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Keywords:

  • cumulus convection;
  • predictability;
  • quasi-equilibrium;
  • convective time-scale

Abstract

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Classification of severe rainfall events
  5. 3.  Computation of convective time-scale
  6. 4.  Results
  7. 5.  Conclusions
  8. A.  Appendix
  9. References

Raingauge data over Italy for the period January 2006–February 2009 have been used to classify severe rainfall events into two types using a recently developed methodology. The types are defined as either long-lived and spatially distributed (Type I) if lasting more than 12 h and larger than 50 × 50 km2 or brief and localized (Type II) if having shorter duration or smaller spatial extent. A total of 81 events were identified, with 51 classified as Type I and 30 as Type II. The work presented here examines the hypothesis that the two types of event are associated with different dynamical regimes distinguished by differing degrees of control of convective precipitation by the synoptic-scale flow. For each of the 81 events, a time-scale for convective adjustment is computed, based on gridded hourly precipitation rates derived from rain-gauge data and ECMWF analysis (ERA-Interim) of convective available potential energy (CAPE). Values of the convective adjustment time-scale, τc, shorter than 6 h indicate convection that is responding rapidly to to the synoptic environment (equilibrium), while slower time-scales indicate that other, presumably local, factors dominate. It was anticipated that τc > 6 h would correspond to brief and localized Type II events, while τc < 6 h would indicate Type I events. This hypothesis was largely confirmed, with 45 of the 51 Type I events having time-scales shorter than 6 h and 20 of the 30 Type II events having time-scales longer than 6 h. Copyright © 2011 Royal Meteorological Society


1.  Introduction

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Classification of severe rainfall events
  5. 3.  Computation of convective time-scale
  6. 4.  Results
  7. 5.  Conclusions
  8. A.  Appendix
  9. References

The need for a deeper understanding of the properties of Mediterranean flash-flood-producing storms, occurring over complex orography regions and often convective in nature, is a long-standing and important issue in hydrometeorology research. This problem has been tackled in the literature according to two different but complementary approaches.

On one hand, efforts have been devoted to the assessment of the predictive ability of meteorological models with respect to severe rainfall events (Petroliagis et al., 1997; Romero et al., 2005; Hohenegger et al., 2006, 2008; Davolio et al., 2007; Hohenegger and Schär, 2007a, 2007b; Argence et al., 2008; Lebeaupin et al., 2008; Amengual et al., 2009; Lapeyre and Talagrand, 2009): their goal is to evaluate how closely a particular model can predict the true state of a certain severe rainfall scenario as a function of observational data quality and availability, parametrization of the subgrid processes, model coupling, model approximations and resolution. On the other hand, some studies have investigated the dynamical, kinematical and microphysics properties of observed systems (Leckebusch and Ulbrich, 2004; Grazzini, 2007; Miglietta and Regano, 2008; Sanchez-Gomez et al., 2008). A central challenge in both of these approaches is posed by the great variety of meteorological circumstances and processes associated with intense precipitation.

A useful classification of intense precipitation events has been introduced by Molini et al. (2009), who examined the duration, spatial extent and large/small-scale triggering of events in a high-resolution precipitation dataset. The study employed the full set of rain-gauges over Italy in order to identify severe rainfall events that occurred within the period 2006–2009 (about 1700 stations). The rain-gauge network consists of about 1700 stations, giving a density ranging between 1/50 km2 and 1/200 km2 with an average of 1/100 km2. A precipitation event was designated as severe if it contained at least one hourly rain-gauge reading exceeding 50 mm. An objective classification system for these events was developed, and two typologies were identified: Type I –long-lived (duration ddS = 12 h) and spatially distributed (more than AS = 50 × 50 km2); and Type II –brief and localized, having a shorter duration (d < dS = 12 h) and a spatial extent smaller than AS. Although the analysis was restricted to Italy, these categories were considered as representative of flash-flood-producing storms over the whole Mediterranean area.

The distinction between the two types of events is of considerable importance for hydrological applications, since the greater size and duration of Type I events has important implications from a civil defence point of view. Presumably, the two types of events are related to some difference or differences in the meteorological environments in which they occur, and even in the absence of an accurate precipitation forecast there would be considerable value in knowing which type of event could be anticipated.

In parallel to this work, Done et al. (2006) investigated the dynamical role of the synoptic and mesoscale environment in controlling the local characteristics of convective precipitation. They argued that two regimes are possible. First equilibrium convection, where it is assumed that production of CAPE by large-scale processes is nearly balanced by its consumption by convective phenomena, and thus CAPE values stay small. In this case the overall size, location and intensity of the precipitating region will be determined by the large-scale flow (cf. Arakawa and Schubert, 1974). This occurs since the convection is dependent on and responds to thermodynamical destabilization induced by boundary conditions and physical processes, such as radiative cooling, adiabatic cooling by large-scale ascent and surface fluxes. Then time-scales of the convective processes can be assumed small compared with the time-scales of forcing changes and, consequently, the convection may be considered to be in a state of statistical equilibrium with the forcing itself (Emanuel, 1994, 2000).

In the second, non-equilibrium regime, a larger amount of CAPE is available, as a result of building up from large-scale processes over long time-scales, but the extent to which it produces convection and precipitation is restricted by the need for a trigger sufficient to overcome the convective inhibition energy (CIN). Triggers included boundary-layer convergence regions or local maxima in temperature or moisture (Charney and Elyassen, 1964; Ooyama, 1971). Since these are typically driven by local orographic or surface-flux variability, they may be hard to predict, even if the large-scale meteorological situation is known: in this case the convection behaves as an initial-value problem.

Done et al. (2006) suggested that the presence or absence of convective equilibrium could be identified by considering a time-scale of convective adjustment, τc. This scale (defined in section 3, below) is an estimate of the rate at which CAPE is being consumed by convective heating. If the convective time-scale is only a few hours, and thus short compared with the time-scale over which the large-scale environment evolves (say 1 day) the convection will remove CAPE as fast as it is created, and the rate of creation of CAPE controls the amount of convection. On the other hand, if the convective time-scale is similar to, or longer than, 1 day, convection is acting too slowly to remove CAPE and there must be local factors controlling its rate. Although Done et al. (2006) applied this diagnostic to model data, it is based only on CAPE and precipitation rate and could also be determined directly from radiosonde and rain-gauge data. It is worth noting that the value of CAPE on its own is a poor predictor of convective properties, as discussed by Lucas etal. (1994) and Zipser (2003). The convective time-scale, in contrast, uses the ratio of CAPE over precipitation rate to estimate a rate of change of CAPE that is directly related to the definition of convective equilibrium given above.

This article explores the hypothesis that the two categories of precipitation events identified by Molini et al. (2009) solely on the basis of area and duration of precipitation correspond to the two dynamical regimes of equilibrium and non-equilibrium convection. The convective time-scale, τc, will be calculated for each of the events in the database of Molini et al. (2009), now extended through 2009, to see whether short values indicating equilibrium convection are associated with Type I (long-lived, large-scale) events and long values indicating non-equilibrium convection are associated with Type II (short-lived, smaller-scale) events. A complicating factor in this analysis is the possibility of non-convective precipitation events. It will be seen in section 3 that since such events are characterized by little or no CAPE, they will result in τc values that are zero or very small and will thus be included in the equilibrium category. This is reasonable since non-convective precipitation is clearly under the control of the large-scale flow.

In section 2, the classification procedure for observed precipitation events is summarized and examples of Type I and II events are presented. Section 3 describes how the convective time-scale τc was calculated. Section 4 presents the results of the comparison between convective time-scale and event type, while section 5 is devoted to a discussion and conclusions.

2.  Classification of severe rainfall events

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Classification of severe rainfall events
  5. 3.  Computation of convective time-scale
  6. 4.  Results
  7. 5.  Conclusions
  8. A.  Appendix
  9. References

Severe rainfall events are selected according to the methodology described in Molini et al. (2009), applied to the hourly rainfall data provided by the Italian rain-gauge network which includes about 1700 sensors.

The first stage in the method is to identify a precipitation period, the onset of which is defined as the hour in which at least one rain-gauge over Italy records an hourly rainfall depth greater than or equal to 2 mm. A precipitation period ends when no rain-gauge exceeds the same threshold for at least 6 h. However this preliminary selection includes precipitation periods that are not significant from a hydrometeorological viewpoint, so a second criterion is applied to identify periods of intense precipitation, namely that the period contains at least one hourly rainfall value greater than 50 mm. This threshold corresponds to a return period of around 50 year, based on a regionalization study of annual rainfall maxima over Italy (Boni et al., 2006, 2008). Through direct inspection of the spatio-temporal evolution of the precipitation field, the areal extent and temporal duration of the rainfall event, or events, contained in a given rainfall period are determined. For visualization, and for calculation of the convective time-scale below, the rain-gauge data are linearly interpolated on to a 7 km spaced grid, which is consistent with the mean density of the Italian rain-gauge network.

Applying this approach results in the identification of 81 events over the period January 2006–February 2009,

  • (i)
    51 events were ascribed to Type I, i.e. lasting more than 12 h and striking an area larger than 50 × 50 km2.
  • (ii)
    30 events were ascribed to Type II, i.e. lasting less than 12 h and striking an area smaller than 50 × 50 km2.

The average duration of the Type I events is roughly 24 h, compared with about 9 h for the Type II events.

An example of a Type I event occurred in December 2008 in the northeastern part of Italy and lasted 19 h: the maximum observed rainfall depth over the event duration was around 150 mm (Figure 1). A typical Type II event occurred in October 2008 in the central part of Italy and lasted 8 h: the maximum observed rainfall depth over the event duration was over 90 mm (Figure 2).

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Figure 1. Total observed rainfall depth for the event that started on 10 December 2008 (d = 19 h, Type I).

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Figure 2. Total observed rainfall depth for the event that started on 28 October 2008 (d = 8 h, Type II).

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3.  Computation of convective time-scale

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Classification of severe rainfall events
  5. 3.  Computation of convective time-scale
  6. 4.  Results
  7. 5.  Conclusions
  8. A.  Appendix
  9. References

The convective adjustment time-scale τc used in this study is defined by Done etal. (2006). First the rate of change of CAPE due to release of latent heat is estimated from the rainfall rate by the following formula:

  • equation image

where iR is the rainfall intensity (mm h−1), Lv the latent heat of vaporization, g the acceleration due to gravity, cp the specific heat of air at constant pressure and T0 and ρ0 reference values of temperature and density, respectively. Assuming Lv = 2.5 × 106 J kg−1, cp = 4186 J kg−1 K−1, T0 = 300 K and ρ0 = 1.2 kg m−3, we may derive the following expression for τc:

  • equation image

A threshold value of the convective time-scale, τcs, must be identified to distinguish between equilibrium and non-equilibrium convection. Done et al. (2006) suggest that a typical synoptic time-scale would be a day or more. Over land, changes in forcing associated with the diurnal cycle are likely to be important, so a shorter threshold time-scale τcs of around 6 h is used in this study. Some confirmation that this is an appropriate value is provided in the next section, where the time evolution of τc is compared for the the example events of Figures 1 and 2. The hypothesis of this work is that the convective adjustment time-scale may allow one to distinguish between Type I and Type II events, with Type I having τc lower than 6 h and Type II having higher values.

The spatial and temporal coverage of the Italian atmospheric radiosounding network is rather coarse: only seven stations are available, with measurements made twice daily (0000 and 1200 UTC). Therefore it was decided to use the ERA-Interim reanalysis product to estimate the CAPE values over the area and for the duration corresponding to each severe precipitation event. ERA-Interim is the most recent European Centre for Medium-Range Weather Forecasts (ECMWF) global atmospheric reanalysis, covering the period 1989 to the present, and provides CAPE values at a horizontal resolution of 60 km and temporal resolution of 3 h (Simmons et al., 2007). To compute the convective time-scale, the ERA CAPE fields are linearly interpolated in time and space to the same hourly resolution and 7 km grid as the precipitation data.

The use of CAPE from a model analysis product is not ideal, since the CAPE values in any numerical simulation used as a background field will be strongly influenced by the model numerics and parametrizations, especially the convection scheme. These deficiencies will be significantly reduced by the assimilated observations, but the quality of the resulting CAPE values remains suspect. A comparison of the ERA-Interim CAPE with the available radiosonde values was therefore undertaken (see the appendix). While the differences between the two CAPE values are not negligible, the errors take the form of a random scatter rather than a systematic bias, making the test conservative in the sense that the degree of correlation between convective time-scale and event type will be reduced rather than a spurious correlation being introduced.

Pixel values of τc were calculated at all rainy grid points (hourly rainfall intensity iR > 2 mm h−1) belonging to each event. It should be noted that the rain-gauge-based precipitation was used in all calculations; the ERA-Interim precipitation was not used. This rainfall intensity threshold was adopted to be consistent with the equivalent threshold adopted for the identification of the rainfall periods. At each hourly time step, a spatial mean value τCE of the convective adjustment time-scale was computed over the aforementioned rainy points. In this way it was also possible to study the temporal evolution of τCE over the duration and area of each event. The relatively coarse resolution of the CAPE provided by ERA-Interim prevents proper consideration of the spatial variability of CAPE for a convective storm, as nicely discussed in Perica and Foufoula-Georgiou (1996): future work will be devoted to the use of finer-resolution analysis CAPE products, when available, and measured CAPE values as provided during the Mid-Latitude Continental Convective Clouds Experiment (MC3E) to be held in Oklahoma in late spring/early summer of 2011.

4.  Results

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Classification of severe rainfall events
  5. 3.  Computation of convective time-scale
  6. 4.  Results
  7. 5.  Conclusions
  8. A.  Appendix
  9. References

Before considering the precipitation events in their entirety, we first present the time evolution of τCE, together with the CAPE and rainfall intensity values averaged over the same set of rainy points, for the example Type I and II events for which total rainfall maps were shown in Figures 1 and 2.

For the Type I event, which started on 10 December and lasted d = 19 h, the τCE values are lower than the 6 h threshold throughout the system's lifetime. This is an indicator of equilibrium convection according the the criterion of the preceding section (Figure 3). No systematic trend in time is apparent.

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Figure 3. Temporal evolution of the spatial mean of CAPE (upper panel), rainfall intensity iR (middle panel) and convective adjustment time-scale (τCE, lower panel) for the event started on 10 December 2008 (d = 19 h, Type I). The 95% confidence interval for τCE is shown by dashed lines.

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For the Type II event, which started on 28 October and lasted d = 8 h, the τCE values are higher than the 6 h threshold over the duration of the event (Figure 4). In this case, however, there is a systematic decrease in τCE over time, reaching a value of about 10 h towards the end of the precipitation period. As discussed by Done et al. (2006), this is consistent with a situation in which convection is inhibited and CAPE builds up, but once convection is established the system begins to adjust towards equilibrium. The plots also show the confidence interval for statistical significance α = 95%, estimated with the jackknife technique by averaging τc values for subsampled portions of rainy points (iR > 2 mm h−1) at each time step. This helps, albeit in a simple way, in accounting for the effect of spatial variability of CAPE and τc. It is worth mentioning that the reciprocal significance of both variables in the process is clearly shown by the trend of CAPE and rainfall intensity for the two events: examination of Figures 3 and 4 does not show either factor to be dominant, at least not over the whole lifetime of an event.

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Figure 4. Temporal evolution of the spatial mean of CAPE (upper panel), rainfall intensity iR (middle panel) and convective adjustment time-scale (τCE, lower panel) for the event started on 28 October 2008 (d = 8 h, Type II). The 95% confidence interval for τCE is shown by dashed lines.

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Time series of τCE were computed for each of the 81 events in the dataset. As a measure of the equilibrium or non-equilibrium character of each severe event, we adopted the average value τCM of each τCE time series. A scatter plot of τCM versus the duration d of each severe event (Figure 5) shows the following.

  • Type I: 45 events out of 51 (about 90%) are characterized by τCM values lower than 6 h, thus corresponding to equilibrium conditions.

  • Type II: 20 events out of 30 (about 66%) are characterized by τCM values higher than 6 h, thus corresponding to non-equilibrium conditions.

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Figure 5. Scatter plot of τCM versus the duration d for each intense rainfall event in the dataset January 2006–February 2009.

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Very few events are found in the upper right quadrant of Figure 5, indicating that it is rare to find an intense convective event of long duration where a long convective time-scale indicates non-equilibrium conditions. Somewhat more events are found in the lower left quadrant. Here, a short time-scale suggests equilibrium convection but the event is short-lived. These are likely to be events that travelled into or out of the analysis domain (recall that the rain-gauge-based dataset is available only over land).

Another way to look at the results in Figure 5 is to evaluate τCM as a predictor for a Type I event. That is, a contingency table is constructed from the four quadrants of Figure 5 by defining a Type I event to be forecast if τCM < 6 h and observed if d > 12 h. This results in a hit rate of H = 0.82 and a false-alarm ratio of FAR = 0.13, indicating quite a skilful prediction. Overall, the initial hypothesis of this study seems to be supported by these findings: Type I events are largely associated with equilibrium conditions, while Type II events appear to be characterized by non-equilibrium conditions.

5.  Conclusions

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Classification of severe rainfall events
  5. 3.  Computation of convective time-scale
  6. 4.  Results
  7. 5.  Conclusions
  8. A.  Appendix
  9. References

This article describes an attempt to relate two classifications of precipitation events, one motivated by hydrological applications and based on duration and extent of heavy rain (Molini et al., 2009) and another motivated by the dynamical coupling between cumulus convection and its synoptic environment (Done et al., 2006). Intense precipitation events over Italy for the period from January 2006–February 2009 were classified following the method of Molini et al. (2009) into long-lived and spatially widespread Type I events and short-lived, localized Type II events. The same set of events was then classified according to whether the convective adjustment time-scale of Done et al. (2006) was less than or greater than a threshold value of 6 h. This threshold is expected to be dynamically significant, since short convective adjustment times imply that the convection is responding rapidly to changes in the synoptic environment (equilibrium) whereas longer adjustment times suggest that other, presumably local, processes are acting to prevent the rainfall from tracking changes in the large-scale environment (non-equilibrium).

A strong degree of consistency was found between the two classifications, with 90% of Type I systems being associated with short convective time-scales and two-thirds of Type II events associated with longer time-scales. This result was obtained despite the limited quality of the ERA-Interim CAPE values that were used in computation of the convective adjustment time-scale. A more accurate CAPE analysis might well produce even better results.

The agreement between the hydrometeorological and dynamical classifications found here is currently being exploited to develop a method for regime-dependent downscaling of precipitation analyses and forecasts, where the convective time-scale is used to select a statistical model of precipitation appropriate for the expected event morphology. Work is ongoing to apply the classifications to other regions of the Mediterranean area.

Future work is planned to explore the use of the proposed methodology for diagnostic versus prognostic studies by introducing a new metric that measures the tendency or rate of temporal evolution of the convective time-scale τCE: this approach will be possible when fine-resolution analysis CAPE products or measured CAPE values, as provided during the Mid-Latitude Continental Convective Clouds Experiment (MC3E) to be held in Oklahoma in late spring/early summer of 2011, become available to better explore storm dynamics.

A.  Appendix

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Classification of severe rainfall events
  5. 3.  Computation of convective time-scale
  6. 4.  Results
  7. 5.  Conclusions
  8. A.  Appendix
  9. References

A comparison of radiosonde-based and ERA-Interim CAPE values over the full dataset of events was undertaken to assess whether the quality of the reanalysis data was adequate for the purposes of this study. First, radiosounding stations associated with each event were identified. Subsequently, the ERA-Interim CAPE values were interpolated to the radiosounding station locations at times 0000 and 1200 UTC. The comparison is shown in terms of a scatter plot of ERA-Interim and predicted values for the 2006–2009 events (Figure A1). The correlation is modest, with a coefficient of determination R2 ∼ 60%. Most importantly for present purposes, the small BIAS of about 50 J kg−1 and the mean absolute error (MAE) of around 200 J kg−1 show that the errors are random, rather than showing a systematic skew that would bias the resulting convective adjustment time-scale τc.

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Figure A1. Scatter plot of ERA-Interim and radiosonde-based CAPE values for the January 2006–February 2009 events.

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References

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Classification of severe rainfall events
  5. 3.  Computation of convective time-scale
  6. 4.  Results
  7. 5.  Conclusions
  8. A.  Appendix
  9. References
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