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Mathematical Theories and Models in Environmental Science

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A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (20 October 2023) | Viewed by 21331

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Special Issue Editors

Prof. Dr. Fei Qi

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Guest Editor

School of Environmental Science and Engineering, Beijing Forestry University, Beijing 100083, China
Interests: AOPs for water purification; non-point pollutants modelling; reaction kinetics and modelling in water purification

Dr. Chao Liu

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Guest Editor

Xuzhou Institute of Technology, School of Environmental Engineering, Xuzhou 221018, China
Interests: water pollution models

Dr. Yiping Wang

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Guest Editor

State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029, China
Interests: nanomaterials; applied chemistry heterogeneous catalysis

Special Issue Information

Dear Colleagues,

Entering the new century, the planet faces various problems, such as natural disasters, a shortage of resources, environment pollution and food safety, and so on. To solve these environmental problems, environmental mathematics comes into being, which is a mathematical theory and method involved in solving environmental science problems. Mathematical models are the basis of solving quantitatively environmental pollution control. This Special Issue welcomes both research articles and review articles dealing with the impact of mathematic models and methods on the environment and on sustainable development. Interdisciplinary works are accepted, related to economics, education, environment, materials, etc., as long as they are based on mathematical methods and models. This includes, among others, new mathematical methods or models that allow for a better understanding of sustainable development and that are beneficial for realizing environmental pollution control. The practical applications derived from these developed models and their possible policy implications will also be considered.

Prof. Dr. Fei Qi
Dr. Chao Liu
Dr. Yiping Wang
Guest Editors

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Keywords

mathematical models
environmental pollution
mathematical method
comprehensive evaluation
theoretical calculation

Published Papers (11 papers)

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Research

23 pages, 3855 KiB

Open AccessArticle

Modeling Asymmetric Dependence Structure of Air Pollution Characteristics: A Vine Copula Approach

by Mohd Sabri Ismail, Nurulkamal Masseran, Mohd Almie Alias and Sakhinah Abu Bakar

Mathematics 2024, 12(4), 576; https://doi.org/10.3390/math12040576 - 14 Feb 2024

Viewed by 631

Abstract

Contaminated air is unhealthy for people to breathe and live in. To maintain the sustainability of clean air, air pollution must be analyzed and controlled, especially after unhealthy events. To do so, the characteristics of unhealthy events, namely intensity, duration, and severity are studied using multivariate modeling. In this study, the vine copula approach is selected to study the characteristics data. Vine copula is chosen here because it is more potent than the standard multivariate distributions, and multivariate copulas, especially in modeling the tails related to extreme events. Here, all nine different vine copulas are analyzed and compared based on model fitting and the comparison of models. In model fitting, the best model obtained is Rv123-Joint-MLE, a model with a root nodes sequence of 123, and optimized using the joint maximum likelihood. The components for the best model are the Tawn type 1 and Rotated Tawn type 1 180 degrees representing the pair copulas of (intensity, duration), and (intensity, severity), respectively, with the Survival Gumbel for the conditional pair copula of (duration, severity; intensity). Based on the best model, the tri-variate dependence structure of the intensity, duration, and severity relationship is positively correlated, skewed, and follows an asymmetric distribution. This indicates that the characteristic’s, including intensity, duration, and severity, tend to increase together. Using comparison tests, the best model is significantly different from others, whereas only two models are quite similar. This shows that the best model is well-fitted, compared to most models. Overall, this paper highlights the capability of vine copula in modeling the asymmetric dependence structure of air pollution characteristics, where the obtained model has a better potential to become a tool to assess the risks of extreme events in future work. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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25 pages, 3746 KiB

Open AccessArticle

Metapopulation Modeling of Socioeconomic Vulnerability of Sahelian Populations to Climate Variability: Case of Tougou, Village in Northern Burkina Faso

by Malicki Zorom, Babacar Leye, Mamadou Diop and Serigne M’backé Coly

Mathematics 2023, 11(21), 4507; https://doi.org/10.3390/math11214507 - 1 Nov 2023

Viewed by 966

Abstract

Since the droughts of the 1970s–1980s, populations in the Sahel region have opted for a mass exodus to more humid urban or rural centers. Migrations or exoduses have accelerated in recent decades due to environmental degradation and unfavorable climatic conditions. Insufficient harvests are the main reason for migration for the majority of migrants in the Sahelian areas. Migration is a major adaptation strategy to cope with extreme climatic conditions, thus requiring quantification in the destination area. The aim of this paper is to propose a metapopulation model to approximate reality by identifying the transition from one socioeconomic vulnerability group to another, from a less favorable area to favorable area in terms of natural resources, depending on the strategies, policies, and climate variability. The model was used to analyze the dynamics of socioeconomic vulnerability to study the impact of migration on the dynamics of socioeconomic vulnerability. The developed mathematical model was analyzed. Up to 2050, simulations applied to the Tougou village in northern Burkina Faso show that migration has a positive impact on the socioeconomic vulnerability of the destination area, thereby reducing the vulnerability of the population by 10% when resources are increased by up to 30%. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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18 pages, 3192 KiB

Open AccessArticle

Risk Assessment of Mining Heritage Reuse in Public–Private-Partnership Mode Based on Improved Matter–Element Extension Model

by Shan Yang, Shengyuan Zhuo, Zitong Xu and Jianhong Chen

Mathematics 2023, 11(16), 3599; https://doi.org/10.3390/math11163599 - 20 Aug 2023

Cited by 1 | Viewed by 847

Abstract

With the development and utilization of resources, mineral-resource cities face the dilemma of resource depletion, the environmental restoration of mines, and industrial transformation. Reusing their mining heritage is a good way for these cities to change their mono-industrial structure and vigorously develop successor industries. Due to the complexity of reusing mining heritage, introducing the “Public–Private-Partnership” (PPP) mode can be a good solution to the problems of the government’s mining heritage reuse, such as large capital investment and a long construction-cycle time. To accurately classify the risk of reuse of mining heritage in the PPP mode, 26 indicators are selected to construct the evaluation index system of mining heritage reuse in the PPP mode based on five aspects: social capital-side, contractor-side, government-side, civilian-side, and the natural environment. The path coefficients of the structural equation model are used to calculate the weights of the indicators. The improved matter–element extension model is constructed to evaluate the reuse of mining heritage in the PPP mode. The Jiaozuo-Centennial Mining Heritage Park project is the object of research for applying the model. The results show that the risk evaluation index system combines the risk factors from the stakeholders’ perspective. The risk-evaluation model of the mining heritage reuse PPP project is constructed based on the combination of the improved matter–element extension model, the calculation of the asymmetric closeness, and the structural equation modeling method, which solves the drawbacks of the traditional model, such as the difficulty of determining the weights of the indicators, the incomplete scope of the material element domains, and the poor calculation of the comprehensive correlation degree. The case analysis shows that the risk level of the Jiaozuo-Centennial Mining Heritage Park project is Level II. This aligns with the actual situation and verifies the feasibility of the risk-evaluation model applied to the actual project. The research in this paper fills the gap in the risk model of mining heritage reuse in the PPP mode, enriches the theoretical system of risk evaluation of mining heritage reuse projects, and provides reference significance for similar mining heritage development projects in the future. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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20 pages, 2023 KiB

Open AccessArticle

Dynamic Analysis of Delayed Two-Species Interaction Model with Age Structure: An Application to Larch-Betula Platyphylla Forests in the Daxing’an Mountains, Northeast China

by Xuan Huang, Yuting Ding and Ning Pan

Mathematics 2023, 11(11), 2485; https://doi.org/10.3390/math11112485 - 28 May 2023

Viewed by 1004

Abstract

Since plant–plant interaction has been the fundamental issue of the ecology community and is essential for the multispecies forest community, it is necessary to analyze the interaction mechanisms and provide suggestions for collaborative management of multispecies forests with the background of double carbon goals in China. To explore the interaction mechanisms in different interaction modes and assist China’s green development, we choose the most promising area, the Daxing’an Mountains, and its dominant species, Larch and Betula platyphylla, as research objects and establish a delayed two-species interaction model with an age structure. First, we calculate the equilibria of our model and analyze the stability of equilibria. Then, we study the existence of the Hopf bifurcation near the equilibria. Furthermore, we determine reasonable parameter values based on official data through mathematical methods, such as cluster analysis and model fitting. Finally, we carry out numerical simulations from three aspects, the evolution of a stand structure without interactions, the population dynamics in different interaction modes, and the influences of the parameters on the equilibria. Combined with simulation results, we provide biological interpretations for simulations of the stand structure evolution process and the interactions between Larch and Betula platyphylla; we also give reasonable values of the growth rates and mortalities for developing forest strategies. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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20 pages, 1801 KiB

Open AccessArticle

A Mathematical Analysis of 4IR Innovation Barriers in Developmental Social Work—A Structural Equation Modeling Approach

by Paramjit Singh Jamir Singh, Ayodeji Emmanuel Oke, Ahmed Farouk Kineber, Oludolapo Ibrahim Olanrewaju, Olayinka Omole, Mohamad Shaharudin Samsurijan and Rosfaraliza Azura Ramli

Mathematics 2023, 11(4), 1003; https://doi.org/10.3390/math11041003 - 16 Feb 2023

Cited by 11 | Viewed by 1945

Abstract

The fourth industrial revolution (4IR) era also known as digital age is central to the advancement of the construction industry as the industry is currently facing a myriad of challenges, including poor productivity and project failure. Therefore, there is an urgent need for industry to adopt 4IR innovations to increase the building business’s performance. The study explored the relationship between the critical barriers to 4IR innovations to foster sustainable development. The study embraced a numerical exploration approach which employed a questionnaire to obtain information from building industry experts. The questionnaire data were used to classify the 4IR barriers into policy and structure, readiness, and acquisition, using Exploratory Factor Analysis (EFA). Likewise, a predictive model was developed using Structural Equation Modelling-Partial Least Square (SEM-PLS). It explained the relationship between the barrier categories and the barriers to 4IR innovation adoption for sustainable development. The results showed that policy and structure were critical components of 4IR adoption that the stakeholders of the construction industry must pay close attention to. The study also provided valuable areas for future research to enhance 4IR innovation adoption for sustainable development. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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21 pages, 1412 KiB

Open AccessArticle

Modeling the Impact of Overcoming the Green Walls Implementation Barriers on Sustainable Building Projects: A Novel Mathematical Partial Least Squares—SEM Method

by Ahmed Farouk Kineber, Ayodeji Emmanuel Oke, Mohammed Magdy Hamed, Ehab Farouk Rached and Ali Elmansoury

Mathematics 2023, 11(3), 504; https://doi.org/10.3390/math11030504 - 17 Jan 2023

Cited by 5 | Viewed by 1866

Abstract

The sustainable building concept must be implemented throughout the project lifecycle to achieve the highest proceeds without lowering the standard. Although implementing green walls in emerging nations is partial, such studies have concentrated on drivers for implementing green walls. Conversely, there is less proof to comprehensively study the impact of implementing green walls’ overall sustainable success (OSS) concerning the lifecycle of projects. This research focuses on the green wall adoption barriers in construction projects in third-world nations. It assesses the effect of addressing green wall (GW) adoption obstacles on OSS throughout the project lifespan. Therefore, a broader review of the literature is needed for conceptual model development. Structural equation modelling and partial least square (SEM-PLS) have been developed employing a survey evaluation tool (i.e., questionnaire). Information was derived from one hundred and five building professionals in Nigeria. The model output revealed that eradicating GWs barriers had a slight to intermediate influence on OSS during the construction scheme’s lifespan. These results offer the foundation for policymaking in third-world nations regarding successful project completion through evading barriers to green wall adoption. Similarly, green walls implementation will enhance the building project’s success. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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18 pages, 5380 KiB

Open AccessArticle

Modeling Non-Point Source Nutrient Loads with Different Cropping Systems in an Agricultural Lake Watershed in Southwestern China: From Field to Watershed Scale

by Jiayu Peng, Chunling Jin, Yue Wu, Zeying Hou, Sijia Gao, Zhaosheng Chu and Binghui Zheng

Mathematics 2022, 10(21), 4047; https://doi.org/10.3390/math10214047 - 31 Oct 2022

Cited by 7 | Viewed by 1500

Abstract

Understanding the influence of cropping systems on non-point source pollution (NPSP) is crucial, since NPSP has become the major nutrient source of lake eutrophication. How to identify the characteristics of the N and P balance at different spatial and temporal scales remains a challenge in pollution control and decision-making. In this study, we built a soil and water assessment tool (SWAT) model coupled with an export coefficient model for a NPSP simulation in the North of Erhai Lake Basin (NELB). A method was proposed to study the N and P transport from fields and the individual sub-basins to Erhai Lake using SWAT simulation. The results showed that the N and P loss fields were mainly situated in the vicinity of the Fengyu river and along the mainstream of the Miju and Mici rivers. N and P loss fields were mainly occupied by rice–broad bean/rice–rapeseed crops and vegetables. While the critical N and P load contribution areas were situated in the vicinity of downstream of the Miju, Yong’an, and Luoshi rivers. The effects of different cropping systems on the N and P export to the watershed were insignificant in the NELB and decreased by 4–9% when changing cropping system compared to the original crops. The NPSP discharged from the critical areas was retained and purified by the flow and the reservoirs scattered along the rivers, and it was noticed that the N and P loss was mainly from the critical pollution discharge areas located downstream of Miju river. This study can provide an important simulation method for understanding NPSPs and, therefore, can help authorities improve agricultural land use and reduce lake pollution. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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15 pages, 1532 KiB

Open AccessArticle

Deep Learning Model for Global Spatio-Temporal Image Prediction

by Dušan P. Nikezić, Uzahir R. Ramadani, Dušan S. Radivojević, Ivan M. Lazović and Nikola S. Mirkov

Mathematics 2022, 10(18), 3392; https://doi.org/10.3390/math10183392 - 19 Sep 2022

Cited by 5 | Viewed by 2432

Abstract

Mathematical methods are the basis of most models that describe the natural phenomena around us. However, the well-known conventional mathematical models for atmospheric modeling have some limitations. Machine learning with Big Data is also based on mathematics but offers a new approach for modeling. There are two methodologies to develop deep learning models for spatio-temporal image prediction. On these bases, two models were built—ConvLSTM and CNN-LSTM—with two types of predictions, i.e., sequence-to-sequence and sequence-to-one, in order to forecast Aerosol Optical Thickness sequences. The input dataset for training was NASA satellite imagery MODAL2_E_AER_OD from Terra/MODIS satellites, which presents global Aerosol Optical Thickness with an 8 day temporal resolution from 2000 to the present. The obtained results show that the ConvLSTM sequence-to-one model had the lowest RMSE error and the highest Cosine Similarity value. The advantages of the developed DL models are that they can be executed in milliseconds on a PC, can be used for global-scale Earth observations, and can serve as tracers to study how the Earth’s atmosphere moves. The developed models can be used as transfer learning for similar image time-series forecasting models. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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17 pages, 45589 KiB

Open AccessArticle

Numerical Simulation Analysis of Difference from a Radial Resistivity Testing Method for Cylindrical Cores and a Conventional Testing Method

by Jiahuan He, Tangyan Liu, Long Wen, Tingting He, Min Li, Jin Li, Li Wang and Xin Yao

Mathematics 2022, 10(16), 2885; https://doi.org/10.3390/math10162885 - 12 Aug 2022

Cited by 2 | Viewed by 1056

Abstract

Rock resistivity is a major geophysical technical parameter in geological and geotechnical engineering, geothermal prospecting, and oil and gas exploration. Its accurate measurement is of great significance to achieve the goal of “carbon peak and carbon neutrality”. To solve anisotropic problems, a method to test the radial resistivity in cylindrical core samples has been proposed and has been deemed the universal method, as it has the virtues of no specially processed sample being needed and nondestructive testing. However, there is still a difference in the radial resistivities obtained from this method and another testing method that is commonly used for cuboid samples. Furthermore, the differences between these methods have not yet been made clear in China or elsewhere. Therefore, we compared the results of the above-two testing methods via numerical simulations after establishing the potential field distribution, and, in combination with their methodological principles, illustrated the differences between the resistivities determined in samples with distinct shapes obtained using the two testing methods, summarized the conditions when there was zero difference and considerable difference when using the two methods, and provided a theoretical basis for the reasonable selection of an appropriate method to test the resistivity anisotropy. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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19 pages, 1341 KiB

Open AccessArticle

Effect of Green Supply Chain Management Practices on Environmental Performance: Case of Mexican Manufacturing Companies

by Jorge Luis García Alcaraz, José Roberto Díaz Reza, Karina Cecilia Arredondo Soto, Guadalupe Hernández Escobedo, Ari Happonen, Rita Puig I Vidal and Emilio Jiménez Macías

Mathematics 2022, 10(11), 1877; https://doi.org/10.3390/math10111877 - 30 May 2022

Cited by 25 | Viewed by 4213

Abstract

Managers implement several Green Supply Chain Management (GSCM) practices to improve sustainability and economic performance, such as environmental management systems (EMS), eco-design (ED), source reduction (SR) and attending to external environmental management (EEM) requirements; however, the relationship among them requires a deep study. This paper reports the case of the Mexican maquiladora industry, analyzing the main relationships among GSCM practices with environmental impact (EI) and environmental cost savings (ECS). The analysis reports three structural equation models (SEM) developed as simple, second-order, and mediating models. Those relationships are tested using 160 responses to a survey applied to the Mexican maquiladora industry and with partial least squares algorithms (PLS), where conditional probabilities for different scenarios in latent variables are also reported. Findings indicate that EMS has a direct effect on EI (β = 0.442) and ECS (β = 0.227), indicating that EMS reduces EI and cost associated with the production process; however, ED has no direct effect on EI (β = 0.019) and ECS ((β = 0.006), and it can be due to the maquiladora nature as foreign companies focused on manufacturing and not to product design. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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17 pages, 1994 KiB

Open AccessArticle

Modeling Semiarid River–Aquifer Systems with Bayesian Networks and Artificial Neural Networks

by Ana D. Maldonado, María Morales, Francisco Navarro, Francisco Sánchez-Martos and Pedro A. Aguilera

Mathematics 2022, 10(1), 107; https://doi.org/10.3390/math10010107 - 29 Dec 2021

Cited by 4 | Viewed by 1514

Abstract

In semiarid areas, precipitations usually appear in the form of big and brief floods, which affect the aquifer through water infiltration, causing groundwater temperature changes. These changes may have an impact on the physical, chemical and biological processes of the aquifer and, thus, modeling the groundwater temperature variations associated with stormy precipitation episodes is essential, especially since this kind of precipitation is becoming increasingly frequent in semiarid regions. In this paper, we compare the predictive performance of two popular tools in statistics and machine learning, namely Bayesian networks (BNs) and artificial neural networks (ANNs), in modeling groundwater temperature variation associated with precipitation events. More specifically, we trained a total of 2145 ANNs with different node configurations, from one to five layers. On the other hand, we trained three different BNs using different structure learning algorithms. We conclude that, while both tools are equivalent in terms of accuracy for predicting groundwater temperature drops, the computational cost associated with the estimation of Bayesian networks is significantly lower, and the resulting BN models are more versatile and allow a more detailed analysis. Full article

(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)

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