Mathematical, Physical, Chemical and Biological Methods for Ice and Water Problems

1. Introduction

High-latitude and cold-region environments feature tightly coupled hydrological, cryospheric, and ecological subsystems, where seasonal freeze–thaw cycles, snow cover, permafrost, and river and lake ice fundamentally shape water flows and ecosystem processes [1,2]. However, the warming climate is disrupting these linkages. The Arctic and subarctic regions are warming at rates well above the global average, leading to accelerated permafrost thaw and altering drainage connectivity [3,4]. Consequently, ice-driven hazards have become more frequent and unpredictable. Ice-jam floods, often more destructive than open-water floods, are posing increasing risks to riverside communities due to changing winter regimes [5,6]. Furthermore, seasonal ice cover on lakes is diminishing globally, and recent pan-Arctic studies indicate that ice-covered lakes are highly sensitive to winter warming; the loss of ice cover greatly amplifies light penetration and thermal shifts, triggering cascading effects on aquatic biodiversity and water quality [7,8].

To tackle these emerging challenges, researchers have achieved significant advancements by utilizing cutting-edge technologies, and integrated numerical modeling and physical experiments have been widely adopted to analyze the mechanical behavior of ice and its interactions with offshore structures, providing insights critical for the design of safety systems in ice-covered waters [9,10]. Concurrently, the application of remote sensing and geospatial analysis has enabled comprehensive monitoring of cryospheric changes, and high-resolution satellite imagery now allows for the precise tracking of river ice evolution and sea ice drift, offering data support for disaster early warning [11,12]. Additionally, artificial intelligence has revolutionized hydrological forecasting, and deep learning algorithms, such as Long Short-Term Memory (LSTM) networks, have shown superior performance compared to traditional statistical approaches in processing nonlinear time series data for the prediction of variables like sea ice thickness and river break-up dates [13,14]. Beyond physics, interdisciplinary studies are also quantifying the transport of emerging contaminants in cold waters and assessing the physiological stress of aquatic organisms under extreme thermal variability, thereby informing integrated ecological management strategies [15].

This Special Issue brings together these and related modern methodologies to improve safety and sustainability in high-latitude environments. Through advanced numerical modeling, physical experiments, and integrated monitoring techniques, the collected studies analyze critical issues ranging from ice mechanics and hydrodynamic processes to biological responses. The findings provide critical theoretical foundations and technical support for ensuring infrastructure resilience, mitigating environmental risks, and optimizing water resource management in high-latitude regions.

2. An Overview of Published Articles

The monitoring, simulation, and risk assessment of hydrological dynamics and ice engineering processes are important in terms of ensuring the safety of infrastructure and the preservation of aquatic environments in cold regions. These complex systems, characterized by the interplay of riverine and sea ice, hydrodynamics, and environmental stressors, pose significant challenges to navigation, flood control, and ecological stability. To address these challenges, cutting-edge methodologies—ranging from machine learning algorithms and numerical modeling to high-resolution remote sensing and in situ mechanical testing—are increasingly being adopted. This Special Issue compiles ten innovative studies that delve into the mechanisms of ice formation and break-up, the interaction between waves and sea ice, and the environmental responses of aquatic systems, offering new theoretical insights and practical guidelines for disaster prevention and water resource management.

Tan et al. (Contribution (5)) provided a comprehensive review of the mathematical models and methods used for studying ice in the Yellow River, highlighting the unique uncertainties associated with the river’s mixed ice–water–sediment transport. The study summarizes universal thermodynamic and hydrodynamic equations while addressing specific parameterization schemes that reflect the Yellow River’s distinctive characteristics. Their results indicate that, while significant progress has been made in deterministic and stochastic modeling, challenges remain in predicting freeze-up and break-up times and in early warning for ice disasters. The findings point toward future research directions focused on integrating multi-source data to improve the accuracy of ice simulations and disaster forecasting in sediment-laden rivers.

Liu et al. (Contribution (2)) developed a forecasting model for river ice break-up dates in the upper reaches of the Heilongjiang River using advanced machine learning techniques. By comparing various feature selection methods and models, including XGBoost and Random Forest, the study identified that ice reserves and accumulated temperature during the break-up period are the most critical predictors. The results of their study show that the XGBoost model combined with Pearson Correlation Coefficient feature selection achieved the highest prediction accuracy. The findings provide a more effective and scientific approach for forecasting ice-jam floods, thereby enhancing disaster management capabilities in high-latitude river basins.

Leng et al. (Contribution (8)) investigated the spatiotemporal variations in open water and ice microstructure in the Inner Mongolia reaches of the Yellow River using Sentinel-2 satellite imagery and field sampling. The study reveals that open water transformation is distinct across different channel morphologies and is significantly driven by temperature fluctuations. Microstructural analysis indicates that ice crystals predominantly exist as columnar or granular forms, with their distribution and equivalent diameters systematically varying with channel configuration and ice thickness. These findings offer quantitative data on river ice physical properties, which are essential to understanding the heterogeneity of ice cover and its implications for river mechanics.

Li et al. (Contribution (9)) derived refined design parameters for sea ice engineering in the southern Bohai Sea using the NEMO-LIM2 ice–ocean coupling model. By partitioning the region into a high-resolution grid, the study calculated key parameters such as ice thickness, concentration, and strength for return periods ranging from 1 to 100 years. The results demonstrate that ice conditions exhibit a distinct spatial gradient, with the most severe conditions occurring in nearshore zones like Bohai Bay. The derived design strengths—specifically compressive and shear strengths—are comparable to current standards, while the refined grid captures more detailed spatial variations, providing accurate data support for the anti-ice design of offshore structures.

Gao et al. (Contribution (4)) proposed a novel Wasserstein Generative Adversarial Network–Long Short-Term Memory (WGAN-LSTM) model to hindcast Arctic sea ice thickness (SIT) under conditions of data scarcity. By integrating the data generation capabilities of WGAN with the temporal prediction strengths of LSTM, and utilizing a comprehensive index (DISO) in the loss function, the model significantly outperforms traditional methods. The team’s experimental results show that the WGAN-LSTM model improves prediction performance by over 50% compared to standard LSTM models, effectively capturing nonlinear changes in sea ice. The study advances short-term SIT prediction techniques, offering a robust tool for Arctic climate research and navigation safety.

Tan et al. (Contribution (6)) established a statistical optimization model to analyze the spatial distributions of ice ridge keels in the northwestern Weddell Sea, Antarctica. Using data from helicopter-borne electromagnetic induction surveys, the researchers determined an optimal keel cutoff draft of 3.8 m to differentiate keels from level ice. Their results indicate that the Wadhams’80 function and lognormal function effectively describe keel draft and spacing distributions, respectively, across different ridging intensity regimes. These findings provide a solid theoretical foundation for inverting sea ice thickness from surface data, improving the accuracy of remote sensing algorithms in polar regions.

Yu and Tian (Contribution (7)) simulated the interactions between regular waves and ice floes using the Coupled Eulerian–Lagrangian (CEL) method. The study quantitatively analyzed wave propagation and ice floe dynamics, revealing that ice floe motion is synchronized with incident wave periods and that wave height attenuation increases significantly with rising ice concentration. Furthermore, the simulation identified that ice fragmentation predominantly occurs at wave trough phases due to the concentration of flexural stress. The findings clarify energy transfer mechanisms between waves and ice, which is critical to assessing navigation safety in marginal ice zones.

Ji et al. (Contribution (10)) conducted full-scale in situ cantilever beam tests to determine the flexural strength and effective elastic modulus of brackish ice in a generic lake environment. By covering the growth, stable, and melt periods, the tests revealed that the square root of bulk porosity is the optimal predictor for flexural performance, and the results show that both strength and modulus decrease systematically with increasing porosity, being significantly lower during the melt period. This study provides valuable field data on brackish ice mechanics, filling a gap between freshwater and sea ice research and supporting ice load assessments in estuarine environments.

Li et al. (Contribution (3)) explored the transport of microplastics in open channels through flume experiments and, by tracking the trajectories of polyethylene, polypropylene, and polystyrene particles, established relationships among the Reynolds number, particle density, and floating velocity. The results of the study show that the Reynolds number dominates the horizontal migration velocity, while particle density primarily affects dispersion. The findings offer a theoretical framework for predicting the transport and fate of microplastics in water bodies, contributing to pollution control strategies in riverine ecosystems.

Li et al. (Contribution (1)) examined the immunochemical response of the Manila clam to extreme temperature reductions and, by measuring the activity of key immune enzymes under rapid cooling conditions, developed a mathematical model describing the stress and direct temperature responses. The research team’s results indicate that enzyme activity fluctuates significantly as a stress response before stabilizing or changing due to low temperatures. The study provides a mathematical description of aquatic organism immunity under thermal stress, which is vital for assessing the ecological impacts of cold weather events on aquaculture.

3. Conclusions

This Special Issue integrates mathematical, physical, chemical, and biological methodologies to address complex challenges in cold region environments. Ranging from deep learning-based sea ice hindcasting to the immunochemical analysis of aquatic organisms, these studies elucidate critical water–ice dynamics and ecological responses. By synthesizing advanced numerical modeling with in situ physical and chemical experiments, this collection establishes a robust scientific framework for enhancing disaster prediction, infrastructure resilience, and environmental preservation in high-latitude waters.

The main conclusions are as follows:

(1) Advanced data-driven models, particularly those utilizing deep learning, significantly outperform traditional methods in forecasting sea ice thickness and river break-up events;

(2) Refined grid systems and porosity-based mechanical indices provide essential design parameters for ensuring infrastructure safety in ice-covered waters;

(3) The synchronization of wave-ice interactions and stress-induced fragmentation governs energy attenuation dynamics and navigation safety in marginal ice zones;

(4) Channel morphology and thermal regimes are the fundamental drivers regulating the spatiotemporal heterogeneity and microstructural evolution of river ice;

(5) Hydrodynamic forces and thermal stress critically influence both the transport mechanisms of pollutants and the physiological resilience of aquatic ecosystems.

Looking ahead, a promising direction is the integration of multi-physics coupling models with artificial intelligence to address the increasing complexity of cold region environments. As global warming alters ice phenology, developing integrated monitoring systems that combine high-resolution remote sensing with in situ mechanical testing will be crucial. Solutions based on these high-precision predictive frameworks, together with comprehensive ecological risk assessments, will be indispensable for sustainable engineering and environmental protection in high-latitude regions.