1. Introduction
The initiation of deep convection is often characterized by a variety of processes interacting on different spatiotemporal scales, from Rossby waves down to cyclonic systems, mesoscale circulations, and ultimately the cloud microscale. Under weak synoptic forcing, boundary layer and soil-surface processes exert strong influence over convective initiation (e.g., Banta 1990). Even when the convection is driven mainly by synoptic-scale features, mesoscale and local-scale processes can still influence the exact location(s) and timing of initiation. Thus, a broad range of scales must be accurately represented by operational forecasting models to enable accurate prediction of deep convection.
Advances in computer power have made numerical weather prediction (NWP) possible over limited-area domains with O(1 km) grid spacing, allowing for convection to be represented explicitly rather than by a convection parameterization. Although such grid spacings are able to explicitly represent large convective clouds, they fail to fully resolve important turbulent features at smaller scales that regulate cloud development and precipitation production (Bryan et al. 2003). Even so, Lean et al. (2008), Roberts and Lean (2008), Kain et al. (2008), Weisman et al. (2008), and Schwartz et al. (2009) have all shown that convection-permitting models yield qualitatively more realistic precipitation fields and are quantitatively more skillful than lower-resolution simulations with parameterized convection.
One factor limiting convective-scale predictability is the sensitivity of convective processes to the errors inherent to numerical models, i.e., initial condition (IC) and lateral boundary condition (LBC) uncertainties, errors introduced by parameterized physics and numerical errors introduced by discretizing the fluid-dynamical equations of the atmosphere. Of particular interest to this study are uncertainties in the large-scale meteorological conditions that drive convective-scale NWP models, which can lead to errors in the moist instability and the vertical motions that initiate convection (among other things).
Ensemble prediction is a promising technique for dealing with these uncertainties. The success of short-range limited-area ensemble prediction systems with grid spacing of order 10 km in improving quantitative precipitation forecasts (e.g., Marsigli et al. 2004, 2005) led Kong et al. (2006, 2007) to develop convective-scale ensembles with a horizontal grid length of 3 km. They found that even a small ensemble provided greater skill than a single deterministic forecast with the same grid spacing. Numerous techniques have been proposed for generating convective-scale ensembles, including perturbing the initial state (e.g., Hohenegger et al. 2006; Hanley et al. 2011), varying the parameterized physics (e.g., Berner et al. 2011; Leoncini et al. 2010), and using a combination of the above techniques (e.g., Clark et al. 2010; Gebhardt et al. 2011). These studies suggest that physics uncertainties determine the spread during the first few hours of the simulation, while the LBCs become more important later.
The precise impact of different sources of uncertainty depends strongly on the larger-scale conditions in which convection develops. Stensrud et al. (2000) compared the performance of a perturbed initial condition ensemble with a perturbed model physics ensemble for two mesoscale convective systems (MCSs) using a limited-area model with 25-km horizontal grid spacing. They found that the initial condition ensemble was more skillful than the perturbed model physics ensemble when the large-scale forcing for ascent was strong, but the perturbed physics ensemble was more skillful when the large-scale forcing was weak. Similarly, Vié et al. (2011) studied convective-scale ensembles for two Mediterranean heavy precipitating events (HPEs). Three ensembles were downscaled from a global ensemble, thus assessing the uncertainty in ICs and LBCs, and an additional ensemble was created by assimilating randomly perturbed observations at the convective scale. They found that when the synoptic-scale dynamics were predominant in driving the HPE, the precipitation forecast was more sensitive to the LBCs, whereas when the HPE was driven by local processes, the forecast was more sensitive to convective-scale uncertainties.
Ensembles are not only useful as a technique for improving forecasts—they can also provide physical insight into the mechanisms leading to severe weather and their multiscale sensitivities. Compared to the common approach of manually modifying deterministic simulations to evaluate hypothesized mechanisms (e.g., Lean et al. 2009), ensembles allow for a more natural identification of these mechanisms and a robust quantification of their sensitivities. Emerging studies have adopted this approach to demonstrate how subtle errors inherited through ICs and LBCs transfer down to the small scale (Argence et al. 2008; Reinecke and Durran 2009; Hanley et al. 2011). Advancing on this theme, this paper investigates the mechanisms and large-scale sensitivities of an intense squall line observed during the Convective and Orographically Induced Precipitation Study (COPS; Wulfmeyer et al. 2008). The main objective is to physically interpret the role of large-scale uncertainties on the quantitative precipitation forecast (QPF) skill of a convective-scale ensemble. Section 2 provides an overview of the event and the numerical setup. The ensemble is verified against observations in section 3, and section 4 discusses the physical mechanisms and sensitivities of the simulated convection. Conclusions are provided in section 5.
2. Case overview
The French Vosges and German Black Forest Mountains, which straddle the Rhine valley in west-central Europe, were chosen as the focus for the COPS campaign (e.g., Wulfmeyer et al. 2008, 2011). The geography of this region and its relation to other relevant geographic landmarks is shown in Fig. 1. This region is characterized by a high frequency of summertime convection initiation through slope and valley wind systems (Barthlott et al. 2006), but a low skill of operational convection forecasts. For example, Schwitalla et al. (2008) performed simulations of 13 cases of summertime convection over this region using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). They found that with parameterized deep convection the simulations suffered from three types of systematic errors: the windward/lee effect (where precipitation is overestimated on the windward side and underestimated on the lee), convection initiation occurred several hours too early, and the peak rain rates were underestimated. For simulations with explicit convection these errors were strongly reduced; however, precipitation was underestimated and the timing error changed into a lag of about 2 h. Another example of poor forecast skill over this region was provided by Barthlott et al. (2011), who analyzed an ensemble of eight cloud-permitting-model realizations of a thunderstorm event over the Black Forest. The models produced a wide range of results: only five of them simulated convective precipitation in the COPS region, with only three simulating an intense storm in approximately the correct location.
(a) Map of western Europe. The rectangle indicates the area shown in (b). (b) Terrain of the COPS and near upstream region. The Rhone valley separates the Massif Central and the Alps and the Rhine valley separates the Vosges and the Black Forest. The rectangle indicates the COPS domain and the black circle indicates the radiosonde station at Burnhaupt le Bas. Orography height is shown in m.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
The COPS intensive observing period 9c (IOP9c) case on the morning of 20 July 2007 was selected for this study because the development of deep convection was influenced by a variety of processes on different spatiotemporal scales. Forcing associated with a midlatitude cyclone led to the formation of an MCS overnight over France, which transitioned into an intense squall line as it approached the COPS region. Using the extensive COPS observational network, Kottmeier et al. (2008) and particularly Corsmeier et al. (2011) provide detailed analyses of the mechanisms behind the squall-line evolution over the COPS region. However, as will be seen in the sections to follow, a much broader view of this event is required to understand its predictability and large-scale sensitivities.
a. Operational analyses and observations
The synoptic-scale evolution during 1800–0600 UTC 19–20 July 2007 is depicted by the Met Office analysis fields in Fig. 2. The 500-hPa geopotential height and 1000–500-hPa thickness fields reveal an upper-level trough centered south of Ireland at 50°N, 7.5°E, along with a baroclinic zone extending across continental Europe (Fig. 2a). As shown by the mean sea level pressure pmsl and 850-hPa wet-bulb potential temperature θw fields at this time, a broad and weak trough of surface low pressure extended northwest from the baroclinic zone across northern France and the British Isles (Fig. 2c). Ageostrophic ascent over northwest France overnight, in the left-exit region of the jet streak on the forward edge of the upper-level trough, deepened the surface low, leading to a strengthened cyclonic circulation (Figs. 2b,d). This developing system drew high-θw air into its central core as the thermal gradient tightened over central France (Fig. 2d).
Met Office analysis fields. (a),(b) 1000–500-hPa thickness (m, gray contours) and 500-hPa height (m, black contours); (c),(d) θw on 850 hPa (K, filled contours), U850 (m s−1, vectors), and pmsl (hPa, black contours). (a),(c) 1800 UTC 19 Jul 2007 and (b),(d) 0600 UTC 20 Jul 2007. The thin black lines show the 0.5-km terrain contours. The solid and dashed white lines in (d) roughly show the position of the surface cold front and the midlevel front, respectively.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
Snapshots from the Met Office 5-km European radar composite (Nimrod; Golding 1998) during the morning hours in Fig. 3 show the MCS propagating eastward across central France along with a cyclonically rotating rainband centered over the southern United Kingdom. Whereas the former coincides with a region of strong cyclonic vorticity advection aloft, the latter forms near the surface low center and beneath the jet-exit region (see Figs. 3b and 2b).
Rain rate (mm h−1) from the Met Office’s Nimrod system at (a) 0300, (b) 0700, (c) 1000, and (d) 1100 UTC. The thin black lines show the 0.5-, 1-, and 1.5-km terrain contours, and the boxed area represents the COPS region.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
The MCS evolved from a broad and disorganized system at 0300 UTC into a tighter, more linear band at 1000 UTC as it crossed the COPS terrain (Figs. 3a–c). Although Fig. 3 gives the impression of continuous propagation across France and Germany, this propagation consisted more of a sequence of discrete forward-initiation events. Notably, the intense “primary” squall line just to the west of the Vosges at 0700 UTC (Fig. 3b) developed suddenly ahead of the weakening MCS, and the new band of intense cells over the Black Forest at 1100 UTC (the “secondary” squall line) developed ahead of the primary squall line after it dissipated within the Rhine valley. The latter cells were initiated when the cold pool ahead of the decaying squall line encountered the thermally driven upslope flow on the eastern side of the Black Forest (Corsmeier et al. 2011).
The vertical structure of the convective inflow is shown by a high-resolution COPS sounding from Burnhaupt le Bas at the southern end of the Rhine valley (see Fig. 1 for location) at 0800 UTC in Fig. 4. This sounding shows a strong nocturnal inversion overlaid by a residual boundary layer from the previous day, topped by a deep layer of nearly saturated and conditionally unstable south-southwesterly flow. Although the convective available potential energy (CAPE) of a surface-based parcel in this sounding is moderate (1052 J kg−1), the convective inhibition (CIN) for that parcel is over 100 J kg−1. By contrast, a parcel originating at 2500 m has a much lower CIN (10 J kg−1; and a lower CAPE of 252 J kg−1), suggesting that the convection was initiated well above the boundary layer (as is common for nocturnal convection).
Rawinsonde from Burnhaupt le Bas (47.7°N, 7.17°E) at 0800 UTC 20 Jul 2007. The solid (dashed) line shows the temperature (dewpoint). Wind vectors are plotted in kt (1 kt = 0.5144 m s−1), with short (long) barbs representing 5 (10) kt, and filled flags representing 50 kt.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
b. Model description and ensemble setup
The ensemble simulations are performed using the Met Office Unified Model (MetUM), version 7.3. The model uses a semi-implicit, semi-Lagrangian numerical scheme to solve the nonhydrostatic, deep atmosphere dynamics (Davies et al. 2005). The horizontal grid is rotated in latitude–longitude and uses Arakawa C staggering, while the vertical grid uses a terrain-following hybrid-height coordinate with Charney–Philips staggering. The model uses a comprehensive set of parameterizations, including a convection scheme based on Gregory and Rowntree (1990), a nonlocal boundary layer scheme (Lock et al. 2000), a surface layer scheme (Essery et al. 2001), a radiation scheme (Edwards and Slingo 1996), and a mixed-phase cloud microphysics scheme (Wilson and Ballard 1999).
The ensembles are generated using the Met Office Global and Regional Ensemble Prediction System (MOGREPS; Bowler et al. 2008). The ensemble setup is explained in detail in Hanley et al. (2011) so only a brief description is given here. During the COPS period the Met Office operationally produced a global ensemble consisting of one unperturbed control forecast along with 23 members with perturbed ICs and model physics. The IC perturbations are generated using an ensemble transform Kalman filter. To address model error two stochastic schemes are used to perturb the parameterized model physics. The “random parameters” scheme targets uncertainty caused by the choice of tunable parameters within the microphysics, convection, and boundary layer parameterization schemes and the “stochastic convective vorticity” scheme addresses uncertainty due to organized convection that is unresolved on the model grid.
The global ensemble provides LBCs for the regional ensemble on the North Atlantic and European (NAE) domain (see Fig. 5). This grid has 300 × 180 horizontal grid points with a spacing of 0.22° (approximately 24 km) and 38 vertical levels. The NAE ensemble is initialized from the 1800 UTC 19 July 2007 regional analysis, which includes operational data assimilation and excludes any special observations from the COPS network. The NAE ensemble uses IC perturbations derived from the global ensemble. These perturbations are introduced in small increments during the first 2 h of the simulations to avoid impulsively shocking the model. Model-physics error is also addressed in the NAE ensemble using only the random parameters scheme; the stochastic convective vorticity scheme is not used.
Domains used for the NAE, 12-, 4-, and 1-km models. The orography height (m) of the NAE domain is shown in grayscale.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
Bowler et al. (2008) have shown that MOGREPS provides good spread-skill performance on the NAE domain, thus it serves as a reliable parent ensemble from which to downscale to the convective scale. The NAE ensemble is dynamically downscaled using a suite of one-way nested models of 12-, 4-, and 1-km horizontal resolution that gradually zoom in on the COPS domain (Fig. 5). The LBCs for the 12-km domain, which has 150 × 150 horizontal grid points and 38 vertical levels, are produced by the NAE ensemble. Similarly, the 4-km domain is driven by LBCs from the 12-km ensemble and has 370 × 300 points in the horizontal, and the 300 × 190 horizontal grid point 1-km domain uses LBCs from the 4-km ensemble. Whereas the NAE and 12-km grids use 38 vertical levels, the 4- and 1-km domains both use 70 vertical levels for improved explicit representation of convective storms. The control simulation is started at 1800 UTC on all domains and the perturbed simulations are started at 2100 UTC on the 12-, 4-, and 1-km domains, immediately after the IC perturbations are fully added to the NAE domain. The simulations are run for 24 h without any additional data assimilation or model physics perturbations. The neglect of the latter is justified by the strong large-scale forcing in this case and the 6–12-h lead time before deep convection developed. In such cases, the impact of model physics perturbations is generally much smaller than that of IC and LBC perturbations (e.g., Stensrud et al. 2000; Gebhardt et al. 2011).
The Gregory and Rowntree (1990) mass flux convection scheme is used on the NAE and 12-km domains with a CAPE adjustment time scale of 30 min. A modified version of the Gregory–Rowntree convection scheme is used in the 4-km model (Roberts 2003). This restricts the parameterized convective cloud-base mass flux except when the CAPE is very small, allowing the model to explicitly represent most of the deep convection. The 1-km model does not use a deep convection scheme.
3. Comparison with observations
Figure 6 compares the instantaneous rain rates at 1100 UTC from a few members of the NAE ensemble with radar-derived values from the Met Offices’s Nimrod European radar composite at 5-km resolution. The NAE rain rates are a summation of the resolved and parameterized rain rates. For ease of reference, the simulations are named according to their member number within the ensemble (control, Pert01, Pert02, etc). Pert06 and Pert20 have been chosen for comparison because, as will be seen in section 3a, they lie at opposite ends of the ensemble verification and therefore help to characterize the ensemble spread (note that the term “spread” herein is broadly defined as the range of ensemble forecast realizations and is not assigned a quantitative value). At this time, the primary squall line that developed over eastern France and crossed the Vosges has weakened within the Rhine valley, but a new band of convective cells have developed over the lee of the Black Forest (Fig. 6a), which shortly thereafter organizes to form the secondary squall line. The simulations capture the organized convection to the north of the COPS region reasonably well, albeit with some mesoscale errors (Figs. 6b–d). However, the position of the simulated convection within the COPS region lags the observations by up to 200 km. The initiation of new cells over the Black Forest has not occurred in any of these members, owing to a delayed arrival of the primary squall line over the COPS region. The cold pool from this squall line, which was a primary mechanism behind the secondary initiation over the Black Forest (Corsmeier et al. 2011), has yet to cross the Rhine valley.
Rain rate (mm h−1) at 1100 UTC 20 Jul 2007 from (a) the Met Office’s Nimrod system, (b) the NAE control simulation, (c) Pert06, and (d) Pert20. The thin black lines show the 0.5-, 1-, and 1.5-km terrain contours, and the boxed area represents the COPS region.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
To ascertain whether increased grid resolution improves the simulated squall-line timing, Fig. 7 shows the instantaneous rain rate from the same three members of the 1-km ensemble compared with that derived from the Deutscher Wetterdienst (DWD) radar composite (with a horizontal resolution of 2.8 km). Among these members, only in the Pert20 case does the simulated convection keep pace with the observations and develops over the Black Forest at roughly the correct time (Fig. 7d). Despite providing a better representation of the initiation, Pert20 is still not perfect: it develops too much precipitation in the Rhine valley, and the intensity and placement of the Black Forest convection disagrees slightly with the radar observations.
Rainfall rate (mm h−1) at 1100 UTC 20 Jul 2007 from (a) the DWD radar composite, (b) the 1-km control simulation, (c) Pert06, and (d) Pert20. The thin black lines show the 0.5-, 0.75-, and 1-km terrain contours. The black dashed lines in (b)–(d) show the estimated squall line position as plotted in Fig. 8. The rectangle in (a) shows the region used for rainfall verification in section 3.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
To view the ensemble as a whole, Fig. 8 shows the position of the squall line at 1100 UTC in each member of the 1-km resolution ensemble compared with that from the DWD radar composite (these positions were subjectively estimated by finding a line that best represented the maximum rain rates across the main precipitation band). To show how this was done, the lines for the Control, Pert06, and Pert20 have been added to the corresponding panels in Fig. 7. Each line is clearly characterized by a positional uncertainty of ±30 km or so. Nonetheless, two clusters are apparent: one over the Vosges and one over the Black Forest. This gap between the two clusters is owing to the strong suppression of convection within the Rhine valley, which causes the heaviest precipitation to fall on either side of it. Although a couple of members (including the aforementioned Pert20) accurately simulate the observed squall-line position, the convection in most simulations trails the observations by 50–200 km. Thus, although finer resolution does improve the simulated positioning of the convection, most of the members are still plagued by significant errors that, as will be seen, are inherited from the larger grids and propagate into the domains through their lateral boundaries. Despite these positional errors, all members of the high-resolution ensemble captured the secondary squall-line initiation, revealing that the model was sufficiently accurate on the large-scale and possessed sufficiently fine resolution to resolve the terrain features. The success of this ensemble in that aspect is notable given that models failed to represent this case as accurately without the benefit of high-resolution data assimilation (e.g., Schwitalla et al. 2011).
Position of the squall line at 1100 UTC 20 Jul 2007 for each member of the 1-km resolution ensemble. The solid black line shows the position of the observed squall line, the gray dashed line shows the control, the black dashed line shows Pert06, and the black dot–dashed line shows Pert20. The thin black lines show the 0.5-, 0.75-, and 1-km terrain contours.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
a. The SAL method
Traditional rainfall verification methods such as mean-square error are based on gridpoint comparisons between modeled and observed precipitation. Such methods can be problematic for high-resolution precipitation forecasts with finescale structure as they are unfairly penalized due to small positional errors (the “double penalty” problem; e.g., Baldwin et al. 2001; Roebber et al. 2004; Wernli et al. 2008; Roberts and Lean 2008). To address these issues, new verification techniques have been developed specifically for higher spatial and temporal resolution forecasts. These largely fall into three categories: neighborhood based (e.g., Roberts and Lean 2008), scale decomposition (e.g., Casati et al. 2004), and feature based (e.g., Ebert and McBride 2000). Here we consider a feature-based rainfall verification technique called structure, amplitude, and location (SAL; Wernli et al. 2008). This method identifies features in the simulated and observed fields and then assesses their structure, amplitude and location (as the name suggests). Here we provide only a brief description of the SAL diagnostics and refer interested readers to Wernli et al. (2008) for the full mathematical formulation.
The amplitude component A corresponds to the difference of the domain-averaged precipitation values of the modeled rain rates, D(Rmod), and the observed rain rates, D(Robs), normalized by D(Rmod) + D(Robs). Values of A range from −2 to 2, where 0 denotes a perfect forecast and A = 1 (−1) indicates that the model overestimates (underestimates) the precipitation by a factor of 3.
The structure component S compares the area of the modeled and observed precipitation fields normalized by their sum, providing a measure of both the size and shape of the precipitation objects. The values of S lie within ±2. Positive values of S occur if the model predicts too large or too flat precipitation objects and negative values occur if the model predicts too small or too peaked objects.
The location component L consists of two parts (L1 and L2) that are added together to measure the accuracy of the precipitation placement within the domain. The first component L1 measures the distance between the centers of mass of the modeled and observed precipitation fields, normalized by d, the largest distance across the domain. The values of L1 are bounded by 0 and 1, where 0 denotes that the two precipitation fields share the same center of mass. Since it is possible for two very different precipitation fields to have the same center of mass, the second component L2 distinguishes such fields by considering the averaged distance between the center of mass of the total precipitation fields and the individual precipitation objects. The values of L2 are also bounded by 0 and 1, so that L is in the range 0–2. Note that L2 is only nonzero if there is more than one precipitation object in the domain.
To compute the L2 and S components, individual precipitation objects are first identified in both the modeled and observed domains. Following Wernli et al. (2009), the threshold value used to define coherent precipitation objects is defined as R* = R95/15, where R95 is the 95th percentile of all gridpoint values in the domain exceeding 0.1 mm h−1. To compute the SAL diagnostics we compare the modeled rainfall data with that derived from the DWD radar composite. For verification of the 4- and 1-km ensembles, the model rain rates and the radar-derived rain rates are all smoothed to a 4-km horizontal resolution grid for fair comparison. For verification of the NAE ensemble, the radar rain rates are smoothed to the model grid length of 24 km. To focus on the COPS region, this verification is initially computed over the region 47.6°–48.8°N and 6.4°–10°E, which is encompassed within all the model domains and also the DWD radar composite (see Fig. 7).
b. Accumulated rainfall
Figure 9a shows the three SAL components computed using the accumulated precipitation over 0800–1400 UTC 20 July from the 4-km ensemble. For the entire ensemble, A lies between 0 and 1, indicating that the precipitation accumulation during this period is overestimated by up to a factor of 3. On average A ≈ 0.75, which corresponds to an overestimation factor of 2.2. Note that it is well documented (e.g., Hitschfield and Bordan 1954) that radar generally underestimates heavy rainfall because of attenuation, so the simulations may not be overestimating the rainfall as much as the verification suggests. The S component is distributed around zero, in the range ±0.75, with the ensemble mean very close to zero. This indicates that the size and shape of the accumulated precipitation is generally accurately simulated in a mean sense. Squall lines in the members with the largest A overestimation tend to possess a significantly larger spatial extent than the observed squall line, as indicated by the positive values of S. Despite exhibiting a lag in the timing of the precipitation, most of the ensemble members have L < 0.25. This is because the temporal error of ≈2 h is less than the accumulation period and because the simulated precipitation falls mainly over the Vosges and northern Black Forest, as in reality.
SAL components computed over the COPS region using the 0800 to 1400 UTC rainfall accumulations derived from the DWD radar composite and (a) the 4-km ensemble and (b) the 1-km ensemble.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
The SAL components computed using the accumulated precipitation from the 1-km ensemble are similar to those from the 4-km ensemble (Fig. 9b). As expected from Fig. 7, all members overestimate the total amount of rainfall, although by a very small amount in a few members. The ensemble mean accumulation is slightly lower for the 1-km ensemble than for the 4-km ensemble, suggesting a slight bias reduction through the use of finer grid resolution. The values of S lie around zero, as in the 4-km ensemble, and most members also have L < 0.25. A pattern which is more noticeable in the 1-km ensemble but still evident in the 4-km ensemble is that members with negative values of S tend to have lower values of A than members with S > 0. Thus, as seen in other studies (e.g., Wernli et al. 2009), the cumulative rainfall over the domain is larger when the precipitation is more widespread.
c. Instantaneous rainfall
To examine the time evolution of the ensemble precipitation verification, Fig. 10 shows the A component for the NAE, 4- and 1-km ensembles during the period 0800–1400 UTC. Initially, all members of the NAE ensemble underestimate the rainfall amount (Fig. 10a), which is due to the ≈2-h time lag of the simulated squall line. Between 1000 and 1200 UTC a larger spread is found in the NAE simulations with some members overpredicting the domain-averaged rainfall and others underpredicting it. However, the ensemble mean is close to zero, reflecting an unbiased instantaneous rainfall forecast. By 1200 UTC most members of the NAE ensemble overestimate the rainfall because the simulated squall line, which in reality has already passed through the COPS region, remains within this region. A larger initial spread is found in both the 4- and 1-km ensembles compared with the NAE ensemble, because the squall line in some members has advanced farther east, in some cases into the COPS region (Figs. 10b,c). However, most members still lag reality and thus underestimate the rainfall. By 1000 UTC the spread narrows in the high-resolution ensembles as the convective precipitation is fully contained within the COPS domain, with all members overestimating the rainfall. Few obvious differences are apparent between the 4- and 1-km ensembles apart from one outlier in the 1-km ensemble where the squall line leaves the domain just after 1200 UTC.
The A component of SAL computed over the COPS region using the DWD radar derived rain rates and the rain rates from (a) the 24-km NAE ensemble, (b) the 4-km ensemble, and (c) the 1-km ensemble. The gray lines show the ensemble members and the black line is the ensemble mean.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
The S component (not shown), indicates that once the simulated squall lines reach the verification domain, the ensembles tend to predict rainfall objects that are too large and flat (S > 0), as was qualitatively evident in Figs. 6 and 7. However, the high-resolution ensembles provide more accurate representations of the object sizes and shapes compared to the NAE ensemble, with S values closer to zero.
Figure 11 shows the L1 and L2 components for the NAE, 4-, and 1-km ensembles, in which the values of L1 are converted into a distance (in km) by multiplying by d = 307.8 km, the size of our verification domain. The L1 component is initially modest in all ensembles, with errors of less than 100 km in the NAE ensemble (Fig. 11a) and less than 50 km in the high-resolution ensembles (Figs. 11c,e). All ensembles show an increase in L1 between 0900–1100 UTC, gradually exposing the simulated errors in squall-line position as the observed squall line propagates through the domain. After 1100 UTC, the location errors are comparable in each ensemble. In all of the NAE simulations, and most of the high-resolution simulations, the squall line entered the domain too late, and the new convective cells in the Black Forest initiated too late. However, because of their improved performance (see Fig. 8), L1 remains relatively small (<50 km) in a few members of the high-resolution ensembles (including Pert20). This improvement is particularly noticeable between 0900–1200 UTC, the period over which the observed squall line moved across the domain. The L2 component is larger in the NAE ensemble (Fig. 11b) than the high-resolution ensembles (Figs. 11d,f), indicating that the high-resolution ensembles better represent the position of the individual precipitation objects, particularly when convection initiated over the Black Forest between 1000–1300 UTC. Both components of L increase after 1300 UTC when the simulated squall line remained within the COPS domain after having exited this area in reality.
As in Fig. 10, but for the L1 and L2 components. The black dashed line shows Pert06 and the black dot–dashed line shows Pert20.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
Because the L1 component provides the most direct representation of the positional error of the simulated squall line, we study its time evolution in more detail. At 0900 UTC most of the simulated squall lines have entered the verification domain and the L1 profiles in Fig. 11 range from very small values to nearly 100 km. Examination of the subsequent error trajectories on the high-resolution grids show that the simulations with the smallest L1 at 0900 UTC continued to yield the best verification scores throughout the 0900–1300 UTC period (Figs. 11c,e). Thus, the proficiency of the different members in representing the convection over the COPS region was apparently linked to positional errors as the squall line entered the COPS domain through its lateral boundaries.
To investigate the origin of these lateral boundary errors, we have computed the L1 component over a large part of France (see region denoted in Fig. 13a) using the rain rates derived from the Met Office’s Nimrod system and the instantaneous rain rates from the 4-km ensemble. Figure 12a shows that although initially most members have errors of less than ≈50 km in the position of the original MCS, the ensemble diverges after 0500 UTC, with the ensemble mean L1 increasing from 25 km to more than 100 km. Note that this larger L1 value (cf. those found in the COPS domain; see Fig. 11) follows from the consideration of a different verification region with more precipitation objects. Figure 12b shows both the absolute standard deviation of L1 (
(a) SAL L1 component computed over the box in Fig. 13 using the Nimrod radar derived rain rates and the rain rates from the 4-km ensemble. The black solid line shows the ensemble mean, the dashed lines show the poor-performing members with Pert06 in black (i.e., composite B), and the dotted–dashed lines show the best-performing members with Pert20 in black (i.e., composite A). (b) Standard deviation of the SAL L1 component computed in (a) (solid line) and standard deviation of the SAL L1 component computed in (a) normalized by the mean instantaneous rain rate (dashed line).
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
Comparison of radar-derived rain rates at 0730 UTC with three 4-km ensemble members in Fig. 13 reveals that all members capture the basic structure of the convection but tend to err in its location. Pert20 best captures the forward initiation ahead of the MCS (shown by the circled region just to the west of the Vosges in Fig. 13a), although the leading edge of the convection is still weaker and less organized than in reality on this grid (Fig. 13d). A weak precipitation band also forms in the control simulation (Fig. 13b), but it does not subsequently develop into an intense squall line (not shown). A primary squall line ultimately does develop in all of the members, but generally 1–2 h too late. Both Pert20 and Pert10 (not shown) capture the timing of this initiation more accurately, and henceforth continue to outperform other members of the ensemble throughout most of the forecast period. This reinforces that the accurate representation of the primary squall-line initiation over France was critical for accurately simulating the secondary squall line over the Black Forest.
Rainfall rate (mm h−1) at 0730 UTC 20 Jul 2007 from (a) the Met Office’s Nimrod system, (b) the 4-km control simulation, (c) the 4-km pert06 simulation, and (d) the 4-km pert20 simulation. The thin black lines show the 0.5-, 0.75-, and 1-km terrain contours. The black rectangle in (a) shows the region over which the L1 component is computed in Fig. 12 and the black ellipse highlights the primary squall line.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
4. Mechanisms and large-scale sensitivities
In this section we focus on physically interpreting the difference in the precipitation forecasts of the ensemble members. We begin by closely analyzing the convection initiation mechanism for the primary squall line over France, which, as previously shown, controlled the timing of convective precipitation over and upstream of the COPS region. We then apply this understanding to analyze the ensemble spread. This analysis begins with a decomposition of the ensemble into two small performance-based clusters, from which we compare composite fields. These composites help to qualitatively link errors in QPF on the convective scale to uncertainties in the representation of meso- and synoptic-scale features, which, as stated in section 1, is the main objective of this study. Finally, we test our emerging hypotheses for the multiscale sensitivities of this event using an ensemble sensitivity analysis that considers the whole 24-member ensemble.
a. Squall-line initiation
Figure 14 shows the overnight evolution of the specific humidity and vertical velocity (q and w) fields for the 4-km ensemble Pert20 member at 700 hPa, roughly the level with minimum CIN in Fig. 4. Also shown is the θ = 307-K contour, which roughly indicates the position of the midlevel front, along with areas where surface precipitation rates exceed 1 mm h−1. While the main moisture anomaly associated with the MCS was located behind (i.e., to the west of) the midlevel front, a mesoscale moisture anomaly extending eastward from the MCS moved north through the Rhone valley ahead of the front and expanded in coverage (Figs. 14a,c). This anomaly served as the site of convection initiation at around 0700 UTC (Fig. 14e). Because this branch of enhanced moisture was already present in the model initialization at 1800 UTC, we are unable to identify its exact origin from these simulations. However, we speculate that its strengthening over time reflects an increased rate of frontal ascent, which brings moister low-level flow up to the 700-hPa level.
Progression of the midlevel moisture anomaly in the Pert20 simulation at 700 hPa at (a),(b) 0400; (c),(d) 0600; and (e),(f) 0730 UTC 20 Jul 2007. (a),(c),(e) Filled contours show q in g kg−1, vectors show the winds, the black line (θ = 307 K) represents the midlevel frontal position, and the white contours show surface precipitation exceeding 1 mm h−1. In (a) “M” denotes the mesoscale moisture anomaly and “F” denotes the midlevel front. (b),(d),(f) Filled contours show w in m s−1 with the frontal position indicated by the black line. In all panels the thin black lines show the 0.5-km orography contours.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
As shown by the w field in Figs. 14b,d, a region of organized ascent developed ahead of the midlevel front between 0400–0600 UTC with a more chaotic vertical motion pattern associated with the MCS behind the front. As the prefrontal moisture anomaly was advected northward, the frontogenetical ascent lifted it enough to overcome the weak midlevel CIN. Soundings at the leading edge of the moisture anomaly (not shown) showed an elevated layer of moist air rising from 715 hPa at 0400 UTC to 675 hPa by 0600 UTC. For Pert20 the CIN of an air parcel lifted from within this layer decreased from 29.7 J kg−1 at 0400 UTC to 14.5 J kg−1 at 0600 UTC and the level of free convection dropped from 4.13 to 3.66 km. Thus, the forward initiation in this event appears to be associated with a transition from postfrontal convection behind the midlevel front to prefrontal convection ahead of it. This mechanism also explains why the precipitation pattern transitioned from a disorganized MCS (within a broad area of large-scale ascent and moist instability) into a quasi-linear convection band (within a narrower area of frontal ascent).
The robustness of the above mechanism across the ensemble is illustrated in Fig. 15 by back trajectories that terminate at cloud base near the center of the developing squall line and extend backward 3 h. Four members of the 4-km ensemble are considered: two that verified well using the SAL L1 component (Pert10 and Pert20) and two that verified poorly (Pert03 and Pert06). Although the timing of initiation differs among these ensemble members, the back trajectories reveal similar patterns: q remains roughly constant as z gradually increases, indicating nearly adiabatic lifting. Note that the initial values of q are relatively large (6–8 g kg−1), which reflects that they all possess similar moisture contents as that within the mesoscale moisture anomaly ahead of the front (see Fig. 14). This moist air undergoes ≈0.5–1 km of prefrontal slantwise ascent as it travels northward, which increases over time as the front strengthened. Note that this gradual frontal lifting contrasts from the rapid and sudden ascent that might be expected from a propagating cold pool ahead of the MCS and therefore argues against cold pools as the initiation mechanism of the primary squall line.
Back trajectories from the cloud base near the center of the developing squall line of (a) q in g kg−1 and (b) z in km MSL, for Pert10 (black solid line), Pert20 (black dashed line), Pert03 (gray dashed line), and Pert06 (gray solid line).
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
b. Composites
We present composites of q and w on 700 hPa on the 4-km domain at 0600 UTC in Fig. 16. The compositing is not meant to be a rigorous statistical analysis, but a means to generate a hypothesis that can then be tested using the full ensemble in section 4c. For this purpose we want a very clear signal to emerge that excludes any marginal members. Thus, we only choose three representative members for each composite: composite A is an average of Perts 04, 10, and 20, which all verify well using the SAL method, and composite B is an average of Perts 02, 03, and 06, which all verify poorly (see Fig. 11). Compared to composite B, the entire frontal development appears to be 1–2 h ahead in composite A. The frontal ascent is generally stronger and located farther to the east, and the moisture anomaly is farther north. The higher values of q and the wider extent of the moisture anomaly at this time appear to result from a stronger cross-frontal circulation, which draws more moisture into the elevated prefrontal region. The more northward placement of this feature in composite A is associated with stronger advection in the faster along-frontal southerly flow. These differences give rise to significant improvements in the squall-line representation in composite A. The timing is improved because the stronger frontal lifting more rapidly brings the prefrontal air to saturation, and the positioning is improved because the prefrontal moisture anomaly and the front itself are situated closer to the Vosges.
Comparison of composite representations of 700-hPa moisture and vertical motion. (a),(c),(e) q in g kg−1 and (b),(d),(f) w in m s−1 at 0600 UTC for (a),(b) composite A (Perts 04, 10, and 20); (c),(d) composite B (Perts 02, 03, and 06); and (e),(f) the difference between composite A and composite B. In (f) the difference field has been smoothed to a horizontal resolution of 24 km. The white contours in the left-hand panels show the rain rate exceeding 2.5 mm h−1 and the thick black line (θ = 307 K) represents the midlevel frontal position. The thin black lines show the 0.5- and 1-km orography contours.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
The sensitivity of the squall-line position to the broader development of the parent midlatitude cyclone is shown by composite averages of pmsl on the NAE domain in Fig. 17 at 0600 UTC. Composite A possesses a deeper low pressure center over northern France and the southeast United Kingdom (Figs. 17a,b), which is associated with a stronger cyclonic circulation. Although composite A already possessed a slightly lower minimum MSLP over a small part of this region on the previous evening (not shown), the two composites diverged substantially overnight as surface cyclogenesis occurred more rapidly in composite A. Figures 17c and 17d, which subtract the Met Office 0600 UTC analysis of pmsl from the two composites, show that the stronger circulation in composite A agrees better with the analysis, with errors of ±0.5 hPa in the vicinity of the low pressure center (Fig. 17c). By contrast, composite B has a weaker low pressure center by up to 2 hPa along with lower pressure over the Massif Central (Fig. 17d). The stronger cyclonic circulation in composite A, which extends throughout the troposphere, helps to explain why the midlevel front develops faster (stronger geostrophic forcing), why the MCS and midlevel front propagate faster to the east (stronger westerly advection over France), and why the moisture anomaly propagates more quickly northward (stronger southerly advection in the warm sector).
Comparison of composite representations of pmsl. (a),(b) Composites of pmsl (mb, thick black contour), rain rate exceeding 2.5 mm h−1 (gray contour), and orography height (km, filled contours) at 0600 UTC for (a) composite A (Perts 04, 10, and 20) and (b) composite B (Perts 02, 03, and 06). (c),(d) The difference in mb between each composite and pmsl from the Met Office analysis at 0600 UTC for (c) composite A and (d) composite B. The thin black lines show the 0.5- and 1-km orography contours and the black rectangle shows the outline of the COPS region.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
Next we look at the composites of larger-scale features at upper levels. The upper-level trough over the eastern Atlantic in Figs. 2a,c is associated with a strongly positive potential vorticity (PV) anomaly, a feature that was responsible for flooding precipitation over the southern United Kingdom on 20 July (Blackburn et al. 2008). Figure 18 shows PV on the θ = 330-K surface (PV330) on the NAE grid at 2100, 0300, and 0600 UTC for each composite, as well as the differences between composites A and B. The PV anomalies in the two composites are similar at 2100 except for subtle differences in their internal PV distribution. Whereas the initial PV gradients are strongest along the eastern and southern edge of the anomaly in composite A (Fig. 18a), they are the strongest along the western edge in composite B (Fig. 18d). This gives rise to a dipole structure in the composites differences (Fig. 18g), with positive values along the eastern edge of the anomaly and negative values over the western edge. At later times, the PV maximum shifts to the western United Kingdom and the Irish Sea and consolidates into a stronger “S shaped” core in composite A (Figs. 18b,c). By contrast, this central PV maximum is weaker in composite B, with a secondary maximum persisting along the western edge of the anomaly (Figs. 18e,f). The PV anomaly also becomes more cyclonically wrapped over time in composite A compared to the more meridionally elongated anomaly in composite B, penetrating farther into Europe along its southern flank (by approximately 1° or 100 km) but retrograding over the United Kingdom. These uncertainties in the initial PV representation and its evolution on the low-resolution grid are transferred to the higher-resolution grids through their ICs and the LBCs.
Composite representation of PV on the θ = 330-K surface in potential vorticity units (PVU; 1 PVU = 10−6 K m2 kg−1 s−1) for (a)–(c) composite A, (d)–(f) composite B, and (g)–(i) the difference between composite A and B. (a),(d),(g) 2100, (b),(e),(h) 0300, and (c),(f),(i) 0600 UTC. The thick black contours in (a)–(f) show the regions where the rain rate exceeds 2.5 mm h−1. In all panels the black lines show the 0.5- and 1-km orography contours and the black rectangle shows the outline of the COPS region.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
To relate the differences in initial PV330 on the low-resolution domain to differences in the squall-line timing on the high-resolution domain for the ensemble, Fig. 19 shows a scatterplot of the time (in UTC) that the squall line crossed the Black Forest on the 1-km grid against PV330 (in PVU) averaged over the eastern flank of the anomaly (43.5°–52.5°N, 7.25°–2.5°W) at 2100 UTC on the NAE grid for each ensemble member. The time the squall line crossed the Black Forest was estimated as the time when the 1-km rain rate averaged over a box covering the northern Black Forest exceeded 1 mm h−1. The negative correlation (shown by the linear regression line excluding two outlying members) indicates that the members with higher PV330 over the eastern flank of the anomaly simulated squall lines that crossed the Black Forest earlier, and thus showed improved timing relative to those members with lower PV330 over this region. This reinforces the findings of the compositing analysis.
Scatterplot showing the time in UTC that the squall line crossed the Black Forest on the 1-km grid against PV330 in PVU averaged over 43.5°–52.5°N, 7.25°–2.5°W on the NAE grid at 2100 UTC. The black line shows a linear regression line fitted to the data (excluding two outliers).
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
Based on the composite analysis presented herein, we hypothesize a chain of processes by which the subtle initial differences in the upper-level PV between the two composites may have led to their substantial differences in QPF. The tighter initial PV gradient along the southeast edge of the anomaly in composite A was associated with a stronger jet streak across eastern Spain and southern France (see Fig. 2 for the jet streak position). Stronger upper-level diffluence in the jet left-exit region over northern France and the United Kingdom was associated with stronger ageostrophic ascent (this has been confirmed but is omitted here for brevity) and faster cyclogenesis (Fig. 17a). The increased upper-level forcing and low-level cyclogenesis in composite A led to increased precipitation: the 2100–0600 UTC accumulated precipitation over the United Kingdom and northern France is 24% higher than in composite B. This resulted in a stronger diabatically generated PV minimum aloft, which noticeably strengthened the upper-level PV gradients over the United Kingdom by 0600 UTC (see rightmost column of Fig. 18). Combined with the action of the stronger low-level circulation, this caused the PV anomaly to become more cyclonically wrapped in composite A, with its southern flank bulging farther eastward into northern France and its northern flank retrograding westward. The faster cyclogenesis and deeper propagation of the PV anomaly into continental Europe strengthened the midlevel front and forced it to propagate farther east in composite A (Fig. 16). As a consequence, the prefrontal convection developed earlier and farther to the east in this composite.
Note that the ensemble error growth found here may be slightly less than that obtained from a two-way nesting procedure. Although feedback between diabatic heating (within the cyclone core and the nocturnal MCS) and the larger scales is permitted on the larger convection-parameterizing grids, it is only partially represented on the grids with explicit convection (the 4-km grid likely captures most, but not all, of these feedbacks). As shown by Zhang et al. (2003) and others, convective-scale uncertainties can propagate upscale and influence the parent cyclone dynamics. Thus, the more chaotic explicit convection on the smaller grids, when fed back to the larger grids, may lead to faster overall error growth. Nonetheless, because both the 12- and 4-km grids are likely to have adequately captured the dominant feedbacks, we are confident in the robustness of our results.
c. Ensemble sensitivity analysis
The above compositing analysis suggests that the faster squall-line development in composite A is linked to variations in the large-scale dynamics, specifically upper-level PV structures. To more quantitatively demonstrate this sensitivity for the whole ensemble, we have adopted the ensemble sensitivity analysis technique of Ancell and Hakim (2007), which was developed as an ensemble analog to adjoint sensitivity analysis. Ensemble sensitivity analysis has been applied to determine optimal locations for observation targeting and to evaluate climatological sensitivities (Ancell and Hakim 2007; Torn and Hakim 2008; Garcies and Homar 2009). It consists of a linear regression to compute the change in a chosen forecast metric J to a unitary perturbation in the initial condition field x so that the raw sensitivity is given by S = ∂J/∂x. A correction factor R is applied to S to deemphasize points with a low correlation coefficient r. Following Garcies and Homar (2009), we set R = r2/c2 at all points where r2 < c2 and R = 1 when r2 ≥ c2, where c is the minimum correlation coefficient for which the sensitivities remain unaltered. In the sensitivities computed here, a relatively high value of c = 0.5 is used to remove points with small sensitivity values and highlight the areas with large sensitivity (although the results presented are robust to the value chosen for c).
Finally, to link the sensitivity to the ensemble skill, the raw sensitivity is multiplied by the standard deviation σx of x at each location. This allows us to look at the projection of initial uncertainty onto the ensemble sensitivity. The final sensitivity field, S = ∂J/∂x × Rσx, is the response of J to a perturbation in x of typical amplitude σx at each location. The units of the final sensitivity are thus the same as those of J. The comparison between the raw sensitivity and the variance-weighted sensitivity shows similar large-scale patterns around the PV anomaly but more mesoscale details over eastern Europe. Some of these small-scale details are likely a by-product of our small ensemble size (24 members). Moreover, given the dominant westerly flow of this event, these mesoscale features are unlikely to have a causal link to convection initiation over France 6–12 h later. Thus, the weighted sensitivity analysis gives a cleaner view of the synoptic-scale sensitivities that we hypothesize control the evolution of convection over France.
Here we apply ensemble sensitivity analysis (again, using all 24 ensemble members) to determine the sensitivity of mesoscale features on the higher-resolution grids (e.g., squall-line position) to the initial representation of synoptic-scale features on the coarser grids. Because this technique is most applicable for output metrics that vary linearly on the input state, its utility to highly nonlinear convective flows is uncertain. However, as will be seen, it does provide meaningful signals if suitable metrics are chosen. Figure 20a shows the sensitivity of pmsl averaged over a box covering northern France and southeast United Kingdom on the 4-km grid at 0600 UTC, just before the primary squall line develops, to PV330 on the NAE grid at 2100 UTC the previous day (just after the initial perturbations are fed into the ensemble). Large negative sensitivities along the southeast boundary of the PV anomaly and within its core (extending southward from the Irish Sea) indicate that the higher values of PV330 there are associated with smaller pmsl over the target region. By contrast, positive values to the west of the main PV anomaly indicate that those higher values of PV330 are associated with larger pmsl over the target region. This agrees with the compositing analysis of section 5b in that the presence of larger PV along the anomaly’s east-southeastern edge gives rise to stronger low-level cyclogenesis (the opposite is true when larger PV is positioned along the western flank of the anomaly).
Ensemble sensitivity of (a) pmsl (hPa), (b) w (m s−1), (c) U700 (m s−1), and (d) the SAL L1 component (km) all on the 4-km grid at (a)–(c) 0600 and (d) 0900 UTC to PV330 on the NAE grid at 2100 UTC. The pink line shows the 7-PVU contour of the ensemble mean PV330. The rectangle shows the area over which the forecast metric has been averaged on the 4-km domain. The thin black lines show the 0.5- and 1-km orography contours.
Citation: Monthly Weather Review 141, 1; 10.1175/MWR-D-12-00013.1
We now examine the sensitivities in the prefrontal region where the convection develops. Because the ascent and southerly winds ahead of the midlevel front are tied to the strength of the cyclonic circulation, they are also strongly linked to the upper-level PV structure. This is reinforced by Figs. 20b,c, which show the sensitivities of the mean w and the horizontal wind magnitude U at 700 hPa on the 4-km grid at 0600 UTC to PV330 on the NAE grid at 2100 UTC (where the output metrics are averaged over a small box directly ahead of the midlevel front). The sensitivity pattern is similar to that in Fig. 20a but with the signs reversed, suggesting that the presence of high PV along the southeastern edge of the anomaly leads to stronger cross-frontal and along-frontal circulations.
Finally, to directly relate the squall-line position to the upper-level PV, we show the ensemble sensitivity of the SAL L1 component (computed over the COPS region on the 4-km domain at 0900 UTC) to PV330 on the NAE grid, again at 2100 UTC (Fig. 20d). Because L1 is calculated from the highly nonlinear precipitation field, the sensitivity field is rather noisy. However, a dominant pattern still emerges that is similar to Figs. 20a–c: strong negative sensitivity (i.e., L1 is reduced) is found when the initial PV is higher along the eastern anomaly edge and when its interior values over the United Kingdom and the Irish Sea are larger. As in Fig. 18, this sensitivity pattern moves with the PV anomaly through the overnight hours (not shown).
5. Summary and conclusions
Convective-scale ensemble simulations carried out with the Met Office Unified Model have been used to study the mechanisms and large-scale sensitivities of a squall line over western Europe as it initiated and crossed over mountainous terrain. The high-resolution ensembles were obtained by downscaling from the 24-km MOGREPS regional ensemble through a series of embedded finer nests (12, 4, and 1 km). The case study was IOP9c of the COPS field campaign where a “primary” squall line developed ahead of a decaying MCS and then propagated over the COPS region. The squall line dissipated as it descended into the Rhine valley, then regenerated as a “secondary” squall line over the Black Forest as its low-level cold pool collided with thermally driven upslope flow. The use of a high-resolution ensemble allowed us to investigate the sensitivities of the simulated squall-line representation to the larger-scale dynamics.
The suite of ensembles captured the primary and secondary squall lines, but were generally plagued by a 1–2-h delay in the primary and secondary squall-line initiations, which led to a 50–150-km positional error over the COPS domain and a phase error in the onset of intense precipitation. The use of high resolution improved the numerical representation of the squall line, with a few members of the 4- and 1-km ensembles predicting the squall-line timing and position much more accurately. However, most members of those ensembles still suffered from significant positional and timing errors.
The forward initiation of the primary squall line occurred upstream of the COPS domain as a meridionally oriented midlevel cold front strengthened ahead of the MCS over central France. This resulted in a transition in the convective organization from a disorganized region of cellular precipitation into a more focused frontal band. The initiation was facilitated by a midlevel moisture anomaly ahead of the front that became more pronounced as it propagated northward through the prefrontal environment upstream of the Vosges.
To explain the differences in the squall-line representation across the ensemble, we first created two three-member clusters based on their verification scores and compared composite fields derived from these clusters. Because this event was largely driven by synoptic-scale processes, the focus was placed on the sensitivity of the squall-line representation to uncertainties in broader meso- and synoptic-scale features. A subtle but critical difference between the composites was found in their representation of a large-scale potential vorticity (PV) anomaly over the Atlantic Ocean. The more accurate composite possessed a stronger initial PV gradient along its southeastern flank and a stronger jet streak across eastern Spain and western France. This gave rise to stronger ageostrophic ascent in the jet left-exit region above a developing surface low over northern France and the southern United Kingdom, which promoted low-level cyclogenesis. The stronger geostrophic flow aloft over Europe and faster cyclogenesis in this composite hastened the development and propagation of both the midlevel frontal circulation and the midlevel moisture anomaly. As a consequence, the squall line initiated earlier and farther to the east, which agreed better with observations. The sensitivity of the system development and squall-line initiation to the initial upper-level PV distribution was reinforced through ensemble sensitivity analysis.
This study suggests that subtle differences in synoptic-scale features may have a substantial impact at the meso- and convective scales, which here manifests as positional and timing errors in the simulated convective storms. Such sensitivities to the large-scale were also observed by Roebber et al. (2002). Thus, events that are broadly predictable at the synoptic scale may be significantly more uncertain at the convective scale, even when model-physics uncertainty is neglected. This is consistent with the notion of increasing error-growth rates on the convective scale, as discussed by Lorenz (1969) and Hohenegger and Schär (2007). It also helps to explain the results of Vié et al. (2011) and Gebhardt et al. (2011), who showed that larger-scale uncertainty begins to dominate forecast error at lead times of 6–12 h and depends on the synoptic regime. Once larger-scale errors grow to sufficient amplitude, the strong convective-scale sensitivities to these errors begin to dominate the ensemble error growth. Thus, convective-scale uncertainties should always be viewed not just in the context of uncertainties in small-scale features and model-physics parameterizations, but also in the context of larger-scale uncertainties. In the present case, such an analysis was used to successfully identify the relevant meteorological processes controlling ensemble error growth. Routine evaluation of ensemble prediction systems should also incorporate such analyses, beyond simple domainwide statistics.
Acknowledgments
This work was funded through the Natural Environment Research Council through Grant NE/E016391/1. We are grateful to the Met Office for making the MetUM available and for archiving the ensemble perturbations during the COPS period. We thank the National Centre for Atmospheric Science (NCAS) Computational Modelling Support (CMS) for their technical support throughout this study. We thank Klaus Stephan of Deutscher Wetterdienst (DWD) for providing the German radar data used for verification over the COPS region, and the British Atmospheric Data Centre (BADC) for providing the Met Office Nimrod radar data. The radiosonde data from COPS were collected by Martin Kohler of Forschungszentrum Karlsruhe. We also thank Lorena Garcies and Sue Gray for valuable input at different stages of this project.
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