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Flood frequency analysis is crucial for understanding flood risks in specific regions. This study applied the Gumbel Distribution Method to analyze flood frequency using river discharge data from the Kadamaian and Wariu Rivers in Kota Belud, Sabah, Malaysia. The analysis involved data collection, parameter estimation, goodness-of-fit testing, and determination of annual recurrence intervals (ARIs). The study found that the ARIs for the Kadamaian and Wariu Rivers are 50 years and 30 years, respectively, highlighting the need for targeted flood mitigation strategies in these areas. These findings emphasize the higher flood risk in the Kadamaian River basin, necessitating more robust flood control measures compared to the Wariu River basin. The Gumbel distribution provided accurate flood frequency estimations validated by the Kolmogorov-Smirnov test and correlation coefficient (R2). The calculated ARIs offer valuable insights for flood hazard assessment and contingency planning. These findings underscore the importance of accurate flood frequency analysis in enhancing flood mitigation strategies and disaster preparedness. It is recommended that local authorities incorporate these results into flood management and urban planning initiatives.

Regional flood frequency analysis (RFFA) is a powerful method for interrogating hydrological series since it combines observational time series from several sites within a region to estimate risk-relevant statistical parameters with higher accuracy than from single-site series. Since RFFA extreme value estimates depend on the shape of the selected distribution of the data-generating stochastic process, there is need for a suitable goodness-of-distributional-fit measure in order to optimally utilize given data. Here we present a novel, least-squares-based measure to select the optimal fit from a set of five distributions, namely Generalized Extreme Value (GEV), Generalized Logistic, Gumbel, Log-Normal Type III and Log-Pearson Type III. The fit metric is applied to annual maximum discharge series from six hydrological stations along the Sava River in South-eastern Europe, spanning the years 1961 to 2020. Results reveal that (1) the Sava River basin can be assessed as hydrologically homogeneous and (2) the GEV distribution provides typically the best fit. We offer hydrological-meteorological insights into the differences among the six stations. For the period studied, almost all stations exhibit statistically insignificant trends, which renders the conclusions about flood risk as relevant for hydrological sciences and the design of regional flood protection infrastructure.

Flood is one of the worst natural disasters, which causes significant damage to economy and society. Flood risk assessment helps to reduce flood damage by managing flood risk in flood affected areas. For ungauged catchments, regional flood frequency analysis (RFFA) is generally used for design flood estimation. This study develops a Convolutional Neural Network (CNN) based RFFA technique using data from 201 catchments in south-east Australia. The CNN based RFFA technique is compared with multiple linear regression (MLR), support vector machine (SVM), and decision tree (DT) based RFFA models. Based on a split-sample validation using several statistical indices such as relative error, bias and root mean squared error, it is found that the CNN model performs best for annual exceedance probabilities (AEPs) in the range of 1 in 5 to 1 in 100, with median relative error values in the range of 29–44%. The DT model shows the best performance for 1 in 2 AEP, with a median relative error of 24%. The CNN model outperforms the currently recommended RFFA technique in Australian Rainfall and Runoff (ARR) guideline. The findings of this study will assist to upgrade RFFA techniques in ARR guideline in near future.

In traditional flood frequency analysis, a minimum of 30 observations is required to guarantee the accuracy of design results with an allowable uncertainty, however, there has not been a recommendation for the requirement on the length of data in NFFA (nonstationary flood frequency analysis). Therefore, this study has been carried out with three aims: (i) to evaluate the predictive capabilities of nonstationary (NS) and stationary (ST) models with varying flood record lengths; (ii) to examine the impacts of flood record lengths on the NS and ST design floods and associated uncertainties; and (iii) to recommend the probable requirements of flood record length in NFFA. To achieve these objectives, 20 stations with record length longer than 100 years in Norway were selected and investigated by using both GEV (generalized extreme value)-ST and GEV-NS models with linearly varying location parameter (denoted by GEV-NS0). The results indicate that the fitting quality and predictive capabilities of GEV-NS0 outperform those of GEV-ST models when record length is approximately larger than 60 years for most stations, and the stability of the GEV-ST and GEV-NS0 is improved as record lengths increase. Therefore, a minimum of 60 years of flood observations is recommended for NFFA for the selected basins in Norway.

With global climate change and human activities, environmental uncertainties are increasing, and extreme flood events are occurring more frequently. The reliability of traditional hydrological frequency analysis theories, based on the assumption of stationarity, is being increasingly questioned. This study aims to develop a non‐stationary flood frequency analysis model using the Generalized Additive Models for Location, Scale, and Shape (GAMLSS) framework, with time and climate indices as covariates. The model calculation and frequency analysis are conducted using 2000 years of climate indices reconstructed by the Paleo Hydrodynamics Data Assimilation product (PHYDA). Design floods for different return periods are then quantified based on the reconstructed data. The results show that the nonstationary model established with climate indices as covariates can accurately identify the trend of first decreasing and then increasing flood series at the FP and ZJG stations in the Daqing River Basin, achieving the best model performance. Moreover, using the PHYDA‐reconstructed climate indices from the past 2000 years to extrapolate floods and calculate design floods provides higher safety for certain return periods than observed series. However, under longer return periods, the design values are smaller than those of the existing observed series. Overall, the nonstationary model proposed in this study can serve as a tool for flood frequency analysis under climate change. Additionally, incorporating the climate indices from the past 2000 years into nonstationary flood frequency analysis provides design results that can offer valuable references for regional water infrastructure design.

Multivariate flood frequency analysis has been widely used in the design and risk assessment of hydraulic structures. However, analytical solutions are often obtained based on an idealized linear reservoir model in which a linear routing process is assumed, and consequently, the flood risk is likely to be over- or underestimated. The present study proposes a nonlinear reservoir model in which the relationships of reservoir water level with reservoir volume and discharge are assumed to be nonlinear in order to more accurately describe the routing process as it takes into consideration the interactions between hydrological loading and different discharge structures. The structure return period is calculated based on the copula function and compared with that based on the linear reservoir model and the bivariate return period based on the Kendall distribution function. The results show that the structure return period based on the linear model leads to an underestimation of the flood risk under the conditions of high reservoir water level. For the same reservoir, linear and nonlinear reservoir models give quite different reservoir volume-water level and discharge-water level curves; therefore, they differ substantially in the sensitivity to flood events with different combinations of flood peak and volume. We also analyze the effects of the parameters involved in the reservoir volume-water level and discharge-water level relationships on the maximum water level at different return periods in order to better understand the applicability and effectiveness of the proposed method for different hydraulic projects.

Non-stationary flood frequency analysis (FFA) is applied to statistical analysis of seasonal flow maxima from Polish and Norwegian catchments. Three non-stationary estimation methods, namely, maximum likelihood (ML), two stage (WLS/TS) and GAMLSS (generalized additive model for location, scale and shape parameters), are compared in the context of capturing the effect of non-stationarity on the estimation of time-dependent moments and design quantiles. The use of a multimodel approach is recommended, to reduce the errors due to the model misspecification in the magnitude of quantiles. The results of calculations based on observed seasonal daily flow maxima and computer simulation experiments showed that GAMLSS gave the best results with respect to the relative bias and root mean square error in the estimates of trend in the standard deviation and the constant shape parameter, while WLS/TS provided better accuracy in the estimates of trend in the mean value. Within three compared methods the WLS/TS method is recommended to deal with non-stationarity in short time series. Some practical aspects of the GAMLSS package application are also presented. The detailed discussion of general issues related to consequences of climate change in the FFA is presented in the second part of the article entitled “Around and about an application of the GAMLSS package in non-stationary flood frequency analysis”.

Computational advances have made atmospheric modeling at convection‐permitting (≤4 km) grid spacings increasingly feasible. These simulations hold great promise in the projection of climate change impacts including rainfall and flood extremes. The relatively short model runs that are currently feasible, however, inhibit the assessment of the upper tail of rainfall and flood quantiles using conventional statistical methods. Stochastic storm transposition (SST) and process‐based flood frequency analysis are two approaches that together can help to mitigate this limitation. SST generates large numbers of extreme rainfall scenarios by temporal resampling and geospatial transposition of rainfall fields from relatively short data sets. Coupling SST with process‐based flood frequency analysis enables exploration of flood behavior at a range of spatial and temporal scales. We apply these approaches with outputs of 13‐year simulations of regional climate to examine changes in extreme rainfall and flood quantiles up to the 500‐year recurrence interval in a medium‐sized watershed in the Midwestern United States. Intensification of extreme precipitation across a range of spatial and temporal scales is identified in future climate; changes in flood magnitudes depend on watershed area, with small watersheds exhibiting the greatest increases due to their limited capacity to attenuate flood peaks. Flood seasonality and snowmelt are predicted to be earlier in the year under projected warming, while the most extreme floods continue to occur in early summer. Findings highlight both the potential and limitations of convection‐resolving climate models to help understand possible changes in rainfall and flood frequency across watershed scales. Plain Language Summary High‐resolution “convection‐permitting” regional climate model simulations hold great promise in projection of climate change impacts including extreme rainfall and flooding. The relatively short (~10‐year) model runs that are currently feasible, however, are insufficient for examining very rare events like 100‐year storms and floods. Meanwhile, existing rainfall and flood data sets have a number of shortcomings that make it difficult to understand how floods have and will continue to change. In this study, we use several novel computer modeling methods to help mitigate these limitations. We apply these methods together with detailed simulations of flood hydrology and high‐resolution regional climate simulation results to examine current and future extreme rainfall and flooding in an agricultural watershed in northeastern Iowa, in the Midwestern United States. Floods there are projected to become more severe, driven by complex seasonal changes in rainfall, temperature, and snow. The magnitude of these changes depends on upstream watershed area. This work demonstrates how cutting‐edge climate and hydrology simulations and methods, together with flood theory and data, can help to predict future changes in flooding. Key Points Process‐based frequency analysis framework is coupled with convection‐permitting RCM outputs to study rainfall and flood nonstationarity We examine current and future rainfall and flood quantiles up to the 500‐year recurrence interval in a medium‐sized watershed Extreme rainfall enhancement is identified across scales, while changes in flood hazards are highly dependent on scale and magnitude

The non-stationarity of hydrologic processes due to climate change or human activities is challenging for the researchers and practitioners. However, the practical requirements for taking into account non-stationarity as a support in decision-making procedures exceed the up-to-date development of the theory and the of software. Currently, the most popular and freely available software package that allows for non-stationary statistical analysis is the GAMLSS (generalized additive models for location, scale and shape) package. GAMLSS has been used in a variety of fields. There are also several papers recommending GAMLSS in hydrological problems; however, there are still important issues which have not previously been discussed concerning mainly GAMLSS applicability not only for research and academic purposes, but also in a design practice. In this paper, we present a summary of our experiences in the implementation of GAMLSS to non-stationary flood frequency analysis, highlighting its advantages and pointing out weaknesses with regard to methodological and practical topics.