The Red River of the North is vulnerable to floods, which have caused significant damage and economic loss to inhabitants. A better capability in flood-event prediction is essential to decision-makers for planning flood-loss-reduction strategies. Over the last decades, classical statistical methods and Machine Learning (ML) algorithms have greatly contributed to the growth of data-driven forecasting systems that provide cost-effective solutions and improved performance in simulating the complex physical processes of floods using mathematical expressions. To make improvements to flood prediction for the Red River of the North, this paper presents effective approaches that make use of a classical statistical method, a classical ML algorithm, and a state-of-the-art Deep Learning method. Respectively, the methods are seasonal autoregressive integrated moving average (SARIMA), Random Forest (RF), and Long Short-Term Memory (LSTM). We used hourly level records from three U.S. Geological Survey (USGS), at Pembina, Drayton, and Grand Forks stations with twelve years of data (2007–2019), to evaluate the water level at six hours, twelve hours, one day, three days, and one week in advance. Pembina, at the downstream location, has a water level gauge but not a flow-gauging station, unlike the others. The floodwater-level-prediction results show that the LSTM method outperforms the SARIMA and RF methods. For the one-week-ahead prediction, the RMSE values for Pembina, Drayton, and Grand Forks are 0.190, 0.151, and 0.107, respectively. These results demonstrate the high precision of the Deep Learning algorithm as a reliable choice for flood-water-level prediction.

Flooding in cold regions, particularly driven by snowmelt and climate variability, presents complex challenges for accurate prediction and effective risk management. The current study aims to bridge these gaps by integrating all three components – cold region river systems, long short-term memory (LSTM) modeling, and a broader set of climate variables. Specifically, we incorporate additional climate parameters, including air temperature, humidity, solar radiation, and wind speed, into the LSTM model. Using 12 years of hourly water level data (2007–2019) from three USGS stations along the Red River – Pembina, Drayton, and Grand Forks – the model predicts water levels at lead times of 6, 12 h, 1 day, 3 days, and 1 week. The incorporation of climate variables significantly improved short-term prediction accuracy, achieving R2 values of 0.999 for 6-h forecasts across all stations, demonstrating the potential for real-time flood warning systems. For 1-week predictions, R2 values were 0.778 for Grand Forks, 0.816 for Drayton, and 0.864 for Pembina, reflecting a decrease in accuracy with longer prediction horizons. These findings highlight the effectiveness of LSTM models for short-term flood forecasting in snowmelt-prone regions and underscore the need for further refinement to address long-term hydrological forecasting challenges, particularly under variable climatic conditions.

This research paper presents the development of a nonlinear Muskingum model which achieves precise flood routing through river reaches while considering lateral inflow conditions. Fourteen pairs of flood hydrograph found at two specific United States Geological Survey (USGS) stations located along the Red River of the North, namely Grand Forks and Drayton, are used for the calibrations and validations of the Muskingum model. To enhance the accuracy of the procedure, a reach is divided into multiple sub-reaches, and the Muskingum model calculations are performed individually for each interval using the distributed Muskingum method. Notably, the model development process incorporates the use of the Salp Swarm algorithm. The obtained results demonstrate the effectiveness of the developed nonlinear Muskingum model in accurately routing floods through the very gentle river with a bed slope of (0.0002–0.0003). The events were categorized into three groups based on their dominant drivers: Group A (Snowmelt-driven floods), Group B (Rain-on-snow-induced floods), and Group C (Mixed floods influenced by both snowmelt and rainfall). For the sub-reaches in Group A, single sub-reach (NR = 1), the Performance Evaluation Criteria (PEC) yielded the highest value for SSE, amounting to 404.9 × 10⁶. In Group B, when NR = 2, PEC results the highest value were SSE = 730.2 × 10⁶. The number of sub-reaches in a model has a significant influence on parameter estimates and model performance, as demonstrated by the analysis of hydrologic parameters and performance evaluation criteria. Optimal performance varied across case studies, emphasizing the importance of selecting the appropriate number of sub-reaches for peak discharge predictions.

This research introduces a novel nonlinear Muskingum model for river flood routing, aiming to enhance accuracy in modeling. It integrates lateral inflows using the Whale Optimization Algorithm (WOA) and employs a distributed Muskingum model, dividing river reaches into smaller intervals for precise calculations. The primary goal is to minimize the Sum of Square Errors (SSE) between the observed and modeled outflows. Our methodology is applied to six distinct flood hydrographs, revealing its versatility and efficacy. For Lawler's and Dinavar's flood data, the single-reach Muskingum model outperforms multi-reach versions, demonstrating its effectiveness in handling lateral inflows. For Lawler's data, the single-reach model (NR = 1) yields optimal parameters of K = 0.392, x = 0.027, m = 1.511, and β = 0.010, delivering superior results. Conversely, when fitting flood data from Wilson, Wye, Linsley, and Viessman and Lewis, the multi-reach Muskingum model exhibits better overall performance. Remarkably, the model excels with the Viessman and Lewis flood data, especially with two reaches (NR = 2), achieving a 21.6% SSE improvement while employing the same parameter set. This research represents a significant advancement in flood modeling, offering heightened accuracy and adaptability in river flood routing.

This study aimed to map the 2022 flood with a 16.5-year return period near a bridge on the Red River, close to Grafton City, North Dakota, and evaluate the scour potential around the bridge. The Red River Basin (RRB) near Grand Forks, ND, and Emerson, ND, is a cold region river vulnerable to floods. Local scouring around bridge piers during floods can lead to hydraulic structure failure. An Autonomous Surface Vehicle (ASV) equipped with LiDAR DEM data from the ND DWR’s LiDAR dataset was used to collect comprehensive bathymetry and discharge data, including the 2022 flood. The HEC-RAS model was used to create flood maps, and the Colorado State University (CSU) methodology was employed to assess local scour around the bridge pier. The study area recorded maximum velocities of 1.71 m/s, 1.87 m/s, and 1.56 m/s for discharge values of 368 m³/s, 784 m³/s, and 1335 m³/s, respectively, with higher velocities recorded upstream of the bridge. The maximum water depth reached 13.14 m during the peak discharge of 1335 m³/s. Higher discharge resulted in increased Froude number and contraction scour depth, with the latter continuing to increase even when the Froude number decreased as water reached the bridge deck. The study highlights the effectiveness of integrating ASVs, bathymetry, and LiDAR data to comprehensively understand flood dynamics and bridge scour in cold region rivers, offering the way for the development of effective flood control measures and strategies to safeguard critical infrastructure.