Special Issue "Applications of Information Theory in the Geosciences"
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A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (21 January 2013)
Special Issue Editor
Guest Editor
Prof. Benjamin L. Ruddell
Department of Engineering, College of Technology and Innovation, and Senior Sustainability Scientist, Global Institute of Sustainability, Arizona State University, USA
Website: https://technology.asu.edu/index.php?q=directory/818971
E-Mail: bruddell@asu.edu
Interests: complex systems; information theory; climate and urban microclimate; ecohydrology; water resources; water policy; statistics; engineering ethics; environmental data informatics; engineering education
Special Issue Information
Dear Colleagues,
Information Theory is gaining many new applications in broad areas of Science, particularly the in the domain of Complex Adaptive Systems. These new applications often blend theoretical developments of Information Theory with innovative applications to complex-systems problems in the geosciences. This special issue specifically emphasizes research that addresses Geoscience problems using Information Theory approaches, by introducing a novel development of Information Theory for specific applications, and/or by solving a new Geoscience problem using the tools of Information Theory. Submissions at the boundaries of Information Theory, the Geosciences, and other disciplines are also welcome.
Prof. Benjamin L. Ruddell
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 1200 CHF (Swiss Francs).
Keywords
- geoscience
- life science
- physics
- complex adaptive systems
- Shannon entropy
- information theory
- nonlinearity
- statistics
- applications
Published Papers (10 papers)
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Received: 28 November 2012; in revised form: 20 December 2012 / Accepted: 14 January 2013 / Published: 22 January 2013
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Abstract: Recent years have witnessed an increased interest towards compression-based methods and their applications to remote sensing, as these have a data-driven and parameter-free approach and can be thus succesfully employed in several applications, especially in image information mining. This paper expands the algorithmic information theory frame, on which these methods are based. On the one hand, algorithms originally defined in the pattern matching domain are reformulated, allowing a better understanding of the available compression-based tools for remote sensing applications. On the other hand, the use of existing compression algorithms is proposed to store satellite images with added semantic value.
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Received: 1 January 2013; in revised form: 15 January 2013 / Accepted: 29 January 2013 / Published: 6 February 2013
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Abstract: Comparisons of eddy covariance (EC) tower measurements of CO2 concentration with mid-tropospheric observations from the Atmospheric Infrared Sounder (AIRS) allow for evaluation of the rising global signal of this greenhouse gas in relation to surface carbon dynamics. Using an information theory approach combining relative entropy and wavelet multi-resolution analysis, this study has explored correlations and divergences between mid-tropospheric and surface CO2 concentrations in grasslands of northeastern Kansas. Results show that surface CO2 measurements at the Kansas Field Station (KFS) and the Konza Prairie Biological Stations 1B (KZU) and 4B (K4B) with different land-cover types correlate well with mid-tropospheric CO2 in this region at the 512-day timescale between 2007 and 2010. Relative entropy further reveals that AIRS observations are indicative of surface CO2 concentrations for all land-cover types on monthly (32-day) and longer timescales. AIRS observations are also similar to CO2 concentrations at shorter timescales at sites KFS and K4B experiencing woody encroachment, though these results require further investigation. Differences in species composition and microclimate add to the variability of surface concentrations compared with mid-tropospheric observations.
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Received: 15 January 2013; in revised form: 25 February 2013 / Accepted: 27 February 2013 / Published: 5 March 2013
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Abstract: Boundary line models for N2O emissions from agricultural soils provide a means of estimating emissions within defined ranges. Boundary line models partition a two-dimensional region of parameter space into sub-regions by means of thresholds based on relationships between N2O emissions and explanatory variables, typically using soil data available from laboratory or field studies. Such models are intermediate in complexity between the use of IPCC emission factors and complex process-based models. Model calibration involves characterizing the extent to which observed data are correctly forecast. Writing the numerical results from graphical two-threshold boundary line models as 3×3 prediction-realization tables facilitates calculation of expected mutual information, a measure of the amount of information about the observations contained in the forecasts. Whereas mutual information characterizes the performance of a forecaster averaged over all forecast categories, specific information and relative entropy both characterize aspects of the amount of information contained in particular forecasts. We calculate and interpret these information quantities for experimental N2O emissions data.
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Received: 1 February 2013; in revised form: 1 April 2013 / Accepted: 2 April 2013 / Published: 8 April 2013
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Abstract: The one-dimensional (1D) power law velocity distribution, commonly used for computing velocities in open channel flow, has been derived empirically. However, a multitude of problems, such as scour around bridge piers, cutoffs and diversions, pollutant dispersion, and so on, require the velocity distribution in two dimensions. This paper employs the Shannon entropy theory for deriving the power law velocity distribution in two-dimensions (2D). The development encompasses the rectangular domain, but can be extended to any arbitrary domain, including a trapezoidal domain. The derived methodology requires only a few parameters and the good agreement is confirmed by comparing the velocity values calculated using the proposed methodology with values derived from both the 1D power law model and a logarithmic velocity distribution available in the literature.
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Received: 31 January 2013; in revised form: 27 March 2013 / Accepted: 1 April 2013 / Published: 10 April 2013
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Abstract: From algorithmic information theory, which connects the information content of a data set to the shortest computer program that can produce it, it is known that there are strong analogies between compression, knowledge, inference and prediction. The more we know about a data generating process, the better we can predict and compress the data. A model that is inferred from data should ideally be a compact description of those data. In theory, this means that hydrological knowledge could be incorporated into compression algorithms to more efficiently compress hydrological data and to outperform general purpose compression algorithms. In this study, we develop such a hydrological data compressor, named HydroZIP, and test in practice whether it can outperform general purpose compression algorithms on hydrological data from 431 river basins from the Model Parameter Estimation Experiment (MOPEX) data set. HydroZIP compresses using temporal dependencies and parametric distributions. Resulting file sizes are interpreted as measures of information content, complexity and model adequacy. These results are discussed to illustrate points related to learning from data, overfitting and model complexity.
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Received: 25 October 2012; in revised form: 22 March 2013 / Accepted: 1 April 2013 / Published: 10 April 2013
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Abstract: The temporal interactions between water and carbon cycling and the controlling environmental variables are investigated using wavelets and information theory. We used 3.5 years of eddy covariance station observations from an abandoned agricultural field in the central U.S. Time-series of the entropy of water and carbon fluxes exhibit pronounced annual cycles, primarily explained by the modulation of the diurnal flux amplitude by other variables, such as the net radiation. Entropies of soil moisture and precipitation show almost no annual cycle, but the data were collected during above average precipitation years, which limits the role of moisture stress on the resultant fluxes. We also investigated the information contribution to resultant fluxes from selected environmental variables as a function of time-scale using relative entropy. The relative entropy of latent heat flux and ecosystem respiration show that the radiation terms contribute the most information to these fluxes at scales up to the diurnal scale. Vapor pressure deficit and air temperature contribute to the most information for the gross primary productivity and net ecosystem exchange at the daily time-scale. The relative entropy between the fluxes and soil moisture illustrates that soil moisture contributes information at approximately weekly time-scales, while the relative entropy with precipitation contributes information predominantly at the monthly time-scale. The use of information theory metrics is a relatively new technique for assessing biosphere-atmosphere interactions, and this study illustrates the utility of the approach for assessing the dominant time-scales of these interactions.
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Received: 19 February 2013; in revised form: 12 April 2013 / Accepted: 15 April 2013 / Published: 22 April 2013
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Abstract: The quantification and analysis of uncertainties is important in all cases where maps and models of uncertain properties are the basis for further decisions. Once these uncertainties are identified, the logical next step is to determine how they can be reduced. Information theory provides a framework for the analysis of spatial uncertainties when different subregions are considered as random variables. In the work presented here, joint entropy, conditional entropy, and mutual information are applied for a detailed analysis of spatial uncertainty correlations. The aim is to determine (i) which areas in a spatial analysis share information, and (ii) where, and by how much, additional information would reduce uncertainties. As an illustration, a typical geological example is evaluated: the case of a subsurface layer with uncertain depth, shape and thickness. Mutual information and multivariate conditional entropies are determined based on multiple simulated model realisations. Even for this simple case, the measures not only provide a clear picture of uncertainties and their correlations but also give detailed insights into the potential reduction of uncertainties at each position, given additional information at a different location. The methods are directly applicable to other types of spatial uncertainty evaluations, especially where multiple realisations of a model simulation are analysed. In summary, the application of information theoretic measures opens up the path to a better understanding of spatial uncertainties, and their relationship to information and prior knowledge, for cases where uncertain property distributions are spatially analysed and visualised in maps and models.
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Received: 30 January 2013; in revised form: 11 May 2013 / Accepted: 14 May 2013 / Published: 24 May 2013
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Abstract: Across geosciences, many investigated phenomena relate to specific complex systems consisting of intricately intertwined interacting subsystems. Such dynamical complex systems can be represented by a directed graph, where each link denotes an existence of a causal relation, or information exchange between the nodes. For geophysical systems such as global climate, these relations are commonly not theoretically known but estimated from recorded data using causality analysis methods. These include bivariate nonlinear methods based on information theory and their linear counterpart. The trade-off between the valuable sensitivity of nonlinear methods to more general interactions and the potentially higher numerical reliability of linear methods may affect inference regarding structure and variability of climate networks. We investigate the reliability of directed climate networks detected by selected methods and parameter settings, using a stationarized model of dimensionality-reduced surface air temperature data from reanalysis of 60-year global climate records. Overall, all studied bivariate causality methods provided reproducible estimates of climate causality networks, with the linear approximation showing higher reliability than the investigated nonlinear methods. On the example dataset, optimizing the investigated nonlinear methods with respect to reliability increased the similarity of the detected networks to their linear counterparts, supporting the particular hypothesis of the near-linearity of the surface air temperature reanalysis data.
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Received: 25 March 2013; in revised form: 7 May 2013 / Accepted: 15 May 2013 / Published: 10 June 2013
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Abstract: The entropy of shortest distance (ESD) between geographic elements (“elliptical intrusions”, “lineaments”, “points”) on a map, or between "vugs", "fractures" and "pores" in the macro- or microscopic images of triple porosity naturally fractured vuggy carbonates provides a powerful new tool for the digital processing, analysis, classification and space/time distribution prognostic of mineral resources as well as the void space in carbonates, and in other rocks. The procedure is applicable at all scales, from outcrop photos, FMI, UBI, USI (geophysical imaging techniques) to micrographs, as we shall illustrate through some examples. Out of the possible applications of the ESD concept, we discuss in details the sliding window entropy filtering for nonlinear pore boundary enhancement, and propose this procedure as unbiased thresholding technique.
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Received: 16 February 2013; in revised form: 3 June 2013 / Accepted: 5 June 2013 / Published: 13 June 2013
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Abstract: We applied information theory to quantify parameter uncertainty in a groundwater flow model. A number of parameters in groundwater modeling are often used with lack of knowledge of site conditions due to heterogeneity of hydrogeologic properties and limited access to complex geologic structures. The present Information Theory-based (ITb) approach is to adopt entropy as a measure of uncertainty at the most probable state of hydrogeologic conditions. The most probable conditions are those at which the groundwater model is optimized with respect to the uncertain parameters. An analytical solution to estimate parameter uncertainty is derived by maximizing the entropy subject to constraints imposed by observation data. MODFLOW-2000 is implemented to simulate the groundwater system and to optimize the unknown parameters. The ITb approach is demonstrated with a three-dimensional synthetic model application and a case study of the Kansas City Plant. Hydraulic heads are the observations and hydraulic conductivities are assumed to be the unknown parameters. The applications show that ITb is capable of identifying which inputs of a groundwater model are the most uncertain and what statistical information can be used for site exploration.
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Last update: 16 April 2013
