Marek Kaspar *, Miloslav Müller Institute of Atmospheric Physics ASCR, Prague, Czech Republic

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1 1.16 NUMERICAL SIMULATIONS OF CONVECTIVE EVENTS THE EFFECT OF PROPAGATING GUST FRONTS Marek Kaspar *, Miloslav Müller Institute of Atmospheric Physics ASCR, Prague, Czech Republic 1. INTRODUCTION Propagating gust fronts are of interest in a shortrange forecasting and nowcasting. The interaction of downdraft outflows with environmental air can initiate convective cells and thus affect the dynamical structure and life cycle of long-lasting and organised convective systems (Thorpe et al., 1982; Rotuno et al., 1988). When applied to the real atmosphere, the results of the extensive laboratory (e.g. Simpson and Britter, 1980) and numerical modelling (e.g. Chen, 1995) approaches of the density current phenomenon have made it possible to understand an array of fundamental processes that are connected with the outflow dynamics and morphology. On the basis of these experiments and the analytical studies concerning the effects of base-state stratification, latent heating and surface drag (Liu and Moncrieff, 2000; Liu and Moncrieff, 1996b; Liu and Moncrieff, 1996a), two-dimensional analytical models, so called regimes of propagation, have been developed. The models describe both the morphology and the propagation of an outflow and the structure of forced upward motions in dependence on the properties of an ambient wind field (Moncrieff and Liu, 1999; Xue et al., 1997). The research reported herein is part of a systematic study aimed at examining the role of gust fronts in the developement and organisation of convection, which occurred in the territory of the Czech republic, by means of the non-hydrostatic limited area NWP model LM COSMO (Doms and Schättler, 1999). As previous experiments had shown, the proposed model for the Objective Analysis of Gust Fronts (OAGF) is a suitable tool for postprocessing studies of the evolution and organisation of various convective systems observed (Kaspar, 2003). On the other hand, it emerged that the objective methods needed further development, tuning and testing. Apart from determining the gust front position and the speed of its movement, the OAGF enables the assessment of the vertical structure of objective gust fronts and their potential for convection initiation. The Radar Simulation Model (RSM; Haase and Fortelius, 2001) is applied to monitor simulated convective systems in arbitrary PPI and RHI scans through the LM COSMO domain and to verify the LM COSMO runs. Section 2 contains a brief description of the constituent OAGF procedures. Section 3 deals with numerical simulations and the example of the postprocessing analysis of a summer convective case. Finally, section 4 summarises the first results and conclusions of the existing work and mentions our future plans. We also tend to present some of the near future results at the meeting. 2. METHODOLOGY OF THE OBJECTIVE ANALYSIS OF GUST FRONTS Kaspar (2003) fully described the fundamental methodology of the OAGF by which mathematical and graphical techniques can be combined to enable a computer to draw gust fronts entirely automatically in arbitrary horizontal and vertical cross sections through the LM COSMO domain. In this section, we will summarise all the OAGF products. * Corresponding author address: Marek Kaspar, IAP ASCR, Bocni II/1401, Prague, Czech Republic; kaspar@ufa.cas.cz. 2.1 Spatial Location of Objective Gust Fronts The OAGF utilises the most primary (i.e. thermal) definition of the gust front position. The objective gust front (hereafter OA gust front) is defined as the line

2 adjacent to the warm air side of a boundary region, across which the magnitude of the moist potential temperature gradient is changing most abruptly. This definition is mathematically expressed by means of a locating equation and two masking inequalities and is analogous to the definition of objective atmospheric fronts on the synoptic scale published by Hewson (1997, 1998). The set of defining equation and inequalities is reproduced from Kašpar (2003) and is summarised below. (I) The second spatial derivative, in the direction perpendicular to the OA gust front, of the magnitude of the moist potential temperature gradient, must equal zero: L ( τ ) sˆ s ± τ = 0, ŝ =, (1) τ where τ is a thermal parameter (here moist potential temperature), ŝ is a unit axis, and is the operator of the horizontal gradient. (II) The rate of change of the moist potential temperature gradient, perpendicular to the OA gust front and in the direction of the cold air, must be greater than a pre-defined non-negative masking threshold : K 1 M 1 τ > K τ τ. 1. (2) (III) The moist potential temperature gradient in the baroclinic zone adjacent to the OA gust front must be greater than a pre-defined non-negative masking threshold : K 2 M2 τ (, ) + mκ τ > K i j ( ) 2, (3) where = 1 2 i, j m, κ is the gridlength, and ( i, j ) are the horizontal coordinates of a gridpoint. The first tuning tests showed that the workable values of the masking thresholds K1 and K2 may be obtained on the knowledge of the statistical characteristics of the masking variables within the limited area containing OA gust fronts and source convective cells. 2.2 Movement and Morphology of OA Gust Fronts The second part of the OAGF consists of the procedures that assess the propagation speed and the vertical range of an OA gust front head. The direction of the propagation speed vector is always perpendicular to the OA gust front and its magnitude is primarily determined by the ambient-wind speed, the magnitude of the horizontal pressure gradient and the height of the OA gust front head (Bluestein, 1993): c = K gh ( Θ Θ ) Θ + 0. u. (4) w c c 62 In (4), we use the non-constant Froude number K depending on latent heating occurrence and stability conditions (e.g. Liu and Moncrieff, 1996b; Nicholls at al., 1988; Wakimoto, 1982), is the gravity acceleration, H is the head height and u is the vertical average of the horizontal-wind component normal to the OA gust front below H. Θw and Θ c are the moist potential temperatures on the warm side and cold side of the OA gust front, respectively. The head height H is defined as the height of a LM COSMO level above earth surface, up to which the OA gust front can be localised with the aid of the OAGF. 2.3 Objective Analysis of Vertical Shear, Stability and Humidity Conditions Firstly, the vectors of propagation speed are compared with the relative background wind field to assign a defined regime of propagation to the OA gust front. The fundamental classification of the flow relative to the propagating OA gust front covers the upshear and downshear propagating regimes and the steering-level regime with an overturning updraft, which is considerably effective for convection initiation. The knowledge of the regime makes it possible to estimate the structure and the vertical extent of forced upward motions and forecast the spatial organisation of incipient convective cells (see Fig. 1). In order to evaluate the probability of convection initiation, the procedure also identifies the occurrence of potential instability in the lower troposphere and the height of the lifting condensation level (LCL). Under the conditions with a low LCL and potentially unstable layers in the lower troposphere, either upshear- or downshear-moving gust fronts could initiate convection. Under the conditions with a high LCL and/or potentially stable lower layers, however, only the downshear-moving gust fronts may be effective for convection initiation. g

Fig. 1. Schematic of the relative flow in a reference frame moving along with the downdraft outflow in the idealized analytical model. The upper figure: Propagating regime (upshear-moving outflow).

3 Fig. 1. Schematic of the relative flow in a reference frame moving along with the downdraft outflow in the idealized analytical model. The upper figure: Propagating regime (upshear-moving outflow). The middle figure: Propagating regime (downshear-moving outflow). The bottom figure: Steering-level regime (downshear-moving outflow). Here, z=h s is the steering level. The thick arrow denotes the velocity c 0 of propagation of the outflow in ground-relative coordinates. 3. CASE STUDY In this section, we will present an example of the application of the OAGF in the numerical simulation of a summer convective case during which objectively identifiable gust fronts occurred. Our object is to evaluate the impact of propagating gust fronts in decaying or regenerating convective cells and to assess the contribution to the prolongation of convection lifetime.in this case. 3.1 LM COSMO Computations We employed the experimental runs of the LM COSMO version The configuration of the run consists of two parts. Firstly, a driving model, which we marked as the LLM, is integrated over a large part of Europe with the horizontal resolution of 14 km. The LLM domain consists of grid points and 21 vertical levels. The integration time step is 120 s. The LLM integration starts at 00 UTC on the day of interest. Initial and boundary conditions are derived from the objective analysis of aerological measurements from European stations (Sokol, 1993). The LLM receives the boundary data at a 12h interval. The LLM is integrated with convection parameterisation. In the second step, a nested model, which we marked as the SLM, runs with a horizontal resolution of 2.8 km. The SLM domain is defined in dependence on the localisation of a simulated weather event and consists of grid points and 36 vertical levels. The integration time step is 30 s. The SLM integration starts from 6 to 10 hours before the precipitation onset. Initial and boundary conditions are obtained from LLM forecasts. The boundary data are received in a 1h interval. The SLM is integrated without convection parameterisation. Further details about the configuration of the LM COSMO runs including the verification of convective precipitation forecast by radar-derived rainfall fields can be found in (Řezáčová and Sokol, 2003). 3.2 Case Characteristics Shortly after the midday, a cold front lying within a shallow pressure trough began to move across the Czech Republic from the southwest. The midtropospheric synoptic-scale pattern was characterised by a weak ridge of high pressure and westerly flow (e.g. Berliner Wetterkarte, 2000). During the passage of the front, showers and isolated thunderstorms occurred. The reported daily precipitation from 06 UTC on 2 July to 06 UTC on 3 July mostly hovered around 10 mm with the maximum of 17 mm. Fig. 2 shows the spatial distribution of the maximum radar reflectivity in the affected area during the afternoon, as detected by the Czech radar Skalky. There can be seen two large convective cells that rapidly move to the southeast. The northerly of the two cells successively decays. It is depicted by black arrow. On the other hand, the southerly cell, whose position is depicted by the red arrow, regenerates. The observations confirm that these long-lasting cells were accompanied by the appearance of a downburst along with microbursts, tiny hail and intensive precipitation.

Fig. 2. The horizontal and vertical projection of maximum radar reflectivity Z max [dbz] measured by the weather radar Skalky with the pixel size of 2 2 km on July 2, 2000.

The OAGF and RSM were applied to the prognostic fields from the 10h, 11h and 12h forecasts, which are valid at 13 UTC, 14 UTC and 15 UTC, respectively.

The well-defined OA gust fronts are correctly plotted along the warm air boundaries of regions with enhanced potential temperature gradient and move away from cold air sources colliding with each

4 Fig. 2. The horizontal and vertical projection of maximum radar reflectivity Z max [dbz] measured by the weather radar Skalky with the pixel size of 2 2 km on July 2, The black and red arrows mark the decaying and regenerating convective cells, respectively. 3.3 Discussion of results The SLM was integrated for the initial analysis from 03 UTC on 2 July. The OAGF and RSM were applied to the prognostic fields from the 10h, 11h and 12h forecasts, which are valid at 13 UTC, 14 UTC and 15 UTC, respectively. Firstly, we will present the main products of a few validation tests with the OAGF. Fig. 3 depicts surface OA gust fronts and the contours of moist potential temperature. The well-defined OA gust fronts are correctly plotted along the warm air boundaries of regions with enhanced potential temperature gradient and move away from cold air sources colliding with each other. Next, Fig. 4 shows that the propagating OA gust fronts coincide with the local maxima of vertical velocities at low levels, which is in accordance with observations. Finally, as it can be seen in Fig. 5, the OA gust fronts ring the local maxima of the instantaneous precipitation rates at the surface, which confirms the convection downdraft origin of cold air pools. The vertical cross-section AB (see Fig. 5) through the decaying and regenerating cells examined are displayed in Fig. 6. The Fig. 6 indicates how the northerly positioned cell (i.e. the right cell in the crosssection) successively decays and on the contrary, how the southerly positioned cell that is located on the front side of the outflow from the other one intensifies. There is a sheared relative flow with no steering level ahead of the outflow. Since the OA gust front move in the direction of the shear vector in the immediate vicinity of the OA gust front head, it was assigned a downshear propagating regime. In Table 1, the results of the vertical cross-section analysis are summarised, including the information about the objective head height and the speed of movement of OA gust fronts propagating into the area where new convection forms also for 11h and 12h forecasts. Fig. 7 depicts how the vertical gradient of equivalent potential temperature and the height of the LCL vary according to the height above earth surface ahead of the OA gust front head in Fig. 6. The curves reveal the potential instability and relatively low LCL at lower SLM levels at the time when convection forms. Moreover, since the OA gust front propagates downshear, the incipient convective cell tends to remain within the area of forced upward motions. The downshear dynamical organisation, together with the favourable stability and humidity conditions, signals the propagating OA gust front has the potential for triggering convection. Fig. 3. The OA gust fronts (blue lines) and the SLM outputs of potential temperature [K] at the surface. From the left: 10h, 11h, and 12h forecast with the start of integration at 03 UTC on July 2, Fig. 4. The surface OA gust fronts and the SLM outputs of vertical velocities [m/s] at the altitude of 1km. Fig. 5. The OA gust fronts and the SLM outputs of instantaneous precipitation rates [mm/h] at the surface. The black and red arrows mark the decaying and regenerating simulated convective cells, respectively.

The right figure: the SLM outputs of wind components [m/s] in a reference frame moving along with the OA gust front head.

5 Fig. 6. The vertical cross-sections along the abscissa AB (see Fig. 5) containing the OA gust front head that moves in the direction of the arrow above. The left figure: the simulated radar reflectivity [dbz] for a hypothetic radar at the point A. The right figure: the SLM outputs of wind components [m/s] in a reference frame moving along with the OA gust front head. Date of forecast UTC UTC UTC Regime Propagating regime (downshear) Propagating regime (downshear) Propagating regime (downshear) Head height [m] Speed of movement [m/s] Table 1. The regime of propagation, head height and the speed of movement of the OA gust fronts propagating into the area where convective cells regenerate (see Figs. 5 and 6). Fig. 7. The variation of the vertical gradient of equivalent potential temperature DEPTZ [K/m] and the height of lifting condensation level LCL [m] with the height H above earth surface. The quantities are computed on the nearest grid point ahead of the OA gust front head depicted in Fig SUMMARY We employed two objective postprocessing tools - the OAGF and RSM models allowing the comprehensive gust front analysis to examine particularly the organizing function of vertical shear and the effect of stability as well as humidity conditions on convection initiation during a summer convective case that was numerically simulated by the LM COSMO. The validation tests confirmed the applicability of the LM COSMO-OAGF chain and RSM in the objective analysis of gust fronts, and hence also in nowcasting and short-range forecasting of such hazardous weather phenomena. The LM COSMO proved to forecast precipitation in nearly correct subregions and times. The OA gust fronts were correctly plotted along the warm air boundaries of regions with enhanced potential temperature gradient, coincided with the local maxima of vertical velocities at low levels and ringed the local maxima of instantaneous precipitation rates at the surface. In presented simulation, the propagating OA gust fronts had the potential for the regeneration of convective cells as they travelled downshear, i.e. into the vertical shear-favourable environment. In addition to the dynamical organisation, there were favourable stability and humidity conditions characterized by potentially unstable lower layers and relatively low LCL in the area of forced upward motions ahead of the OA gust fronts. Regarding future activities, the tuning and verification of the OAGF procedures will continue. The OAGF will be applied within the numerical simulations of selected convective events, where we plan to utilise both the outputs from the RSM and the techniques of radar data assimilation. The enhancement of the horizontal resolution of the LM COSMO application down to 1km is one of the crucial tasks for future, too. The additional locating procedures based on the analysis of wind field will be tested. The parametres that are derived from convergence, vorticity and shear would be helpful in the cases when the thermal definition of an OA gust front does not allow its unambiguous localisation. Furthermore, the products of the OAGF are assumed to be used in formulating decision criteria. The final output could be, for instance, a total index quantifying the potential of an OA gust front to trigger new convective cells. The examination of such potential is also possible by the numerical experiments with artificial initial conditions (Ducrocq et al., 2002). For this purpose, special runs of the LM COSMO will be performed. The experiments will be

6 designed to evaluate particularly the effects of vertical shear. The obtained results can be then applied to modify the LM COSMO convection parameterization scheme. Acknowledgements The study is supported by GA ASCR B and GACR 205/04/0114 projects. The German Weather Service is acknowledged for the provision of the LM COSMO and RSM codes for research purposes. The radar pictures were kindly provided by the Czech Hydrometeorological Institute. References Berliner Wetterkarte 2000: Institute für Meteorologie der Freien Universität Berlin. Bluestein, H. B., 1993: Synoptic-dynamic meteorology in midlatitudes. Vol. 2. Oxford Univ. Press, New York, Chen, C., 1995: Numerical simulations of gravity currents in uniform shear flows. Mon. Weather Rev., 123, Doms, G., Schättler, U., 1999: The Nonhydrostatic Limited-Area Model LM of DWD. Part I: Scientific Documentation, DWD, Offenbach, Germany, 172 pp., available at Ducrocq, V., Ricard, D., Lafore, J. P., Orain, F., 2002: Storm-scale numerical rainfall prediction for five precipitating events over France; On the importance of the initial humidity field. Weather and Forecasting, 17, Haase, G., Fortelius, C., 2001: Simulation of radar reflectivity using HIRLAM forecasts. Working document COST717 - STSM_03_200106_1, available at Hewson, T. D., 1997: Objective identification of frontal wave cyclones. Meteor. Appl., 4, Hewson, T. D., 1998: Objective fronts. Meteor. Appl. 5, Kašpar, M., 2003: Analyses of gust fronts by means of limited area NWP model outputs. Atmos. Res., 67-68, Liu, C., Moncrieff, M. W., 1996a: A numerical study of effects of ambient flow and shear on density currents. Mon. Weather Rev., 124, Liu, C., Moncrieff, M. W., 1996b: An analytical study of density currents in sheared, stratified fluids including the effects of latent heating. J. Atmos. Sci., 53, Liu, C., Moncrieff, M. W., 2000: Simulated density currents in idealised stratified environments. Mon. Weather Rev., 128, Moncrieff, M.W., Liu, C., 1999: Convection initiation by density currents: role of convergence, shear, and dynamical organization. Mon. Weather Rev., 127, Nicholls, M. E., Johnson, R. H., Cotton, W. R., 1988: The sensitivity of two-dimensional simulations of tropical squall lines to environmental profiles. J. Atmos. Sci., 45, Rotunno, R., Klemp, J. B., Weisman, M. L., 1988: A theory for strong, long-lived squall lines. J. Atmos. Sci., 45, Řezáčová, D., Sokol, Z., 2003: A Diagnostic study of a summer convective precipitation event using a nonhydrostatic NWP model. Atmos. Research, 67-68, Simpson, J. E., Britter, R. E., 1980: A laboratory model of an atmospheric mesofront. Quart. J. Roy. Meteor. Soc., 106, Sokol, Z., 1993: Objective analysis on a limited area. PhD Thesis, Charles University, Prague, 135 pp. (in Czech; English abstract available from Math. and Phys. Faculty, Charles University, Prague, Czech Republic) Thorpe, A. J., Miller, M. J., Moncrieff, M. W., 1982: Two-dimensional convection in non-constant shear. Quart. J. Roy. Meteor. Soc., 108, Wakimoto, R. M., 1982: The life cycle of thundrstorm gust fronts as viewed with Doppler radar and rawinsonde data. Mon. Weather Rev., 110, Xue, M., Xu, Q., Droegemeier, K. E., 1997: A theoretical and numerical study of density currents in nonconstant shear flows. J. Atmos. Sci., 54,

Theories on the Optimal Conditions of Long-Lived Squall Lines

Theories on the Optimal Conditions of Long-Lived Squall Lines References: Thorpe, A. J., M. J. Miller, and M. W. Moncrieff, 1982: Two-dimensional convection in nonconstant shear: A model of midlatitude