Application of a Limited-Area Short-Range Ensemble Forecast System to a Case of Heavy Rainfall in the Mediterranean Region

566 WEATHER AND FORECASTING VOLUME 19 Application of a Limited-Area Short-Range Ensemble Forecast System to a Case of Heavy Rainfall in the Mediterranean Region P. A. CHESSA AND G. FICCA Servizio Agrometeorologico della Sardegna, Sassari, Italy M. MARROCU Center for Advanced Studies, Research and Development in Sardinia, Parco Scientifico e Technologico della Sardegna, Pula, Italy R. BUIZZA European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, United Kingdom (Manuscript received 16 January 2003, in final form 3 September 2003) ABSTRACT Severe weather risk assessment is becoming an increasing component of the daily operational activity at advanced meteorological forecasting centers. To improve its forecast capabilities and develop a severe weather warning system, the Sardinian Regional Meteorological Service (SAR) and the Centre for Advanced Studies, Research and Development in Sardinia (CRS4) have been testing a Limited-area Ensemble Prediction System (SAR-LEPS). The SAR-LEPS system is described and preliminary results of its use to predict the intense and localized flooding event of 12 13 November 1999 are discussed. Results for this specific case study indicate that SAR-LEPS provided valuable, additional information to the ECMWF ensemble system. This suggests that the operational use of SAR-LEPS could prove to be an important component in the decision making process in issuing threat warnings for severe weather conditions. 1. Introduction Economic and societal losses due to extreme weather events are steadily increasing (Easterling et al. 1999). Local institutions, governmental agencies, and the private sector are increasing the pressure on the meteorological community to develop more effective early detection systems that could be used to reduce and/or manage the risk associated with extreme weather events (Pielke and Landsea 1998; Pielke and Downton 2000). At the European Centre for Medium-Range Weather Forecasts (ECMWF), for example, the development of a severe weather prediction system has become one of its main objectives. Extreme weather events are rare and contribute to the tail(s) of the probability distribution function of atmospheric states. Thus, to be effective, a severe weather prediction system must be able to simulate the time evolution of the probability distribution function of forecast states in great detail, and cannot be limited to predicting its first-order moment. In other words, a high Corresponding author address: Piero A. Chessa, Servizio Agrometeorologico della Sardegna, Viale Porto Torres 119, 07100 Sassari, Italy. E-mail: chessa@sar.sardegna.it resolution in probability space is also required (Buizza and Chessa 2002), where high resolution means that the ensemble probability density function should be defined at the maximum resolution with the available ensemble (specifically, given an ensemble with 51 forecasts, defining and using 50 equivalent intervals from 0 to 1). Furthermore, users are often not interested in the most probable weather scenario (e.g., described by a single deterministic forecast or by the ensemble-mean forecast) but need to assess and quantify the risk of occurrence of climatologically rare but destructive events (Buizza 2001). High resolution in physical space (i.e., high horizontal and vertical resolution) is also very important when predicting severe weather events, since severe weather is often associated with rapidly developing small-scale systems and can be strongly influenced by local terrain characteristics (orographic forcing, land sea interaction). The severe flooding event that affected the Aude River basin in southern France (Gaume et al. 2001; Bechtold and Bazile 2001) and the island of Sardinia between 12 and 13 November 1999 is a typical example of this type of events. In theory, the time evolution of the atmosphere probability distribution function can be described by inte- 2004 American Meteorological Society

JUNE 2004 CHESSA ET AL. 567 grating the associated Liouville equation (Gleeson 1966; Epstein 1969; Ehrendorfer 1994a, b), but in practice this equation is solvable only for very simple systems with a very coarse geographical resolution. Ensemble prediction systems based on a finite number of numerical integrations provide a practical tool for estimating the probability distribution function of the forecast states, with ensemble resolution and membership limited by computer power availability. The Ensemble Prediction System (EPS) operational at ECMWF since December 1992 (Molteni et al. 1996) can provide this type of information. At the time of the November 1999 Sardinian and French floods, the EPS included fifty-one 10-day forecasts run with a T L 159L31 [spectral triangular truncation T159 with a linear grid and 31 vertical levels, Buizza et al. (1998)] version of the ECMWF model, which has an equivalent gridpoint spacing of about 120 km. The EPS was upgraded on 21 November 2000 to T L 255L40 resolution [80-km gridpoint spacing and 40 vertical levels; Buizza et al. (2003)]. For this study, EPS forecasts have been rerun at the current T L 255L40 resolution. The EPS upgrade of November 2000 improved the quality of the EPS. Mullen and Buizza (2002) concluded that the system upgrade produced an improvement equivalent to shortening the forecast lead time by 12 36 h, when considering precipitation prediction, and Buizza and Hollingsworth (2002) showed that forecasts from the new system have smaller intensity and position errors in predicting mean sea level pressure. Despite this improvement, Mullen and Buizza (2002) and Buizza and Hollingsworth (2002) pointed out that the coarse resolution (80 km) of the current EPS still limits its forecast capabilities in predicting intense precipitation or small-scale, rapidly moving vortices. These limitations are known and will continue to affect global ensemble systems for the next few years, since spatial resolution will continuously be limited by computer power availability. Limited-area ensemble prediction systems nested into global ensembles have been developed in recent years to overcome this and related problems. Tracton et al. (1998) have shown that the National Centers for Environmental Prediction Short-Range Ensemble Forecasting system, based on high-resolution versions of the Eta and the Regional Spectral Models, can provide accurate precipitation forecasts with lead times of up to 72 h. Molteni et al. (2001) and Marsigli et al. (2001) proposed a strategy for the development of a high-resolution ensemble system based on a six-member limited-area ensemble prediction system, and documented improved precipitation predictions during four cases of flooding over Europe. Other related studies (see, e.g., Hamill and Colucci 1997, 1998; Du et al. 1997; Hersbach et al. 2000; Stensrud et al. 1999, 2000; Grimit and Mass 2002) confirmed that the Limited-area Ensemble Prediction Systems (LEPS) nested into a global ensemble can provide the forecasters with extra, skillful information, with a higher spatial resolution than is available with global ensemble systems. This paper describes the research activity in limitedarea ensemble prediction of the Sardinian Regional Meteorological Service (SAR) and the Centre for Advanced Studies, Research and Development (CRS4), and discusses the performance of the SAR-LEPS during the November 1999 flooding event that hit the island of Sardinia and southern France. Since the study is limited to a single event, strong conclusions cannot be drawn; nevertheless, this work documents the potential value of using limited-area forecasting in cases of intense mesoscale activity in the Mediterranean region. The paper is organized as follows: SAR-LEPS is described in section 2, the synoptic situation that lead to the 12 13 November 1999 flooding is discussed in section 3, EPS and SAR-LEPS forecasts are compared in section 4, sensitivity results are discussed in section 5, and some conclusions are drawn in section 6. 2. The SAR Limited-area Ensemble Prediction System SAR-LEPS is based on 51 integrations of the Bologna Limited Area Model (BoLAM) developed at the Institute of Atmospheric Sciences and Climate (ISAC) of the Italian National Research Council (Buzzi et al. 1994; Malguzzi and Tartaglione 1999). A brief description of BoLAM is provided in the appendix. The initial and boundary conditions of SAR-LEPS members are provided by the corresponding ECMWF EPS members. At the time of the event, the ECMWF operational model for EPS was the T L 159L31 (resolution equivalent to approximately 120-km grid spacing at midlatitudes with 31 vertical levels), but for this study, EPS forecasts have been rerun at the current T L 255L40 resolution (equivalent to approximately 80- km grid spacing at midlatitudes with 40 vertical levels). The limited-area model (BoLAM) used has been nested on each EPS member with the one-way technique. BoLAM s integration area is 29 56 N and 19 W 31 E over a rotated C grid with a 0.2 horizontal grid spacing (equivalent to approximately 22 km) and 30 vertical sigma levels. The integration area has been chosen to be quite a bit larger than the domain of interest with the aim of limiting the influence of the driving boundary conditions. The SAR-LEPS numerical integrations have been performed at CRS4 using an IBM SP3 with 16 POW- ER3 nodes (approximately 9.5 h, using all 16 nodes, were required to complete the SAR-LEPS 72-h forecast experiment, corresponding to a total CPU time of about 150 h). 3. The case study and the deterministic forecast Between 11 and 13 November 1999 intense precipitation affected some regions of the western Mediter-

568 WEATHER AND FORECASTING VOLUME 19 ranean, with Sardinia and southern France experiencing heavy rainfall during the night of 12 13 November. The severity of this precipitation was such that the consequent flooding killed 35 people in France (Bechtold and Bazile 2001) and 2 in Sardinia, where the main town was only marginally affected. On 11 November, an upper-level trough was positioned over France and Spain, while at low levels a cutoff low developed over the Mediterranean Sea between the Gibraltar Channel and the Balearic Islands, and an anticyclone was centered over Great Britain (Fig. 1). This situation favored low-level advection of warm and moist air from the southeast and upper-level advection of cold and wet air into the cyclonic system. On 12 November, the axis of the upper-level cutoff low started rotating cyclonically, its southern side moved from the Iberian Peninsula to the Mediterranean Sea while its northern part moved from France to the Atlantic region off of Portugal, inducing a cold-air intrusion aloft over the Mediterranean Sea while low levels were still affected by a strong warm advection. Over Sardinia, this strong vertical gradient triggered deep convection. Two radiosounding profiles (Fig. 2) from Cagliari (i.e., very close to one of the flooded areas; see Fig. 3), launched at 1800 UTC 12 November and 0000 UTC 13 November (representative of one of the most active spells of deep convection during the event), show the presence of a notable amount of convective available potential energy from 900 hpa all the way up to 300 hpa (about 424 and 256 J kg 1, respectively) and of moisture at least up to 100 hpa. The strong orographic forcing induced by the mountains of southeastern Sardinia, coupled to the heat fluxes due to the relatively warm Mediterranen Sea, further strengthened the convective system and intensified the precipitation. As a result, intense rainfall hit the southern part of Sardinia between 12 and 13 November, causing severe disruption, heavy property damage, and loss of lives. The observed rainfall peaked at about 340 mm 24 h 1, where 24 h 1 means per 24 h throughout (Fig. 3) with about 100 mm recorded in less than an hour at Pelau in the eastern part of Sardinia (Fig. 4). Over southern France, the situation was very similar, with maximum rainfall exceeding 500 mm 24 h 1 and peaks of more than 100 mm h 1 (Gaume et al. 2001; Bechtold and Bazile 2001). The operational forecasts produced at SAR at that time were based on the ECMWF model and on a deterministic run of BoLAM nested in the ECMWF model, version T L 319L60 and starting from the t 12 t 0 12 h forecast, where t 0 stands for the time of the 1200 UTC ECMWF analysis. The choice of the 12-h forecast as the initial condition for the limited-area model is based on the assumption that after that period the model produced adjusted scales of motion compatible with the higher resolution of the LAM. Figure 5 shows the t 0 72 h precipitation forecasts (i.e., the amount of precipitation accumulated between t 0 48 and t 0 72 h) given by the ECMWF T L 319L60 and the nested BoLAM models, verifying between 1200 UTC on 12 November and 1200 UTC on 13 November, while Fig. 6 shows the same fields but for the t 0 48 h forecasts. Note that ECMWF forecasts (Figs. 5a, 6a) had some useful indications of intense precipitation over southern France both in the 72- and the 48-h forecasts but predicted only a few millimeters per 24 h of rain over Sardinia. In this area, by contrast, the t 12 60 h BoLAM forecast had up to 40 mm 24 h 1 on the east coast of the island where part of the floods took place with peaks between 60 and 80 mm 24 h 1 slightly to the north and offshore of the right spot (Fig. 5b). The t 12 36 h forecast instead showed a precipitation field with a shape corresponding to the actual rainfall pattern and with values up to 40 mm 24 h 1 over the flooded area in the southern part of the island (fig. 6b). Although the peaks (about 80 mm 24 h 1 ) were slightly out of position, the signal could be considered useful for warning (and prewarning) purposes (this is of course completely true when information about the false alarm rate is available). It is worth mentioning that no rainfall was forecast by either models 96 h before the event (not shown). As for southern France, BoLAM forecasts 3 and 2 days in advance were rather good and estimated up to 100 mm 24 h 1 very close to the area where the most intense rainfall was localized. 4. Ensemble forecasts Figures 7 9 show EPS and SAR-LEPS t 0 96, t 0 72, and t 0 48 h probabilistic precipitation predictions. Due to the severity of the event under investigation, attention is focused on probabilistic predictions of rainfall amounts in excess of 20, 40, and 60 mm 24 h 1. For all forecast times (t 0 96, t 0 72, and t 0 48 h), the T L 255 EPS gives little indication of intense precipitation over Sardinia. All EPS forecasts give a null probability of more than 60 mm 24 h 1 and 40 mm 24 h 1 over Sardinia, and only a 2% 25% probability of precipitation in excess of 20 mm 24 h 1 is forecast at t 0 48 h (Fig. 9). Note that 2% 25% probabilities of rainfall in excess of 60 mm 24 h 1 are predicted over southern France at all forecast ranges. The SAR-LEPS probability forecasts over Sardinia and over France appear to be more indicative of intense precipitation than are those of the EPS. However, the relative gain seems to be larger for the precipitation over Sardinia than over southern France. This is probably due to the different scales of the phenomena and the differences in the forcing sources for the convective systems. The t 0 96 h SAR-LEPS probability forecasts (Fig. 7) indicate a 2% 25% probability of rainfall in excess of 20 mm 24 h 1 and 40 mm 24 h 1 over the areas of eastern Sardinia affected by intense precipitation. The probabilities of rainfall in excess of 40 mm 24 h 1 increase by up to 50% in the t 0 72 h forecast (Fig. 8), with a 2% 25% probability of rainfall over the southern part of Sardinia. Some weak signals are also

JUNE 2004 CHESSA ET AL. 569 FIG. 1. The analyzed synoptic situation at (left column) 0000 UTC 12 Nov and (right column) 13 Nov 1999. The fields represented are geopotential height (solid lines), temperature (shaded contours), and wind (barbs) at (a), (b) 250- and (c), (d) 500-hPa levels; (e), (f) mean sea level pressure (solid lines), 850-hPa temperature (shaded contours), and wind (barbs). The scales beside the plots refer to the corresponding temperature fields.

570 WEATHER AND FORECASTING VOLUME 19 FIG. 2. Cagliari/Elmas radiosonde plots at (a) 1800 UTC 12 Nov and (b) 0000 UTC 13 Nov 1999. These plots show strong convective instability from lower levels up to 300 hpa.

JUNE 2004 CHESSA ET AL. 571 FIG. 3. Accumulated precipitation (shaded contours) across Sardinia, interpolated using data recorded by the 55 SAR weather stations between 1200 UTC 12 Nov and 1200 UTC 13 Nov 1999. The local peak values are indicated (at triangles) in the plot. The values shown in the grayscale are expressed in mm.

572 WEATHER AND FORECASTING VOLUME 19 increase to 50% 75% at t 0 72 h and to 100% at t 0 48 h, while the EPS T L 255 probabilities are always under 25%. For both areas affected by the intense rainfall the SAR-LEPS probability forecasts are also in good spatial agreement with the position of the cloud tops in the Meteosat infrared image (Fig. 10). Overall, SAR-LEPS gives probabilities of intense rainfall higher than the ECMWF EPS probability forecasts, with distinct evidence of a potential risk of intense precipitation. Referring to the operational problems that sparked our interest in conducting an ensemble simulation, it can be easily seen that if SAR-LEPS were operational at the time of the Sardinian flooding, the fact that consecutive SAR-LEPS forecasts from t 0 96htot 0 48 h (Figs. 7d f, 8d f, and 9d f) had consistently indicated an increasing probability that intense precipitation could occur would have triggered warning and prealarm procedures at least 2 days in advance of the event. Considering the nature of the event, this would have been sufficient time to take corrective actions to limit damage and possibly prevent the loss of lives. FIG. 4. Rainfall time series for hourly data recorded at (a) Decimomannu and (b) Pelau (see Fig. 3 for locations) during 12 13 Nov 1999. present for rainfall in excess of 60 mm 24 h 1. The SAR-LEPS t 0 48 h forecasts (Fig. 9) more correctly identify southeastern Sardinia as a region of possible intense rainfall, and indicate at least a 50% 75% probability of rainfall in excess of 60 mm 24 h 1. These results should be compared to the best EPS forecasts, which give not more than an 8% rainfall probability for the first threshold (probability of rainfall in excess of 20 mm 24 h 1 ) and which are also slightly out of position at t 0 72 and t 0 48 h. For southern France the EPS works better with distinct, though decreasing, rainfall probability for all the thresholds. Quite importantly, this signal appears to be, for 20 and 40 mm 24 h 1, reinforcing itself as the forecast time approaches the verification time. However SAR-LEPS substantially improves these forecasts since it gives a clear indication of intense precipitation (probability of rainfall in excess of 60 mm 24 h 1 ) that is almost absent in the EPS probabilities. As a matter of fact a 25% 50% probability of precipitation in excess of 60 mm 24 h 1 is given, for the French flooded area, starting with the t 0 96 h forecast. These probabilities 5. Forecast sensitivity to resolution and physical processes Two deterministic experiments were performed to investigate whether horizontal resolution or the different physical packages used in the BoLAM and the ECMWF models could explain the remarkable difference between the SAR-LEPS and the ECMWF EPS forecasts over Sardinia. These deterministic experiments have been carried out with the nesting in operational use at SAR, that is, using ECMWF model version T L 319L60 and, as the initial condition, the t 12 forecast. In the first experiment (BoLAM E ), the Kain and Fritsch (1990) scheme for deep convection normally used by BoLAM is replaced with the Emanuel (1991) scheme. In the second experiment (BoLAM L ), BoLAM has been run in the usual operational setup but with a horizontal resolution of 45 km 45 km, which is closer to the T L 319L60 model resolution. Parameterization schemes for cumulus convection in large-scale and mesoscale models are one-dimensional representations of the updrafts and downdrafts for subcloud-scale motion in every grid box. Considering the experimental evidence that individual clouds show an extraordinary degree of inhomogeneity, Emanuel (1991) proposed a parameterization of the vertical transport of small-scale drafts with initial diameters between 100 and 1000 m. There are two main closure parameters of this nonexplicit scheme: the first is the efficiency with which an air parcel, lifted to the neutral buoyancy level within the cloud, is converted into precipitable water; the second is the precipitation amount that falls through unsaturated air. Emanuel (1991) argued in his paper that mass fluxes within the convective cells are essentially

JUNE 2004 CHESSA ET AL. 573 FIG. 5. Forecast of accumulated precipitation between 1200 UTC 12 Nov and 1200 UTC 13 Nov 1999, issued 3 days before the event by (a) ECMWF (model: T L 319L60) and (b) SAR (model: BoLAM). Values on the grayscales are expressed in mm.

574 WEATHER AND FORECASTING VOLUME 19 FIG. 6. As in Fig. 5 but for the forecasts issued 2 days in advance.

JUNE 2004 CHESSA ET AL. 575 FIG. 7. Probability of 24-h cumulated precipitation exceeding 20, 40, and 60 mm 24 h 1, as obtained by the t 0 96 h (a) (c) EPS forecast and (d) (f) SAR-LEPS forecast. Precipitation from 1200 UTC 12 Nov to 1200 UTC 13 Nov 1999. The values on the scales represent the probability thresholds. controlled by parcel instability and the possible influence of mass and moisture convergence is not taken into account in his scheme. On the other hand, in their parameterization Kain and Fritsch (1990) used a lateral entrainment in the vertical column, proportional to the cloud-base mass, and a detrainment related to the probability of mixed air to be negatively buoyant. Detrainment, entrainment,

576 WEATHER AND FORECASTING VOLUME 19 FIG. 8. As in Fig. 7 but for the t 0 72 h forecasts. and the associated convective upward and downward motion are used to determine the amount of mixing and the net effect of convection onto the model variables. The ECMWF model uses a cumulus convection parameterization based on the bulk mass flux scheme originally described by Tiedtke (1989). The scheme considers deep, shallow, and midlevel convection where clouds are represented by a single pair of entraining detraining plumes that describes updraft and downdraft

JUNE 2004 CHESSA ET AL. 577 FIG. 9. As in Fig. 7 but for the t 0 48 h forecasts. processes. In this scheme momentum transport by convection is also included. Figures 11 and 12 show that t 12 36 h precipitation predicted by BoLAM L and BoLAM E, respectively. Results show that the spatial location of the BoLAM L (Fig. 11) and BoLAM (Fig. 6b) forecasts are very similar, with BoLAM L predicting lower maximum values but basically keeping a spatial distribution similar to the one obtained by a simple interpolation from a highresolution grid to a coarser one (cf. Fig. 11 to Figs. 6a and 6b). By contrast, BoLAM E wrongly forecasts the position of the precipitation band over the Sardinian area (cf. Fig. 12 to Fig. 6b). These results suggest that, for this case, the more

578 WEATHER AND FORECASTING VOLUME 19 FIG. 10. Meteosat infrared image at 0000 UTC 13 Nov 1999. accurate BoLAM precipitation prediction might be related to the use of the Kain and Fritsch (1990) physical representation of deep convection, more so than to the higher spatial resolution. However, this can be taken as an endorsement for further investigation more than as an explanation for the different behaviors of the two models. The ECMWF forecast done with the T L 319L60 model, which gave no more than 10 mm 24 h 1 for the Sardinian area, is not very different from the T L 255L40 EPS probabilities forecasts in comparison to the T L 159L31 EPS forecasts (not shown here). This seems to indicate a reduced role for model resolution with respect to the physical parameterizations. Thus, even though the very preliminary results obtained with BoLAM have to be considered valid only for the deterministic forecasts and might well be inside the natural spread of an ensemble, they raise some questions. In particular a multimodel approach should be carefully evaluated in terms of accuracy and ability to estimate the forecast skill, especially for severe weather events like the one studied here. 6. Conclusions The Sardinian Regional Meteorological Service Limited-area Ensemble Prediction System (SAR-LEPS) has been described, and preliminary results of the prediction of a flooding event that hit Sardinia (and southern France) between 12 and 13 November 1999 have been discussed. SAR-LEPS is based on 51 integrations of BoLAM, the limited-area model developed at the Institute for Atmospheric Sciences and Climate of the Italian National Research Council, run with a gridpoint spacing of about 22 km. All these integrations use, as initial and boundary conditions, fields from the 51 members of the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS). Results obtained from three consecutive SAR-LEPS forecasts of the November 1999 Sardinian and southern France floods confirm the conclusions of Marsigli et al. (2001) that nesting a limited-area high-resolution model into the ECMWF EPS can provide valuable, more accurate predictions, especially in areas of strong oro-

JUNE 2004 CHESSA ET AL. 579 FIG. 11. The 2-day forecast of accumulated precipitation between 1200 UTC 12 Nov and 1200 UTC 13 Nov 1999, obtained using the BoLAM model with a spatial resolution of about 45 km 45 km. Values are expressed in mm. graphic forcing. However it is not possible to draw definite conclusions from one simple event, and more case studies are required to quantify such a statement from a statistical point of view. Sensitivity experiments based on single deterministic forecasts have indicated that, for the case under discussion, different convection schemes produce forecast differences greater than those obtained through a simple change of model resolution. These results suggest that, especially at high resolution, the effect on the forecast error of model uncertainties might become as important as the effect of initial uncertainties earlier in the forecast, and thus high-resolution, limited-area ensemble systems should include both effects to provide effective and skillful probabilistic predictions. Although stronger, statistically significant conclusions cannot be drawn, the results of this sensitivity analysis may suggest that another development strategy would be to follow a multimodel approach (e.g., Harrison et al. 1999), or at least diversify the use of parameterization schemes in the SAR-LEPS members (Stensrud et al. 2000; Alhamed et al. 2002). Acknowledgments. We wish to acknowledge the authors of the BoLAM model, Andrea Buzzi and Piero Malguzzi. Suggestions made by three careful reviewers helped to improve the quality of the paper. Marino Marrocu acknowledges support from the Sardinian Regional Authorities and from the Italian Ministry of the University (Project ISR8, C11-B). APPENDIX The Bologna Limited Area Model BoLAM, the limited-area model developed at the Institute for Atmospheric Sciences and Climate of the Italian National Research Council, is a primitive equation model using p/p s as its vertical coordinate and a horizontal staggered Arakawa C grid. The prognostic variables are the horizontal wind components u and, potential temperature, specific humidity q, and surface pressure p s. The evolution of these five variables are computed by integrating the two equations for components of the horizontal momentum, u u R T lnp ( f ) t ahx d s 1 ( E) Ku Fu and ahx

580 WEATHER AND FORECASTING VOLUME 19 FIG. 12. The 2-day forecast of accumulated precipitation between 1200 UTC 12 Nov and 1200 UTC 13 Nov 1999 obtained using the BoLAM model with Emanuel s parameterization of convection. Values are expressed in mm. RT lnp ( f )u t ahy d s 1 ( E) K F ; ahy the vertically integrated continuity equation, 1 p p s Vh d ; t the thermodynamic equation, u K F ; t ahx ahy and the equation for water conservation, q u q q q Kq F q. t ahx ahy The diagnostic equations are the hydrostatic equation, RT d p, t p and the continuity equation solved at each vertical level for the vertical velocity, 1 p p ps p h s 1 V d. p t This set of equations is completed with the law of ideal gases and the standard definitions of potential and virtual temperatures (, T ). The variable and constants reported in the equation are the scale factors h x, h y (equivalent to cos and 1 in spherical coordinates); the constant for ideal gases R d ; the mean radius of the earth a; the Coriolis parameter f 2 sin ; the vertical component of relative vorticity ; the geopotential ; the kinetic energy of the horizontal motion E; the contributions to the tendencies coming from the parameterization of the physical processes (such as solar and terrestrial radiation, convection, cloud processes, surface friction and heat flux, etc.), F u, F, F, and F q ; and the contribution from the horizontal and vertical diffusion (K u, K, K, K q ). A second-order horizontal diffusion operator is applied to the divergence of the horizontal velocity field in order to reduce the growth of gravity waves and the development of unbalanced components in the meteorological fields. A time-splitting integration method is used, with a second-order Eulerian scheme for the advection equation followed by a forward backward integration for the gravity wave part of the primitive equations. The lateral boundary conditions are imposed via a relaxation scheme (Davies 1976; Kallberg 1981). Parameterized physical processes include vertical diffusion, soil water and energy balance (Charnock 1955),

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