Intra-event extreme rainfall characterization in the tropical Andes: a high-resolution weather radar approach

Hydrological hazards, such as floods and landslides are frequently driven by extreme rainfall events (ERE). Thus, understanding the spatio-temporal patterns and intra-event behavior of these events is important for identifying vulnerable regions, improving early warning systems, and enhancing water management. This study aimed to analyze the spatio-temporal intra-event characteristics of ERE, using high-resolution (5min) weather radar data focusing on their internal structure and spatial distribution. The study was conducted in the headwaters of the Paute basin (2,200–4,400 m a.s.l.) in southern Ecuador. Based on three ERE classes, four intra-event rainfall features were analyzed: area, maximum rainfall, cohesion, and the locations of rainfall hotspots. These features revealed different rainfall patterns for the three distinct rainfall classes. Class 1 is characterized by the highest rainfall peaks, concentrated between 12:00 and 19:00 (afternoon). Class 3 shows the lowest rainfall peaks. Class 2 shows the least cohesive rainfall core and a mixed behavior in features. Regarding the locations of rainfall hotspots, classes 1 and 2 show hotspots located at the catchment outlets and at the urban (City of Cuenca) areas of the sub-catchments (around 2,500 m a.s.l), while those in class 3 are found at headwaters (above 3,500 m a.s.l). Identifying these rainfall characteristics and hotspot location provides a better understanding of extreme rainfall behavior in the tropical Andes, which enhances knowledge of hydrological processes, and improves flood forecasting.

Extreme rainfall is considered the key driver of many hazards (Zscheischler et al., 2018; Rosin et al., 2024) such as droughts, floods, and landslides, which, in turn, lead to severe economic, environmental and human losses (Zscheischler et al., 2018; Poveda et al., 2020; Ridder et al., 2020). Understanding extreme rainfall patterns is crucial for identifying areas prone to impacts of such extreme events. This helps in establishing early warning systems and improving monitoring in these areas. Moreover, this knowledge is valuable for water management and planning flood mitigation strategies.

There is no unique definition of extreme rainfall. In spite of the increasing use of the term extreme, a unified definition has never been achieved (Gimeno et al., 2022). For instance, Field et al. (2012) define extreme events as the occurrence of a climate variable such rainfall above a threshold near the upper ends of the observed data series of the rainfall. Conversely, Gimeno et al. (2022) relate the definition of extremes to the impacts that they produce such as economic losses or social effects. Furthermore, statistical methods such as parametric and non-parametric methods are widely used to define extreme events (Anagnostopoulou and Tolika, 2012; Liu et al., 2013; Flores-Rojas et al., 2021; Gimeno et al., 2022). However, the choice between parametric and non-parametric remains a point of discussion (Gimeno et al., 2022). In addition, Serinaldi (2024) selected extreme rainfall in midlatitude areas using a daily percentage threshold based on the at-site empirical cumulative distribution function (ECDF). Then, that study applied a test based and model based to fit the extreme data and assess annual trends. However, the author emphasize that mathematical assumptions must not be overlooked when performing statistical tests to avoid incorrect conclusions.

In tropical areas like Peru and Ecuador, non-parametric methods are used for defining extreme rainfall (Flores-Rojas et al., 2021; Urgilés et al., 2024). In Peru, extreme rainfall, defined as rainfall exceeding a specific threshold (e.g., 90th percentile) within a data series (Flores-Rojas et al., 2021), is characterized by high spatio-temporal variability. These variability is particularly pronounced in the tropical Andes, where strong altitudinal gradients influence rainfall distribution (Buytaert et al., 2006; Espinoza et al., 2015). In relation to extreme rainfall, most studies in tropical regions have analyzed the influence of large-scale atmospheric patterns (Espinoza et al., 2015; Segura et al., 2019; Hermawan et al., 2022; Purwaningsih et al., 2022; Villalobos-Puma et al., 2022; Gómez-Rios et al., 2026). For instance, in Indonesia, atmospheric patterns of both oceanic and terrestrial moisture sources play an important role in extreme rainfall (Hermawan et al., 2022; Purwaningsih et al., 2022). Similarly, in the Peruvian Andes, orographic effects, easterly winds, and moisture flows drive rainfall variability (Espinoza et al., 2015; Villalobos-Puma et al., 2022). Gómez-Rios et al. (2026) identified two main spatio-temporal patterns in the Colombian Andes driven by regional atmospheric mechanisms and orographic characteristics. Furthermore, Segura et al. (2019) linked extreme monthly events to convection over the western Amazon. However, beyond the large-scale atmospheric patterns, lifecycles of ERE and intra-event characteristics has been less explored. Characterizing ERE spatial coverage and peak intensity is important for better understanding their local impacts.

Analyzing ERE in the Andes remains challenging due to data constraints. Studies often rely on rain gauges, satellite imagery or reanalysis products (Ferreira and Reboita, 2022; Villalobos-Puma et al., 2022). For instance, daily and monthly rainfall data from satellite and reanalysis sources (Global Precipitation Climatology Project, Climate Prediction Center, National Center for Environmental Prediction- National Center for Atmospheric (NCEP–NCAR) and ERA5) covering a period of approximately 40 years, have been used to evaluate the intensification of the hydrological cycle on a global scale (Koutsoyiannis, 2020). Although these datasets effectively capture seasonal and annual variations, substantial uncertainties remain in the rainfall estimation (Koutsoyiannis, 2020). Furthermore, while satellite images such as IMERG offer global coverage, they often fail to capture topographic effects, particularly during extreme rainfall (Malamos et al., 2025). In addition, Longo-Minnolo et al. (2022) evaluated rainfall using reanalysis data (ERA5-Land) and suggested that adjustments are necessary to reduce site-specific uncertainties driven by local climate conditions. Consequently, both satellite and reanalysis data (e.g., ERA5 and IMERG) require careful calibration with ground-based data to properly reproduce rainfall variability and avoid the over or underestimation of rainfall (Koutsoyiannis et al., 2023).

Specifically in Ecuador, recent evaluations of gridded precipitation and reanalysis datasets indicate that global gridded datasets struggle to capture local variability due to complex topography (Turini et al., 2021; Fernandez-Palomino et al., 2022; Huber Magoffin et al., 2023). These datasets are often hindered by coarse resolution and a lack of in-situ data for calibration in Ecuador, making them more suitable for assessing long-term averages (i.e., monthly) rather than specific intra-event timing. This limitation is critical in southern Ecuador, where ERE durations are usually under 7 h (Seidel et al., 2019; Urgilés et al., 2021). Additionally, scarce ground monitoring and low spatial resolution data impede the capture of intra-event processes. To address this, Sokol et al. (2021) and Thomassen et al. (2022) highlight the importance of high spatio-temporal resolution data, noting that weather radar is a better option for extreme precipitation analysis. Radar data have been used in mountain regions worldwide, including the Swiss Alps (Grazioli et al., 2015; Gabella et al., 2017), the central Himalayan region (Talchabhadel et al., 2022) and the tropical Andes (Valdivia et al., 2021; Gómez-Rios et al., 2026), where high spatio-temporal resolution is essential for capturing different rainfall characteristics. The use of radar data has increased over the last decade. For instance, Gómez-Rios et al. (2026) used maxima and mean rain rates to identify the spatio-temporal patterns of extreme rainfall. Similarly, Morin et al. (2006) used rain cell features such as area, intensity, local maxima rainfall to characterize the spatial track of rainstorms, showing that extreme rainfall cells moving over watershed tributaries toward the outlets triggered high flows. Also, Peleg and Morin. (2012) analyzed convective rain cells using radar data in the eastern Mediterranean (Israel). The authors identified three types of extreme events and analyzed their spatial and temporal features (area, intensity, major and minor radius). Furthermore, Panziera et al. (2016), analyzed extreme rainfall to identify thresholds for nowcasting systems, finding that the spatial rainfall distribution depends on the accumulation period, highlighting the importance of high-resolution data.

Despite efforts to analyze ERE, these events have typically been studied as single entities. This means that rainfall characteristics (i.e., total rainfall accumulation, total duration) representing the whole event are prioritized, while a detailed analysis of the intra-event variability (i.e., variability within the event) remains limited. ERE have usually focus on rainfall amounts at fixed durations, for example, per day or multiple days (Grimm and Tedeschi, 2009; Chen et al., 2011) rather than complete ERE with different durations (Yin et al., 2022). Consequently, their intra-event variability remains unknown, and the use of radar data provides a unique spatial and temporal resolution to characterize event rainfall at a detailed scale. In this context, the objective of this study is to analyze the spatio-temporal intra-event characteristics of ERE by using 5min weather radar data, focusing on evaluating their internal structure and organization. The study was conducted in the headwaters of the Paute basin (2,200–4,400 m a.s.l.) in southern Ecuador. ERE were analyzed based on a clustering approach previously applied in the tropical Andes of Ecuador by Urgilés et al. (2024), in which ERE characteristics (e.g., total rainfall, duration, month of occurrence) were used as inputs for clustering. Urgilés et al. (2024) identified three classes of events that are the starting point of our current work: i) events with high intensity and short duration, ii) events with low intensity and long duration, and iii) events combining the previous classes. This approach enables a deeper understanding of how rainfall is distributed over complex terrain, providing a high-resolution characterization of ERE behavior.

Study area

The study site has an area of 5,500 km 2 within the Inter-andean zone, located in southern Ecuador in the tropical Andes. The study site covers the Machangara (M), Tomebamba (T), Yanuncay (Y), and Tarqui (T1) sub-catchments, which form the headwaters of the Paute basin near the city of Cuenca (Figure 1).

These sub-catchments are essential providers of ecosystem services to surrounding communities, including hydropower generation, and water for both drinking and irrigation purposes (Célleri and Feyen, 2009); consequently, they constitute a source of important economic value. These mountain ecosystems also provide great ecological value to the study site. The presence of different microhabitats fosters ideal conditions for the evolution of plant and animal species (Célleri and Feyen, 2009). Furthermore, neighboring towns and cities, such as Cuenca, are exposed to flash floods that cause human and economic losses.

The study area shows a bimodal rainfall regime, characterized by two rainfall peaks occurring in April and October, and dry seasons occurring between June-August and December-January (Campozano et al., 2016). Mean annual rainfall ranges from 660 mm to 1,200 mm at lower elevations, and from 1,000 to 1800 mm in the upper elevations of the study area (Célleri et al., 2007; Silva et al., 2025). Rainfall is driven by the displacement of the Intertropical Convergence Zone (ITCZ) (Poveda and Mesa, 1997; Espinoza Villar et al., 2009; Campozano et al., 2016), the Pacific regime from the west, and the tropical Amazon air masses originating from the east (Urdiales-Flores et al., 2025). The study area covers slopes, peaks, and isolated valleys (Célleri and Feyen, 2009). It features a complex topography, with elevations ranging from 2,300 to 4,450 m a.s.l. The mean temperature ranges from 6.5 °C (4,000 m a.s.l) to 14 °C (2,600 m a.s.l) while the relative humidity is around 80%–95% (Córdova et al., 2016). According to the Köppen-Geiger climatic classification, the study area is characterized by temperate climate, humid with warm summer (Cfb) (Kottek et al., 2006; Beck et al., 2023).

Data

Weather radar

As part of the Radar Net-Sur weather radar network, a single-polarized X-band radar (CAXX) was installed in southern Ecuador (2.75°S, 79.26°W) (Bendix et al., 2017). It is located in the Cajas National Park on Paragüillas Peak at 4,450 m a.s.l. (Figure 1). The system has a transmission frequency of 9,410 ± 30MHz, a bandwidth of 2.5MHz, and a pulse length of 1.2–0.5 μs. It reaches a maximum range of 100 km. A parabolic antenna with vertical and horizontal beam widths of 2° is the main component of the system. The radar provides polar images of radar reflectivity with 5min resolution. Further details about the radar and its components can be found in (Bendix et al., 2017; Guallpa et al., 2019; Orellana-Alvear et al., 2019).

The CAXX weather radar began operating in April 2015; however, due to operation issues, it was turned off from June 2017 to November 2020. These issues were associated with logistical challenges related to its remote mountain location, energy supply instability and maintenance delays caused by the COVID-19 pandemic. For this study, we used ERE identified across 3 years of data, specifically from April 2015 to June 2017 and December 2020 to March 2022. The weather radar provides polar images of reflectivity, which must be converted into Quantitative Precipitation Estimation (QPE).

Although radars data offer an unprecedent opportunity to observe rainfall events, there are recognized limitations such as beam blockage, clutter, and attenuation (Rollenbeck, 2006; Rollenbeck and Bendix, 2011; Orellana-Alvear et al., 2019) which must be addressed to improve reliability on radar QPE especially in a complex topography such as tropical Andes. The CAXX is located on Paragüillas Peak at 4,450 m a.s.l., the antenna elevation angle was set to −2° during installation. This aligns the main beam horizontally at 0°, which effectively overcomes beam blockage from surrounding peaks (Orellana-Alvear et al., 2019). Next, the raw polar images were corrected using a step-wise correction method that addressed the correction of reflectivity value by considering the specific location of the radar and study area (Orellana-Alvear et al., 2019). The step wise correction method consists of: (i) removing ground clutter by filtering static and dynamic clutter (Marra and Morin, 2015), and (ii) correcting attenuation using a gate-by-gate iterative approach (Krämer and Verworn, 2009). The maximum reflectivity was set to 95.5 dBZ, consistent with the maximum values of reflectivity observed by the radar in this study. The maximum Path Integrated Attenuation (PIA) was set to 20 dB, as suggested by Jacobi and Heistermann. (2016). The parameters for the k-Z relationship were locally derived from a disdrometer located in the city of Cuenca, ensuring the correction is representative of the study area. Additionally, Jacobi and Heistermann. (2016) evaluated three procedures for constraining attenuation effects and the method by Krämer and Verworn. (2009) showed the best performance in cases of heavy rainfall. According to Krämer and Verworn. (2009), this method significantly improves rainfall estimates and preserves the structure of the rain fields. In our study, to evaluate the performance of the step wise correction method, a comparison between corrected reflectivity values of the radar and the reflectivity records of two Thies Laser Precipitation Monitor (disdrometer) (Thies Clima, 2007) located at 7 km (Virgen 3,600 m a.s.l) and 30 km (Balzay 2,600 m a.s.l) was carried out (Figure 1). Reflectivity data of the disdrometers were collected at 5min resolution and it was used only for comparison purposes. More detail about disdrometers can be found in Thies Clima. (2007). Two extreme events were selected based on the location occurrence over the disdrometers and data availability.

In Figure 2, the radar and disdrometer reflectivities show good agreement, with correlation values ranging between 0.5 and 0.8 consistent with values found in Orellana-Alvear et al. (2019). Furthermore, the p-values show statistical significance (p < 0.01) for the relationship between the reflectivities obtained from the radar and the disdrometer. This strong agreement in correlation values is related to two main factors: i) Both instruments derive the same variable (reflectivity). In the case of the radar, the reflected energy (the echo that returns after interacting with the raindrops) is transformed into reflectivity (Rollenbeck and Bendix, 2006). On the other hand, the disdrometer consists of a transmitter and a receiver; a light beam is emitted by the transmitter, and when the beam intercepts a rainfall particle, the received signal is reduced, allowing the estimation of the diameter and velocity of raindrops (Thies Clima, 2007). From these measurements, reflectivity is calculated. ii) The datasets from both instruments were selected from the same geographic location, and the data was synchronized and used the same temporal resolution (5min). It minimized the spatial mismatch and ensuring that they captured the same rainfall fields. At Virgen station, the lower RMSE and bias indicate strong agreement with the disdrometer; at this close range (7 km), the radar accurately captures the rainfall patterns. Conversely, at Balzay station, the attenuation effect is observed in the underestimation of the values. This underestimation of rainfall may also be a result of the small-scale heterogeneity of the events (Jacobi and Heistermann, 2016). Additionally, other deviations such as wind effects will occur when comparing the volume integrated measurements (smoothed area-wide) to the point observations (disdrometer) (Jacobi and Heistermann, 2016). Although attenuation plays an important role in radar measurements, the sensor is still able to capture rainfall fields and their variability.

The reflectivity values obtained from the radar were converted into rainfall rates following the Z = a R b relationship (Marshall and Palmer, 1948). In this study, locally derived coefficients, a and b, for the Z-R relationship were used to convert reflectivity into rainfall rates (Orellana-Alvear et al., 2017).

In Equation 1, Z is the reflectivity value in mm 6 /m 3, and R is the rain rate in mm/h.

Rain gauges have been used to evaluate the quality of the radar data (Morin et al., 2006; Jacobi and Heistermann, 2016; Gómez-Rios et al., 2026). Bournas and Baltas. (2022) evaluated multiple relationship Z-R derived from rain gauges-based relationships, highlighting the spatial variability of the rainfall. In the context of Ecuador, in the tropical Andes, where rain gauge networks are sparse and unevenly distributed, implementing comparison and adjustment methods are difficult to apply specially at sub-hourly scales. To evaluate the quality of the radar dataset despite these limitations, we compare the complete rainfall radar data set (averaged over 3 × 3 pixel window of 500 m centered on the locations of each rain gauge) against three rain gauges located at different distances within the study area: Toreadora 5.5 km, OPNC 20 km and Zona 33 km (Figure 1). Nine metrics were calculated to assess radar data quality: percentage of missing values, percentage of zero values, maximum rainfall, root mean square error (RMSE), bias, mean, variance, kurtosis and skewness.

The metrics summarized in Table 1 showed the performance and validity of the radar QPE dataset across different distances from the radar. First, the radar presents a high capability in detecting rain/no rain, its percentage of zero values is consistent with rain gauge, showing a maximum difference of 0.8% in the furthest rain gauge (Zona). Maximum values revealed underestimation of the values. Furthermore, there are differences in the metrics such as mean, variance, kurtosis and skewness, showing the dominant presence of values near-zero in the radar. This suggests that the radar struggles to capture low-intensity rainfall which are important in the rain-gauge accumulations over long time periods. However, while the radar effectively captures the rainfall fields and maximum values, it tends to underestimate low rain rate. Additionally, the RMSE increased from 0.27 to 0.78 at largest distances. These error magnitudes are in agreement with other radar literature, for instance previous studies reported RMSE values ranging from 0.23–1.19 (Bournas and Baltas, 2022), 3.14 (Mapiam, 2008), 0.77 (Jacobi and Heistermann, 2016), and around 3 (Dzwonkowski et al., 2025) Regarding bias, values of −2.48 (Dzwonkowski et al., 2025) and −0.246 (Zeng et al., 2021) were reported in literature, while our results showed values of −0.17 and −0.44. This general underestimation is in agreement with the values reported in literature. Additionally, the values of RMSE and bias increase at ranges from 5.5 to 33 km showing that the attenuation influence in the QPE. Although attenuation is a recognized limitation of X-band radar, other error sources such as instrumental limits of the tipping buckets, small scale rainfall variability and different measures volumes affect the comparison with rain gauges (Kitchen and Blackall, 1992; Krämer and Verworn, 2009; Gires et al., 2014). Rain gauge measurements rely on a threshold of rainfall accumulation (typically 0.1 mm) which could be distributed in 5min or in 1 h, while the radar captures instantaneous volumetric in a defined time (e.g., 5min) (Kitchen and Blackall, 1992). Furthermore, Kitchen and Blackall. (1992) emphasize than evaluating radar data with a limited number of rain gauges force a point to volume correction, it often introduces biases in the radar field. However, the overall consistency in rain detection and error magnitude (Table 1) validates that the step wise correction method (Orellana-Alvear et al., 2019) is an effective method given the constraints of the available rain gauge network in Ecuador.

According to Guallpa et al. (2019), a spatial resolution of 500 m is adequate to capture rainfall for hydrological studies. Thus, the polar images were transformed into Cartesian coordinates with a spatial resolution of 500 m. As a result, radar images with 5min and 500 m resolution were used.

Extreme rainfall events

We analyzed 67 ERE that were previously identified and classified by Urgilés et al. (2024). In that study, the ERE were selected from the weather radar database based on a daily rainfall threshold (i.e., the 90th percentile). Those authors applied the k-means algorithm to cluster the events based on 14 rainfall characteristics extracted from each event (e.g., rainfall accumulation, intensity, reflectivity, among others). Urgilés et al. (2024) identified three classes of events: i) events with high intensity and short duration (class 1: 29 events), ii) events with low intensity and long duration (class 3: 16 events), and iii) events with a combination of the characteristics of the other two classes (class 2: 22 events) (Table 2).

Methods

First, we used the 67 ERE identified by Urgilés et al. (2024), Supplementary Table S1 details the statistical summary of the ERE. Then, we eliminated the isolated rain cells from each event (Section 3.1). Finally, intra-event features were extracted for each ERE (Section 3.2) (Figure 3).

Extreme rainfall events

In order to eliminate isolated rain cells within each extreme event, a rain cell identification method was applied following the approach of Peleg and Morin. (2012) and Bournas and Baltas. (2024). This method assigns a null value to any rain cell value falling below a rainfall/reflectivity threshold (Peleg and Morin, 2012). While the choice of threshold typically depends on the target features (i.e., rainfall core, convective part, stratiform part) and the climatological conditions of the study area (Barnolas et al., 2010; Peleg and Morin, 2012; Bournas and Baltas, 2024), the threshold for this study was determined through a sensitivity analysis.

Convective cells typically show reflectivities above 30–35 dBZ, while stratiform cells generally fall within 20–30 dBZ. Consequently, a threshold of 25 dBZ was selected as an optimal trade-off. This threshold maintains the main structure of the ERE (i.e., capturing both stratiform and convective rainfall) while removing isolated rain patches. This threshold value is consistent with Bournas and Baltas. (2024), and was further validated through visual inspection.

Extreme rainfall characterization (spatio-temporal features)

The ERE were characterized spatially and temporally using intra-event features that synthesize their key aspects. In the literature, there is no conventional list of features to be considered; however, the selection of the features relies on the measured variables and the scope of the study (Dilmi et al., 2017). As shown in Table 3, several authors select features covering intensities, spatial and temporal characteristics to describe ERE and their dynamics. For instance, Schumacher and Johnson. (2006) used specific characteristics to capture extreme events associated with tropical, synoptic and mesoscale convective systems. In the context of tropical Andes, the presence of convective cores, mesoscale convective systems and mesoscale convective complexes highlights the complex dynamics of extreme rainfall. Additionally, the life cycle of these events changes over time (e.g., young and mature stages) (Bendix et al., 2009). Consequently, capturing rainfall organization, concentration and dynamics needs a detailed representation of intra-event structure. In this context and based on Table 3, four key intra-event features were selected: i) extreme rainfall area, ii) local maxima rainfall intensity, iii) core cell cohesion and iv) the locations of rainfall hotspots. These features are described below.

Extreme rainfall area

The identification of extreme rainfall areas is important for analyzing flood generation and delimiting ERE (Morin et al., 2006; Peleg and Morin, 2012). It identifies the location of the start and the end of an extreme rainfall event. This feature combined with the rainfall intensity threshold, is useful for delineating ERE in the tropical Andes. In this study, two parameters representing area were selected: i) the 5min extreme rainfall area (km 2 /5min) and ii) the total extreme rainfall area (km 2 /event), as explained in the following paragraphs. The 5min extreme rainfall area (i.e., area at each time step), was determined during the ERE identification. This area was quantified by counting the total number of pixels (spatial blocks) that exceeded the reflectivity threshold for each 5min (Supplementary Figure S1 in Supplementary material). This provided a dynamic tracking of the spatial extent of the event over the time. Then, we obtained one area value (km 2 /5min) for each image.

The total extreme rainfall area (i.e., the area of each extreme rainfall event), was calculated using the rainfall accumulation of the 5min images for the entire duration of the event. Then, we counted the number of pixels that comprised the accumulated rainfall for the event. Finally, we obtained one area value (km 2 /event) for each event (Supplementary Figure S2 in Supplementary material).

Local maxima rainfall intensity

In this study, we used the local maxima of rainfall at each time step to track the extreme rainfall core and identify the hours of occurrence of the highest values. The core cell tracking is useful for identifying the local maxima rainfall intensity, hereafter referred to as local maxima rainfall (Yakir and Morin, 2011; Peleg and Morin, 2012; Bournas and Baltas, 2024). Yakir and Morin (2011) proposed a segmentation method to perform this identification. In this method, we identified the local maximum rainfall (mm/5min) and its location (WGS84 UTM Zone 17S) (i.e., coordinates x,y) at each time step. The local maxima values (maximum intensity mm/5min) values were identified in consecutive images with a time resolution of 5 min, for each event (Supplementary Figure S3 in Supplementary material).

Core cell cohesion

The core cell cohesion is a complementary feature to the area description. It is an indicator of the spatial concentration of an event (Naghizadeh and Metaxas, 2020). It quantifies the spatial dispersion of local maxima rainfall values around the highest rainfall value of the event. In this study, cohesion of the extreme rainfall event was analyzed using the spatial coordinates (i.e., x,y) of the local maxima rainfall (mm/5min) identified in the previous section. Cohesion features measure the distances between these points, allowing for the identification of the maximum spatial extent covered by the rain event core during a specific event (referred to hereafter as the distance buffer). Two parameters were used to analyze cohesion: the within-cluster sum of squares (WCSS) and proximity analysis (distance buffer). WCSS is a feature used to evaluate the cohesion between points within a cluster (Naghizadeh and Metaxas, 2020). It is calculated as the sum of the squared distances between the points and the cluster centroid (Naghizadeh and Metaxas, 2020; Wickramasinghe et al., 2022). In this study, WCSS was used to analyze the spatial cohesion among the local maxima rainfall (mm/5min) points, with each event evaluated as a cluster. While WCSS is typically calculated using the geometric centroid of the cluster (Naghizadeh and Metaxas, 2020; Wickramasinghe et al., 2022); in this study, the centroid was defined as the location of the maximum of local maxima rainfall over the entire event. This centroid is a static point. Consequently, the WCSS is a metric used to measure of the spatial cohesion around the maximum of local maxima rainfall per event.

In Equation 2, e is the number of event, wcss e (km 2) is the within-cluster sum of squares for event e, n is the number of time steps within each event, p i (km) is the coordinates (x,y) of the local maxima rainfall in each time step, and c e (km) represents the coordinates of the centroid (maximum of local maxima rainfall) for each event. Then, we compared the WCSS between all events of the same class. The WCSS ranges from 0 upward. A low value of WCSS indicates that the local maxima rainfall points within each event are closer together, reflecting higher cohesion. In contrast, a high WCSS value indicates lower cohesion (Supplementary Figure S3 in Supplementary material). Proximity Analysis (Distance Buffer) is a spatial analysis used to evaluate the distance between points relative to a centroid (Chatterjee et al., 2025). This proximity analysis was used to determine the distance buffer of the rainfall core. It is defined as the distance from the maximum value of the local maxima rainfall (centroid) to the farthest local maxima. It represents the maximum distance traveled by the rainfall core.

In Equation 3, d e (km) is the distance buffer, e is the event number, c e (km) is the position of the centroid (maximum of local maxima rainfall, it is a static point for each event), and f e (km) is the position of the farthest local maxima for each event. The distance buffer ranges from 0 upward. High values of the distance buffer indicate a greater distance covered, while low values indicate a shorter distance covered by the ERE (Supplementary Figure S3 in Supplementary material).

Locations of rainfall hotspots

The identification of rainfall hotspot locations is useful for revealing the geographical regions where the highest amounts of rainfall are concentrated (Espinoza et al., 2015; Zhang and Meng, 2019). Kernel Density Estimation (KDE) is a non-parametric approach (Lall, 1995) used to identify the spatial locations of hotspots in different hydrological applications, such as soil pollution, flood and drought analysis (Lall, 1995; Lin et al., 2011; Jiang et al., 2022; Wu et al., 2023). KDE estimates the spatial probability density function (PDF) of a variable (e.g., rainfall) from a data series.

In Equation 4, f(x) is the spatial density of the variable x (rainfall in mm), n is the number of data points, h is the bandwidth also known as the smoothing variable, and K is the kernel function. Cao et al. (2023), and Chen (2017) highlighted that the choice of kernel function has little influence on the KDE values. Nevertheless, the Gaussian Kernel was selected for this study due to its superior smoothing capabilities (Ren et al., 2014; Steininger et al., 2021; Lawal et al., 2024).

In Equation 5, K h is the Gaussian kernel function, x is the variable (rainfall), and h is the bandwidth.

According to Cao et al. (2023), the selection of the bandwidth is an important task. In this study, the spatial resolution of the data (500 m) was used as a first approximation for the bandwidth. However, the bandwidth was selected based on the spatial details obtained and the cohesion of the hotspots. Then a value of h = 1,000 was selected.

KDE is used to evaluate the spatial density of high rainfall amounts within each class. To complement the hotspot analysis, KDE application considers the spatial probability density function of the relevant areas to determine whether high rainfall values cluster together or whether these values remain isolated.

Regarding ERE, KDE allows for the visualization and identification of areas with the highest risk for ERE. In this study, KDE was applied to the three cases: extreme rainfall accumulation for ERE of class 1, class 2, and class 3.

Statistical analysis

To evaluate the statistical significance of the differences between the identified ERE classes, the Kruskal–Wallis test was applied. This non-parametric method was selected because no assumptions are required regarding data distribution (Helsel et al., 2020). The test evaluated if the distributions of the features were significantly different among the three classes. A p-value <0.1 indicated significant differences, while a p-value >0.1 showed that there were no significant differences among the compared classes. When significant differences were found (p-value <0.1), Dunn´s post hoc test with a Bonferroni correction was applied to identify significant differences between pairs of classes (Dinno, 2015).

Extreme rainfall area

The extreme rainfall area distributions of the ERE for each class are presented in Figures 4, 5. Figure 4a shows that a 5min extreme rainfall area of around 6 km 2 is predominant (approximately 17% of all events). Furthermore, around 60% of the 5min ERE have an area smaller than 100 km 2. This feature (Figure 4b) shows significant differences (p-value<0.001). Additionally, the post hoc test indicates no significant differences between class 2 and 3 (Table 4). Figure 4b shows that class 1 events have larger areas than classes 2 and 3. Here, around 10% of the 5min extreme rainfall areas of class 1 are over 300 km 2. Moreover, class 1 events show the highest mean and median area values, at approximately 120 km 2 and 80 km 2 respectively. The mean and median area values of classes 2 and 3 are similar, these are around 90 km 2 (mean) and 60 km 2 (median). Furthermore, for all three classes, around 60% of the 5min extreme rainfall areas have values below their respective mean values.

Figure 5 shows the total ERE area distributions for all extreme events and the three extreme rainfall classes. Figure 5a illustrates that the mean and median values are around 1700 km 2. However, 50% of the extreme events have areas lower than the mean value. This suggests that ERE typically have a spatial track (life cycle) between the first and third quartiles (1,200–2,300 km 2) in our study area, from their start until their end.

In Figure 5b, the three classes reported similar distributions in their mean and median values. This feature shows no significant differences (p-value>0.1) between the classes. Class 1 shows a mean total area (1800 km 2) while class 2 (1700 km 2) and class 3 (1,500 km 2). Class 3 shows that the 50% of the events have total areas below 1,500 km 2. In class 2, the distribution of values shows that 45% of the values are below the mean. For class 1, the median value is close to the mean (around 1700 km 2).

Local maxima rainfall

The local maxima rainfall (mm/5min) for the three classes of ERE are presented in Figure 6. This feature shows significant differences (p-value<0.001). Additionally, the post hoc test indicates significant differences between classes (Table 4). Class 1 events present the highest local maxima value (up to 38 mm/5min) compared to classes 2 and 3. Additionally, the local maxima of class 1 events occur between 10:00 and 24:00, showing higher values between 12:00 and 19:00.

Class 2 shows an isolated local maxima value of up to 30 mm/5min. Moreover, classes 2 and 3 show similar ranges for their local maxima values (10–20 mm/5min). Furthermore, class 2 and 3 events occur throughout the day. In class 2, the higher values are concentrated between 12:00 and 23:00. In class 3, the higher values are concentrated from 12:00 to 19:00. Furthermore, both classes show a rainfall tail (values below 1 mm/5min) at dawn.

In addition, the highest local maxima rainfall across the three event classes occur between 12:00 and 19:00. For this reason, to evaluate the hours of occurrence of the events, we divided the day into three-time periods: 0–12 (morning), 12–19 (afternoon), and 19–24 (evening). The three classes show a dominance during the afternoon hours. On the other hand, in class 1, the morning hours represent less than 10% of occurrences, whereas class 2 shows higher percentages of occurrence in both the morning and evening (Table 5).

Core cell cohesion

Within-cluster sum of squares (WCSS) – cell cohesion

Figure 7 shows the distribution of the WCSS for all ERE. Figure 7a shows that the mean and median values are different. This feature (Figure 7b) shows significant differences (p-value<0.1). Additionally, the post hoc test indicates no significant differences between class 1 and 3 (Table 4). Figure 7b shows that events in class 2 are the least cohesive. Here, the mean and median values are the highest, indicating a higher spatial area covered by the rainfall core. In addition, the mean and median of class 3 are lower than those of class 1. However, in class 1, the presence of outliers affects the mean values showing a similar distribution. These outliers represent atypical ERE, reflecting the variability within each class.

In Figure 8 the most cohesive events occurred in January and June which can be observed in the lower mean values of WCSS. In addition, the WCSS in June has the lowest mean value, representing 5% of the total number of events. These events belong to classes 1 and 3. Furthermore, the least cohesive events occurred in February, March, and April. The mean values in those months show higher values. Furthermore, the WCSS in February has the highest mean value, with 11% (8) of the total number of events. These events belong to class 2 and 3.

Regarding the classes, 75% of the events in class 2 occur in the months of February-April, showing that class 2 has the least cohesive events. Class 1 shows that the 95% of its events occur in October-December. Class 3 shows that the 60% of its events occur in January, June, and October-December. Therefore, class 1 and class 3 are associated with more cohesive events.

Proximity analysis - cell cohesion

Figure 9 shows the distance buffer of the rainfall cores of the ERE. Figure 9a shows that 55% of the events have a distance buffer below 55 km. This feature shows no significant differences (p-value>0.1) between the classes. As shown in Figure 9b, Class 1, class 2 and class 3 show similar mean distance buffers (54, 57 and 56 km, respectively) and follow a similar distribution. The spatial area covered remains similar across all the ERE events classes.

Locations of rainfall hotspots

The accumulated rainfall of the extreme events for each class is shown in Figure 10. The three classes have different local maxima and spatial distributions of rainfall. The maximum accumulated rainfall values are 149, 104, and 78 mm in classes 1, 2, and 3 respectively. Figure 10a shows the presence of high amounts of rainfall at the lower elevations of the sub-catchments and at the confluence of the sub-catchments (i.e., the inter-Andean valley). In contrast, class 2 (Figure 10b), shows that the high amounts of rainfall are located only near the outlets of the sub-catchments. Although the rainfall values in class 3 (Figure 10c), are lower than the values in classes 1 and 2, this class shows high amounts of rainfall located in the upper parts of the sub-catchments.

The hotspot areas of high amount of rainfall were identified for each class by applying KDE (Figure 11). In comparison with Figure 10, the KDE (Figure 11) allows for a clear spatial delimitation of areas with high amounts of rainfall that are surrounded by similarly high value pixels. This reduces the influence of spurious areas with high local variability.

In addition, the identified intra-event hotspots (i.e., KDE values above the 99th percentile) were labeled using numbers for visualization purposes only. The numerical labels do not reflect the relative importance of the hotspots. We provide the hotspot maps side by side (Figure 11). However, since kernel density values are image dependent (see legends), they cannot be compared among clusters.

For class 1, Figure 11a illustrates the presence of four main rainfall hotspots, three (2,3,4) located at the outlets of the sub-catchments and one (1) located at the confluence of two sub-catchments. These four main hotspots are regions where the highest amounts of rainfall are most concentrated and, therefore, have a higher probability of occurrence. Also, the two hotspots in the eastern part (2 and 3) could be considered as one, due these are surrounded by high values of KDE. Class 2 (Figure 11b) occurs more frequently in two main rainfall hotspots areas; the most intense hotspot is located at the outlet (1) of the sub-catchment.

For class 3, Figure 11c illustrates the presence of three main rainfall hotspots. The highest value is located in the upper parts (1) of the sub-catchments, but also a relevant hotspot is found at the confluence (2) of the sub-catchments. Also, there is a hotspot (3) in the headwaters with a lower value than (1).

The three classes show different hotspot characteristics which are summarized in Table 6. First, rainfall accumulation is the highest in class 1. Regarding the elevation of occurrence of the hotspots, a marked difference is shown between class 3 and the other classes. Class 3 hotspots are located at elevations above 3,500 m a.s.l., in the headwaters of the sub-catchments. In contrast, hotspots of class 1 and class 2 are located in urban areas at lower elevations.

When analyzing the intra-annual variability of the identified hotspots, class 1 events occurred in the last 3 months of the year. Class 2 events occur in the first 4 months of the year, and class 3 events occur throughout the year, except during July, August, and September.

Our study analyzed 67 ERE in the tropical Andes. Three classes of extreme events were identified using the methodology of Urgilés et al. (2024). The results reveal differences in the spatio-temporal characteristics of each class, suggesting different dynamics and rainfall processes. These results align with the International Association of Hydrological Sciences (IAHS) scientific view, which highlights that hydrological systems are characterized by complex interactions and natural variability that must be understood to improve predictability in a changing world (Montanari et al., 2013). Before analyzing our results, the p-values of the different parameters indicate that the classification successfully captures meaningful distinctions (p-value <0.1) in most parameters (5min area (p < 0.001), local maxima rainfall (p < 0.001), and WCSS (p < 0.1)), while others (total area (p = 0.46), distance buffer (p = 0.63) show overlaps, reflecting the complex nature of rainfall processes.

Regarding spatial extent, a minimum area threshold of 6 km 2 was established. It was derived from the violin plots of the 5min extreme rainfall area (Figure 4a). This threshold aligns with the range observed in similar studies where the selection of this area value is constrained by the specific data and study site (Morin et al., 2006; Peleg and Morin, 2012). For instance, Morin et al. (2006) in North America and Peleg and Morin (2012) in northern Israel selected minimum areas of 9 km 2, while Bournas and Baltas (2024) in Greece used 4 km 2. In contrast to Bournas and Baltas (2024) who used visual inspection to determine this value, our study identified that 6 km 2 is a 5min area threshold that, when combined with the reflectivity threshold of 25 dBZ, can be useful to delimit 5min extreme rainfall areas without requiring visual inspection.

Furthermore, 60% of the 5min extreme rainfall areas were smaller than 100 km 2, indicating a high concentration of values under this value. This is in agreement with Peleg and Morin (2012), who analyzed convective cells of three storm classes and found that rainfall event areas in the eastern Mediterranean (Israel) ranged between 36 and 64 km 2. However, despite of the 5min areas being concentrated below 100 km 2, the total extreme rainfall area in our study area ranged from 1,200 to 2,300 km 2. These results show that while 5min extreme rainfall areas were localized at any given moment, the ERE track across the study area, spanning multiple sub-catchments (325–476 km 2). This highlights the importance of tracking the entire lifecycle of the ERE.

The temporal distribution of local maxima rainfall reveals different characteristics across the ERE classes. The concentration of local maxima rainfall between 12:00 and 19:00 across all classes, but most dominantly in class 1, highlights the role of the diurnal cycle. This aligns with previous studies in the tropical Andes (Colombia, Ecuador, and Peru), which identified a marked rainfall peak and dominant convective activity in the afternoon (Poveda et al., 2005; Bendix et al., 2006; Endries et al., 2018; Chavez et al., 2020; Urdiales-Flores et al., 2025; Gómez-Rios et al., 2026). The dominance of afternoon peaks across all three classes points to solar heating as the primary trigger for convection in the inter-Andean valleys (Campozano et al., 2018). Specifically, these afternoon peaks are driven by locally induced thermal convection resulting from the effect of heating (solar insolation) the valley slopes throughout the day and the subsequent development of an up-slope breeze system (Mapes et al., 2003; Bendix et al., 2006; Silva et al., 2025; Gómez-Rios et al., 2026). However, the differences observed in classes 2 and 3 such as the presence of long rainfall tails in the morning and evening, suggest the influence of additional mechanisms. While solar heating remains a key driver, other factors such as external moisture sources, katabatic flows, and local climate drivers (e.g., topography, local winds and micro-climates) may play a role in these classes (Campozano et al., 2018; Ballari et al., 2020). For instance, Bendix et al. (2006), Bendix et al. (2009) and Trachte et al. (2010) found that the formation of nocturnal convective clouds is related to the interaction among katabatic flows, complex Andean topography and warm moist air from the Amazon. Furthermore, when katabatic flows interact with the complex topography of the tropical Andes, the resulting mechanism is strong enough to generate mesoscale convective complexes (Bendix et al., 2009). To show the diurnal pattern beyond ERE, Supplementary Figure S4 shows the diurnal distribution of the complete dataset (extreme and non-extreme) of hourly rainfall accumulation for the three rain gauges located in the study area (Figure 1). The complete rainfall dataset shows a clear peak concentrated between 12:00 and 19:00, with lower rainfall amounts during the morning hours. This aligns with our findings, confirming that this pattern remains applicable across the complete rainfall dataset and not only for ERE.

The classification of events into three classes reveals distinct physical behaviors related to seasonality, topography, and intensity.

Class 1: This class represents the most hazardous events in terms of instantaneous intensity (38 mm/5min) and rainfall accumulation. These events were highly cohesive (low WCSS) and spatially concentrated in the lower valleys and urban areas (confluence and outlet of the sub-catchments). These events occurred primarily in the period of October-December. The high local maxima rainfall values observed in class 1 suggest the presence of strong convective cells triggered by the solar heating cycle. These events are characterized as intense, and short-lived events, which are characteristics of convective events. In addition, the location of hotspots near the city of Cuenca (2,600 m a.s.l) might suggest the role of the urban heat island effect in these events. In summary, this class shows intense and cohesive valley events.

Class 2: This class dominates during February-April. While they have high total areas similar to class1, they are less cohesive (highest WCSS). This implies that class 2 events are likely associated with larger, more widespread events. While class 1 seems to be a result of pure convective cells, class 2 shows a morning rainfall tail and lower local maxima rainfall. This suggests a transition from convective mechanisms to complex interactions associated with local topography and external moisture sources. The morning and evening rainfall observed in this class is likely driven by the interaction between katabatic flows and moisture from the Amazon basin (Trachte et al., 2010). In summary, this class shows widespread and dispersed events.

Class 3: The main difference from the other classes is location. Class 3 hotspots are located in the headwaters at high elevations (>3,500 m a.s.l). These events show lower intensities and smaller total areas. In concordance with our results, Escobar-González et al. (2022) found that lower elevations were related to higher rainfall accumulation, while higher elevations were related to lower rainfall accumulation. The presence of hotspots at high elevations suggests an orographic mechanism, resulting in lower intensity compared with rainfall in the valley. While class 1 seems to be a result of pure convective cells, class 3 shows a morning rainfall tail and lower local maxima rainfall. This suggests a similar behavior to class 2 (complex interactions associated with local topography and external moisture sources).

Furthermore, the seasonality and the spatial distribution of the three classes align with the migration of the Intertropical Convergence Zone (ITCZ). The months with the highest number of ERE are March, October and November, which correspond to the bimodal regime in the study area. These months are related to the influence of humidity from the Amazon (October -November) and the migration of the ITCZ (February–April) (Garreaud and Wallace, 1997; Segura et al., 2019). The presence of the ITCZ and Amazon moisture promotes atmospheric conditions favorable for deep convection over the upper elevations of the equatorial Andes (Segura et al., 2019), explaining the presence of hotspots in the headwaters areas (class 3).

Urdiales-Flores et al. (2025) identified two dominant moisture source trajectories in the study area: the northern Amazon basin and the Andes mountains at elevations between 1,000–2000 m a.s.l., which could be related to the location of these hotspots. In addition, the authors (Urdiales-Flores et al., 2025) pointed out that the low-level jets (Orinoco and South American) seem to play a key role in the local precipitation. The location of the hotspots suggests a complex relationship between rainfall and elevation. Turini et al. (2021) and Iza-Wong et al. (2026) found that elevation plays a key role in rainfall estimation. For instance, the performance of rainfall models decreases in Ecuadorian regions above 3,500 m a.s.l. (Turini et al., 2021). Similarly, rainfall estimation accuracy declines in mountain areas in Ecuador above 2,400 m a.s.l. (Iza-Wong et al., 2026). However, evaluating this relationship especially in mountain areas of Ecuador presents limitations, including a sparse rain gauge network, different temporal and different spatial aggregation of rainfall (Turini et al., 2021). Therefore, future studies should investigate this relationship in more detail by including alternative methodologies such as elevation-based model (Malamos et al., 2025).

Although the current study is based on 67 ERE, these findings provide a better understanding of the behavior and variability of extreme rainfall in the tropical Andes. The 5min area, local maxima rainfall, WCSS, and hotspot identification underscore the spatial variability among the event classes. Class 1 events are highly cohesive and located in urban areas, highlighting the elevated risk of urban flash floods. In contrast, class 3 events are located at high elevations (hotspots above 3,500 m a.s.l), pointing to the necessity of expanding monitoring networks to capture these headwater events. Therefore, as monitoring networks improve and data availability increases, further statistical analyses (including statistical measures such as autocorrelation and cross-correlation) and long-term persistence evaluations will be worthwhile to perform. Additionally, while Vázquez-Patiño et al. (2020) explored the relationship between rainfall, wind and moisture at a larger scale (for the whole country Ecuador), our results open the door for further exploring these relationships at the local scale using reanalysis and satellite data.

This study analyzed intra-event rainfall characteristics such as area, cohesion, local maxima rainfall and location of hotspots for three classes of ERE in the tropical Andes using X-band weather radar data. It is one of the first efforts to study intra-event variability in the tropical Andes. The analysis of the rainfall characteristics revealed marked differences among the three classes of ERE, revealing different behaviors of the ERE in the tropical Andes. From this study, we derived the following conclusions:

ERE could be identified using rainfall and area thresholds. For the tropical Andes, a threshold of 25 dBZ and 6 km 2 in 5min can be used to delimit an extreme rainfall event.

Class 1 rainfall events are characterized by the largest areas at 5min resolution. Also, these events have a more cohesive rainfall core, suggesting that the core cell is more stable (i.e., moves less) than the in the other classes. This class shows the highest local maxima rainfall values, occurring mostly in the afternoon (12:00–19:00). Furthermore, the hotspots are located at lower elevations, in urban areas and near the outlets of sub-catchments. These events occurred principally in the last 3 months of the year (Oct–Dec).

Class 3 rainfall events are characterized by the smaller areas (5min area) than class 1. They also show a more cohesive core than class 2. Furthermore, the local maxima rainfall is lower than class 1, and these values are distributed throughout the day. The higher concentration of these occurs in the afternoon. The hotspots are located at elevations above 3,500 m a.s.l, in the headwaters. In addition, these events occur throughout the year.

Class 2 rainfall events are characterized by areas similar to class 3 and the least cohesive rainfall core. In addition, this class shows similar characteristics to both class 1 and class 3. The local maxima rainfall values are similar to those in class 3, and the location of the hotspots is similar to class 1. These events occur in the first 5 months of the year (Jan- May).

The identification of urban areas with highly cohesive events highlighting the elevated risk of urban flash floods. Consequently, the necessity of implement nowcasting algorithms for short-term prediction of extreme rainfall by including tracking (area, cohesion) and intensity (location of hotspots, local maxima rainfall) of ERE are essential for flood early warning systems. Additionally, while this study utilizes the k-means clustering established by Urgilés et al. (2024) to analyze spatio-temporal patterns, we suggest a comparative analysis using other classification methodologies (rainfall threshold, morphology, tracking and machine algorithms) (Sreekanth et al., 2019; Hirockawa et al., 2020; Pu et al., 2020) as a direction for further research to gain complementary insights into the characterization of ERE.

Our study highlights the importance of high spatio-temporal resolution data for capturing intra-event rainfall patterns. Specifically, the location of the hotspots suggests a complex relationship between rainfall and elevation, providing the basis for future research to use elevation-based models. Furthermore, the location of hotspots (above 3,500 m a.s.l, and within the city of Cuenca), shows the necessity of ground monitoring at these elevations. These locations are suggested as important areas for long-term monitoring to evaluate the strength of the long-term persistence in future studies. In addition, monitoring at high elevations will be useful as input for hydrological models, water resource management, risk assessment, and flood forecasting in mountain regions, making this study a baseline for developing localized nowcasting systems in the tropical Andes.

Finally, although this study employed a non-parametric method (percentile threshold) to define ERE due to limitations in the sample size, future research with extended time series should explore the application of parametric methods such as Generalized Extreme Value or Generalized Pareto distribution to evaluate their performance and the trade-offs in characterizing extreme rainfall in the complex topographic and climatic conditions of the tropical Andes.