Relative impact of polar-orbiting and geostationary satellite radiances in the Aladin/France numerical weather prediction system

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1 QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 33: 6 67 (7) Published online in Wiley InterScience ( DOI:./qj.34 Relative impact of polar-orbiting and geostationary satellite radiances in the Aladin/France numerical weather prediction system Thibaut Montmerle*, Florence Rabier and Claude Fischer Météo-France/CNRM, Toulouse, France ABSTRACT: For its short-range forecasts over Western Europe, Météo-France runs the limited-area model ALADIN operationally with four daily analyses obtained with a 3D-Var data assimilation system. This system includes, among other observation types, radiances from AMSU-A, AMSU-B, HIRS and SEVIRI radiometers. SEVIRI is on board the geostationary platform Meteosat-8 and provides continuous observations in space and in time over the region of interest at several wavelengths, while the others, which are on board polar-orbiting satellites, have poorer temporal and horizontal resolutions but a better spectral resolution than SEVIRI. Observing System Experiments (OSEs) have been performed with the operational 3D-Var to assess the impact of such satellite data on analyses and on forecasts. DFS (Degrees of Freedom for Signal) have been computed and have shown the complementarity between WV channels from the different radiometers. In the operational version of the 3D-Var, DFS values show that analyses are strongly controlled by SEVIRI data in the mid to high troposphere. This is consistent with the large number of assimilated SEVIRI radiances. HIRS and AMSU-B WV data would provide more information if SEVIRI data were not assimilated and if ATOVS data were used with a higher density. However, using ATOVS data with a higher horizontal resolution makes the analyses more dependent on these data, and it does not appear to be beneficial in this particular context, probably because of a non-optimal bias correction. In that case however, the individual impact of each pixel decreases because of the horizontal correlation lengths of the structure functions. Forecast scores and predicted precipitation patterns display the positive impact of SEVIRI data. Copyright 7 Royal Meteorological Society KEY WORDS 3D-Var; SEVIRI; ATOVS; radiance assimilation Received February 6; Revised 3 November 6; Accepted 8 November 6. Introduction Infrared and microwave radiance data such as those from the Advanced TIROS Operational Vertical Sounder (ATOVS) have been shown to be beneficial to NWP global model forecasts because they provide valuable information on atmospheric temperature and humidity (English et al., ; Bouttier and Kelly, ). For global models, these data affect large scales and are dominant over the tropical and southern oceans, since satellite observations are often the only available data in these areas. At present, these data are far more useful over the oceans than over land, since information about emissitivity and surface temperature over land is not very accurate and induces the removal of low-peaking channels in the assimilation process. Improvements in both assimilation techniques and instruments will push the benefit of radiances further. In particular, sounders such as the Advanced Infrared Sounder (AIRS) and the Infrared Atmospheric Sounding Instrument (IASI) show more potential than ATOVS observations through * Correspondence to: Thibaut Montmerle, Météo-France/CNRM, 4 av. G. Coriolis, 37 Toulouse, France. montmerle@cnrm.meteo.fr their much finer spectral and vertical resolution (Prunet et al., 998). Limited-area models (LAMs) can also benefit from polar-orbiting satellite data for short-term forecasting at the mesoscale, provided they are at an adequate horizontal and temporal resolution. Radiometers such as ATOVS have a horizontal resolution which seems well suited for regional studies (between and 4 km, depending on instruments). However, their potential impact strongly depends on their availability within the domain of interest. Despite their lower spectral resolution, radiometers on board geostationary satellites are particularly well adapted to weather predictions at the mesoscale to the convective scale, since they allow almost continuous access to information about the evolution of temperature and humidity fields at a high horizontal resolution. For instance, the Spinning Enhanced Visible and Infrared Imager (SEVIRI) on board Meteosat-8 has a horizontal resolution between 4 and 6 km over Western Europe. Assimilation of geostationary data in NWP global models is quite recent, e.g. GOES imager data at the US National Centers for Environmental Prediction (NCEP, Derber, 3), at the Canadian Meteorological Centre (CMC, Garand and Wagneur, ) and at the European Copyright 7 Royal Meteorological Society

2 66 T. MONTMERLE ET AL. Centre for Medium-range Weather Forecasts (ECMWF, Köpken et al., 3); Meteosat-7 and -8 at ECMWF (Köpken et al., 3; Szyndel et al., 4, respectively). In these studies at global scale, the main impact of geostationary radiances is generally a small improvement in the analysis and in the forecasts of mid- to high-tropospheric humidity. The scope of our study is to investigate the relative impact of geostationary versus polar-orbiting satellites and their possible complementarity in a context of weather forecasting at regional scale. For that purpose, radiances from SEVIRI and from ATOVS on board AQUA and the NOAA satellites are considered. To evaluate the impact of a specific observation type on the forecast, Observing System Experiments (OSEs), which consist of comparing forecast scores from experiments that use different observation scenarios, are performed. The drawback of such a method is the large amount of computational resource which is required. Other methods have been implemented to diagnose the impact of observations on analyses, i.e. to infer the statistical variance reduction induced by the assimilation of one particular type of observations. These methods are mainly based on measurements of the so-called DFS (Degrees of Freedom for Signal) that allow the amount of information brought by subsets of observations in assimilation systems to be quantified. The DFS computation has been implemented in the four-dimensional variational (4D-Var) assimilation scheme of operational global models such as the ECMWF model (Cardinali et al., 4) and the French ARPEGE model (Action de Recherche Petite Echelle Grande Echelle, Chapnik et al., 6) using an extension of a randomization procedure initially described by Desroziers and Ivanov (). These methods seem particularly well suited to this study, since they give an objective way to diagnose the relative impact of assimilated radiances coming from different platforms, and they have been adopted here to the LAM context. The LAM ALADIN/France (Aire Limitée Adaption Dynamique et dévelopement International), which has been running operationally at Météo-France since July, is used with four daily analyses obtained with a 3D-Var data assimilation system. The operational suite provides short-range forecasts over Western Europe, with a km horizontal resolution. An overview and an evaluation of this complete assimilation/forecast system is given by Fischer et al. (, F below). Different OSEs, based on this configuration, have been performed to study the relative impacts of the assimilated radiances. The main characteristics of the ALADIN/France operational suite are presented in section, with special emphasis put on the set-up of satellite radiance. The relative impact of the radiances in the analysis is then discussed in the following sections. Section 3 focuses on the sensitivity of the analysis with respect to the different types of data using DFS; section 4 presents the relative impact of polar-orbiting and geostationary satellite data in weather forecasting at regional scale, using forecast scores against conventional data and comparing precipitation forecasts for a case-study. Finally, section presents some concluding remarks.. Experimental framework.. The ALADIN 3D-Var The variational code of the ALADIN 3D-Var is based on the incremental formulation originally introduced in the ARPEGE/Integrated Forecast System global assimilation (Courtier et al., 994). In F, the specification of the background-error covariance matrix is discussed and has led to the selection of ensemble-based covariances that were sampled from an ensemble of ALADIN forecasts, with initial conditions taken from an ensemble of analyses from the coupling model ARPEGE (Ştefănescu et al., 6). This background-error covariance matrix includes finer-scale structure functions than those used for the global model. For instance, the horizontal correlation lengths for temperature and specific humidity are around 7 km in the mid-troposphere for ALADIN compared to more than km for ARPEGE (Berre et al., 6). Compared to ARPEGE, the shorter length-scales in ALADIN 3D-Var lead to finer structures in the analysis increments. The operational version of ALADIN/France has been evaluated on a daily basis by computing forecast scores against observations and by analyzing simulated precipitation patterns. Montmerle () and F have shown encouraging results compared to the spin-up model (i.e. ALADIN used as a dynamical adaptation of ARPEGE), in particular for short-range precipitation forecasts... Main features of the operational suite As in the global model ARPEGE, the operational suite of ALADIN 3D-Var (OPER in the following) consists of two parallel cycles. The assimilation cycle uses a ±3-hour assimilation window and is coupled with the ARPEGE assimilation cycle that uses long cut-off times. This cycle produces 6-hour forecasts which are used as background fields for the next analysis in both assimilation and production cycles. The production cycle also uses a ±3-hour assimilation window but it is coupled with the ARPEGE production cycle that has a short cutoff time ( h min for the UTC analysis). Shortrange forecasts are run from each production cycle. Each ALADIN analysis uses surface fields that have been analyzed for ARPEGE for the same assimilation time, i.e. no surface analysis is formed specifically for ALADIN. In ALADIN, the same observations as in ARPEGE are used, with the addition of SEVIRI radiances and of surface measurements. The latter two are presented in sections.3 and.4, respectively. Radiosondes, surface observations, buoys, ship and aircraft measurements, wind profilers, horizontal winds from atmospheric motion vectors (AMVs) and the QuikSCAT scatterometer, AMSU-A radiances from NOAA-, NOAA-6 and Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

3 IMPACT OF SATELLITE DATA IN ALADIN 67 AQUA, AMSU-B radiances from NOAA-6 and NOAA- 7, and High-Resolution Infrared Sounder (HIRS) radiances from NOAA-7 are common to both systems. Details about the use of ATOVS radiances (channel selection, quality control, cloud detection, etc.) in ARPEGE can be found in Gérard et al. (3). Innovations (i.e. observation minus guess) in brightness temperature (T b ) have been bias-corrected following the method developed at ECMWF by Harris and Kelly (). Biases due to scan angle and those dependent on air mass have been removed. The air-mass-dependent biases have been computed using multiple linear regressions based on four predictors: thicknesses between and 3 hpa and between and hpa, surface temperature and the total column water vapour (WV). It has to be noted that, for all experiments presented herein, the regression coefficients are the same as for ARPEGE, assuming that they are valid for the limited-area domain. For AMSU-A data, Randriamampianina () has shown that this hypothesis might lead to more variable daily forecast scores compared to coefficients computed especially from LAM innovations. For the sake of simplicity, the same coefficients are used in this study. The values of specified observation error variances for ATOVS radiances are between. and.7 K for HIRS 4,, 6, 7, 4 and ; and K for HIRS WV and respectively; 3,. and K for AMSU-B 3, 4 and respectively; and between.3 and.8 K for AMSU-A channels. As shown in Figure, there is a large difference in the number of active data (i.e. data that enter the minimization) between the ATOVS and SEVIRI radiances in the OPER configuration. This is due to the different initial data sampling and to the large thinning lengths used in ARPEGE for ATOVS data (6 km) whereas 7 km is used for SEVIRI. No HIRS radiances are present for the 6 and 8 UTC analysis and almost no AMSU-B data are used at 8 UTC. In a 3D-Var context, the time differences of ATOVS measurements relative to analysis time can reach a few hours. In fact, NOAA-6 and NOAA- 7 fly over western Europe around 43 and 4 UTC and around, 9 and UTC, respectively. This time difference between observations and analysis can possibly lead to an analysis degradation, e.g. in cases of rapidly developing mesoscale convective systems. However, on average, extra data such as these time-shifted ATOVS data generally add valuable information in datavoid regions. Furthermore, and as is demonstrated in section 3, the imbalance between numbers of active data from geostationary and polar-orbiting satellites implies that the resulting analyses are strongly controlled by SEVIRI radiances, which mitigates the potential negative effect of the time-shifted ATOVS observations. Mean weighting functions of channels that are considered in the assimilation, computed for midlatitude atmospheric profiles using the fast radiative transfer model RTTOV (Radiative Transfer for TIROS Operational Vertical sounder; Saunders et al., 999), are plotted in Figure for the four radiometers. These plots show that mid- to high-tropospheric humidity-sensitive HIRS 3 UTC 6 8 SEVIRI AMSU-A AMSU-B HIRS Figure. Number of assimilated satellite radiances for the four daily analysis steps for OPER on June. channels and, AMSU-B channels 3 and 4 and SEVIRIchannelsand3arecharacterizedbyweighting functions that have similar shapes and intensities. As a consequence, the individual impact of one single observation from these different WV channels should be comparable, provided their specified errors are similar. On the contrary, SEVIRI low-peaking infrared channels seem to be more sensitive to surface conditions than those from HIRS. Finally, the AMSU-A channels are sensitive to high-tropospheric/low-stratospheric temperature variations, and thus their impacts are expected to be different from those of the other three radiometers..3. SEVIRI radiances The first Meteosat Second Generation (MSG) satellite, known as Meteosat-8, has been operational since January 4. It carries the SEVIRI composed of twelve channels, eight of which are in the infrared spectrum with wavelengths of 3.9, 6., 7.3, 8.7, 9.7,.8, and 3.4 µm. The 6. and 7.3 µm are designated as WV channels and 3 in Figure. More details about this particular instrument can be found in Schmetz et al. (). A clear-sky radiance (CSR) product is operationally produced by EUMETSAT and assimilated in the ECMWF model (Szyndel et al., 4). It is generated by averaging radiances from cloud-free pixels over segments of 6 6 pixel squares. In our study, the higher spatial resolution of the analysis motivated us to use these observations directly at high resolution. The details of the data processing are as follows. The near-ir 3.9µm channel is blacklisted because of possible solar contamination and because of its broad spectral resolution that makes its modelling by the radiative transfer model difficult. The ozone IR 9.7 µm channel is also blacklisted because the model does not consider ozone as a prognostic variable and because of the poor vertical resolution of the model in the high troposphere/low stratosphere. Finally, the CO 3.4 µm channel has also been blacklisted because of a persistent bias-correction problem, explained below. Of the remaining channels, one pixel out of five is extracted and thinning to 7 km is applied. The relevance of this choice is discussed in detail Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

4 68 T. MONTMERLE ET AL. AMSUA Weighting functions AMSUB Weighting functions Pressure level 4 6 # 3.6 GHz #6 4.4 GHz #8. GHz #9 7.3 GHz # 7.3 GHz # 7.3 GHz # 7.3 GHz Pressure level 4 6 #3 83 +/ GHz #4 83 +/3 GHz # 83 +/7 GHz (a) dt/dlnp..... (b) dt/dlnp HIRS Weighting functions SEVIRI Weighting functions Pressure level 4 6 #4 4. µm # 3.9 µm #6 3.6 µm #7 3.3 µm # 7.3 µm # 6. µm #4 4. µm # 4.4 µm Pressure level 4 6 # 6. µm #3 7.3 µm #4 8.7 µm #6.8 µm #7. µm (c) dt/dlnp..... (d) dt/dlnp Figure. Mean weighting functions (or variations of the transmittance per vertical layer) for midlatitude summertime profiles for channels that are used in the assimilation process for (a) AMSU-A, (b) AMSU-B, (c) HIRS and (d) SEVIRI. WV channels are in bold lines. in section.. Observation error variances of and.7 K have been used for IR and WV channels respectively, which is comparable to what has been set for ATOVS channels, as seen in the previous section. For SEVIRI, the bias due to the scan angle is not relevant because of small scan angle values inherent to the geostationary scanning strategy. The remaining airmass-dependent bias is then deduced from multiple linear regressions as in Harris and Kelly () on a volume of data which is sufficient to get statistically stable results over the ALADIN domain. The coefficients of the bias correction used in this study were computed from a onemonth period of innovations (April May ) for which comparable weather regimes for those of the experiments were observed. The predictors of that regression are the same as for ATOVS (see section.). To correct biases of the two WV channels from the SEVIRI CSR product in the ECMWF global model, Szyndel et al. (4) use only three predictors, the surface temperature not being taken into account since they do not take into consideration the low-peaking IR channels in the assimilation. The corrected innovation biases present a narrow Gaussian distribution centred on zero for all the assimilated channels except the 3.4 µm. For the CO 3.4µm channel, this distribution is constantly centred on +.4 K, perhaps because of unsuited predictors for this particular channel which is sensitive to the temperature throughout most of the troposphere. Consequently, this channel has been temporarily blacklisted. If a radical change of weather regime occurs over the limited area covered by the model, the results can be degraded, the regression coefficients being misfitted. In that particular case, new coefficients should be computed (typically every new season). The cloud-type product developed by CMS (Centre de Météorologie Spatiale, Lannion, France) in the framework of the MSG Satellite Application Facility to Nowcasting has been used (Derrien et al., ) to avoid contamination by clouds and to keep in the assimilation process channels whose weighting functions peak above the cloud top. The two WV channels are kept above low clouds, for which the fixed cloud-top pressure levels are Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

5 IMPACT OF SATELLITE DATA IN ALADIN 69 below the tail of the weighting functions, and the lowpeaking channels 8.7,.8 and µm are used over sea, only in clear-sky conditions..4. m measurements The m measurements of temperature and humidity, coming mainly from the French RADOME (Réseau d Acquisition de Données et d Observations Météorologiques Étendues) network consisting of synoptic and automatic surface measurements, are another observation type assimilated in ALADIN/OPER and not in the global model. In addition to the fact that these data give a better analysis of the boundary layer, a strong complementarity with SEVIRI WV channels has been found. The information brought by the latter on the mid-tropospheric humidity can artificially propagate downwards too stongly, because the background-error vertical correlations poorly represent the height of the boundary layer. The addition of these ground-based data somehow allows this anomaly to be corrected... Observing system experiments OSEs have been carried out and run for three weeks, from to 3 June, with the same cycling strategy as OPER. This time period was chosen because of the large sample of precipitating cases that were observed over the ALADIN domain. Three main precipitating periods occurred during that period: from the 7 to 9 and around 3 June, when unstable conditions prevailed in the south of France leading to strong convective activity, and from 3 to 8 June, when a more synoptic-scale weather regime brought successive westward-propagating rain bands over Western Europe. The different OSEs considered in this study are as follows: nosev denotes OPER without SEVIRI data. moreatovs denotes OPER with additional ATOVS data used with a finer thinning (see next section for details). For the UTC assimilation cycle, this configuration inserts in the assimilation process approximately eight times more HIRS, AMSU-A and AMSU- BdatathaninOPER. moreatovsnosev denotes moreatovs without SEVIRI data. This experiment has been carried out to study the impact of additional ATOVS data independently of SEVIRI. OPER SEVnoIR denotes OPER without SEVIRI IR radiances (e.g. only considering WV channels). These experiments have been run to infer the relative impact of SEVIRI and of denser ATOVS radiances in an operational configuration. Discussion will be carried out mainly using the nosev and moreatovs OSEs, the two other OSEs helping to draw conclusions reported in section Thinning of satellite observations Using denser data in the variational process does not necessarily mean an improvement of the analyses. In fact, and as pointed out by Liu and Rabier (3), if the error correlation between two adjacent pixels becomes greater than a threshold value (around. in their study) and if the observation-error covariance matrix R is diagonal (which is the case here), then the system becomes sub-optimal which degrades the analyses and the resulting forecasts. On the contrary, if observations are uncorrelated, adding new data generally improves the results. The thinning lengths for SEVIRI and ATOVS radiances have thus been chosen in order to find a good compromise between the spatial resolution of the data and a sufficiently small correlation value between selected observations to ensure the optimality hypothesis made in the variational process. For that purpose, the tuning coefficients s o for observation-error variances described by Desroziers and Ivanov () and Chapnik et al. (4) have been used indirectly. This method aims at producing tuned variances consistent with the innovations (i.e observation minus guess), assuming that the correlation patterns of the specified matrices are correct. As a consequence, if the observational error is spatially correlated while the corresponding specified observation-error matrix R is diagonal, after some iterations the tuning coefficients will drop to zero. This behaviour has been used as a tool to tune the thinning. For instance, Chapnik et al. (6) have used this particular property to point out the high spatial correlations of geostationary wind vectors. The theory and the method that has been used to compute this tuning coefficient are detailed in Appendix A. In practice, the tuning coefficients computed for each SEVIRI channel in OPER and for each ATOVS channel in moreatovs have been re-injected in new analyses. With 7 and 8 km thinning lengths for SEVIRI and ATOVS data respectively (while OPER uses 6km for ATOVS), the values of s o that have been diagnosed after that second iteration were larger than their initial value and were converging towards unity, which is specific to uncorrelated data. This test confirmed the relevance of the different thinning intervals selected in this study. As displayed in Figure 3, moreatovs uses a coverage for ATOVS data more comparable to that of SEVIRI which seems better suited for regional-scale studies within the ALADIN domain. 3. Sensitivity of the analysis to observations 3.. Verification versus ATOVS and SEVIRI observations For nosev and moreatovs, the fit of the model first guess and the analysis to conventional observations remains mostly unchanged compared with OPER. However, discrepancies appear for statistics involving AMSU- B and HIRS channels. Figure 4 shows such statistics Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

6 66 T. MONTMERLE ET AL. (a) (b) (c) Figure 3. Example of the localization of active data that enter the minimization at UTC with a long cut-off time for (a) AMSU-B in OPER, (b)amsu-b in moreatovs (c) SEVIRI WV 6.4µm in both experiments, all plotted over brightness temperature observed by the SEVIRI.8 µm channel. This figure is available in colour online at for nosev compared with OPER. For HIRS channels and and AMSU-B, smaller background departure r.m.s. errors are displayed for OPER, which indicates that 6-hour forecasts are closer to these observations when SEVIRI radiances are considered. On the contrary, the corresponding analysis departure r.m.s. errors are larger for OPER than for nosev because of the high number of assimilated SEVIRI data which highly constrains the cost function. One can see that AMSU-B 3 and 4 are poorly bias corrected. The monitoring of this bias (not shown), as well as for HIRS channels, displays highly variable features (typically between ± K) because of the low number of data that are taken into account in the statistics, and also probably because the regression coefficients were not computed specifically over the ALADIN domain explained in section.. Concerning this last point, the relevance of those coefficients is difficult to evaluate precisely, because the low number of assimilated ATOVS data is making the statistics unstable. However, biased ATOVS observations are less problematic for OPER than for nosev, because of the small influence of ATOVS data in the OPER analyses, as shown in the next section. Figure 4 shows that adding a high number of correctly bias-corrected SEVIRI data seems to improve the guess since r.m.s. errors and biases have lower values for AMSU-B 3 and 4. In nosev, the larger innovation biases thus seem to be mainly due to poorer short-term forecasts of mid- to high-level humidity. The same statistics are plotted in Figure for more- ATOVS compared to OPER. Concerning background and analysis departure r.m.s. errors, the same characteristics as for nosev are observed, but in a much less pronounced manner; adding extra ATOVS data to an experiment that assimilates high-resolution SEVIRI data has far less impact than adding SEVIRI data to an experiment that uses only sparse ATOVS data. It seems that (observation minus guess) biases are generally degraded for HIRS when more ATOVS data are used, although smaller values for AMSU-B 3 and 4 are shown. This indicates that the background becomes poorer and poorer throughout the cycling when using biased and/or weakly correlated data, as pointed out in the previous section. In fact, statistics computed for the initial analysis time show smaller biases and background departures for more- ATOVS than for OPER, whereas the contrary is obtained for the last analysis time (not shown). This drawback could be partly solved by using greater observation-error variances σo for ATOVS data in order to decrease their weight in the minimization. For that purpose (and also to check the relevance of the thinning lengths, as mentioned in section.6), tuning factors have been computed as in Chapnik et al. (6) in order to get prescribed covariance matrices that fulfil an optimality criterion, and have been applied to an extra experiment (see Appendix A for more details). Unfortunately, no significant impact either on the analysis or on forecasts has been obtained for this experiment, although the resulting observationerror variances per channel seem to be realistic too. This result shows that covariance matrices are globally finely tuned in moreatovs. As a consequence, only results from moreatovs will be discussed below. Another issue when using denser ATOVS data would be to compute the regression coefficients used for the bias correction Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

7 IMPACT OF SATELLITE DATA IN ALADIN exp - ref RMS RMS... 3 exp - ref nobsexp 887 BIAS background departure (ref) background departure analysis departure (ref) analysis departure nobsexp BIAS Figure 4. Brightness temperature (a) r.m.s. error and (b) bias (K) of observation minus guess (solid line) and observation minus analysis (dashed line) for nosev (black) and OPER (grey) between 6 and June, for HIRS on board NOAA-7. (c) and (d) are as (a) and (b), but for AMSU-B on board NOAA-6. The vertical axis represents the channel number and numbers in the middle the amount of assimilated data. This figure is available in colour online at specifically over the ALADIN/France domain, in order to ensure a better fit to predictors, instead of using coefficients computed over the global ARPEGE domain, as is the case for the three OSEs. 3.. Use of the DFS 3... Theory The relative influence of each type of observation can be quantified by computing Degrees of Freedom for Signal (DFS), which is equal to the trace of the derivative of the analysis written in the observation space with respect to the observations: { } δ(hxa ) DFS = Tr, () δy where x a represents the analysis, and y the observations. H is the tangent linear operator of H, which is the observation operator that writes model variables in observation space (spatial interpolations and radiative transfer model RTTOV-8; Saunders et al. 999). More information on the theory and on the properties of the DFS can be found in Rodgers (996). This diagnostic has been recently used by Rabier et al. () to perform channel selection on simulated IASI observations and by Cardinali et al. (4) to study the respective influence of different types of observations in the ECMWF data assimilation system. More recently, Fourrié et al. (6) have also used this quantity to diagnose the contribution of targeted observations on analyses in the context of the international programme THORPEX (The Observing system Research and Predictability Experiment). For an optimal case, the analysis increment δx can be written as δx = x a x b = (B + H T R H) H T R (y H [x b ]) = K(y H [x b ]), () where x b represents the background, B is the backgrounderror covariance matrix and R is the observation-error covariance matrix composed of instrumental errors and errors in the observation operator H, already presented in section.4. K is the Kalman gain matrix. In a linear case, we can deduce from () and (): DFS = Tr(HK). (3) Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

8 66 T. MONTMERLE ET AL RMS exp - ref exp - ref RMS nobsexp 648 BIAS nobsexp BIAS background departure (ref) background departure analysis departure (ref) analysis departure Figure. As Figure 4, but for moreatovs (black) and OPER (grey). This figure is available in colour online at This diagnostic can be computed for a subset of observations y i, as long as they are uncorrelated, by using a projection operator o i : DFS i = Tr( o i HK o i T ). (4) It is difficult to estimate the DFS using (3), because of the size of the matrices that are involved and because the Kalman gain matrix is unavailable in a variational scheme. As in Chapnik et al. (6), a Monte Carlo method to approximate the trace of the operator is therefore used (Girard, 987). This method requires a random perturbation of the observation vector y.letδy be this random vector of the same size as y that follows a normalized Gaussian probability density function δy N(,I). If the size of this vector is sufficiently large, the following relationships hold: δy T HKδy = Tr(HKδy δy T ) Tr(HK). () This method needs two parallel analyses: the original x a retrieved from the available observations y and the background state x b, and a second one x a from the very same set of observations but randomly perturbed y = y + Rδy and the same guess x b. After applying () for the two cases, and considering (4): DFS = Tr(HK) = (y y) T R H(x a x a) Results As pointed out by Sadiki and Fischer (), a sufficient number of samples is needed to compute a reliable estimate of the Tr(HK) with this kind of Monte Carlo method. While applying the projection operator o i to a particular set of data (humidity from radiosondes for instance), the sample size can drop and corrupt the result. To solve this potential problem, the Monte Carlo estimate has been generalized for a series of trace operators valid for four different analysis dates (,, and June at UTC) by simply adding all the individual random estimates. Analyses taken five days apart have been chosen following the recommendation given by Sadiki and Fischer () to ensure the ergodicity of the signal that requires the data of each analysis step to be uncorrelated with other analysis times. This decorrelation time probably results from the meteorological variability over Western Europe and from the propagation time of a synoptic system inside the computational domain. Figure 6 shows DFS values per observation type for the three experiments. For OPER and for the UTC assimilation time, SEVIRI radiances are as informative as either ground-based data (SYNOP) or the sum of temperature and humidity from radiosonde data (TEMP). Other satellite observations (HIRS, AMSU-A and AMSU-B) have much less impact on the analyses, with values of 9, 8 and 63 respectively, compared to 368 for Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

9 IMPACT OF SATELLITE DATA IN ALADIN OPER more ATOVS nosev 3 3 DFS tempu tempt tempq pilot aireu airet synop hirs amsua amsub sevirl satob Figure 6. DFS values per observation type for OPER, moreatovs and nosev OPER more ATOVS nosev.3 DFS/p..... tempu tempt tempq pilot aireu airet synop hirs amsua amsub sevirl satob Figure 7. DFS values per observation type normalized by the number of observations for OPER, moreatovs and nosev. SEVIRI. As stated in section for ATOVS data, the same thinning lengths as for ARPEGE have been kept (6 km) which reduces drastically the number of radiances entering the minimization. Furthermore, the fact that these radiometers are on board polar-orbiting satellites makes the number of available data over Western Europe strongly dependent on time of day. For instance, as has been pointed out in section., no HIRS and almost no AMSU-B data are present for the 6 and 8 UTC assimilation times. The high temporal resolution and the fast reception of SEVIRI radiances are thus an obvious advantage for regional-scale data assimilation compared to polar-orbiting satellites. For conventional data, the moreatovs experiment displays comparable DFS values to OPER. However, as expected, ATOVS data and especially AMSU-B data have more impact on the analyses, with values reaching 39. On the contrary, SEVIRI data show smaller DFS values of 33 in that case. This result is due to the fact that the new observations, radiances from HIRS and AMSU-B, are sensitive to the mid- to high-tropospheric humidity. As a consequence, the influence of SEVIRI WV channels is impaired. For the same reason, adding more ATOVS data reduces the impact of one single radiance, as plotted in Figure 7 which shows the DFS normalized by the number of associated observations: for HIRS, AMSU-A and AMSU-B, this normalized DFS drops from.8 to.7, from. to. and from. to., respectively. Such a decrease of DFS coupled with an increase of the number of data has also been shown for targeted observations by Fourrié et al. (6). This behaviour is due to a redundancy of data Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

10 664 T. MONTMERLE ET AL. and to the structure functions in the background-error covariance matrix which have a dissolving effect on the information brought by one single pixel. For AMSU- A, this reduction is accentuated because this radiometer is mostly sensitive to temperature variations from the high troposphere to the low stratosphere (Figure ), altitudes at which these structure functions are broader, with horizontal correlation lengths around 8 km for temperature and humidity compared to 7 km in the mid-troposphere, as stated in subsection.. (Ştefănescu et al., 6, give more details.) Without any SEVIRI radiances (nosev experiment), the DFS associated with HIRS and AMSU-B increase, with respective values of 3 and 6 (Figure 6). In parallel, the DFS per single observation notably increases with values reaching.6 and.4 respectively (Figure 7), especially for AMSU-B. The impact of humidity from radiosondes (TEMPQ) also increases slightly from.8 to.3. This shows the complementarity between datasets that are sensitive to the same atmospheric components. When all radiances are available, the information brought by each pixel become somehow redundant and their relative impact decreases. DFS are also useful to study the sensitivity of the analysis to different channels of a particular radiometer (Figure 8). For each AMSU-A channel, the normalized DFS decrease when the number of pixels that enter the minimization increases, but they do not change depending on the use of SEVIRI observations since this radiometer is not sensing the same atmospheric levels (Figure 8(a)). As shown in Figure 8(c), WV channels and have the largest DFS for HIRS, especially channel. This result confirms the findings of Cardinali et al. (4) for the ECMWF data assimilation system. For nosev, the DFS associated with the latter HIRS channels have larger values, which denotes a higher impact of these particular channels whose spectral responses are close to the 7.3 and 6.4 µm SEVIRI channels respectively. The large number of additional AMSU-B data in moreatovs (ten times more than in OPER) implies a loss of the potential individual information for every channel compared to the operational configuration (Figure 8(b)). The AMSU- B pixels that are more comparable to SEVIRI WV channels (channels 3 and 4) become more informative in nosev. As one could expect, the two WV channels are the most informative for SEVIRI, especially the 6. µm (Figure 8(d)) that has a DFS of.36, while the three remaining IR channels have almost the same DFS values of around.3. For moreatovs, these values decrease slightly by about % Impact on specific humidity increments Mean increments for specific humidity have been computed over the 3-week period of interest. OPER has been compared to nosev to infer the relative mean impact of SEVIRI data on the analyses. However it is difficult to draw conclusions about the individual impact of denser ATOVS data, considering only the three OSEs presented above. The moreatovs experiment indeed uses both SEVIRI and ATOVS data. For that purpose and for the particular point discussed in this section, an extra experiment, denoted moreatovsnosev, has been.3.. AMSUA Aqua OPER more ATOVS nosev.6..4 AMSUB NOAA-7 OPER more ATOVS nosev DFS/p (a) DFS/p (c) channels HIRS NOAA-7 OPER more ATOVS nosev channels DFS/p DFS/p.3.. (b) (d) 3 4 channels SEVIRI OPER more ATOVS channels Figure 8. As Figure 7, but for each channel of (a) AMSU-A, (b) AMSU-B, (c) HIRS and (d) SEVIRI. Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

11 IMPACT OF SATELLITE DATA IN ALADIN 66 run considering only denser ATOVS data in the assimilation process. Differences of the mean specific increments between OPER and nosev, and between moreatovsno- SEV and nosev are plotted in Figure 9. At hpa, the shape and localization of the resulting fields are comparable; the assimilation of SEVIRI and denser ATOVS data allows moistening of an area covering northern Spain, southern France, and around Gibraltar and Sicily, and drying over the sea (Figures 9(a) and (c)). Some discrepancies appear over Northern Europe and over the inflow region located west of Ireland where the denser ATOVS data seem to accentuate the moistening and the drying over these regions respectively. In general, however, the impacts of these radiometers are consistent at hpa, which shows that the information brought by their WV channels in the analyses is comparable. In the analyses at lower levels, strong discrepancies appear: at 7 hpa, while SEVIRI data produce a global drying mostly over the Mediterranean Sea and the Bay of Biscay (Figure 9(b)), denser ATOVS data have the opposite effect (Figure 9(d)). The corresponding zonal average displayed in Figure confirms that this affects the analysis from 7 hpa to sea level, mainly south of 48 N. This strong difference of behaviour is obviously linked to the assimilation of low-peaking channels whose weighting functions have different shapes and intensities, as is shown in Figure 3. The individual impacts of SEVIRI IR channels is displayed in Figure, where we show a comparable zonal average of mean specific humidity increments between OPER and a second extra experiment that corresponds to OPER without IR channels (OPER- SEVnoIR in the plot). This picture shows that SEVIRI IR channels are responsible for the relatively strong drying over the Mediterranean Sea and that the background-error vertical correlations spread out this low-level information up to 6 hpa in that area. The very different features found with the moreatovsnosev experimentcanbe due to the different shapes of the HIRS and SEVIRI weighting functions for the low-peaking channels (Figures 3(c) and (d)). An alternative explanation would be a poor simulation of those channels in the assimilation because of a bad representation of surface emissitivity and of surface (a) (b) (c) (d) Figure 9. Difference of mean specific humidity increment (OPER minus nosev ) at (a) hpa and (b) 7 hpa, over the period 3 June. (c) and (d) are as (a) and (b), but for (moreatovsnosev minus nosev ). The contour interval is kg kg, with the zero contour omitted. This figure is available in colour online at Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

12 - 666 T. MONTMERLE ET AL. (a) 3 Pressure levels Pressure levels (b) N N 48 N 44 N 4 N 36 N Figure. Zonal average of the difference of the mean specific humidity increment for (a) OPER minus nosev and (b) moreatovsnosev minus nosev, for 3 June. The contour interval is.4 kg kg, with the zero contour omitted. 3 Pressure levels E 6 N N 48 N 44 N 4 N 36 N Figure. As Figure but for (OPER minus OPER-SEVnoIR), with contour interval. kg kg and the zero contour omitted. Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

13 IMPACT OF SATELLITE DATA IN ALADIN 667 temperature in the model, this non-realistic information in the low-troposphere being spread by the backgrounderror vertical correlations. The assimilation of IR channels indeed requires a realistic evaluation of these two surface parameters, which explains why no IR channels are considered over land where their modelled values are known to be often far from the truth. The fact that SEVIRI IR channels are strongly constrained by surface conditions (cf. Figure 3(d)) raises the question of the relevance of their use in the 3D-Var, even over sea. For instance, Szyndel et al. (4) use only WV channels in the ECMWF global model. This particular point has been addressed during the set-up of satellite observations in the pre-operational version of ALADIN. The conclusions of these tests were that adding SEVIRI IR channels in the variational process generally improved forecast scores, which seems to indicate that surface emissitivity values diagnosed by the model (using wavelength-dependent precomputed tables) are reasonable. These latter channels have thus been kept in the assimilation process. 4. Impact on forecasts Forecast scores against conventional data for each OSE are discussed in the first part of this section. Precipitation forecasts are then compared for a particular case-study. 4.. Forecast scores As discussed in Montmerle (), using the 3D-Var with the OPER configuration presented in section generally improves the forecast scores compared with the spin-up model, i.e. ALADIN without data assimilation. For instance, this allows the initial (i.e. up to 8-hour forecasts) r.m.s. error and biases of m humidity and of 3-hour accumulated precipitation to be reduced. Reduction of r.m.s. error for forecasts up to hours in the tropospheric temperature, humidity and wind have also been obtained compared with radiosonde measurements. On the other hand, some deterioration has been noticed on high-tropospheric/low-stratospheric biases of temperature and humidity and of low-tropospheric bias of temperature at all forecast ranges. During the set-up of the configuration of the 3D-Var, F have shown that this high-level temperature bias is produced by the model integration and is maintained through the cycling. Concerning the three OSEs presented here, comparisons between radiosonde data and forecasts interpolated at the observation s location show very comparable behaviour. Adding SEVIRI data or denser ATOVS observations has no particular impact on this kind of score. A small degradation of the relative humidity bias ( 3%) around 3 hpa for forecasts up to hours is however visible with SEVIRI data, which indicates that SEVIRI data are constraining the analyses towards a new solution which is, on average, slightly different from what the radiosonde observations indicate (not shown). Table shows the only significant discrepancies between the three experiments for forecast scores against ground-based data over the whole test period. SEVIRI data indeed lead to better short-range forecasts of 3-hour accumulated precipitation over the ALADIN domain, especially at the 6-hour forecast range where the corresponding r.m.s. error is significantly smaller for OPER than for nosev. The likely non-optimality of more- ATOVS, already pointed out in section 3., seems to be thecauseofworsescoresthanoper; using a better ATOVS coverage does not improve the short-range precipitation forecast, as the larger r.m.s. errors at 6 hours for moreatovs indicate. A slight deterioration of the meansea-level pressure bias for forecasts up to hours has also been noticed for moreatovs (not shown). Biases displayed in Table are almost unchanged. Scores for m temperature, for m humidity and for m wind show similar values for the three OSEs, which indicates that the additional mid- to high-tropospheric information brought by new satellite data has no significant impact on the model s lowest vertical levels. After 8 hours, OPER shows slightly degraded r.m.s. scores against the two other experiments (not shown), mainly because of two particular precipitating cases that occurred during the test period. However, it has to be noted that, at those ranges, forecasts are more sensitive to the growing influence of lateral boundary conditions. 4.. Precipitation forecast For the precipitating cases within the period, the three OSEs produce their own solution. However, some conclusions on the general behaviour can be drawn from the examination of the simulated precipitating patterns. For example, Figure shows accumulated rainfall forecast between and 8 hours of simulation for 3 June by the three experiments, compared with rain-gauge observations (Figure (e)). This case was characterized by easterly and south-easterly winds in the south-east of France, bringing unstable moist air from the Mediterranean Sea. During the day, these unstable conditions triggered convective activity, mainly over the mountains of the Massif Central, the Pyrenees and the Alps. For that particular case, the spin-up model generally underestimates the precipitation, especially over the Massif Central. The strong convective activity that has developed along a north south convergence line that links the Pyrenees to the Massif Central is well represented in intensity, but is located too far east. These drawbacks are typical for the spin-up model which often captures the large-scale precipitation pattern but is less accurate for smaller scales. For all the precipitating cases of the 3-week experiment, OPER and moreatovs show very similar patterns for the simulated precipitation. For example, Figures (b) and (d) display comparable forecasts. These two experiments represent quite well the main bow-shaped precipitation line with a realistic amount, which is also reflected by better quantitative precipitation forecast scores than the spin-up model and nosev over Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj

14 668 T. MONTMERLE ET AL. Table I. Mean biases and r.m.s. errors of OPER, nosev and moreatovs against ground-based observations of 3-hour accumulated precipitation. Forecast OPER nosev moreatovs range (hours) r.m.s bias Values were computed over France using hourly observations from 47 rain gauges. (a) Spin-Up (b) OPER (c) nosev (d) moreatovs (e) Raingauges Figure. Accumulated rainfall (mm) between and 8 hours of the forecast over France on 3 June from (a) the spin-up model, (b) OPER, (c) nosev, (d) moreatovs, and (e) rain-gauge observations. This figure is available in colour online at Copyright 7 Royal Meteorological Society Q. J. R. Meteorol. Soc. 33: 6 67 (7) DOI:./qj