Flash floods are hydrometeorological disasters that are increasingly common and have a major impact on people's lives. This study uses a systematic literature review to evaluate various methods for determining rainfall thresholds, including empirical, hydrological, and machine learning approaches, as part of a flash flood early warning system. This study uses systematic literature review to evaluate various methods for determining rainfall thresholds, including empirical and hydrological approaches. Empirical methods use historical data to find patterns of relationships between rainfall and flood events, while hydrological approaches take into account the physical characteristics of the watershed to model the hydrological response to rainfall. The results show that empirical methods, although easy to implement, often unable to adequately handle spatial and temporal variations in rainfall. In contrast, hydrological approaches provide better accuracy but require more detailed and comprehensive data. Machine learning offers a promising solution with its ability to analyze big data adaptively and in real-time, improving prediction accuracy. The integration of these three approaches can result in a more effective early warning system, especially in facing the challenges of climate change. This study concludes that the combination of traditional methods and advanced technologies can significantly reduce the impact of flash flood disasters.

  • The rainfall threshold-based approach serves as a globally applied early warning system for flash floods.

  • Empirical, hydrological, and machine learning methods are employed to determine rainfall thresholds for early flash flood warning.

  • Flash Flood Guidance System (FFGS) and hydrological modeling offer advancements in flash flood prediction.

Flash floods are a major problem in flood control and management of small river basins worldwide as they are considered one of the most hazardous types of floods due to their highly destructive nature, causing significant damage to infrastructure and socio-economic aspects, and threatening human lives and property in various regions of the world (Douben 2006; Anagnostou et al. 2010; Javelle et al. 2010; Modrick & Georgakakos 2015; Bezak et al. 2016; Miao et al. 2016; Nguyen et al. 2016; Dahri & Abida 2017; Zhai et al. 2018; Ahmadalipour & Moradkhani 2019; Das 2019; Wu et al. 2023). Globally, more than 5,000 people die due to flash floods every year. This number is four times higher than other types of floods (Jonkman 2005; Bui et al. 2019). Flash floods are flood events that have a rapid response that occur in water catchment areas of several hundred square kilometers or less with water levels in the drainage network reaching critical levels within minutes to hours (usually <6 h) after rainfall (Borga et al. 2007; Norbiato et al. 2008; Miao et al. 2016; Jalayer et al. 2018). This results in very short flood warning times, causing enormous socio-economic damage (Luong et al. 2021). Flash flood events tend to be exacerbated by natural and anthropogenic activities, such as heavy rainfall, steep topography, deforestation, land reclamation and excessive urbanization, and global climate change (Špitalar et al. 2014; Strauch et al. 2015; Pham et al. 2020). Flash floods are often associated with other natural hazards such as landslides, soil erosion, debris flows, and building collapse, which can increase the potential threat to human life and property (Miao et al. 2016).

Reducing the potential impacts of flash floods has become a priority for several national authorities responsible for risk management (Javelle et al. 2010). Therefore, the World Meteorological Organization emphasizes the need for flash flood forecasts that take into account the socio-economic impacts that may be caused by the event (WMO 2015). Unfortunately, flash flood forecasting is one of the most difficult tasks in operational hydrology (Norbiato et al. 2008). This is due to the short time available to produce flash flood forecasts and the small catchment areas also add to the difficulty of flash flood forecasting (Javelle et al. 2010; Miao et al. 2016).

Flash flood forecasting can be done using hydraulic models, but these models require large amounts of data and computational resources. This modeling must be run on each rainfall scenario to produce flash flood forecasts, a process that certainly takes a long time to provide warning information (Ke et al. 2020). To meet the needs of timeliness and effectiveness of warning information delivery, the rainfall threshold method is the most commonly used approach in flash flood forecasting (Jang 2015; Chu et al. 2022). Compared with rainfall observations or predictions, threshold rainfall can be used as an initial reference to initiate flood warnings before hydrological simulations are carried out so that areas that will experience flash floods can be directly predicted (Martina et al. 2009; Golian et al. 2010; Montesarchio et al. 2011; Yang et al. 2016; Tian et al. 2019). Several studies using rainfall thresholds in flash flood forecasting have been successfully carried out in several countries in the world (WMO 2022). The Flash Flood Guidance System (FFGS) developed by the US National Weather Service (NWS) produces flood-related discharge using estimates of rainfall depth (Young et al. 2021). This system produces a high probability of flood detection and warnings are issued based on different rainfall thresholds by considering soil moisture factors (Georgakakos 2006). Another rainfall threshold-based early warning system is the Meteo-alarm. Meteo-alarms are implemented in 30 countries in Europe and warnings are issued based on a comparison of rainfall and local thresholds (Young et al. 2021). In addition, there is the ‘FLOODsite’ project which uses rainfall thresholds as an alternative to conventional early warning systems (Borga et al. 2011) and has proven successful in identifying several flash floods across Europe (Alfieri & Thielen 2015).

The rainfall threshold is defined as the amount of rainfall required to reach the critical water depth at certain points. This point does not have to be located at a river crossing but can also be located at a place where rapid inundation occurs in lowlands or slow floodwater accumulation at river junctions (Jang 2015). Determining the cumulative rainfall threshold can apply various methods such as data-based analysis (Carpenter et al. 1999; Martina et al. 2006; Golian et al. 2010; Montesarchio et al. 2011) or a physical-based model that is usually needed to calculate the critical rainfall threshold over time (Norbiato et al. 2008; Montesarchio et al. 2015; Yang et al. 2016). However, on the one hand, physical models have shortcomings in short-term prediction capabilities, while flash flood predictions require a short lead time to provide timely warnings to residents (Zhang et al. 2018). On the other hand, data-based models have limitations in prediction accuracy (Fawcett & Stone 2010; Filho et al. 2021). In addition, watersheds that require flash flood forecasting generally do not have sufficient hydrological data for calibration, making it difficult to estimate rainfall thresholds (Miao et al. 2016; Yang et al. 2016). In addition, rainfall estimates for hydrological use require rainfall bias correction, which can be answered by machine learning (ML) (Ko et al. 2020). Recently, a number of researchers have used ML to improve the accuracy of rainfall threshold analysis (Zagorecki et al. 2013; Chang & Guo 2020; Park et al. 2020). There is a growing body of literature studying flood estimation using ML techniques, as this approach does not require any assumptions (Chang & Tsai 2016; Zhou et al. 2019; Chang et al. 2020; Kao et al. 2020; Chu et al. 2022). Mosavi et al. (2018) have made an important contribution in summarizing the use of ML for flood prediction in general. This study focuses on the use of ML to determine specific rainfall thresholds associated with flash floods, which has not been widely discussed in previous literature. Mosavi et al.'s review focuses more on various ML models applied to flood prediction and their performance comparison but does not specifically discuss aspects such as uncertainty in determining rainfall thresholds and the interrelationship of hydrological and meteorological variables in the context of flash flood early warning systems. Our review not only presents existing methods but also highlights the challenges and limitations of applying ML in determining rainfall thresholds in gauged and ungauged watersheds and provides recommendations to improve prediction performance by integrating new technologies and multi-source data.

Despite the extensive research, there are still some important gaps that need further investigation. One of the major gaps is the inability of existing thresholds to accurately reflect ongoing climate change, which significantly affects rainfall patterns. Most of the existing models are based on historical data and may not be flexible enough to accommodate future climate shifts. In addition, there is growing recognition of the need for integrating rainfall thresholds with modern early warning systems that utilize emerging technologies, such as ML and big data analytics. While traditional approaches to determining rainfall thresholds have proven effective, their limitations in accounting for the increasing variability in climate and rainfall patterns necessitate the use of more advanced techniques. Therefore, this study attempts to present a comprehensive overview of the research developments on rainfall thresholds for flash floods. The focus is on the methods used to determine rainfall thresholds, the effectiveness of various models, and how these thresholds are applied in the context of early warning. In addition, this study also aims to identify weaknesses that still exist in the current approach and propose a more effective and adaptive method. Thus, this study has the potential to make a significant contribution to the development of a more reliable and proactive early warning system capable of providing timely warnings and minimizing flash flood risks.

In conducting this literature review, a systematic approach was used that aims to identify, evaluate, and synthesize relevant research on rainfall thresholds for flash floods as a form of early warning. The systematic approach was chosen because it is able to provide a comprehensive and transparent analysis of developments in this field. The literature collection procedure was carried out through several structured stages. The procedure begins with determining keywords that are relevant to the topic being discussed, such as ‘rainfall threshold’, ‘flash flood’, ‘early warning’, and ‘flood prediction’. Furthermore, a literature search was conducted through trusted academic databases that are often used in scientific research, such as Google Scholar, Scopus, Web of Science, and IEEE Xplore. The search was conducted using predetermined keywords, with a greater focus on articles published in the past 10 years to ensure the relevance and topicality of the research results. The search results were then selected based on previously established inclusion and exclusion criteria. Inclusion criteria include literature that examines the methodological or applicative aspects of rainfall threshold in the context of flash floods and early warning, as well as research published in recognized journals. The exclusion criteria included irrelevant literature, such as studies that only discussed flooding without any relation to rainfall threshold.

Each selected article was evaluated for quality using the critical appraisal approach (Crombie 2022). This evaluation covers three main aspects: methodological validity, quality of data analysis, and relevance of findings. This process begins with determining methodological validity, where the articles being assessed must have clear and well-defined research objectives, and be relevant to the topic being discussed, for example, determining rainfall thresholds for flash floods. The research design is also evaluated to ensure that it is in accordance with the research question, including the use of appropriate statistical methods or hydrological models. In addition, sampling and data sources must be described in detail, and the authors evaluate the quality and representativeness of the data. Variables that may affect the results must be identified and controlled. Good methodology must also be reproducible by other researchers, so clearly described research procedures are essential.

Next, the quality of the data analysis is evaluated. The analysis methods used must be appropriate to the type of data and the research question. The depth of analysis is also important, where the article must consider factors that affect the results as well as uncertainty in the data. The use of analysis tools, such as statistical software or hydrological models, is also checked to see whether they are applied correctly. Interpretation of results must be supported by data and must not be overinterpreted. Finally, the relevance of the findings is the focus of the assessment. Articles must be relevant to the topic discussed and make significant contributions to the scientific literature. The findings produced must be generalizable or applicable in various regional contexts and have practical implications.

In this literature review, articles were categorized based on the main focus of the study, namely empirical, hydrological, and ML-based methods. In total, 55 studies were included, with 20 focusing on empirical methods, 25 on hydrological methods, and 10 on ML applications in flash flood prediction. These articles were selected after going through a selection process based on quality criteria. Articles that met the standards were then analyzed and synthesized. The synthesis process was carried out thematically to identify key trends, important findings, and areas that still need further research.

The empirical method is an approach that has been widely used to predict and warn of hydrological disasters such as floods, flash floods, and landslides (Filho 2021). Empirical method rainfall thresholds are relational values based on a statistical analysis of the relationship between rainfall and historical flood events (Campbell 1975; Caine 1980; Larsen & Simon 1993; Crozier 1999).

One of the key elements in this method is rainfall intensity, which is the amount of rainfall that falls in a given time period, usually measured in millimeters per hour (mm/h). In the context of flash floods, rainfall intensity is used to identify how fast rain falls and how much potential it has to trigger surface runoff that can cause flooding. In addition, rainfall duration, or the length of time that rain occurs, is an important variable in empirical analysis. This duration helps us understand how long rain can increase surface runoff and contribute to flash floods. Flash flood frequency is also a key factor in empirical analysis. This frequency refers to the number of flash flood events in an area over a given time period. By analyzing historical data, empirical methods can identify recurring rainfall patterns associated with flash flood events, which ultimately helps establish rainfall thresholds.

Rain gauges are the primary source of data in this method, providing daily or hourly measurements. While highly accurate in a given location, their limitations include limited spatial coverage, and may not reflect variations in rainfall over a wider area. Additionally, data from remote sensing satellites, such as tropical rainfall measuring mission (TRMM) and global precipitation measurement (GPM), are used to complement data from ground gauges. These satellites provide broader global coverage of rainfall, allowing analysis in hard-to-reach areas, although their resolution and accuracy can vary and require bias correction. Weather radars are also important in this method, as they are able to detect rainfall and its movement at high temporal resolution, mapping rainfall distribution during flash floods. While helpful in providing real-time data, radar measurements can be affected by factors such as topography and distance from the radar.

In general, empirical methods compare rainfall events with past flash flood events to determine rainfall thresholds (Crosta 1998). Georganta et al. (2022) divided empirical method rainfall thresholds into three categories, namely rainfall intensity–duration (I–D) thresholds, rainfall event–duration (E–D) thresholds, and rainfall event–intensity (E–I) thresholds. The I–D and E–D thresholds are the most commonly used approaches worldwide (Georganta et al. 2022). From the set of events, each flood and non-flood event is represented on a curve according to the selected categoryand then separated by a critical line determined by a power law equation (Caine 1980; Cannon et al. 2008). This line separates critical conditions, where rainfall is more likely to cause flooding, from non-critical conditions where rainfall is unlikely to cause flooding. The collected rainfall data were analyzed to obtain the necessary parameters. These parameters are then used to establish catchment-specific thresholds (Bezak et al. 2016).

The rainfall threshold obtained from this analysis is then used as a reference for issuing early warnings. The early warning system monitors rainfall in real time using rain gauges, weather radars, and satellites. The data collected in real time is then compared to the established empirical threshold. When the monitored rainfall data exceeds the empirical threshold, the early warning system will identify an increased risk of flash floods. In other words, the empirical threshold functions as a risk indicator. If the rainfall exceeds the established threshold, the system can automatically issue an early warning. Typically, this method is used for short-term predictions, which is especially important in the context of flash flood early warning (Filho et al. 2021; Deng et al. 2022). Thus, this method allows local governments to issue timely warnings based on relevant historical data.

Empirical methods provide quite effective results in providing early warning of flash floods, especially in areas with adequate historical data (Filho et al. 2021). By utilizing rainfall data from radar and satellites, this method is able to capture spatial and temporal variations in rainfall, thereby increasing prediction accuracy, especially in areas with limited rainfall measuring instruments. The flexibility of empirical methods allows their application to various catchments with long historical rainfall and river flow data, not only urban areas, making them versatile for different geographic locations and types of catchments (Dao et al. 2020; Mentzafou et al. 2023; Gambini et al. 2024). However, empirical methods are highly dependent on quality historical data, limiting their application in areas with limited data. In addition, empirical methods are also relatively simple and efficient, as they do not require complex hydrological models and extensive geospatial data. This can reduce the operational costs involved in determining rainfall thresholds.

At the local scale, empirical methods have great potential in providing effective early warning. Rainfall thresholds set based on empirical analysis are very specific to the characteristics of a particular area, such as topography and soil conditions. This makes empirical methods very suitable for areas with relatively uniform environmental conditions. When applied at a wider scale, such as regional or national, empirical methods face challenges related to the heterogeneity of environmental conditions. To overcome this, it is necessary to segment the area and adjust the rainfall threshold for each zone or region based on local characteristics. In addition, it can also be combined with other methods, such as hydrological models or ML.

Although widely used in predicting hydrological disaster events, empirical methods have several limitations that need to be considered. The accuracy of the results of empirical method analysis is highly dependent on the quality and quantity of data used. Uneven distribution of rainfall gauges, inaccurate observation data or lack of historical data can limit the reliability of the resulting thresholds. In addition, the temporal variability of rainfall and the assumption of spatial homogeneity of rainfall are also important factors to consider (Guzzetti et al. 2008; Bordoni et al. 2019). Empirical methods often assume that the average rainfall in an area represents the entire area. However, this assumption may not be valid, especially for large catchments with diverse land uses and topographic features. Therefore, empirical methods will provide more effective early warning at a local scale than at a wider regional or national scale. To overcome this, it is necessary to segment the area and adjust the rainfall threshold for each zone or region based on local characteristics. In addition, it can also be combined with other methods such as hydrological models or ML.

Empirical methods are more statistical in nature and pay less attention to the complex physical processes that govern the relationship between rainfall and runoff. Factors such as previous soil moisture conditions, land use, topography, and soil type have significant effects on the hydrological response of an area but are often ignored in empirical analyses (Miao et al. 2016). As a result, these methods may not have the ability to accurately predict disaster events under complex conditions. In some cases, such as flash floods, the performance of empirical methods is less than optimal because historical data may not include rare extreme events (Filho et al. 2021). In addition, the static nature of empirical thresholds makes them less able to accommodate climate change and spatial variability of rainfall (Bordoni et al. 2019; Filho et al. 2021; Deng et al. 2022). Thus, thresholds generated by empirical methods tend to be location-specific and difficult to generalize to other areas with different characteristics. This requires new data collection and analysis if the method is to be applied in different locations.

To ensure the reliability of the generated threshold, validation needs to be carried out by comparing the prediction results with disaster events from different time periods (Dao et al. 2020). Good validation will increase confidence in the early warning system built based on empirical methods. There are several efforts that can be made to improve the performance of empirical methods. Improving the quality and quantity of data used will increase the accuracy of the model. Integration of historical data related to flash flood events and rainfall data with spatial data such as elevation, land use, and soil type can provide more detailed information about the hydrological conditions of an area. In practical applications, spatial data can map zones that are highly vulnerable to flash floods. An example of a study that applies this spatial data can be found in the FLOODsite project in Europe, which combines rainfall data with spatial data to estimate flash flood risk and develop an early warning system (Alfieri & Thielen 2015).

The development of more adaptive empirical methods, which refers to the ability of empirical methods to adjust to changes in meteorological and hydrological conditions in a particular area, can be done by integrating local meteorological variability with long-term observational data from various regions. This can be achieved by using advanced technologies such as ML and big data, which are able to analyze and predict rainfall patterns more accurately. The use of numerical weather prediction that uses physical principles and atmospheric observation data such as pressure and temperature for weather forecasting can be considered to provide more accurate and adaptive weather forecasts.

Closer international collaboration is also needed to collect weather and flash flood disaster data from various countries, thereby expanding data coverage and improving the reliability of predictive models. Various efforts have been made to do this, such as the International Disaster Database, the Global Landslide Catalog, and the Space-based Weather and Climate Extremes Monitoring. This international collaboration plays a role in increasing the coverage and resolution of data used in empirical methods so that rainfall thresholds can be more accurate and adjusted to local and global conditions. In addition, it can accelerate the development of early warning systems with various technologies and resources for data analysis, enabling more responsive, adaptive, and reliable prediction systems, especially in facing the challenges of climate change and extreme weather in the future.

Validation of empirical methods across different geographic and climatic conditions should also be a priority, with case studies covering regions with different geological and meteorological characteristics. Furthermore, climate change leading to increased frequency and intensity of extreme events further underscores the importance of developing more robust methods that can accommodate high uncertainties (IPCC 2023). By integrating these approaches, the limitations of previous studies can be overcome and empirical methods can be developed to be more comprehensive and accurate in determining rainfall thresholds, which will ultimately improve the effectiveness of natural disaster mitigation.

One approach that is widely used to determine this threshold is through a hydrological model. Hydrological models allow simulation of the response of a watershed to various rainfall conditions and soil moisture status so that it can estimate the magnitude of flow and the potential for flash floods. In this context, the selection of the right hydrological model is very important, especially in watersheds that have complete hydrological, meteorological, and geographic information data. This model considers antecedent soil conditions and rainfall patterns that occur in the study area. Soil moisture has a significant influence because, during periods of low-intensity and long-duration rainfall, the soil tends to become saturated. With increasingly saturated soil conditions, surface runoff and peak flows will increase, potentially causing flash floods. In addition, the sensitivity of rainfall thresholds to antecedent soil conditions tends to decrease as the duration of rainfall increases, while the temporal pattern of rainfall becomes increasingly sensitive to the threshold.

Shorter time-scale rainfall thresholds refer to thresholds that are determined to predict and warn of flash floods in a short time duration, usually in the range of minutes to hours. This shorter time-scale is important because flash floods tend to occur immediately after high-intensity rainfall, especially in watersheds with a rapid response to surface runoff. Therefore, these thresholds are designed to be sensitive to short-term rainfall events that can quickly cause flash floods (Miao et al. 2016; Zhai et al. 2018). Shorter time-scale rainfall thresholds are more suitable for flood early warning, especially in small mountain watersheds in humid regions, because the uncertainty of rainfall thresholds increases sharply with time scales for different rainfall patterns (Nikolopoulos et al. 2011; Miao et al. 2016). This is consistent with several studies that the application of hydrological models produces better performance in humid watersheds than in dry watersheds. However, we must be careful in estimating and updating the initial soil saturation in humid regions, either by running hydrological models or through field observations.

Caution is needed because antecedent soil conditions directly affect how much runoff is generated during a rainfall event. Inaccurate estimates of antecedent soil saturation can lead to erroneous flood predictions, such as overestimating or underestimating the potential for flash flooding. Specific concerns in estimating antecedent soil saturation include spatial and temporal variability of soil moisture, data uncertainty, the effect of soil moisture on runoff, and handling of extreme conditions. Soil moisture varies significantly within the same watershed and changes over time, depending on factors such as rainfall patterns, temperature, and land use. If hydrologic models do not account for this variability, their results can be less accurate (Blöschl 2005; Ntelekos et al. 2006). In addition, soil moisture data obtained through field observations or hydrologic models often have limited spatial and temporal coverage, which increases uncertainty in estimating antecedent soil conditions. Inaccurate estimates of soil saturation can lead to errors in predicting the timing of runoff and the magnitude of peak flows.

The negative impact of soil moisture conditions in determining rainfall thresholds using hydrological models lies in the inaccuracy of the resulting runoff estimates. High soil moisture conditions, if not measured properly, can cause hydrological models to predict greater runoff than actually occurs, resulting in excessive early warnings. Conversely, if soil moisture is considered too low, the model may fail to detect the potential for actual runoff, thus underestimating the risk of flash floods. Previous studies have shown that inappropriate soil moisture conditions can cause significant errors in peak flow and rainfall threshold estimates (Nikolopoulos et al. 2011; Miao et al. 2016). Therefore, it is important to handle and update soil moisture estimates carefully to ensure better flood prediction accuracy.

One step that can be taken to overcome these challenges is adequate data collection, such as field observations, soil moisture sensors, or satellite data to obtain a representative picture of soil moisture conditions. In addition, hydrological model calibration must be carried out properly using historical soil moisture and river flow data to ensure that the model can capture the relationship between soil moisture, rainfall, and runoff correctly. Real-time soil condition updates through monitoring systems are also important to improve prediction accuracy (Luong et al. 2021). Conducting sensitivity analysis on soil moisture parameters in hydrological models can help understand the extent to which small changes in initial soil saturation estimates affect flash flood predictions. Thus, hydrological models can produce better estimates of flash flood potential, making early warning more accurate and effective.

Probability of detection evaluations show that rainfall thresholds determined through hydrological simulations generally perform quite well, especially for radar-based models (Filho et al. 2021). However, it is important to note that the use of radar data often results in a higher false alarm rate compared to other methods. This indicates the need for improvements in the calibration of hydrological models, especially in determining parameters relevant to rainfall–runoff models. Uncertainties in model calibration are caused by the complexity of hydrological processes involving multiple variables and interactions that influence each other, as well as the limited data available (Blöschl 2005; Ntelekos et al. 2006).

Hydrological models require a variety of physical and meteorological parameters to accurately determine rainfall thresholds. These parameters include physical characteristics of the watershed such as slope, soil type, and soil retention capacity, as well as rainfall conditions such as rainfall intensity and duration (Miao et al. 2016). Initial parameters such as soil moisture and initial watershed conditions also affect model accuracy. Variations in the selection of parameter combinations can produce significant differences in peak discharge simulations, which impact the accuracy of rainfall threshold determination (Nikolopoulos et al. 2011).

To overcome the limitations of radar data and improve the accuracy of rainfall estimates, integration with other rainfall data sources, such as satellite data and rainfall station data, can be done. Satellite data, such as TRMM and GPM, offer wide spatial coverage but with lower temporal resolution compared to radar data. In contrast, rainfall station data provides accurate rainfall measurements at the measurement point, although their coverage is often limited and uneven (Filho et al. 2021). The use of a combination of data from various sources can help reduce uncertainty in rainfall estimates and improve the performance of hydrological models in predicting flood events.

Another challenge in predicting flash flood events is the lack of hydrological data in the watersheds that really need such predictions. Many flood-prone watersheds are inadequately quantified and, as a result, lack sufficient hydrological data for accurate model calibration (Miao et al. 2016). When hydrological models are applied to ungauged basins, model parameters and soil moisture status are usually taken from other basins with more complete data. This approach can lead to a significant decrease in the performance of the prediction system.

One major problem is the poor estimation of the temporal variability of soil moisture, which can be significantly increased when soil moisture data are unavailable or inaccurate. Without sufficient information on the previous soil moisture status, flood predictions become unstable and can be misleading (Blöschl 2005; Ntelekos et al. 2006). In addition, geomorphological factors such as the impact of lakes and karst in the study area can be difficult to accurately describe with standard hydrological models. This phenomenon can lead to bias in simulations, reduce model accuracy, and affect the critical success index in predicting flood events (Miao et al. 2016).

Since historical data are often limited or unavailable in ungauged areas, calibrating model parameters is a major challenge. Limited historical data leads to uncertainties in model parameters, which in turn affect the model's ability to accurately represent hydrological dynamics. To address this issue approaches such as collecting additional field data, using satellite data, and integrating with data from watersheds with similar characteristics can help improve model accuracy. These approaches are essential to reduce simulation bias and improve the reliability of flash flood prediction systems in under gathered areas.

ML has been widely used in hydrology, especially to improve flash flood prediction by processing large and complex data. Unlike traditional methods that rely on physical or empirical models, ML techniques are able to learn patterns from historical rainfall and flash flood data to determine rainfall thresholds more accurately and adaptively. One of the advantages of ML is its ability to combine multiple data sources, such as rainfall, soil moisture, topography, and satellite data, making flash flood predictions more effective.

Recent studies have shown that methods such as random forest, support vector machines (SVMs), and neural networks can identify nonlinear relationships between rainfall and hydrological responses in catchments. Chang & Tsai (2016) and Ke et al. (2020) showed that ML can estimate rainfall thresholds based on historical data, resulting in more accurate and relevant predictions. In addition, ensemble methods can overcome data limitations in areas with minimal hydrological measurements, allowing early warning systems to work more effectively even though field data limitations remain.

Recently, several studies have applied ML to improve the accuracy of rainfall threshold analysis. For example, Chang & Guo (2020) used a random forest model to identify rainfall thresholds in urban areas, while Park et al. (2020) used the SVM technique to combine rainfall data from multiple sources. Zagorecki et al. (2013) also applied artificial neural networks (ANNs) in analyzing historical rainfall data, finding that this method is better able to accommodate temporally varying rainfall patterns. This approach emphasizes the importance of combining data from multiple sources to improve prediction accuracy.

In addition, a growing body of literature examines the relationship between rainfall and runoff, the impact of rainfall damage, and flood estimation using ML and deep learning instead of conventional hydrological models. Chang & Tsai (2016) developed a deep learning model to predict peak flows based on multi-resolution rainfall data, which allows for more accurate identification of rainfall thresholds. Kao et al. (2020) found that the use of multi-resolution rainfall intensity data processed through ML helps reduce uncertainty in flood prediction, especially in ungauged coastal areas. This is especially important because coastal areas often face more complex hydrological measurement challenges (Chu et al. 2022).

ML has the ability to determine rainfall thresholds based on rainfall characteristics and historical data, without the need to understand the underlying physical processes (Mosavi et al. 2018; Ke et al. 2020). This approach is particularly useful in areas lacking direct measurement data, such as ungauged watersheds, where traditional hydrological models struggle to produce accurate predictions. Ke et al. (2020) used an ensemble method to address data scarcity by combining multi-resolution rainfall intensities and improving flood threshold prediction results. Similarly, Sitokonstantinou et al. (2018) applied a technique of combining rainfall data from multiple sources with different temporal resolutions to improve the accuracy of their prediction model.

Although ML models have shown better performance than empirical methods in some cases, there are some limitations that need to be considered. ML is a method that is highly dependent on the quality and quantity of data (Liu et al. 2017; Mosavi et al. 2018), so the availability of sufficient data is a major determinant of the success of these models. Quantitative validation using real flood events is needed to provide more meaningful and accurate results. Chu et al. (2022) emphasized that despite the uncertainties in the ML model, this method can provide a solid basis for setting rainfall thresholds, which can be used in flood early warning and emergency response systems. Rainfall threshold prediction using ML can be applied sustainably if it can provide accurate information on the impact of damage due to previous rainfall. This will help stakeholders make better decisions in flash flood disaster control and risk mitigation (Chu et al. 2022).

Several ML methods have been effectively applied to determine rainfall thresholds in the context of flash flood early warning. ANNs, for example, has been shown to be able to model complex nonlinear patterns between rainfall, watershed characteristics, and flash flood events. With its ability to capture relationships that are difficult to predict by conventional models, ANN is used to identify rainfall thresholds that can trigger floods (Ke et al. 2020). Random forest, which is a development of the decision tree algorithm, is used to improve the accuracy of rainfall threshold prediction by combining several decision trees. This is very helpful in identifying important variables such as rainfall intensity and soil saturation levels that contribute to flood events (Kan et al. 2020).

In addition, SVM is often applied because of its ability to generalize limited data and prevent overfitting problems, which are often encountered in determining rainfall thresholds in areas with limited measurement data. Gradient boosting machines (GBMs) are also used to handle data with high dimensions and significant complexity, such as multi-resolution rainfall, which allows for more accurate and responsive rainfall threshold determination to climate change (Liu et al. 2018).

The selection of the right algorithm depends on the characteristics of the data and the specific purpose of the study. For example, for areas with complex feature interactions such as a combination of rainfall intensity and topographic changes, GBM or ANN may provide better results in determining rainfall thresholds. Conversely, if model interpretability is more important, such as to communicate results to stakeholders in disaster management, random forest or decision trees may be more suitable choices because of their ability to provide a more transparent explanation of the factors that trigger flooding (Ko et al. 2020).

Validation of rainfall thresholds generated from ML models is a crucial step to ensure the reliability of flash flood early warning systems. This validation should be done by comparing model predictions with real flash flood data and past rainfall events. This not only ensures that the generated thresholds are reliable but also allows for better adjustment to local conditions, such as spatial and temporal variability of rainfall and specific hydrological characteristics of the watershed (Ke et al. 2020). In this context, the use of multi-source data such as rainfall stations, radar, and satellite data, as well as model testing at different temporal resolutions, can improve prediction accuracy and reduce uncertainty (Chu et al. 2022).

In line with the objectives of this study, which emphasize the importance of developing more adaptive and effective rainfall threshold determination methods, ML-based approaches offer great potential. However, to ensure the sustainable implementation of these methods in early warning systems, it is important to conduct quantitative validation using verified flash flood event data. In addition, the development of flexible models that are able to adapt to changing weather patterns due to climate change should continue to be a major focus of this study. The results of this validation will help create a more responsive early warning system and be able to provide more accurate information to stakeholders in disaster risk mitigation decision-making.

The integration of empirical and hydrological methods, coupled with the use of ML, offers great potential to improve early warning systems for flash floods. ML enables faster and more accurate analysis of complex and diverse data, such as rainfall, soil moisture, and topographic characteristics. With the ability to process large amounts of data and identify patterns that may not be visible with traditional methods, ML can significantly improve the accuracy of flash flood predictions. In addition, ML can also adjust predictions based on changing conditions, including weather variability and the impacts of climate change.

A key advantage of this technology is its ability to adapt to real-time data, allowing for rapid updates to warnings as conditions on the ground change. This is a significant improvement over conventional methods that often rely on rigid historical models. With stronger integration of ML technologies, early warning systems will be more responsive, predictive, and proactive in responding to flash flood threats, ultimately reducing the impact of disasters and saving more lives.

Accurate determination of rainfall threshold is a key element in developing an effective flash flood early warning system. Based on the literature review conducted, there are three main approaches that can be used, namely empirical, hydrological, and ML methods, each of which has advantages and limitations. Empirical methods are widely used because of their simplicity and efficiency in identifying rainfall patterns based on historical data. Although this method is quite effective in areas with adequate data, this approach tends to be less accurate in handling spatial and temporal variability of rainfall and does not take into account more complex physical factors. The hydrological approach, on the other hand, offers higher accuracy by considering the specific hydrological conditions of a watershed. This method can predict the response of a watershed to rainfall in more detail but requires more comprehensive data and is difficult to apply in areas with limited data.

ML opens up new opportunities to improve the accuracy of rainfall threshold predictions. With the ability to analyze complex and varied data, this technology is able to provide more adaptive and real-time predictions. This technology enables faster and more accurate data analysis through processing large and diverse data, including rainfall, soil moisture, and topography data. One of the main advantages of ML is its ability to adjust predictions in real time, allowing warning systems to respond dynamically to changing weather conditions. ML also allows systems to identify complex nonlinear patterns, which are difficult to capture by traditional methods. With the ability to process data continuously and provide more timely predictions, this technology is considered a significant advancement in improving the reliability of flash flood early warning systems.

The integration of these three approaches, coupled with the use of historical and real-time data, can produce a more effective flash flood early warning system. This more adaptive and integrated approach is also able to face the challenges of climate change and increasingly dynamic weather variability. Thus, efforts to develop an early warning system that combines various advanced methods and technologies will be able to significantly reduce the risk and impact of flash flood disasters.

The authors would like to thank Direktorat Jenderal Pendidikan Tinggi, Kementrian Pendidikan dan Kebudayaan as a funder of this study, and Jember University for the support of this study.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

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