Implementation of a 3D Variational Data Assimilation System at the ...

Implementation of a 3D Variational Data Assimilation System at the Canadian Meteorological Centre. Part II: The Regional Analysis Stéphane Laroche* and Pierre Gauthier Meteorological Research Branch, Atmospheric Environment Service, Dorval, Québec. and Judy St-James and Josée Morneau Canadian Meteorological Centre, Atmospheric Environment Service, Dorval, Québec.

[Original manuscript received 13 October 1998; in revised form 30 March 1999]

abstract This paper describes the implementation of the 3D variational (3D-var) analysis in the Regional Data Assimilation System (RDAS) of the Canadian Meteorological Centre. The RDAS, a 12-h data assimilation cycle, is run twice daily to provide analyses to the variable resolution Global Environmental Multi-scale (GEM) model. The same incremental 3D-var algorithm is used for both the regional and global data assimilation systems. In this algorithm, the innovations are calculated with respect to the full-resolution model while the analysis increments are calculated at a lower resolution on a Gaussian grid. Background error correlations for the global and regional data assimilation systems are examined. It is shown that the resolution of the analysis increments is determined to a great extent by the horizontal correlation lengths. Although the horizontal resolution of the regional model is three times higher than the global model, the correlation lengths for both models are similar. Consequently, the same horizontal resolution for the analysis increments is used in both data assimilation systems. A pre-implementation evaluation showed that the RDAS maximizes the coherence between the analysis and the forecast model. This results in a higher-resolution and more consistent analysis with respect to the regional model. The forecasts issued from the RDAS are generally improved, especially the temperature and the geopotential above 300 hPa. The RDAS also reduces the precipitation spin-up observed during the first 12 hours when initiated with an *Corresponding author address: Stéphane Laroche, Data Assimilation and Satellite Meteorology Division, Atmospheric Environment Service, 2121 Trans-Canada Hwy., Dorval, P.Q. CANADA H9P 1J3

ATMOSPHERE-OCEAN 37 (3) 1999, 281–307 0705-5900/99/0000-0281$1.25/0 © Canadian Meteorological and Oceanographic Society

282 / Stéphane Laroche et al. analysis from the global data assimilation system. Finally, the impact of the digital filter on the analysis from the RDAS is small, indicating that the regional analysis is already well balanced. résumé Cet article décrit la mise en place de la nouvelle analyse variationnelle tridimensionnelle (3D-var) dans le système régional d’assimilation des données (RDAS), utilisé au Centre météorologique canadien. Le RDAS est un court cycle d'assimilation de données d'une durée de 12 heures qui utilise le modèle régional pour générer ses champs d’essai. Ce cycle est exécuté deux fois par jour pour fournir des analyses au modèle Global Environnemental Multi-échelle (GEM), utilisé pour les prévisions régionales. Le même algorithme d'analyse 3D-var est employé dans les systèmes régional et global d’assimilation des données. Dans cet algorithme, les innovations sont calculées à partir du champ d'essai à pleine résolution alors que les incréments d'analyse sont calculés à plus faible résolution, sur une grille Gaussienne. Les corrélations d'erreur de prévision pour les systèmes régional et global d’assimilation de données sont examinées. On montre que la résolution des incréments d'analyse est largement dictée par les longueurs de corrélation horizontales. Bien que la résolution du modèle régional soit trois fois plus élevée que celle du modèle global, on montre que les longueurs de corrélation horizontales sont similaires. Par conséquent, la même résolution horizontale des incréments d’analyse est utilisée dans les deux systèmes d’assimilation des données. L’évaluation du RDAS, avant sa mise en opération, montre que le système maximise la cohérence entre l’analyse et le modèle de prévision. Les analyses sont définies à plus haute résolution et sont en meilleur accord avec le modèle de prévision régional. Les prévisions initialisées à partir du RDAS sont généralement améliorées, surtout les prévisions de température et du géopotentiel au-dessus de 300 hPa. Le RDAS réduit la sous-estimation de la précipitation observée durant le 12 premiéres heures de prévision lorsque le modèle est initialisé à partir d’un système d’analyse statique. Finalement, l’impact du filtre digital sur l’analyse issue du RDAS est faible, indiquant que l'analyse régionale est déjà dynamiquement bien balancée.

1 Introduction A medium-range global model and a short-range regional model are run twice daily at the Canadian Meteorological Centre (CMC), to provide weather offices with atmospheric predictions. The companion paper by Gauthier et al. (1999) (Part I) presents the three-dimensional variational (3D-var) analysis as implemented in the global variational data assimilation. The present paper is the second part and describes how the same 3D-var analysis is implemented in the Regional Data Assimilation System (RDAS). In the beginning of regional modelling at CMC in 1985, initial conditions were provided by the hemispheric analysis (Mitchell et al., 1990) interpolated to the regional model grid. This strategy, referred to as static analysis by Rogers et al. (1996), was used until December 1992 for the Regional Finite-Element (RFE) model (Benoit et al., 1989). However, this analysis was not consistent with the regional forecast model and produced a spin-up of the dynamical and physical processes, typically during the first 12 hours of the forecast. Based on the work of DiMego et al. (1992), Chouinard et al. (1994) developed an RDAS driven by the RFE model. They showed that the RDAS provides more detailed and dynamically consistent analyses

Implementation of a 3D Variational Data Assimilation System / 283 to the regional model and improves the forecast during the first 24 h. This RDAS for the RFE model was in operation from December 1992 to February 1997. In the last few years, a variable-resolution Global Environmental Multi-scale (GEM) model was developed and then implemented at CMC with a static analysis system on 24 February 1997. Noticeable improvements in the GEM forecasts were noted when compared to the RFE model with its own RDAS, which motivated its operational implementation (see Côté et al., 1998b for details). Meanwhile, the RDAS presented in this paper was being tested and was implemented on 24 September 1997. The 3D-var analysis of the RDAS is based on an incremental approach (Courtier et al., 1994) in which the innovations (difference between observations and background field) are computed with respect to the full-resolution of the background field while the analysis increments are produced on a global Gaussian grid at a different resolution. Using this strategy, it is possible to provide an analysis for both the global spectral model (Part I) and a grid-point regional model like the GEM model. Hence, the same 3D-var analysis system can be employed for all forecasting models at CMC. Furthermore, the global variable-resolution grid of the GEM model requires an analysis outside the uniform high resolution window; a condition that is fulfilled by a global Gaussian grid of the analysis increments. Most atmospheric data analysis methods act as low-pass filters (Daley, 1991 and references therein) and the degree of filtering is controlled to a great extent by the background-error correlations. Hollingsworth and Lönnberg (1986) and Mitchell et al. (1990) have shown that the horizontal correlation lengths of the background-error statistics for global forecast models typically range from 200 to 600 km in the troposphere. With such correlation lengths, a spectral truncation of T108 is sufficient to represent the analysis increments properly, as will be shown in this paper. The incremental formulation exploits this property by calculating the analysis increments at a lower resolution than the resolution of the forecast model, making the analysis computationally more efficient. In addition, it will be shown that the background-error correlations estimated from forecasts obtained from the RDAS are similar to those obtained from the global data assimilation system. Following the argument presented in Part I, this is largely related to the background-error covariance model used in the 3D-var which is representative of forecast error averaged in time over a period of at least one month and in space over large areas. This makes the characteristic lengths of the correlations relatively insensitive to the resolution of the model. The paper is organized as follows. Section 2 describes the main components of the RDAS. The incremental 3D-var formulation is presented in Section 3. Background-error statistics from the global and regional data assimilation system are then compared in Section 4. The filtering effect of the background-error correlations on the analysis increments is also discussed. Pre-implementation results are presented in Section 5 and the RDAS performance is compared with the static analysis system for the two-month evaluation period during the summer of 1997. Analyses from both systems, valid at 1200 utc on 24 September 1997, are compared to highlight some of the benefits of the RDAS. Conclusions are drawn in Section 6.

284 / Stéphane Laroche et al. 2 The regional data assimilation system (RDAS) Figure 1 depicts both the global and regional data assimilation systems during a 24-h period. The global data assimilation system is a self-contained continuous cycling system (see Part I) in which the analysis is updated every 6 hours. A continuous assimilation system requires that the model performs well when integrated over long periods of time and forced by the observations. Preliminary results (not shown) from a continuous cycle for the regional model were generally not as good as those from a 12-h intermittent data assimilation system, particularly near the model’s upper lid. The results from the regional continuous cycle also showed that an important degradation occurs in the coarse regions of the model. Addressing these problems would require changes to the model. As an alternative, it was decided to develop an intermittent data assimilation cycle similar to the one described in Chouinard et al. (1994). This is the RDAS that will be described here in which two periods of 12 hours of data assimilation are performed every day to provide analyses at 0000 and 1200 utc to the regional GEM model (Fig. 1). If to denotes the initial time for a 48-h regional forecast (0000 or 1200 utc), the regional cycle begins at to – 12 h with a first 3D-var analysis. Its trial field, which is a 6-h forecast initiated at to – 18 h from the global data assimilation system is interpolated directly to the regional model’s grid. The analysis is then followed by a 6-h regional forecast and this procedure is repeated to provide the final regional analysis using a more detailed and dynamically consistent trial field. A 12-h data assimilation cycle prior to the regional forecast is long enough to provide an analysis which is dynamically consistent with the model, as will be shown here, while short enough to limit the emergence of problems associated with long-term integrations of the regional GEM model. The observations assimilated and the quality control algorithm used in the RDAS are the same as those described in Section 5 of Part I for the global data assimilation system and these were inherited from the previous Optimal Interpolation (OI) system (Mitchell et al., 1996). In summary, the observations assimilated are the horizontal winds, geopotential height and dewpoint depression from radiosondes and some surface stations, buoys and ships, winds from aircrafts (AIREP/AMDAR). The following satellite observations are also assimilated: SATEM geopotential height thicknesses, SATOBS horizontal wind, and dewpoint depression from the HUMSAT system (Garand and Hallé, 1997). Observation error characteristics are described in detail in Appendix B of Part I. The surface analyses used by the RDAS are briefly described here. The soil moisture analysis, run daily at 1800 utc (Mailhot et al., 1997), is performed on the regional grid. Through statistical relationships by a regression technique, a 5-day average of the 6-h forecast error, obtained from an analysis of dewpoint temperature, gives the correction to be made to the soil moisture field. The ice analysis, run daily on a global 1/38 grid, is a simple averaging of the Special Sensor Microwave Imager (SSMI) derived data and ice cover data from the Canadian Ice Service of Environment Canada. Where there are no data, monthly climatology is used. The

Schematic diagram illustrating the global and regional data assimilation systems at CMC over a 24-h period. The global system is a continuous cycling procedure in which the analysis is updated every 6 hours. Two periods of 12-h regional data assimilation cycles are connected above and below the global data assimilation cycle. The data cutoff is indicated above the OBS symbol.

Implementation of a 3D Variational Data Assimilation System / 285

Fig. 1

286 / Stéphane Laroche et al. screen-level temperature and the snow depth analyses are performed every six hours using a statistical interpolation methodology (Brasnett, 1999). The analyses resolutions are 0.98 and 1/38 respectively. The analyzed screen-level temperature is used in turn to produce a deep soil temperature analysis through relationships established from statistical regression. The sea surface temperature analysis, performed on the departure from climatology, is performed daily with a statistical interpolation algorithm (Brasnett, 1997). The analysis resolution is 0.98. The GEM model is a global variable-resolution grid-point model (Côté et al., 1998a,b). It solves the hydrostatic primitive equations using an implicit, semiLagrangian time treatment on an arbitrarily-rotated variable-resolution latitudelongitude mesh. A cell-integrated finite-element discretization on an Arakawa C grid is used in the horizontal. The vertical discretization is the same as in the RFE model (Tanguay et al., 1989). The model has 28 levels from the surface up to 10 hPa. The horizontal resolution is approximately 35 km over North America and some of its adjacent waters (Fig. 2). The resolution varies smoothly outside the uniform resolution window (each successive mesh length is approximately 10% larger than its predecessor). The physical parametrizations included in the model are described in Mailhot et al. (1997). The digital filter described in Fillion et al. (1995) is used as the initialization procedure. It is a variant of the digital-filter method proposed by Lynch and Huang (1994), which is suitable for regional modelling. Using a 6-h time series obtained from a forward integration of the complete model, the digital filter is applied and yields a filtered state at t + 3 h: this is referred to as a finalization procedure by Fillion et al. (1995). The initialization step is usually a distinct component in a data assimilation system. However, due to the nature of the digital-filter method, this initialization step is considered here as part of the forecast model. 3 The incremental 3D-var formulation The 3D-var analysis used in the RDAS is the same as the one described in Part I. Here, we recall the main equations of the incremental formulation and its key features. In addition, the analysis steps performed in the RDAS are summarized. In the incremental formulation (see Part I for more details), the analysis xa is expressed as xa = xb + δxa,

(3.1)

where x is the background field and δx represents the analysis increments obtained by minimizing: b

a

J(δxL) = ½δxLTB–1δxL + ½(H9(Xref)ΠTδxL – y0)TO–1(H9(Xref)ΠTδxL – y0).

(3.2)

Here B and O are the covariance matrices of background-error and observation-error respectively, H9(Xref) is a low-resolution and linear approximation of the forward interpolation operator H and ΠT is the projection operator from the full to low-resolution grids. The innovations y0 are defined as:

Implementation of a 3D Variational Data Assimilation System / 287

Fig. 2

The 289 × 255 variable-resolution horizontal grid on the globe: resolution is approximately 35 km over North America. For clarity, only every other line of the mesh is shown.

y0 = y – H(xb),

(3.3)

where y represents the observations. The analysis increments δxL are expressed in terms of spectral components of the streamfunction (Ψ), the velocity potential (χ), dewpoint depression and the geopotential departure from geostrophy (Φ9) defined as: Φ9 = Φ – f Ψ,

(3.4)

where f = 2Ωsin ϕ is the Coriolis parameter, ϕ is the latitude and Ω is the angular frequency of the earth. These variables are used to introduce a multivariate covariance model. However, in the final output of the 3D-var analysis, the increments are expressed in terms of the horizontal wind components, geopotential and dewpoint depression (see Part I for details).

288 / Stéphane Laroche et al. Steps in the regional analysis can then be summarized as follows: i.

Calculate the innovations y0. This is done by first interpolating horizontally the full-resolution background field from its own grid to the observation locations. This produces vertical profiles of the model state which serve as input to the observation operator (i.e., Vh(xb), see Part I); ii. Calculate the analysis increments δxL at a spectral resolution of T108, on the 16 mandatory pressure levels [1000, 925, 850, 700, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, 10 hPa] with the 3D-var algorithm; iii. Transform and interpolate the analysis increments to the model grid (δxL → δxa). These processes include horizontal linear interpolations from a 240 × 120 Gaussian grid to the variable-resolution GEM grid, vertical linear interpolations from pressure levels to the model vertical coordinate, derivation of temperature and surface pressure increments from the geopotential increments using the hydrostatic equation, and a transformation of the dewpoint depression into specific humidity. For model levels with pressure higher than 1000 hPa, values of winds, temperature and dewpoint depression at l000 hPa are used; iv. Add the resulting analysis increments δxa to the background field xb. In the previous operational OI system used at CMC, all observations were preprocessed so that they were located exactly on these levels. This approach has been kept in the current implementation of the 3D-var at CMC in order not to alter the preprocessing of the observations (including quality control). As discussed in Part I, this also makes our implementation of the 3D-var incremental in the vertical since the analysis increments are produced on pressure levels and need to be interpolated back to the model levels. However, as shown in Part I, this vertical interpolation destroys some of the constraints imposed by the analysis through the covariance model. Moreover, the analysis increments are too coarse particularly near the surface. A similar incremental formulation of the 3D-var has been adopted by MétéoFrance (Thépaut et al., 1998). In their data assimilation system, the innovations are computed with respect to the ARPEGE model, which is a spectral variable resolution model T149/L27 with a stretching factor of 3.5 and rotation of the North Pole over France. This transformation gives an equivalent resolution of 33 km over Europe. The analysis increments are calculated at a lower uniform resolution T95/ L27 with no rotation with respect to the North Pole. The analysis increments are produced directly on the model's vertical levels and subsequently, horizontally interpolated to the variable resolution grid. No vertical interpolation is then needed. Currently, the 3D-var algorithm is being modified at CMC to produce the analysis increments directly on the model’s own vertical levels (Gauthier et al., 1998). The merit of the incremental 3D-var formulation is that the minimization of the cost function (3.2) is performed with respect to the analysis increments rather than the full model state as in the original 3D-var formulation (see Part I, equation 2.1).

Implementation of a 3D Variational Data Assimilation System / 289 Consequently, the representation of analysis increments and the background field can be different. For instance, in the RDAS described in the present paper, the analysis increments are produced at a spectral resolution of T108, represented on a 240 × 120 Gaussian grid, while the background field is defined on a variable-resolution latitude-longitude grid. Thus, the same analysis system can be used for different models or different model configurations. As shown in Fig. 2, the grid of the GEM model is quite different from the Gaussian grid of the global spectral model used in Part I. In addition, the innovations are obtained by horizontally interpolating the full-resolution background field to the observation locations. There are several advantages to doing so. Firstly, the error in the innovations due to the interpolation of the background field to the observation locations is reduced. Secondly, since the low-resolution analysis increments are simply added to the background field, all the small-scale features developed by the regional model are retained in the analysis. Those features generated by stationary forcing such as the orography and land-water boundaries are meaningful and contribute to reducing the representativeness error. They also contribute to a better representation of the atmospheric state in the planetary boundary layer, as will be shown in Section 5. Thirdly, the spin-up of the dynamical and physical processes of the analysis is considerably reduced since the full-resolution background field, already in equilibrium on the forecast model grid, remains so throughout the process. Three experiments were carried out to demonstrate the advantage of computing the innovations with respect to the background field at its full-resolution. These experiments were conducted with a trial field from the global data assimilation system because the Gaussian grid of a global model can be the same as the analysis. In the control analysis, the analysis increments are calculated at the full resolution of the background field (i.e., T199). In the second experiment, the incremental formulation uses the T199 background field to compute the innovations while the analysis increments are calculated at T108. In the third experiment, the innovations are computed with respect to the background field filtered at T108. This is referred to as the non-incremental analysis. The three analyses are valid on 24 September 1997, 1200 utc. Figure 3a shows the control analysis increments of the dewpoint depression at 700 hPa over the western part of North America. The difference between the dewpoint depression increments from the control and those from the two other experiments are shown in Fig. 3b and Fig. 3c. The differences obtained from the incremental formulation (Fig. 3b) are at least an order of magnitude smaller than the amplitude of the increments of the control analysis. On the other hand, the differences obtained from the non-incremental analysis are significant (Fig. 3c), especially over the western part of the continent where the terrain is complex. The errors generated by using the coarser background field are therefore much greater than those due to a lower resolution representation of the analysis increments. It will be shown in the next section that the effective resolution of the analysis increments is controlled by the background-error correlations and, beyond a certain resolution, the response of the analysis scheme becomes independent of the resolution at which the

290 / Stéphane Laroche et al.

Fig. 3

(a) Analysis increments of dewpoint depression at 700 hPa from the control experiment valid at 1200 utc on 24 September 1997; (b) Difference between analysis increments shown in (a) and those from the incremental experiment; (c) Difference between analysis increments shown in (a) and those from the non-incremental experiment.

Implementation of a 3D Variational Data Assimilation System / 291 increments are actually computed. For instance, with the background-error statistics used in the global data assimilation system, a resolution of T108 is sufficient to represent the variability allowed by the statistics. An additional benefit of the incremental formulation is that the computational cost is cut by half without a significant degradation of the quality of the analysis. 4 Background-error statistics The argument of the preceding section is that the resolution of the analysis increments is dictated by the filtering properties of the background-error statistics. The purpose of this section is to present recent estimates of these statistics and show the filtering properties they have on the analysis increments. In the context of the Kalman filter, the background-error covariances evolve in time and show flow-dependent structures that make them non-homogeneous and anisotropic (Gauthier et al., 1993; Bouttier, 1993). For instance, the correlation structures are horizontally stretched and vertically tilted along frontal zones (Thépaut et al., 1996). However, in the present context of the 3D-var, the background-error covariances are considered to be representative of their averages over a period of a month to a season in which case, their correlations can be reasonably approximated as being isotropic and homogeneous (Mitchell et al., 1990). In a previous study conducted at CMC (Richard Hogue, personal communication), the background-error statistics were estimated for the global Spectral Finite Element (SFE) model and the RFE model. The method employed uses innovations sequences and is described in Mitchell et al. (1990). In short, the debiased innovations ε(p) are used to compute an ensemble average of the error covariance between station pairs. Under the homogeneity and isotropy assumptions, these are taken to depend only on the horizontal distance between the two stations. The parameters characterizing a correlation function (including the characteristic length) are obtained through a least-squares fit to these data. Although the resolution of both models was quite different (50 km for the regional model and ∼150 km for the global model), the horizontal correlation lengths were found to be similar for both models. To realize these estimates, the background-error statistics were reestimated for the current regional and global models using the same methodology. The results presented here are based on innovations from the North American radiosonde network at 0000 utc and 1200 utc from 15 December 1997 to 1 March 1998. Stable estimates of the correlation structures require 100 reports or more per station. With only two common reports each day, 50 days of reports are required. It is thus the limited number of station pairs, especially those less than 1000 km apart, that makes it necessary to consider the time-averaged background-error statistics. Figure 4 shows the correlation lengths of the streamfunction and dewpoint depression as a function of pressure for the global and regional models. We employed the correlation model described in Part I, namely a second-order autoregressive correlation function was used to represent the streamfunction and a Gaussian was used for the dewpoint depression. The results presented in Fig. 4 show that the correlation

292 / Stéphane Laroche et al.

Fig. 4

Correlation lengths of the streamfunction and dewpoint depression for the global and regional data assimilation system.

Implementation of a 3D Variational Data Assimilation System / 293

Fig. 5

Normalized power spectra of the streamfunction increments (solid curve) and the dewpoint depression increments (dashed curve) at 500 hPa obtained from the analysis valid at 1200 utc on 24 September 1997.

lengths are very similar for both the global and regional models, even though the horizontal resolution of the regional model is approximately three times that of the global model. Also shown are the error bars corresponding to the standard deviation obtained by a bootstrap method. These results agree well with those of Desroziers et al. (1995) who used lagged forecasts (the so-called NMC method) to estimate the correlation lengths over Europe obtained from the regional ARPEGE and global European Centre for Medium-Range Weather Forecasts (ECMWF) models. The filtering properties can be easily understood in the context of a simple example. In the Appendix, a one-dimensional problem is introduced to illustrate the filtering properties of the background-error statistics on the analysis increments. It is shown in particular that the analysis increments are strongly damped above wavenumber 60 and this is due mostly to the filtering effect of the background-error correlations. For the experiments described below, the background-error statistics used are identical to those presented in Part I. Figure 5 shows normalized power spectra of analysis increments of the streamfunction and dewpoint depression in response to a complete set of observations used operationally on 24 September 1997, 1200 utc. These increments were obtained with the global data assimilation system using its full resolution of T199. As in the one-dimensional case, the amplitude of the increments decreases rapidly above total wavenumber 60, the decrease being steeper for the dewpoint depression. This is explained by the steeper slope of the spectrum of a

294 / Stéphane Laroche et al. Gaussian function in the small scales. For both variables, the amplitude decreases by about five orders of magnitude at n = 100. The results presented here show that, due to the filtering properties of the background-error statistics, we are justified in producing analysis increments on a coarser uniform grid provided the innovations are computed with respect to the background state at its full resolution. The large scale structure of the correlations stems from the fact that the background-error covariances used in the 3D-var are representative of their spatial and temporal averaging. Covariances with finer scales can be obtained within the framework of truly 4D data assimilation schemes which make use of flowdependent covariance models either explicitly (in a Kalman filter) or implicitly (in 4D-var). Alternatively, flow-dependent background-error covariances can also be obtained by using an isentropic (Benjamin et al., 1991) or a semi-geostrophic (Desroziers, 1997) coordinate transformation in the analysis scheme. The filtering properties of such covariance models may require that the analysis increments be produced at a higher resolution. However, the approach taken here is well justified for the current formulation of the background-error statistics. 5 Performance evaluation The RDAS was evaluated against the static analysis system during the summer of 1997 before its implementation in the CMC operational suite on 24 September 1997. The background and observation error statistics in the RDAS are the same as in the global data assimilation system (Part I). In the static analysis system, the global analysis is directly interpolated to the regional model grid and used as initial conditions. Figure 6 depicts the root mean square error (RMS) and bias differences for the static analysis system (solid curve) and the RDAS (dashed curve). The thick and thin lines represent the analysis and 6-h forecast error estimates respectively. The RMS and bias differences are generally smaller for the RDAS except for the dewpoint depression where the results are comparable. The main improvements are found near 1000 and 200 hPa which correspond roughly to the surface and jet stream levels respectively. The improvements near the surface come from the higher-resolution representation of the orography and land-water boundaries in the RDAS. Figure 7 compares temperature and wind analyses at the surface from the RDAS and the static analysis system. The surface wind and temperature fields are significantly modified during the 12-h RDAS providing a better representation of the warmer lake surface temperature in the fall season. Moreover, the higher horizontal resolution in the regional model allows a better representation of tropospheric jets. Figure 8 shows the verification statistics for the 24-h and 48-h forecast during the pre-implementation experimentation. The main improvements are found in the temperature and geopotential near the jet stream level. The wind biases are also improved at most levels throughout the 2-day forecast. In the static analysis, the regional model is initialized with an analysis from the global data assimilation, which is driven by a model that is significantly different. This creates spurious gravity waves which makes it necessary to use a digital filter.

Implementation of a 3D Variational Data Assimilation System / 295

Fig. 6

Verification scores (RMS and Bias errors) against the North American radiosonde network obtained for the static analysis system (solid curves) and the RDAS (dashed curves). The thin curves correspond to verifications of the background fields whereas the thick curves correspond to verifications of the analysis. The errors are averaged over the two-month evaluation period.

Figure 9 shows a 24-h time series of surface pressure at a point near Montréal for different experiments. This point is representative of what is observed elsewhere. The presence of spurious gravity waves is clearly seen in the time series of an integration that uses the analysis from the static analysis system without the digital filter (dashed-dotted curve). By comparison, the same integration with the digital filter (dashed curve) leads to a time series that is devoid of such oscillations. The two remaining curves are the results of integrations using the RDAS analysis when the

296 / Stéphane Laroche et al.

Fig. 7

Wind and temperature analyses on the first model level over the Great Lakes on 24 September 1997 from (a) the RDAS and (b) the static analysis system.

digital filter is used (dotted curve) or not (solid curve). The analysis from the RDAS is significantly better balanced than the one from the static analysis system, particularly during the 12- to 24-h period. Its degree of balance is even similar to that of the integration with the digital filter turned on. A short data assimilation cycle therefore seems sufficient to bring the analysis into dynamical equilibrium with the regional

Implementation of a 3D Variational Data Assimilation System / 297

Fig. 8

RMS (thin curves) and bias (thick curves) forecast errors as measured against the North American radiosonde network for the pre-implementation period as a function of time. The solid (dashed) curves correspond to the forecast runs with the static analysis (RDAS). The errors are averaged over the two-month evaluation period.

298 / Stéphane Laroche et al.

Fig. 9

Time series of surface pressure for a point located near Montréal, Canada (458N, 748W).

GEM model. Moreover, after 12 hours of data assimilation, the resulting regional 3D-var analysis does not seem to require any initialization for the final 48-h forecast. This is also the case for the global analysis (see Part I). An important consequence of the RDAS is the significant reduction of the precipitation spin-up during the first 12-h forecast (Fig. 10). A deficit of 20% is noted for the mean precipitation rate over North America in the static analysis system (dashed curve in Fig. 10) at the beginning of the integration compared to the RDAS. However, after 12 hours of integration, the mean rain rates in both systems are the same. Figure 11 shows the mean sea level (MSL) pressure and the accumulation of precipitation over the first 3 hours of integration initiated on 24 September 1997 at 1200 utc with the RDAS (a) and the static analysis system (b). The corresponding horizontal divergence fields at 925 hPa are presented in Fig. 12. The higher quantities of precipitation obtained from the RDAS are explained by the stronger and more detailed divergence, as seen in Fig. 12a. The horizontal divergence is built up and preserved by the model during the 12-h regional data assimilation cycle which increases the deep convective part of the precipitation, parametrized by a Kuo-type scheme (Mailhot et al., 1997), at the beginning of the ensuing forecast. The amount of precipitation is, however, not always higher over the first hours of integration, as seen in the southwestern part of the precipitation line in Fig. 11. Verification of the 48-h total precipitation forecasts of the RDAS and the static analysis system were compared at over 90 Canadian observing stations. Contin-

Implementation of a 3D Variational Data Assimilation System / 299

Fig. 10

Mean rain rate over North America obtained from forecasts issued at 0000 utc during the evaluation period. The solid (dashed) curves correspond to the forecast runs with the static analysis (RDAS).

gency tables over 6-h intervals up to 48 h were calculated for a total of 55 forecast cases. Six categories of precipitation amounts were used (25 mm). Table 1 shows the percentage of correct precipitation forecasts for categories less than 10 mm and greater than or equal to 10 mm. When the model is initiated from the RDAS, the large precipitation amounts are improved while the smallest are degraded over the first 12-h forecast. We found that the model overestimates the small quantities (less than 10 mm) of precipitation. This indicates the presence of a precipitation bias in the model which is partially compensated for in the beginning of the integration when the model is initiated from the static analysis system. Beyond the 12-h forecast, results from both systems are similar. 6 Discussion and conclusions A 12-h regional data assimilation system using a 3D-var analysis has been implemented at CMC to provide initial conditions to the regional GEM model. The incremental 3D-var analysis requires that the innovations be computed with respect to the full-resolution regional forecast. By first interpolating it horizontally to observation locations, vertical profiles of model states are obtained and used as input to the observation operators of the 3D-var. This computation then becomes independent of the definition of the grid of the regional model. Due to the filtering properties of the background-error statistics, the analysis increments can be calculated at a lower resolution on the same uniform grid as that used for the global analysis. These two ele-

300 / Stéphane Laroche et al.

Fig. 11

(a) MSL pressure field (solid contours) valid at 1200 utc on 24 September 1997 and the first three-hour precipitation accumulation (shaded areas) obtained from the RDAS and ensuing forecast; (b) Same as (a) but from the static analysis system.

Implementation of a 3D Variational Data Assimilation System / 301

Fig. 12

(a) Divergence field at 925 hPa valid at 1200 utc on 24 September 1997 obtained from the RDAS; (b) Same as (a) but from the static analysis system.

302 / Stéphane Laroche et al. Table 1

Percentage of correct precipitation forecasts over 6-h intervals measured at over 90 stations in Canada for precipitation amounts less than 10 mm and greater than or equal to 10 mm. Only forecasts issued at 0000 utc during the evaluation period are used. The highest percentage of correct forecasts for each 6-h interval and each category are indicated in bold. $10 mm