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Entropy Theory and its Application in Environmental and Water Engineering responds to the need for a book that deals with basic concepts of entropy theory from a hydrologic and water engineering perspective and then for a book that deals with applications of these concepts to a range of water engineering problems. The range of applications of entropy is constantly expanding and new areas finding a use for the theory are continually emerging. The applications of concepts and techniques vary across different subject areas and this book aims to relate them directly to practical problems of environmental and water engineering. The book presents and explains the Principle of Maximum Entropy (POME) and the Principle of Minimum Cross Entropy (POMCE) and their applications to different types of probability distributions. Spatial and inverse spatial entropy are important for urban planning and are presented with clarity. Maximum entropy spectral analysis and minimum cross entropy spectral analysis are powerful techniques for addressing a variety of problems faced by environmental and water scientists and engineers and are described here with illustrative examples. Giving a thorough introduction to the use of entropy to measure the unpredictability in environmental and water systems this book will add an essential statistical method to the toolkit of postgraduates, researchers and academic hydrologists, water resource managers, environmental scientists and engineers.  It will also offer a valuable resource for professionals in the same areas, governmental organizations, private companies as well as students in earth sciences, civil and agricultural engineering, and agricultural and rangeland sciences. This book: * Provides a thorough introduction to entropy for beginners and more experienced users * Uses numerous examples to illustrate the applications of the theoretical principles * Allows the reader to apply entropy theory to the solution of practical problems * Assumes minimal existing mathematical knowledge * Discusses the theory and its various aspects in both univariate and bivariate cases * Covers newly expanding areas including neural networks from an entropy perspective and future developments.

Accurate and fast measurements of thermal properties are frequently required for characterizing the heat‐water dynamics in frozen soil. Measuring the thermal properties of frozen soil without inducing ice thaw has proven challenging with conventional heat pulse (HP) methods. In this study, based on an Infinite Line Source (ILS) semi‐analytical model that applies a constant temperature lower than the freezing point at the heat source to prevent the initiation of ice thaw in the frozen soil, we propose a novel HP‐based approach to measure thermal properties, applicable at temperatures below or above 0°C. Laboratory experiments and numerical modeling were utilized to validate the applicability of the approach and optimization strategies of the measurement. We found that the proposed HP‐based approach effectively maintained the maximum spatial temperature below the freezing point and therefore estimated the bulk thermal properties of quartz sand and ice contents. An optimized measurement strategy was proposed to monitor the temperature variations 2–4 cm away from the center of the heat probe after 60 s. This progress can largely facilitate the determination of the thermal properties of multi‐phase and ‐component frozen soil such as thermal conductivity, heat flux, and ice content in cold areas across soil science, hydrology, engineering, and climate science. Plain Language Summary Frozen soil thermal properties are essential for understanding the potential impacts of varying temperatures on water and heat exchange within the surface soil and the subsurface environment. The conventional method, using the single pulse heating strategy to measure the thermal properties of frozen soil, has difficulty avoiding the ice‐melt process. Ice melt may lead to biased outputs due to the ice melting around the heating probe. In this study, we proposed a novel method to maintain a constant temperature on the heat source surface to avoid the overheating challenge within the measurement. The mathematical model and the proposed workflow can successfully estimate the bulk soil thermal conductivity, heat flux, and soil ice content in cold regions. Key Points A novel approach has been developed using an Infinite Line Source model to predict frozen soil thermal properties and water/ice contents The proposed method offers distinct advantages for measurements, especially in frozen soil with temperatures near the freezing point Further application is valuable regarding its potential merits in minimizing ice melting in the measurement

Lake ecosystems, and the organisms that live within them, are vulnerable to temperature change 1 – 5 , including the increased occurrence of thermal extremes 6 . However, very little is known about lake heatwaves—periods of extreme warm lake surface water temperature—and how they may change under global warming. Here we use satellite observations and a numerical model to investigate changes in lake heatwaves for hundreds of lakes worldwide from 1901 to 2099. We show that lake heatwaves will become hotter and longer by the end of the twenty-first century. For the high-greenhouse-gas-emission scenario (Representative Concentration Pathway (RCP) 8.5), the average intensity of lake heatwaves, defined relative to the historical period (1970 to 1999), will increase from 3.7 ± 0.1 to 5.4 ± 0.8 degrees Celsius and their average duration will increase dramatically from 7.7 ± 0.4 to 95.5 ± 35.3 days. In the low-greenhouse-gas-emission RCP 2.6 scenario, heatwave intensity and duration will increase to 4.0 ± 0.2 degrees Celsius and 27.0 ± 7.6 days, respectively. Surface heatwaves are longer-lasting but less intense in deeper lakes (up to 60 metres deep) than in shallower lakes during both historic and future periods. As lakes warm during the twenty-first century 7 , 8 , their heatwaves will begin to extend across multiple seasons, with some lakes reaching a permanent heatwave state. Lake heatwaves are likely to exacerbate the adverse effects of long-term warming in lakes and exert widespread influence on their physical structure and chemical properties. Lake heatwaves could alter species composition by pushing aquatic species and ecosystems to the limits of their resilience. This in turn could threaten lake biodiversity 9 and the key ecological and economic benefits that lakes provide to society. Modelling and remote sensing show that by the end of the twenty-first century, lake heatwaves will be several degrees Celsius warmer and some will be months longer, with potentially major adverse consequences for lake ecosystems.

Local thermal nonequilibrium (LTNE) effects in heterogeneous media can affect subsurface temperature distributions, as well as the capacity of the heat transport model to solve the inverse problem of estimating groundwater fluxes. We present a synthetic coupled flow and heat transport numerical model with five scenarios to analyze the influence of subsurface hydraulic and thermal property variations on heat transport in heterogeneous streambed sediments, while also evaluating the role of LTNE effects in heat transport processes within heterogeneous streambed sediments and their impact on streambed fluxes estimation. Heterogeneous streambed sediments with varying sand‐gravel‐clay fractions are stochastically generated using a Markov Chain model. Synthetic streambed temperature‐time series are produced to estimate effective thermal diffusivity and thermal front velocity using a heat transport model based on homogeneous and local thermal equilibrium assumptions, and these estimates were compared to known values from numerical models of flow fields analogous to losing streams. Results show that neglecting thermal heterogeneity in streambed sediments leads to significant errors in streambed fluxes estimation, where the effective thermal diffusivity can be underestimated by about 40%, while the thermal front velocity can be overestimated by more than two times. In addition to the effects of streambed heterogeneity, LTNE effects further amplify these errors. Furthermore, the influences of streambed heterogeneity on LTNE effects are primarily influenced by flow velocity, with higher clay content reducing Darcian velocity and weakening LTNE effects.

The Tibetan Plateau (TP) has the largest areas of permafrost terrain in the mid- and low-latitude regions of the world. Some permafrost distribution maps have been compiled but, due to limited data sources, ambiguous criteria, inadequate validation, and deficiency of high-quality spatial data sets, there is high uncertainty in the mapping of the permafrost distribution on the TP. We generated a new permafrost map based on freezing and thawing indices from modified Moderate Resolution Imaging Spectroradiometer (MODIS) land surface temperatures (LSTs) and validated this map using various ground-based data sets. The soil thermal properties of five soil types across the TP were estimated according to an empirical equation and soil properties (moisture content and bulk density). The temperature at the top of permafrost (TTOP) model was applied to simulate the permafrost distribution. Permafrost, seasonally frozen ground, and unfrozen ground covered areas of 1.06  ×  106 km2 (0.97–1.15  ×  106 km2, 90 % confidence interval) (40 %), 1.46  ×  106 (56 %), and 0.03  ×  106 km2 (1 %), respectively, excluding glaciers and lakes. Ground-based observations of the permafrost distribution across the five investigated regions (IRs, located in the transition zones of the permafrost and seasonally frozen ground) and three highway transects (across the entire permafrost regions from north to south) were used to validate the model. Validation results showed that the kappa coefficient varied from 0.38 to 0.78 with a mean of 0.57 for the five IRs and 0.62 to 0.74 with a mean of 0.68 within the three transects. Compared with earlier studies, the TTOP modelling results show greater accuracy. The results provide more detailed information on the permafrost distribution and basic data for use in future research on the Tibetan Plateau permafrost.

iFLOW is a free, open‐source, and python‐based framework and graphical user interface to visualize and analyze temperature time series, and extract one dimensional thermal velocity, vT, and bulk effective thermal diffusivity, ke. Information of thermal properties of the sediment‐water mixture (bulk) and water allows quantifying the one‐dimensional Darcian flux, q, and seepage velocity, v, from vT. Available software packages were developed to quantify q and ke only based on a specific mathematical model or focused on specific data processing or parameter estimation techniques, and all these steps were lumped together preventing users to identify potential source of errors. iFLOW proposes a novel organizational philosophy with a modular framework that parses the analysis process into three fundamental steps: (a) the mathematical model, (b) signal processing, and (c) parameter estimation. iFLOW houses a suite of models and analysis techniques. This suite can be readily added to and expanded through its modular framework. iFLOW contains a wizard to guide users through the selection process with respect to the three fundamental steps. Users can analyze and visualize intermediate results to identify problematic issues in the time series data and improve data interpretation. Here, we present iFLOW and summarize its performance using a set of one‐dimensional synthetic heat transport simulations. Plain Language Summary iFLOW is a free, open‐source computer application to help users visualize and analyze temperature data. It calculates the water velocity within sediment along with thermal diffusivity from measured temperature data. Unlike other applications, iFLOW is flexible, allowing users to check for errors by breaking down the analysis into three parts: mathematical model selection, signal processing, and estimating parameters. It includes various models and methods that users can easily expand on. iFLOW also guides users through the analysis and in choosing options for these three analysis stages. We introduce iFLOW through a set of examples with simulated heat transport data. Key Points iFLOW is a novel framework for temperature time series analysis iFLOW helps users estimate advective flux and effective thermal diffusivity with their uncertainty The analysis is parsed into the mathematical model selection, signal processing, and parameter estimation steps

Research on phase change material (PCM) for thermal energy storage is playing a significant role in energy management industry. However, some hurdles during the storage of energy have been perceived such as less thermal conductivity, leakage of PCM during phase transition, flammability, and insufficient mechanical properties. For overcoming such obstacle, researchers have been concentrating on composite PCM, where PCM is combined with metal or non-metal particles, fibrous materials, expanded or porous materials, and flame retardants. The main purpose of the current paper is to review the properties enhanced paraffin-based composite PCM. In the literature review, paraffin is selected as a thermal energy storage material, which is mixed with property-enhancing material to prepare composite. Structural and thermal properties of composite have been explored with the help of scanning electron microscope, X-ray diffractometer, transmission electron microscope, polarizing optical microscope, Fourier transform infrared spectroscopy, thermogravimetric analysis, and differential scanning calorimetry. Mechanical properties of the material are also portrayed using different testing techniques. Nevertheless, numerical methods have also been adopted for characterization of composite. It is found from the literature review that with incorporation of property-enhancing material, thermal conductivity, phase transition rate, and shape stability of PCM increased at the same time flammability, heat storage capacity, and mechanical properties reduced. Graphical abstract

This paper delves into the engineering applications of lime-stabilized red clay, a highly water-sensitive material, particularly in the context of the climatic conditions prevalent in the Dalian region. We systematically investigate the impact of water content, dry density, and freeze-thaw cycles (with a freezing temperature set at -10°C) on the thermal conductivity of stabilized soil, a crucial parameter for analyzing soil temperature fields that is influenced by numerous factors. By developing and validating both empirical and machine learning prediction models, we unravel the evolution of thermal conductivity in response to these factors: within the range of influencing variables, thermal conductivity exhibits an exponential or linear increase with rising water content and dry density, while it decreases exponentially with increasing freeze-thaw cycles. Furthermore, we quantitatively analyze the specific influence of water content and other factors on the thermal conductivity of stabilized soil and construct a comprehensive prediction model encompassing BP neural network, gradient boosting decision tree, and linear regression models. Comparative analysis highlights the significant enhancement in prediction accuracy achieved by the proposed ensemble model over single machine learning models, with root mean square error (RMSE) values below 0.05 and mean absolute percentage error (MAPE) values remaining under 2.5% in both frozen and unfrozen states. Additionally, a secondary validation using experimental data from other researchers confirms the model’s good agreement with previous results, demonstrating its robust generalization ability. Our findings provide valuable insights for engineering studies in the Dalian region and red clay areas subjected to extreme climatic conditions.

Climate change is expected to increase stream temperatures and the projected warming may alter the spatial extent of habitat for cold-water fish and other aquatic taxa. Recent studies have proposed that stream thermal sensitivities, derived from short-term air temperature variations, can be employed to infer future stream warming due to long-term climate change. However, this approach does not consider the potential for streambed heat fluxes to increase due to gradual warming of the shallow subsurface. The temperature of shallow groundwater is particularly important for the thermal regimes of groundwater-dominated streams and rivers. Also, recent studies have investigated how land surface perturbations, such as wildfires or timber harvesting, can influence stream temperatures by changing stream surface heat fluxes, but these studies have typically not considered how these surface disturbances can also alter shallow groundwater temperatures and streambed heat fluxes. In this study, several analytical solutions to the one-dimensional unsteady advection–diffusion equation for subsurface heat transport are employed to estimate the timing and magnitude of groundwater temperature changes due to seasonal and long-term variability in land surface temperatures. Groundwater thermal sensitivity formulae are proposed that accommodate different surface warming scenarios. The thermal sensitivity formulae suggest that shallow groundwater will warm in response to climate change and other surface perturbations, but the timing and magnitude of the subsurface warming depends on the rate of surface warming, subsurface thermal properties, bulk aquifer depth, and groundwater velocity. The results also emphasize the difference between the thermal sensitivity of shallow groundwater to short-term (e.g., seasonal) and long-term (e.g., multi-decadal) land surface-temperature variability, and thus demonstrate the limitations of using short-term air and water temperature records to project future stream warming. Suggestions are provided for implementing these formulae in stream temperature models to accommodate groundwater warming.