We have named the proposed rainfall-runoff event identification method the Robust Variance-based Event Identification Method (RVEIM). RVEIM adopts the definition of runoff event from Fischer et al. (2021) who defined runoff event as “a temporally limited exceedance of normal discharges”. Similar to Fischer et al. (2021), we used a moving window to estimate streamflow variance, which is used to identify sudden movement of streamflow. However, RVEIM adopts a different approach to detect runoff events beyond Fischer et al. (2021) by detection and pairing rainfall-runoff events while only using two parameters. Figure 2 present a flowchart of the developed method. Each major and minor step is explained in detailed in the following sections.

To demonstrate the advantages of the RVEIM, we compare our results with existing methods. Since there are numerous rainfall-runoff event identification methods we benchmark RVEIM against two complementary methods. First, we implemented a commonly used method which uses local maxima to identify events before pairing the streamflow to the driving rainfall (Wasko and Guo, 2022). Following the recommendation by Mohammadpour Khoie et al. (2025) which compared event identification methods, the local maxima method generally had less uncertainty in its outputs; and as such, we included the local maxima as one benchmark method. Second, the Detrending Moving-average Cross-correlation Analysis (DMCA) method developed by Giani et al. (2022) is included as its methodological complexity is closer to that of RVEIM, providing a more comparable benchmark for assessing the performance and transferability of the proposed method.

To detect runoff events, the local maxima method firstly detects local maximum values in streamflow/runoff timeseries. Then, by comparing each peak with the next valley it decides about a new runoff event: if the difference between a peak with the next valley is higher than a user-defined value (delta.y), a new runoff event is detected. Otherwise, the peak is part of a multi-peak runoff event. To filter out small runoff, the local maxima method considers a minimum threshold above which runoff is considered. A minimum spacing between two consecutive runoff events (delta.x) is considered to ensure independency of runoff events.

DMCA identifies rainfall-runoff events by analysing rainfall and streamflow time series simultaneously. The method estimates a characteristic catchment response time and uses it to detect event cores where rainfall and streamflow fluctuations are jointly active. Event boundaries are then refined using the behaviour of the individual rainfall and streamflow fluctuations, with a rainfall fluctuation tolerance used to prevent negligible rainfall from merging otherwise separate events. This allows DMCA to define events as coupled rainfall-runoff system realizations.

Baseflow separation is handled differently across the three event identification methods used in this study and may be applied either before or after runoff event detection. In the local maxima method, baseflow is usually separated before runoff event detection so that runoff events are identified from quickflow (the part of streamflow which directly comes from rainfall). However, in RVEIM and DMCA, the baseflow volume is subtracted after detecting the runoff event. Further, DMCA estimate the baseflow by connecting the streamflow values at the beginning and the end of each detected runoff event (Giani et al., 2022) while RVEIM and local maxima use a digital baseflow filter (as described in Sect. 3.1.1 and 3.1.2). The Lyne and Hollick (1979) baseflow filter which is widely used in the literature (Wasko and Guo, 2022; Ladson et al., 2013; Kemp and Alankarage, 2023; Miao et al., 2020; Ho et al., 2022) was used in this study. The filter separates baseflow with the help of a parameter called the “filter parameter”. The filter parameter varies between 0 and 1 and defines how the digital filter should respond to streamflow variation. Lower values of the filter parameter indicate on a quicker response to streamflow changes. Nathan and McMahon (1990) investigated the best choice of filter parameter. They showed the range of 0.9–0.95 for filter parameter works better and recommended the value of 0.925 for better performance of the filter.

The pairing process differs slightly among the methods used: RVEIM and DMCA identify rainfall-runoff event pairs jointly, whereas local maxima detects rainfall and runoff events separately and pairs them afterwards. In local maxima, the pairing uses a search window to pair each rainfall to a corresponding runoff event. Five pairing strategies are included in local maxima which are different in their directions and start points used for searching. Pairing type 1 searches from the start of rainfall event to the peak of runoff event. Pairing type 2 searches from the start of rainfall event to the end of runoff event. Pairing type 3 searches from the peak of runoff event to the peak of rainfall event. Pairing type 4 searches from the start of runoff event to the start of rainfall event. Pairing type 5 searches from the peak of rainfall event for the peak of runoff event both forwards and backwards. The pairing type and length of search window (lag) are both user-specified.

To assess the uncertainty associated with parameter value selection in all methods, a sensitivity analysis is performed for the sites representing different climates and regions listed in Table 2. A plausible range is specified for each parameter for each rainfall-runoff event identification method. Then, random samples within the parameter range are drawn and used for identifying rainfall-runoff events. The changes in characteristics of rainfall-runoff events are then analyzed to understand the uncertainty in rainfall-runoff event detection due to parameter change. The characteristics here are the mean annual number, volume, length, and RCs of paired runoff events (i.e., runoff events matched to rainfall events and having runoff volumes greater than zero). This combination of characteristics was selected to determine which method yields acceptable variability in the identified event characteristics while maintaining an acceptable level of physical plausibility. We estimate the ECDF of RCs for each sampled parameter set and then across each catchment considering the 95 % confidence interval (between 2.5th percentile and 97.5th percentile) as it reveals how each method represents the characteristics of individual catchment across the full distribution of RCs.

Two parameters are associated with the development of RVEIM: the length of the moving variance window, d_var (Sect. 3.1.1) and the filter parameter of the baseflow digital filter, alpha. For the benchmarking methods, local maxima event identification method uses six parameters: alpha for rainfall event detection, Threshold, delta.x, delta.y for runoff event detection, and type and lag for pairing rainfall and runoff events, and DMCA uses two parameters: rain_min, which is the minimum rainfall intensity threshold, and max_window, which is the maximum search window for estimating the catchment response time.

The parameter ranges adopted for the three rainfall-runoff event identification methods were selected based on previous studies and the methodological characteristics of each approach. Therefore, for the local maxima method, the parameter ranges were adopted from Mohammadpour Khoie et al. (2025) based on the dynamics of streamflow in different climate zones. For DMCA, the ranges for the rain_min and the max_window were derived from the example implementation provided with the original method (Giani et al., 2022). For RVEIM, the alpha range is considered between 0.9 and 0.95 as recommended by Lyne and Hollick (1979). To specify a plausible range for the length of moving variance window (Sect. 3.1.1) we used the range of 3–10 d. The maximum 10 d was chosen to capture the temporal variability of runoff events without excessively smoothing the data. This range was informed by the range specified by Fischer et al. (2021) which proposed another variance-based runoff event detection method. We generated 300 random samples (i.e., parameter sets) for RVEIM and DMCA and 600 samples for local maxima to properly cover the parameter space for each method.

Rainfall event detection is considered a deterministic process in RVEIM and local maxima methods meaning uncertainty is not investigated. Here, the POT method with 1 mm threshold is appropriate to identify rainfall events (Ashcroft et al., 2019; Wasko and Guo, 2022; Zhang et al., 2011).

To demonstrate the performance of the proposed rainfall-runoff event identification method, we chose catchment 306119 in Tasmania. Within the eight representative catchments, 306119 has the third highest annual rainfall and the largest annual streamflow (Table 2). As one of the wetter catchments, identifying rainfall-runoff events is more challenging as there are a higher number of rainfall-runoff events and usually a higher baseflow contribution to streamflow through year which makes it harder for statistical rainfall-runoff event identification methods to identify events precisely. Consequently, adequate performance of a rainfall-runoff event identification method in such a catchment means it will likely obtain satisfactory performance in other catchments. Here an example event identification with RVEIM with alpha 0.904 and d_var 3 (one random sample of the 300 random parameter sample sets drawn, as detailed in Sect. 3.3) is presented. Figure 5 shows identified rainfall-runoff events from 1 June 1973 to 1 September 1973, with each pair of identified rainfall and runoff events highlighted in the same color on top of the original time-series in black. Within the selected period, 11 rainfall events are recognized with 8 runoff events detected and paired with rainfall. Although some rainfall events have suitable volume for generating runoff, they did not lead to runoff events because the variance does not exceed the var_lim (Sect. 3.1). Both small and large runoff events including single-peak and multi-peak runoff events are detected and paired demonstrating the power and flexibility of RVEIM. Some streamflow peaks (for example, the small peak after the first runoff event toward mid-June) are not detected since the variance is lower than var_lim. Note that such events have minor effects on streamflow analysis even if they are detected and paired, and the key point demonstrated here is that the pairing appears plausible and consistent with our physical understanding.

Although the same runoff event identification rules are applied consistently to all events, some events may appear visually truncated, such as the third and fourth runoff events in Fig. 5 (shown in green). This mainly reflects the temporal discretization involved in delineating runoff events from daily data. Shifting the runoff event start one time step earlier could make the runoff events appear more visually complete, but it produces only negligible changes in event characteristics and may incorrectly double-count time steps by creating overlap between the beginning of one runoff event and the end of the preceding event.

Mean annual characteristics of paired runoff events are extracted from all three methods over all samples. Figure 6 demonstrates that local maxima generally exhibits the greatest uncertainty in the characteristics of the identified paired runoff events, whereas RVEIM consistently produces lower uncertainty across the representative catchments, highlighting the higher robustness of the proposed method against parameter value change. The uncertainty of RVEIM and DMCA are similar to each other for most cases, but RVEIM generates lower uncertainty for some sites and event characteristics (for example, the mean volume of paired runoff events in Fig. 6c). The uncertainty associated with DMCA varies depending on both the considered characteristic and the catchment. For example, DMCA shows markedly higher uncertainty in the mean length of paired runoff events for the desert catchment A0020101 than for the other catchments (Fig. 6b), suggesting that its performance may vary considerably under certain climatic conditions. Boxplots of paired runoff event characteristics detected by the local maxima method includes many outliers, with much fewer when using the RVEIM. Noticeably there are fewer outliers in the average annual number rainfall-runoff events identified by RVEIM (Fig. 6a) providing more confidence on number of paired runoff events. Considering the mean length and volume of paired runoff events (Fig. 6b and c), it can be concluded that local maxima generally finds shorter but larger runoff events meaning local maxima probably biases towards large runoff events while RVEIM and DMCA perform better in identifying a broader range of runoff events.

Assuming the measured rainfall and runoff are accurate, errors in rainfall-runoff event identification can come from detecting the start and end of rainfall and runoff events, and pairing runoff events to rainfall, which lead to uncertainties in estimating the runoff events' volume. Here, to examine the reliability of implemented methods, we compare the percentage of RCs > 1. A higher percentage of RCs > 1 means there are more physically implausible rainfall-runoff events and hence a lower reliability in the identified events.

Figure 7 shows the percentage of RCs > 1 for rainfall-runoff events identified by the three methods for the 8 representative catchments. Each boxplot presents the variability of percentage of RCs > 1 over the full sample of parameter sets. The percentage of RCs > 1 is generally lowest for DMCA, while RVEIM also produces substantially lower percentage of RCs > 1 than local maxima across most catchments. All catchments identified by DMCA and RVEIM show very low percentage of RCs > 1 (except for catchment 306119 – below 4 % for RVEIM and 0 % for DMCA) with limited sensitivity to parameter values change (shown by the interquartile range of the boxplot). However, the percentage of RCs > 1 in local maxima is consistently higher and vary across a wider range for all catchments with changing parameter values. Among all catchments, the three wettest catchments (306119, 926002A and G8150018) have both higher percentages and variability of RCs > 1 in all methods (especially, local maxima). This highlights the challenge for rainfall-runoff event identification in wetter catchments, which is further discussed in Sect. 5.

As a signature of catchment response, the Empirical Cumulative Distribution Function (ECDF) of RCs informs the event-scale rainfall-runoff relationship. Here we compare the uncertainties in the ECDFs of RCs obtained using the implemented methods, over all parameter samples used (Fig. 8). Since rainfall-runoff events with RCs > 1 are physically implausible, we have estimated the ECDFs of RCs with rainfall-runoff events with 0 < RCs ≤ 1. As demonstrated in Fig. 7, with the RVEIM there is generally only a small number of identified events with RCs > 1 (less than 4 % for most catchments), therefore omitting rainfall-runoff events with RCs > 1 is not expected to greatly impact the ECDF of RCs for an individual catchment.

The RVEIM and DMCA have a significantly narrower uncertainty band in the ECDFs compared to using local maxima for event identification across all representative catchments. For example, the probability of identifying a rainfall-runoff event with RC < 0.25 in catchment 926002A is roughly between 0.3–1 when the local maxima method is used (Fig. 8g). However, the probability of identifying rainfall-runoff events with RC < 0.25 is approximately 0.48–0.65 when the RVEIM is used and approximately 0.96–0.98 when DMCA is used, indicating greater confidence. The uncertainty in the ECDF of RCs varies considerably between catchments among all methods. For example, the uncertainty in catchment A0020101 is much lower than catchment 306119 for all methods (Fig. 8a and f). The change of uncertainty across catchments is likely due to differing catchment responses and climatic conditions. Rainfall-runoff events are identified with greater certainty for drier catchments, where there are fewer number of rainfall/runoff events and a steady contribution of baseflow throughout a year (e.g. catchment A0020101 in Fig. 8a).

The shape of the ECDF of RCs contains important information regarding the rainfall-runoff events in a catchment. A steeper ECDF emphasizes that there is a mass of rainfall-runoff events with a limited range of RCs. A more gradually increasing ECDF represents a wider range of RCs with a more uniform distribution. For example, in catchment A0020101 (Fig. 8a), there is a sharp increase in the slope of the ECDFs between RC ≈ 0 and approximately 0.125, reaching around 70th percentile, meaning that all methods agree that most rainfall-runoff events (around 70 % of rainfall-runoff events) have the RC between 0-0.125. However, in catchment G8150018 (Fig. 8h), the ECDF increases smoothly between RC ≈ 0 to 0.25 up to around 50th percentile meaning a more uniform distribution of rainfall-runoff events with RCs between 0 and 0.25.

The median of ECDFs for all methods are quite close for some catchments, like catchment 707002 (Fig. 8b). However, in some catchments, like catchment 204041 or 926002A (Fig. 8e and g), there is a meaningful separation between methods. The separation among the methods indicates the contrasting representation of the catchment behavior. For example, in catchment 926002A, for low RCs, the median of local maxima method increases relatively gradually, suggesting that identified rainfall-runoff events are distributed relatively evenly across this range (approximately 17 % of rainfall-runoff events have RCs < 0.05 – Fig. 8g). In contrast, the median of DMCA rises sharply near zero, indicating a greater concentration of rainfall-runoff events with zero or very low RCs (around 69 % of rainfall-runoff events have RCs < 0.05). The median of RVEIM remains considerably below the other two curves over much of the low-RC range, indicating fewer rainfall-runoff events with near-zero RCs (only around 3 % of rainfall-runoff events have RCs < 0.05). Consequently, RVEIM physically represents this catchment as having a greater potential to convert event rainfall into runoff. Given that catchment 926002A is Equatorial in climate and relatively wet (the second highest mean annual rainfall and streamflow according to Table 2), the event representation by RVEIM is likely more hydrologically plausible. This disagreement between methods is also evident in catchment 204041 (Fig. 8e). In catchment 204041, DMCA shows around 69 %, local maxima shows around 26 %, and RVEIM suggests only 2 % of rainfall-runoff events with RCs ≤ 0.05. As shown in Fig. 8, the disagreement between methods are more pronounced when moving towards wetter catchments (i.e. catchments presented in later panels, as they are ordered by annual rainfall as per Table 2), where RVEIM consistently indicates a greater potential for runoff generation, which appears hydrologically plausible. Considering the demonstrated robustness and reliability of RVEIM in producing more realistic rainfall-runoff event behavior, the subsequent sections focus only on results generated from RVEIM.

The RVEIM is applied to all 467 HRS catchments in Australia. The characteristics of rainfall and runoff events are extracted and the mean value over 300 parameter samples are plotted in Fig. 9. There is a clear increase of the average annual number of rainfall events from northwestern to southeastern Australia (Fig. 9a). There is a positive correlation between the average annual number of rainfall and runoff events except for catchments in the north and south-west of Australia. For these regions, although the average annual number of rainfall events is lower (Fig. 9a), the average annual number of runoff events is similar to other catchments in southern Australia (Fig. 9b). A positive correlation between mean length of rainfall and runoff events is also seen except for western Tasmania (see Fig. A1 in Appendix A). Although catchments in western Tasmania have longer rainfall events than other catchments (Fig. 9c), their corresponding runoff events are shorter compared to other catchments (Fig. 9d). The shorter duration of runoff events in Tasmania can be explained by the steeper slopes of catchments in Tasmania which develop quick flow paths (Douinot et al., 2022). A high positive correlation between the mean volume of runoff and rainfall events is also detected (Fig. A2) with some inconsistencies for catchments in northern WA. Catchments in northern WA have the lowest mean volume of rainfall (Fig. 9e), however they have relatively larger mean annual volume of runoff (Fig. 9f) pointing to lower losses in these catchments compared to others. This can be explained by the relatively lower evapotranspiration (Fig. A3) and higher soil moisture (Fig. A4) in northern WA (Bureau of Meteorology, 2025b, c) meaning lower rainfall losses and higher potential of runoff generation. Figure 9g presents mean RC values of identified rainfall-runoff events across Australia. Higher RC values are concentrated around coasts pointing out that catchments around coasts have higher potential of runoff generation. Among all catchments, catchments in Tasmania obtained highest RCs which can be a combined effect of the lower evapotranspiration and significantly higher soil moisture in Tasmania (Bureau of Meteorology, 2025c, b). The percentage of RCs > 1 within all events identified for each catchment is shown in Fig. 9h. The mean percentage of RCs > 1 is below 6 % for almost all catchments (around 90 % of catchments). However, the ∼ 10 % of catchments that have 6 %–25 % of RCs > 1 are mostly concentrated in the east of Australia and Tasmania. Catchments in east coast of Australia and Tasmania which generally have higher soil moisture (highest in Tasmania). Higher soil moisture increases the runoff volume and the RC as well (Song and Wang, 2019; Schoener and Stone, 2019). The increase in RC, on the other hand, increases the potential of estimating RCs > 1 because of errors in runoff volume estimation (Mohammadpour Khoie et al., 2025). The potential errors leading to RCs > 1 are further discussed in Sect. 5.2.

Figure 10 compares the ECDF of RCs in each climate region by presenting the median of ECDFs of RCs across the 300 parameter samples of individual catchments within each climate region. This provides the first Australia-wide summary of the distribution of event RCs. Where the ECDF of RCs has a sharp increase at the beginning it means that there is a mass of rainfall-runoff events with low RC values. According to Fig. 10, there is a clear gradient of the shapes of ECDFs of RCs from dryer to wetter climate regions. For example, at RC = 0.02, the ECDF of desert climate is around 50 % meaning 50 % of rainfall-runoff events in desert climate region have RC < 0.02. In grassland climate (wetter than desert), the ECDF of RC = 0.02 is roughly 40 %. The ECDF at RC = 0.02 for temperate, subtropical, and tropical climate regions is around 10 % while it decreases to 2 % in equatorial. The similar relationship between RC distribution and climate is observed for other RC values. Although we acknowledge that the number of catchments in equatorial regions are much fewer than others with just 2 catchments, a clear large-scale pattern across Australia emerges: in wetter catchments, during each event rainfall contributes more to runoff, highlighting increasing potential for runoff generation. Studies in other places around the world have shown that the spatial distribution of RCs is strongly correlated with precipitation and align with our findings (Norbiato et al., 2009; Merz and Blöschl, 2009; Merz et al., 2006).

Figure 10 exhibits a climatic signature that can be used to categorize Australian catchments in three different groups across climates based on their dominant runoff generation mechanism. In desert and grassland regions, the ECDF rises sharply at RC ≈ 0, indicating that high proportion of rainfall-runoff events produce negligible runoff, meaning rainfall is largely lost due to infiltration and evaporation. This points to less potential for rainfall to produce runoff via saturation excess, and thus suggests the potential dominance of infiltration-excess runoff generation mechanism in these regions. In subtropical, temperate, and equatorial regions, however, the ECDFs rise most gradually towards higher RCs, suggesting a high proportional rainfall becoming runoff in general. This pattern is often seen in regions with greater antecedent soil moisture and the predominance of saturation-excess processes. Tropical catchments show an intermediate pattern: the ECDF increases smoothly from RC ≈ 0 and is right-shifted relative to arid zones, indicating a mixed regime of runoff generation. Saturation-excess may dominate during wet periods, while infiltration-excess can occur under high-intensity rainfall (Kidron, 2021; Johnson et al., 2016; Mirus and Loague, 2013; Trancoso et al., 2016). Moreover, runoff events in desert and grassland regions have longer duration than runoff events in temperate, subtropical, and equatorial regions (Fig. 9d) confirming this categorization.

Moving from dryer to wetter catchments, the ECDF of RCs become less skewed (Fig. 10). This is consistent with (Merz and Blöschl, 2009) who reported that RC in dryer catchments is more skewed. RCs between 0 to 0.25 become more evenly distributed moving from dryer to wetter climates. In equatorial climate region, the ECDF of RCs between 0 to 0.25 resemble to follow a uniform distribution. For RCs more than 0.5, the ECDF of RCs almost follows a linear relationship with steeper slope for wetter catchments. The steeper slope of ECDF of RCs in wetter catchments reveals that there is a higher probability of occurrence of hydrologic extremes in wetter catchments which is align with what reported in Norbiato et al. (2009) and Breinl et al. (2021).

In the process of identifying rainfall-runoff events, the use of parameters to specify “rules” to define events is usually unavoidable, however, decreasing the number of parameters is beneficial for reducing uncertainty (Mohammadpour Khoie et al., 2025). In this study, we presented RVEIM which attempts to address the challenges with conventional rainfall-runoff event identification methods while using a fewer number of parameters. RVEIM's key benefit is incorporating a physical understanding of runoff-generation processes into statistical event identification with the fewest parameters within known methods, which are unlikely to differ across different hydro-climatic conditions, making the method less uncertain and more transferable across different hydro-climatic conditions.

Independence of runoff events is always an important consideration in identifying rainfall-runoff events with parameters used to define periods of time without an event usually used to define independence (Tang and Carey, 2017). Although such parameters might be useful, they increase the uncertainty, as there is no standard to select such a time period, as it may vary between catchments and the events themselves. To address this, RVEIM identifies runoff events based on independent rainfall events; hence it ensures the independence of corresponding runoff events while minimizing the number of parameters.

A threshold value is usually necessary to detect/delineate a runoff event. The threshold, in some cases, is applied directly to the streamflow records (Tang and Carey, 2017; Wasko and Guo, 2022), sometimes to the variance of streamflow data (Fischer et al., 2021), or in other cases, to the rainfall records (Giani et al., 2022). This also adds uncertainty and reduces transferability. For example, in DMCA, a threshold is considered for detecting rainfall events (rain_min which is distinct from the peak-over-threshold approach). They showed that change in the threshold value can significantly change the characteristics of identified rainfall-runoff events. They showed that lower values of the threshold lead to fewer but longer and larger rainfall-runoff events, while larger values lead to more but shorter and smaller ones. The variability introduced by threshold value change leads to substantial uncertainty, complicating subsequent analyses.

Compared with the existing approaches, the proposed approach to specify the variance threshold of streamflow is more robust across different climates while relying on less parameters. The proposed approach tries to find the variance of baseflow-dominated streamflow. In RVEIM, there is only one alpha parameter which affects the estimation of baseflow, and hence, the variance threshold var_lim. To show the robustness of variance threshold against parameter value change, we tested the changes of the average annual number of rainfall-runoff events against changing alpha value (d_var is fixed). Figure A5 shows the variability of average annual number of rainfall-runoff events across alpha values for 8 representative catchments. In all catchments, the variability of average annual number of rainfall-runoff events is low (where the standard deviation for each catchment is within ±3.48 % of the corresponding mean). This approach to threshold selection enhances the transferability of RVEIM while reducing uncertainty.

RVEIM simultaneously detects and pairs runoff events on the basis of detected rainfall events. The dynamic detection and pairing of rainfall and runoff events has several advantages. By detecting runoff events from rainfall events, RVEIM mirrors the natural hydrologic process. In RVEIM, each rainfall event is matched with its corresponding runoff event (if one can be identified) before moving to the next rainfall event reducing the risk of mispairing. Existing methods vary the direction of pairing (many studies pairing from runoff to rainfall), and they may also vary the statistics used to pair (peak of rainfall/runoff, start/end of rainfall/runoff) (Wasko and Guo, 2022). However, RVEIM considers the temporal runoff generation causality and searches for runoff from the start of each rainfall event.

RVEIM also enhances the way of determining the length of search window and the way of finding corresponding runoff for each rainfall. Conventional methods usually use a time-invariant search window should be defined by the user. Using a time invariant search window may force rainfall-runoff event identification to identify specific types of events, such as shorter runoff events (Mohammadpour Khoie et al., 2025), which may bias towards specific runoff generation mechanism. However, in RVEIM, the length of search window is not user-defined and changes across rainfall events. This allows RVEIM to capture runoff events with various lengths which has higher potential of capturing a fuller range of mechanisms of runoff generation. Moreover, including the length of rainfall in the search window can maximize the probability of correctly capturing multi-peak runoff events. The number of peaks in a runoff event is usually dependent on number of peaks in the corresponding rainfall event and wetness conditions during the runoff event (Tarasova et al., 2018b; Gao et al., 2025); hence, incorporating rainfall length as well as best_lag in the search window implicitly considers the temporal pattern of the rainfall and helps ensure that the associated runoff is accurately captured. This also eliminates the parameter usually considered to ensure the independency of two consecutive runoff peaks (Wasko and Guo, 2022).

RVEIM could, in principle, be applied to sub-daily data because its identification rules are based on physically meaningful changes in streamflow. However, because runoff event detection is initiated from independently identified rainfall events, the definition and consistent delineation of rainfall events at sub-daily resolutions would be critical. Although the underlying rules should remain physically applicable, the greater variability and noise at finer temporal resolutions may require adjustments to parameter definitions and thresholds.

The use of RVEIM is still associated with some errors. Although it is challenging to identify errors due to a lack of “ground truth” data, analyzing RC values may help, as RCs > 1 indicate physically implausible events. We must acknowledge that there might be some rainfall-runoff events with valid RC values that are still incorrectly identified or paired, however, a high percentage of rainfall-runoff events with RCs > 1 generally indicates greater errors in rainfall-runoff event identification.

Values of RC ≥ 1 can occur for various reasons. The first reason is overestimation of runoff volume. For some alpha values, the baseflow filter may estimate lower baseflow locally/generally which causes an overestimation of runoff volume leading to RCs > 1. This situation is more probable in wet catchments. Wet catchments usually have lower rainfall losses (higher RC values) which increases the probability of RC values exceeding 1. Secondly, in some cases, the rainfall-runoff event identification method may pair a runoff event with the incorrect runoff leading to identifying a rainfall-runoff event with RC > 1. This is, again, more probable in wetter catchments where there is higher number of rainfall and runoff events. When the number of rainfall/runoff events increases, there can be less clear separation of rainfall-runoff events which confuses rainfall-runoff event identification.

Underestimation of rainfall volume is the third potential reason for RCs > 1, most likely due to disinformation in the observations (Beven, 2019). In some cases (especially regions where rainfall is highly spatially variable, such as mountainous regions) not all rainfall events may be captured by the rainfall gauges. In this case, a large volume of runoff might be correctly paired to a small recorded rainfall event, which is actually an underestimate of a larger rainfall event, causing RC to exceed. Here we have assumed rainfall events to be deterministic. However, it may be that two consecutive rainfall events are both part of a single multi-peak event but are separated by a rainfall amount below the 1 mm threshold. In this case the POT detects two smaller rainfall events, and it is probable that one rainfall event is paired to the runoff with the other one left unpaired. However, this can be accommodated through post processing of unpaired rainfall events. Finally, errors in streamflow gauging, rating curve extrapolation, and the use of daily data (which may not accurately capture the timing or dynamics of rainfall-runoff events) can also contribute to RC values exceeding 1 (Beven, 2012) but the impacts of such errors are beyond the scope here.

Considering Fig. 9, catchments which are in regions with more rainfall/runoff events do indeed have higher uncertainty and percentage of RCs > 1. For example, catchment G8150018 has relatively higher percentage of RCs > 1 according to Fig. 7. Tasmanian catchments are usually the worst cases with the highest percentages of RCs > 1, and they satisfy all above-mentioned contributing conditions. For example, catchment 306119 located in western Tasmania where there is high number of rainfall/runoff events, the soil moisture is the highest (Fig. A4), and the elevation is high. In such catchments, improving the temporal resolution of data (i.e. sub-daily data) may enhance the correct identification of rainfall-runoff events but will also likely introduce more noise in the measurements.

We used the RVEIM to generate a first Australia-wide summary of rainfall-runoff event characteristics, as well as the distribution of event RCs (Sect. 4.3). Catchments showing a gradual/slow increase of ECDF of RCs at RC ≈ 0 suggest dominance of the saturation‐excess runoff process, distinguishing them from those governed by infiltration‐excess runoff (sharp increase of ECDF at RC ≈ 0). The results closely align with hydrologic understanding of climate variations in Australia. In northern Australia (tropical and equatorial climates) catchment responses highly vary based on rainfall intensity and soil moisture during wet seasons. So, it is expected to see a wider variety of rainfall-runoff events with various RCs comparing to other regions (Duvert et al., 2022). In the desert climate in Australia, the rainfall losses are high, meaning there is lower potential for catchments in arid climate to generate runoff (Zaman et al., 2012). Therefore, it is expected to see rainfall-runoff events have lower RCs (i.e., ECDF of RCs shifts to left) in Fig. 7. Comparing catchments in different climates, catchments with higher soil moisture and lower actual evapotranspiration are expected to have less rainfall losses and thus higher RCs. ECDFs of RCs obtained from all methods indicate that RVEIM better presents rainfall-runoff relationships (Fig. 8). For example, catchment 306119 in western Tasmania, where soil moisture is extremely high, should generate rainfall-runoff events with relatively high RCs. Among the three methods, the ECDF derived from RVEIM suggests a greater runoff generation potential in the Tasmanian catchment, as it assigns less probability mass to very low RCs than local maxima and DMCA (Fig. 8f). Results are broadly consistent with (Merz et al., 2006) demonstrating that the shape of ECDF of RCs can relate to climatic conditions (such as mean annual rainfall or soil moisture).

More broadly, accurate identification of rainfall-runoff events across the full spectrum of event magnitudes and climates is crucial for characterizing catchment responses at large/national scale. Australia has a highly diverse runoff patterns, ranging from water-limited regions in central Australia to regions with frequent rainfall/runoff events such as Tasmania. Existing rainfall-runoff event identification methods are often highly sensitive to parameter values, which can lead to biased identifying of event characteristics. For example, some settings may capture only very large events (Leenman et al., 2023), while others may force the identification of only short-duration runoff responses (Mohammadpour Khoie et al., 2025) and identification of only a limited number of runoff processes that exist in a catchment (Merz et al., 2006). These biases reduce comparability across regions and may obscure the climatic gradients that shape runoff response. However, the RVEIM provides a more consistent basis for comparing runoff processes across contrasting climates, thus offering a systematic classification of runoff response.

Many regions worldwide face the challenge of understanding hydrological response under changing conditions, whether due to droughts, land-use change, or climate change. As the RVEIM reduces uncertainty and captures both small and large runoff events, it provides a transferable framework for exploring how catchments respond to rainfall in different hydroclimatic settings. Future studies can further investigate the key climatic and catchment-scale drivers of rainfall-runoff event characteristics identified by RVEIM. Linking event-scale characteristics (RC, for example) to such drivers would help explain regional variations in runoff generation. RVEIM can be also used to classify rainfall-runoff events based on dominant runoff mechanisms (e.g., infiltration- versus saturation-excess) and to explore how these behaviors evolve under different hydroclimatic conditions (such as climate change). Such analyses would facilitate systematic understanding of catchment response and enhance predictive rainfall-runoff models at large spatial scales. Using RVEIM, therefore, improves confidence in runoff characteristics used for infrastructure design and flood risk assessment, and allows researchers to better assess how event-scale processes shift under climate change in large sample studies.