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Uncertainty in prediction of deep moist convective processes: Turbulence parameterizations, microphysics and grid-scale effects
Atmospheric Research 100 (2011) 447–456
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Atmospheric Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a t m o s
Uncertainty in prediction of deep moist convective processes: Turbulence parameterizations, microphysics and grid-scale effects E. Fiori a,⁎, A. Parodi a, F. Siccardi a,b a b
CIMA Research Foundation, Via Magliotto 2, 17100 Savona, Italy DIST, University of Genova, Via all'Opera Pia 13, 16145, Genova, Italy
a r t i c l e
i n f o
Article history: Received 20 January 2010 Received in revised form 1 October 2010 Accepted 2 October 2010 Keywords: Microphysics High resolution Turbulence parameterizations Deep moist convection Numerical modeling
a b s t r a c t A line of development of numerical meteorological forecast, common to many European and American Meteorological Organizations, schedules a drastic reduction of the grid spacing for the realization of limited-area predictions. The scientific community has been discussing such an issue whether this approach can be of real advantage for the solution of the problems of the uncertainty of the decision-maker. The extraordinary enhancement of the computer power could indeed promote this drastic reduction of the modeling horizontal resolution just because “nowadays it is possible”. However this “brute-force” approach to the question of the solution of the problem of nowcasting does not guarantee a priori improvement of forecast skill. In this framework, deep moist convective processes in simplified atmospheric scenarios (e.g. supercell) are studied in this paper by means of high-resolution numerical simulations with COSMO-Model. Particular attention is paid to determine whether and at which extent the convection-resolving solutions, in the range of grid spacing between 1 km and 100 m, statistically converge from a turbulence perspective with respect to flow field structure, transport properties and precipitation forecast. Different turbulence closures, microphysics settings and grid spacings are combined and their joint impact on the spatial–temporal properties of storm processes is discussed. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The increasing availability of computational power makes possible the numerical modeling of severe weather events at unprecedented fine mesh-scale (Xue et al., 2007). While the rapid progress of high-resolution numerical modeling has the potential for enabling a deeper understanding of the spatial– temporal properties of deep moist convective processes and related intense rainfall phenomena, it also calls for a better understanding of the uncertainty associated with the adoption of different physical parameterizations. In this respect, the assessment of effects of subgrid-scale closures such as those associated with microphysics and turbulence processes
⁎ Corresponding author. E-mail address: elisabetta.fi[email protected] (E. Fiori). 0169-8095/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2010.10.003
on fine mesh-scale modeling has been subjected to growing attention. From a microphysics perspective and in a direct numerical simulation (DNS) limit, several studies have focused their attention on the interaction between turbulence and microphysics to gain an in-depth understanding of the broadening cloud-droplet spectra. Among others, Ayala et al. (2008a,b) and Wang et al. (2008) tried to quantify the effects of the vertical motion on the droplet growth and the liquid-water transport. Hence, some investigations aimed at the evaluation of both the turbulence effects on the motion and the concentration of the droplets as well as of the collision efficiency (Franklin et al., 2005) and the stochastic coalescence (Wang et al., 2005). In a large-eddy simulation (LES) framework, Jiang and Cotton (2000) studied the sensitivity of shallow marine cumulus convection to different microphysics and radiation
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schemes to understand how drizzle affects the turbulent fluxes and surface precipitation. Morrison and Grabowski (2007), instead, developed a two-moment warm rain bulk microphysics scheme suitable for addressing the indirect impact of atmospheric aerosols on ice-free clouds. The focus was on the prediction of supersaturation, activation of cloud droplets, and the representation of microphysical transformations associated to parameterized turbulent mixing. For horizontal resolutions ranging from the cloud permitting (CPM) to the cloud resolving (CRM) limits (e.g. 4– 0.1 km), many studies have tried to assess the precipitation uncertainty due to variations in precipitating species parameters (Grabowski, 2003; Gilmore et al., 2004; Grubišić et al., 2005; Liu and Moncrieff, 2007; Hong et al., 2009). Grabowski (2003) investigated the impact of cloud microphysics on global radiative–convective quasi-equilibrium in a constantSST aquaplanet, with simulations at 1 km grid spacing. The results show that cloud microphysics affects mainly the quasi-equilibrium temperature and moisture profiles while the relative humidity is only marginally influenced. In their study, instead, Gilmore et al. (2004) reported on the sensitivity of accumulated precipitation to the microphysical parameterization in simulations of deep convective storms at 1 km grid spacing with a single-moment bulk liquid–ice microphysics scheme. Various intercept parameters from a prescribed Marshall–Palmer exponential size distribution are evaluated along with two particle densities for the hail/ graupel species. The results suggested that the amount of accumulated ground precipitation is very sensitive to the way the hail/graupel category is parameterized. Distributions characterized by larger intercepts and/or smaller particle density have a smaller mass-weighted mean terminal fall velocity and produce smaller hail/graupel mixing ratios spread over a larger area. With respect to the prediction of precipitation over complex orography areas, Grubišić et al. (2005) examined the skill of a MM5 model, run at 1.5 km grid spacing, during high-impact precipitation events in the Sierra Nevada, and the sensitivity of that skill to the choice of the microphysical parameterization and horizontal resolution. Again, at convection-permitting grid spacing, Liu and Moncrieff (2007) investigated the effects of cloud microphysics parameterizations on simulations of warm-season precipitation The objective was to assess the sensitivity of summertime convection predictions to the bulk microphysics parameterizations at fine-grid spacings applicable to the next generation of operational numerical weather prediction models. Based on their results, a general conclusion about the desirable degree of sophistication in the microphysics treatment and their performance was not achievable. Hong et al. (2009) examined the relative importance of ice-phase microphysics and sedimentation velocity for hydrometeors in two bulk microphysics schemes, the Single-Moment 6-Class Microphysics Scheme (WSM6) and the Purdue–Lin scheme, for a 2D idealized storm case and for a 3D heavy rainfall event over Korea. This study provided the relative role of ice-phase microphysics and fall velocity for ice particles in the bulk-type parameterization approach of clouds and precipitation, and allows to gain a deeper understanding of the cloud and radiation interaction in forming precipitating convection. Furthermore, it appears clear that the impact of the number of prognostic water species variables on simulated convective
processes is smaller than the effects of the formulation of each microphysical process in the same category of prognostic water species variables. From a turbulence parameterization point of view, some recent studies tackled the novel research issue in the modeling of deep convective processes at a very fine resolution (Bryan et al., 2003; Wyngaard, 2004; Fiori et al., 2009, 2010): the joint choice of the turbulence parameterization (or closure) and grid spacing. Two important categories of meteorological numerical approaches exist for the simulation of severe weather events with domain size ranging between 3000 km and 1 km (Wyngaard, 2004): mesoscale modeling on the larger domains and large-eddy simulation (LES) on the smaller ones. The mesoscale modeling aims to weather prediction at horizontal grid spacing of the order of O(10 km) while LES is, traditionally, focused on fine scale Planetary Boundary Layer (PBL) convective processes with a resolution of the order of O (0.1 km). In traditional mesoscale modeling, the typical mesoscale grid spacing largely exceeds the energy-containing turbulence scale l so that little or no turbulence is resolved. Contrary, in LES, the energy and flux-containing turbulence eddies are resolved. The recent possibility of simulating convective systems with very fine resolution makes the distinction between mesoscale and LES model disappearing and since neither mesoscale nor LES turbulence closures were designed to operate in this range, Wyngaard (2004) named it “terra incognita”. Thus a new scientific question arises about the source of uncertainties associated with the use of such two turbulence closure approaches in the “terra incognita”. In this respect, looking for convergence solution for squall lines, Bryan et al. (2003) studied the spatial resolution appropriate for the simulation of deep moist convection from a turbulence perspective. Numerical simulations of squall lines were conducted with grid spacing between 0.125 and 1 km. The results revealed that simulations with 1 km grid spacing do not produce equivalent squall line structures and evolution as compared to the higher-resolution simulations, in terms of precipitation amount, system phase speed, cloud depth, thunderstorm cells size, and organizational mode of convective overturning. Wyngaard (2004) addressed the topic of numerical modeling in the “terra incognita”, corresponding to grid spacing between 0.1 and 1 km, to assess the pertinence for this scales range of turbulent parameterizations valid in the mesoscale (1D, also known as boundary-layer approximation type, Stull, 1988) and LES limits. Along the same lines, Fiori et al. (2010) tried to understand how the uncertainty in the modeling of deep moist convective processes is affected by adoption of smaller grid spacing and by the choice of the turbulent closure used to represent subgrid-scale processes. Bearing in mind this overview, to the best authors knowledge, the potential joint effects of different turbulence closures, microphysics parameterizations and grid spacings on the modeling of the deep moist convective processes, in the “terra incognita” range (0.1–1 km), has been never addressed. This topic is here tackled for a simplified convective scenario corresponding to a supercell. Different turbulent closures, microphysics settings and grid spacing are combined
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in order to create an “ensemble” of fine resolution numerical simulations and their joint impact on the spatial–temporal properties of storm processes is discussed by using appropriate graphics and statistics analysis to study the simulations results. The paper is organized as follows. Section 2 provides a brief overview about the convective scenario considered, the limited-area model used, and its setting in terms of turbulence and microphysics parameterizations. Section 3 describes the results that arise by comparing the numerical experiments in terms of supercell trajectories and rainfall patterns. In Section 4 the conclusions are given. 2. The case study A supercell convection scenario is adopted in this study. This convective scenario has been largely analyzed and studied in literature (Weisman and Klemp, 1982, 1984, 1986; Rotunno and Klemp, 1985). The well-known dynamics and thermodynamics allow an effective comparison of the different numerical simulations in order to evaluate the sensitivity of the convective phenomenon in relation to the changes in the settings of the model. The model is initialized with a thermal bubble superimposed on a homogeneous field. The bubble setting is defined according to Fiori et al. (2010). The horizontal radius of the bubble is 10 km. The vertical one is 1.4 km and the temperature excess is of 2 °C at the center decreasing gradually to 0 °C at the edge. The bubble is placed at (25 km, 25 km) in the horizontal domain to avoid influence of the boundary on its development in the first time steps of integration. The vertical profile of moisture and temperature are those adopted in Weisman and Klemp (1982, 1984), corresponding to a CAPE value around 1600–1700 J/kg: they are depicted in Fig. 1. A directionally varying wind shear is one of the main factors that
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determine supercell motion: in this study the shear vector turns through 180° over the lowest 5 km of the atmosphere, while the wind becomes constant in direction and speed above 5 km. The curvature of the clockwise-curved hodograph is strong enough to favor a right-moving supercell. From a computational point of view, we adopt COSMOModel which is a nonhydrostatic and fully compressible numerical weather prediction model created in 1998 by the Deutsche Wetterdienst (DWD, German National Weather Service) and developed to provide a flexible tool for various scientific applications on a broad range of spatial scales (Steppeler et al., 2003). The model is run over a three-dimensional domain that is of 150 km in both horizontal directions and it is extended to 20 km in height. The vertical coordinates are stretched gradually from ~80 m near the bottom boundary to ~ 500 m near the top one. Four horizontal grid spacings are considered: Δ = 1 km, 0.5 km, 0.25 km and 0.2 km. The model is integrated up to 3 h and the time steps are set to 6, 3, 1.5 and 1 s, respectively, from 1 km to 0.2 km runs. The experiments are realized neglecting orography and Coriolis forces. Davies (1976) and free-slip conditions are applied to the lateral and ground boundaries, respectively. Rayleigh layer characterizes the top-5 km of the atmosphere. Three turbulent parameterizations are adopted in this study, in agreement with the companion paper of Fiori et al. (2010): the first one is called 1D turbulent closure which makes use of the so-called boundary-layer approximation (Steppeler et al., 2003) for the computation of the vertical H diffusion coefficients for momentum KM V and heat KV and it is complemented by a horizontal computational mixing term (Smolarkiewicz et al., 1997) designed to remove shortwave grid-scale noise from fields. The second one is called 3D turbulent closure in which the vertical diffusion coefficients H for momentum KM V and heat KV are computed as in the 1D
Fig. 1. Skew-T diagram depicting dew point temperature (heavy dashed line) and temperature (heavy solid line) profiles used in numerical simulations. The green lines depict the saturation mixing ratio. Blue ones, the dry adiabats. Red ones, the moist adiabats. Tilted black ones, the isotherms.
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case, while the horizontal turbulent coefficients are assumed M H H equal to the vertical ones (K M V = K H , K V = K H), thus no additional numerical computational mixing operator is active in such a closure. The last one is called LES turbulent closure which uses a three-dimensional subgrid-scale model instead of the boundary-layer approximation, so that both vertical and horizontal turbulent coefficients are active (Herzog et al., 2002). With respect to microphysics, simulations have been performed using a single-moment bulk microphysics scheme with two different microphysical settings (Table 1). As shown in Table 1, differences are in terms of the intercept parameter N0x of the exponential Drop Size Distribution (DSD) with x corresponding alternatively to the two solid precipitating water categories investigated, i.e. graupel (x = G) and hail (x = H), the values of the density ρx and the parameters a, b, c and e of velocity–size and mass–size relationships: VT = aDb m = cDe where VT is the terminal velocity and m the mass (Doms et al., 2007). The choice of the aforementioned parameters aims to mimic graupel and hail as defined in Straka (2009) and in according to the parameters values and methodological approach already adopted in Gilmore et al. (2004), Liu and Moncrieff (2007), Reinhardt and Seifert (2006) and Snook and Xue (2008) for grid spacing in the range of 0.1–1 km: graupel/hail category may be a very important species that influences the quantity and type of precipitation received at the ground in many types of severe thunderstorms. Thus, small Nx0 and large values of density change the properties of the particle ensemble: more hail-like behavior appears, particles fall faster and melting is reduced. More unmelted graupel/hail can reach the ground (Lin et al., 1983; Cheng et al., 1985; Heymsfield and Kajikawa, 1987; Rutledge and Hobbs, 1984). For sake of clarification, the plot of the adopted velocity–size relationship for graupel (x = G) and hail (x = H) are shown (Fig. 2). 3. Results 3.1. The trajectory The path of the main convective core entire was captured by tracking the pixel which contains the maximum vertical velocity at the elevation of 5 km. The paths for graupel and hail cases, determined over the two hours of simulations, are plotted in Fig. 3. For the graupel case, the LES-driven paths, corresponding to Δ = 0.5, 0.25 and 0.2 km, collapse each on the other. For the 1D closure, the convergence is not yet reached at Δ = 0.2 km.
Table 1 Parameters adopted for graupel and hail species.
Graupel Hail
ρx g cm− 3
Nx0 m− 4
a m(1 − b)s− 1
b
c kg m− e
e
0.2 0.9
4·106 4·104
442 140
0.89 0.5
169.6 471.2
3.1 3.0
It is worth to highlight that the horizontal spatial distance between the 1 km-1D path and the 0.2 km-LES ones in the final stages of the simulation is about 20 km, largely exceeding the original size of the supercell. For the hail case, instead, the convergence is faster, and, whatever is the adopted turbulence parameterization, the paths collapse each on the other when Δ = 0.25 km. Furthermore, the paths for the LES-driven runs exhibit a smaller curvature with respect to the graupel LES-driven ones, and also the horizontal spatial distance between the 1 km-1D path and the 0.2 km-LES is reduced to 10 km. Thus, the hail-driven experiments show a smaller spread in the trajectory of main convective core corresponding to the supercell: this result suggests that the microphysical setting largely determines the properties of this convective scenario and also their convergence from a turbulence closure perspective. A deeper understanding of the differences induced by the graupel and hail settings can be gained by investigating the structure of the cold pool for the experiments that exhibit the farthest trajectories, which are 1 km-1D and 0.2 km-LES. The cold pool intensity and low-level storm dynamics are found to be very sensitive to the intercept parameters of graupel/hail category drop size distributions (Snook and Xue, 2008). Snook and Xue (2008) argue that DSDs favoring smaller (larger) hydrometeors result in stronger (weaker) cold pools due to enhanced (reduced) evaporative cooling/ melting over a larger (smaller) area. To evaluate this issue, we considered the horizontal cross-sections of potential temperature θ [K] at 0.5 km AGL after 5400 s (Fig. 4). The strength and the size of the cold area related to the downdraft of dry air on the back side of the updraft give in fact a measure of the high pressure due to the ground level spreading of the cold downward. At first glance, Fig. 4 suggests that cold pool extension is more sensitive to changes in horizontal resolution and turbulence parameterization when we consider the graupel microphysical setting, while for the hail one it stays almost the same. In fact, for graupel simulations, there is a general increase of the cold area towards the west part of the domain when finer resolutions and LES closure are used. This is connected to the intensification in the vertical velocity field particularly on the left flank of the system. For the hail simulations, instead, the achievement of more stable configuration appears to be faster, since all the main “large” scale cold pool features are already present in the 1 km-1D closure, when compared with the 0.2 km-LES ones, and this may explain also results of Fig. 3 (lower panel) in terms of faster convergence of the supercell trajectory. It is also worth to mention that hail experiments, due to the larger size of hydrometers and higher terminal velocity, produce more intense updrafts in agreement with some recent theoretical arguments (Parodi and Emanuel, 2009) and as supported by Fig. 5. From Fig. 5, it appears that the mid-level updrafts are similar in magnitude in the 1 km-1D graupel and hail runs, and similar in the 0.2 km-LES graupel and hail runs. Thus, updraft strength is strongly influenced by the grid spacing but not so much by the different microphysics schemes. However, from Fig. 4 it appears that the magnitude of the cold pool is similar in the two hail runs, which are yet much weaker in the
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Fig. 2. Velocity–size relationship for graupel and hail. An approximate identification of the size range for the two ice species is also provided.
1 km-1D graupel run compared to the 0.2 km-LES graupel run. Thus, the grid spacing influences the structure of the cold pool while the magnitude/strength of the cold pool is influenced by both the grid spacing and the microphysics. 3.2. The rainfall field The analysis of the supercell trajectory for different simulations suggested that different microphysical settings,
concerning graupel and hail respectively, may strongly affect the dynamical and thermodynamical structures of the convective flow field, and also the convergence of the convection-resolving solutions from a turbulence closure perspective. Bearing in mind this framework, we tried also to quantify if and to which extent similar arguments are valid for the predicted rainfall field. Thus, the maps of rainfall depth over the time window between the 1 h and 2 h from the initialization of the process are depicted (Fig. 6): the maps
Fig. 3. Path of the core of the right-moving cell in its relative motion in the first two hours of all 12 simulations (upper panel: graupel, lower panel: hail).
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Fig. 4. Horizontal cross-sections of the potential temperature field at z = 500 m and t = 5400 s (upper row: graupel, lower row: hail).
are prepared for both microphysical settings (graupel and hail) and for a subset of the possible turbulence closure/grid spacing combinations, that is 1 km-1D, 1 km-1D, 0.25 km-LES, 0.2 km-1D and 0.2 km-LES. First, for a prescribed turbulence closure–grid spacing combination, the influence of microphysical parameterization is evident both in terms of spatial distribution and intensity of the rainfall depth fields. Indeed, in hail-driven maps the peaks of rainfall are twice of those produced by graupel-driven ones. The parameters of the fall speed–size relationships for graupel/ hail category are the most responsible for the differences in maps of Fig. 6 in agreement with findings of Grabowski (2003), and Parodi and Emanuel (2009). Second, at fine-grid spacing (0.25–0.2 km), the rainfall spatial rainfall distribution is different: it appears to move from a classical supercell structure (graupel cases) to a multicell one (hail cases), composed of a cluster of convective cells at various stages of their life (Fovell and Tan, 1998). Finally, from a turbulence perspective and within each microphysical setting (graupel and hail), some degree of
convergence in the hourly rainfall depth fields seems to be achieved for LES-driven experiments and for finer grid spacings (0.25–0.2 km): in this respect, both for graupel and hail cases, the hourly rainfall depth field as predicted by the 0.2 km-LES experiment is assumed as “ground truth”. In order to evaluate the degree of convergence of the rainfall depth fields in Fig. 7, we adopted the Rousseau index (RI, Barancourt et al., 1992), as a method to cluster simulation results (Giuli et al., 1999; Sangati and Borga, 2009): h RIðthr Þ =
2
4⋅p11 ⋅p00 −ðp10 + p01 Þ
i
½2⋅p11 + p10 + p01 ⋅½2⋅p00 + p10 + p01
where: • thr: predefined threshold (related to the weather field choice) for the calculation of the RI between the reference field (“ground truth” by 0.2 km-LES experiment) and the target (prediction provided by another experiment) on the
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Fig. 5. Horizontal cross-sections of the vertical velocity field at z = 5000 m and t = 5400 s (upper panel: graupel, lower panel: hail).
•
•
•
•
common selected domain. In this work the threshold is equal to 4 mm; p11: percentage of pixels in the spatial domain in which both the reference field and the target field are both greater than the specified threshold; p10: percentage of pixels in the spatial domain in which the target field is above the threshold while the reference one is below this threshold; p00: percentage of pixels in the spatial domain in which both the reference and the target fields are both lower the threshold choice; p01: percentage of pixels in the spatial domain in which the target field is below the threshold while the reference one is above this threshold.
The RI may range between 1 (complete agreement) and −1 (complete disagreement) between the reference field and the target one. The RI has been evaluated, both for graupel and hail cases, by comparing the 0.2 km-LES hour rainfall depth (Fig. 6) with
the other 4 rainfall depth-cases (after spatial interpolation over the same grid spacing if necessary), as summarized in the following: • • • •
Case Case Case Case
I: 0.2 km-LES versus 1 km-LES II: 0.2 km-LES versus 1 km-1D III: 0.2 km-LES versus 0.25 km-LES IV: 0.2 km-LES versus 0.2 km-1D.
Fig. 7 confirms that hail-driven experiments (lower panel) are more effective in the convergence of the spatial structure of the rainfall depth field as already observed in the case of the supercell trajectory. For case III, the RI values for the hail case are higher than graupel ones whatever is the rainfall threshold, thr. Furthermore, Fig. 7 (lower panel) supports the idea that hail-driven cases exhibit more similar rainfall depth fields at finer grid spacings (case IV) even if characterized by 1D closure. Consequently, once more, microphysics seems to determine the convergence of convective flow field properties from a turbulence closure perspective.
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Fig. 7. Rousseau index plot for 1 h rainfall depth map (upper panel: graupel, lower panel: hail).
4. Conclusions Turbulence closures and microphysical parameterizations are recognized to be important sources of uncertainty in highresolution numerical modeling of deep moist convection processes (Bryan et al., 2003; Gilmore et al., 2004). In this respect, this study has tackled the challenging problem of assessing the sensitivity of a modeled supercell to different combination of physical parameterizations for subgrid processes (turbulence and microphysics) and the grid spacing in the resolution ranges between 0.1 and 1 km. The results suggest that differences in supercell propagation and the uncertainty in its physical representation are reduced when a suitable grid spacing in combination with an adequate turbulent and microphysical parameterization are chosen. The use of the LES closure, with both microphysics settings, implies a more intense turbulent activity at fine-grid scale with respect to the other two closures, 1D and 3D. Furthermore, for this case study, microphysics largely determines deep moist convective properties, as found also in another study by Gilmore et al. (2004). In this respect, for graupel-driven runs, the convective-resolving solutions does “converge”, with respect to the overall flow field structure,
and precipitation patterns when Δ ≈ 0.2–0.25 km and LES closure are adopted. In hail-driven ones, the horizontal spread of the trajectories is reduced with respect to the graupel-driven ones and the convergence of the trajectories and precipitation field is shown at Δ ≈ 0.2–0.25 km whatever is the adopted turbulent closure. Acknowledgements This work was supported by the Italian Civil Protection Department. The authors are grateful to Richard Rotunno for the useful comments and discussions. References Ayala, O., Rosa, B., Wang, L.-P., Grabowski, W.W., 2008a. Effects of turbulence on the geometric collision rate of sedimenting droplets: Part 1. Results from direct numerical simulation. New J. Phys. 10, 075015. doi:10.1088/ 1367-2630/10/7/075015. Ayala, O., Rosa, B., Wang, L.-P., 2008b. Effects of turbulence on the geometric collision rate of sedimenting droplets: Part 2. Theory and parameterization. New J. Phys. 10, 075016. doi:10.1088/1367-2630/10/7/075016. Barancourt, C.J., Creutin, D., Rivoirard, J., 1992. A method for delineating and estimating rainfall fields. Water Resour. Res. 28 (4), 1133–1144. Bryan, G.H., Wyngaard, J.C., Fritsch, J.M., 2003. Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev. 131, 2394–2416.
Fig. 6. Hourly rainfall depth field for selected turbulence parameterization/grid spacing combinations and for microphysical settings corresponding to graupel (left column) and hail (right column).
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Atmospheric Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a t m o s
Uncertainty in prediction of deep moist convective processes: Turbulence parameterizations, microphysics and grid-scale effects E. Fiori a,⁎, A. Parodi a, F. Siccardi a,b a b
CIMA Research Foundation, Via Magliotto 2, 17100 Savona, Italy DIST, University of Genova, Via all'Opera Pia 13, 16145, Genova, Italy
a r t i c l e
i n f o
Article history: Received 20 January 2010 Received in revised form 1 October 2010 Accepted 2 October 2010 Keywords: Microphysics High resolution Turbulence parameterizations Deep moist convection Numerical modeling
a b s t r a c t A line of development of numerical meteorological forecast, common to many European and American Meteorological Organizations, schedules a drastic reduction of the grid spacing for the realization of limited-area predictions. The scientific community has been discussing such an issue whether this approach can be of real advantage for the solution of the problems of the uncertainty of the decision-maker. The extraordinary enhancement of the computer power could indeed promote this drastic reduction of the modeling horizontal resolution just because “nowadays it is possible”. However this “brute-force” approach to the question of the solution of the problem of nowcasting does not guarantee a priori improvement of forecast skill. In this framework, deep moist convective processes in simplified atmospheric scenarios (e.g. supercell) are studied in this paper by means of high-resolution numerical simulations with COSMO-Model. Particular attention is paid to determine whether and at which extent the convection-resolving solutions, in the range of grid spacing between 1 km and 100 m, statistically converge from a turbulence perspective with respect to flow field structure, transport properties and precipitation forecast. Different turbulence closures, microphysics settings and grid spacings are combined and their joint impact on the spatial–temporal properties of storm processes is discussed. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The increasing availability of computational power makes possible the numerical modeling of severe weather events at unprecedented fine mesh-scale (Xue et al., 2007). While the rapid progress of high-resolution numerical modeling has the potential for enabling a deeper understanding of the spatial– temporal properties of deep moist convective processes and related intense rainfall phenomena, it also calls for a better understanding of the uncertainty associated with the adoption of different physical parameterizations. In this respect, the assessment of effects of subgrid-scale closures such as those associated with microphysics and turbulence processes
⁎ Corresponding author. E-mail address: elisabetta.fi[email protected] (E. Fiori). 0169-8095/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2010.10.003
on fine mesh-scale modeling has been subjected to growing attention. From a microphysics perspective and in a direct numerical simulation (DNS) limit, several studies have focused their attention on the interaction between turbulence and microphysics to gain an in-depth understanding of the broadening cloud-droplet spectra. Among others, Ayala et al. (2008a,b) and Wang et al. (2008) tried to quantify the effects of the vertical motion on the droplet growth and the liquid-water transport. Hence, some investigations aimed at the evaluation of both the turbulence effects on the motion and the concentration of the droplets as well as of the collision efficiency (Franklin et al., 2005) and the stochastic coalescence (Wang et al., 2005). In a large-eddy simulation (LES) framework, Jiang and Cotton (2000) studied the sensitivity of shallow marine cumulus convection to different microphysics and radiation
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schemes to understand how drizzle affects the turbulent fluxes and surface precipitation. Morrison and Grabowski (2007), instead, developed a two-moment warm rain bulk microphysics scheme suitable for addressing the indirect impact of atmospheric aerosols on ice-free clouds. The focus was on the prediction of supersaturation, activation of cloud droplets, and the representation of microphysical transformations associated to parameterized turbulent mixing. For horizontal resolutions ranging from the cloud permitting (CPM) to the cloud resolving (CRM) limits (e.g. 4– 0.1 km), many studies have tried to assess the precipitation uncertainty due to variations in precipitating species parameters (Grabowski, 2003; Gilmore et al., 2004; Grubišić et al., 2005; Liu and Moncrieff, 2007; Hong et al., 2009). Grabowski (2003) investigated the impact of cloud microphysics on global radiative–convective quasi-equilibrium in a constantSST aquaplanet, with simulations at 1 km grid spacing. The results show that cloud microphysics affects mainly the quasi-equilibrium temperature and moisture profiles while the relative humidity is only marginally influenced. In their study, instead, Gilmore et al. (2004) reported on the sensitivity of accumulated precipitation to the microphysical parameterization in simulations of deep convective storms at 1 km grid spacing with a single-moment bulk liquid–ice microphysics scheme. Various intercept parameters from a prescribed Marshall–Palmer exponential size distribution are evaluated along with two particle densities for the hail/ graupel species. The results suggested that the amount of accumulated ground precipitation is very sensitive to the way the hail/graupel category is parameterized. Distributions characterized by larger intercepts and/or smaller particle density have a smaller mass-weighted mean terminal fall velocity and produce smaller hail/graupel mixing ratios spread over a larger area. With respect to the prediction of precipitation over complex orography areas, Grubišić et al. (2005) examined the skill of a MM5 model, run at 1.5 km grid spacing, during high-impact precipitation events in the Sierra Nevada, and the sensitivity of that skill to the choice of the microphysical parameterization and horizontal resolution. Again, at convection-permitting grid spacing, Liu and Moncrieff (2007) investigated the effects of cloud microphysics parameterizations on simulations of warm-season precipitation The objective was to assess the sensitivity of summertime convection predictions to the bulk microphysics parameterizations at fine-grid spacings applicable to the next generation of operational numerical weather prediction models. Based on their results, a general conclusion about the desirable degree of sophistication in the microphysics treatment and their performance was not achievable. Hong et al. (2009) examined the relative importance of ice-phase microphysics and sedimentation velocity for hydrometeors in two bulk microphysics schemes, the Single-Moment 6-Class Microphysics Scheme (WSM6) and the Purdue–Lin scheme, for a 2D idealized storm case and for a 3D heavy rainfall event over Korea. This study provided the relative role of ice-phase microphysics and fall velocity for ice particles in the bulk-type parameterization approach of clouds and precipitation, and allows to gain a deeper understanding of the cloud and radiation interaction in forming precipitating convection. Furthermore, it appears clear that the impact of the number of prognostic water species variables on simulated convective
processes is smaller than the effects of the formulation of each microphysical process in the same category of prognostic water species variables. From a turbulence parameterization point of view, some recent studies tackled the novel research issue in the modeling of deep convective processes at a very fine resolution (Bryan et al., 2003; Wyngaard, 2004; Fiori et al., 2009, 2010): the joint choice of the turbulence parameterization (or closure) and grid spacing. Two important categories of meteorological numerical approaches exist for the simulation of severe weather events with domain size ranging between 3000 km and 1 km (Wyngaard, 2004): mesoscale modeling on the larger domains and large-eddy simulation (LES) on the smaller ones. The mesoscale modeling aims to weather prediction at horizontal grid spacing of the order of O(10 km) while LES is, traditionally, focused on fine scale Planetary Boundary Layer (PBL) convective processes with a resolution of the order of O (0.1 km). In traditional mesoscale modeling, the typical mesoscale grid spacing largely exceeds the energy-containing turbulence scale l so that little or no turbulence is resolved. Contrary, in LES, the energy and flux-containing turbulence eddies are resolved. The recent possibility of simulating convective systems with very fine resolution makes the distinction between mesoscale and LES model disappearing and since neither mesoscale nor LES turbulence closures were designed to operate in this range, Wyngaard (2004) named it “terra incognita”. Thus a new scientific question arises about the source of uncertainties associated with the use of such two turbulence closure approaches in the “terra incognita”. In this respect, looking for convergence solution for squall lines, Bryan et al. (2003) studied the spatial resolution appropriate for the simulation of deep moist convection from a turbulence perspective. Numerical simulations of squall lines were conducted with grid spacing between 0.125 and 1 km. The results revealed that simulations with 1 km grid spacing do not produce equivalent squall line structures and evolution as compared to the higher-resolution simulations, in terms of precipitation amount, system phase speed, cloud depth, thunderstorm cells size, and organizational mode of convective overturning. Wyngaard (2004) addressed the topic of numerical modeling in the “terra incognita”, corresponding to grid spacing between 0.1 and 1 km, to assess the pertinence for this scales range of turbulent parameterizations valid in the mesoscale (1D, also known as boundary-layer approximation type, Stull, 1988) and LES limits. Along the same lines, Fiori et al. (2010) tried to understand how the uncertainty in the modeling of deep moist convective processes is affected by adoption of smaller grid spacing and by the choice of the turbulent closure used to represent subgrid-scale processes. Bearing in mind this overview, to the best authors knowledge, the potential joint effects of different turbulence closures, microphysics parameterizations and grid spacings on the modeling of the deep moist convective processes, in the “terra incognita” range (0.1–1 km), has been never addressed. This topic is here tackled for a simplified convective scenario corresponding to a supercell. Different turbulent closures, microphysics settings and grid spacing are combined
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in order to create an “ensemble” of fine resolution numerical simulations and their joint impact on the spatial–temporal properties of storm processes is discussed by using appropriate graphics and statistics analysis to study the simulations results. The paper is organized as follows. Section 2 provides a brief overview about the convective scenario considered, the limited-area model used, and its setting in terms of turbulence and microphysics parameterizations. Section 3 describes the results that arise by comparing the numerical experiments in terms of supercell trajectories and rainfall patterns. In Section 4 the conclusions are given. 2. The case study A supercell convection scenario is adopted in this study. This convective scenario has been largely analyzed and studied in literature (Weisman and Klemp, 1982, 1984, 1986; Rotunno and Klemp, 1985). The well-known dynamics and thermodynamics allow an effective comparison of the different numerical simulations in order to evaluate the sensitivity of the convective phenomenon in relation to the changes in the settings of the model. The model is initialized with a thermal bubble superimposed on a homogeneous field. The bubble setting is defined according to Fiori et al. (2010). The horizontal radius of the bubble is 10 km. The vertical one is 1.4 km and the temperature excess is of 2 °C at the center decreasing gradually to 0 °C at the edge. The bubble is placed at (25 km, 25 km) in the horizontal domain to avoid influence of the boundary on its development in the first time steps of integration. The vertical profile of moisture and temperature are those adopted in Weisman and Klemp (1982, 1984), corresponding to a CAPE value around 1600–1700 J/kg: they are depicted in Fig. 1. A directionally varying wind shear is one of the main factors that
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determine supercell motion: in this study the shear vector turns through 180° over the lowest 5 km of the atmosphere, while the wind becomes constant in direction and speed above 5 km. The curvature of the clockwise-curved hodograph is strong enough to favor a right-moving supercell. From a computational point of view, we adopt COSMOModel which is a nonhydrostatic and fully compressible numerical weather prediction model created in 1998 by the Deutsche Wetterdienst (DWD, German National Weather Service) and developed to provide a flexible tool for various scientific applications on a broad range of spatial scales (Steppeler et al., 2003). The model is run over a three-dimensional domain that is of 150 km in both horizontal directions and it is extended to 20 km in height. The vertical coordinates are stretched gradually from ~80 m near the bottom boundary to ~ 500 m near the top one. Four horizontal grid spacings are considered: Δ = 1 km, 0.5 km, 0.25 km and 0.2 km. The model is integrated up to 3 h and the time steps are set to 6, 3, 1.5 and 1 s, respectively, from 1 km to 0.2 km runs. The experiments are realized neglecting orography and Coriolis forces. Davies (1976) and free-slip conditions are applied to the lateral and ground boundaries, respectively. Rayleigh layer characterizes the top-5 km of the atmosphere. Three turbulent parameterizations are adopted in this study, in agreement with the companion paper of Fiori et al. (2010): the first one is called 1D turbulent closure which makes use of the so-called boundary-layer approximation (Steppeler et al., 2003) for the computation of the vertical H diffusion coefficients for momentum KM V and heat KV and it is complemented by a horizontal computational mixing term (Smolarkiewicz et al., 1997) designed to remove shortwave grid-scale noise from fields. The second one is called 3D turbulent closure in which the vertical diffusion coefficients H for momentum KM V and heat KV are computed as in the 1D
Fig. 1. Skew-T diagram depicting dew point temperature (heavy dashed line) and temperature (heavy solid line) profiles used in numerical simulations. The green lines depict the saturation mixing ratio. Blue ones, the dry adiabats. Red ones, the moist adiabats. Tilted black ones, the isotherms.
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case, while the horizontal turbulent coefficients are assumed M H H equal to the vertical ones (K M V = K H , K V = K H), thus no additional numerical computational mixing operator is active in such a closure. The last one is called LES turbulent closure which uses a three-dimensional subgrid-scale model instead of the boundary-layer approximation, so that both vertical and horizontal turbulent coefficients are active (Herzog et al., 2002). With respect to microphysics, simulations have been performed using a single-moment bulk microphysics scheme with two different microphysical settings (Table 1). As shown in Table 1, differences are in terms of the intercept parameter N0x of the exponential Drop Size Distribution (DSD) with x corresponding alternatively to the two solid precipitating water categories investigated, i.e. graupel (x = G) and hail (x = H), the values of the density ρx and the parameters a, b, c and e of velocity–size and mass–size relationships: VT = aDb m = cDe where VT is the terminal velocity and m the mass (Doms et al., 2007). The choice of the aforementioned parameters aims to mimic graupel and hail as defined in Straka (2009) and in according to the parameters values and methodological approach already adopted in Gilmore et al. (2004), Liu and Moncrieff (2007), Reinhardt and Seifert (2006) and Snook and Xue (2008) for grid spacing in the range of 0.1–1 km: graupel/hail category may be a very important species that influences the quantity and type of precipitation received at the ground in many types of severe thunderstorms. Thus, small Nx0 and large values of density change the properties of the particle ensemble: more hail-like behavior appears, particles fall faster and melting is reduced. More unmelted graupel/hail can reach the ground (Lin et al., 1983; Cheng et al., 1985; Heymsfield and Kajikawa, 1987; Rutledge and Hobbs, 1984). For sake of clarification, the plot of the adopted velocity–size relationship for graupel (x = G) and hail (x = H) are shown (Fig. 2). 3. Results 3.1. The trajectory The path of the main convective core entire was captured by tracking the pixel which contains the maximum vertical velocity at the elevation of 5 km. The paths for graupel and hail cases, determined over the two hours of simulations, are plotted in Fig. 3. For the graupel case, the LES-driven paths, corresponding to Δ = 0.5, 0.25 and 0.2 km, collapse each on the other. For the 1D closure, the convergence is not yet reached at Δ = 0.2 km.
Table 1 Parameters adopted for graupel and hail species.
Graupel Hail
ρx g cm− 3
Nx0 m− 4
a m(1 − b)s− 1
b
c kg m− e
e
0.2 0.9
4·106 4·104
442 140
0.89 0.5
169.6 471.2
3.1 3.0
It is worth to highlight that the horizontal spatial distance between the 1 km-1D path and the 0.2 km-LES ones in the final stages of the simulation is about 20 km, largely exceeding the original size of the supercell. For the hail case, instead, the convergence is faster, and, whatever is the adopted turbulence parameterization, the paths collapse each on the other when Δ = 0.25 km. Furthermore, the paths for the LES-driven runs exhibit a smaller curvature with respect to the graupel LES-driven ones, and also the horizontal spatial distance between the 1 km-1D path and the 0.2 km-LES is reduced to 10 km. Thus, the hail-driven experiments show a smaller spread in the trajectory of main convective core corresponding to the supercell: this result suggests that the microphysical setting largely determines the properties of this convective scenario and also their convergence from a turbulence closure perspective. A deeper understanding of the differences induced by the graupel and hail settings can be gained by investigating the structure of the cold pool for the experiments that exhibit the farthest trajectories, which are 1 km-1D and 0.2 km-LES. The cold pool intensity and low-level storm dynamics are found to be very sensitive to the intercept parameters of graupel/hail category drop size distributions (Snook and Xue, 2008). Snook and Xue (2008) argue that DSDs favoring smaller (larger) hydrometeors result in stronger (weaker) cold pools due to enhanced (reduced) evaporative cooling/ melting over a larger (smaller) area. To evaluate this issue, we considered the horizontal cross-sections of potential temperature θ [K] at 0.5 km AGL after 5400 s (Fig. 4). The strength and the size of the cold area related to the downdraft of dry air on the back side of the updraft give in fact a measure of the high pressure due to the ground level spreading of the cold downward. At first glance, Fig. 4 suggests that cold pool extension is more sensitive to changes in horizontal resolution and turbulence parameterization when we consider the graupel microphysical setting, while for the hail one it stays almost the same. In fact, for graupel simulations, there is a general increase of the cold area towards the west part of the domain when finer resolutions and LES closure are used. This is connected to the intensification in the vertical velocity field particularly on the left flank of the system. For the hail simulations, instead, the achievement of more stable configuration appears to be faster, since all the main “large” scale cold pool features are already present in the 1 km-1D closure, when compared with the 0.2 km-LES ones, and this may explain also results of Fig. 3 (lower panel) in terms of faster convergence of the supercell trajectory. It is also worth to mention that hail experiments, due to the larger size of hydrometers and higher terminal velocity, produce more intense updrafts in agreement with some recent theoretical arguments (Parodi and Emanuel, 2009) and as supported by Fig. 5. From Fig. 5, it appears that the mid-level updrafts are similar in magnitude in the 1 km-1D graupel and hail runs, and similar in the 0.2 km-LES graupel and hail runs. Thus, updraft strength is strongly influenced by the grid spacing but not so much by the different microphysics schemes. However, from Fig. 4 it appears that the magnitude of the cold pool is similar in the two hail runs, which are yet much weaker in the
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Fig. 2. Velocity–size relationship for graupel and hail. An approximate identification of the size range for the two ice species is also provided.
1 km-1D graupel run compared to the 0.2 km-LES graupel run. Thus, the grid spacing influences the structure of the cold pool while the magnitude/strength of the cold pool is influenced by both the grid spacing and the microphysics. 3.2. The rainfall field The analysis of the supercell trajectory for different simulations suggested that different microphysical settings,
concerning graupel and hail respectively, may strongly affect the dynamical and thermodynamical structures of the convective flow field, and also the convergence of the convection-resolving solutions from a turbulence closure perspective. Bearing in mind this framework, we tried also to quantify if and to which extent similar arguments are valid for the predicted rainfall field. Thus, the maps of rainfall depth over the time window between the 1 h and 2 h from the initialization of the process are depicted (Fig. 6): the maps
Fig. 3. Path of the core of the right-moving cell in its relative motion in the first two hours of all 12 simulations (upper panel: graupel, lower panel: hail).
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Fig. 4. Horizontal cross-sections of the potential temperature field at z = 500 m and t = 5400 s (upper row: graupel, lower row: hail).
are prepared for both microphysical settings (graupel and hail) and for a subset of the possible turbulence closure/grid spacing combinations, that is 1 km-1D, 1 km-1D, 0.25 km-LES, 0.2 km-1D and 0.2 km-LES. First, for a prescribed turbulence closure–grid spacing combination, the influence of microphysical parameterization is evident both in terms of spatial distribution and intensity of the rainfall depth fields. Indeed, in hail-driven maps the peaks of rainfall are twice of those produced by graupel-driven ones. The parameters of the fall speed–size relationships for graupel/ hail category are the most responsible for the differences in maps of Fig. 6 in agreement with findings of Grabowski (2003), and Parodi and Emanuel (2009). Second, at fine-grid spacing (0.25–0.2 km), the rainfall spatial rainfall distribution is different: it appears to move from a classical supercell structure (graupel cases) to a multicell one (hail cases), composed of a cluster of convective cells at various stages of their life (Fovell and Tan, 1998). Finally, from a turbulence perspective and within each microphysical setting (graupel and hail), some degree of
convergence in the hourly rainfall depth fields seems to be achieved for LES-driven experiments and for finer grid spacings (0.25–0.2 km): in this respect, both for graupel and hail cases, the hourly rainfall depth field as predicted by the 0.2 km-LES experiment is assumed as “ground truth”. In order to evaluate the degree of convergence of the rainfall depth fields in Fig. 7, we adopted the Rousseau index (RI, Barancourt et al., 1992), as a method to cluster simulation results (Giuli et al., 1999; Sangati and Borga, 2009): h RIðthr Þ =
2
4⋅p11 ⋅p00 −ðp10 + p01 Þ
i
½2⋅p11 + p10 + p01 ⋅½2⋅p00 + p10 + p01
where: • thr: predefined threshold (related to the weather field choice) for the calculation of the RI between the reference field (“ground truth” by 0.2 km-LES experiment) and the target (prediction provided by another experiment) on the
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Fig. 5. Horizontal cross-sections of the vertical velocity field at z = 5000 m and t = 5400 s (upper panel: graupel, lower panel: hail).
•
•
•
•
common selected domain. In this work the threshold is equal to 4 mm; p11: percentage of pixels in the spatial domain in which both the reference field and the target field are both greater than the specified threshold; p10: percentage of pixels in the spatial domain in which the target field is above the threshold while the reference one is below this threshold; p00: percentage of pixels in the spatial domain in which both the reference and the target fields are both lower the threshold choice; p01: percentage of pixels in the spatial domain in which the target field is below the threshold while the reference one is above this threshold.
The RI may range between 1 (complete agreement) and −1 (complete disagreement) between the reference field and the target one. The RI has been evaluated, both for graupel and hail cases, by comparing the 0.2 km-LES hour rainfall depth (Fig. 6) with
the other 4 rainfall depth-cases (after spatial interpolation over the same grid spacing if necessary), as summarized in the following: • • • •
Case Case Case Case
I: 0.2 km-LES versus 1 km-LES II: 0.2 km-LES versus 1 km-1D III: 0.2 km-LES versus 0.25 km-LES IV: 0.2 km-LES versus 0.2 km-1D.
Fig. 7 confirms that hail-driven experiments (lower panel) are more effective in the convergence of the spatial structure of the rainfall depth field as already observed in the case of the supercell trajectory. For case III, the RI values for the hail case are higher than graupel ones whatever is the rainfall threshold, thr. Furthermore, Fig. 7 (lower panel) supports the idea that hail-driven cases exhibit more similar rainfall depth fields at finer grid spacings (case IV) even if characterized by 1D closure. Consequently, once more, microphysics seems to determine the convergence of convective flow field properties from a turbulence closure perspective.
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Fig. 7. Rousseau index plot for 1 h rainfall depth map (upper panel: graupel, lower panel: hail).
4. Conclusions Turbulence closures and microphysical parameterizations are recognized to be important sources of uncertainty in highresolution numerical modeling of deep moist convection processes (Bryan et al., 2003; Gilmore et al., 2004). In this respect, this study has tackled the challenging problem of assessing the sensitivity of a modeled supercell to different combination of physical parameterizations for subgrid processes (turbulence and microphysics) and the grid spacing in the resolution ranges between 0.1 and 1 km. The results suggest that differences in supercell propagation and the uncertainty in its physical representation are reduced when a suitable grid spacing in combination with an adequate turbulent and microphysical parameterization are chosen. The use of the LES closure, with both microphysics settings, implies a more intense turbulent activity at fine-grid scale with respect to the other two closures, 1D and 3D. Furthermore, for this case study, microphysics largely determines deep moist convective properties, as found also in another study by Gilmore et al. (2004). In this respect, for graupel-driven runs, the convective-resolving solutions does “converge”, with respect to the overall flow field structure,
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Fig. 6. Hourly rainfall depth field for selected turbulence parameterization/grid spacing combinations and for microphysical settings corresponding to graupel (left column) and hail (right column).
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