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

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "New Sensors, New Technologies and Machine Learning in Water Sciences".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 2630

Special Issue Editors

Prof. Dr. Zhijun Li

E-Mail Website
Guest Editor
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
Interests: ice physical and mechanical properties; ice engineering; polar sciences and technology; ecosystem under ice; physical modeling
Special Issues, Collections and Topics in MDPI journals
Dr. Fang Li

E-Mail Website
Guest Editor
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Interests: ice mechanics; ice-structure interaction; ice loads; ice navigation; ship performance in ice
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are excited to announce a Special Issue titled "Mathematical, Physical, Chemical, and Biological Methods for Ice and Water Problems" in Water. Ice and water, though two distinct physical states of the same substance, have traditionally been studied in isolation across various disciplines. However, recent advances in cryospheric science and technology underscore their intrinsic interdependence and the need for integrated research approaches.

The interconnectedness of ice and water arises from several critical phenomena. Phase transitions link the dynamic energy and mass exchanges between ice and water that drive processes such as freezing and melting. Under ice-covered conditions, ecosystems and water environments are tightly coupled with the ice, forming unique ecological systems. Thermodynamic processes are inherently governed by the interplay between ice and water, particularly in cold-region hydrology. Moreover, the interactions between ice and engineering structures often exhibit complex coupled behaviors, emphasizing the need for multidisciplinary investigations. These interactions highlight the importance of mathematical, physical, chemical, and biological approaches in addressing water-ice-related challenges.

This Special Issue aims to provide a platform for showcasing cutting-edge research on ice and water systems using diverse methodologies. We encourage submissions covering topics such as ice–water phase transition processes, phase-transition-influenced properties (e.g., thermal, mechanical, optical, and electrical), ecosystems under ice covers, ice–water thermodynamics, shipping in ice-covered waters, surface icing on structures in cold regions, and wastewater purification through freezing. Contributions employing theoretical studies, case analyses, field investigations, data analyses, physical simulations, or numerical modeling are particularly welcome.

We invite you to share your valuable research in this Special Issue, advancing our understanding of the complex dynamics between ice and water through multidisciplinary methods and innovative techniques.

Prof. Dr. Zhijun Li
Dr. Fang Li
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Water is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • lake ice
  • river ice
  • sea ice
  • ice engineering
  • observations and investigations
  • water environment
  • ecology
  • mathematical method
  • numerical modeling
  • physical modeling
  • chemical analysis
  • biological analysis
  • data analysis

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Published Papers (5 papers)

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Research

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20 pages, 8397 KiB  
Article
Advancing Sea Ice Thickness Hindcast with Deep Learning: A WGAN-LSTM Approach
by Bingyan Gao, Yang Liu, Peng Lu, Lei Wang and Hui Liao
Water 2025, 17(9), 1263; https://doi.org/10.3390/w17091263 - 23 Apr 2025
Viewed by 177
Abstract
The thickness of the Arctic sea ice constitutes one of the crucial indicators of global climate change, and while deep learning has shown promise in predicting sea ice thickness (SIT), the field continues to grapple with the challenge of limited data availability. In [...] Read more.
The thickness of the Arctic sea ice constitutes one of the crucial indicators of global climate change, and while deep learning has shown promise in predicting sea ice thickness (SIT), the field continues to grapple with the challenge of limited data availability. In this study, we introduce a Wasserstein Generative Adversarial Network–Long Short-Term Memory (WGAN-LSTM) model, which leverages the data generation capabilities of WGAN and the temporal prediction strengths of LSTM to perform single-step SIT prediction. During model training, the mean square error (MSE) and a novel comprehensive index, the Distance between Indices of Simulation and Observation (DISO), are used as two metrics of the loss function to compare. To thoroughly assess the model’s performance, we integrate the WGAN-LSTM model with the Monte Carlo (MC) dropout uncertainty estimation method, thereby validating the model’s enhanced generalization capabilities. Experimental results demonstrate that the WGAN-LSTM model, utilizing MSE and DISO as loss functions, improves comprehensive performance by 51.9% and 75.2%, respectively, compared to the traditional LSTM model. Furthermore, the MC estimates of the WGAN-LSTM model align with the distribution of actual observations. These findings indicate that the WGAN-LSTM model effectively captures nonlinear changes and surpasses the traditional LSTM model in prediction accuracy. The demonstrated effectiveness and reliability of the WGAN-LSTM model significantly advance short-term SIT prediction research in the Arctic region, particularly under conditions of data scarcity. Additionally, this model offers an innovative approach for identifying other physical features in the sea ice field based on sparse data. Full article
(This article belongs to the Special Issue Mathematical, Physical, Chemical, and Biological Methods for Ice and Water Problems)
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13 pages, 2946 KiB  
Article
Impact of the Reynolds Numbers on the Velocity of Floating Microplastics in Open Channels
by Jiachen Li, Zhichao Wang, Weiping Li, Shuangyi Jing, Caio Graco-Roza and Lauri Arvola
Water 2025, 17(4), 588; https://doi.org/10.3390/w17040588 - 18 Feb 2025
Viewed by 464
Abstract
Quantitatively analyzing the factors influencing the horizontal migration of microplastics (MPs) in water bodies and understanding their movement patterns are crucial for explaining and predicting their transport principles and final destinations. This study used nearly spherical polyethylene (PE), polypropylene (PP), and polystyrene (PS) [...] Read more.
Quantitatively analyzing the factors influencing the horizontal migration of microplastics (MPs) in water bodies and understanding their movement patterns are crucial for explaining and predicting their transport principles and final destinations. This study used nearly spherical polyethylene (PE), polypropylene (PP), and polystyrene (PS) MPs as experimental subjects. By tracking their motion characteristics through video recording, we established relationships among the Reynolds number (Re), MP density, and floating velocity. The results showed that the Re and MP density jointly affect the horizontal drift of MPs. The horizontal floating velocity of MPs significantly increases with the increase in the Re and shows a power function growth trend. The difference in density of MPs mainly affects their dispersion during the floating process. Moreover, the coefficient of variation (CV) of PP’s horizontal floating velocity increased with the Re, suggesting PP’s motion is more random and discrete than that of PE and PS. Ultimately, we fitted the horizontal floating velocity of MPs to the equation to comprehensively evaluate the relationship between the floating velocity, Re, and density of MPs. This analysis underscores that the Re predominantly influences the MP velocity in water, while the MP density chiefly impacts the discrete nature of their motion. Full article
(This article belongs to the Special Issue Mathematical, Physical, Chemical, and Biological Methods for Ice and Water Problems)
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23 pages, 16066 KiB  
Article
Forecasting the River Ice Break-Up Date in the Upper Reaches of the Heilongjiang River Based on Machine Learning
by Zhi Liu, Hongwei Han, Yu Li, Enliang Wang and Xingchao Liu
Water 2025, 17(3), 434; https://doi.org/10.3390/w17030434 - 4 Feb 2025
Viewed by 928
Abstract
Ice-jam floods (IJFs) are a significant hydrological phenomenon in the upper reaches of the Heilongjiang River, posing substantial threats to public safety and property. This study employed various feature selection techniques, including the Pearson correlation coefficient (PCC), Grey Relational Analysis (GRA), mutual information [...] Read more.
Ice-jam floods (IJFs) are a significant hydrological phenomenon in the upper reaches of the Heilongjiang River, posing substantial threats to public safety and property. This study employed various feature selection techniques, including the Pearson correlation coefficient (PCC), Grey Relational Analysis (GRA), mutual information (MI), and stepwise regression (SR), to identify key predictors of river ice break-up dates. Based on this, we constructed various machine learning models, including Extreme Gradient Boosting (XGBoost), Backpropagation Neural Network (BPNN), Random Forest (RF), and Support Vector Regression (SVR). The results indicate that the ice reserves in the Oupu to Heihe section have the most significant impact on the ice break-up date in the Heihe section. Additionally, the accumulated temperature during the break-up period and average temperature before river ice break-up are identified as features closely related to the river’s opening in all four feature selection methods. The choice of feature selection method notably impacts the performance of the machine learning models in predicting the river ice break-up dates. Among the models tested, XGBoost with PCC-based feature selection achieved the highest accuracy (RMSE = 2.074, MAE = 1.571, R2 = 0.784, NSE = 0.756, TSS = 0.950). This study provides a more accurate and effective method for predicting river ice break-up dates, offering a scientific basis for preventing and managing IJF disasters. Full article
(This article belongs to the Special Issue Mathematical, Physical, Chemical, and Biological Methods for Ice and Water Problems)
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11 pages, 1747 KiB  
Article
Mathematical Description of the Immunochemical Response of the Manila Clam (Ruditapes philippinarum) to Extreme Temperature Reductions
by Runling Li, Jianjun Wang, Wei Han, Jianying Gong and Jun Ding
Water 2025, 17(1), 93; https://doi.org/10.3390/w17010093 - 1 Jan 2025
Viewed by 654
Abstract
The activity levels of superoxide dismutase (SOD), catalase (CAT), lysozyme (LZM), acid phosphatase (ACP), and alkaline phosphatase (AKP) can reflect the immune status of an organism. The immune status may be affected by extreme changes in the weather, especially rapid declines in temperature. [...] Read more.
The activity levels of superoxide dismutase (SOD), catalase (CAT), lysozyme (LZM), acid phosphatase (ACP), and alkaline phosphatase (AKP) can reflect the immune status of an organism. The immune status may be affected by extreme changes in the weather, especially rapid declines in temperature. In this study, the SOD, CAT, LZM, ACP, and AKP activity levels of the Manila clam (Ruditapes philippinarum) were measured for 24 h while the seawater temperature rapidly decreased to the freezing point from 8 °C, 4 °C, and 2 °C to analyze its immunochemical response to temperature decline. The results showed that the enzyme activity levels fluctuated with time as the temperature declined. By fitting the data, a model was obtained to describe the variation in immune enzyme activity within a short time period as temperature declined. The mathematical description included the stress response and the direct temperature response. The enzyme activity was adjusted rapidly as a stress response in the short term as the temperature declined, before it tended to stabilize. The direct temperature response also caused the enzyme activity to change as the temperature declined to the freezing point. The correlation coefficient between the fitted model and the actual enzymatic activity levels exceeded 0.87, which demonstrated that the mathematical description was adequate. Full article
(This article belongs to the Special Issue Mathematical, Physical, Chemical, and Biological Methods for Ice and Water Problems)
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Review

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36 pages, 1439 KiB  
Review
Review and Prospect of the Uncertainties in Mathematical Models and Methods for Yellow River Ice
by Bing Tan, Chunjiang Li, Shengbo Hu, Zhijun Li, Honglan Ji, Yu Deng and Limin Zhang
Water 2025, 17(9), 1291; https://doi.org/10.3390/w17091291 - 25 Apr 2025
Viewed by 99
Abstract
Mathematical models and methods serve as fundamental tools for studying ice-related phenomena in the Yellow River. River ice is driven and constrained by hydrometeorological and geographical conditions, creating a complex system. Regarding the Yellow River, there are some uncertainties that manifest in unique [...] Read more.
Mathematical models and methods serve as fundamental tools for studying ice-related phenomena in the Yellow River. River ice is driven and constrained by hydrometeorological and geographical conditions, creating a complex system. Regarding the Yellow River, there are some uncertainties that manifest in unique features in this context, including ice–water–sediment mixed transport processes and the distribution of sediment both within the ice and on its surface. These distinctive characteristics are considered to different degrees across different scales. Mathematical models for Yellow River ice developed over the past few decades not only encompass models for the large-scale deterministic evolution of river ice formation and melting, but also uncertainty parameter schemes for deterministic mathematical models reflecting the Yellow River’s particular ice-related characteristics. Moreover, there are modern mathematical results quantitatively describing these characteristics with uncertainty, allowing for a better understanding of the unique ice phenomena in the Yellow River. This review summarizes (a) universal equations established according to thermodynamic and hydrodynamic principles in river ice mathematical models, as well as (b) uncertainty sources caused by the river’s characteristics, ice properties, and hydrometeorological conditions, embedded in parametric schemes reflecting the Yellow River’s ice. The intractable uncertainty-related problems in space–sky–ground telemetric image segmentation and the current status of mathematical processing methods are reviewed. In particular, the current status and difficulties faced by various mathematical models in terms of predicting the freeze-up and break-up times, the formation of ice jams and dams, and the early warning of ice disasters are presented. This review discusses the prospects related to the uncertainties in research results regarding the simulation and prediction of Yellow River ice while also exploring potential future trends in research related to mathematical methods for uncertain problems. Full article
(This article belongs to the Special Issue Mathematical, Physical, Chemical, and Biological Methods for Ice and Water Problems)
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