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Special Issue "Entropy in Hydrology"

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A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (28 February 2015)

Special Issue Editor

Guest Editor
Dr. Nathaniel A. Brunsell

Department of Geography,University of Kansas, Lawrence, KS 66045, USA
Website | E-Mail
Interests: information theory; maximum entropy production; scale; mutual information; land atmosphere interactions

Special Issue Information

Dear Colleagues,

The hydrological system is inherently complex and exhibits variability across a range of temporal and spatial scales. Understanding and predicting this variability is essential for assessing future changes in response to such changes as climate and anthropogenic land cover.

Entropy and associated methods may help to understand the range of variability of the hydrological system and the scales at which system organization occurs. In addition, understanding the propagation of uncertainty across scales, model-data comparisons and other relevant aspects of the application of entropy is of interest. These may include both thermodynamic as well as information theoretic applications of entropy to the hydrological sciences.

Key areas of interest include hydrological applications of:
Maximum entropy production
Extremum principles in hydrology
Information theory metrics: Shannon entropy, mutual Information, transfer entropy, etc.
Using entropy to assess scale issues
Entropy applications to model-data comparisons, particularly across scales

We seek to highlight the application of entropy techniques to the hydrological sciences and welcome your contributions to the special issue.

Dr. Nathaniel Brunsell
Guest Editor

Submission

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

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

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs).


Published Papers (12 papers)

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Research

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Open AccessArticle Broad Niche Overlap between Invasive Nile Tilapia Oreochromis niloticus and Indigenous Congenerics in Southern Africa: Should We be Concerned?
Entropy 2015, 17(7), 4959-4973; doi:10.3390/e17074959
Received: 26 February 2015 / Revised: 7 July 2015 / Accepted: 8 July 2015 / Published: 14 July 2015
Cited by 1 | PDF Full-text (2868 KB) | HTML Full-text | XML Full-text
Abstract
This study developed niche models for the native ranges of Oreochromis andersonii, O. mortimeri, and O. mossambicus, and assessed how much of their range is climatically suitable for the establishment of O. niloticus, and then reviewed the conservation implications
[...] Read more.
This study developed niche models for the native ranges of Oreochromis andersonii, O. mortimeri, and O. mossambicus, and assessed how much of their range is climatically suitable for the establishment of O. niloticus, and then reviewed the conservation implications for indigenous congenerics as a result of overlap with O. niloticus based on documented congeneric interactions. The predicted potential geographical range of O. niloticus reveals a broad climatic suitability over most of southern Africa and overlaps with all the endemic congenerics. This is of major conservation concern because six of the eight river systems predicted to be suitable for O. niloticus have already been invaded and now support established populations. Oreochromis niloticus has been implicated in reducing the abundance of indigenous species through competitive exclusion and hybridisation. Despite these well-documented adverse ecological effects, O. niloticus remains one of the most widely cultured and propagated fish species in aquaculture and stock enhancements in the southern Africa sub-region. Aquaculture is perceived as a means of protein security, poverty alleviation, and economic development and, as such, any future decisions on its introduction will be based on the trade-off between socio-economic benefits and potential adverse ecological effects. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Open AccessArticle Modeling Soil Moisture Profiles in Irrigated Fields by the Principle of Maximum Entropy
Entropy 2015, 17(6), 4454-4484; doi:10.3390/e17064454
Received: 26 April 2015 / Revised: 4 June 2015 / Accepted: 18 June 2015 / Published: 23 June 2015
Cited by 1 | PDF Full-text (9523 KB) | HTML Full-text | XML Full-text
Abstract
Vertical soil moisture profiles based on the principle of maximum entropy (POME) were validated using field and model data and applied to guide an irrigation cycle over a maize field in north central Alabama (USA). The results demonstrate that a simple two-constraint entropy
[...] Read more.
Vertical soil moisture profiles based on the principle of maximum entropy (POME) were validated using field and model data and applied to guide an irrigation cycle over a maize field in north central Alabama (USA). The results demonstrate that a simple two-constraint entropy model under the assumption of a uniform initial soil moisture distribution can simulate most soil moisture profiles that occur in the particular soil and climate regime that prevails in the study area. The results of the irrigation simulation demonstrated that the POME model produced a very efficient irrigation strategy with minimal losses (about 1.9% of total applied water). However, the results for finely-textured (silty clay) soils were problematic in that some plant stress did develop due to insufficient applied water. Soil moisture states in these soils fell to around 31% of available moisture content, but only on the last day of the drying side of the irrigation cycle. Overall, the POME approach showed promise as a general strategy to guide irrigation in humid environments, such as the Southeastern United States. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Open AccessArticle A Hybrid Physical and Maximum-Entropy Landslide Susceptibility Model
Entropy 2015, 17(6), 4271-4292; doi:10.3390/e17064271
Received: 28 February 2015 / Revised: 28 May 2015 / Accepted: 12 June 2015 / Published: 19 June 2015
Cited by 3 | PDF Full-text (8771 KB) | HTML Full-text | XML Full-text
Abstract
The clear need for accurate landslide susceptibility mapping has led to multiple approaches. Physical models are easily interpreted and have high predictive capabilities but rely on spatially explicit and accurate parameterization, which is commonly not possible. Statistical methods can include other factors influencing
[...] Read more.
The clear need for accurate landslide susceptibility mapping has led to multiple approaches. Physical models are easily interpreted and have high predictive capabilities but rely on spatially explicit and accurate parameterization, which is commonly not possible. Statistical methods can include other factors influencing slope stability such as distance to roads, but rely on good landslide inventories. The maximum entropy (MaxEnt) model has been widely and successfully used in species distribution mapping, because data on absence are often uncertain. Similarly, knowledge about the absence of landslides is often limited due to mapping scale or methodology. In this paper a hybrid approach is described that combines the physically-based landslide susceptibility model “Stability INdex MAPping” (SINMAP) with MaxEnt. This method is tested in a coastal watershed in Pacifica, CA, USA, with a well-documented landslide history including 3 inventories of 154 scars on 1941 imagery, 142 in 1975, and 253 in 1983. Results indicate that SINMAP alone overestimated susceptibility due to insufficient data on root cohesion. Models were compared using SINMAP stability index (SI) or slope alone, and SI or slope in combination with other environmental factors: curvature, a 50-m trail buffer, vegetation, and geology. For 1941 and 1975, using slope alone was similar to using SI alone; however in 1983 SI alone creates an Areas Under the receiver operator Curve (AUC) of 0.785, compared with 0.749 for slope alone. In maximum-entropy models created using all environmental factors, the stability index (SI) from SINMAP represented the greatest contributions in all three years (1941: 48.1%; 1975: 35.3; and 1983: 48%), with AUC of 0.795, 0822, and 0.859, respectively; however; using slope instead of SI created similar overall AUC values, likely due to the combined effect with plan curvature indicating focused hydrologic inputs and vegetation identifying the effect of root cohesion. The combined approach––using either stability index or slope––highlights the importance of additional environmental variables in modeling landslide initiation. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Open AccessArticle Kolmogorov Complexity Based Information Measures Applied to the Analysis of Different River Flow Regimes
Entropy 2015, 17(5), 2973-2987; doi:10.3390/e17052973
Received: 14 January 2015 / Revised: 26 March 2015 / Accepted: 6 May 2015 / Published: 8 May 2015
Cited by 3 | PDF Full-text (4703 KB) | HTML Full-text | XML Full-text
Abstract
We have used the Kolmogorov complexities and the Kolmogorov complexity spectrum to quantify the randomness degree in river flow time series of seven rivers with different regimes in Bosnia and Herzegovina, representing their different type of courses, for the period 1965–1986. In particular,
[...] Read more.
We have used the Kolmogorov complexities and the Kolmogorov complexity spectrum to quantify the randomness degree in river flow time series of seven rivers with different regimes in Bosnia and Herzegovina, representing their different type of courses, for the period 1965–1986. In particular, we have examined: (i) the Neretva, Bosnia and the Drina (mountain and lowland parts), (ii) the Miljacka and the Una (mountain part) and the Vrbas and the Ukrina (lowland part) and then calculated the Kolmogorov complexity (KC) based on the Lempel–Ziv Algorithm (LZA) (lower—KCL and upper—KCU), Kolmogorov complexity spectrum highest value (KCM) and overall Kolmogorov complexity (KCO) values for each time series. The results indicate that the KCL, KCU, KCM and KCO values in seven rivers show some similarities regardless of the amplitude differences in their monthly flow rates. The KCL, KCU and KCM complexities as information measures do not “see” a difference between time series which have different amplitude variations but similar random components. However, it seems that the KCO information measures better takes into account both the amplitude and the place of the components in a time series. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Open AccessArticle Sensitivity Analysis for Urban Drainage Modeling Using Mutual Information
Entropy 2014, 16(11), 5738-5752; doi:10.3390/e16115738
Received: 13 July 2014 / Revised: 26 September 2014 / Accepted: 11 October 2014 / Published: 3 November 2014
Cited by 2 | PDF Full-text (867 KB) | HTML Full-text | XML Full-text
Abstract
The intention of this paper is to evaluate the sensitivity of the Storm Water Management Model (SWMM) output to its input parameters. A global parameter sensitivity analysis is conducted in order to determine which parameters mostly affect the model simulation results. Two different
[...] Read more.
The intention of this paper is to evaluate the sensitivity of the Storm Water Management Model (SWMM) output to its input parameters. A global parameter sensitivity analysis is conducted in order to determine which parameters mostly affect the model simulation results. Two different methods of sensitivity analysis are applied in this study. The first one is the partial rank correlation coefficient (PRCC) which measures nonlinear but monotonic relationships between model inputs and outputs. The second one is based on the mutual information which provides a general measure of the strength of the non-monotonic association between two variables. Both methods are based on the Latin Hypercube Sampling (LHS) of the parameter space, and thus the same datasets can be used to obtain both measures of sensitivity. The utility of the PRCC and the mutual information analysis methods are illustrated by analyzing a complex SWMM model. The sensitivity analysis revealed that only a few key input variables are contributing significantly to the model outputs; PRCCs and mutual information are calculated and used to determine and rank the importance of these key parameters. This study shows that the partial rank correlation coefficient and mutual information analysis can be considered effective methods for assessing the sensitivity of the SWMM model to the uncertainty in its input parameters. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Open AccessArticle Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy
Entropy 2014, 16(8), 4626-4647; doi:10.3390/e16084626
Received: 28 January 2014 / Revised: 26 May 2014 / Accepted: 7 August 2014 / Published: 18 August 2014
Cited by 3 | PDF Full-text (1249 KB) | HTML Full-text | XML Full-text
Abstract
Because of high variation in mountainous areas, rainfall data at different spatiotemporal scales may yield potential uncertainty for network design. However, few studies focus on the scaling effect on both the spatial and the temporal scale. By calculating the maximum joint entropy of
[...] Read more.
Because of high variation in mountainous areas, rainfall data at different spatiotemporal scales may yield potential uncertainty for network design. However, few studies focus on the scaling effect on both the spatial and the temporal scale. By calculating the maximum joint entropy of hourly typhoon events, monthly, six dry and wet months and annual rainfall between 1992 and 2012 for 1-, 3-, and 5-km grids, the relocated candidate rain gauges in the National Taiwan University Experimental Forest of Central Taiwan are prioritized. The results show: (1) the network exhibits different locations for first prioritized candidate rain gauges for different spatiotemporal scales; (2) the effect of spatial scales is insignificant compared to temporal scales; and (3) a smaller number and a lower percentage of required stations (PRS) reach stable joint entropy for a long duration at finer spatial scale. Prioritized candidate rain gauges provide key reference points for adjusting the network to capture more accurate information and minimize redundancy. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Open AccessArticle The Role of Vegetation on the Ecosystem Radiative Entropy Budget and Trends Along Ecological Succession
Entropy 2014, 16(7), 3710-3731; doi:10.3390/e16073710
Received: 1 March 2014 / Revised: 6 June 2014 / Accepted: 12 June 2014 / Published: 3 July 2014
Cited by 1 | PDF Full-text (2660 KB) | HTML Full-text | XML Full-text
Abstract
Ecosystem entropy production is predicted to increase along ecological succession and approach a state of maximum entropy production, but few studies have bridged the gap between theory and data. Here, we explore radiative entropy production in terrestrial ecosystems using measurements from 64 Free/Fair-Use
[...] Read more.
Ecosystem entropy production is predicted to increase along ecological succession and approach a state of maximum entropy production, but few studies have bridged the gap between theory and data. Here, we explore radiative entropy production in terrestrial ecosystems using measurements from 64 Free/Fair-Use sites in the FLUXNET database, including a successional chronosequence in the Duke Forest in the southeastern United States. Ecosystem radiative entropy production increased then decreased as succession progressed in the Duke Forest ecosystems, and did not exceed 95% of the calculated empirical maximum entropy production in the FLUXNET study sites. Forest vegetation, especially evergreen needleleaf forests characterized by low shortwave albedo and close coupling to the atmosphere, had a significantly higher ratio of radiative entropy production to the empirical maximum entropy production than did croplands and grasslands. Our results demonstrate that ecosystems approach, but do not reach, maximum entropy production and that the relationship between succession and entropy production depends on vegetation characteristics. Future studies should investigate how natural disturbances and anthropogenic management—especially the tendency to shift vegetation to an earlier successional state—alter energy flux and entropy production at the surface-atmosphere interface. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Open AccessArticle Three Methods for Estimating the Entropy Parameter M Based on a Decreasing Number of Velocity Measurements in a River Cross-Section
Entropy 2014, 16(5), 2512-2529; doi:10.3390/e16052512
Received: 27 February 2014 / Revised: 15 April 2014 / Accepted: 7 May 2014 / Published: 9 May 2014
Cited by 7 | PDF Full-text (471 KB) | HTML Full-text | XML Full-text
Abstract
The theoretical development and practical application of three new methods for estimating the entropy parameter M used within the framework of the entropy method proposed by Chiu in the 1980s as a valid alternative to the velocity-area method for measuring the discharge in
[...] Read more.
The theoretical development and practical application of three new methods for estimating the entropy parameter M used within the framework of the entropy method proposed by Chiu in the 1980s as a valid alternative to the velocity-area method for measuring the discharge in a river is here illustrated. The first method is based on reproducing the cumulative velocity distribution function associated with a flood event and requires measurements regarding the entire cross-section, whereas, in the second and third method, the estimate of M is based on reproducing the cross-sectional mean velocity  by following two different procedures. Both of them rely on the entropy parameter M alone and look for that value of M that brings two different estimates of , obtained by using two different M-dependent-approaches, as close as possible. From an operational viewpoint, the acquisition of velocity data becomes increasingly simplified going from the first to the third approach, which uses only one surface velocity measurement. The procedures proposed are applied in a case study based on the Ponte Nuovo hydrometric station on the Tiber River in central Italy. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Open AccessArticle Ensemble Entropy for Monitoring Network Design
Entropy 2014, 16(3), 1365-1375; doi:10.3390/e16031365
Received: 21 January 2014 / Revised: 25 February 2014 / Accepted: 26 February 2014 / Published: 4 March 2014
Cited by 8 | PDF Full-text (1127 KB) | HTML Full-text | XML Full-text
Abstract
Information-theory provides, among others, conceptual methods to quantify the amount of information contained in single random variables and methods to quantify the amount of information contained and shared among two or more variables. Although these concepts have been successfully applied in hydrology and
[...] Read more.
Information-theory provides, among others, conceptual methods to quantify the amount of information contained in single random variables and methods to quantify the amount of information contained and shared among two or more variables. Although these concepts have been successfully applied in hydrology and other fields, the evaluation of these quantities is sensitive to different assumptions in the estimation of probabilities. An example is the histogram bin size used to estimate probabilities to calculate Information Theory quantities via frequency methods. The present research aims at introducing a method to take into consideration the uncertainty coming from these parameters in the evaluation of the North Sea’s water level network. The main idea is that the entropy of a random variable can be represented as a probability distribution of possible values, instead of entropy being a deterministic value. The method consists of solving multiple scenarios of Multi-Objective Optimization Problem in which information content is maximized and redundancy is minimized. Results include probabilistic analysis of the chosen parameters on the resulting family of Pareto fronts, providing additional criteria on the selection of the final set of monitoring points. Full article
(This article belongs to the Special Issue Entropy in Hydrology)
Figures

Open AccessArticle Entropy: From Thermodynamics to Hydrology
Entropy 2014, 16(3), 1287-1314; doi:10.3390/e16031287
Received: 13 January 2014 / Revised: 8 February 2014 / Accepted: 12 February 2014 / Published: 27 February 2014
Cited by 4 | PDF Full-text (1265 KB) | HTML Full-text | XML Full-text
Abstract
Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a) to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b) to show the power of entropy and
[...] Read more.
Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a) to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b) to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron) from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy. Full article
(This article belongs to the Special Issue Entropy in Hydrology)

Review

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Open AccessReview Integrating Entropy and Copula Theories for Hydrologic Modeling and Analysis
Entropy 2015, 17(4), 2253-2280; doi:10.3390/e17042253
Received: 12 March 2015 / Revised: 8 April 2015 / Accepted: 10 April 2015 / Published: 15 April 2015
Cited by 7 | PDF Full-text (828 KB) | HTML Full-text | XML Full-text
Abstract
Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula
[...] Read more.
Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula theories provides new insights in hydrologic modeling and analysis, for which the development and application are still in infancy. Two broad branches of integration of the two concepts, entropy copula and copula entropy, are introduced in this study. On the one hand, the entropy theory can be used to derive new families of copulas based on information content matching. On the other hand, the copula entropy provides attractive alternatives in the nonlinear dependence measurement even in higher dimensions. We introduce in this study the integration of entropy and copula theories in the dependence modeling and analysis to illustrate the potential applications in hydrology and water resources. Full article
(This article belongs to the Special Issue Entropy in Hydrology)

Other

Jump to: Research, Review

Open AccessTechnical Note Discharge Estimation in a Lined Canal Using Information Entropy
Entropy 2014, 16(3), 1728-1742; doi:10.3390/e16031728
Received: 20 December 2013 / Revised: 10 February 2014 / Accepted: 19 March 2014 / Published: 24 March 2014
Cited by 3 | PDF Full-text (518 KB) | HTML Full-text | XML Full-text
Abstract
This study applies a new method and technology to measure the discharge in a lined canal in Taiwan. An Acoustic Digital Current Meter mounted on a measurement platform is used to measure the velocities over the full cross-section for establishing the measurement method.
[...] Read more.
This study applies a new method and technology to measure the discharge in a lined canal in Taiwan. An Acoustic Digital Current Meter mounted on a measurement platform is used to measure the velocities over the full cross-section for establishing the measurement method. The proposed method primarily employs Chiu’s Equation which is based on entropy to establish a constant ratio the relation between the maximum and mean velocities in an irrigation canal, and compute the maximum velocity by the observed velocity profile. In consequence, the mean velocity of the lined canal can be rapidly determined by the maximum velocity and the constant ratio. The cross-sectional area of the artificial irrigation canal can be calculated for the water stage. Finally, the discharge in the lined canal can be efficiently determined by the estimated mean velocity and the cross-sectional area. Using the data of discharges and stages collected in the Wan-Dan Canal, the correlation of stage and discharge is also developed for remote real-time monitoring and estimating discharge from the pumping station. Overall, Chiu’s Equation is demonstrated to reliably and accurately measure discharge in a lined canal, and can serve as reference for future calibration for a stage-discharge rating curve. Full article
(This article belongs to the Special Issue Entropy in Hydrology)

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