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Floods are the most frequent types of natural disasters. From the perspective of disaster management, indicators associated with floods are important for accurate flood risk assessment. However, the application of all indicators related to flood risk assessment decreases the evaluation efficiency, because the definitions of the indicators may overlap. Moreover, the volume of data required for collection and evaluation is significantly large, making the evaluation practically impossible. Thus, a scientific and objective method to select indicators for flood risk assessment based on the entropy theory was developed herein. First, the existing 28 assessment indicators were analyzed and probability‐based data were constructed for each indicator considering 28 districts in a midwestern region of Korea. The information quantity for each indicator was then obtained using marginal entropy and mutual information generated in the entropy theory. Next, the total information quantity based on the numbers of combination of indicators was derived by considering the information quantity for each indicator and the overlapping mutual information between the indicators. The maximum amount of information (161.55) was obtained by combining 18 out of the 28 flood risk indicators. The selected 18 indicators reflected regional characteristics better than those used in the existing method, demonstrating that the flood risk of the target area could be adequately assessed. [ABSTRACT FROM AUTHOR]

Abstract Floods are the most frequent types of natural disasters. From the perspective of disaster management, indicators associated with floods are important for accurate flood risk assessment. However, the application of all indicators related to flood risk assessment decreases the evaluation efficiency, because the definitions of the indicators may overlap. Moreover, the volume of data required for collection and evaluation is significantly large, making the evaluation practically impossible. Thus, a scientific and objective method to select indicators for flood risk assessment based on the entropy theory was developed herein. First, the existing 28 assessment indicators were analyzed and probability‐based data were constructed for each indicator considering 28 districts in a midwestern region of Korea. The information quantity for each indicator was then obtained using marginal entropy and mutual information generated in the entropy theory. Next, the total information quantity based on the numbers of combination of indicators was derived by considering the information quantity for each indicator and the overlapping mutual information between the indicators. The maximum amount of information (161.55) was obtained by combining 18 out of the 28 flood risk indicators. The selected 18 indicators reflected regional characteristics better than those used in the existing method, demonstrating that the flood risk of the target area could be adequately assessed.

Marginal entropy is one of the distances based on the graph entropy. Then, this entropy is computed by the Wiener index of graphs. In this paper, we obtain the marginal entropy of paths, stars, double stars, cycles and vertex-transitive graphs. [ABSTRACT FROM AUTHOR]

Hyperspectral remote sensing across multiple spatio-temporal scales allows for mapping and monitoring mangrove habitats to support urgent conservation efforts. The use of hyperspectral imagery for assessing mangroves is less common than for terrestrial forest ecosystems. In this study, two well-known measures in statistical physics, Mean Information Gain (MIG) and Marginal Entropy (ME), have been adapted to high spatial resolution (2.5 m) full range (Visible-Shortwave-Infrared) airborne hyperspectral imagery. These two spectral complexity metrics describe the spatial heterogeneity and the aspatial heterogeneity of the reflectance. In this study, we compare MIG and ME with surface reflectance for mapping mangrove extent and species composition in the Sierpe mangroves in Costa Rica. The highest accuracy for separating mangroves from forest was achieved with visible-near infrared (VNIR) reflectance (98.8% overall accuracy), following by shortwave infrared (SWIR) MIG and ME (98%). Our results also show that MIG and ME can discriminate dominant mangrove species with higher accuracy than surface reflectance alone (e.g., MIG–VNIR = 93.6% vs. VNIR Reflectance = 89.7%).

Histograms have extensively been used as a simple tool for nonparametric probability density function estimation. However, practically, the accuracy of some histogram-based derived quantities, such as the marginal entropy (ME), the joint entropy (JE), or the mutual information (MI) depends on the number of bins chosen for the histogram. In this paper, we investigate the binning problem of bi-histogram for the estimation of JE. By minimizing a theoretical mean square error (MSE) of JE estimation, we derive a new formula for the optimal number of bins of bi-histogram for continuous random variables. This novel JE estimation has been used in the MI estimation to avoid the error accumulation of joint MI between the class variable and feature subset in the feature selection. In a synthetic Gaussian feature selection problem, only the proposed method permits to retrieve the exact number of relevant features that explain the class variable when compared to a concurrent univariate estimator based on binning formula that has been proposed for ME estimation. In speech and speaker recognition applications, the proposed method permits to select a limited number of features which guaranties approximately the same or an even better recognition rate than using the total number of features. [ABSTRACT FROM AUTHOR]

The spatial and temporal variability of precipitation time series were investigated for the Hexi Corridor, in Northwest China, by analyzing the entropy information. The examinations were performed on monthly, seasonal, and annual timescales based on 29 meteorological stations for the period of 1961-2015. The apportionment entropy and intensity entropy were used to analyze the regional precipitation characteristics, including the intra-annual and decadal distribution of monthly and annual precipitation amounts, as well as the number of precipitation days within a year and a decade. The regions with high precipitation variability are found in the western part of the Hexi corridor and with less precipitation, and may have a high possibility of drought occurrence. The variability of the number of precipitation days decreased from the west to the east of the corridor. Higher variability, in terms of both of precipitation amount and intensity during crop-growing season, has been found in the recent decade. In addition, the correlation between entropy-based precipitation variability and the crop yield is also compared, and the crop yield in historical periods is found to be correlated with the precipitation intensity disorder index in the middle reaches of the Hexi corridor. [ABSTRACT FROM AUTHOR]

Oozing of groundwater in Jodhpur city in the desert area of Rajasthan, India has caused weakening of foundations and cellars of buildings and shops. It has become more significant since 1996 when Kaylana lake was connected with Rajiv Gandhi Lift Canal (RGLC) water supply and filling of the lake had started. This has resulted in fear among dwellers about any future calamity. The hydrogeological, hydrochemical and isotopic studies clearly indicated that the lake water is responsible for the oozing phenomenon in the area. This article highlights a landscape entropy approach to assess pathways causing rise in the level of groundwater integrating the measured lake water level and groundwater table in a few selected wells in the city. With the fractional information of lake water and groundwater, marginal entropies of lake water and depths to groundwater in the selected wells sites are calculated. Mutual information, on common uncertainty associated in the measurements of lake water and groundwater, is also provided. Subsequently, ratios of mutual information to marginal entropy of the lake water are used as a measure for demarcating the pathways of weak zones, which correlate well with the lineaments delineated from satellite imagery. The results of this study represent a base for additional insight on future work, which will help in tracing the connectivity of weak zones causing oozing of water in Jodhpur city, and evolving a plan for remedial measures. [ABSTRACT FROM AUTHOR]

A discrete entropy-based approach is used to assess the groundwater monitoring network that exists in Kodaganar River basin of Southern India. Since any monitoring system is essentially an information collection system, its technical design and evaluation require a quantifiable measure of information and this measure can be derived using entropy. The use of information-based measures of groundwater table shows that the existing monitoring network contains a sufficient number of wells but is not well designed for the measurement of groundwater level. Entropy-based results show that 15 wells are vital to measure regional groundwater level, not 28 wells which are being monitored effectively in this basin. [ABSTRACT FROM AUTHOR]

Summary: Employing the entropy concept spatial and temporal variability of precipitation time series were investigated for the State of Texas, USA. Marginal entropy was used to investigate the variability associated with monthly, seasonal and annual time series. Also, apportionment entropy and intensity entropy were used for investigating the intra-annual and decadal distributions of monthly and annual precipitation amounts and numbers of rainy days within a year and decade respectively. Finally, the Hurst exponent and the Mann–Kendall test were used to evaluate the long-term persistence and trend in the variability of precipitation. Distinct spatial patterns in annual series and different seasons were observed. The variability of precipitation amount as well as number of rainy days within a year increased from east to west of Texas. The results also indicated that highly disorderliness in the amount of precipitation and number of rainy days caused severe droughts during the 1950’s in whole of Texas. [Copyright &y& Elsevier]

Hyperspectral remote sensing across multiple spatio-temporal scales allows for mapping and monitoring mangrove habitats to support urgent conservation efforts. The use of hyperspectral imagery for assessing mangroves is less common than for terrestrial forest ecosystems. In this study, two well-known measures in statistical physics, Mean Information Gain (MIG) and Marginal Entropy (ME), have been adapted to high spatial resolution (2.5 m) full range (Visible-Shortwave-Infrared) airborne hyperspectral imagery. These two spectral complexity metrics describe the spatial heterogeneity and the aspatial heterogeneity of the reflectance. In this study, we compare MIG and ME with surface reflectance for mapping mangrove extent and species composition in the Sierpe mangroves in Costa Rica. The highest accuracy for separating mangroves from forest was achieved with visible-near infrared (VNIR) reflectance (98.8% overall accuracy), following by shortwave infrared (SWIR) MIG and ME (98%). Our results also show that MIG and ME can discriminate dominant mangrove species with higher accuracy than surface reflectance alone (e.g., MIG–VNIR = 93.6% vs. VNIR Reflectance = 89.7%). [ABSTRACT FROM AUTHOR]

• A normalized entropy measure, Standardized Variability Index, is proposed. • Trend analysis shows one-third of the country experienced a significant increase. • More extreme rainfall events in the near future are anticipated. Understanding the spatiotemporal variability of rainfall is vital for water resources planning and management, flood and drought mitigation, and erosion control, among others. Despite the progress in this direction, through proposal of many different approaches and their applications to rainfall data at various regions around the world, our knowledge of the spatiotemporal variability of rainfall remains limited. Studies in this direction have largely focused on the amount of rainfall and its spatial patterns, and investigations of spatiotemporal variability at multiscale are limited. In this study, we introduce a novel measure, Standardized Variability Index (SVI), based on the concept of entropy to investigate the spatiotemporal variability of gridded rainfall in the Indian subcontinent at different timescales. The results show distinct spatial patterns in the inter-annual rainfall variability at all timescales. Also, the intra-annual variability of rainfall amount, as well as rainy days, is found to increase from east to west of India. The Mann-Kendall trend test at different timescales reveals significant increase in rainfall variability. In addition, coupling the mean annual rainfall with SVI enables a relative assessment of the water resources availability. [ABSTRACT FROM AUTHOR]