Linear Rainfall Features and Their Association with Rainfall Extremes near Melbourne, Australia

Stacey M. Hitchcock aSchool of Geography, Earth and Atmospheric Sciences, The University of Melbourne, Melbourne, Victoria, Australia
bARC Centre of Excellence for Climate Extremes, Melbourne, Victoria, Australia

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Todd P. Lane aSchool of Geography, Earth and Atmospheric Sciences, The University of Melbourne, Melbourne, Victoria, Australia
bARC Centre of Excellence for Climate Extremes, Melbourne, Victoria, Australia

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Robert A. Warren bARC Centre of Excellence for Climate Extremes, Melbourne, Victoria, Australia
cSchool of Earth, Atmosphere and Environment, Monash University, Melbourne, Victoria, Australia

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Joshua S. Soderholm dAustralian Bureau of Meteorology, Melbourne, Victoria, Australia
bARC Centre of Excellence for Climate Extremes, Melbourne, Victoria, Australia

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Abstract

Linear precipitation systems are a prominent contributor to rainfall over Melbourne, Australia, and the surrounding region. These systems are often convective in nature, frequently associated with cold fronts, and in some cases can lead to significant rainfall and flash flooding. Various types of linearly organized systems (e.g., squall lines, quasi-linear convective systems) have been the subject of much research in the United States and elsewhere, but thus far relatively little analysis has been done on linear systems in Australia. To begin to understand rainfall extremes and how they may change in this region in the future, it is useful to explore the contribution of these types of systems and the characteristics that define them. To this end, we have examined the recently developed Australian Radar Archive (AURA), identifying objects that meet a specific set of relevant criteria, and used multiple methods to identify heavy and extreme daily rainfall. We found that on average, days with linear systems contribute over half of the total rainfall and 70%–85% of heavy/extreme rainfall in the Melbourne region. The linear systems that occur on heavy rainfall days tend to be larger, slower-moving, and longer-lived, while those on extreme rainfall days also tend to be more intense and have a greater degree of southward propagation than linear systems on other days.

Warren’s current affiliation: Australian Bureau of Meteorology, Melbourne, Victoria, Australia.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Stacey Hitchcock, Stacey.Hitchcock@unimelb.edu.au

Abstract

Linear precipitation systems are a prominent contributor to rainfall over Melbourne, Australia, and the surrounding region. These systems are often convective in nature, frequently associated with cold fronts, and in some cases can lead to significant rainfall and flash flooding. Various types of linearly organized systems (e.g., squall lines, quasi-linear convective systems) have been the subject of much research in the United States and elsewhere, but thus far relatively little analysis has been done on linear systems in Australia. To begin to understand rainfall extremes and how they may change in this region in the future, it is useful to explore the contribution of these types of systems and the characteristics that define them. To this end, we have examined the recently developed Australian Radar Archive (AURA), identifying objects that meet a specific set of relevant criteria, and used multiple methods to identify heavy and extreme daily rainfall. We found that on average, days with linear systems contribute over half of the total rainfall and 70%–85% of heavy/extreme rainfall in the Melbourne region. The linear systems that occur on heavy rainfall days tend to be larger, slower-moving, and longer-lived, while those on extreme rainfall days also tend to be more intense and have a greater degree of southward propagation than linear systems on other days.

Warren’s current affiliation: Australian Bureau of Meteorology, Melbourne, Victoria, Australia.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Stacey Hitchcock, Stacey.Hitchcock@unimelb.edu.au

1. Introduction

In Melbourne and the surrounding region of Victoria, Australia, linear precipitation systems are a frequent and noticeable characteristic of the often bemoaned “Melbourne weather,” which is said by locals to change frequently and sometimes drastically at a moment’s notice. Linear precipitation systems in the region are often associated with a “cool change,” which is a local phrase used by early studies (e.g., Berson et al. 1957), to describe a series of front-like discontinuities that often successively pass through the region. These discontinuities are thought to result from prefrontal squall lines or quasi-linear convective systems (QLCSs), where the final transition associated with a steady pressure rise and often the strongest temperature gradient marks the passage of the surface cold front (Reeder and Smith 1987). Like air mass boundaries elsewhere in the world, those associated with the passage of a cool-change can provide a source of lift for the precipitation systems that frequently accompany them (e.g., Catto and Pfahl 2013; Pepler et al. 2020, 2021). These linear systems are an important source of rainfall in the region, but can also lead to flooding/flash-flooding, severe winds, and even hail and tornadoes in some cases. Surprisingly, there is limited research into the occurrence of these linear/quasi-linear systems, their characteristics, and their specific contribution to rainfall. Documenting some details of these systems, including their contribution to extreme rainfall, is the focus of this study.

In different regions around the world, the large-scale conditions and local environments may differ, but one theme of extreme rainfall is convection–environment interactions that lead to organized structures where convection repeatedly passes over (i.e., trains) or redevelops over (i.e., back-builds) the same location for an extended period of time (Schumacher 2017). In the United States, this often occurs with mesoscale convective systems (MCSs). MCSs can be supported by different physical mechanisms (e.g., cold pools, gravity waves, large-scale ascent) in different environments, but the relationship between the low-level vertical wind profile and the particular support mechanism has been consistently identified as important (e.g., Schumacher 2009; Keene and Schumacher 2013; Peters and Schumacher 2015; Blake et al. 2017; Liu and Moncrieff 2017; Hitchcock and Schumacher 2020). In Argentina, storms with deep convective cores contribute ~44% of the total warm season rain, and tend to demonstrate back-building characteristics that keep them tied to the terrain (Rasmussen and Houze 2016). In China, heavy rainfall is often produced by quasi-stationary convection along the mei-yu front (Zheng et al. 2013), where multiple wave modes may act together to support back-building in an environment with very moist low levels and unidirectional vertical wind shear. Melbourne is surrounded by modest terrain in three directions and the Southern Ocean coastline to the south (Fig. 1a), that make it different from the more often studied regions mentioned above. Its Southern Ocean coastline makes it particularly unique—the land–sea contrast can lead to exceptionally strong cold fronts [Ryan et al. (1985) reported a change of 16°C in 3 h for one event], different dynamics to fronts that approach from over land (e.g., Muir and Reeder 2010), and only a few radar sites in the world directly observe fronts off the Southern Ocean.

Fig. 1.
Fig. 1.

(a) Topography of Melbourne and surrounding region [source: 30-arc-s resolution Global Multiresolution Terrain Elevation Data (GMETED2010) by U.S. Geological Survey, prepared by National Center for Atmospheric Research/Mesoscale and Microscale Meteorology Laboratory for use with Weather Research and Forecasting (WRF) Model (Skamarock et al. 2019)]. Relevant locations discussed in the text are labeled. (b) AWAP (shaded) and rain gauge (shaded circles) mean annual precipitation in a 200 × 200 km2 Melbourne region domain centered on the Melbourne (Laverton) radar (white star). The 200- and 500-m terrain is in white and black contours, respectively.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

In southern Australia, anecdotal evidence suggests much of the organized precipitation is linear in structure, but details about the precipitation systems themselves remain largely unknown, including their contributions to heavy precipitation and precipitation totals. Few studies, especially in recent years, have focused on convective organization, synoptic/mesoscale/convective scale environment, or the dynamics of those systems. The Cold Fronts Research Programme (CRFP; Ryan et al. 1985) was a coordinated field project designed to observe and better understand the summertime cool changes and their associated weather extremes, and led to a number of studies in the 1980s (e.g., Wilson and Stern 1985; Garratt et al. 1985; Ryan et al. 1985; Ryan and Wilson 1985; Physick et al. 1985; Reeder and Smith 1987; Smith and Reeder 1988; Garratt 1988; Ryan et al. 1989). Only one of these, Physick et al. (1985), analyzed a prefrontal squall line in great detail as it passed over the Mt. Gambier station (~400 km west of Melbourne), where multiple wind shifts were associated with convectively produced boundaries. The squall line was described as generally similar to U.S. squall lines at the time, but with lower average rain rates [~1 mm h−1 over 90 min that include the peak period, compared with 4 mm h−1 over a nonpeak period in the U.S. squall line described by Ogura and Liou (1980)].

Other studies of the larger-scale contributions to Victorian precipitation, including Wright (1988), Wright (1989), Pook et al. (2006), Landvogt et al. (2008) focused on quantifying seasonal rainfall and identifying the dominant synoptic regimes in different subregions. Each identify fronts and low pressure systems as important for rainfall, though the degree of importance varied by study and region. Of particular interest, Wright (1989) found that in general, local rainfall in the dominant synoptic types was governed by the relationship between low-level winds and local topography, using a small number of stations deemed representative of a particular subregion of Victoria. More recent studies use more comprehensive objective methods to broadly link rainfall and extremes to specific synoptic- to mesoalpha-scale features like fronts, cyclones (e.g., Pepler et al. 2020), and northwest cloud bands (Reid et al. 2019). Fronts and clouds bands, especially, are conducive to forming linear precipitation structures, but many questions remain about the details of their organizational structure, intensity, duration, propagation, and the role of local topography.

Although a number of systematic studies of organized convection have been performed for other regions of the world, especially the United States [e.g., Smith et al. (2012), Haberlie and Ashley (2019), and those listed in Table 1], none of this scale have yet been published for anywhere in Australia; Potts et al. (2000) completed a more general analysis using the Dixon and Wiener (1993) method on 12 thunderstorm days in Sydney, Peter et al. (2015) did similar for southeast Queensland over a 5-yr period, while Soderholm et al. (2019) and Warren et al. (2020) focused on hail in their radar based climatologies in eastern parts of Australia. If in fact, most Melbourne rain comes from systems with specific organizational structure, identifying these systems and their characteristics has useful forecasting implications, especially if we can begin to differentiate between systems that bring more/less rain.

Table 1.

Criteria used to define linearly organized precipitation systems (e.g., MCSs/QLCSs) in previous studies and this work. Parts are adapted from Meng et al. (2013).

Table 1.

In Melbourne, convection is often organized linearly. Existing literature ties much of Melbourne region extreme rainfall to fronts/cyclones, but these are also the features that dominate the large-scale weather patterns in the midlatitudes. The organization of precipitation associated with these larger-scale features depends on a variety of other factors, and as described through existing literature in other parts of the world, a combination of this organization and environmental conditions play an important role in the occurrence of extreme rainfall. This means that linearly organized systems often occur in concert with lows and fronts, but can also form separately from those systems. The goals of this work are to 1) explore the occurrence of linearly organized precipitation systems and their relationship to total, heavy, and extreme rainfall and 2) examine the characteristics of linear systems that occur on heavy and extreme rainfall days. To this end, we objectively identified linear rainfall features in the Australian Radar Archive [AURA; Soderholm et al. (2019)] and used Australian Water Availability Project [AWAP; Jones et al. (2009)] data to explore their contributions to daily rainfall. The next section (section 2) will include information about the radar and rainfall datasets, as well as the methods used for object and extreme event identification. The results begin with an analysis of linear system frequency, followed by the contribution of linear system days to rainfall, heavy and extreme events, and finally, a look at the linear system characteristics on all, heavy, and extreme days.

2. Methods

a. Australian Radar Archive

The newly released operational dataset from the Australian Radar Archive (AURA; Soderholm et al. 2019) comprises archived data from the Bureau of Meteorology operational radar network and provides a unique opportunity for analysis of a number of phenomena, including linear precipitation systems. In this analysis, we use data from the Melbourne (Laverton) weather radar (located: 37.86°S, 144.76°W; black star in Fig. 1a) for the period 2003–18. Absolute calibration using the GPM satellite Ka-band radar as ground truth was applied to the Melbourne radar reflectivity dataset from March 2014 to December 2018 using the volume matching technique described by Warren et al. (2018). Prior to the period with GPM coverage, no calibration was applied. Removal of permanent ground echoes was performed onsite before the dataset was archived, and additional clutter was removed using the Gabella and Notarpietro (2002) echo continuity and minimum area filter. The corrected horizontal reflectivity is gridded to Cartesian coordinates centered on the radar location with 1-km horizontal and 500-m vertical grid spacing and a range of 150 km. Regridding was performed using the Py-ART python package (Helmus and Collis 2016) with a constant 2.5-km radius of influence and a Barnes weighting function. Steiner classifications (Steiner et al. 1995) were applied to the gridded dataset to identify convective pixels, which are used to quantify the convective fraction of the identified systems.

Despite the quality control described above, some residual nonstationary ground clutter still remains that is difficult to remove in the absence of Doppler velocity or polarimetric data. These pixels may be identified as convective pixels by the Steiner classification and impact radar reflectivity. Lower elevations in the Melbourne radar data are partially blocked by the mountain ranges that surround the city (Fig. 1a). The radar is also impacted by towers in the central business district (located to the northeast of the radar), leading to missing returns and spurious clutter. To reduce these effects, clear air days were used to create a mask for each year. Clear air days were defined as days with a grid maximum of less than 1 mm of rainfall in Australian Water Availability Project (AWAP) rainfall data (described in section 2c), and less than 100 pixels (~ the size of a small convective cell) with reflectivity values greater than 20 dBZ. If any pixel was identified as convective on any clear air day, it was considered clutter on that day. If more than 5% of all clear air days had clutter at a particular location, it was masked in the analysis of radar derived quantities like linear system frequency and convective fraction.

Two major upgrades of the Melbourne radar took place during the analysis period. In July 2007 the conventional C band radar was upgraded to a Doppler S band radar, and then in August 2017 upgraded to a polarimetric S band (denoted by black lines in Fig. 2). During this period incremental improvements in the gate resolution (from 1 km to 250 m), scan time (from 10 to 6 min) and data resolution (from 16 levels to 256 vertical levels) have also taken place. These changes result in some additional caveats and limitations. Compared with the S band radar, the C band radar system is expected to experience higher attenuation within and behind areas of heavy precipitation and when the radome is coated in water. Our analysis uses data from 2003 to 2018, except 2007, which had data for less than half of the year. While some data are available prior to 2003, reflectivity is available on 16 levels, which is not suitable for the assessment of reflectivity gradients required for the Steiner classification. This was upgraded to 64 levels in 2003, 160 in 2004, and 256 in 2018. The frequency of linear systems identified (method described in section 2b below) in the analysis period is shown in Fig. 2. To understand the impacts of the radar upgrade from C to S band, the results were compared for subsets of 2003–06 and 2008–18, and the fundamental conclusions did not change (not shown).

Fig. 2.
Fig. 2.

Frequency of linear systems identified on wet days between 2003 and 2018 (excluding 2007) each year. Black lines denote known radar updates.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

b. Linear system identification

In this work, we use the following criteria (given in Table 1) to define a linear system: a contiguous area with greater than 30-dBZ reflectivity anywhere in the column, a major axis longer than 100 km, and an axis ratio of more than 3:1 at two times at least 30 min apart. This is generally consistent with definitions of QLCSs/squall lines in the literature, a sample of which are listed in Table 1. The exception, perhaps, is the use of a 30-dBZ reflectivity threshold. After exploring a number of thresholds, we chose to use 30 dBZ rather than the 40-dBZ threshold more commonly used to identify U.S. storms, based on subjective analysis of the resulting identification’s ability to consistently capture the range of linear systems observed in this region. It is worth noting that this is the same threshold used in objective identification of Sydney convection by Potts et al. (2000), and further supported by evidence of lower reported rain rates than in the United States (Physick et al. 1985). As 30-dBZ rainfall is not necessarily convective, we choose to use the term “linear system” rather than squall line or QLCS. Additional discussion is provided in section 6.

We use TINT [https://github.com/openradar/TINT; Fridlind et al. (2019)], a relatively simple object identification method based on Thunderstorm Identification, Tracking, Analysis and Nowcasting (TITAN; Dixon and Wiener 1993), to identify objects with reflectivity greater than 30 dBZ anywhere in the column in the gridded radar dataset. Objects were then fit with ellipses and the linear system criteria were applied. Because of the relatively simplistic method used for object identification, we have chosen to use a discontinuous time requirement to allow for short-term discontinuities that may occasionally arise. For example, occasionally, handling of object merges and splits may result in temporary periods where an object does not meet all above requirements.

There will always be caveats and limitations to objective or subjective identification of different types of convective systems, and it is useful to understand them in order to contextualize the results. Here, the reflectivity threshold may lead to an underestimation of wintertime linear systems in Melbourne, as these events are more often characterized by shallower convection (and consequently have lower rain rates/reflectivity) than during other seasons. In some cases, an object’s size and proximity to the domain edge might lead to a missed identification if large proportions of the linear system are outside of the radar’s domain. Tracking is performed on each day individually, so cells are not tracked from one day to the next. In the diurnal cycle analysis, linear systems observed less than 30 min before or after 0000 UTC (1000/1100 local time, depending on the time of year) may have escaped identification initially, but have been manually included; the largest impact was a <2% increase at 1000 local time. In other analyses, the impact is negligible. There are sometimes multiple modes of convection present on a given day. If any of these meets the criteria for a linear system, they will be counted as such. This means that the presence of a linear system does not guarantee that it is the primary contributor to precipitation at a particular location on that day. Finally, there is some sensitivity to the set of parameters used to identify the linear systems, though the overall conclusions remain the same. Section 5b provides additional details about the sensitivity tests.

The panels in Fig. 3 were subjectively selected to demonstrate the identification algorithm in different scenarios and provide insight into the range in size, orientation, intensity, and structure of identified linear systems. Figure 3a represents a fairly typical linear system associated with a frontal passage, where a single line of moderate intensity convection is the only or largest precipitation feature. The linear system in Fig. 3b is embedded in larger stratiform region, while that in Fig. 3d is a roughly linear collection of more discrete cells. These less traditional examples still suggest larger scale linear organization.1 The example in Fig. 3c was identified as extreme by metrics described in both sections 2c and 5a, and has two large regions of precipitation with different characteristics that each met the linear system criteria at several times (though only the stronger line meets the criteria at the time shown). Note that while linear systems were identified in the entire region of available radar data, the analysis primarily focuses on a 200 × 200 km2 region centered on the Melbourne radar (the region displayed in Fig. 1b) in order to mitigate some of the radar range issues described previously.

Fig. 3.
Fig. 3.

Examples of identified objects (thick solid lines) and fit ellipses (dashed blue lines) in Melbourne radar reflectivity at the lowest vertical level (dBZ; shading). Panels include identified linear systems with different orientation, from different months and years, and represent a variety of identified linear systems. Times are in UTC.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

c. Identification of heavy and extreme rainfall events

In this paper, the 95th and 99th percentiles of domain-average daily wet-day rainfall from the Australian Water Availability Project (AWAP) are used to define heavy and extreme rainfall events (HREs and EREs), respectively, where the domain is the 200 × 200 km2 region in Fig. 1b described above, and wet days are defined as any day where the domain maximum rainfall was greater than 1 mm. The Australian Water Availability Project (AWAP) includes a gridded daily rainfall dataset that uses Barnes successive correction technique that applies a weighted averaging process to the station data, which is interpolated to a 0.05° × 0.05° grid (Jones et al. 2009). The annual mean rainfall for both AWAP and individual gauges is shown in Fig. 1b. Percentiles were computed for the set of days which radar data were available. Two other metrics, including one based directly on gauge data lead to similar results. For brevity, they will not be detailed here, but a description of those methods and their impact on results can be found in section 5a. The domain-average metric (described above) is the strictest of the three metrics, and identified 184 HRE and 37 ERE events over the 15-yr study period. It is more heavily weighted by places where it rains more and biased toward days with more widespread precipitation, which both may act as limitations to interpretation, though sensitivity analysis described in section 5a found that other definitions lead to similar results.

AWAP daily rainfall totals are available for 24-h periods ending at 0900 local time on the day the observations recorded, consistent with historical rain gauge data in Australia. To analyze rainfall contributions of days with linear systems, we define a “linear system day” as a day where the largest object at any given time meets the requirements of a linear system described in section 2b above. The “day,” is defined by data availability, so linear system object dates are first adjusted to be consistent with the AWAP “day.”

Finally, an important caveat to the analysis of rainfall contributions on linear system days in sections 3b and 3c) is that the AWAP dataset is a daily rainfall dataset. Therefore, contributions reflect all of the rainfall for the days on which linear systems occur. This does not necessarily mean that all of the rainfall on these days is attributable to linear systems. As part of our future work we plan to examine subdaily rainfall to provide an improved measure of the link between the rainfall and the linear systems.

3. Frequency and contribution of linear systems

a. Linear system frequency

On average, linear systems were identified somewhere in the analysis region (pink box in Fig. 4a) once every ~6.5 days (15.3% of all days) and on 22.1% of wet days, for a total of 812 linear system days over the 15-yr period. More than 75% of these days have convective fractions (within the linear system) of more than 10%, and the median day has a convective fraction of 19.2% (Fig. 5a). So while we have chosen to use the term linear system rather than the more familiar QLCS or squall line to account for linearly organized precipitation systems that have little-to-no convection, many of the linear systems could also be considered QLCSs.2 In fact, in the effort to choose an appropriate naming convention, we found ourselves asking questions such as, how much convection does an organized precipitation system need to be considered convective? Additional discussion to this end is in section 6.

Fig. 4.
Fig. 4.

Average number of days with a linear system observed at each point in grid (a) per year and per season, where seasons are (b) December–February (DJF), (c) June–August (JJA), (d) March–May (MAM), and (e) September–November (SON), or austral summer, winter, autumn, and spring, respectively. This does not account for the possibility of multiple linear systems passing the same point in one day. The 200- and 500-m terrain is in black and white contours, respectively. The thin orange outline is the Melbourne metro area. The pink rectangle shows the 200 × 200 km2 domain used in the analysis. The number in the top-right corner is the domain average.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

Fig. 5.
Fig. 5.

(a) Distribution of average fraction of pixels within identified linear systems that are convective by case. Mean and median for all cases given by solid and dashed black lines, respectively. (b) Average convective fraction in each season for all, heavy, and extreme events.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

While at least one linear system was identified within the analysis region every 6.5 days, an observer in central Melbourne will not necessarily experience a linear system every 6–7 days. In reality, there may be longer stretches with no events, but then several linear systems over a multiday period. Furthermore, many linear systems will only traverse a fraction of the analysis domain. In a frequency map computed from masks of observed linear systems, this translates to at least one linear system on 15 days per year (roughly one event every 24 days; Fig. 4a). Most linear systems were observed over land, to the east and north of Melbourne, with a maximum of more than 20 days in the Yarra Valley region, and extending southwest into the Mornington Peninsula (See Fig. 1a for locations). The Yarra Valley maximum is south and west of the annual mean precipitation maximum in this region (located over the Yarra ranges; Fig. 1b),3 but the east–west gradient is present in both linear system frequency and mean annual precipitation. The decrease in the number of observed linear systems toward the edge of the radar domain is likely a result of the limitations of the radar described in section 2a rather than a true lack of observed systems.

The seasonal cycle of days with linear systems somewhere in the domain is modest (Fig. 6a), but some locations have several more days with linear systems in winter/spring (JJA/SON; on average 1–2 more days); this is maximized in the Yarra Valley (Figs. 4b–e).4 In contrast, the average convective fraction is nearly twice as large in summer (DJF) compared to winter (Fig. 5b). So while linear systems occur more often in winter, they are likely to be more convective in summer.

Fig. 6.
Fig. 6.

(a) Seasonal and (b) diurnal cycles of frequency of linear systems in the domain. If multiple linear systems are identified in the same hour of the same day, they are each counted once.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

The modest seasonal cycle of the domain-wide occurrence of linear systems is consistent with Pook et al. (2006) and more general findings that Southern Hemisphere storm tracks have weaker seasonality than those in the Northern Hemisphere (Hoskins and Hodges 2005). However, spatial differences between summer/autumn and winter/spring could indicate that linear systems more consistently impact the same regions in winter/spring. Larger convective fractions also suggest that summer environments are more conducive to convection, which may not have the same spatial dependence as nonconvective events.

Linear systems have a diurnal cycle that peaks in the late afternoon–evening hours (Fig. 6b). This is consistent with the cycle of daytime heating and subsequent initiation of convection over land, which can be enhanced by topographically driven circulations (e.g., land/sea and slope/valley breezes). In cases where linear systems are closely connected to cold fronts, the coastline impact on the cold front may also impact the diurnal cycle. Turbulent mixing over land associated with daytime heating can inhibit the ability of a front to move onshore during the day, but once this mixing decreases in the evening, the roughness length change at the coastline can act to strengthen the front (increasing its speed) and the associated vertical motion at its leading edge (Muir and Reeder 2010).

b. Linear system day contributions to rainfall

On average, days with linear systems contribute 58.6% of wet day rainfall in the analysis domain, and have up to 10% higher contributions in locations where average rainfall is lower (cf. Figs. 7b and 1b). Similarly, higher contributions from linear system days occur where there are also, perhaps surprisingly, fewer linear systems (cf. Figs. 7b and 4a). Linear system days also have higher relative contributions in the Kilmore Gap region and to the north (Fig. 7b), but these regions (especially to the north of the mountain ranges) are not well captured by the radar data (Fig. 4a).

Fig. 7.
Fig. 7.

Linear system frequency and contribution by grid point. (a) Fraction of wet days that are also linear system days. (b) Percent contribution of rainfall on days with linear systems to wet day rainfall at each grid point. (c),(d) Percent contribution of days with linear systems to rain that falls on heavy and extreme rainfall days, respectively. The 250- and 500-m land surface heights are shown by white and black lines, respectively. The number in the top-right corner of (b), (c), and (d) is the domain average.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

Seasonal variations of linear system day contribution to wet day rainfall range from 2.5% to 12.5% on average (Fig. 8), and while linear systems occur more frequently in winter, their contributions are greater in summer. The spatial variations generally resemble those of the annual contributions (Figs. 7b and 8), but in autumn and winter the largest contribution near the city is shifted to the west relative to the annual contribution (Figs. 8b,c). The lower contributions in winter could be due to more frequent low-intensity cases that are not captured by the 30-dBZ threshold, more rainfall associated with broad stratiform regions without noteworthy convection or linear organization, or postfrontal cellular convection.

Fig. 8.
Fig. 8.

Percent contribution of rainfall on days with linear systems to wet day rainfall at each grid point, as in Fig. 7b, but separated into seasons (a) summer, (b) winter, (c) autumn, and (d) spring. The number in the top-right corner is the domain average.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

Figure 7a suggests that the frequency of more than 1 mm of rainfall on a linear system day is nearly equally likely at any grid point (even if the linear system does not pass over that point). Put another way, if a linear system occurs, most locations are likely to see rain, even if a linear system is not responsible for it, which provides some evidence for the caveat described in section 2c. This said, linear systems can lead to locally intense rainfall, and their presence provides insight into the organizational mechanisms on the days they occur. Future analysis that focuses on subdaily time scales would certainly be insightful, however, this will require an accurate source of subdaily rainfall information.

c. Heavy and extreme events

Frequency maps of linear systems on heavy/extreme days indicate that most places can expect to see one to two linear systems associated with heavy rain events per year, and one linear system associated with extreme events once in three years (Fig. 9). Interestingly, these frequency maps do not share much resemblance to the annual or seasonal frequency maps. Rather, HRE linear systems have relatively similar frequency across much of the domain, fragmented by a minimum southwest of the Macedon ranges in the same location as the annual precipitation minimum, and linear systems on EREs occur more frequently in the Kilmore gap region. A total of 83.6% (81.1%) of HRE (ERE) days have at least one linear system somewhere in the domain, and those days contribute 82.8% (77.8%) of the rain that falls during HRE/EREs. This consistency between the frequency and contribution suggests that a similar amount of rain falls on linear system days as other types of HRE (ERE) days.

Fig. 9.
Fig. 9.

Average number of days with a linear system that are also (a) HREs and (b) EREs. Does not account for the possibility of multiple different linear systems passing the same point in one day. The 200- and 500-m terrain is in black and white contours, respectively. The thin orange outline is the Melbourne metro area. The pink rectangle shows the 200 × 200 km2 domain used in the analysis.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

Spatial variations in the contribution of heavy/extreme linear system day rainfall to total rainfall (not shown) are similar to those for all linear system days (e.g., Fig. 7b), but the relative contributions to rainfall on heavy/extreme days appear to be influenced by local coastlines and terrain; differences are on the order of a few percent (Figs. 7c,d). Heavy linear system days contribute more to HRE rainfall in the ranges to the north and west and along the coastline. Extreme linear system days have relatively higher contribution in the east and toward the north of the Macedon and Yarra Ranges.

To contextualize the seasonal contributions of heavy and extreme linear system rainfall, we examined all HREs and EREs (with or without linear systems, Fig. 10b). HREs occur most frequently in spring, are more consistent across the other seasons (Fig. 10a), and they have the largest contributions to seasonal rainfall in spring and summer (Fig. 10b). HREs with linear systems follow a similar trend in frequency (Fig. 10c), but contribute the most to heavy rainfall in winter (Fig. 10d), when the heavy rainfall contribution to the seasonal total is lowest (Fig. 10b).

Fig. 10.
Fig. 10.

Seasonal bulk rainfall statistics: (a) fraction of heavy/extreme rainfall days by season, (b) gridpoint mean contribution heavy/extreme rainfall day rainfall to seasonal rainfall, and (c) fraction of days with linear systems and fraction of days that overlapped with heavy and extreme rainfall events by season. The former is shown by the left axis, the latter (overlap with heavy and extreme events) is shown by the right axis. (d) Contribution of rainfall on days in (c) to wet day/heavy/extreme rainfall totals by season.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

EREs occur more frequently in spring and summer (Fig. 10a), and their relative contributions are similarly higher in those seasons (Fig. 10b). EREs with linear systems also occur most frequently in spring and summer (Fig. 10c), but 100% (8 cases) of extreme rainfall events that occurred during winter months had linear systems (Fig. 10d).

4. Linear system characteristics for all, heavy, and extreme events

If we wish to identify the characteristics of linearly organized heavy and extreme events in this region, it is useful to consider the fundamental ingredients of heavy rainfall. The precipitation P at a particular location is simply the product of the mean rain rate R¯ and rainfall duration D or P=R¯D (Doswell et al. 1996). Duration is a function of the storm system lifetime, size, organization, and propagation. These, along with rain rate, are driven by complex relationships between the system dynamics, microphysics, and the environment. In this section, we use information from the linear system objects to create distributions of the day-median characteristics described in Table 2 (characteristics for every time level are used to determine the median for each day). We also provide an indication of significant differences between distributions at the 95th percentile based on the nonparametric Kolmogorov–Smirnov test (Wilks 2011), and Kuiper’s test for angular variables (Stephens 1970). Significance was computed between HREs and nonevents (days with linear systems that were not HREs), and between EREs and the subset of HREs that excludes EREs.

Table 2.

Description of linear system characteristics and a measure of whether different categories are significantly different. The H designates parameters where differences between HRE linear systems and nonevents are significant at 95% by nonparametric Kolmogorov–Smirnov test (Kuiper’s test for angular variables). [The Kuiper statistic is nonparametric and resembles the Kolmogorov–Smirnov test but is also invariant under cyclic permutations and therefore more appropriate for circular data. It was computed using the Python package (Astropy Collaboration 2013, 2018).] Likewise for E, but for differences between ERE linear systems and the subset of HRE linear systems that does not include EREs. E* indicates where ERE linear systems are significantly different from nonevents.

Table 2.

a. Orientation and propagation

The majority of cases have a negative slope (~−20°), indicating that their major axis is aligned north-northwest–south-southeast (Fig. 11a). This is consistent with the typical orientation and progression of cold fronts in this region (which approach from the southwest). The distribution of orientation is shifted closer to zero in heavy and extreme cases, indicating a more north–south orientation. The distribution shifts lead to modest increases in the mean (median) orientation from −20.7° (−27.1°) to −14.9° (−17.2°) to −11.8° (−14.7°) between nonevents, HREs, and EREs, respectively, and differences between HREs and nonevents are significant.

Fig. 11.
Fig. 11.

Violin plots of case-median linear system characteristics. Black lines are distribution means, colored lines are distribution minima, maxima, and medians. (a) Orientation, (b) propagation direction, (c) angle difference between orientation and propagation direction, (d) propagation speed, (e) area, (f) major axis, (g) minor axis, (h) longest duration, (i) reflectivity, (j) echo top height, (k) convective fraction, and (l) number of unique linear systems. A star in the space between two categories indicates statistical significance between the adjacent columns. A triangle above the ERE column indicates statistical significance between ERE and nonevents. Significance between HRE and ERE distributions was computed using the subset of HREs that excludes EREs. Additional information about the individual characteristics can be found in Table 2.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

On average, linear systems propagate at 14.1 m s−1 toward the east (95.6°) (Figs. 11b,d). Heavy and extreme events are ~2 m s−1 slower and differences between HRE/EREs and nonevents are significant. Propagation is slightly more southward in heavy events (by 7.5°), but much more so in extreme events. There is an 21.7° shift toward more southward propagation from heavy to extreme events and 29.0° shift from nonevents to extreme events. These differences are both meaningful and statistically significant (Table 2; Fig. 11b).

The more north–south orientation and southerly propagation in heavy/extreme events suggests a greater component of along-line propagation. This relationship was analyzed directly by computing the acute angle between the major axis and the axis of propagation. On average, this angle is around 54°, but the distribution is skewed toward 90°, indicating that many cases move largely perpendicular to their major axis (Fig. 11c). The mean and median angles in all subsets are relatively similar, and differences between the distributions are not significant. However, it is interesting that the distribution in ERE cases is bimodal, with peaks around 70° and 35°. While the other distributions have some bimodality, that the ERE peaks are comparable in amplitude is notable and may suggest different regimes of extreme events. Specifically, it is possible that clusters of orientation/propagation characteristics based on larger scale flow could exist, but this is an area of future work. It is worth mentioning here, that while the 30-dBZ threshold is useful for identifying the linear systems, a higher threshold or method to track individual convective cells may better identify training events. Our use of daily precipitation and lack of attribution to specific systems are also limitations to the analysis of these aspects.

b. Size

When propagation and orientation are more perpendicular, a larger minor axis leads to higher precipitation totals; where they are more parallel, a larger major axis leads to heavier precipitation [see Fig. 3 in Doswell et al. (1996)]. The average linear system has both line-parallel and line-perpendicular components of propagation, so those with larger major axes, minor axes, and area might be expected to lead to heavier rainfall, as is shown by Fig. 11e. Indeed, the mean (median) HRE has a 45.7% (40.4%) larger area than the mean (median) nonevent, but the difference between EREs and HREs is smaller, ~7.6% (9.0%). The major and minor axes are both larger in HRE/EREs than in nonevents, but similar in HREs and EREs (Figs. 11f,g). The percent change in the minor axes length from nonevents to HREs is slightly larger than the change in the major axis, ~24.1% and 16.3%, respectively, which suggests that in this definition of extreme events, the width of the linear system may have a greater role in distinguishing an HRE from a nonevent, though both the length and width are important.

There are two important limitations to the interpretation of this analysis. First, both major and minor axes of all linear systems are limited by a combination of the selection criteria and the coverage of the radar data. Second, the choice of a HRE/ERE definition favors more widespread events, so perhaps it should be expected that HRE/EREs tend to be larger. However, as described earlier, there are also physical reasons that larger events can lead to heavy/extreme rainfall at individual locations too. When other definitions (discussed in section 5a) were used, area remained a significant indicator of differences between HRE/EREs and nonevents.

c. Intensity

Reflectively, echo top height, and convective fraction were explored as measures of intensity, as rain rates have not yet been published for this dataset. Reflectively of EREs is significantly higher when compared to nonevents, but differences in mean/median are less than 1 dBZ (Fig. 11i). EREs have echo-top heights that are significantly different from HREs and nonevents, but differences are less than 1 km. While these differences are small in the median, the shifted distributions (especially of echo-top heights) and statistical significance suggest that linear systems on ERE days have an increased likelihood of deeper, more intense convection, even if the fraction of convective cells is similar to linear systems on other days. The domain-average and temporal scale of the definition of HRE/EREs that favors widespread over locally extreme precipitation may also impact this result.

d. Duration and multiple occurrences

In addition to the area and degree of along-line propagation, the storm lifetime can also impact the duration of a storm (in the domain and at an individual location). As there are often multiple lines of varying lifetimes associated with linear systems, we use the duration of the longest-lived linear system to focus on the most likely “main event.” To counteract the discontinuous time requirement used in linear system identification and ensure continuity in linear systems considered for longest duration, if a “break” between consecutive classifications of the same object as linear is longer than 20 min (this is a single 10-min scan prior to 2007 and approximately three 6-min scans after), the duration before and after the break are considered separately.

The average duration of all, heavy, and extreme events is 50, 57, and 70 min, respectively, where HRE and ERE event durations are both significantly longer than nonevents (Fig. 11h). Duration is limited by the time linear systems are within the radar range, even if their true life-span is much longer. Consequently, duration may also be a reflection of size, propagation speed, and degree of along line propagation.

Because fronts, one of the synoptic features previously associated with linear systems, often contain multiple linear systems, we also decided to look at the number of uniquely identified objects that met the linear system criteria in each case. The vast majority of cases have only one to two unique objects, but heavy and extreme days have 2.4 and 3.2 (Fig. 11l). This suggests HRE and ERE events are often characterized by wide, slow-moving precipitation systems with multiple embedded, long-lived linear structures.

5. Sensitivity of results to definitions and parameters

a. Sensitivity to the definition of heavy and extreme rainfall events

For robustness, two different datasets and three different metrics were initially used to identify and compare HRE/EREs. In addition to the domain-average method described in the methods section (hereafter, AWAP_AVG), an AWAP domain maximum (hereafter AWAP_MAX) wet day rainfall was also explored. A third metric, using daily gauge data from the Global Historical Climate Network-Daily (GHCN-D) (Menne et al. 2012), defines HREs/EREs where two gauges, separated by at least 50 km, exceed their 95th/99th percentile of wet day rainfall (hereafter GAUGE) similar to Warren et al. (2021). In this method, the gauge time series are considered independently in defining percentiles, and wet days at a given gauge are days where rainfall is greater than 1 mm. Unlike the methods used on the AWAP data, GAUGE events were identified over a 30-yr period for better consistency with climatological identification of HRE/EREs, and then only days with available radar data were considered for analysis.

In both other definitions, linear system days still have a large overall contribution to HREs/EREs (Fig. 12), and spatial frequency and contribution are relatively consistent with Figs. 7 and 9. Of the linear system characteristics, sizes are similar in both definitions, while duration and orientation become insignificant (not shown). In the GAUGE definition, propagation speeds during EREs become even more significant (and significantly different from HREs), and in the AWAP_max definition, EREs have significantly more along-line propagation, but are not necessarily deeper than nonevents (not shown).

Fig. 12.
Fig. 12.

Linear system day frequency and contribution to total, heavy, and extreme rainfall using AWAP_AVG, AWAP_MAX, and GAUGE methods to identify heavy/extreme rainfall days. (a) Percent of wet days, heavy rainfall, and extreme rainfall days where a linear system was identified. (b) Contribution of rainfall on those days to the wet-day, heavy, and extreme rainfall. Contributions are calculated by taking the grid average rainfall on relevant linear system days divided by the grid-averaged rainfall on wet days identified as all/heavy/extreme. Overall frequency and contribution values computed just once but displayed in each set for consistency.

Citation: Monthly Weather Review 149, 10; 10.1175/MWR-D-21-0007.1

b. Sensitivity to select parameters

The overall frequency and contribution of linear system days was somewhat sensitive to the linear system selection criteria, but as with the definition of heavy and extreme events, linear system days have a large contribution to rainfall in each. The sensitivity tests are listed in Table 3.

Table 3.

Sensitivity to different system definitions.

Table 3.

Almost by definition, less restrictive criteria lead to identification of more linear system days and larger contributions (not shown). Likewise, more restrictive criteria result in fewer linear system days and smaller contributions. When the definition which results in the smallest number of linear system days (35 dBZ) is used, those days contribute 32.3% of the total rainfall and 42% (53%) of HRE (ERE) rainfall. However, early subjective analysis suggested that this definition missed many events.

Regardless of the criteria, days with linear systems contribute at least 40% of HRE and at least 45% of ERE rainfall. When the 35-dBZ threshold was used, spatial distributions of linear system frequency and contribution (e.g., like Figs. 4 and 7) are also consistent (not shown). Extreme event contributions are least similar, but also represent smaller numbers of cases, where individual days have more impact.

Size is a distinguishing feature of HRE/EREs (note AWAP_AVG defined HRE/EREs), while reflectivity and echo-top height are significantly higher in EREs than nonevents in most of the sensitivity tests. The increase in southward propagation between nonevents and HREs, HREs and EREs, or both, is significant in nearly all definitions, and interestingly, in the majority of definitions it is a distinguishing factor between HREs and EREs. Several definitions also lead to greater degrees of along-line propagation (35 dBZ, 50 km, day largest), which were significant for the group defined by a 50-km major axis. At the same time, cases in this group are mostly dominated by many smaller linear systems, where more extreme events tended toward more separate, larger, and longer-lived lines.

6. Discussion

Some discussion occurred around the decision of what to call the linearly organized precipitation systems common to this region. Although QLCS is often used interchangeably with squall line, while not defined in the AMS Glossary, it is sometimes distinguished as a more generic term that captures those systems that might not be truly linear. QLCS also implies that a system is convective, though it is less clear how much convection there is, how deep the convection is, or if it must be driven by that convection to be a QLCS. The measure of convective fraction is more commonly applied to tropical studies,5 of which some explore areal fractions over different regions of different sizes (e.g., Schumacher and Houze 2003; Kumar et al. 2013), while others explore system relative fractions of individual events. Those which explore system relative fractions have found convective fractions of MCSs and squall lines are anywhere between 15% and 75% [summarized by Schumacher and Houze (2003), and citations therein], though the individual methods for determining system convective fractions are not consistent. Nearly all of the linear systems in the Melbourne region had some convective pixels, and 75% had convective fractions of at least 10%. However, anecdotal observations indicate that they are often of weaker intensity than similar systems elsewhere (especially in wintertime, like Fig. 3b); the median reflectivity of slightly more than 30 dBZ and 4–7-km echo tops in Figs. 11i and 11j are consistent with these observations. Ultimately, we chose to use the more generic term “linear system.”

One of the themes evident in the spatial analyses, is the role of the coastline and orography. Linear system frequencies highlight coastlines and the western slope of the Yarra Ranges, indicating invigoration or even initiation by orographic and/or sea-breeze circulations. Though somewhat counterintuitively, these spatial differences are amplified in winter. At the same time, linear system day contributions to rainfall are lower in a similar region, because orography, especially windward slopes, is conducive to rainfall that in many cases may not be linear. Shifts in seasonal contributions suggest differences in dominant low-level flow and its interactions with orography are important, as described by Wright (1989).

As most linear systems have north-northwest–south-southeast orientation (becoming increasingly north–south in HRE/EREs) and propagate toward the east-southeast (and increasingly toward the south in EREs), minima southeast of the Macedon Ranges (seen in many analyses), including in the frequency of HRE linear systems, may be linked with down-slope effects. In contrast, much of the largest linear system day contributions to rainfall (for any subset of events) are to the north of the mountain ranges. The Kilmore gap is a region of relatively lower terrain, where ERE linear systems are maximized. While it is not entirely clear exactly why this occurs, potential explanations include deepening of the moist inflow and convective outflow layers as convection moves off of the higher terrain leading to increased organization, zones of enhanced convergence resulting from channeling of northerly flow through the region, or other kinematic effects due to the impact of the terrain on the local wind field; these may be worth future investigation. Northerly flow is more likely to originate in the tropics or subtropics (Wright 1988), and transport air that is both moist and warm (as opposed to cooler, more southerly, marine air), and so perhaps extreme events are ones that are able to make use of favorable topographic interactions and northerly flow.

This work highlights some important questions. For example, we focused on daily rainfall extremes, but linear systems have strong spatial tendencies and relatively short life-spans (approximately a few hours). It is reasonable to wonder how much of the rain on days with linear systems originates from the system itself. Similarly, many flash-flooding events occur on subdaily time scales. What are the linear system contributions to subdaily extremes? Do these events have different characteristics from the case-averaged characteristics based on daily extremes? While we suspect that many cases are frontal in nature, gravity waves, cold pools, sea breezes, and other similar boundaries can organize convection linearly. In frontal cases, linear systems may occur ahead of, along, or behind the front. Distinguishing between organizational mechanisms and the location of precipitation relative to fronts could prove useful. Finally, seasonal patterns and orientation characteristics are likely connected to the synoptic scale environments, and the bimodality of along-line propagation suggest clusters of specific flow regimes which could be explored.

7. Summary and conclusions

An objective method was used to identify linearly organized precipitation systems in 15 years of Australian radar data for the Melbourne region. The resulting set of linear system objects and the 812 days they occurred were used to explore their annual, seasonal, and diurnal characteristics, as well as their contribution to regional rainfall on all, heavy, and extreme days. Characteristics of linear systems on HRE/ERE days were compared with those on nonevents days in order to identify those that define the heavy and extreme cases.

Linear systems occur frequently (every ~6–7 days somewhere in the domain, and every ~15 days at a point on average), and the days on which they occur contribute more than half of the total rainfall and more than three-quarters of the rain on HRE/ERE days. Linear systems are more common in the east, but contribute more rain where the total rain is smaller and the systems occur less often. Seasonal differences suggest that summertime linear systems are more convective, while wintertime events are more likely strongly forced by cold fronts. Spatial variability suggests that linear systems (and their rainfall) are impacted by the local coastline and orography.

Linear systems associated with the type of widespread daily heavy/extreme rainfall events explored here are generally oriented north-northwest–south-southeast, propagate toward the east between 10 and 20 m s−1, and have components of propagation both perpendicular and parallel to their orientation. With the caveats of the selection criteria, linear systems tend to be between 110 and 150 km long, and 30–40 km wide with moderate (~30–35 dBZ) reflectivity, 4–7-km echo tops, and convective fractions of 10%–30%. Those that contribute to daily heavy rain events have more north–south orientation and are significantly larger, slower, and long lived. Those that contribute to extreme events are still larger, slower and longer lived, but also have more southward propagation, and are more likely to be associated with deeper, more intense convection.

Despite the questions that remain, this study confirms that frequently observed linear systems are not simply anecdotal, and more importantly, that the rainfall on days when they occur has a significant contribution to both the total and extreme rainfall in the region due to both their size and motion. Exploring subdaily rainfall extremes and their links to linear systems is a natural extension of this work and should be a topic for future research.

Acknowledgments

Thanks to three anonymous reviewers and Editor Angela Rowe for their time and helpful suggestions. Thanks to Jordan Brook and Ewan Short for sharing their methods of TINT modification and bug fixes, to Andrew King and Christian Jakob for helpful discussions, and to the Mesoscale and CLEX Extreme Rainfall groups for feedback and support. Thanks also to the CLEX administration and Computational Modeling Systems teams, especially Scott Wales for their assistance and support. This work is supported by the ARC Centre of Excellence for Climate Extremes (CE170100023) and also benefited from computing provided by the National Computational Infrastructure (NCI) facility.

Data availability statement

The Australian Radar Archive data (Soderholm et al. 2019) is available through the National Computational Infrastructure (NCI) THREDDS data server, and additional information can be found at https://www.openradar.io/. TINT (Fridlind et al. 2019) is available on github: https://github.com/openradar/TINT. The Australian Water Availability Project data (Jones et al. 2009) is maintained by the Australian Bureau of Meteorology http://www.bom.gov.au/metadata/catalogue/19115/ANZCW0503900567. Daily rain gauge data are available through the Global Historical Climate Network-Daily [GHCN-D; Menne et al. (2012)].

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1

The linear structure of identified objects was more clear at times other than the one shown in Fig. 3d, which was selected to demonstrate a borderline case.

2

We also avoided terms like frontal, as rainfall can be organized linearly by other mechanisms including sea breezes, gravity waves, and cold pools, which imply different dynamics.

3

Beam blockage may be partially responsible for the decrease beyond the front range.

4

In winter, the strong range dependence is likely a reflection of the brightband contribution to the column maximum reflectivity.

5

Jirak et al. (2003) explored the convection fraction of different MCS types in the U.S. Great Plans, but based on reflectivity thresholds alone, so their results are not particularly comparable here.

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