Comparison of instability indices from COSMO-I7 and ECMWF-IFS analyses over the Piedmont Region, Italy, and new modifications to the K Index

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1 METEOROLOGICAL APPLICATIONS Meteorol. Appl. 23: (2016) Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: /met.1582 Comparison of instability indices from COSMO-I7 and ECMWF-IFS analyses over the Piedmont Region, Italy, and new modifications to the K Index Paolo A. Bertolotto* and Guido Roggero ARPA Piemonte Sistemi Previsionali, Turin, Italy ABSTRACT: This paper presents a statistical analysis of heavy rain events recorded by the high resolution network of ARPA Piemonte (Piedmont Region Environmental Protection Agency) rain gauges between 2007 and In order to define convective heavy rain events over the region, a rainfall threshold of 10 mm in 20 min was chosen. Events were sampled at intervals of 6 h for the warning areas of the Piedmont Region, Italy, and their distribution was studied in relation to the values of instability indices obtained from the European Centre for Medium Range Weather Forecasts Integrated Forecasting System and the COnsortium for Small-scale MOdeling (COSMO)-I7 operational analyses. The performances of the indices of the two meteorological models were investigated for the different warning areas in a pseudo-operational weather forecasting context, obtaining useful information in the phase of issuing thunderstorm early warnings. The second part of the work had the goal of improving the performance of these indices, modifying the one that showed better verification results in terms of receiver operating characteristic (ROC) area increase and the K Index (K I ). This was done by introducing dependences on the thickness of geopotential height and wind direction at different levels. K I modifications that displayed better results were called reduced K Index (K R ), obtained by dividing K I by the thickness of geopotential height between 500 and 850 hpa, and K W, obtained by adjusting the K R value with additive constants depending on the wind direction at different levels. K W in particular led to a net improvement of the performance of the original K I over the region. KEY WORDS instability; indices; thunderstorm; Italy; performance; ROC; diagram; Alps Received 8 April 2015; Revised 2 March 2016; Accepted 16 March Introduction Forecasting convective heavy rain events in the Alps is a difficult challenge. Past studies have shown that although the Alps are essential for synoptic forcing (Cacciamani et al., 1995), their complex orography plays an important role in the formation and development of storm cells (Costa et al., 2001). The use of high resolution Numerical Weather Prediction (NWP) convective precipitation fields can be counterproductive because it can lead to more realistic, but not always more accurate, rainfall patterns (Roberts et al., 2008; Morgillo, 2011). NWP convective precipitation patterns often show large errors, both in intensity and in localization (Anquetin et al., 2005). There is an evident predictability problem for convective precipitation NWP, even with a perfect representation of synoptic conditions; this phenomenon seems due mainly to the Alpine region complex orography (Walser and Schär, 2004; Walser et al., 2004; Hohenegger et al., 2006). The best approach for Alpine region thunderstorm and heavy rain forecasting seems to be based on initial analysis of synoptic forcing with subsequent evaluation of the environmental instability. Convective precipitation NWP should be used only as another predictor of thunderstorm occurrence (Schmeits et al., 2005). Atmospheric instability in the Alps must be evaluated mainly by instability indices; these should not be used alone as magic bullets but, instead, combined with the experience of weather forecasters and their knowledge of Alpine complex terrain. Therefore, it is necessary that weather forecasters have * Correspondence: P. A. Bertolotto, Via Pio VII 9, Torino, Italy. paolo.bertolotto@arpa.piemonte.it complete knowledge of atmospheric instability indices that best discriminate between potential convective heavy rain conditions and noncritical conditions. Every day at Piemonte Regional Functional Centre, ARPA Piemonte (Piedmont Region Environmental Protection Agency), thunderstorm early warnings are issued over the whole region, which is divided into 11 geographical areas with different characteristics, from the plains around 200 m above mean sea level (amsl) to alpine areas up to 3000 and 4000 m amsl. The present work follows on the limited literature concerning the verification of instability indices, which has produced results that are not always aligned in terms of best indicators and threshold values (see, for example, Jacovides and Yonetani, 1990; Huntrieser et al., 1997; Haklander and Van Delden, 2003; Kunz, 2007). The approach of the previous work is useful, keeping in mind (Doswell and Schultz, 2006) that there is no perfect thunderstorm index and one will probably never exist; however, the experience of forecasters is essential for interpreting the indices. The focus of this work is directed towards operational meteorology, thus taking into account the instability indices visualized and used daily by the forecasters of the Piemonte Regional Functional Centre in order to obtain solid results from the analysis data sample. The data sample for this study consists of 7 years of rain gauge records from a high-resolution network (more than 400 rain gauges across the Piedmont Region, measuring ca km 2 of surface area). The present work relates the rainfall observations to values of atmospheric instability indices obtained from COSMO-I7 and the European Centre for Medium Range Weather Forecasts Integrated Forecasting System (ECMWF-IFS) analysis. COSMO-I7 is the Italian version of the COSMO (COnsortium for Small-scale MOdeling) nonhydrostatic model with resolution of (around 7 km). These two numerical models are the 2016 Royal Meteorological Society

2 606 P. A. Bertolotto and G. Roggero reference models for the Italian Functional Centres System (DPCM, 27/02/2004); further information about their specification and analysis is reported in Section 3. The aim of the present study was to investigate the skill of various instability indices in discriminating between heavy rain events and non-events of atmospheric instability indices used operationally during weather forecasting and issuing early warnings in the Piedmont Region. A rainfall threshold of >10 mm in 20 min during each 6 h forecast interval ( , , , UTC) was used for analysis in every part of the Piedmont Region. 2. Model variables and indices The ECMWF-IFS analyses had of resolution from 2010 onwards and 0.25 of resolution between 2007 and 2010; the COSMO-I7 analyses had resolution. ECMWF-IFS analyses are issued every 6 h each day with 4DVar Global Telecommunication System (GTS) assimilation. COSMO-I7 analyses are issued every 12 h with a 12 h GTS assimilation cycle with nudging technique. In the present study, model analyses were used instead of model forecasts, in order to eliminate the forecast lead time error while maintaining the model resolution and structure. It should be pointed out that the model analysis used in the study does not dispose of high-resolution soil temperature and soil moisture assimilation data. This is definitely a source of errors, negatively affecting mainly instability indices such as CAPE and lifted index (LI), calculated over the whole vertical profile. Figure 1 presents an example of comparison, just before a heavy convective rain event over the city of Cuneo (34 mm in 20 min) on 4 July 2014, between a radiosonde Skew-T chart and ECMWF-IFS and COSMO-I7 Skew-T chart analyses at the same location and time. While the K Index (K I ) is similar (35 C for both model analyses, 37 C for the radiosonde), the error in CAPE and LI is more consistent (ECMWF analysis shows a CAPE value less then a third that of the radiosonde CAPE, while COSMO-I7 CAPE is 80% of the observed one). These errors are definitely connected with temperature and moisture errors at the surface (the observed temperature was 24.2 C, while COSMO-I7 and ECMWF-IFS gave 22.1 and 20.6 C, respectively). Several meteorological variables and indices of instability were analysed at four intervals every day (0000, 6000, 1200 and 1800 UTC), in order to study the pre-convective environment which sustained (or not) thunderstorm formation. Each index extracted from the analyses was associated with the events recorded within the corresponding 6 h interval (between 0000, 0600, 1200 and 1800 UTC). The ECMWF-IFS model provided analyses every 6 h, whereas the limited area model COSMO-I7 provided analyses only every 12 h (0000 and 1200 UTC). In order to create a homogeneous set of the two models data sets, COSMO-I7 forecasts at +6 h (0600 and 1800 UTC) were added. For every atmospheric variable and instability index considered, the average and the extreme value over each Piedmont warning area (warning areas are the zones into which the Piedmont Region is divided when meteorological alerts are issued) were calculated, for every 6 h interval. The analysed variables over the warning areas were the following: average and maximum wind speed and direction at 925 (or 950), 850, 700, 500, 300 hpa; average relative humidity at 925 (or 950), 850, 700 hpa; average temperature at 700, 500, 300 hpa; average geopotential height at 925 (or 950), 850, 700, 500, 300 hpa; average equivalent potential temperature at 925 (or 950), 700, 500 hpa; average relative vorticity at 500 hpa; average and maximum K I ;average and maximum surface based CAPE (SBCAPE); average and maximum SWEAT index; average and minimum surface LI; and minimum equivalent potential temperature difference in profile between 500 and 925 (or 950) hpa. The extrapolation of the extreme values over a Piedmont warning area in every interval T (between 0000, 0600, 1200 and 1800 UTC) was calculated by taking into consideration the grid point within the area that showed the extreme value of the field, whereas the average value was calculated by averaging the values of all the grid points of the model contained within each warning area (without making corrections for boundary points, because of the high spatial resolution of the analyses). Averaging instability indices is not a common practice; however, the fact that the warning areas are relatively small (around 2000 km 2 each) and the presence of model errors in representing complex orography and surface fields led to the decision to carry out the study using average values. 3. The observed values The problem of defining convective heavy rain events is still open. Because of the good availability and the high quality of Piedmont rain gauge data and the lower quality or availability of other types of data (radar observations, lightning detection networks), a decision was made to focus the research on heavy precipitation events between March and November. An event over a warning area was defined as a 6 h interval during which at least 10 mm of rainfall occurred in 20 min. Choosing a short time-defined precipitation threshold (20 min) allowed inclusion in the dataset not only of the summer months, but also spring and autumn months, thus reducing the risk of mistakenly including some nonconvective precipitation events. Although there is no unequivocal definition of a critical rain threshold typical of heavy convective events, the link between lightning and heavy rainfall has been analysed extensively (Sheridan et al., 1996; Peterson and Rutledge, 1998; Soula and Chaouzy, 2001). In Canada, for example, rainfall rate >50 mm (2 in.) in 1 h, or 75 mm (3 in.) in 3 h is also used to indicate severe thunderstorms (Environment Canada Ontario Region Fact Sheet, 2005); in hydrology, some studies correlate the core storm intensity with runoffs, choosing arbitrary thresholds on small timescales such as 50 mm in 10 min (Syed et al., 2003). In radar meteorology, convective cells are often identified with reflectivity of dbz, conventionally associated with a rainfall rate of 30 mm h -1 (see, for example, Rinehart and Garvey, 1978). The choice of 10 mm in 20 min seemed to be a good compromise with which to perform the analysis. The rainfall data considered are relative to months between March and November during the period from 2007 to For each of the four 6 h intervals in which a given day was divided, the occurrence or not of a heavy precipitation event (in each individual warning area) was recorded, setting every interval for each area as event or non-event. When multiple rain gauges in the same area recorded rainfall above the threshold, it was considered as a single event. This method of analysis thus reduces the observations to binary variables. In total, considering all the areas and the intervals, 3220 events were defined and their distribution across the Piedmont warning areas is shown in Figure 2. It can be seen that warning areas near the southern border of the region (near Liguria Region) had fewer events than the central and northern areas: this is in accordance with the Piedmont rainfall regime, where

3 607 Analysis of convective heavy rain events in the Piedmont Region Figure 1. Skew-T diagrams for the location of Cuneo Airport on 12 July 2014 at 1200 UTC before a convective heavy rain event: (a) radiosonde data, (b) ECMWF-IFS analysis and (c) COSMO-I7 analysis. Figure 2. Piedmont Region warning areas and numbers of convective heavy rain events for each area. northern areas are subject to an amplification of the phenomena through an interaction of moist southerly fluxes with Alpine orography (ARPA Piemonte, 2013). Figure 3 shows the trend of the number of total events (summing all warning areas different events) as a function of the rainfall threshold per 20 min Royal Meteorological Society Figure 3. Total number of events over all the Piedmont warning areas as a function of the rainfall in 20 min; the threshold selected for the present work, 10 mm, is indicated. 4. Instability indices over warning areas The analysis was performed on events that can be defined as very rare : the dataset consists of about 3220 intervals with an event Meteorol. Appl. 23: (2016)

4 608 P. A. Bertolotto and G. Roggero out of total intervals, for a base rate of (around 3%). Dichotomic verification based on contingency tables are one conceivable way to proceed with this kind of analysis (Doswell et al., 1990), but, when dealing with verification of uncalibrated forecasts of rare events (i.e. when forecasts of events tend to be different from the event s base rate; see Ferro and Stephenson, 2011), another way to perform the verification is to derive a receiver operating characteristic (ROC) curve (Mason, 1982) of the parameter under investigation. The ROC curve correlates POD (probability of detection) and POFD (percentage of false detection, or false positive rate), varying the threshold of the forecasting parameter (see for example Figure 4(b)). Together with the ROC curve, in order to find the correlation between the distribution of events and instability indices, the performance diagram, a diagram that displays POD versus success ratio (i.e. 1 FAR), was investigated (Roebber, 2009). These two diagrams facilitated comparison of the reliability of ECMWF-IFS and COSMO-I7 analysis fields in predicting events, depending on the chosen discriminating threshold between events and non-events (Figure 4(a)). The normalized distributions (density plots and boxplots) for every index were calculated for both models, also, in order to evaluate the parameters discriminating powers (Figure 5). These analyses were made for each index and for each Piedmont warning area. Figure 4(a) presents an exemplar performance diagram over a warning area: this diagram shows on the x-axis the success ratio (1 FAR) and on the y-axis the POD. The curved isolines in the graph are threat score (TS) isolines and the broken isolines are BIAS isolines; the perfect forecast is at the top right, while near the top left there are forecasts corresponding to low thresholds of instability indices, with very high POD but also very low success ratio (many false alarms). The corresponding ROC diagram (Figure 4(b)) shows the true positive rate (or POD) on the y-axis and the POFD on the x-axis: the area under the curve (ROC area) is therefore a good indication of how the variable in question, considering all of the thresholds together, discerns between events and non-events. A variable unrelated to the probability of occurrence of the events would have linear ROC curves corresponding to the bisector of the graph and an ROC area equal to 0.5. Therefore, in the following, the ROC area will be used as the main objective parameter for assessing the overall quality of the forecast variable under consideration. A comparison between the ROC diagrams for all of the warning areas, comparing the two model analyses for every instability index (Table 1), revealed that COSMO-I7 appeared to have slightly better performance than ECMWF-IFS: considering the nine best indices analysed in the study (i.e. the nine indices with highest ROC area values, reported in Table 1) for 11 areas, COSMO-I7 analyses gave better results in 73 out of 99 cases. Similar trends were found for all Piedmont warning areas, but for warning areas D, E, F, G, H and M (i.e. areas of the southern and western Alps and the Apennines) the performances were generally lower, with ROC area values 0.8. For K I,aswellasforall of the other instability indices, the use of the averaged values over the warning areas provided slightly better results than the maximum values. For this reason, all of the following considerations will refer to warning area average indices (see Table 1 for a complete résumé of the results). However, a general and encouraging conclusion at this point is that the instability indices used most operationally discriminate sufficiently between the distributions of events versus non-events. Comparing the performance of the various indices (Table 1), SBCAPE performed worse than K I, but was generally better for areas A, B, C, D, I and L (northern areas and plains) than for areas D, E, F, G, H and M (southern areas of the region). It should be pointed out that SBCAPE discriminated threshold values between events and non-events obtained from ECMWF-IFS were much lower (sometimes by a factor of 10) than COSMO-I7 values. This difference could be due to surface field errors, as explained in Section 2. The SWEAT index and surface lifted index (SLI) showed similar results, but for southern areas, in particular the Apennines area near the Liguria Region, the performance of ECMWF-IFS was better than that of COSMO-I7 (see Table 1). The minimum equivalent potential temperature difference between 500 and 950 hpa (i.e. the maximum difference in stability profile on a warning area gridpoint, termed DeltaThetaE) showed slightly lower performance than SBCAPE; in this comparison, for areas G, H and F (southern mountains near the border with the Liguria Region) ECMWF-IFS showed better results compared to COSMO-I7. The instability index with the best performance in general was K I, with ROC area values between 0.85 and 0.9 for areas A, B, I and L (plains and northern Alps). The K I ROC areas over southern areas were generally lower compared to northern and central parts of the region, but still higher than the best values of other instability indices. Also for K I, ECMWF-IFS performed better than COSMO-I7 in the small southern areas (F, G, H and M) (Table 1). The main result up to this point is that the COSMO-I7 average K I showed the best performance over almost all Piedmont warning areas (in terms of ROC area values) with respect to the other indices or the other atmospheric variables taken into account. In other words, COSMO-I7 average K I can be defined as the best predictor for convective heavy rain events across the Piedmont Region. See Figure 6 for an example of the comparison, by means of performance diagram, of the average K I with two other indices calculated from COSMO-I7 (in this case SWEAT index and SBCAPE) on another warning area of the set (area B), where the superiority of K I is apparent. Furthermore, it is shown that the indices based on COSMO-I7 analyses displayed better results for warning areas distant from the sea (northern areas and plains) and the difference between the two models was greater (to the advantage of COSMO-I7) for the indices calculated over the whole profile, such as SLI and SBCAPE. ECMWF-IFS performed better for the southern areas, which are more strongly influenced by the Tyrrhenian Sea and have a smoother orography (except for SLI and SBCAPE). Results from performance and ROC diagrams were in line and ROC area values were used as the quantitative measure of comparison, summarized in Table The reduced K Index (K R ) The threshold values of K I associated with the occurrence of convective rain events depend strongly on the baric configuration: in anticyclonic conditions or periods with higher geopotential thickness, typical of summer months, these values are much higher than in cyclonic conditions or periods with lower geopotential thicknesses (spring, autumn, winter). This follows from the definition of K I, which contains the temperature and humidity at three pressure levels (850, 700, 500 hpa) but has no explicit dependence on the geopotential thickness. The original K I definition is: K I = T 850 T T d850 ( ) T 700 T d700 The sample analysed in this work included spring, summer and autumn months and the average values of geopotential height appeared to be variable in the dataset, resulting in a reduced

5 Analysis of convective heavy rain events in the Piedmont Region 609 (a) (b) Figure 4. (a) Performance diagram and (b) ROC diagram referred to averaged K I for Piedmont warning area A (Toce Basin), varying the threshold, for COSMO-I7 and ECMWF-IFS analyses. The K I thresholds that provide better performances and higher ROC areas are highlighted. (a) (b) Figure 5. Normalized distributions (a) and boxplot distributions (b) for average K I for Piedmont warning area I (Northern Plains). The lines in (a) refer to COSMO-I7 values for event cases (solid-dotted line), COSMO-I7 for non-event cases (dotted line), ECMWF-IFS for event cases (solid line) and ECMWF-IFS for non-event cases (dashed line). reliability of K I in its original definition. In order to overcome the seasonal dependence of typical K I values, a reduced K Index (K R ) was defined as: K R = 10 4 K I ( ) Z 850 Z 500 where Z 850 and Z 500 are geopotential height (in metres) at 850 and 500 hpa. This new index version was analysed using the process listed above (ROC and performance diagrams) and showed slightly better performance compared to the traditional K I value (see Table 2), with a small but unequivocal ROC area improvement for all of the areas; K R showed optimal threshold values (typical of convective cases) of around 75 or 80, as can be observed, for example, in the performance diagram in Figure Wind fields on Piedmont warning areas Another important contribution to atmospheric instability comes from the wind field, in particular from the shear and the convergence in the lower and middle layers of the atmosphere, where flows interact with the Alpine orography. In order to add information about the wind field to the K R (and implicitly to the K I ), K R was modified in the following ways: 1. For each warning area, a higher K R threshold still sufficient to guarantee a POD 0.6 was determined (i.e. the value that, regardless of false alarms, forecasted successfully at least 60% of the observed events). 2. After having limited the dataset to those intervals with K R bigger than the threshold values specified in point 1 (above), the mean wind distributions were determined for events and non-events for each area, for pressure levels 700, 850 and 950 hpa of the COSMO-I7 analysis. 3. Wind directions were chosen arbitrarily that better discriminate between events and non-events, after having observed the discriminating graphs and having discussed the choice with operational forecasters. Most frequent discriminating

6 610 P. A. Bertolotto and G. Roggero Table 1. ROC area values for the main instability indices from COSMO-I7 and ECMWF-IFS analyses, in different Piedmont warning areas. Average K I Maximum K I Average surface LI Minimum surface LI Average SWEAT index Maximum SWEAT index Average CAPE Maximum CAPE Minimum DThetaE hpa COSMO-I7 Area A Area B Area C Area D Area E Area F Area G Area H Area I Area L Area M ECMWF Area A Area B Area C Area D Area E Area F Area G Area H Area I Area L Area M K I, K Index; LI, lifted index. The best ROC area values for every warning area are in bold. Note that this new K I modification introduces an implicit counterclockwise shear dependence (down with height) in the original index. The next step was to add a constant v to K R according to the wind direction (if the direction was identified as discriminating in the previous paragraph) at different pressure levels, selecting the optimum value of this constant in order to optimize the performance of the index (once again, with the criterion of the maximum ROC area). From all diagrams obtained, the one with the greatest ROC area was chosen, thus identifying the optimal values of the parameter v. The optimal choice for parameter v was found to be v = 6 at all pressure levels analysed (see Table 2 with all values of the improvement in terms of ROC area for the warning areas). Essentially, this index modification could be summarized on each warning area as: K W = K R + v(dir (V)) p Figure 6. Performance diagram for Piedmont warning area B (Sesia Basin) comparing the performances of three instability indices (average K I, average SWEAT index, average SBCAPE) derived from COSMO-I7 analysis. Significant threshold values are highlighted on the graph. directions were then selected from south to westsouthwest ( ) at 700 hpa, from southeast to south ( ) at 850 hpa and from east to southeast ( ) at 950 hpa. An example of a discriminating graph for winds, at a pressure level of 700 hpa for one of the warning areas (Area H, Scrivia Basin), is presented in Figure 8, wherein the better discriminating directions are highlighted. where K W is the new index with the wind correction and the correction parameter v is 0 or 6 depending on the average wind direction dir(v) over each level of pressure p. The corrections of K W at the three pressure levels were then joined together to further optimize the total gain of the ROC area (Table 2). This further modification to K I added basic information about the wind field, implicitly selecting the meteorological situation with a cyclonic curvature of the profile. This is similar to adding basic information about the cyclonic curvature of the flow at a single pressure level, as performed in other studies in the literature (e.g. Jacovides and Yonetani, 1990). This further modification takes into account three pressure levels of the profile. It will be interesting in the future to add fuller information about the wind shear to the index, such as the storm relative helicity, and see how this changes the verification results.

7 Analysis of convective heavy rain events in the Piedmont Region 611 Table 2. ROC area increase in th safterthek I modifications. Type of correction Area A Area B Area C Area D Area E Area F Area G Area H Area I Area L Area M Sum K I to K R K R to K W 700 hpa hpa hpa K R to K W +6 at three levels Increases of ROC area relative to COSMO-I7 indices K I, K R and K W on all warning areas. Bold values represent the choices made in the work in defining K R and K W. Figure 7. Performance diagram of K R averaged on the Piedmont warning area A (Toce Basin) used as events predictor. K R values refer to COSMO-I7 (triangles) and ECMWF-IFS (circles). Better performing threshold values are highlighted on the graph. 7. Performance of the new index K W The K W modification, reported above in Section 6, was performed from the fields calculated on the variables of COSMO-I7 analysis, which is the model that generally has provided the most reliable results (Table 1). Figures 9 and 10 display a comparison between the performance (in terms of both performance and ROC diagram) of K I, K R and K W. From this comparison, the net improvement of K W can be seen: this appeared to be true for almost all of Figure 8. Normalized distributions for Piedmont warning Area H (Scrivia Basin) of wind direction at pressure level 700 hpa for events (solid line) and non-events (dotted line), considering the intervals in which the index K R > 70 (from COSMO-I7 analysis). An approximation of the directions in which K R could be improved with an additive constant is highlighted on the graph. the warning areas on which the correction was carried out, apart from the areas D and E (small areas of the southwestern Alps). A summary of results can be seen in Table 2. On 9 out of 11 warning areas, computing K W from K R led to an improvement greater than the one obtained in the previous step, computing K R from K I.

8 612 P. A. Bertolotto and G. Roggero Piedmont warning areas. A second correction factor was added to the K R, dependent on wind direction, averaged on the warning areas, resulting in a further increase of the receiver operating characteristic (ROC) area on almost all warning areas. This new index, K W, is now being used operationally to help ARPA Piemonte weather forecasters in identifying potential convective heavy rain events due to thunderstorm occurrence. A similar verification to that reported in this study was subsequently made for all Italian regions, albeit with a less dense network of rain gauges over the whole territory, with similar results. The index K W is currently displayed and operationally used by the functional centres of Civil Protection in the main Italian regions and by the main meteorological office of the Civil Protection Department in Rome. Figure 9. Diagram for Piedmont warning area A displaying the performances of the three versions of the index K I, K R and K W. Acknowledgements The authors want to thank all of the weather forecasters of ARPA Piemonte, Umberto Pellegrini (ARPA Lombardia), and Alexander Toniazzo (Civil Protection Department, Rome) for their valuable suggestions. They also state that they have no conflict of interests to declare. Figure 10. ROC diagram for Piedmont warning area A displaying the performances of the three versions of the index K I, K R and K W in terms of ROC area. 8. Conclusions The present work in analysing the key indicators of instability has allowed identification of the best predictor yet devised for convective heavy rain events over the Piemond Region warning areas. A very large data sample was examined, consisting of the analysis of the two main meteorological models used operationally at the Piemonte Regional Weather Centre and the ARPA Piemonte rain gauge data. The K Index (K I ) average value (over each Piedmont warning area) was first reckoned as the best overall predictor. An attempt to improve its performance was then made by introducing a dependence on the hpa geopotential thickness, with the intention of obtaining an instability index with values less dependent on the synoptic regime and seasonality. This correction, K R, showed a slight but unequivocal improvement for all References Anquetin S, Yates E, Ducrocq V, Samouillan S, Chancibault K, Davolio S, et al The 8 and 9 September 2002 flash flood event in France: a model intercomparison. Nat. Hazards Earth Syst. Sci. 5: ARPA Piemonte Le Precipitazioni Intense in Piemonte. ARPA Piemonte Agency: Piemonte; ISBN: Cacciamani C, Battaglia F, Patruno P, Pomi L, Selvini A, Tibaldi S A climatological study of thunderstorm activity in the Po Valley. Theor. Appl. Climatol. 50(3 4): Costa S, Mezzasalma P, Levizzani V, Alberoni PP, Nanni S Deep convection over Northern Italy: synoptic and thermodynamic analysis. Atmos. Res. 56(1): Doswell CA III, Davies-Jones R, Keller DL On summary measures of skill in rare event forecasting based on contingency tables. Weather Forecast. 5(4): Doswell CA III, Schultz DM On the use of indices and parameters in forecasting severe storms. Electron. J. Severe Storms Meteorol. 1(3): Environment Canada Ontario Region Fact sheet summer severe weather warnings ( ). Ferro CAT, Stephenson DB Extremal dependence indices: improved verification measures for deterministic forecasts of rare binary events. Weather Forecast. 26(5): Haklander AJ, Van Delden A Thunderstorm predictors and their forecast skill for the Netherlands. Atmos. Res : Hohenegger C, Lüthi D, Schär C Predictability mysteries in cloud-resolving models. Mon. Weather Rev. 134(8): Huntrieser H, Schiesser HH, Schmid W, Waldvogel A Comparison of traditional and newly developed thunderstorm indices for Switzerland. Weather Forecast. 12(1): Jacovides CP, Yonetani T An evaluation of stability indices for thunderstorm prediction in Greater Cyprus. Weather Forecast. 5: Kunz M The skill of convective parameters and indices to predict isolated and severe thunderstorms. Nat. Hazards Earth Syst. Sci. 7(2): Mason I A model for assessment of weather forecasts. Aust. Meteorol. Mag. 30: Morgillo A Preliminary results with very high resolution COSMO model for the forecast of convective events. COSMO News Lett. 11: Peterson AW, Rutledge SA On the relationship between cloud-to-ground lightning in mesoscale convective rainfall. J. Geophys. Res. 103(D12, 14): Rinehart RE, Garvey ET Three-dimensional storm motion detection by conventional weather radar. Nature 273:

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