polar-orbiting satellites; CSRs from the water vapour channels on five geostationary satellites; sea surface winds from the Advanced Scatterometer (ASCAT); and atmospheric refractivity from Global Positioning System (GPS) occultations. Radiance data affected by clouds or precipitation were not assimilated into the operational system. Data were thinned to one point in a 250 km box in every time slot for microwave temperature sounders, one per 180 km box for microwave humidity sounders, and one per 200 km box for microwave imagers. CSRs were thinned to one per 220 km box in every other time slot. New pre-processing steps for OSRs were included in the operational assimilation system. We implemented a spatial thinning of three grid boxes (approximately 180 km) in every time slot. Note that OSRs existed in only five of the six slots because full-disk imaging begins every hour just after the half hour; consequently, no OSR was recorded during the first half-hour-long slot. OSRs do not virtually depend on surface conditions because overcast clouds block most surface radiation. This study, however, assimilated OSRs only over the sea because estimating cloud parameters becomes more uncertain over land and sea ice. OSRs were removed when their local zenith angle exceeded 62.5 because the radiative transfer calculation has potentially lower accuracy for the long slant view. OSRs composed of fewer than ten pixels, which can occur at the outer edge of the image disk, were also rejected because auxiliary cloud information, such as the clear-sky rate, was of poor quality, and the central limit theorem assumption may have been violated, resulting in a non-gaussian observation error. Finally, gross error QC checks removed OSRs with O B greater than three times the observational error. This error was determined from the SD of O B and assigned to be 0.2 K. We assimilated OSRs of channel IR1 in this study, and possible use of more channels will be discussed in section 6. For comparison, in the operational system and this study, CSRs of water vapour channels from five geostationary satellites were assimilated with observation error of 1.5 K over both sea and land (Toshiyuki Ishibashi, personal communication; Okamoto et al. 2008). CSRs were bias-corrected using variational bias correction (VarBC) with predictors of their background BTs, near-jet-level wind speed and a constant term, and were screened out by clear-sky identification QC (pixel SD > 1.0 K and clear-sky rate > 35%) and gross error QC checks ( O B > 4.5 K). ThenumberofOSRs(andoforiginalsuper-obs)ateach data-screening step in the analysis for 25 July 2009 is shown in Table 3. Only one-seventh of the super-obs over the sea were identified as OSRs and then, only one-third of the OSRs passed all the QC checks. The number of OSRs that were assimilated was much smaller than the number of microwave sounder data (1.6% of AMSU-A and 6.9% of MHS data) or imager data (15% of AMSR-E), and was about half the number of CSRs. The analysis variables of the 4D-Var assimilation are temperature, vector wind, logarithm of specific humidity, surface pressure, and coefficients of VarBC. No cloud variables are analysed in our 4D-Var system. We retrieved the cloud parameters for OSRs (P c and N e ) in the preprocessing stage and kept them constant in the main analysis. This configuration allows OSRs to have a direct impact on the temperature and humidity through the adjoint model of RTTOV-9. It is expected that OSRs affect other analysis variables through dynamical and physical processes in the model, a balance constraint of background error covariance, and assimilation cycles. 5. Impact of assimilation of OSRs The OSRs from geostationary satellites are expected to have three distinctive advantages: (i) temperature information with high vertical resolution at the cloud top, (ii) high temporal resolution, and (iii) high availability in regions too cloudy for other radiance measurements. The high vertical resolution is because the radiation from below the cloud top is almost completely blocked. McNally (2009) showed that assimilation of cloudy radiances from hyperspectral sounder data made temperature and humidity analysis increments (i.e. departure from background) sharper. In order to verify these features, we carried out two sets of observation system experiments (OSEs). Set A consisted of one-cycle experiments at 0600 UTC on 29 July 2009 that started from virtually no satellite baseline, making it easier to illustrate the impact of each observation type. We performed several experiments with different data configurations at 0600 UTC on 25 July 2009 (Table 4). In the Base run of the set A, neither AMSU-A radiances, CSRs, nor geostationary satellite AMVs were assimilated. Then OSRs of channel IR1

8 722 K. Okamoto Table 3. Number of super-obs and OSRs selected by each QC procedure in the analyses at 0000, 0600, 1200 and 1800 UTC on 25 July UTC 06UTC 12UTC 18UTC Super-obs or OSRs of MTSAT-1R All at every three grids Super-obs over the sea Super-obs with N e 0.8 over the sea OSRs over the sea OSRs over the sea passing cloud height QC (160 P c 650 hpa) Assimilated OSRs (pass all QCs) Assimilated channels of AMSU-A on NOAA MHS on NOAA AMSR-E on Aqua Assimilated CSRs from MTSAT-1R Assimilated AMVs from MTSAT-1R Numbers of assimilated data are also shown for AMSU-A and MHS on NOAA-18, AMSR-E on Aqua, and MTSAT-1R CSRs and AMVs. Table 4. Configuration of data used in data assimilation experiments. OSRs AMSU-A CSRs geo AMVs conventional, other satellites scatterometer, MODIS AMV MTSAT other geo Operation X O O O O O O set A (one cycle) Base X X X X X O X Base+OSR O X X X X O X 3grd5slot 3grd3slot 4grd5slot 2grd3slot Base+AMSU-A67 X O X X X O X Base+CSR X X O X X O X Base+AMV X X X X O O X set B (51-day cycle) TEST O O O O O O O TEST2 (3grd3slot) O O O O O O O CNTL X O O O O O O The experiments including OSRs employ 3grd5slot (generated at every three model grid points ( 180 km) and assimilated in five slots of the assimilation window), unless otherwise specified: for example, 3grd3slot run assimilates OSRs at the same grid points but in every second time slot (3 slots). In Base+AMSU-A 67 run, only channels 6 and 7 data from NOAA-18, which were simultaneous with MTSAT-1R measurements at the assimilation time of 0600 UTC 25 July 2009, were added to Base run. In Base+CSR and Base+AMV runs, only MTSAT-1R products were added. were added to Base run in Base+OSR run. To see the effect of temporal resolution, we performed four Base+OSR runs: one employed standard data sampling (generated at every three model grid points and assimilated in five slots of the assimilation window, hereafter called 3grd5slot ), and the other three used different temporal and spatial sampling ( 3grd3slot, 4grd5slot, and 2grd3slot ). CSRs and AMVs from the MTSAT-1R satellite were added to the Base run in the Base+CSR and Base+AMV runs, respectively. The Base+AMSU-A 67 run included channels 6 and 7 of AMSU-A from NOAA-18 within the MTSAT-1R coverage area. Those channels have a peak in their temperature weighting function at around 400 and 300 hpa, respectively, which correspond to the sensitivity levels of most of the OSRs (Figure 4(c)). Set B consisted of full OSEs, including all operational data and OSRs of channel IR1. We performed assimilation cycles from 20 July through to 9 September 2009 with 219 h forecasts made at 1200 UTC 1 31 August The CNTL run assimilated all operational data, and the TEST run added OSRs to the CNTL run. Moreover, to see the impact of the frequency of assimilation, we performed another full OSE (the TEST 2 run) including less frequent OSRs. First, we compared the general impacts of OSRs, AMSU- A clear radiances, CSRs and AMVs on analyses in the Set A runs. We examined the differences between the Base run and Base+OSR, Base+AMSU-A67, Base+CSR and Base+AMV at 300 hpa (Figure 5). The analysis difference was identical to the analysis increment difference because all experiments of Set A used the same first-guess. OSRs were generated at low latitudes where cumulus clouds and anvils were developed, and south of Australia, northeast of New Zealand, and around Japan where overcast clouds due to a frontal system had expanded in area. The OSRs produced a change in temperature, then a change in the wind (Figure 5(a)). Hardly any change in humidity was produced (not shown). AMSU-A caused a greater temperature impact over more area than OSRs did, because it included more assimilated data (Figure 5(b)). The impact of AMSU-A on wind was large at high- and mid-latitudes but small at low latitudes in the western Pacific Ocean. These wind increments arose from the distribution of assimilated data, which are relevant to satellite orbit and results of QC checks,

9 Assimilation of Cloudy Radiances from MTSAT-1R 723 as well as from the effect of geostrophic constraints, which is weak at low latitude. CSRs had a profound impact on the upper tropospheric humidity (Figure 5(c)) but little on the temperature (not shown). The wind impact was generated by tracing advected humidity in the adjoint model as a result of assimilation of very frequent humidity measurements (Peubey and McNally, 2009). AMVs had much larger impact on the wind than other experiments (Figure 5(d); note that the scale of wind velocity is different from that in other figures) even though the number of their assimilated data points was comparable to CSRs (Table 3). This larger impact probably resulted from the assignment of larger observation errors to radiance data in the JMA assimilation system, where more weight is given to AMV and radiosonde data than to radiances (Ishibashi, 2010). Even though both OSRs and AMVs were derived from infrared cloud images of MTSAT-1R, there was little agreement in the wind increment pattern between the Base+OSR and Base+AMV runs, except southwest of Australia. The discrepancy was possibly caused by hour-by-hour differences in the representativeness of the observations (the AMVs were derived in 64 km 64 km boxes at the four main synoptic observation times of 0000, 0600, 1200 and 1800 UTC but in 96 km 96 km boxes at other times), or differences in the observation variables, the target clouds, the method of data thinning (AMVs are thinned to one per 200 km box in the whole assimilation window). We calculated Jacobians of BT with respect to temperature and humidity for channel IR1 in a typical tropical atmosphere in the presence of a single layer of cloud with an effective cloud fraction of 0.0, 0.6, 0.8 or 1.0 at 300 hpa (Figure 6(a) and (b)). The Jacobians were calculated for changes of temperature of 1 K and 10% of background humidity (ppmv) by using the RTTOV-9 K- matrix calculation model. The Jacobian for temperature had a sharp peak at the cloud-top pressure, and the peak amplitude increased with the effective cloud fraction. There was a small sensitivity to lower tropospheric temperature in clear conditions, but that decreased as the effective cloud fraction increased, and disappeared in completely cloudy conditions. The Jacobian for humidity was sensitive to humidity in the middle and low troposphere and, in contrast to the Jacobian for temperature, did not show a sharp peak at the cloud-top pressure. The sensitivity became smaller in the presence of clouds and it reached approximately zero below the clouds when the effective cloud fraction was 1.0. In summary, the simulated Jacobian analysis showed that OSRs were highly sensitive to temperature at the cloud top in a sharply defined layer and had much smaller sensitivity to temperature and humidity below the cloud except for the completely overcast condition, in which no sensitivity was observed. The sharpness is distinctive when compared with a Jacobian of temperature from the AMSU-A clear-sky BT (Figure 6(c)). To see the impact of a sharp Jacobian, we examined temperature analysis increments averaged over a small area (141 E 144 Eand48 S 52 S) among the Base, Base+OSR, and Base+AMSU-A67 runs (Figure 7). In this area, one radiance of channel 6, six radiances of AMSU-A channel 7, and 17 OSRs were assimilated. Most of the OSRs exhibited negative O B values (up to 0.21 K) and estimated clouds between 250 and 351 hpa, although one OSR had an O B value of K at 351 hpa, whereas AMSU-A had O B values ranging from 0.26 to 1.11 K. The bell-shaped curve of the increment for the Base run became W-shaped after OSRs lowered the temperature near the 300 hpa level, because of the OSR sharp Jacobian peaks at the cloud tops. In AMSU-A, by contrast, the temperature increment was shifted to the negative side over a wide altitude range of height because of the broad shape of its Jacobian. The second expected distinctive advantage of OSRs derives from their frequent measurement, a benefit we will now verify. The direct benefits of frequent measurements by geostationary satellites are certainly the increase in assimilated data and better analyses of changes in time in the atmosphere. In fact, the average quantity of assimilated data in each analysis increased greatly from 337 in the TEST2 run to 565 in the TEST run. Furthermore, a tracer effect from the frequent measurements is expected to have a positive impact on the wind analysis results (Peubey and McNally, 2009). We investigated the relationship between measurement frequency and quality of wind analyses in OSR assimilations. We compared the zonal mean average of the analysis error of wind speed at 300 hpa between the 3grd5slot run and the 3grd3slot run, which was temporally thinned (Figure 8). We defined the analysis error here as the difference from the operational analysis. Overall, there was a small difference ( m s 1 in the area average) except for smaller errors at around 20 Nand30 Nlatitude, in the 3grd5slot run. This difference can arise not only from the assimilation frequency but also from increasing number of OSRs. To avoid this ambiguity, we performed two further sets of OSE comparisons (3grd3slot to 4grd5slot; 3grd5slot to 2grd3slot) in which the numbers of assimilated OSRs were nearly identical. The wind error differences were still small ( m s 1 and m s 1, respectively) and seemed to depend more on the distribution of the assimilated data than on the assimilation frequency (not shown). Furthermore, we compared the performance of the wind forecasts of the full OSEs between TEST and TEST2. The forecast skill of wind speed at 300 hpa showed no statistically significant difference for TEST and TEST2 (Figure 9). These findings suggest that high-frequency measurements in the OSR assimilation had a very small impact on the wind analyses, perhaps because in limited areas only a small number of OSRs are assimilated. Possible another reason is the fact that OSRs of channel IR1 have impact on cloudtop temperature instead of humidity. In contrast, Lupu and McNally (2012) showed that overcast radiances of four infrared channels including two water vapour channels (6.2, 7.3, 10.8 and 13.4 µm) from Meteosat-9 had clear impact on the wind field as CSRs and cloudy AMVs did. Investigating the capability of tracing overcast cloud through temperature advection is an interesting future study. Regarding the third advantage of OSR assimilation (the availability of data in very cloudy regions), we examined the distribution of assimilated data by comparing the availability of OSR, AMSU-A and CSR data. We compared the ratio of assimilated data to all data for OSRs, AMSU-A channels 6 and 7 on the NOAA-18 satellite, and CSRs from MTSAT- 1R (Figure 10, right panels). For OSRs, the ratio was calculated against all super-obs, rather than all OSRs, their number being much smaller than the number of AMSU-A and CSRs. AMSU-A6 was rejected mainly by cloud QC (the rejection criterion is that retrieved total-column cloud liquid water (TCCLW) > 100 g m 2 ), and AMSU-A7 by rain QC (TCCLW > 300 g m 2 ). Neither AMSU-A6 nor -A7 was assimilated in high terrain or coastal areas. OSRs

10 724 K. Okamoto Figure 5. Differences of the 300 hpa analysis between the Base run at 0600 UTC 25 July 2009 and the (a) Base+OSR run, (b) Base+AMSU-A67 run, (c) Base+CSR run, and (d) Base+AMV run. Wind vector differences that exceeded 0.2 m s 1 are plotted as arrows superimposed on the temperature differences (colour shading) for the runs in (a), (b) and (d), and on the dew-point depression (T TD) forthebase+csr run in (c). were prominently observed south of Australia, around New Zealand, east of Japan and in the Bay of Bengal, and, in lesser numbers, east of the Philippines (Figure 10(a)). Comparison of Figure 10(b) and (d) reveals that OSRs complemented the observations in areas where AMSU-A6 was relatively lacking, such as south of Australia, around New Zealand, and in the northern Pacific Ocean. AMSU-A7 covered most ocean areas rather homogeneously except its coverage was somewhat lower near 15 N latitude east of the Philippines (Figure 10(f)). In contrast, a slight increase in the number

11 Assimilation of Cloudy Radiances from MTSAT-1R 725 Figure 6. (a) Jacobian of channel IR1 BT with respect to a temperature change of 1 K, for a typical tropical atmosphere with a single layer of cloud having an effective cloud fraction of 0.0, 0.6, 0.8 or 1.0 at the 300 hpa level. (b) As in (a) but with respect to a change of 10% of background humidity (ppmv). (c) As in (a) but for BT of AMSU-A channel 7 in clear conditions. Figure 7. Vertical profile of the temperature increment for the Base run (dotted), Base+OSR run (solid line), and Base+AMSU-A67 run (dashed line). Temperatures were averaged over the area within the box 141 E 144 Eand48 S 52 S at time 0600 UTC on 25 July of OSRs used was noticeable in this area (Figure 10(b)). CSRs complemented OSRs very well, especially northwest of and over Australia, and south of Japan (Figure 10(g)). Thus, OSRs complement CSRs and even, to some extent, microwave soundings, which are available for modestly cloudy regions. Finally we verified the impact of assimilation of OSRs on analyses and forecasts by comparing the results of the TEST and CNTL runs. From the Jacobian of BT (Figure 6(a)) and the distribution of cloud-top pressures of assimilated OSRs (Figure 4(c), horizontal axis), we expected OSRs to have a large impact on the upper and middle tropospheric temperature. In a verification against radiosonde data (not shown), the bias was slightly reduced for the 6 h forecast of the u-component of wind in the middle troposphere in the Tropics and the Southern Hemisphere, even though there was almost no difference in the temperature skills of the analysis and 6 h forecast. Although the impact on the forecasts was small and neutral for most geophysical fields, we found an improvement in the temperature at 300 hpa (T300) and the wind velocity at 850 hpa (WV850). Forecast improvements were statistically significant (t-test at the 95% confidence level) for T300 in the Tropics, and for WV850 in the Northern Hemisphere (Figure 11). Given a similar improvement in WV850 in TEST2 (not shown), and the fact that there were few OSRs that were sensitive to the lower troposphere, the improvement in WV850 is attributable mostly to the assimilation cycle of the temperature increment rather than to frequent measurements. During the OSE period, five typhoons provided 30 cases for the verification of typhoon tracks. Although improved tracks were seen for several cases such as Vongfon that approached Japan in mid- August, there was no statistically significant improvement in averaged track error. 6. Conclusion and discussion We have simulated and assimilated super-ob radiances of the MTSAT-1R imager in cloudy conditions. Each super-ob was constructed by weighted averages of infrared pixels within a circle of a predefined size. The frequency distribution of super-ob BTs and the SD of pixel BTs in each super-ob varied with the size of the super-ob. This points out how important appropriate selection of the super-ob size is for the representative scale of assimilation, if model cloud variables are used. In this study, we simply set the radius of a super-ob to the model resolution (30 km) because instead of using model cloud variables we derived the cloud parameters from measurements. In order to assimilate the super-ob radiances in cloudy conditions, we employed a simple RTM with the assumption of a single-layer cloud. The simple RTM calculated cloudy radiance using cloud-top pressure and effective cloud fraction. These two cloud parameters were estimated by the minimum residual method using the MTSAT-1R 10.8 µm (IR1) and 12.0 µm (IR2) channels and assuming

12 726 K. Okamoto Figure 8. (a) Zonal mean error of wind speed (m s 1 ) at 300 hpa over the MTSAT-1R satellite coverage area (60 E 160 Wand60 N 60 S) for the 3grd5slot run (solid line) and 3grd3slot run (dashed line), and (b) their difference. Figure 9. Forecast improvement of the wind speed vector at 300 hpa in (a) (b) the extratropical Northern Hemisphere, (c) (d) the Tropics, and (e) (f) the extratropical Southern Hemisphere. For the left panels (a), (c), (e), the improvement is defined by CNTL RMSEs minus TEST RMSEs normalized by CNTL RMSEs, and is positive when the forecast is improved by assimilating OSRs. Vertical error bars indicate the statistical confidence (t-test) at the 95% level. (b), (d), (f) As in the left panels, but improvement is calculated for the TEST2 run instead of the TEST run.

13 Assimilation of Cloudy Radiances from MTSAT-1R 727 Figure 10. (a), (c), (e), (g) Total number of assimilated data points, and (b), (d), (f), (h) ratio of assimilated data to all data, for (a) (b) OSRs, (c) (d) AMSU-A channel 6, and (e) (f) AMSU-A channel 7 on the NOAA-18 satellite, and (g) (h) CSRs from MTSAT-1R. The data were counted in 4 4 grid boxes in August 2009 in the TEST run. no difference in cloud emissivity between the channels. These assumptions were nearly satisfied where the effective cloud fraction exceeded 0.8; there was a small SD of pixel BTs and a low proportion of clear-sky pixels. We call these radiances the overcast super-ob radiances (OSRs). To reduce the dependence on spectral wavelength of O B of channels IR1 and IR2, we removed OSRs if their cloud-tops were below the level of 650 hpa or above the level of 160 hpa. Advantages of OSRs from geostationary satellites include having temperature information that is highly vertically resolved at the cloud top, frequent measurements, and availability in cloudy regions. We have largely confirmed

14 728 K. Okamoto Figure 11. Forecast improvement of (a), (c), (e) the temperature at 300 hpa and (b), (d), (f) wind speed at 850 hpa, as a function of time into the forecast. The improvement is defined by CNTL RMSEs minus TEST RMSEs normalized by CNTL RMSEs in (a) (b) the extratropical Northern Hemisphere, (c) (d) the Tropics and (e) (f) the extratropical Southern Hemisphere. Vertical error bars indicate the statistical confidence (t-test) at the 95% level. these features with several one-cycle experiments that started from a baseline virtually without satellite data, and cycled OSEs that included all operational datasets. While frequent measurements increased the number and the temporal resolution of observations to be assimilated, we found little clear evidence of a benefit from the tracer effect on wind, probably because a small number of OSRs of channel IR1 only were assimilated in limited areas. In the full OSE runs we showed that assimilation of OSRs of channel IR1 improved the forecast skill of upper tropospheric temperature and lower tropospheric wind velocity, although the impact was small and neutral for most geophysical variables. This study is unique in that it has characterized a super-ob BT as a function of the radius of the super-ob and applied an assimilation technique used for hyperspectral sounder data (McNally, 2009) to geostationary imager data. For the latter, we examined the assumptions of the simple RTM and the estimation of cloud parameters, and devised qualitycontrol procedures. Although this relationship between super-ob size and its BT has not yet been fully utilized in this study because we did not use any model cloud variables in the simple RTM, it will guide a more advanced approach that will use model cloud variables in our future study. While previous studies demonstrated a clear impact on temperature analysis in the low troposphere (McNally, 2009; Bauer et al., 2011b), we have shown that the main impact is in the high troposphere due to the different data usage, including cloud height QC. Several issues related to short- and long-term improvement of the OSR assimilation remain. This study focused on assimilating channel IR1 BT using cloud parameters extracted from both IR1 and IR2 BTs. Since the cloud parameters are calculated to minimize the radiance difference between measurement and background, systematic and random errors in NWP models, RTMs and measurements can affect the resulting estimate. The parameters may be adjusted excessively so that these errors cancel out. For example, warm biases in NWP models or cold biases in measurements would lead to estimates of higher cloud tops and/or larger effective cloud fractions than really exist. These wrong cloud parameters might cause serious deterioration of analysis through, for example, the sharp temperature Jacobian at the wrong height and with wrong amplitude. One approach to handling this overfitting problem is to correct as many biases in models and measurements as possible before estimating the cloud parameters. Another approach is to analyse cloud parameters in 4D-Var to be consistent with other measurements and analysis variables, instead of treating them as fixed parameters as was done in this study. For better consistency, it is important to find the appropriate background error covariance for all cloud parameters, including their correlation with other analysis variables. Although only channel IR1 BT of MTSAT-1R was assimilated in this study, more channels should be utilized to extract more observations. OSRs from the water vapour