1. Introduction
Accurate quantitative forecasting of precipitation, especially during severe weather episodes, is one of the most challenging tasks of meteorological modeling and has a direct impact on the management of such events in areas at risk. The frequent assimilation of variables directly related to the formation of precipitation and the water cycle may contribute to a better definition of model moisture, divergence (vertical velocity), and latent heating, and could therefore lead to an improvement in short-range precipitation forecasts. Over recent years, increasing attention has been focused on the assimilation of precipitation data into meteorological models.
In pioneering precipitation assimilation studies, rainfall data were used only in tropical areas, in order to alleviate the impact of large deficiencies in moisture analysis, due mainly to the lack of a proper conventional data coverage over land and ocean areas (Krishnamurti et al. 1991) and the difficulties in prescribing error covariances for moisture fields. At low latitudes, large errors in the humidity distribution and the divergent component of the wind field heavily impinged on the specification of the diabatic forcing, resulting in poor forecasts of deep convection, which is almost totally responsible for tropical rainfall. The inadequate accuracy of the initial conditions also resulted in the well-known spinup problem (Davidson and Puri 1992): numerical meteorological models tend to underforecast precipitation during the first few hours of integration (Turpeinen et al. 1990). Against this background, a procedure that could use rainfall data to improve moisture analyses was viewed as a very promising development as far as tropical forecasting was concerned.
While the grid resolution of limited area models has largely increased in recent years, the spatial density of conventional observational networks has not progressed at the same pace. For this reason, present operational analysis fields, used to initialize limited area models, are often not adequate to represent relevant mesoscale features that the models can resolve. Therefore, rainfall assimilation has become an attractive prospect also in midlatitudes, where there is a need to improve the initial conditions and the balance of the hydrological cycle, especially in the first few hours, in order to obtain better estimates of precipitation on a regional scale.
Precipitation itself cannot be directly introduced into weather prediction models because it is not a prognostic variable but an end result of very complex dynamical and microphysical processes. However, rain observations can be used to correct humidity and/or temperature profiles in order to obtain simulated precipitation closer to reality. Different procedures have been developed to attain this aim. For example, Krishnamurti et al. (1991, 1993) assimilated observed tropical rainfall by means of a physical initialization procedure, based on the inversion of the planetary boundary layer and Kuo convective parameterization schemes, in order to link the surface fluxes and humidity analysis to the observed precipitation. Good results have been obtained, leading to an improvement in forecasting and a reduction of spinup time.
A positive impact on both precipitation forecasting and dynamical fields has also been attained in several studies that employed the nudging method to assimilate vertically integrated water vapor (Kuo et al. 1993; Alexander et al. 1999) or rainfall (Manobianco et al. 1994; Chang and Holt 1994; Falkovich et al. 2000; Macpherson 2001). Even if somewhat empirical, the nudging technique is a straightforward, physically based method that can solve this data assimilation problem and is therefore still widely used. Manobianco et al. (1994) implemented a dynamical assimilation of satellite-derived precipitation for a cyclogenesis event, in a regional-scale model, where the model heating profiles were modified proportionally to the differences between observed and predicted rainfall. In this way, latent heating derived from the observed precipitation was taken into account. The proposed scheme overcame the weaknesses of previous latent heat nudging procedures, because instead of modifying externally derived heating profiles, either parabolic (Wang and Warner 1988) or obtained from cloud models (Fiorino and Warner 1981), it employed model-generated profiles, ensuring consistency with the model's parameterization schemes and allowing the evolution of the profiles with time. Improvements were observed in short-range forecasts of rainfall and storm position. A different latent heating procedure, adopted by Chang and Holt (1994) in a case of winter extratropical cyclogenesis, showed similar benefits from rainfall assimilation, lasting well beyond the assimilation period.
More recently, operational assimilation of rainfall data has been implemented at the U.K. Met Office (UKMO) (Jones and Macpherson 1997; Macpherson 2001), where a latent heat nudging similar to the one proposed by Manobianco et al. (1994) was used to ingest radar data. Falkovich et al. (2000) have developed a new application of nudging for assimilating precipitation in the Tropics, in order to improve the initial fields in the National Centers for Environmental Prediction (NCEP) Medium Range Forecast (MRF) model. Here, specific humidity profiles, rather than temperature, are modified proportionally to the difference between model and target precipitation. Variations of moisture may lead to gradual changes in temperature due to latent heat exchanges produced via the model precipitation scheme, avoiding the model shocks incurred by temperature jumps.
The idea underlying the method of Falkovich et al. (2000) has been adopted in the present study, with the aim of setting up an assimilation procedure to be applied to the Bologna Limited Area Model (BOLAM; see section 2). However, since the technique was originally devised for a global model assimilation in tropical areas, major modifications have been introduced for midlatitude model application.
The choice of a nudging technique mainly stems from the fact that it is computationally much cheaper than variational methods and easily allows for operational implementation. In spite of its simplicity, nudging has proved to be efficiently applicable to many synoptic-scale and mesoscale cases. Even if rainfall assimilation using four-dimensional variational assimilation (4DVAR) has already been performed, sometimes successfully (Zupanski and Mesinger 1995; Guo et al. 2000; Marecal and Mahfouf 2000), it requires huge resources. The scheme only assimilates the precipitation, which is the end product of the interaction of all the dynamical and thermodynamical processes occurring in the model. However, it is shown below that the impact of the nudging positively affects not only the forecast rainfall field itself, but to some extent also the fields of pressure, wind, and temperature.
Different rainfall data sources are available nowadays, including surface observations (rain gauges and radar networks), which are limited to restricted areas of continental landmasses, and satellite estimates. Satellites represent a powerful tool, as they provide a unique global coverage over both land and sea. For example, some recent techniques are available which blend low-earth-orbiting passive microwave rainfall estimates from the Special Sensor Microwave Imager (SSM/I) and the Tropical Rainfall Measuring Mission (TRMM) with geostationary earth-orbiting infrared satellite data, yielding rainfall information with a temporal frequency suitable for regional-scale modeling. However, satellite data suffer from some drawbacks, depending on the sensor type [infrared (IR), visible (VIS), or microwave (MW)]. It is therefore important to take into account the characteristics of the assimilated data and the associated errors and limitations. A detailed analysis of the data source variety and of the problems connected to the retrieval of rainfall information from satellite data is outside the scope of this study, which addresses another challenging issue: assimilating precipitation in such a way that the model can recover the observed distribution. The scheme, originally aimed at ingesting satellite-retrieved precipitation data, can be applied in principle to other sources of rainfall observations, provided that data are properly interpolated to obtain a continuous areal distribution at high temporal frequency.
Our intent is to explore the impact of rainfall assimilation at relatively high resolution, with a view to improving the short-range forecasts of two episodes of mesoscale phenomena typical of the Mediterranean area: a case of orographic precipitation over the Alps, and an occurrence of a “hurricane-like” vortex (Rasmussen and Zick 1987) forming over the sea.
In the section below a description of the meteorological model is provided. After a section devoted to the presentation of the nudging procedure, section 4 gives an overview of the employed methodologies and of the two meteorological events. In section 5 the results of the simulations are shown, while sensitivity tests are described and discussed in section 6. Finally, concluding remarks are drawn in section 7.
2. The model
All the simulations were carried out with the primitive equation, σ-coordinate, hydrostatic model BOLAM. A detailed description of the dynamics and numerical schemes of the model can be found in Buzzi et al. (1994), Buzzi and Foschini (2000), and Malguzzi and Tartaglione (1999).
The water cycle for stratiform precipitation is described by means of five prognostic variables (cloud ice, cloud water, rain, snow, graupel), with a simplified approach similar to that proposed by Schultz (1995). Deep convection is parameterized, using the Kain–Fritsch (Kain and Fritsch 1990) convective scheme, with some modifications, including those suggested by Spencer and Stensrud (1998) to improve the effect of the downdraft.
The orography used in the simulations was derived from the interpolation and smoothing of the 1-km (1/ 120°) resolution Global Land One-km Base Elevation (GLOBE) Project Digital Elevation Model (DEM). The initial and lateral boundary conditions were supplied by European Centre for Medium-Range Forecasts (ECMWF) 6-hourly analyses available at 0.5° × 0.5° resolution. Hybrid model level data were directly interpolated on the limited area model grid. Snow cover, sea surface temperature, and soil temperature and wetness were also derived from the ECMWF analyses.
All the experiments were performed with a horizontal resolution of about 18 km (0.16° in rotated coordinates) and 38 vertical levels. The spacing between levels is variable, with the highest resolution in the lower portion of the atmosphere.
The model was tested and favorably compared with many other mesoscale limited area models in the course of the Comparison of Mesoscale Prediction and Research Experiments (COMPARE) World Meteorological Organisation (WMO) Project. Model intercomparison was conducted on a case of midlatitude explosive cyclogenesis (Compare I) (Gyakum et al. 1996), on a well-documented case of flow over orography in the presence of lee waves and wakes (Compare II) (Georgelin et al. 2000), and, finally, on a case of explosive development of a tropical cyclone (Nagata et al. 2001).
3. The assimilation scheme
The scheme starts with a comparison between the forecast (Rm) and target (Rt) total precipitation, followed by the appropriate modification of the model specific humidity profiles at grid points where the two values differ. In principle, this comparison should be made after every model time step. In practice, no data are available at such a high temporal resolution, and overly short intervals may be influenced by observation and sampling errors. Therefore, it is better to accumulate the observed precipitation, bearing in mind that the period of rain accumulation depends on the model resolution (the higher the model resolution, the shorter the accumulation interval), and that overly long intervals would lead to an excessive time averaging of the precipitation field. The best accumulation interval was established to lie in the range of 1–3 h, a choice confirmed by the experimental results (see section 6). Within this selected interval, a mean constant rainfall rate was assumed for the observed precipitation. The model's characteristics also impose some constraints: for example, since the convective scheme is activated about every 20 min, the total forecast precipitation becomes available only at this time frequency. Once available, the scheme compares the forecast and observed rainfalls, accumulated up to the current time step, and consequently modifies the humidity profiles. Once the selected accumulation interval is over, the subsequently observed accumulated rainfall is used as the target. Therefore, the scheme does not instantaneously adjust the rain rate at each time step but rather compares and adjusts the rain accumulated up until the current time step, seeking to recover the observed precipitation at the end of the accumulation interval.
The method also has to address the partitioning problem, that is, whether the observed precipitation corresponds to convective or stratiform model precipitation (Manobianco et al. 1994). Since the present study deals with extratropical phenomena, it is not possible to consider all the precipitation as convective, as is usually the case in the Tropics. For this reason, the scheme handles convective and large-scale rain differently, even though the evaluation of rain-rate differences is carried out for the total precipitation.
The modification of the humidity profiles depends on the sign of the precipitation difference (target minus forecast) and, as indicated by the subscribed s and c, on the type of precipitation (stratiform or convective). Model-generated rainfall is used in order to discriminate the precipitation type at a specific grid point, assuming that the model is simulating the appropriate type of precipitation. Although this implies that the partitioning of precipitation becomes dependent on the convective parameterization scheme implemented in the model, the final results should not be excessively influenced by this choice. Different vertical modulation profiles νs,c and different coefficients εs,c are used in cases of stratiform and convective precipitation, in order to introduce or remove humidity only where necessary. In the case of pure stratiform precipitation, νs is such that humidity is changed only in the middle-lower troposphere (Fig. 1), where most of the large-scale condensation takes place. If the total model rainfall (Rm) (accumulated up to the current time step) is less than the observed rainfall (Rt), the humidity is increased gradually toward a value 10% higher than the saturation value [
If the model fails to forecast rainfall, both types of rainfall are provisionally considered. However, when the adjacent grid points are exclusively experiencing one type of precipitation, the proper modification is applied.
The possibility of acting when no precipitation is predicted has proved to be very important elsewhere: for example, Manobianco et al. (1994) found that the use of observations only where Rm > 0 limits the ability of the precipitation data to affect the simulation.
As for the computed convective (and all physical) tendencies, the nudging adjustment is distributed over all the time steps within the interval between two times at which rain rates are compared.
4. Experimental setup and description of the precipitation events
A preliminary phase in defining the nudging procedure was devoted to the optimization of the empirical coefficients. A “simulated nudging test,” as proposed by Falkovich et al. (2000), was used for this purpose. Assuming a perfect model, a control forecast (C) was performed in order to obtain 2 (or 3)-hourly accumulated precipitation for use as target data. For the same period and from the same initial condition of (C), another forecast (S) was carried out by adjusting the forecast precipitation toward the “pseudotarget” data of (C). This procedure, which can only deteriorate the forecast, allows the characterization of the differences between a fully time dependent latent heating (C) and a latent heating that is forced to be nearly constant over the selected 2 (or 3)-hourly interval (S). In this test, small deviations from (C) are expected for a proper assimilation scheme. A limited set of “good” coefficients was selected during the test phase by comparing precipitation fields and evaluating the convergence of the scheme, in terms of the number of grid points at which the difference between target and forecast precipitation exceeded prescribed thresholds. The values of the nudging coefficients were subsequently tested also in a realistic assimilation framework (see the case studies below). This double-check, in principle, should assure that the scheme can improve the short-range precipitation forecast by introducing a “minimal” forcing to the model “trajectory.” A test phase was also required for the tuning of the vertical profiles νs,c(k).
During the subsequent verification phase, an (Observing System Simulation Experiment) OSSE-type strategy was adopted in order to evaluate the scheme's performance. Sensitivity to different factors, such as the length of the accumulation period and the impact of errors in magnitude and position of precipitation data were explored. Sensitivity tests are facilitated by the fact that the “synthetic” observations of an OSSE can be assumed as perfect (no observing system errors) and are known at the same spatial resolution of the model [no interpolation is needed; Chang and Holt (1994)]. The OSSE was set up through a lagged forecast scheme in which two simulations, starting from initial conditions 12 (or 24) h apart, were considered. It was therefore possible to obtain two different forecasts for a given time: the first was the control run, representing the reference state and providing the target rain rate, while the second (perturbed run) was considered the “real” forecast, which differed from the control and had to be improved. The nudging procedure was then applied for 12 h in a third simulation, starting from the same initial condition of the perturbed run, with the aim of forcing the “real” forecast toward the control run, whose accumulated precipitation was used as target rainfall.
Two precipitation events, usually harbingers of heavy rainfall in the Mediterranean area, were chosen and analyzed in order to test the nudging procedure. Although the practical implementation of the lagged forecast scheme in the two cases is slightly different, the goal is the same: to produce a perturbed run for comparison with a reference control run and assess the capability of the nudging procedure to force the perturbed simulation back toward the control simulation.
a. The first event: MAP IOP2
The event of heavy precipitation that occurred in the region south of the Alps in the period 19–21 September 1999 was extensively observed during the Mesoscale Alpine Programme (MAP) field-phase IOP2 (Medina and Houze 2003; Rotunno and Ferretti 2003). A deep baroclinic trough affected northern Italy, and a southwesterly strong flow, ahead of the trough axis, lay directly over the Lago Maggiore region, where most of the precipitation occurred, mainly forced by the orography. Associated with the trough, a frontal and prefrontal cloud system, with embedded convective cells, swept across northern Italy between 19 and 20 September (Fig. 2).
The lagged forecast scheme implementation is shown in Fig. 3a. The 48-h control run was initialized at 0000 UTC 19 September 1999, while the 36-h perturbed run started 12 h later, at 1200 UTC 19 September. The 36‐h assimilation run was also initialized at 1200 UTC 19 September and assimilated precipitation during the first 12 h. For this purpose, accumulated precipitation values from the control forecast were stored and then used as target rainfall data.
b. The second event: Algerian flood 2001
The second event analyzed is a case of severe weather over the southern part of the Mediterranean area in the form of a flood that struck Algeria between 9 and 12 November 2001, and very strong winds over the sea. This event, which caused the loss of human lives and extensive economic damage, was characterized by a high-level deep trough that started to develop on 9 November over the western Mediterranean, extending from northeast to southwest (Fig. 4). On the following days an intense cyclone, associated with a pronounced tropopause fold (Fierli et al. 2003), was responsible for heavy precipitation over northern Algeria (mainly on 10 November) and a severe wind storm, especially over the Balearic Islands. The BOLAM operational forecasts for that period (available online at http://www.meteoliguria.it/archivio21.asp) suggest that the cyclone evolution might have closely resembled an “hurricane-like” event, where characterizing features are a warm core and a potential vorticity (PV) maximum at low tropospheric levels. Although this evolution of the forecast is consistent with the ECMWF analysis at 0000 UTC 11 November, it seems unlikely that such a development actually occurred. However, model runs indicated high instability in this respect, as a function of the sensitivity to the initial conditions.
As shown in Fig. 3b, the lagged forecast scheme consisted of a 36-h control run, initialized at 1200 UTC 10 November 2001, while the other two 48-h simulations were initialized 12 h before, at 0000 UTC on the same day. It was decided not to consider at this point the first part of the event1 (9 November), in order to focus on the development of the deep low over the Mediterranean Sea, the purpose also being to assess the impact of rainfall assimilation on the development of such an intense cyclone.
Unlike the previous event, the assimilation started after 12 h of free forecast at 1200 UTC 10 November and, as before, lasted for 12 h. Although the lagged forecast scheme implementation is different with respect to the previous case, the philosophy is the same. Two forecasts have to be compared (with respect to the reference, that is, the control run). While one is free to evolve, the second (nudging run) is forced, through the rainfall assimilation, toward the control run. Therefore, the only difference between these two simulations is due to the assimilation and not to the initialization.
5. Model simulation results
For both events, target rainfall data were accumulated over periods of 2 h. No assessment of forecast skill was attempted in this context. Since the control run was adopted as reference, all the comparisons considered it as representing the “reality.”
a. MAP IOP2
The 12-hourly accumulated precipitation for the control run (reference state) in Fig. 5a shows the effects of the cold front on approaching the Alpine barrier: a wide rainfall area is visible over western Europe, with localized strong orographic precipitation during the second part of 19 September. Over the Mediterranean Sea, west of Sardinia, in advance of the main frontal system, a well-defined rainband is moving eastward. The comparison with the perturbed run precipitation field (Fig. 5b) reveals marked differences. In particular, the perturbed simulation does not reproduce the extensive rainband over the western Mediterranean Sea; moreover, the areas of heavy precipitation over southern France are displaced, and the maximum of rain appears over central-western France. These differences with respect to the control run have to be considered as forecast errors. The nudging procedure (using 2-hourly data from the control run) is able to correct most of the forecast errors, during the 12-h forcing period (Fig. 5c). The precipitation field is now closer to that of the control case: the missing rainband over the Mediterranean Sea is recovered, and areas of heavy rainfall are now better reproduced. In particular, cross sections over the Mediterranean Basin (not shown) show that, at this time, in correspondence to the rainband, mesoscale vertical motion was created and the vertical potential temperature distribution was consequently modified, becoming closer to that of the control run.
The improvements are confirmed by objective verification results (Fig. 6). Equitable threat score (ETS) and false alarm rate (FAR) (Figs. 6a and 6b) display remarkably better skills at the end of the assimilation period, with an improvement in both the amount and location of precipitation.
Despite these encouraging results during the assimilation, the impact on the quality of the subsequent free forecast is rather limited in duration. Indeed, the evolution of the ETS in time, as observed in Figs. 6c and 6d, shows how the adjustments become negligible about 10 h after the end of the assimilation. At variance with the results of Rogers et al. (2000), a longer assimilation period, of 24 h, does not prolong the improvement during the unconstrained forecast, following the nudging phase. However, impact of the assimilation is observed not only in the precipitation field but also in the geopotential, especially in the lower troposphere. The root-mean-square error (rmse) computed for the mean sea level pressure (MSLP) is reduced by the nudging (Fig. 7), the positive adjustment lasting for almost 18 h after the end of the assimilation period (the same behavior was found for the geopotential height at 850 and 700 hPa, not shown). The improvement seems mainly due to a better representation of the cyclone over Ireland (Fig. 8a) (too deep in the perturbed run), which is observed to persist after 12 h of free forecast (cf. Figs. 8b and 8c).
b. Algerian flood
On analyzing the 12-hourly accumulated precipitation field at 0000 UTC 11 November 2001 for the control and the perturbed simulations shown in Figs. 9a and 9b, respectively, the differences are evident. Over Algeria, as well as between the Algerian coast and the Balearic Islands, the rainfall patterns differ greatly in shape and location. The target (control run) displays an intense precipitation area over the western Algerian coast, which is weaker and displaced eastward in the perturbed forecast. Moreover, the latter completely misses an arc-shaped rainband southeast of the Balearic Islands. Moving eastward, toward the Italian coast, another rainband east of Sardinia and the Corsican Islands is visible in the reference but not well captured by the perturbed forecast.
As in the previous case, the nudging was applied for 12 h, using 2-hourly accumulated precipitation from the control run. The impact of the nudging is considerable. At the end of the 12-h forcing period (Fig. 9c) the precipitation field resembles the target. Over the western Mediterranean Basin, the nudging has been able to suppress the intense rainfall (displaced eastward) and to generate partially the precipitation in the area indicated by the target data. The two above-mentioned rainbands are now well defined in the forced forecast. Although the westernmost one is shifted slightly eastward, it is almost correct in intensity (84 against 85 mm 12 h−1), as a consequence of a better reproduction of the associated vertical motion. The other is generated in phase, but the maximum intensity of rainfall is too low (35 instead of 67 mm 12 h−1). Finally, also the area of light rainfall around Sardinia has been positively modified by the nudging procedure.
The objective scores again confirm the improvements in terms of precipitation forecasting: both the ETS and FAR (not shown) are better during the forcing phase. Moreover, the evolution of ETS in time (Figs. 10a and 10b) points to the benefit of the nudging, extending well after the end of the nudging period, for both high and low values of the rain rate. In this case the impact seems to last at least 18 h during the free forecast.
The different behavior of the scheme for the two analyzed cases confirms that the persistence of any impact depends on the particular situation (Jones and Macpherson 1997).
As demonstrated by Genovès and Jansà (2003), the latent heat release and its interaction with surface heat fluxes played a crucial role in the development of the cyclone during this severe weather event. It was therefore expected that the nudging procedure would have an appreciable impact on the cyclogenesis. That this is indeed the case emerges from the intercomparison of Figs. 11a, 11b, and 11c. The control run (reference “data”) displays a very deep low (985 hPa) (Fig. 11a), resembling a hurricane-like cyclone (with a warm core and a PV maximum in the lower troposphere), surrounded by an area of more leveled pressure and, farther off, by a large-scale pressure gradient area. In the perturbed run (forecast of the event), the cyclone appears as a weaker large-scale pressure system (Fig. 11b), with a less intense core. The sensitivity to the initial condition confirms that this case is close to a transition between a “normal” cyclone development and a hurricane-like event (note that also the ECMWF analysis at 0000 UTC 11 November showed a small-scale deep low). The cyclone development is modified by the nudging procedure: 12 h after the end of the forcing, the cyclone center position and its intensity are still markedly better represented in the adjusted forecast (Fig. 11c) than in the perturbed one (with respect to the control run). The cyclone is deeper (MSLP value of 985 hPa), and its center is displaced southward in agreement with the reference run.
Figure 12a shows that the motion of the low center is positively modified, in addition to its intensity. The modification of the environment in which the deep cyclone develops produces a clear shift in the cyclone trajectory. Computing the distance between forecast cyclone centers for the perturbed and nudging simulations with respect to the control indicates that the modification is positive, since the positional error of the cyclone is clearly reduced. Finally, as displayed in Fig. 12b, the evolution of central pressure is also better captured in the nudging run, in terms of both the magnitude and the timing of the peak intensity.
6. Sensitivity tests
For both the analyzed events, three sets of sensitivity tests were performed in order to determine the dependence of the nudging procedure on different accumulation intervals (1, 2, 3, and 6 h), to assess the impact on performance of data errors in position and intensity, and to address the impact of model error. For brevity, only the main results are presented in this section.
a. Sensitivity to accumulation interval
Implementing the same lagged forecast scheme, three more “nudged” forecasts were performed for each of the two cases, using as target rainfall, hourly, 3-hourly, and 6-hourly rainfall data from the control run.
As far as the 6-hourly accumulated precipitation target is concerned, a clear reduction in the nudging impact is found. Analyzing the MAP case (Fig. 13a), the objective scores are worse with respect to the results obtained with 2-hourly target rainfall, both during and after the forcing period. The limited positive impact on the precipitation forecast, emerging from a comparison of the predicted rain fields, also reflects on the quality of the whole forecast. The rmse computed for the MSLP demonstrates that improvements obtained using 2-hourly data completely disappear if the accumulation period is too long (not shown), mainly because of the failure of the nudging procedure to correct the intensity of the cyclone located over Ireland. Reducing the accumulation interval to 3 h, results become better, and the quality of the nudging forecast is comparable, though slightly lower, with that attained using 2-hourly target rainfall. Finally, hourly target data seem slightly better during the first few hours of the forcing but do not reflect better scores during the free forecast.
The same holds for the Algerian flood experiments (Fig. 13b): while 6-hourly accumulated rainfall again produces the worst results, hourly target data behave even better (with respect to 2-hourly data) during the forcing period and during the first few hours of the free forecast, especially for high precipitation rates (not shown). Moreover, the hourly data show a slightly larger positive impact on the cyclone evolution, but again limited to the first few hours of the free forecast.
In conclusion, 2-hourly accumulated rainfall seems appropriate for this nudging scheme, even if the employment of a shorter accumulation period should not be discarded, especially in view of data availability and an increase in model resolution. Bearing this in mind, it is not surprising that analogous results were achieved with the UKMO 12-km resolution mesoscale model, using hourly radar data (Macpherson 2001).
b. Sensitivity to data errors
The impact of data accuracy on the nudging performance was investigated by introducing errors in rainfall data intensity and position. The former were simply obtained by doubling or halving the amount of rain, while for the latter a (westward) shift of the target precipitation pattern of about 100 km was applied.
The effects of doubling the target rainfall data, while keeping the position unchanged, are more evident in the MAP case, at least on the ETS. During the nudging period, for a low rainfall threshold, the ETS (Fig. 14a) does not worsen, but the FAR (not shown) is considerably higher, confirming a deterioration of the precipitation forecast skill. During the free forecast, the ETS displays less skill with respect to the results obtained with “perfect” target data. For the Algerian case, the ETS (Fig. 14b) shows a weaker impact of doubling rainfall, even if it clearly affects the position and depth of the Mediterranean cyclone. The low impact of this kind of data error is due partly to the characteristics of the nudging scheme itself, and partly to the different reproductions of this particular meteorological situation by the two analyzed simulations (control and perturbed). The equation modifying the humidity profiles does not contain a term that is directly related to the difference between target and forecast precipitation. Therefore, if large differences in precipitation are present (as in this case, where an area of heavy rain was displaced in the perturbed forecast and had to be moved accordingly to the target), the forcing is already as high as possible, and a doubling of the target rain rate does not strongly affect performance.
Halving the amount of target rainfall produces a more visible impact on the forecast, reducing the value of the ETS (see again Figs. 14a and 14b). However, it is the lack of accuracy of the exact location of the precipitation area that impacts the forecast most, as emerges again from the scores (Figs. 14a and 14b). In this case the assimilation turns out to be ineffective, if not unfavorable, in terms of forecast skill, and during the free forecast the simulation seems to recover the original model “trajectory.” This convergence of the scores confirms a limit of the nudging procedure: whether the direction is right or wrong, the applied correction does not last much beyond the forcing period.
For the Algerian case, the shift in the precipitation, in particular of the rainband originally located southeast of the Balearic Islands (Fig. 9a), has marked consequences on the dynamics, since the deepening of the low (Fig. 15) and the related wind field are now considerably weaker.
Therefore, data affected by an error of the order of 100 km are unsuitable, since they do not produce improvements, not even during the assimilation. This result is strictly related to that concerning sensitivity to the length of the rainfall accumulation interval. Indeed, the accumulation implies not only a temporal but also a spatial smoothing of the precipitation field. Consequently, it introduces an error in the location of the precipitation pattern—the longer the interval, the larger the error.
In conclusion, the assimilation procedure appears to be more sensitive to errors in position of rainfall than in its amount. This result can be generalized beyond this application, since it has also been found in other assimilation studies (Manobianco et al. 1994; Chang and Holt 1994).
c. Sensitivity to model error
A degraded version of the model was obtained by switching off the convective parameterization scheme, allowing the model to produce only large-scale rainfall. The erroneous model was then used for data assimilation, implementing the same lagged forecast scheme for both the analyzed events. The reference precipitation data, used as target, was still generated by the true model, while the perturbed run and the assimilation run were obtained by the degraded model. A clear reduction of the precipitation forecast skill was observed for the degraded model, in comparison with the correct one (cf. the dashed lines of Fig. 16 with Figs. 6d and 10b).
The ETS in Fig. 16, computed for a threshold of 10 mm/6 h, shows almost the same behavior for the MAP and Algerian events. The nudging scheme actually improves the forecast skill during the assimilation phase. However, the improvement in the ETS is quantitatively reduced with respect to the same experiment using the correct model (cf. again Fig. 16 with Figs. 6d and 10b) and is associated with higher values of FAR and rmse for geopotential and temperature in the lower troposphere (not shown). During the following unconstrained forecast, the positive impact of the assimilation disappears after only 6 h, and the skill of the nudging run becomes even worse (MAP case) or equal (Algerian case) to that of the perturbed run. Therefore, the model error clearly limits the benefits of the assimilation. Suppression of the convective adjustment produces excessive accumulation of humidity in the lower troposphere, which negatively impacts the forecast following the assimilation.
Finally, this sensitivity test confirms the importance of considering separately the two types of precipitation in the nudging procedure. The error introduced in the model only allows production of, and hence assimilation of, large-scale precipitation, which contributes to reducing the forecast skill.
7. Conclusions
In the present study, the impact of rainfall assimilation in a limited area model has been examined. The OSSE strategy provided an idealized framework suitable for evaluating the performance of the assimilation scheme and its sensitivity to different parameters, avoiding the “noisy” contribution of observing system errors. Two events were chosen in order to concentrate the effort on two classes of phenomena that are of particular interest in the Mediterranean area: orographic precipitation systems and “hurricane-like” mesoscale vortices forming over the sea. Since both phenomena are often associated with severe weather episodes, an improvement in the quantitative precipitation forecast, potentially achievable by assimilating precipitation data, could be of benefit to weather forecasting, hydrogeological management, and risk assessment.
The proposed assimilation technique, based on nudging, gradually modifies the model's specific humidity profiles, attempting to bring the forecast as close as possible to reality. The scheme allows the assimilation of precipitation also when the rain is not purely convective, an advantage in midlatitudes with respect to reverse schemes. Indeed, while the latter can act directly only on the convective part of the total rainfall, the nudging may be applied successfully to a much wider range of situations.
Notwithstanding the many limits of such types of idealized experiments and of the nudging technique in general (if compared to the more sophisticated variational assimilation methods), encouraging results are obtained in terms of both improvements in precipitation forecasting and impact on dynamics. The scheme seems able both to reduce and to increase the precipitation patterns, producing improvements in the amount and location of rainfall, even if the positive impact of the assimilation is difficult to retain for a long period after the assimilation phase (6–12 h for the MAP case, 18– 24 h for the Algerian one). In the MAP event, the most important result of the assimilation is the reproduction of the extensive prefrontal rainband over the sea, together with the associated mesoscale updraft. Improvements in precipitation are still noticeable about 10 h after the assimilation, while a more persistent positive impact affects the MSLP field. The Algerian case provides further confirmation, and is even more promising, since the scores show a persistence of the rainfall forecast improvements until 24 h after the assimilation period. Moreover, modification of the three-dimensional humidity field strongly impacts the development of the deep low (perhaps hurricane-like cyclone) off the Algerian coast, in terms of intensity, trajectory, and associated rainfall. At variance with the results of Manobianco et al. (1994), here the MSLP field evolution is very different after the rainfall assimilation, and scores show improvements lasting at least 12–18 h after the end of the forcing period. In part, this is due to the very high sensitivity of the forecast to the initial condition for the particular case: since small errors in the initial field can be responsible for low accuracy of the forecasts, the positive impact of the assimilation can be large. Rogers et al. (2000), in a study concerning the use of radar reflectivity to improve model initialization, found that a 24-h forcing period, instead of only 12 h, was necessary to obtain long-lived significant improvements in forecasting mesoscale convective systems. In our case, sensitivity tests varying the length of the nudging phase (from 12 to 24 h) did not provide the same positive results, at least in the present idealized framework. Additional and longer-lasting modifications, especially in the dynamical variables, are expected if nudging is performed within an assimilation cycle, where the changes in circulation introduced by nudging improve the first guess for the subsequent analysis.
Further experiments, for example, the implementation of a pseudo-operative assimilation chain, are required to extend the analysis and generalize the results. The impact of precipitation assimilation on a developing cyclone represents an interesting issue and deserves more detailed investigation, also by means of idealized experiments. Assimilation experiments with real data are already under way, using satellite-retrieved precipitation. Taking into account the results of the sensitivity tests, satellite data are accumulated over 2-hourly intervals before being assimilated by the model. In addition, particular attention must be paid to errors possibly affecting the position of the precipitation area, rather than those concerning amounts.
Acknowledgments
This work is supported by EURAINSAT (Contract EVG1-2000-00030) and has been partially supported by EU Project “Optimisation des outils de prévision Hydrométéologique - HYDROPTIMET,” Interreg IIIB, and by “Short Term Mobility Program” (CNR). The authors are grateful to Dr. E. Kalnay (University of Maryland) and Dr. A. Falkovich (NCEP) for the fruitful collaboration and discussions.
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Vertical modulation profiles ν(k) for the nudging equation in the case of pure stratiform (solid line) and pure convective (dashed) precipitation
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
Meteosat infrared satellite image at 0300 UTC 20 Sep 1999
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
Lagged forecast scheme implemented for (a) MAP IOP 2 (19–21 Sep 1999) and (b) Algerian flood (10–12 Nov 2001) simulations
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
Analysis from ECMWF (interpolated on BOLAM grid) of 500-hPa heights (contour interval = 30 gpm) at 0000 UTC 10 Nov 2001. The area represents the BOLAM integration domain. Geographical features referred to in the text are indicated
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
The 12-h accumulated precipitation at 0000 UTC 20 Sep 1999 (end of the assimilation period) for the (a) control run (“data”), (b) perturbed run, and (c) nudging run. Shading and contour interval is 10 mm
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
(a) Equitable threat score and (b) false alarm rate, computed at 0000 UTC 20 Sep 1999, after 12-h forecast, corresponding to the end of the 12-h assimilation period, and evolution of the equitable threat score for thresholds of (c) 2 mm 6 h−1 and (d) 10 mm 6 h−1 for the perturbed run (dashed) and the nudging run (solid). All the scores are computed for 6-h accumulated precipitation (MAP event). Numbers in parentheses indicate number of observations (control run) exceeding the corresponding threshold value. The vertical dashed line in (c) and (d) indicates the end of the nudging period
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
Rmse evolution for MSLP for the perturbed (dashed) and the nudging (solid) runs (MAP event). The vertical dashed line indicates the end of the nudging period
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
(a) MSLP field at 1200 UTC 20 Sep 1999 for the control run (“data”) after 36-h forecast. MSLP difference from the control run (after 36-h forecast) for the (b) perturbed run and (c) nudging run, after 24-h forecast, verifying 1200 UTC 20 Sep 1999. Contour interval is 2 hPa
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
As in Fig. 5, but at 0000 UTC 11 Nov 2001 (Algerian event).
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
Evolution of the equitable threat score for thresholds of (a) 2 mm 6 h−1 and (b) 10 mm 6 h−1 for the perturbed run (dashed) and the nudging run (solid), computed for 6-h accumulated precipitation (Algerian event). Number in parentheses indicates number of observations (control run) exceeding the threshold value. The vertical dashed line indicates the end of the nudging period
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
MSLP field at 1200 UTC 11 Nov 2001 for the (a) control run (“data”) after 24-h forecast, (b) perturbed run, and (c) nudging run, after 36-h forecast. Contour interval is 2 hPa
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
(a) Surface low center trajectory and (b) central MSLP (hPa) for the control run (dashed line), perturbed run (thin line), and nudging run (thick line) computed at 2-h intervals, from 1200 UTC 10 Nov to 0000 UTC 12 Nov 2001
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
Evolution of the equitable threat score computed for 6-h accumulated precipitation for thresholds of 2 mm 6 h−1 for (a) MAP and (b) the Algerian event: perturbed run (dashed line) and nudging runs, using hourly (plus sign), 2-h (full dots), 3-h (open circles), and 6-h (stars) accumulated rainfall as target. Number in parentheses indicates number of observations (control run) exceeding the threshold value. The vertical dashed line indicates the end of the nudging period
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
As in Fig. 13, but for the perturbed run (dashed line) and the nudging runs using, as target, 2-h accumulated precipitation (full dots), doubled precipitation (stars), halved precipitation (open circles), and shifted precipitation (plus sign) (see text)
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
As in Fig. 12b, but for the control run (dashed), nudging run (thick line), and nudging run using shifted precipitation (thin line) (see text)
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
Evolution of the equitable threat score computed for 6-h accumulated precipitation for a threshold of 10 mm 6 h−1 for (a) MAP and (b) the Algerian event. The perturbed run (dashed) and nudging run (solid) are performed with the degraded model (see text)
Citation: Weather and Forecasting 19, 5; 10.1175/1520-0434(2004)019<0855:ANSFTA>2.0.CO;2
The same lagged forecast scheme was implemented also for 9 November. Since the results are very similar to those presented in the paper, they are not discussed here.
