Entropy

Research

27 pages, 8663 KiB

Open AccessArticle

Tsallis Entropy for Assessing Spatial Uncertainty Associated with Mean Annual Runoff of Quaternary Catchments of the Middle Vaal Basin in South Africa

by Masengo Ilunga

Entropy 2020, 22(9), 1050; https://doi.org/10.3390/e22091050 - 19 Sep 2020

Viewed by 2541

Abstract

This study assesses mainly the uncertainty of the mean annual runoff (MAR) for quaternary catchments (QCs) considered as metastable nonextensive systems (from Tsalllis entropy) in the Middle Vaal catchment. The study is applied to the surface water resources (WR) of the South Africa [...] Read more.

This study assesses mainly the uncertainty of the mean annual runoff (MAR) for quaternary catchments (QCs) considered as metastable nonextensive systems (from Tsalllis entropy) in the Middle Vaal catchment. The study is applied to the surface water resources (WR) of the South Africa 1990 (WR90), 2005 (WR2005) and 2012 (WR2012) data sets. The q-information index (from the Tsalllis entropy) is used here as a deviation indicator for the spatial evolution of uncertainty for the different QCs, using the Shannon entropy as a baseline. It enables the determination of a (virtual) convergence point, zone of positive and negative uncertainty deviation, zone of null deviation and chaotic zone for each data set. Such a determination is not possible on the basis of the Shannon entropy alone as a measure for the MAR uncertainty of QCs, i.e., when they are viewed as extensive systems. Finally, the spatial distributions for the zones of the q-uncertainty deviation (gain or loss in information) of the MAR are derived and lead to iso q-uncertainty deviation maps. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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23 pages, 2612 KiB

Open AccessArticle

Assessing and Predicting the Water Resources Vulnerability under Various Climate-Change Scenarios: A Case Study of Huang-Huai-Hai River Basin, China

by Yan Chen, Yazhong Feng, Fan Zhang, Fan Yang and Lei Wang

Entropy 2020, 22(3), 333; https://doi.org/10.3390/e22030333 - 14 Mar 2020

Cited by 9 | Viewed by 3354

Abstract

The Huang-Huai-Hai River Basin plays an important strategic role in China’s economic development, but severe water resources problems restrict the development of the three basins. Most of the existing research is focused on the trends of single hydrological and meteorological indicators. However, there [...] Read more.

The Huang-Huai-Hai River Basin plays an important strategic role in China’s economic development, but severe water resources problems restrict the development of the three basins. Most of the existing research is focused on the trends of single hydrological and meteorological indicators. However, there is a lack of research on the cause analysis and scenario prediction of water resources vulnerability (WRV) in the three basins, which is the very important foundation for the management of water resources. First of all, based on the analysis of the causes of water resources vulnerability, this article set up the evaluation index system of water resource vulnerability from three aspects: water quantity, water quality and disaster. Then, we use the Improved Blind Deletion Rough Set (IBDRS) method to reduce the dimension of the index system, and we reduce the original 24 indexes to 12 evaluation indexes. Third, by comparing the accuracy of random forest (RF) and artificial neural network (ANN) models, we use the RF model with high fitting accuracy as the evaluation and prediction model. Finally, we use 12 evaluation indexes and an RF model to analyze the trend and causes of water resources vulnerability in three basins during 2000–2015, and further predict the scenarios in 2020 and 2030. The results show that the vulnerability level of water resources in the three basins has been improved during 2000–2015, and the three river basins should follow the development of scenario 1 to ensure the safety of water resources. The research proved that the combination of IBDRS and an RF model is a very effective method to evaluate and forecast the vulnerability of water resources in the Huang-Huai-Hai River Basin. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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11 pages, 241 KiB

Open AccessArticle

Comprehensive Evaluation on Soil Properties and Artemisia ordosica Growth under Combined Application of Fly Ash and Polyacrylamide in North China

by Jiping Niu, Xiaoling Su, Zejun Tang, Kaiwen Lu, Gengxi Zhang, Fengxin Wang and Jie Wang

Entropy 2020, 22(2), 148; https://doi.org/10.3390/e22020148 - 27 Jan 2020

Cited by 3 | Viewed by 2107

Abstract

A field experiment was conducted to investigate the combined application effects of fly ash (FA) (0, 5%, 10%, and 15% (w/w) soil) and polyacrylamide (PAM) (0, 0.006% and 0.012% (w/w) soil) on the edge of [...] Read more.

A field experiment was conducted to investigate the combined application effects of fly ash (FA) (0, 5%, 10%, and 15% (w/w) soil) and polyacrylamide (PAM) (0, 0.006% and 0.012% (w/w) soil) on the edge of Hobq Desert in Inner Mongolia, China from May 2016 to October 2018. Seven different ratios of FA and PAM were selected as evaluation objects, a total of 14 soil property indices and 9 Artemisia ordosica growth indices were selected as evaluation indicators, and the entropy weight method was employed to evaluate the soil physicochemical properties and vegetation growth performances under FA and PAM amendments. The results showed that the F15P1 (15% FA + 0.006% PAM) and F5P1 (5% FA + 0.006% PAM) were the effective treatments for soil improvement and Artemisia ordosica growth respectively. Considering the soil properties and Artemisia ordosica growth in 2016–2018 synthetically, the highest score was observed in the F5P1, followed by the F5P2 (5% FA + 0.012% PAM) and F10P1 (10% FA + 0.006% PAM) treatments. The optimal amounts for FA and PAM should be recommended as 5% and 0.006%, respectively. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

17 pages, 3531 KiB

Open AccessArticle

Analysis of Streamflow Complexity Based on Entropies in the Weihe River Basin, China

by Weijie Ma, Yan Kang and Songbai Song

Entropy 2020, 22(1), 38; https://doi.org/10.3390/e22010038 - 26 Dec 2019

Cited by 14 | Viewed by 4646

Abstract

The study on the complexity of streamflow has guiding significance for hydrologic simulation, hydrologic prediction, water resources planning and management. Utilizing monthly streamflow data from four hydrologic control stations in the mainstream of the Weihe River in China, the methods of approximate entropy, [...] Read more.

The study on the complexity of streamflow has guiding significance for hydrologic simulation, hydrologic prediction, water resources planning and management. Utilizing monthly streamflow data from four hydrologic control stations in the mainstream of the Weihe River in China, the methods of approximate entropy, sample entropy, two-dimensional entropy and fuzzy entropy are introduced into hydrology research to investigate the spatial distribution and dynamic change in streamflow complexity. The results indicate that the complexity of the streamflow has spatial differences in the Weihe River watershed, exhibiting an increasing tendency along the Weihe mainstream, except at the Linjiacun station, which may be attributed to the elevated anthropogenic influence. Employing sliding entropies, the variation points of the streamflow time series at the Weijiabu station were identified in 1968, 1993 and 2003, and those at the Linjiacun station, Xianyang station and Huaxian station occurred in 1971, 1993 and 2003. In the verification of the above points, the minimum value of t-test is 3.7514, and that of Brown–Forsythe is 7.0307, far exceeding the significance level of 95%. Also, the cumulative anomaly can detect two variation points. The t-test, Brown–Forsythe test and cumulative anomaly test strengthen the conclusion regarding the availability of entropies for identifying the streamflow variability. The results lead us to conclude that four entropies have good application effects in the complexity analysis of the streamflow time series. Moreover, two-dimensional entropy and fuzzy entropy, which have been rarely used in hydrology research before, demonstrate better continuity and relative consistency, are more suitable for short and noisy hydrologic time series and more effectively identify the streamflow complexity. The results could be very useful in identifying variation points in the streamflow time series. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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14 pages, 321 KiB

Open AccessArticle

Intuitionistic Fuzzy Entropy for Group Decision Making of Water Engineering Project Delivery System Selection

by Xun Liu, Fei Qian, Lingna Lin, Kun Zhang and Lianbo Zhu

Entropy 2019, 21(11), 1101; https://doi.org/10.3390/e21111101 - 11 Nov 2019

Cited by 12 | Viewed by 2571

Abstract

The project delivery mode is an extremely important link in the life cycle of water engineering. Many cases show that increases in the costs, construction period, and claims in the course of the implementation of water engineering are related to the decision of [...] Read more.

The project delivery mode is an extremely important link in the life cycle of water engineering. Many cases show that increases in the costs, construction period, and claims in the course of the implementation of water engineering are related to the decision of the project delivery mode in the early stages. Therefore, it is particularly important to choose a delivery mode that matches the water engineering. On the basis of identifying the key factors that affect the decision on the project delivery system and establishing a set of index systems, a comprehensive decision of engineering transaction is essentially considered to be a fuzzy multi-attribute group decision. In this study, intuitionistic fuzzy entropy was used to determine the weight of the influencing factors on the engineering transaction mode; then, intuitionistic fuzzy entropy was used to determine the weight of decision experts. Thus, a comprehensive scheme-ranking model based on an intuitionistic fuzzy hybrid average (IFHA) operator and intuitionistic fuzzy weighted average (IFWA) operator was established. Finally, a practical case analysis of a hydropower station further demonstrated the feasibility, objectivity, and scientific nature of the decision model. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

16 pages, 8536 KiB

Open AccessArticle

Introducing the Ensemble-Based Dual Entropy and Multiobjective Optimization for Hydrometric Network Design Problems: EnDEMO

by Jongho Keum, Frezer Seid Awol, Jacob Ursulak and Paulin Coulibaly

Entropy 2019, 21(10), 947; https://doi.org/10.3390/e21100947 - 27 Sep 2019

Cited by 8 | Viewed by 3230

Abstract

Entropy applications in hydrometric network design problems have been extensively studied in the most recent decade. Although many studies have successfully found the optimal networks, there have been assumptions which could not be logically integrated into their methodology. One of the major assumptions [...] Read more.

Entropy applications in hydrometric network design problems have been extensively studied in the most recent decade. Although many studies have successfully found the optimal networks, there have been assumptions which could not be logically integrated into their methodology. One of the major assumptions is the uncertainty that can arise from data processing, such as time series simulation for the potential stations, and the necessary data quantization in entropy calculations. This paper introduces a methodology called ensemble-based dual entropy and multiobjective optimization (EnDEMO), which considers uncertainty from the ensemble generation of the input data. The suggested methodology was applied to design hydrometric networks in the Nelson-Churchill River Basin in central Canada. First, the current network was evaluated by transinformation analysis. Then, the optimal networks were explored using the traditional deterministic network design method and the newly proposed ensemble-based method. Result comparison showed that the most frequently selected stations by EnDEMO were fewer and appeared more reliable for practical use. The maps of station selection frequency from both DEMO and EnDEMO allowed us to identify preferential locations for additional stations; however, EnDEMO provided a more robust outcome than the traditional approach. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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25 pages, 3442 KiB

Open AccessArticle

Decision-Making of Irrigation Scheme for Soybeans in the Huaibei Plain Based on Grey Entropy Weight and Grey Relation–Projection Pursuit

by Yi Cui, Shangming Jiang, Juliang Jin, Ping Feng and Shaowei Ning

Entropy 2019, 21(9), 877; https://doi.org/10.3390/e21090877 - 9 Sep 2019

Cited by 15 | Viewed by 3449

Abstract

To provide a scientific reference for formulating an effective soybean irrigation schedule in the Huaibei Plain, potted water deficit experiments with nine alternative irrigation schemes during the 2015 and 2016 seasons were conducted. An irrigation scheme decision-making index system was established from the [...] Read more.

To provide a scientific reference for formulating an effective soybean irrigation schedule in the Huaibei Plain, potted water deficit experiments with nine alternative irrigation schemes during the 2015 and 2016 seasons were conducted. An irrigation scheme decision-making index system was established from the aspects of crop water consumption, crop growth process and crop water use efficiency. Moreover, a grey entropy weight method and a grey relation–projection pursuit model were proposed to calculate the weight of each decision-making index. Then, nine alternative schemes were sorted according to the comprehensive grey relation degree of each scheme in the two seasons. The results showed that, when using the entropy weight method or projection pursuit model to determine index weight, it was more direct and effective to obtain the corresponding entropy value or projection eigenvalue according to the sequence of the actual study object. The decision-making results from the perspective of actual soybean growth responses at each stage for various irrigation schemes were mostly consistent in 2015 and 2016. Specifically, for an integrated target of lower water consumption and stable biomass yields, the scheme with moderate-deficit irrigation at the soybean branching stage or seedling stage and adequate irrigation at the flowering-podding and seed filling stages is relatively optimal. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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17 pages, 3506 KiB

Open AccessArticle

Application of the Entropy Spectral Method for Streamflow and Flood-Affected Area Forecasting in the Brahmaputra River Basin

by Xiaobo Wang, Shaoqiang Wang and Huijuan Cui

Entropy 2019, 21(8), 722; https://doi.org/10.3390/e21080722 - 25 Jul 2019

Cited by 1 | Viewed by 2979

Abstract

Reliable streamflow and flood-affected area forecasting is vital for flood control and risk assessment in the Brahmaputra River basin. Based on the satellite remote sensing from four observation sites and ground observation at the Bahadurabad station, the Burg entropy spectral analysis (BESA), the [...] Read more.

Reliable streamflow and flood-affected area forecasting is vital for flood control and risk assessment in the Brahmaputra River basin. Based on the satellite remote sensing from four observation sites and ground observation at the Bahadurabad station, the Burg entropy spectral analysis (BESA), the configurational entropy spectral analysis (CESA), maximum likelihood (MLE), ordinary least squares (OLS), and the Yule–Walker (YW) method were developed for the spectral analysis and flood-season streamflow forecasting in the basin. The results indicated that the BESA model had a great advantage in the streamflow forecasting compared with the CESA and other traditional methods. Taking 20% as the allowable error, the forecast passing rate of the BESA model trained by the remote sensing data can reach 93% in flood seasons during 2003–2017, which was significantly higher than that trained by observed streamflow series at the Bahadurabad station. Furthermore, the segmented flood-affected area function with the input of the streamflow forecasted by the BESA model was able to forecast the annual trend of the flood-affected area of rice and tea but needed further improvement in extreme rainfall years. This paper provides a better flood-season streamflow forecasting method for the Brahmaputra River basin, which has the potential to be coupled with hydrological process models to enhance the forecasting accuracy. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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22 pages, 4938 KiB

Open AccessArticle

A Method for Improving Controlling Factors Based on Information Fusion for Debris Flow Susceptibility Mapping: A Case Study in Jilin Province, China

by Qiang Dou, Shengwu Qin, Yichen Zhang, Zhongjun Ma, Junjun Chen, Shuangshuang Qiao, Xiuyu Hu and Fei Liu

Entropy 2019, 21(7), 695; https://doi.org/10.3390/e21070695 - 15 Jul 2019

Cited by 12 | Viewed by 3932

Abstract

Debris flow is one of the most frequently occurring geological disasters in Jilin province, China, and such disasters often result in the loss of human life and property. The objective of this study is to propose and verify an information fusion (IF) method [...] Read more.

Debris flow is one of the most frequently occurring geological disasters in Jilin province, China, and such disasters often result in the loss of human life and property. The objective of this study is to propose and verify an information fusion (IF) method in order to improve the factors controlling debris flow as well as the accuracy of the debris flow susceptibility map. Nine layers of factors controlling debris flow (i.e., topography, elevation, annual precipitation, distance to water system, slope angle, slope aspect, population density, lithology and vegetation coverage) were taken as the predictors. The controlling factors were improved by using the IF method. Based on the original controlling factors and the improved controlling factors, debris flow susceptibility maps were developed while using the statistical index (SI) model, the analytic hierarchy process (AHP) model, the random forest (RF) model, and their four integrated models. The results were compared using receiver operating characteristic (ROC) curve, and the spatial consistency of the debris flow susceptibility maps was analyzed while using Spearman’s rank correlation coefficients. The results show that the IF method that was used to improve the controlling factors can effectively enhance the performance of the debris flow susceptibility maps, with the IF-SI-RF model exhibiting the best performance in terms of debris flow susceptibility mapping. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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24 pages, 3339 KiB

Open AccessArticle

Invasive Plant Species Establishment and Range Dynamics in Sri Lanka under Climate Change

by Champika S. Kariyawasam, Lalit Kumar and Sujith S. Ratnayake

Entropy 2019, 21(6), 571; https://doi.org/10.3390/e21060571 - 5 Jun 2019

Cited by 47 | Viewed by 7541

Abstract

Plant invasion has been widely recognized as an agent of global change that has the potential to have severe impacts under climate change. The challenges posed by invasive alien plant species (IAPS) on biodiversity and ecosystem stability is growing and not adequately studied, [...] Read more.

Plant invasion has been widely recognized as an agent of global change that has the potential to have severe impacts under climate change. The challenges posed by invasive alien plant species (IAPS) on biodiversity and ecosystem stability is growing and not adequately studied, especially in developing countries. Defining climate suitability for multiple invasive plants establishment is important for early and strategic interventions to control and manage plant invasions. We modeled priority IAPS in Sri Lanka to identify the areas of greatest climatic suitability for their establishment and observed how these areas could be altered under projected climate change. We used Maximum Entropy method to model 14 nationally significant IAPS under representative concentration pathways 4.5 and 8.5 for 2050 and 2070. The combined climate suitability map produced by summing up climatic suitability of 14 IAPS was further classified into five classes in ArcMap as very high, high, moderate, low, and very low. South and west parts of Sri Lanka are projected to have potentially higher climatic suitability for a larger number of IAPS. We observed suitable area changes (gains and losses) in all five classes of which two were significant enough to make an overall negative impact i.e., (i) contraction of the very low class and (ii) expansion of the moderate class. Both these changes trigger the potential risk from IAPS in Sri Lanka in the future. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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22 pages, 8132 KiB

Open AccessArticle

Offshore Platform Extraction Using RadarSat-2 SAR Imagery: A Two-Parameter CFAR Method Based on Maximum Entropy

by Qi Wang, Jing Zhang and Fenzhen Su

Entropy 2019, 21(6), 556; https://doi.org/10.3390/e21060556 - 2 Jun 2019

Cited by 13 | Viewed by 3782

Abstract

The ability to determine the number and location of offshore platforms is of great significance for offshore oil spill monitoring and offshore oil and gas development. Considering the problem that the detection threshold parameters of the two-parameter constant false alarm rate (CFAR) algorithm [...] Read more.

The ability to determine the number and location of offshore platforms is of great significance for offshore oil spill monitoring and offshore oil and gas development. Considering the problem that the detection threshold parameters of the two-parameter constant false alarm rate (CFAR) algorithm require manual and repeated adjustment of the during the extraction of offshore platform targets, this paper proposes a two-parameter CFAR target detection method based on maximum entropy based on information entropy theory. First, a series of threshold parameters are obtained using the two-parameter CFAR algorithm for target detection. Then, according to the maximum entropy principle, the optimal threshold is estimated to obtain the target detection results of the possible offshore platform. Finally, the neighborhood analysis method is used to eliminate false alarm targets such as ships, and the final target of the offshore platform is obtained. In this study, we conducted offshore platform extraction experiments and an accuracy evaluation using data from the Pearl River Estuary Basin of the South China Sea. The results show that the proposed method for platform extraction achieves an accuracy rate of 97.5% and obtains the ideal offshore platform distribution information. Thus, the proposed method can objectively obtain the optimal target detection threshold parameters, greatly reduce the influence of subjective parameter setting on the extraction results during the target detection process and effectively extract offshore platform targets. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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12 pages, 2209 KiB

Open AccessArticle

Regionalization of Daily Soil Moisture Dynamics Using Wavelet-Based Multiscale Entropy and Principal Component Analysis

by Yuqing Sun and Jun Niu

Entropy 2019, 21(6), 548; https://doi.org/10.3390/e21060548 - 30 May 2019

Cited by 3 | Viewed by 3134

Abstract

Hydrological regionalization is a useful step in hydrological modeling and prediction. The regionalization is not always straightforward, however, due to the lack of long-term hydrological data and the complex multi-scale variability features embedded in the data. This study examines the multiscale soil moisture [...] Read more.

Hydrological regionalization is a useful step in hydrological modeling and prediction. The regionalization is not always straightforward, however, due to the lack of long-term hydrological data and the complex multi-scale variability features embedded in the data. This study examines the multiscale soil moisture variability for the simulated data on a grid cell base obtained from a large-scale hydrological model, and clusters the grid-cell based soil moisture data using wavelet-based multiscale entropy and principal component analysis, over the Xijiang River basin in South China, for the period of 2002–2010. The effective regionalization, for 169 grid cells with the special resolution of 0.5° × 0.5°, produced homogeneous groups based on the pattern of wavelet-based entropy information. Four distinct modes explain 80.14% of the total embedded variability of the transformed wavelet power across different timescales. Moreover, the possible implications of the regionalization results for local hydrological applications, such as parameter estimation for an ungagged catchment and designing a uniform prediction strategy for a sub-area in a large-scale basin, are discussed. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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20 pages, 3280 KiB

Open AccessArticle

Quantitative Assessment and Diagnosis for Regional Agricultural Drought Resilience Based on Set Pair Analysis and Connection Entropy

by Menglu Chen, Shaowei Ning, Yi Cui, Juliang Jin, Yuliang Zhou and Chengguo Wu

Entropy 2019, 21(4), 373; https://doi.org/10.3390/e21040373 - 5 Apr 2019

Cited by 17 | Viewed by 3243

Abstract

Assessment and diagnosis of regional agricultural drought resilience (RADR) is an important groundwork to identify the shortcomings of regional agriculture to resist drought disasters accurately. In order to quantitatively assess the capacity of regional agriculture system to reduce losses from drought disasters under [...] Read more.

Assessment and diagnosis of regional agricultural drought resilience (RADR) is an important groundwork to identify the shortcomings of regional agriculture to resist drought disasters accurately. In order to quantitatively assess the capacity of regional agriculture system to reduce losses from drought disasters under complex conditions and to identify vulnerability indexes, an assessment and diagnosis model for RADR was established. Firstly, this model used the improved fuzzy analytic hierarchy process to determine the index weights, then proposed an assessment method based on connection number and an improved connection entropy. Furthermore, the set pair potential based on subtraction was used to diagnose the vulnerability indexes. In addition, a practical application had been carried out in the region of the Huaibei Plain in Anhui Province. The evaluation results showed that the RADR in this area from 2005 to 2014 as a whole was in a relatively weak situation. However, the average grade values had decreased from 3.144 to 2.790 during these 10 years and the RADR had an enhanced tendency. Moreover, the possibility of RADR enhancement for six cities in this region decreased from east to west, and the drought emergency condition was the weak link of the RADR in the Huaibei Plain. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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24 pages, 15865 KiB

Open AccessArticle

The Influence of Different Knowledge-Driven Methods on Landslide Susceptibility Mapping: A Case Study in the Changbai Mountain Area, Northeast China

by Zhongjun Ma, Shengwu Qin, Chen Cao, Jiangfeng Lv, Guangjie Li, Shuangshuang Qiao and Xiuyu Hu

Entropy 2019, 21(4), 372; https://doi.org/10.3390/e21040372 - 5 Apr 2019

Cited by 23 | Viewed by 4171

Abstract

Landslides are one of the most frequent geomorphic hazards, and they often result in the loss of property and human life in the Changbai Mountain area (CMA), Northeast China. The objective of this study was to produce and compare landslide susceptibility maps for [...] Read more.

Landslides are one of the most frequent geomorphic hazards, and they often result in the loss of property and human life in the Changbai Mountain area (CMA), Northeast China. The objective of this study was to produce and compare landslide susceptibility maps for the CMA using an information content model (ICM) with three knowledge-driven methods (the artificial hierarchy process with the ICM (AHP-ICM), the entropy weight method with the ICM (EWM-ICM), and the rough set with the ICM (RS-ICM)) and to explore the influence of different knowledge-driven methods for a series of parameters on the accuracy of landslide susceptibility mapping (LSM). In this research, the landslide inventory data (145 landslides) were randomly divided into a training dataset: 70% (81 landslides) were used for training the models and 30% (35 landslides) were used for validation. In addition, 13 layers of landslide conditioning factors, namely, altitude, slope gradient, slope aspect, lithology, distance to faults, distance to roads, distance to rivers, annual precipitation, land type, normalized difference vegetation index (NDVI), topographic wetness index (TWI), plan curvature, and profile curvature, were taken as independent, causal predictors. Landslide susceptibility maps were developed using the ICM, RS-ICM, AHP-ICM, and EWM-ICM, in which weights were assigned to every conditioning factor. The resultant susceptibility was validated using the area under the ROC curve (AUC) method. The success accuracies of the landslide susceptibility maps produced by the ICM, RS-ICM, AHP-ICM, and EWM-ICM methods were 0.931, 0.939, 0.912, and 0.883, respectively, with prediction accuracy rates of 0.926, 0.927, 0.917, and 0.878 for the ICM, RS-ICM, AHP-ICM, and EWM-ICM, respectively. Hence, it can be concluded that the four models used in this study gave close results, with the RS-ICM exhibiting the best performance in landslide susceptibility mapping. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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17 pages, 1727 KiB

Open AccessArticle

Agricultural Water Resources Management Using Maximum Entropy and Entropy-Weight-Based TOPSIS Methods

by Mo Li, Hao Sun, Vijay P. Singh, Yan Zhou and Mingwei Ma

Entropy 2019, 21(4), 364; https://doi.org/10.3390/e21040364 - 4 Apr 2019

Cited by 39 | Viewed by 5116

Abstract

Allocation and management of agricultural water resources is an emerging concern due to diminishing water supplies and increasing water demands. To achieve economic, social, and environmental goals in a specific irrigation district, decisions should be made subject to the changing water supply and [...] Read more.

Allocation and management of agricultural water resources is an emerging concern due to diminishing water supplies and increasing water demands. To achieve economic, social, and environmental goals in a specific irrigation district, decisions should be made subject to the changing water supply and water demand—the two critical random parameters in agricultural water resources management. This paper presents the foundations of a systematic framework for agricultural water resources management, including determination of distribution functions, joint probability of water supply and water demand, optimal allocation of agricultural water resources, and evaluation of various schemes according to agricultural water resources carrying capacity. The maximum entropy method is used to estimate parameters of probability distributions of water supply and demand, which is the basic for the other parts of the framework. The entropy-weight-based TOPSIS method is applied to evaluate agricultural water resources allocation schemes, because it avoids the subjectivity of weight determination and reflects the dynamic changing trend of agricultural water resources carrying capacity. A case study using an irrigation district in Northeast China is used to demonstrate the feasibility and applicability of the framework. It is found that the framework works effectively to balance multiple objectives and provides alternative schemes, considering the combinatorial variety of water supply and water demand, which are conducive to agricultural water resources planning. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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13 pages, 3112 KiB

Open AccessArticle

Application of Entropy Spectral Method for Streamflow Forecasting in Northwest China

by Gengxi Zhang, Zhenghong Zhou, Xiaoling Su and Olusola O. Ayantobo

Entropy 2019, 21(2), 132; https://doi.org/10.3390/e21020132 - 1 Feb 2019

Cited by 4 | Viewed by 3111

Abstract

Streamflow forecasting is vital for reservoir operation, flood control, power generation, river ecological restoration, irrigation and navigation. Although monthly streamflow time series are statistic, they also exhibit seasonal and periodic patterns. Using maximum Burg entropy, maximum configurational entropy and minimum relative entropy, the [...] Read more.

Streamflow forecasting is vital for reservoir operation, flood control, power generation, river ecological restoration, irrigation and navigation. Although monthly streamflow time series are statistic, they also exhibit seasonal and periodic patterns. Using maximum Burg entropy, maximum configurational entropy and minimum relative entropy, the forecasting models for monthly streamflow series were constructed for five hydrological stations in northwest China. The evaluation criteria of average relative error (RE), root mean square error (RMSE), correlation coefficient (R) and determination coefficient (DC) were selected as performance metrics. Results indicated that the RESA model had the highest forecasting accuracy, followed by the CESA model. However, the BESA model had the highest forecasting accuracy in a low-flow period, and the prediction accuracies of RESA and CESA models in the flood season were relatively higher. In future research, these entropy spectral analysis methods can further be applied to other rivers to verify the applicability in the forecasting of monthly streamflow in China. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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15 pages, 1719 KiB

Open AccessArticle

Estimating the Bed-Load Layer Thickness in Open Channels by Tsallis Entropy

by Zhongfan Zhu and Jingshan Yu

Entropy 2019, 21(2), 123; https://doi.org/10.3390/e21020123 - 29 Jan 2019

Cited by 8 | Viewed by 3467

Abstract

In the research field of river dynamics, the thickness of bed-load is an important parameter in determining sediment discharge in open channels. Some studies have estimated the bed-load thickness from theoretical and/or experimental perspectives. This study attempts to propose the mathematical formula for [...] Read more.

In the research field of river dynamics, the thickness of bed-load is an important parameter in determining sediment discharge in open channels. Some studies have estimated the bed-load thickness from theoretical and/or experimental perspectives. This study attempts to propose the mathematical formula for the bed-load thickness by using the Tsallis entropy theory. Assuming the bed-load thickness is a random variable and using the method for the maximization of the entropy function, the present study derives an explicit expression for the thickness of the bed-load layer as a function with non-dimensional shear stress, by adopting a hypothesis regarding the cumulative distribution function of the bed-load thickness. This expression is verified against six experimental datasets and are also compared with existing deterministic models and the Shannon entropy-based expression. It has been found that there is good agreement between the derived expression and the experimental data, and the derived expression has a better fitting accuracy than some existing deterministic models. It has been also found that the derived Tsallis entropy-based expression has a comparable prediction ability for experimental data to the Shannon entropy-based expression. Finally, the impacts of the mass density of the particle and particle diameter on the bed-load thickness in open channels are also discussed based on this derived expression. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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16 pages, 12541 KiB

Open AccessArticle

Estimation of Soil Depth Using Bayesian Maximum Entropy Method

by Kuo-Wei Liao, Jia-Jun Guo, Jen-Chen Fan, Chien Lin Huang and Shao-Hua Chang

Entropy 2019, 21(1), 69; https://doi.org/10.3390/e21010069 - 15 Jan 2019

Cited by 4 | Viewed by 3988

Abstract

Soil depth plays an important role in landslide disaster prevention and is a key factor in slopeland development and management. Existing soil depth maps are outdated and incomplete in Taiwan. There is a need to improve the accuracy of the map. The Kriging [...] Read more.

Soil depth plays an important role in landslide disaster prevention and is a key factor in slopeland development and management. Existing soil depth maps are outdated and incomplete in Taiwan. There is a need to improve the accuracy of the map. The Kriging method, one of the most frequently adopted estimation approaches for soil depth, has room for accuracy improvements. An appropriate soil depth estimation method is proposed, in which soil depth is estimated using Bayesian Maximum Entropy method (BME) considering space distribution of measured soil depth and impact of physiographic factors. BME divides analysis data into groups of deterministic and probabilistic data. The deterministic part are soil depth measurements in a given area and the probabilistic part contains soil depth estimated by a machine learning-based soil depth estimation model based on physiographic factors including slope, aspect, profile curvature, plan curvature, and topographic wetness index. Accuracy of estimates calculated by soil depth grading, very shallow (<20 cm), shallow (20–50 cm), deep (50–90 cm), and very deep (>90 cm), suggests that BME is superior to the Kriging method with estimation accuracy up to 82.94%. The soil depth distribution map of Hsinchu, Taiwan made by BME with a soil depth error of ±5.62 cm provides a promising outcome which is useful in future applications, especially for locations without soil depth data. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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12 pages, 3576 KiB

Open AccessArticle

Precipitation Complexity and its Spatial Difference in the Taihu Lake Basin, China

by Jian Hu, Yong Liu and Yan-Fang Sang

Entropy 2019, 21(1), 48; https://doi.org/10.3390/e21010048 - 10 Jan 2019

Cited by 13 | Viewed by 3813

Abstract

Due to the rapid urbanization development, the precipitation variability in the Taihu Lake basin (TLB) in East China has become highly complex over the last decades. However, there is limited understanding of the spatiotemporal variability of precipitation complexity and its relationship with the [...] Read more.

Due to the rapid urbanization development, the precipitation variability in the Taihu Lake basin (TLB) in East China has become highly complex over the last decades. However, there is limited understanding of the spatiotemporal variability of precipitation complexity and its relationship with the urbanization development in the region. In this article, by considering the whole urbanization process, we use the SampEn index to investigate the precipitation complexity and its spatial differences in different urbanization areas (old urban area, new urban area and suburbs) in TLB. Results indicate that the precipitation complexity and its changes accord well with the urbanization development process in TLB. Higher urbanization degrees correspond to greater complexity degrees of precipitation. Precipitation in old urban areas shows the greatest complexity compared with that in new urban areas and suburbs, not only for the entire precipitation process but also the precipitation extremes. There is a significant negative correlation between the annual precipitation and its SampEn value, and the same change of precipitation can cause a greater complexity change in old urbanization areas compared with the new urban areas and suburbs. It is noted that the enhanced precipitation complexity in a new urban area during recent decades cannot be ignored facing the expanding urbanization. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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21 pages, 2603 KiB

Open AccessArticle

Noise Reduction Method of Underwater Acoustic Signals Based on CEEMDAN, Effort-To-Compress Complexity, Refined Composite Multiscale Dispersion Entropy and Wavelet Threshold Denoising

by Guohui Li, Qianru Guan and Hong Yang

Entropy 2019, 21(1), 11; https://doi.org/10.3390/e21010011 - 24 Dec 2018

Cited by 30 | Viewed by 5368

Abstract

Owing to the problems that imperfect decomposition process of empirical mode decomposition (EMD) denoising algorithm and poor self-adaptability, it will be extremely difficult to reduce the noise of signal. In this paper, a noise reduction method of underwater acoustic signal denoising based on [...] Read more.

Owing to the problems that imperfect decomposition process of empirical mode decomposition (EMD) denoising algorithm and poor self-adaptability, it will be extremely difficult to reduce the noise of signal. In this paper, a noise reduction method of underwater acoustic signal denoising based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), effort-to-compress complexity (ETC), refined composite multiscale dispersion entropy (RCMDE) and wavelet threshold denoising is proposed. Firstly, the original signal is decomposed into several IMFs by CEEMDAN and noise IMFs can be identified according to the ETC of IMFs. Then, calculating the RCMDE of remaining IMFs, these IMFs are divided into three kinds of IMFs by RCMDE, namely noise-dominant IMFs, real signal-dominant IMFs, real IMFs. Finally, noise IMFs are removed, wavelet soft threshold denoising is applied to noise-dominant IMFs and real signal-dominant IMFs. The denoised signal can be obtained by combining the real IMFs with the denoised IMFs after wavelet soft threshold denoising. Chaotic signals with different signal-to-noise ratio (SNR) are used for denoising experiments by comparing with EMD_MSE_WSTD and EEMD_DE_WSTD, it shows that the proposed algorithm has higher SNR and smaller root mean square error (RMSE). In order to further verify the effectiveness of the proposed method, which is applied to noise reduction of real underwater acoustic signals. The results show that the denoised underwater acoustic signals not only eliminate noise interference also restore the topological structure of the chaotic attractors more clearly, which lays a foundation for the further processing of underwater acoustic signals. Full article

(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)

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