a. Spinup as seen on short-term model forecasts

When the 3DVAR data assimilation was tested and implemented in the ALADIN-France system (see Fischer et al. 2005), the filtering of the initial state was kept the same as in the dynamical adaptation. On the one hand, we have considered that the move toward an assimilation cycle should introduce a smaller amount of spinup and a shorter spinup time, because the initial state (the analysis) then is the addition of a previous (here, 6-h lead time) forecast (as background) plus an analysis increment. The background 6-h forecast fields are in fairly good balance, as we will illustrate below. Some level of mass–wind balance furthermore is present in the increment, via statistical regression coefficients between predictors in the control vector of the 3DVAR following the works of Derber and Bouttier (1999) and Berre (2000). On the other hand, some trials to move away from the DFI specifications used in dynamical adaptation mode, mostly with the goal of diminishing the intensity of filtering the total 3DVAR analysis, lead to mitigated results: on the positive side, the very-short-term forecasts often exhibited a shorter diabatic adjustment time when filtering less; on the negative side, when for instance the stop-band edge period was decreased, we also found cases of spurious onsets of precipitations in nonactive areas. Thus, the decision was made to keep the DFI procedure within the assimilation identical to the dynamical adaptation mode. This choice amounted to starting any actual forecast, either within the assimilation cycle or for the parallel, long-term production runs, from the filtered analysis denoted as f (a) henceforth, where a denotes the analysis.

After the first operational implementation of 3DVAR in ALADIN-France, we reassessed the role of DFI in the model. In doing so, we have considered classical measures for model spinup activity, such as the domain-averaged absolute tendency of the model fields, the root-mean square of the model field tendencies, or time series of model fields at specific gridpoint locations. The latter have appeared to be the most informative diagnostics for our concern, since they provide local information that can give insight into some temporal or spatial aspect of a signal (as will be shown below). Figures 1 and 2 show time series of mean sea level pressure (MSLP) for the five sensitivity experiments listed in Table 1, measured for a model grid point located in the inner core of the ALADIN-France domain and over the sea (here, the Bay of Biscay) for Fig. 1 and a grid point positioned inside the Davies relaxation zone (Fig. 2). The goal here is to assess the traces of inertia–gravity waves, by means of the differences of the various sensitivity runs with respect to a, presumably noise-free, reference. The reference run is EX1, which is an ALADIN forecast started using as its initial conditions a 6-h forecast. As for all five runs, no DFI is applied in EX1. From Fig. 1, it is clear that the time evolution of MSLP is rather smooth. There is no graphical evidence of spinup in this restart experiment, despite the fact that we do not provide all t − dt fields, nor the physics tendencies for the restart time t. Note furthermore that in EX1, we use “old” lateral boundary conditions (LBCs) so that the core and LBC fields do match at the initial time in the relaxation zone. In EX2, we change both the initial conditions (to a 3DVAR analysis) and the LBC data (to LBC obtained from the up-to-date ARPEGE run, which is also denoted as “refreshed” LBC). If DFI was set on, this configuration would be the equivalent of an operational ALADIN-France forecast. In EX2, however, DFI is switched off and one notices the existence of a wavy, rather nonperiodic, pattern on MSLP right from the start of the integration. A fairly parallel MSLP time curve in EX2, compared with EX1, is obtained after about 30 model time steps (about 3.5 h). Thus, the first information in EX2 is that a forecast started from an ALADIN 3DVAR analysis, along with refreshed coupling data from ARPEGE, does possess wavy structures that are not present in a “restart” experiment. This result has also been obtained for several other cases, which shows that these patterns are not just the signature of a meteorological feature that would have been captured by the data analysis process in the particular situation displayed in our graphics. This type of feature corresponds to a pattern of spinup behavior. Operational experience furthermore tells us that these wavy patterns are not seen when DFI is switched on. With DFI and the tunings discussed in section 1, time series of model outputs exhibit a smooth evolution both in their dynamical adaptation and in data assimilation mode.

Another question of interest is to what extent the analysis increment does introduce such wavy, unbalanced, behavior. From other ALADIN studies, especially in relation to so-called blending cycles (e.g., Brožkovà et al. 2001; Širokà et al. 2001), we know that the choice of the LBC data can have an impact on short-term forecast performances and spinup properties. Thus, we have run experiment EX3, which is started from the same initial fields as EX1 but which uses the refreshed LBCs, like EX2. Conversely, we have run an experiment (EX4) that is started from the 3DVAR analysis like EX2, but that uses the same LBCs as in EX1. In Fig. 1 and for EX3, we notice a very clear periodic pattern associated with a wave in MSLP passing over the point in the Bay of Biscay after about seven model time steps. This pattern disappears only after about 30 model time steps, which is slightly beyond the first LBC update time (3 h) in the forecast, since we use a 3-h coupling frequency. The MSLP curve for EX4 first follows the evolution of EX2, until about six or seven time steps, and then becomes dominated by a very periodic wave signal that lasts for about the same duration as in EX3.

Let us now compare the MSLP time series over the Bay of Biscay with the time series for MSLP at a point in the relaxation zone. At the latter location, the model forecast fields will be partially controlled by the coupling model solution. Referring now to Fig. 2, we see a smooth MSLP evolution for EX1, a rather periodic wavy curve for EX2 and EX3 (for about 20–30 time steps and, here, starting right from the beginning of the simulation), and a fairly nonperiodic wavy pattern for EX4 (over about 30 time steps). Thus, similar oscillations are observed at both points, in the relaxation zone and in the interior domain (Bay of Biscay).

Not shown in this paper are the spatial structures of the wavy patterns, as obtained by simply plotting the difference of MSLP between any sensitivity experiment and the reference EX1, which we have done for every 1-h time step. From these plots, we have inferred that the nonperiodic wavy feature obtained for EX2 mostly corresponds to a spatially unstructured field in which no specific horizontal patterns are visible. We interpret the unstructured nature of the MSLP difference maps as being a signature of a complex reequilibration of the analysis in the model spinup phase. Thus, one may consider the hills and valleys for EX2 in Fig. 1 as a signal of the imbalance in the analysis increment. This imbalance generates MSLP variations of about 0.7–0.8 hPa. With regard to EX3 and EX4, the spatial maps of the MSLP forecast differences have shown a fairly structured wavy pattern, though they do not correspond to a pure sinusoidal signal (rather a succession of pluses and minuses in the field, with irregular but smooth contours). Furthermore, we found graphical evidence that the wavy pattern is generated at an inflow boundary of the model domain and very quickly propagates inward. From the plots, and from the time of appearance of the periodic signal on the MSLP time series of EX3 at the two points displayed in Figs. 1 and 2, the speed of the propagation of the corresponding wave is estimated to be about 1200 km h⁻¹. This speed would correspond to the phase velocity of the external inertia–gravity wave for a uniform-density fluid with an equivalent height of about 11 km. The wave graphically appears as a broad (spatial pseudo-wavelength of about 450 km) and deep structure, which is the result of the imbalance within the relaxation zone, and it is sufficient to simply use spatially mismatching fields to produce it. Indeed, in EX3, the wavy pattern is created despite the balanced initial state in the core of the domain. However, the linear combination of that forecast state with the refreshed LBC data used in the Davies formulation is not balanced. A similar problem affects EX4, which also has mismatching lateral boundary and inner domain fields. We further notice that the periodic signals seen in Figs. 1 and 2 are reminiscent of signals obtained, for instance, in noninitialized High Resolution Limited Area Model (HIRLAM) forecasts [see Fig. 6 in Lynch and Huang (1992)].

Previous experimental studies within the ALADIN community, for various types of 3DVAR assimilation cycles, have indicated that spatially consistent (matching) data for the inner domain and the LBC initial fields can reduce the size of the digital filter increment around the lateral boundaries (Širokà et al. 2001). Thus, in order to verify whether a rather straightforward spatial match of core and boundary initial data would be sufficient to reduce the boundary-generated spinup, we have run experiment EX5, where the 3DVAR analysis is used both for the initial inner domain and LBC data. It turns out that EX5 also exhibits wavy structures on the MSLP curves, and that they are about as pronounced as in EX4. In Figs. 1 and 2, the differences between EX1 and EX3 are striking, while the patterns of behavior of EX4 and EX5 remain fairly similar. This graphical evidence suggests that the model balance for the LBC data probably would be even more beneficial than the mere spatial consistency. As an intermediate conclusion, we exhibited two different sources of spinup: one linked with the 3DVAR analysis increment and the other linked with the imperfect match of interior and lateral boundary conditions at initial time.

b. Consequences of the use of digital filters

From the findings summarized in section 2a, we have run alternative assimilation configurations, changing the choices for the initial LBC data (spatially matching or not) and the settings for the digital filtering. Namely, we have tested reducing the filter’s time span and stop-band edge period. Keeping in mind that “boundary waves” might appear occasionally, with time periods between 0.75 and 1.5 h (see Figs. 1 and 2), we have reduced the stop-band edge τ_s from 3 to 2 h but not less. At the same time, the time span also can be slightly reduced from about 2 to 1.6 h setting N = 9 down to N = 7 (N as defined in the appendix). The latter change keeps the response function nearly untouched (similar ripple ratio) while diminishing slightly the numerical cost of the DFI. As concerns the analysis increment oscillations, it is difficult to spot a clear time period associated with them. The new settings proved experimentally to be valid choices for removing these analysis-related signals. In the MSLP time series for EX2 and EX5, one for instance cannot notice any significant oscillatory signal with a period longer than 2 h.

A further change of interest for the ALADIN LAM assimilation was the switch from nonincremental filtering, where forecasts are started with f (a), to incremental filtering, where forecasts are started with g + f (a) − f (g) (g standing for the first guess). Initialization using the incremental formulation and digital filters is denoted here as IDFI. The effective “total increment” for nonincremental filtering is f (a) − g, with both an impact coming from corrections by the observations and the 3DVAR background error covariances, and an effect due to the application of the digital filter. We have found on several occasions that the two signals tend to overlap, especially in meteorologically active areas such as frontal structures, where one still would wish the analysis to remain the dominating process of “correction of the first guess.” Rewriting f (a) − g = f (a) − f (g) − [g − f (g)] shows that the (nonincremental filter) total increment amounts to adding to the first guess the balanced analysis increment, but also to removing the filtered part of the first guess. This is not a problem if the first guess itself is in balance in the sense of the filter f, since then g − f (g) vanishes. However, if we come back to digital filtering, f behaves by definition as a temporal filter and the term g − f (g) is nonzero if one admits that high frequencies can exist in g in relation to rapidly evolving meteorological features, for instance. Consequently, the high frequencies present in the first-guess field will be removed from the initial state in the nonincremental case, although one would hypothesize that these “oscillations” are not of the spinup type. Moreover, the total increment f (a) − g may depart significantly from the optimum in terms of assimilation theory, an aspect that is in principle true regardless of whether DFI or IDFI are used. Conversely, with incremental filtering, the high frequencies in g are kept in the initial state for the subsequent forecast.

The use of incremental filtering for initialization in an assimilation cycle has been promoted in various works in the past. Puri et al. (1982) compared incremental linear normal mode initialization with Machenhauer’s NNMI in a hemispheric nine-level primitive equations model. They showed that the incremental linear version was able to filter gravity wave noise from the analysis while keeping a strong signal of the mean meridional circulation, especially in the model’s tropics. They also noticed some residual transient gravity wave activity, a finding that they presumed to be harmless. Ballish et al. (1992) proposed an alternative method, leaving the context of a linearized initialization and transposing the incremental approach to NNMI. Using the global National Meteorological Center [NMC, now known as the National Centers for Environmental Prediction (NCEP)] model, they applied the NNMI code to the difference of the model tendencies starting with the analysis and the first guess, respectively. The result is added back to the analysis, and a final initialization step follows before the forecast. They claimed that this approach is less sensitive to the way diabatic tendencies are computed, as the potential uncertainties in the model physics, which could lead to incorrect gravity wave removal in NNMI, are partially canceled by the subtraction step. Their results show that the incremental method keeps the signal of tidal waves, especially the semidiurnal wave in their settings, much more untouched than does the nonincremental NNMI. They also show that the incremental NNMI produces a better balanced state within the assimilation cycle than Puri et al.’s linear incremental version, by removing more efficiently transient waves. The benefit, in terms of balances, of incremental initialization has been then further confirmed within the context of 3DVAR global assimilation systems (see, e.g., Courtier et al. 1998). In four-dimensional variational data assimilation (4DVAR) Gauthier and Thépaut (2001) have introduced an incremental filtering formulation directly inside the data assimilation process, by adding a weak-constraint cost function based on digital filters (the so-called Jc-DFI term in 4DVAR, one variant of the J_c term introduced in section 1). This approach allows one to filter the analysis increment while performing the data assimilation step, at a very marginal extra numerical cost. Despite its intrinsic linear formulation, this filtering should control nonmeteorological transient waves thanks to the presence of the observational constraint.

The quantitative effects on objective scores when switching from the operational, nonincremental, DFI toward retuned IDFI are shown in Figs. 3 –5 for MSLP, and 10-m wind direction and wind speed, respectively. We display both error bias and root-mean-square error (RMSE). As an important point here, note that while surface pressure is assimilated in the ALADIN-France 3DVAR, 10-m wind observations are not assimilated in the operational version discussed in this section 2. Accordingly, in our companion experiment using IDFI, 10-m wind observations are not included, and can be considered to be genuine cross-validating data throughout section 2. The scores are obtained with respect to the French mesoscale surface network, for a period of 40 days (20 September–31 October 2006). A further difference, namely the overall tuning of the ratio between background and observation error variances [setting R from 1.5 to 1.2; see Fischer et al. (2005, p. 3481)], is an additional change entering this comparison. This retuning however does not have a significant impact on the statistical scores displayed in this section. The major impact of IDFI is a decrease on the MSLP error bias, with also a fairly small reduction of the RMSE in the short-term forecasts, mostly felt until 6-h lead time (Fig. 3). Note that, at other time periods when the operational MSLP error bias was negative, IDFI further decreased the bias, thus leading to a slightly more negative bias with respect to the observations. Therefore, this effect of IDFI, tending to decrease the MSLP bias, cannot systematically be considered to be an improvement. We rather interpret this signal as an effect of the intrinsically biased nature of the nonincremental formulation of the digital filter (see the appendix). For the 10-m wind direction, the most prominent impact is a much better fit of the 3DVAR + IDFI initial state with respect to the observations, compared with the operational version (Fig. 4). This finding is in accordance with subjective verification, which indicated that the large-scale 10-m wind orientation is more consistent with MSLP structures (gradients) in the IDFI-derived initial model state. An apparent “drawback” of IDFI is the deterioration of the initial and 3-h lead-time 10-m wind speed bias and RMSE (Fig. 5). Thus, IDFI does have opposed effects on the wind field, in terms of scores to observations: a positive impact is obtained for the 10-m wind direction, and a negative one is seen on the 10-m wind intensity.

To be more specific, the overestimation of low-level wind speed, most notably during night, is known as a typical shortcoming of the ALADIN model version used in our study. This overestimation was seen in routine experiments of that time both in ARPEGE and ALADIN, and for any forecast lead time corresponding to nighttime conditions (F. Bouyssel 2009, personal communication). Within the framework of our discussion, this aspect will be considered to be a typical model error term whose investigation is beyond the scope of our work. To understand more in depth, however, the link between this overestimation of wind intensity and the strategy for filtering the initial state, we have run two extra experiments. Both experiments consist of series of forecasts over the full 40-day period, started respectively from archived nonfiltered 3DVAR analyses (initial state is a) and archived (nonincrementally) filtered first guesses [initial state is f (g)]. The archived data originate from the operational ALADIN-France 3DVAR and no assimilation cycle was run for these two extra experiments. The 10-m wind speed scores for the experiment started from nonfiltered analyses superpose almost perfectly with those of the IDFI assimilation experiment. The scores of the f (g) experiment reveal a drop of the bias almost to 0 and a slight decrease of the RMSE, exactly as for the operational assimilation using nonincremental DFI. Thus, it is DFI that brings the initial states closer to the observations of 10-m wind speed, and not the 3DVAR analysis. Nonincremental DFI impacts on the 10-m wind field, regardless of which term is the input state (an analysis a or a forecast g), in a way leading to a better fit toward the observations. This positive impact is however lost after about 3 h of integration. In the IDFI assimilation, as well as in the series of forecasts started from nonfiltered analyses, the low-level wind speed differences between the observations and model initial states are relatively close to the differences between the observations and 6-h forecasts (the backgrounds to the analyses). Eventually, the wind speed error bias and RMSE will tend to approach values representative of forecast errors.

We also checked the two extra series of 40-day forecasts, started from a and f (g), with respect to MSLP and 10-m wind direction scores. The scores of the forecasts that were started from nonfiltered analyses were roughly similar to those of the IDFI assimilation experiment, especially as concerns MSLP and 10-m wind direction biases over the 40 days. The scores of the forecasts started from filtered first guesses revealed increased MSLP bias and RMSE, as well as a clearly increased 10-m wind direction bias at 0 h, with respect to the IDFI assimilation. Actually, the scores for the f (g) experiment were close to those of the operational assimilation with nonincremental DFI [remember that the f (g) experiment is not cycled, so that model errors cannot diverge to large “climatological” values]. Thus, the application of the nonincremental DFI systematically leads to an increase of the MSLP bias along with a slight increase in MSLP RMSE. Conversely, application of no or incremental DFI results in a systematic drop in the MSLP error bias, compared with the nonincremental DFI. In terms of low-level wind direction, subjective verification reveals that low-level wind vectors tend to be more consistent with the isobaric contours in the IDFI case.

Among all aspects, formulation of the filter, tuning of the filter parameters, and tuning of the weighting factor R in the range [1.2, 1.8] (see Fischer et al. 2005), the most prominent impact came from changing the digital filter formulation from nonincremental to incremental. The retuning of the time span and stop-band edge period did have a second-order impact in terms of scores. Other aspects noticed during the comparison of nonincremental DFI versus IDFI were the systematic signal of a drop in the scores of the MSLP bias and the more significant similarity between the total IDFI increments and 3DVAR analysis increments than with simple DFI. As a consequence of the accumulated experience from Fischer et al. (2005) and the present study, we have decided to introduce IDFI inside the ALADIN-France 3DVAR assimilation cycle and forecast production process, accepting the deterioration of the low-level wind speed score in the 0–3-h model states, and the drop observed in the MSLP bias. The previous experiments and results were obtained without assimilating some of the verifying data, namely the 10-m wind observations from the surface synoptic observation (SYNOP) and French mesoscale surface networks. In section 3, we illustrate the impacts of adding the 10-m wind observations into the 3DVAR assimilation.