Effect of mountainous rainfall on uncertainty in flood model parameter estimation

Flooding is one of the most common natural disasters on Earth, and flooding events caused by extreme rainfall are increasing worldwide today, anticipated to occur more frequently as a consequence of the changing climate (Mie Sein et al. 2021; Hailemariam & Alfredsen 2023; Kirsta & Troshkova 2023). The Korean Peninsula has recently experienced frequent occurrences of heavy rainfall and extreme weather conditions close to super typhoons, resulting in significant damages (Lee & Choi 2018). Numerous studies on flood risk prediction indicate an increasing likelihood of future flooding events, with climate change scenarios suggesting a potential rise in both the frequency and magnitude of flood events in many regions (Kundzewicz et al. 2019; Klijn et al. 2022).

Rainfall is one of the most critical factors influencing flooding. The amount and patterns of rainfall can vary significantly from one region to another, influenced by geographical, climatic, and topographical factors (Houze 2012; Furcolo et al. 2016). Rainfall plays a crucial role as an input for hydrological modeling. However, its distribution across the watershed is often non-uniform, resulting in significant uncertainties in estimated model parameters when the detailed spatial variation of input rainfall is not considered (Obled et al. 1994; Zhang & Han 2017). Consequently, the spatial characteristics of rainfall directly affect the results of local flood simulations, determining the scale and impacts of flood damages (Singh 1997; Arnaud et al. 2002; Gabellani et al. 2007; Younger et al. 2009; Emmanuel et al. 2015). One of the main sources of rainfall increase in mountainous watersheds is the orographic effect, also known as the mountain effect, resulting from atmospheric uplift by hills and mountains (Barry 1992; Abbate et al. 2022; Auliagisni et al. 2022). The interaction between atmospheric circulation and relief results, among other effects, in increasing rainfall with elevation (Lloyd 2005; Tobin et al. 2011; Gottardi et al. 2012). Consequently, rainfall in mountainous regions may not be adequately captured by conventional raingauge networks due to the topographical characteristics, which may negatively affect the accuracy of flood estimation. The accurate estimation of the spatial distribution of rainfall requires a very dense network of instruments, which entails large installation and operational costs (Goovaerts 2000). As a result, rainfall estimation in mountainous regions, particularly in ungauged areas and high elevation catchments, remains a true challenge for hydrological modeling (Piman & Babel 2013; Skaugen et al. 2015; Hussain et al. 2018). This challenge is mainly due to the high spatial variability and scarcity of observations in those areas (Krajewski et al. 2000; Gottardi et al. 2012; Stoffel et al. 2016; Ragettli et al. 2021).

In cases where the density of raingauge networks is too low to provide sufficient data, estimations are often generated based on data recorded at nearby gauges. However, in such cases, significant discrepancies can arise (Xiaojun et al. 2021). For instance, in the Namgang Dam area in Korea, there has been a recorded rainfall–runoff ratio exceeding 1 (Lee et al. 2023). Similarly, in Zhouqu, China, a raingauge located 16 km from headwaters recorded 96 mm of rainfall, while only 3 mm was recorded at the outlet raingauge (Hu et al. 2010; Cui et al. 2013). Xiaojun et al. (2021) analyzed the empirical relationship between rainfall and both the elevation and the density of rain gauges based on 52 storm events that occurred in mountainous watersheds. Their study demonstrated that estimating rainfall distribution at high elevations is more challenging, and they analyzed the uncertainty caused by raingauge selection in hydrological hazards forecasting. According to the error analysis, uncertainties increased when the horizontal distance between gauges exceeded 3 km. Such results exemplify the scale of the variation and uncertainty associated with rainfall in mountainous watersheds.

Therefore, recent studies on estimating rainfall in mountainous watersheds, referred to as mountainous rainfall, or flood estimation have been continuously conducted using radar or satellite rainfall data. Gebregiorgis & Hossain (2012) demonstrated that the uncertainty of satellite rainfall data depends more on the topography than on the regional climate. Moreno et al. (2014) aimed to simulate flow rates based on radar rainfall and address the uncertainties associated with rainfall estimation from radar data. Nikolopoulos et al. (2014) sought to define the impact of uncertainties related to mountainous rainfall estimation based on ground raingauge and predict the occurrence probability of debris flows. Adib et al. (2019) performed uncertainty and sensitivity analysis to find the optimal rainfall–runoff model for flood estimation in mountainous watersheds. Saouabe et al. (2020) evaluated the accuracy of satellite rainfall data and its suitability for hydrological modeling in mountainous watersheds, confirming its applicability in ungauged or data-scarce regions. However, these studies mainly focus on the suitability assessment, uncertainties of mountainous rainfall or flood volume, and research regarding the uncertainty of flood estimation associated with mountainous rainfall remains limited.

In this study, we examine the effect of the estimated spatial rainfall field on the uncertainty of flood estimation by comparing two methods: the WREPN (WRF Rainfall-Elevation Parameterized Nowcasting) model and the IDW (Inverse Distance Weighting) method. The WREPN model is developed to estimate the real-time spatial rainfall field considering the mountain effect based on ground raingauge data, while the IDW method is widely used in practice.

The selection of target storm events in the Namgang Dam watershed was carried out by analyzing the time series data from the ground raingauge. To separate the storm events, the Inter-Event Time Definition (IETD) method (Kim & Han 2010; Joo et al. 2013) was applied with a threshold of 12 h. This approach led to the identification of 24 individual storm events characterized by high rainfall depth. Subsequent analyses were then performed for these 24 events, as summarized in Table 1.

The spatial rainfall fields for the target storm events were estimated using two methods: the WREPN model (Lee et al. 2023) and the IDW technique. Both rainfall fields have a spatial resolution of 3 km. The WREPN model is a parameterized model that takes into account the mountain effect on rainfall estimation. It incorporates the Weather Research and Forecasting (WRF) model, which is a regional-scale climate model, to establish the relationship between hourly rainfall and elevation at a regional scale. By utilizing the hourly rainfall data from the ground raingauge network, the WREPN model can provide real-time spatial rainfall field estimates. For a more comprehensive understanding, please refer to the study by Lee et al. (2023).

In the ModClark model, the accumulated excess rainfall from each grid cell is routed through a linear reservoir. The model's parameters consist of three elements: the curve number (CN) for effective rainfall estimation, the time of concentration (t_c), and the storage coefficient (K). As the antecedent soil moisture conditions vary for each heavy rainfall event, the CN values are estimated separately for each storm event.

The ModClark model's ability to incorporate spatially distributed rainfall input makes it suitable for analyzing flood events in different geographical areas, providing a valuable tool for flood estimation in mountainous regions where rainfall distribution can be highly variable.

In the equations mentioned above, represents the linear correlation coefficient between the observed and simulated values, represents the ratio of the standard deviation of the simulated values to the standard deviation of the observed values, and represents the ratio of the mean of the simulated values to the mean of the observed values. For all three metrics, R², NSE, and KGE, values closer to 1 indicate better model performance, meaning that the model's simulated results are closer to the observed values.

In this study, the stream network of the watershed was established by upscaling the digital elevation model with a spatial resolution of 90 m to match the spatial rainfall field with a spatial resolution of 3 km. To achieve this implementation, the D-8 algorithm proposed by O'Callaghan & Mark (1984) was applied.

In this context, A_t represents the contributing area at time t, which is the area that contributes to the flow at a specific time in the watershed. A refers to the total watershed area, which is the entire area of the watershed under consideration.

In this context, CN_o,i represents the initial CN value for cell i. The correction factor f_CN is considered to be a single value applied uniformly across the entire watershed

The Metropolis–Hastings (hereafter MH) algorithm (Hastings 1970) was employed as the sampling algorithm to extract samples from the posterior distribution. The MH algorithm, as a general form of Markov Chain Monte Carlo (MCMC), is an attractive choice for generating samples from the posterior distribution and has proven successful in numerous cases (Wu et al. 2019; Liu et al. 2021).

Table 2 presents the results of the four performance evaluation metrics for the ModClark model. Both the WREPN and IDW spatial rainfall fields show excellent performance, with an average R² of 0.90, NSE of 0.88, and KGE of 0.83. Based on these results, it can be concluded that the ModClark model performs well, and no significant issues were identified regarding the estimation methods for spatial rainfall fields. Overall, the model successfully reproduces the flood timeseries, indicating its robustness and accuracy.

The observed streamflow used for parameter estimation was obtained after baseflow separation from the inflow data of the Namgang Dam. Baseflow separation was conducted using a graphical method. Although various methods for baseflow separation exist, it was found that the choice of method had minimal effect on parameter estimation and overall results. Therefore, the details of the baseflow separation method were excluded.

The estimated parameters for each target storm event using different spatial rainfall estimation methods are shown in Table 3. It can be observed that all three parameters vary for each storm event. Comparing with the IDW spatial rainfall, the WREPN spatial rainfall consistently resulted in lower values of f_CN. For the 12th storm event, the highest CN value was estimated, which is attributed to the influence based on the antecedent 5-day rainfall that resulted in 224.65 mm (refer to Table 1 for details).

The concentration time (t_c) was consistently estimated to be an average of 14.75 h for both spatial rainfall estimation methods. However, there were two storm events (Nos 11, 19) with t_c values exceeding 20 h. This can be attributed to the relatively dry antecedent conditions of the watershed, where the antecedent 5-day rainfall for events 11 and 19 was only 0.99 and 0.17 mm, respectively.

Regarding the storage constant (K), there was no significant difference between WREPN (average 7.15) and IDW (average 7.21). However, the ninth storm event had the highest K value, estimated at 10.6. The considerable variation in these three parameters for different storm events is likely influenced by the antecedent rainfall conditions and other factors affecting the watershed's state during each event.

Table 4 presents the coefficient of variation (CV) for the parameters based on different spatial rainfall estimation methods. Among the three parameters, f_CN exhibited a noticeably lower mean CV when estimated using the WREPN spatial rainfall. However, for t_c and K, there were no significant differences in the CV between the two methods. This can be attributed to the fact that WREPN's rainfall data effectively captures the mountainous rainfall effect, leading to reduced uncertainty in the most rainfall-sensitive parameter, f_CN. Particularly, significant differences in the CV were observed for rainfall events 1 and 6. However, no strong association between antecedent rainfall amounts or rainfall amount of storm events and the CV was evident for other cases.

The performance evaluation of the ModClark model has shown favorable results overall, but some limitations have been observed in Table 2. In the case of PBIAS, the WREPN spatial rainfall field shows an average of −8.18%, and the IDW spatial rainfall field shows an average of −7.93%, indicating that the flood discharge was generally overestimated. Additionally, upon examining Figure S1 (supplementary material), it can be observed that some peak flows were underestimated in certain rainfall events. Nevertheless, considering the main objective of this study, which is to investigate the uncertainty in flood discharge estimation based on different spatial rainfall field estimation methods, it is deemed feasible to proceed with the analysis. More detailed results for each rainfall event and the corresponding simulated time series can be visualized and further assessed in Figure S1.

In Figure S1, we see particular underestimation in certain peak flows, especially the first peak. These limitations could be attributed to various factors.

Firstly, one of the limitations could be related to the application of the NRCS-CN method used to calculate the runoff from rainfall. As it was originally developed to estimate daily runoff, errors may arise when applied at an hourly or sub-hourly time resolution (Verma et al. 2017). Previous studies have highlighted significant uncertainties when applying the NRCS-CN method in complex forested areas with various soil, land cover, and terrain conditions (Tedela et al. 2012). In this study, the initial CN values were determined based on the CN-II condition, and the correction factor f_CN was estimated as a parameter, resulting in the final CN values. However, the process of determining the initial CN values did not consider factors such as antecedent soil moisture, vegetation effects, and terrain, leading to inherent uncertainties.

Secondly, the use of 3 km grid cells to construct the spatial rainfall field could lead to limitations. Local extreme rainfall events might not be captured by the gauge stations, or if captured, the process of estimating spatial average values during interpolation could lead to smoothing, potentially resulting in underestimation or overestimation of the input rainfall. According to Sangati & Borga (2009), an important error source related to spatial rainfall aggregation is the rainfall volume error caused by incorrectly smoothing the rainfall volume either inside or outside of the watershed. Previous studies have shown significant improvement in simulated streamflow dynamics and accuracy when using higher resolution (1 km) spatial rainfall fields (Lobligeois et al. 2014). Especially in mountainous regions with high rainfall variability and low observation density, uncertainties are likely to be significant. Rainfall events 22 and 23 were particularly underestimated at the peak, and there is a possibility that the problem caused by the low resolution was intensified as the rainfall duration was short.

To address these issues, improvements in the spatial rainfall estimation method by incorporating high-resolution radar rainfall or weather model outputs could be considered. However, the high computational cost remains a challenge for flood forecasting applications.

In this study, we aimed to estimate floods using the WREPN model, which was developed to realistically estimate rainfall in mountainous areas that are difficult to capture with ground raingauge networks. We compared the flood estimations using the WREPN-based spatial rainfall field with the commonly used IDW-based spatial rainfall field to examine the effect of spatial rainfall estimation on the uncertainty of flood model parameter estimation. For the hydrological analysis of the spatial rainfall fields, we utilized the ModClark model, which operates on a grid-based approach and demonstrated its capability to accurately reproduce observed flood discharge through performance evaluation. To assess the uncertainty in flood model parameter estimations, we employed Bayesian techniques for parameter estimation in the ModClark model. The results showed that using the WREPN spatial rainfall field reduced the uncertainty in the f_CN parameter estimation for flood estimation.

Indeed, while the WREPN spatial rainfall estimation method, which considers the mountain effect in general rainfall events, showed relatively robust results, it might not be dramatically superior. However, it significantly reduced uncertainty in extreme rainfall events with observation peak rainfall exceeding 500 mm, emphasizing the importance of rainfall data in hydrological modeling. To achieve better results, further studies should explore various rainfall events, watershed conditions, and remote sensing data, aiming to generalize the findings. It is anticipated that such research will provide insights into the impact of rainfall variability and flood model parameter estimation uncertainty in mountainous regions.

This study reaffirmed the significant influence of rainfall on flood estimation and highlighted the need for continuous and related research to better understand the high variability of rainfall and its implications in flood estimation in mountainous areas.

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B01001750).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.