Identification of Rainfall Events and Heavy Rainfall Events From Radar Measurements in Southeastern Australia

Radar data can be of significant utility in investigating characteristics of rainfall events that cannot be studied with rain gauges alone. The recent establishment of a long‐term, quality‐controlled data set covering most of the radars on the Australian continent enables a deeper characterization of rainfall, including heavy rainfall events. This study develops a methodology to identify and characterize rainfall events from radar data and tests its utility by applying it to the regions surrounding the major cities of Brisbane, Sydney, and Melbourne. The event characteristics studied include rainfall accumulation and intensity, event duration and spatial extent, and the contribution convective areas make to the overall event rainfall. Rainfall events in Brisbane and Sydney are found to be more intense, more convective, and smaller in extent whilst producing larger rainfall accumulations than Melbourne rainfall events. Rainfall event duration and total accumulated rainfall are strongly positively correlated, as are the overall event intensity and the intensity of convective rainfall. The events that produce the largest rainfall accumulations exhibit significant differences from the events that produce the highest rainfall intensities. Overall, the study demonstrates that long‐term radar data sets in Australia provide an invaluable and rich source to study rainfall characteristics in a variety of regions at a high spatial and temporal resolution.

accumulated over specific time intervals, making them less useful to study the physical mechanisms involved in rainfall events.In gauge data sets there is also the potential for untagged accumulations, instances where rain gauges have gone unread for a period of multiple days which results in the accumulated rainfall of these days (typically over weekends) being mistakenly recorded as that of a single day (Viney & Bates, 2004).This poses a major issue when analyzing past heavy rainfall events.Gridded data sets derived from gauge data are also subject to spatial errors originating from the interpolation techniques used (Liu et al., 2018;Tozer et al., 2012).
An alternative method to estimate rainfall is the use of weather radars.Operational weather radars provide continuous estimates of rainfall at a high temporal and spatial resolution over a large area, and can provide detailed information about rainfall event duration, spatial extent, and structure, at the expense of quantitative accuracy and long record periods.Radar estimates of instantaneous rain rate R in mm hr −1 are commonly generated from radar reflectivity factor Z using an empirically derived Z-R relation of the form Z = aR b (Rauber & Nesbitt, 2018).Like any remote sensing technique, rainfall estimates from radar are quantitatively uncertain.There are two key areas of error for single-polarization radar rainfall estimation-errors associated with reflectivity retrievals (e.g., calibration, attenuation, ground clutter, anomalous propagation) and errors associated with conversion of retrieved reflectivity into surface rainfall rates (e.g., variability in raindrop size distribution, contamination by ice) (Chumchean et al., 2008;Villarini & Krajewski, 2010).It is possible to mitigate against uncertainties in radar rainfall estimates by adjusting radar rainfall fields to quantitatively match rain gauge measurements while retaining the spatial structure in a process known as gauge adjustment (Bližnák et al., 2018;Rauber & Nesbitt, 2018), and many data sets using this technique exist around the world (Kreklow et al., 2020;Panziera et al., 2018;J. Zhang et al., 2016).
Radar data can also be used to partition rain fields into convective and stratiform areas.Convective precipitation occurs when environmental vertical velocity equals or exceeds the terminal velocity of water droplets, while stratiform precipitation occurs when environmental vertical velocity is less than terminal velocity (Chumchean et al., 2008;Steiner et al., 1995).Regions of stratiform precipitation can also be identified on radar by the presence of a bright band, which is a region of high reflectivity created by the melting ice layer present in stratiform precipitation (Chumchean et al., 2008).Although it is not practically feasible to use vertical motion or bright band presence to separate convective and stratiform precipitation, it is possible to distinguish between these two precipitation types based on the fact that convective areas typically exhibit both higher reflectivity values and higher horizontal spatial variability in reflectivity than stratiform areas (Churchill & Houze, 1984;Houston et al., 2015;Raut et al., 2020;Steiner et al., 1995).While a variety of convective-stratiform partitioning algorithms exist, the algorithm of choice for many different radar studies is the Steiner algorithm (Barnolas et al., 2010;Chumchean et al., 2008;Cifelli et al., 2007Cifelli et al., , 2008;;Hitchcock et al., 2021;Kumar et al., 2013;Louf, Jakob, et al., 2019;Xu & Rutledge, 2015).Developed by Steiner et al. (1995), this algorithm classifies peaks in reflectivity and their surrounding areas out to an intensity-dependent radius as convective precipitation, with the remainder of the reflectivity field classed as stratiform precipitation.To aid in the quantitative accuracy of radar rainfall estimates, different Z-R relations can be used for convective and stratiform precipitation (Chumchean et al., 2008;Goudenhoofdt et al., 2017;Steiner et al., 1995).
There are a multitude of studies that use a single radar to investigate the characteristics of radar echoes in a localized region (Capsoni et al., 2008;Clarke, 1989;Feral et al., 2000;Lagrange et al., 2018;Lang et al., 2007;López, 1976;Lopez et al., 2023).Recently, Hitchcock et al. (2021) used radar data to identify linear rainfall systems in the region surrounding Melbourne, Australia, before using a gridded rainfall data set to link them to rainfall extremes.They were able to obtain valuable information pertaining to the attributes of linear systems in the study region, and found that linear systems occurring on heavy rainfall days tend to be larger and longer-lasting than linear systems on other days.Ayat et al. (2022b) used an object-oriented tracking algorithm to analyze the characteristics of precipitation systems in the Sydney region, and found that precipitation systems are most frequent during autumn and winter, but systems classed as extreme in terms of size, translation speed and rainfall intensity are most common during the spring and summer.
Radars are frequently used to study convective rainfall (Barnolas et al., 2010;Kumar et al., 2013;May & Ballinger, 2007;Moral et al., 2020;Peleg & Morin, 2012;Rigo & Llasat, 2004) and thunderstorms (Birch, 1972(Birch, , 1973;;Peter et al., 2015;Potts et al., 2000).Using the C-band Dual-Polarization (CPOL) research radar in Darwin, Louf, Jakob, et al. (2019) investigated the relationship between convective clouds and their large scale environment.They found that convective rainfall intensity is more closely related to cell area than number of cells, with heavy rainfall almost always associated with large convective cells.Satellite-based radar studies have found that there is a degree of separation between events with extreme rain rates and events with extremely intense convection (Hamada et al., 2015;Zipser & Liu, 2021).This may be attributable to intense rainfall with high precipitation efficiency being favored by a structure known as the low-echo centroid, where the majority of rainfall production occurs below the freezing level through warm rain processes (Hamada et al., 2015;Ryan & Vitale, 2008;Schumacher, 2017).In Australia, convective systems that occur during active monsoon periods in Darwin have been found to have relatively low cloud top heights and minimal electrical activity, indicative of relatively weak updrafts, while convective systems that occur during break (non-monsoon) periods generally have more intense convection (Kumar et al., 2013;May & Ballinger, 2007).Despite lack of strong convective activity during monsoon periods, daily total rain accumulation in Darwin is greatest during these times (Kumar et al., 2013), demonstrating that intense convection does not directly equate to intense rainfall.
In several countries around the world, radar networks have been used to analyze echo characteristics, convection, and rainfall events over larger regions than those covered by a single radar (Karklinsky & Morin, 2006;Lang et al., 2007;López et al., 1984).Fairman et al. (2017) used radar data to create a climatology of precipitation features over the United Kingdom and Ireland and obtained information about feature characteristics such as areal coverage, shape, and mean and maximum precipitation rates.Another notable example is Schumacher and Johnson (2006), who used the radar network in the United States to examine the morphology of extreme rainfall events, with those that were identified as mesoscale convective systems (MCSs) able to be classified into archetypes including trailing stratiform, leading stratiform, and parallel stratiform, amongst others.This allowed investigation of which system types produced the highest 24-hr rainfall totals.Lengfeld et al. (2021) used a nationwide radar archive for Germany to obtain a catalog of heavy rainfall events and their characteristics over a 20-year period, allowing for detailed investigation of individual events and computation of event statistics.In Australia, Ayat et al. (2022a) used a set of three radars in the Sydney region to examine trends in rainfall extremes, discovering a statistically significant increase in sub-hourly maximum rain rates of at least 20% per decade.
While notable work has been done with radar rainfall estimation for flood events (Cusworth, 1997;Hoy, 1975;Liu et al., 2018;Sun et al., 2000) and investigating drop size distributions (Bringi et al., 2009;Thurai et al., 2010) in Australia, there have not yet been any long-term radar studies that focus on rainfall event characteristics on a national scale, despite such studies existing in other parts of the world.Furthermore, initial identification of extreme rainfall events in many studies both in Australia and overseas is performed using a rain gauge network, before radar data is later used to investigate event attributes in more detail (Hitchcock et al., 2021;Lee & Kim, 2007;Moral et al., 2020;Rigo & Llasat, 2004;Schumacher & Johnson, 2006;L. Zhang et al., 2019).Overall, there is a gap in research regarding use of radar networks to both identify and characterize rainfall events and heavy rainfall events across Australia.The Australian Unified Radar Archive (AURA) collates more than a decade of radar rainfall estimates across the operational weather radars deployed by the Bureau of Meteorology using a coherent and well-calibrated methodology (Soderholm et al., 2022).While this data set has been used in previous studies to provide innovative insights into precipitation in specific regions (Ayat et al., 2022a(Ayat et al., , 2022b;;Hitchcock et al., 2021), it also provides an opportunity to exploit radar observations to characterize and compare rainfall events in different regions across the Australian continent for the first time.
The purpose of this study is to develop a simple yet robust algorithm for identifying rainfall events and their key characteristics in the long-term radar observations of the AURA data set.This algorithm is then used to create a large data set of rainfall events and investigate the duration, rainfall accumulation, intensity, spatial extent, and convective characteristics of these events.An additional goal is to contrast heavy rainfall event characteristics with those of non-heavy rainfall events.Given the focus on methodological aspects, this study is confined to three locations-Brisbane, Sydney, and Melbourne-with the extension of the findings to the entire AURA network of radars left to future work.While incorporation of rainfall estimates from rain gauges and satellite platforms is a key task for Australia, doing so is beyond the scope of this paper, and no such data sets with record periods longer than a few years currently exist.Additionally, while use of dual-polarization radar allows for a more physically based conversion from reflectivity to rain rates and more effective removal of non-meteorological echoes (Chandrasekar et al., 2003), only a quarter of the radars currently active in Australia's operational network have dual-polarization capabilities and most of these radars have only been commissioned in the last 3 years (Soderholm et al., 2022).Additionally, dual-polarization radar-specific rainfall retrieval algorithms have not yet been widely deployed in Australia.Overall, the focus of the results presented in this study is less on the precise quantitative accuracy of the radar measurements and more on qualitative comparisons that can be made between different regions.
Section 2 of this paper introduces the AURA data set and the method of identifying rainfall events using radar.Section 3 presents an analysis of the main characteristics of rainfall events in Brisbane, Sydney, and Melbourne.Section 4 introduces identification of heavy rainfall events and contrasts their characteristics to those of all rainfall events.Section 5 describes the implications of uncertainties in the conversion of reflectivity to rain rate and separation of convective and stratiform regions.Finally, Section 6 presents the final conclusions of the study and summarizes the main caveats and opportunities associated with the methods used here.

The Australian Unified Radar Archive
The analysis in this study is performed using AURA.This data set provides a range of radar products from more than 70 weather radars in the Australian operational network (Soderholm et al., 2022).Level 2 data products (which are corrected 2-D fields) are used for the analysis presented in this study.The Level 2 products are interpolated into Cartesian coordinates using the technique described in Dahl et al. (2019) of transforming radial and azimuthal data to x-y coordinates using Cressman interpolation with a cutoff radius of 2.5 km, and using linear interpolation in the vertical direction.The resulting horizontal resolution of the data is 1 km, and the vertical resolution is 0.5 km.Data is available to a maximum horizontal range of 150 km.As this study is mainly concerned with prototyping an algorithm to identify rainfall events, we restrict our analysis to three radars: Brisbane, Sydney, and Melbourne.Each of the three radars is a dual-polarization S-band radar (wavelength approximately 10.5 cm, frequency approximately 2.9 GHz) with a beam width of 1°.Eleven years of data spanning 1 January 2010-31 December 2020 are used from each radar.All three radars were operating with 5-10 min volume sampling, with 6 min being the most common volume sampling time.To avoid range-related artifacts in the data, analysis is limited to pixels within a range of 100 km from the radar site.Ground clutter filtering was first performed by the weather radar signal processor and again prior to interpolation by using thresholds on echo continuity and minimum echo area described by Gabella and Notarpietro (2002).Reflectivity data from March 2014 onwards is calibrated using a technique involving the Global Precipitation Measurement Ku-band Precipitation Radar product, as outlined in Louf, Protat, et al. (2019).Prior to this date, data from the Tropical Rainfall Measuring Mission (TRMM) satellite was used for calibration.This means that data prior to March 2014 from the Melbourne radar, which is located outside of the domain covered by TRMM, is not calibrated.However, there is no statistically significant difference between rainfall event characteristic distributions obtained using data from the Melbourne radar prior to March 2014 and results obtained using data post-March 2014 (not shown).
Two Level 2 products were used directly: estimates of the instantaneous rain rate, and partitioning of the rain fields into convective and stratiform areas (see below).Each of the three radars used in this study has a distinct Z-R relation fitted using observations from rain gauges near the radar.The rain rate data is estimated from the reflectivity at the lowest valid grid value between 0 and 2.5 km above radar level.The Z-R relations for each radar, along with other key attributes, are summarized in Table 1.Some months have reduced data availability due to outages and maintenance, which is illustrated in more detail in Figure 1.Less than 4% of the data over the 11-year period used is missing for each radar, although individual outages were able to exceed a month in length.
The convective-stratiform partitioning product in AURA is based on the algorithm developed by Steiner et al. (1995).The algorithm is applied to the gridded reflectivity values at 2.5 km above radar level, and classifies a point as likely convection if: 1. reflectivity is at least 42 dBZ, or 2. reflectivity exceeds the linear average of non-zero radar echoes within an 11 km radius around the point, or  (Soderholm et al., 2022) 10.1029/2023JD039253 5 of 21 3. the point is located within an intensity-dependent radius of a point that satisfies either of the previous conditions.
All other points are classified as stratiform.Figure 2 provides an example of reflectivity, rain rate and Steiner classification fields for a single scene from the Sydney radar.As the rain rates can be estimated from reflectivity values below the 2.5 km level while the Steiner classification is estimated from the reflectivity at the 2.5 km level, some pixels with non-zero rain rates have no Steiner classification, and some pixels with a defined Steiner classification have a rain rate of 0 mm hr −1 .Only pixels with both a non-zero rain rate and a defined Steiner class were used to compute rainfall characteristics, but ignoring this discrepancy does not significantly impact results.
All three radars used in this study underwent an upgrade from single-to dual-polarization capabilities in 2017, but the effect of this change on the overall conclusions is negligible as dual-polarization variables were not used in the derivation of rain rates.

Defining Rainfall Events Using Radar
The first step in the identification of rainfall events for each city is the computation of several quantities that describe each individual radar scene.Here, we choose five areal quantities we will call time series variables that summarize the overall rainfall behavior as well as the presence of convection in the rainfall event.First, we calculate the areal mean rain rate as the average rain rate across the radar scene including pixels with no measured rain (recall from Section 2.1 that we are applying a 100 km radius limit to define a radar scene).This variable will only be used in defining the start and end times of rainfall events (see below).We also calculate the areal mean rain intensity, which we define as the average rain rate over pixels with non-zero rain rates only.To quantify the  horizontal extent of the rain, we calculate the instantaneous rain area fraction, defined as the number of pixels with non-zero rain divided by the total number of pixels in the scene.Finally, we characterize convection using two quantities.They are the areal mean convective intensity and the instantaneous convective area fraction.These quantities are calculated in the same way as the areal mean rain intensity and the instantaneous rain area fraction, but use only pixels that have been classified as convective by the Steiner algorithm (see Section 2.1).An example of the derivation of these time series variables is shown using Table 2 and Figures 2 and 3.Each time series variable is computed for each radar scan for which data is available, resulting in a time series of resolution 5-10 min of 11 years in length for each time series variable at each of the three locations.
Using the time series of areal mean rain rate (i.e., pixels with zero rain included), rainfall events are identified using a simple thresholding algorithm (Figure 3).The areal mean rain rate is used to identify events rather than the areal mean rain intensity to prevent radar scenes with only a few pixels with extremely high rain rates (likely resulting from ground clutter) from being classed as events.We define the start of a rainfall event as the first time when the areal mean rain rate exceeds a given rain rate threshold (see below).The event continues until the areal mean rain rate drops back below the threshold, at which point the end of the event is identified.Using the event start and end times and the time series variables areal mean rain intensity, instantaneous rain area fraction, areal mean convective intensity, and instantaneous convective area fraction, the characteristics of each rainfall event can be computed.
We use six characteristics to describe each rainfall event.The event duration is defined as the time (in minutes) between the start and end of the event.The average values of the areal mean rain intensity, areal mean convective intensity, and instantaneous rain area fraction over all scenes in the event are calculated, and will be hereafter referred to as intensity, convective intensity, and rain area fraction for purposes of simplicity, though an example of a more descriptive name would be average instantaneous rain fraction (an average over a time series).The   2, and the dashed horizontal line indicates a rain rate threshold of 0.1 mm hr −1 .Note the presence of smaller events likely to be clutter before and after the main identified event.
10.1029/2023JD039253 7 of 21 event total rain is simply the accumulation of the areal mean rain intensity for each scene over the duration of the event.Finally, we calculate the Total Convective Rain Fraction (TCRF) for each event as the ratio of convective total rain to the event total rain.The convective total rain is computed as the accumulation of the product of area-weighted instantaneous convective area fraction (instantaneous convective area fraction divided by instantaneous rain area fraction) and areal mean convective intensity at each time step over the duration of the event.
Hence, the TCRF describes the fraction of the event rainfall volume that can be ascribed to pixels classed as convective, and by definition depends on both the fraction of the event area classed as convective and the intensity of the rain in convective areas.For examples of these event characteristics, refer to Table 2.
A decision must be made regarding the rain rate threshold used to identify events in the time series.If a low rain rate threshold is chosen, there is the potential for non-meteorological radar echoes (clutter) to be misidentified as events.A higher rain rate threshold minimizes this risk but will inevitably result in some less intense or smaller area events being missed.In addition to the number of events, the event duration will also be affected by the choice of threshold, with higher thresholds leading to a split of longer events into several shorter events.A variety of thresholds were tested, and a threshold of 0.1 mm hr −1 was chosen as a compromise between the above advantages and disadvantages of high versus low thresholds.
While radars operate quasi-continuously, there are gaps of varying length in the time series at each location.They are the result of radar maintenance, failure, or incomplete individual scans.Given the most common time step of 6 min, we decided to close gaps of a single time step by linear interpolation using the mean of the values on either side of the gap.Any longer gaps are classified as missing data and all events containing them are omitted from analysis.An additional condition in the event identification algorithm ensures that no identified event immediately follows a time step where there is no data.
A final step in the event identification algorithm is to remove any events with a duration shorter than 1 hr.This step of screening out extremely short events has been used in past studies (Clarke, 1989;Kumar et al., 2013) and aims to further remove clutter mistakenly identified as rainfall events.A final screening of the resulting time series for outliers allows us to identify events that exhibit an average instantaneous convective area fraction of 100% and extremely high intensity values.These events result from non-meteorological sources and are discarded.For each of the three sites, events that are discarded as outliers or for being shorter than 1 hr comprise less than 5% of the total accumulated rainfall across the 11-year study period.Applying the algorithm described in this section leads to the identification of 2,164 rainfall events for Brisbane, 2,142 rainfall events for Sydney, and 1,897 rainfall events for Melbourne.We will investigate the main characteristics of these events in the following section.

Seasonal Event Occurrence
We begin our analysis of the rainfall events identified in the previous section by analyzing the monthly cycle of event occurrence in all three locations (Figure 4).It is evident that there are differences in the monthly occurrence of rainfall events for Brisbane, Sydney, and Melbourne.Brisbane rainfall events exhibit a strong seasonal cycle, with a late warm season peak in frequency between February and April.Brisbane rainfall events are least frequent during July and August.Similar to Brisbane, rainfall events in Sydney have a tendency to be more frequent in the warm season (November-March), and are most common during January and least common during May, August, and September.There is heightened occurrence of Sydney rainfall events in June and July compared to other cool season months, potentially attributable to east coast low occurrence.Melbourne rainfall events also have a strong seasonal cycle with a cool season peak that differs from Brisbane and Sydney, with events most common in July and August, and least common from January to April.Warren et al. (2021) similarly found that rainfall events in Brisbane were most common in March and least common in August, rainfall events in Sydney were most common in warmer months, and rainfall events in Melbourne were most common in July and least common in February.

Comparison of Event Characteristics
Next, we investigate the distributions of the six key characteristics of the rainfall events.They are event total rain, intensity, duration, rain area fraction, convective intensity, and TCRF.The reader is reminded that intensity, rain area fraction, and convective intensity represent an average over a times series of an areal mean variable.Figure 5 shows the distribution shapes of these variables as violin plots comparing the three loca- tions.We note that for plotting purposes rare values of total rain exceeding 60 mm, intensity exceeding 6 mm hr −1 , duration exceeding 25 hr, and convective intensity exceeding 20 mm hr −1 are omitted from the plots.For completeness, the maximum values identified for total rain, intensity, duration, and convective intensity for Brisbane, Sydney, and Melbourne are displayed in Table 3. Ninety-five percent confidence intervals for the median and mean were computed and examined for each city and characteristic by using the 2.5th and 97.5th percentiles of the medians and means of 10,000 bootstrapped samples, with each sample containing 1,000 events.
The distribution of total rain for each city is strongly skewed toward smaller values (Figure 5a).Melbourne events typically have smaller total rain values compared to Sydney and Brisbane events, while Sydney has the largest median total rain value.It was found that the confidence intervals for Brisbane and Sydney overlapped, indicating that the two cities are similar in terms of total rain, while Melbourne events have notably different total rain values.
The distribution of event intensity for each city also exhibits some skewness toward lower intensities (Figure 5b).The intensity distributions for Brisbane and Sydney events are quite similar and have near-identical confidence intervals, while Melbourne events clearly have lower intensities.One potential cause of lower mean and median event intensities in Melbourne could be less frequent occurrence of convection, a process often associated with higher rainfall intensities.Through use of pluviographs in the region surrounding Melbourne, Clarke (1989) found that the distributions of both rainfall amounts and intensities were similarly skewed toward smaller values.
The distribution of event duration for each city shows that most events are relatively short and certainly much shorter than the common rainfall reporting period of 24 hr (Figure 5c).It is also evident that the first quartile and third quartile event duration is highest for Melbourne events, indicating that Melbourne events may be typically longer, and that there are rare events in Brisbane and Sydney that have the potential to be very long-lasting, as indicated by the maximum values highlighted in Table 3.However, all three cities have overlapping confidence intervals for both median and mean duration, indicating that overall inter-city differences in duration are not significant.Past radar studies in Australia and overseas have found that distributions of duration for radar echoes are also strongly skewed toward shorter values (Clarke, 1989;Cruz, 1973;López, 1976;López et al., 1984).
The area covered by the rainfall events exhibits a general increase with latitude (Figure 5d).Overall, Brisbane events have the lowest areal coverage, followed by Sydney events, while Melbourne events typically have the highest areal coverage and their distribution of rain area fraction exhibits less skewness.There is no overlap in the confidence intervals for any of the cities.The increase in both median and mean rain area fraction with latitude may be attributable to increased frequency of large scale stratiform events in the region surrounding Melbourne, with localized storms and showers in this region being less frequent.The distributions of stratiform area fraction for each city (not shown) are almost identical to those of rain area fraction and also show an increase in median and mean values with latitude, supporting this hypothesis.
Brisbane and Sydney rainfall events have similar distributions of convective intensity, while Melbourne events have much lower convective intensities compared to Brisbane and Sydney (Figure 5e).It was observed that the confidence intervals for Brisbane and Sydney again strongly overlap, as was the case for event intensity.
The overall relative contribution of convection pixels to the rainfall accumulation shows a considerable change with location (Figure 5f), with no overlap between confidence intervals.The TCRF for Brisbane rainfall events is skewed toward larger values, indicating that for most events, more than half the rain is falling from convective pixels.The TCRF for Sydney rainfall events is much more uniformly distributed with a slight indication of bi-modality.For Melbourne rainfall events, the TCRF distribution peaks at very small values.Events in which convective pixels contribute more than half the rainfall in Melbourne are quite rare.This indicates that quite a different set of mechanisms are responsible for rainfall events in Melbourne compared to those in Sydney and Brisbane, and supports the earlier assertion that large scale stratiform events could be more frequent in the region surrounding Melbourne.However, we note that some of the stratiform rain in events at any of the locations is likely the result of convective processes that have initiated the formation of a stratiform region (e.g., MCSs) (Markowski & Richardson, 2010), and that formation of such regions may not require large areal coverage of convective cells.

Relationships Between Event Characteristics
Intuitively, we expect several of the rainfall event characteristics to be related to each other.For example, longer events likely also have larger rainfall accumulations.We quantify these relationships by calculating the correlation coefficients of the six key event characteristics with each other (Figure 6).It is evident that the relationships between event characteristics (positive or negative correlation) are qualitatively consistent across all three cities with some quantitative differences.We note that with the exception of duration and TCRF, correlations between all pairs of characteristics while sometimes small are statistically significant at the 5% level.
Total rain and duration are strongly positively correlated (r > 0.8) for all three cities, indicating that longer events generally have larger accumulations of rain, as expected.Intensity and convective intensity are strongly positively correlated for Brisbane events (r = 0.9) (Figure 6a), and moderately positively correlated (r > 0.7) for Sydney and Melbourne events (Figures 6b and 6c).This indicates that convective rainfall intensity contributes significantly to the overall event intensity.Furthermore, overall event intensity and the TCRF are moderately positively correlated for Brisbane rainfall events, potentially indicating a notable contribution made by convection to the rainfall events at this location.While still positive, these correlations are weaker for Sydney and Melbourne rainfall events.Event convective intensity and TCRF are moderately positively correlated for Brisbane and Sydney events, and weakly positively correlated for Melbourne events.
The event characteristic pairs total rain and intensity/convective intensity, total rain and rain area fraction, total rain and TCRF, and duration and rain area fraction exhibit weak positive correlation for all three cities (Figure 6).Meanwhile, rain area fraction and convective intensity, and rain area fraction and TCRF are weakly negatively correlated for all three cities.Therefore events with larger areal coverage are likely to have less intense rain from convective pixels, and a lesser fraction of their accumulated rain is attributed to convective pixels.Intensity and duration are only weakly positively correlated for Melbourne events (Figure 6c), whilst they exhibit no correlation for Brisbane and Sydney events (Figures 6a and 6b).This implies that while the total rain accumulation is strongly related to event length, both long and short events can be intense.Intensity and rain area fraction are weakly negatively correlated for Sydney and Melbourne events, and exhibit no correlation for Brisbane events.This indicates that while smaller events are more likely to be more intense, the relationship is far from strong and/or linear.Finally, duration and convective intensity, and duration and TCRF exhibit no correlation with each other.

Defining Heavy Rainfall Events
Having studied the overall characteristics of rainfall events in the three cities, we extend our analysis to heavy rainfall events only.There are several ways of defining heavy rainfall events from our data set, each with its own advantages and drawbacks.Fixed thresholds are simple to implement and interpret, but are generally only useful for studies of heavy rainfall events focused on a specific region, as a threshold considered heavy in one location may not represent truly heavy rainfall events in another (Schumacher & Johnson, 2006).Rainfall percentiles derived using all days or only days with measurable rainfall can also be used to define heavy events (i.e., using the 95th or 99th rainfall percentile) (Schär et al., 2016).The 95th percentile of total rain for all rainfall events is 52.6 mm for Brisbane, 54.7 mm for Sydney, and 25.8 mm for Melbourne.These values are similar in magnitude to the median 95th percentile rain amounts identified in daily resolution rain gauge networks used in Warren et al. (2021), which gives values of 45.6 mm for Brisbane, 40.5 mm for Sydney, and 21.0 mm for Melbourne.However, the effectiveness of percentiles to identify truly heavy events can be affected by the shape of the overall rainfall distribution.Alternatively, a fixed number of the heaviest events (e.g., the top 100 events) can be used as the set of heavy events, as used in White et al. (2022).This gives each city the same sample size of heavy rainfall events.
As each rainfall event defined in the previous section has a number of characteristics, an additional consideration is the choice of the characteristic used to define heavy events.Here, we use the top 100 events by total rain and the top 100 events by intensity for each location as the sample for heavy rainfall events based on accumulation (hereafter referred to as high accumulation events) and heavy rainfall events based on intensity (high intensity events), respectively.Given the considerable differences in the overall rainfall event characteristics (see Section 3.2), choosing the same number of events enables a direct comparison of the heaviest events at the three locations.The overlap between defining heavy events by total rain and intensity is relatively small, 24% in Brisbane (i.e., 24% of high accumulation events are also high intensity events and vice versa), 17% in Sydney, and 26% in Melbourne, justifying using both definitions separately.

Seasonal Heavy Event Occurrence
As for the analysis of all events, we first present the seasonal cycle of the occurrence of heavy events (Figure 7).High accumulation events in Brisbane are infrequent during cold months (with the exception of June) and are most common from October through to February (Figure 7a).By contrast, high accumulation events in Sydney and Melbourne have a more uniform seasonal cycle with a peak in frequency in May and June.Similarly to the result when analyzing all rainfall events, this winter peak in high accumulation events in Brisbane as well as Sydney and Melbourne may be attributable to east coast low activity.Both Brisbane and Sydney display a very strong seasonal cycle of high intensity events (Figure 7b).Almost all high intensity events in Brisbane occur in the warm season from October to February, and almost all high intensity events in Sydney occur between November and March.High intensity events in Melbourne are also common during warm months, with the highest frequencies in December, January, and February.Overall, high accumulation events and high intensity events have very different seasonal cycles in Sydney and Melbourne, while high accumulation events and high intensity events occur at similar times of the year in Brisbane.This is potentially because the mechanisms responsible for high accumulation events (e.g., east coast lows) and the mechanisms responsible for high intensity events in Sydney and Melbourne peak in frequency at different times of the year, while the mechanisms responsible for high accumulation events and high intensity events in Brisbane (with the exception of east coast lows) tend to peak in frequency at the same time of the year.Fully understanding these differences requires further investigation beyond the scope of this paper.For Brisbane, the monthly distribution of high accumulation events bears some similarity to the results for Brisbane in White et al. (2022), who present the monthly distributions of the top 100 rain days by accumulation defined using Climate Prediction Center Morphing (CMORPH) satellite data.However, the monthly distribution of heavy rain days they found for Melbourne bears greater resemblance to our high intensity event distribution in Melbourne, rather than our high accumulation distribution.

Comparison of Heavy Event Characteristics
The distribution shapes of key variables for high accumulation rainfall events and high intensity rainfall events are displayed in Figure 8. However owing to the small sample sizes of heavy events, we cannot calculate meaningful bootstrapped confidence intervals.
Sydney high accumulation events have the highest total rain amounts, followed by Brisbane high accumulation events.Melbourne high accumulation events have the lowest total rain amounts, which do not exceed 80 mm (Figure 8a).The distribution of total rain for Melbourne high accumulation events is strongly skewed toward smaller values.Melbourne high intensity events also have the lowest total rain amounts.High intensity events for Brisbane and Sydney have much larger accumulations compared to Melbourne.As expected, total rain amounts for high intensity events are typically much smaller than those for high accumulation events across all three cities, with a difference of one order of magnitude noted when comparing mean total rain values for different heavy event types in Brisbane and Sydney.
The intensity of the high accumulation events is similar for Brisbane and Sydney (Figure 8b).Melbourne high accumulation events have much lower intensities, with their intensities not exceeding 10 mm hr −1 .The distribution for Melbourne high accumulation events is again strongly skewed toward lower intensities.Brisbane high intensity events have the highest intensities, while Melbourne high intensity events have the lowest intensities.
The distributions for each city are skewed toward smaller values, particularly in the case of Melbourne.For each 10.1029/2023JD039253 13 of 21 city, high accumulation events typically have lower intensities than high intensity events, but the magnitude of this difference between heavy event types is much lower than that of total rain.
High accumulation events have comparable duration across the three cities (Figure 8c).Duration tends to be largest for Sydney events, followed by Brisbane events, then Melbourne events.By contrast, high intensity events in Melbourne tend to last longest, while high intensity events in Brisbane and Sydney are shorter-lived.The distribution of Sydney high intensity events differs from that of Brisbane in that it is more skewed toward shorter events, but there is also the potential for much longer events compared to Brisbane.It is also clear that high accumulation events are typically much longer lasting than high intensity events across all three cities.The median duration for high accumulation events is also much higher than that of all rainfall events.
Rain area fraction values bear some similarity across the three cities for high accumulation events (Figure 8d).The median rain area fraction is highest for Melbourne high accumulation events, followed by Brisbane and Sydney.The mean and median values in all three cities are higher than those for all events, indicating that high accumulation events tend to be larger in areal extent.
The distributions of rain area fraction for high accumulation events are quite symmetric compared to other event characteristics, particularly for Sydney and Melbourne.Melbourne high intensity events also tend to have the greatest rain area fractions, while rain area fraction for Brisbane and Sydney is lower.Thus Brisbane and Sydney high intensity events typically have smaller areal coverage compared to Melbourne high intensity events.The distributions of rain area fraction for Brisbane and Sydney high intensity events are skewed toward smaller values, while the distribution for Melbourne high intensity events exhibits some bi-modality with modes at approximately 0.1 (10% coverage) and 0.5 (50% coverage).For all three cities, rain area fraction values for high accumulation events are much greater than those of high intensity events, and the distributions are more symmetric.
The distributions of convective intensity for high accumulation events are shown in Figure 8e.Melbourne high accumulation events have much lower convective intensities compared to those of Brisbane and Sydney events.The distributions of convective intensity are also skewed toward lower intensities, particularly in the case of Melbourne.For high intensity events, convective intensity is highest for Brisbane events, followed by Sydney events.Melbourne high intensity events typically have the lowest convective intensities.The distributions of convective intensity for Brisbane and Melbourne high intensity events are strongly skewed toward lower intensities, while the distribution for Sydney high intensity events exhibits more symmetry.Across all three cities, high intensity events have much higher convective intensity values compared to those of high accumulation events.The strong similarities in the distribution of convective intensity across the three locations with that of overall rainfall intensity indicates that convective pixels play a significant role in influencing some of the key event characteristics.
The analysis of the contribution of convective pixels to the total rainfall clarifies this relationship further.The TCRF for high accumulation events is highest for Brisbane, followed by Sydney.Melbourne events have the lowest median TCRF (Figure 8f).The distribution of this characteristic is skewed toward larger values for Brisbane events, is relatively symmetric for Sydney events, and is skewed toward smaller values for Melbourne events.For high intensity events, TCRF is again generally highest for Brisbane events, followed by Sydney events, then Melbourne events.The distribution of TCRF is strongly skewed toward higher values for Brisbane and Sydney high intensity events, and more uniformly spread for Melbourne high intensity events.It is evident for all three cities that TCRF tends to be considerably higher for high intensity events compared to high accumulation events and all events.This indicates that convection may have a stronger influence on the event intensity than it has on the total rainfall accumulation, which is more strongly linked to the duration and rain area fraction of the event.

Uncertainty Assessment
As is the case with any kind of atmospheric observation, use of radar rainfall estimates is subject to uncertainties.Here we explore the impact of the Z-R relation used in conversion of reflectivity to rain rates and the intensity threshold used in the Steiner classification on our results.Due to data processing constraints, we use one year of data from 2020 to examine the effects of parameter changes in the retrievals.This year was chosen as the amount of data missing for each radar was minimal (Figure 1).

Uncertainty in Rain Rate Estimation
To test for uncertainty in the results introduced by changes in the Z-R relation, a variety of different relationships were implemented for each radar site (Table 4).Specifically, for each site we trial three Z-R relations, one derived from the Marshall-Palmer rain drop size distribution (Marshall & Palmer, 1948) as well as the two relationships used at the other two sites in our study.We also experimented with changing the two parameters in each Z-R relation by percentages of 10% and 20%, which yielded similar results.In each case, the original reflectivity field was converted to a new rain rate field using the three trialled Z-R relations for each city.Using the techniques outlined  in Section 2.2, rainfall event identification and characterization was then performed using the new rain rate fields, which then allows us to compare the resulting event data sets to the control data set used so far.
When using any of the alternative Z-R relations, the number of rainfall events identified in the sample year changes by less than 7% for each city.The small changes we do observe are due to changes in the number of times that the areal mean rain rate exceeds the 0.1 mm hr −1 threshold as the Z-R relation parameters are varied.
An example for the impact of using different Z-R relations on the rainfall event characteristics is shown in Figure 9.
Here, we show the distributions of event intensity when applying the original Z-R relation at each city (Figure 9a) against cases where we use different relationships for each city.As might be expected, each Z-R relationship yields small to moderate quantitative differences, especially in the tails of the distributions.However, the overall distribution shape and the qualitative differences between the distributions at the three locations prevail no matter what Z-R relationship is applied.We note that this is true for all event characteristics used in this study (not shown).
To better quantify the distribution similarity when varying Z-R relations, we apply the two-sided two-sample Kolmogorov-Smirnov test with a significance level of 5% to compare each event characteristic distribution to its control distribution.The null hypothesis of this statistical test is that the two given samples come from the same distribution.For most event characteristics and locations, the Kolmogorov-Smirnov test does not identify statistically significant differences in event characteristics between the altered and control Z-R relations.There are some exceptions to this overall result.For example, using the Melbourne Z-R relation at the Brisbane site leads to a rejection of the null hypothesis in the case of event total rain, intensity, and convective intensity (for intensity, compare the Brisbane violin in Figure 9d to that in Figure 9a).This is not unexpected given the very different meteorological and associated rainfall regimes in the two locations.In fact, it highlights and justifies the need to apply different Z-R relations in different locations, as has been done in the AURA data set.Overall, intensity-related characteristics are more strongly affected by Z-R relation changes than duration or rain area characteristics, but the qualitative differences between locations remain unaltered.

Uncertainty in Convective-Stratiform Partitioning
Like all convective and stratiform rainfall classification algorithms, the algorithm developed by Steiner et al. (1995) used in this study contains a set of rules and parameters that are subject to uncertainty.Specifically, the algorithm was developed and tested on 1 month of reflectivity data at a 3 km height from the Darwin operational radar, with the authors noting that data from a lower altitude should be chosen in the midlatitudes (Steiner et al., 1995).In the AURA data set used for our analysis, the Steiner classification product is derived from reflectivity data at 2.5 km above the radar (site altitude plus tower height), and the algorithm uses a 42 dBZ reflectivity threshold as its primary condition for the presence of convection (see Section 2.1).
To investigate the uncertainty resulting from the choice of threshold, new Steiner classification fields and event data sets were generated for each city using 35 and 45 dBZ absolute convective thresholds for the year 2020.The resulting event characteristics are then compared to the control data set.Modifying the Steiner classification field has by design no impact on the number of events identified or on the event characteristics total rain, intensity, duration, or rain area fraction.However, it has the potential to change the convective properties of each event.Figure 10 shows the distributions for convective area fraction (average instantaneous convective area fraction over the duration of the event) for each threshold.When applying the Kolmogorov-Smirnov two-sample test to the distributions of convective intensity, convective area fraction, and TCRF, the null hypothesis that both samples (control and modified threshold) come from the same distribution is not rejected for any characteristic in any city at the 5% level.Hence, the qualitative conclusions about the convective events drawn are insensitive to the choice of reflectivity threshold (Figure 10).
A second concern, especially for the midlatitude locations, is that high reflectivities could be the result of the melting level dropping to near or below a 2.5 km height, leading to a overestimation of convective activity due to bright band effects.To assess this possibility, we use hourly fields of the melting level height from January 2010 to December 2020 from the ERA5 reanalysis data set (Hersbach et al., 2020).We find that the melting level was at a height of 2.5 km above the radar or lower for 7.6% of the timesteps over the grid point closest to the Brisbane radar, 27.9% for Sydney radar, and 34.2% of the timesteps over the Melbourne radar.For the months June to August in both Melbourne and Sydney, the freezing level is at or below 2.5 km more than half the time.This raises the prospect of overestimating convective activity in the winter months at these locations.To further examine this possibility, we assess seasonal differences in convective area fraction and TCRF over all three locations (Figure 11) for the 11 years of data available.We find that convective area fraction is lowest during the winter months (JJA) at all three locations (Figure 11), and in particular for Melbourne.We note that in contrast seasonal changes in stratiform area fraction are small (not shown).TCRF also exhibits a strong seasonal cycle, especially for Melbourne and Sydney, with the lowest values occurring during the winter months.These results show that if present, the bright band's effects are unlikely to negate the conclusions about convective behavior of the rainfall events in the three locations used here.While we cannot exclude that there is an overestimation of winter convection in Melbourne due to bright band effects, the small convective area fractions obtained for Melbourne events in winter suggest that any effect on the conclusions for Melbourne is not major.

Conclusions
This study has presented a technique to identify and characterize rainfall events using a simple thresholding technique on areal variables from weather radar data.Examples of the analysis possible examining all rainfall events and two definitions of heavy rainfall events have also been presented for the Australian cities of Brisbane, Sydney, and Melbourne.The key findings of the study are: 1. Rainfall events in Brisbane and Sydney tend to have higher rainfall accumulations, intensities and convective intensities compared to Melbourne rainfall events, which have the smallest total rain amounts and lowest intensities and convective intensities.2. Brisbane rainfall events have the lowest areal coverage and highest TCRF values, Melbourne events have the greatest areal coverage and the lowest total convective rain fractions, and Sydney events have rain area fraction and TCRF values that are intermediate between Brisbane and Melbourne.It is likely that Melbourne rainfall events are more stratiform in nature, while Brisbane and Sydney events are more convective.3. Event duration and total rain are strongly positively correlated, with longer events resulting in greater rainfall accumulations.Intensity and convective intensity are also strongly positively correlated, indicating that convective rainfall intensity makes a significant positive contribution to overall event intensity.The overall convective contribution to rainfall is also driven by increasing overall intensity and convective intensity, particularly for Brisbane rainfall events.4. High accumulation events and high intensity events exhibit significant differences.High intensity events have smaller accumulations, higher convective intensities, shorter duration, smaller areal coverage, and greater convective contributions than high accumulation events.High intensity events also have higher mean and median total rain amounts than the set of all events.High accumulation events are longer lasting, less convective, and cover a greater area than high intensity events.High accumulation events also have higher mean and median intensities compared to all events.5. Long-term radar data sets can be used to both identify and characterize rainfall events and heavy rainfall events in Australia.

Limitations and Future Work
As the majority of rainfall studies in Australia use rain gauge-based data sets and event definitions based on rain days, it is difficult to quantify the representativeness of the results presented in this paper.Another challenge to the representativeness of results is the relatively short length of radar data sets compared to rain gauge data sets.However, these issues can be addressed with further work identifying and characterizing rainfall events a few decades from now, provided that archiving of radar observations in Australia is continued.
In their work, Jordan et al. (2000) commented "Sources of error in radar measurements of rainfall are legion."While technological advancements in radar meteorology have led to a reduction in error, this statement still holds true in that there are many uncertainties that must be considered.Focus on analysis of areal variables, and preprocessing of the data (as outlined in Section 2.2) can mitigate against some error in reflectivity measurements.Calibration of the radar data set is also crucial, and addressing the need for uniform quality control was one of the primary aims in the creation of the AURA data set.However, further work is still needed to address variability in Z-R relations and improve removal of ground clutter and anomalous propagation.
The use of the threshold approach to identify rainfall events presented in this study can introduce error from areal mean rain rates temporarily dropping just below the threshold and resulting in an event being split into multiple, shorter events.Thus the use of a very low rain rate threshold and later removal of events that are short/small enough to be considered clutter was chosen as a way to avoid incorrectly splitting events as much as possible.Another way of improving quantitative accuracy of radar rainfall estimates is to incorporate rain gauge measurements.While gauge adjustment and multisensor analysis is crucial for improving the use of radar to study rainfall in Australia, it is beyond the scope of this study.Also beyond the scope of this work is incorporation of polarimetric radar variables into radar rainfall estimates in Australia, although this represents an important avenue of future work.
The techniques outlined in this paper and the data yielded from such analysis can be applied in many ways, and will be useful in investigating processes behind heavy rainfall in different regions of Australia.Future research will involve expanding identification of rainfall events to other radars available in AURA, further investigation of the distinction between heavy and non-heavy rainfall events, morphological classification of rainfall systems, and relating rainfall event characteristics to meteorological variables and the large scale state of the atmosphere.Continued maintenance and expansion of AURA will allow for the results presented in this paper to be further investigated, and for more robust rainfall climatologies to be developed.If operational data in AURA continues to be maintained, there is also the potential for associations between climate drivers and rainfall characteristics to be studied.

Figure 1 .
Figure 1.Percentage of data available in each year and month for the (a) Brisbane, (b) Sydney, and (c) Melbourne radar sites.The numbers 1-12 on the y-axis indicate month, with 1 being January and 12 being December.

Figure 2 .
Figure 2. (a) Example reflectivity, (b) rain rate, and (c) Steiner classification fields for a scene taken from the Sydney (Terrey Hills) radar on 13 November 2020 at 04:45 UTC.A star marks the location of the radar in each panel.Note that the reflectivity and Steiner classification fields are at the 2.5 km level, while the rain rate field is at the lowest available level.

Figure 4 .
Figure 4. Percentage of rainfall events occurring in each month for Brisbane, Sydney, and Melbourne.Each calendar month is labeled with a single letter.

Figure 5 .
Figure 5. (a) Violin plots comparing total rain, (b) intensity, (c) duration, (d) rain area fraction, (e) convective intensity, and (f) total convective rain fraction for rainfall events in Brisbane, Sydney, and Melbourne.The box plot within each violin plot indicate the quartiles with sufficiently large values removed (refer to the beginning of Section 3.2), and the white square indicates the mean value.

Figure 6 .
Figure 6.Correlation matrices showing Pearson's correlation between rainfall event characteristics for (a) Brisbane, (b) Sydney, and (c) Melbourne.Abbreviations are: TR = Total Rain, I = Intensity, D = Duration, RAF = Rain Area Fraction, CI = Convective Intensity, and TCRF = Total Convective Rain Fraction.Correlations that are not statistically significant at the 5% level are italicized.

Figure 7 .
Figure 7. Percentage of (a) high accumulation and (b) high intensity rainfall events occurring in each month for each city.Each calendar month is labeled with a single letter.

Figure 8 .
Figure 8. Violin plots comparing (a) total rain, (b) intensity, (c) duration, (d) rain area fraction, (e) convective intensity, and (f) total convective rain fraction for high accumulation (high acc.) and high intensity (high int.) rainfall events in Brisbane, Sydney, and Melbourne.The white square within each boxplot indicates the mean value.

Figure 9 .
Figure 9. Violin plots comparing the distributions of event intensity obtained using (a) the control data set, (b) the Brisbane Z-R relation, (c) the Sydney Z-R relation, (d) the Melbourne Z-R relation, and (e) the Marshall-Palmer Z-R relation.The box plot within each violin plot indicates the quartiles, and the white square indicates the mean value.

Figure 10 .
Figure 10.Violin plots showing the distributions of event convective area fraction for each city for (a) a 35 dBZ absolute convective threshold, (b) the control data (42 dBZ threshold), and (c) a 45 dBZ absolute convective threshold.The box plot within each violin plot indicates the quartiles, and the white square indicates the mean value.

Figure 11 .
Figure 11.Violin plots comparing the distributions of (a, c, and e) event convective area fraction and (b, d, and e) total convective rain fraction across seasons for each city.The box plot within each violin plot indicates the quartiles, and the white square indicates the mean value.

Table 1 Table of the
Attributes of Each Radar Used in This Study

Table 2 Table of Time
Series Variables and Event Characteristics Referred to in This Paper Figure 3.Time series of areal mean rain rate from the Sydney (Terrey Hills) radar showing a rainfall event spanning 02:25 to 07:20 UTC on 13 November 2020.The black vertical lines indicate the event start and end times, the vertical dotted red line indicates a time of 04:45 UTC corresponding to the example radar fields in Figure

Table 3 Table of Maximum
Values of Event Characteristics for All Rainfall Events

Table 4 Table Showing Z
-R Relations Tested for Each Radar