Aguirre, A., Foster, B., and Merali, Z. (Eds.) (2015) “It From Bit or Bit From It?” On Physics and Information. Published in cooperation with the renowned physics “think-tank” Foundational Questions Institute, FQXi. Springer. https://www.springer.com/gp/book/9783319129457

Azmi, E., Ehret, U., Weijs, S.V., Ruddell, B.L., and Perdigão, R.A.P. (2021). Technical note: “Bit by bit”: a practical and general approach for evaluating model computational complexity vs. model performance, Hydrol. Earth Syst. Sci., 25(2), 1103-1115.

Balasis, G., Donner, R., Potirakis, S., Runge, J., Papadimitriou, C., Daglis, I., Eftaxias, K. and Kurths, J. (2013). Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System. Entropy 15 (11), 4844-4888.

Bennett, Andrew, et al. (2019) “Quantifying process connectivity with transfer entropy in hydrologic models.” Water Resources Research. https://doi.org/10.1029/2018WR024555

Bertschinger, N., Rauh, J., Olbrich, E., Jost, J. and Ay, N. (2014). Quantifying Unique Information. Entropy 16, 2161–2183.

Boba, P., Bollmann, D., Schoepe, D., Wester, N., Wiesel, J., and Hamacher, K. (2015). Efficient computation and statistical assessment of transfer entropy. Comput. Phys. 3.

Brunsell, N. A. (2010). “A multiscale information theory approach to assess spatial-temporal variability of daily precipitation.” Journal of Hydrology 385.1: 165-172.

Brunsell, N. A., and Anderson, M. C. (2011). “Characterizing the multi-scale spatial structure of land-atmosphere interactions with information theory.” Biogeosciences Discussions 8.2.

Brunsell, N. A., J. M. Ham, and C. E. Owensby (2008). “Assessing the multi-resolution information content of remotely sensed variables and elevation for evapotranspiration in a tall-grass prairie environment.” Remote Sensing of Environment 112.6 pp. 2977-2987.

Caticha, A. & C. Cafaro (2007). “From information geometry to Newtonian dynamics.” Full Caticha reference.

Cover, T. and Thomas, J. (2006). Elements of Information Theory. Wiley.

Cox, R. T. (1964). Probability, frequency, and reasonable expectation. Am. J. Phys. 14, 1-13. Full Cox reference.

Datcu, M., Seidel, K. and Walessa, M. (1998) “Spatial information retrieval from remote-sensing images. I. Information theoretical perspective,” IEEE Transactions on Geoscience and Remote Sensing, 36(5), pp. 1431-1445.

DelSole, T. & Tippett, MK (2007). Predictability: Recent Insights From Information Theory. Information Theory and Physics. Full DelSole reference.

Donges, Jonathan F., et al. “Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package.” Chaos: An Interdisciplinary Journal of Nonlinear Science 25.11 (2015): 113101.

Emanuel, K. [2020]. The Relevance of Theory for Contemporary Research in Atmospheres, Oceans and Climate. AGU Advances, 1, e2019AV000129. https://doi.org/10.1029/2019AV000129

Garland, Joshua, et al. “A First Step Toward Quantifying the Climate’s Information Production over the Last 68,000 Years.” International Symposium on Intelligent Data Analysis. Springer, Cham, 2016. Full Garland reference.

Garland, J.; Jones, T.R.; Neuder, M.; Morris, V.; White, J.W.C.; Bradley, E. Anomaly Detection in Paleoclimate Records Using Permutation Entropy. Entropy 2018, 20, 931. Full Garland reference.

Garland, J. and E. Bradley (2018), Information Theory in Earth and Space Science, SIAM News, October 1st, 2018. Full Garland reference.

Gencaga, Deniz, Kevin H. Knuth, and William B. Rossow. “A recipe for the estimation of information flow in a dynamical system.” Entropy 17.1 (2015): 438-470.

Gerken, T., Ruddell, B.L., Fuentes, J.D.,  Araujo, A., Brunsell, N.A., Maia, J., Manzi, A., Mercer, J., dos Santos, R.N., von Randow, C., and Stoy, P.C. (2017). Investigating the mechanisms responsible for the lack of surface energy balance closure in a central Amazonian tropical rainforest. Full Gerken reference.

Gerken, T., B.L. Ruddell, R. Yu, P.C. Stoy, and D.T. Drewry (2019), Robust observations of land-to-atmosphere feedbacks using the information flows of FLUXNET, NPJ Climate and Atmospheric Science, 2:37, https://www.nature.com/articles/s41612-019-0094-4.

Gharari, Shervan; Gupta, Hoshin V.; Clark, Martyn P.; Hrachowitz, Markus; Fenicia, Fabrizio; Matgen, Patrick; and Savenije, Hubert H.G. (2021). “Understanding the Information Content in the Hierarchy of Model Development Decisions: Learning from data.” Water Resources Research, https://doi.org/10.1029/2020WR027948

Glymour, Clark, Richard Scheines, Peter Spirtes, and Kevin Kelly. (1987). Discovering causal structure: Artificial intelligence, philosophy of science, and statistical modeling. Academic Press, ISBN 012286961.

Gong, W., Gupta, H. V., Yang, D., Sricharan, K., and Hero, A. O. (2013) ‘Estimating Epistemic & Aleatory Uncertainties During Hydrologic Modeling: An Information Theoretic Approach’, Water Resources Research, 49(4), pp. 2253-2273. Full Gong reference.

Gong, W., Yang, D., Gupta, H. V. and Nearing, G. (2014). Estimating information entropy for hydrological data: One-dimensional case, Water Resour. Res., 50, 5003–5018. Full Gong reference.

Goodwell, Allison E., and Maoya Bassiouni. “Source relationships and model structures determine information flow paths in ecohydrologic models.” Water Resources Research: e2021WR031164. https://doi.org/10.1029/2021WR031164

Goodwell, Allison, and Nicholas Campbell. “An information theory-based approach to characterize drivers of upstream salmon migration.” PloS one 17.6 (2022): e0269193.

Goodwell, A. E., et al. “Dynamic process connectivity explains ecohydrologic responses to rainfall pulses and drought.” Proceedings of the National Academy of Sciences (2018): 201800236. https://doi.org/10.1371/journal.pone.0269193

Goodwell, A. E. and Kumar, P. (2017). “Temporal Information Partitioning Networks (TIPNets): A process network approach to infer ecohydrologic shifts,” Water Resources Research, 53(7), pp. 5899-5919.

Goodwell, A. and Kumar, Praveen (2015). “Information Theoretic Measures to Infer Feedback Dynamics in Coupled Logistic Networks.” Entropy 17.11: 7468-7492.

Goodwell, A. E., Jiang, P., Ruddell, B. L., & Kumar, P. (2020). Debates—Does information theory provide a new paradigm for Earth science? Causality, interaction, and feedback. Water Resources Research, 56, e2019WR024940. https://doi.org/10.1029/2019WR024940

Griffin, A. (2008): Maximum Entropy: The Unviersal Method for Inference. Dissertation at the University of Albany, New York.

Gupta H.V., Ehsani, R.M., Roy, T., Sans-Fuentes, M.A., Ehret, U., and Behrangi, A. (2021). “Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples.” Section on Information Theory, Probability and Statistics, Entropy, 23(6), 740, doi.org/10.3390/e23060740

Gupta, H.V., Ehsani, M. R., Roy, T., Sans-Fuentes, M. A., Ehret, U., & Behrangi, A. (2021). Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples. arXiv preprint arXiv:2102.12675. Full Gupta reference.

Gupta, H.V. and Nearing, G.S. (2014). Debates—The future of hydrological sciences: A (common) path forward? Using models and data to learn: A systems theoretic perspective on the future of hydrological science, Water Resour. Res., 50, 5351–5359. Full Gupta reference.

Hejazi, M.I., X. Cai, and B.L. Ruddell (2008). The role of hydrologic information in reservoir operation – Learning from historical releases, Advances in Water Resources. Full Hejazi reference.

Hlaváčková-Schindler, K.; Paluš, M.; Vejmelka, M.; Bhattacharya, J. (2007). Causality detection based on information-theoretic approaches in time series analysis. Phys. Rep. 441, 1–46.

Hlinka, Jaroslav, et al. “Reliability of inference of directed climate networks using conditional mutual information.” Entropy 15.6 (2013): 2023-2045.

James, R. G., Barnett, N. and Crutchfield, J. P. (2016) ‘Information Flows? A Critique of Transfer Entropies’, Physical Review Letters, 116(23).

Jiang, P. and Kumar, P. (2020) “Bundled Causal History Interaction.” Entropy 2020, 22(3), 360; https://doi.org/10.3390/e22030360

Jiang, P. and Kumar, P. (2019) “Using Information Flow for Whole System Understanding from Component Dynamics.” Water Resources Research. https://doi.org/10.1029/2019WR025820

Jiang, Peishi, and Kumar, P. (2019) “Information transfer from causal history in complex system dynamics.” Physical Review E 99.1: 012306. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.012306

Jiang, P. and Kumar, P. (2018). “Interactions of information transfer along separable causal paths,” Phys. Rev. E 97, 042310.

Kiesel, J., Stanzel, P., Kling, H., Jähnig, S., Fohrer, N., and Pechlivanidis, I.G. (2020). “Streamflow-based evaluation of climate model sub-selection methods for impact assessments.” Climatic Change, https://doi.org/10.1007/s10584-020-02854-8

Knuth, K. H. (2002). “What Is A Question?” In: C. Williams (ed.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Moscow ID 2002, AIP Conference Proceedings vol. 659, American Institute of Physics, Melville NY, pp. 227-242. Full Knuth reference.

Knuth, K. H. (2004) ‘What is a question?’ Full Knuth reference.

Knuth, K. H. (2010). ‘Information physics: The new frontier’. Full Knuth reference.

Knuth, Kevin H., et al. “Revealing relationships among relevant climate variables with information theory.” arXiv preprint arXiv:1311.4632 (2013).

Koutsoyiannis, Demetris. (2005). “Uncertainty, entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling/Incertitude, entropie, effet d’échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d’état.” Hydrological Sciences Journal 50.3.

Krich, Christopher, Jakob Runge, Diego G. Miralles, Mirco Migliavacca, Oscar Perez‑Priego, Tarek S. El-Madany, Arnaud Carrara, and Miguel D. Mahecha. “Causal networks of biosphere–atmosphere interactions.” Biogeosciences, 17, 1033–1061, 2020
https://doi.org/10.5194/bg-17-1033-2020

Kumar, P., & Gupta, H. V. (2020). Debates—Does Information Theory provide a new paradigm for Earth Science?. Water Resources Research, 56, e2019WR026398. https://doi.org/10.1029/2019WR026398

Kumar, P. and Ruddell, B.L. (2010). Information Driven Ecohydrologic Self-Organization. Entropy 2010, 12, 2085–2096.

Larsen, Laurel G., et al. “Complex networks of functional connectivity in a wetland reconnected to its floodplain.” Water Resources Research 53.7 (2017): 6089-6108.

Leung, L. and North, G. (1990). Information Theory and Climate Prediction. Journal of Climate, V 3.

Lindley D.V. (1956). On the measure of information provided by an experiment. Ann. Math. Statist. 27, 986–1005.

MacKay, D. J. (2003) Information theory, inference and learning algorithms. Cambridge University Press.

Majda, A. & Gershgorin, B. (2010). “Quantifying uncertainty in climate change science through empirical information theory.” Proceedings of the National Academy of Sciences 107.34: 14958-14963.

Moges, E. et al., (2022), HydroBench, GitHub. https://github.com/EMscience/HydroBench

Moges, E., et al. (2022), HydroBench: Jupyter supported reproducible hydrological model benchmarking and diagnostic tool, Frontiers in Earth Science, No.30, September 2022. https://doi.org/10.3389/feart.2022.884766

Moges, E., Ruddell, B. L., Zhang, L., Driscoll, J. M., & Larsen, L. G. Strength and memory of precipitation’s control over streamflow across the conterminous United States. Water Resources Research, e2021WR030186. https://doi.org/10.1029/2021WR030186

Nearing, Grey S., et al. (2013). “A philosophical basis for hydrological uncertainty.” Hydrological Sciences Journal 61.9 (2016): 1666-1678.An information-theoretical perspective on weighted ensemble forecasts SV Weijs, N Van De Giesen – Journal of Hydrology.

Nearing, G. S. and Gupta, H. V. (2015). The quantity and quality of information in hydrologic models, Water Resour. Res., 51, 524–538. Full Nearing reference.

Nearing, Grey and Gupta, Hoshin (2017). “Information vs. Uncertainty as the Foundation for a Science of Environmental Modeling.” Full Nearing reference.

Nearing, G. S., Gupta, H. V. and Crow, W. T. (2013). Information loss in approximately Bayesian estimation techniques: A comparison of generative and discriminative approaches to estimating agricultural productivity. Journal of Hydrology 507, 163-173. Full Nearing reference.

Nearing, G. S., Gupta, H. V., Crow, W. T. and Gong, W. (2013b). ‘An approach to quantifying the efficiency of a Bayesian filter’, Water Resources Research, 49(4), pp. 2164-2173.

Nearing, G.S. Moran, M.S. Scott, R.L. & Ponce-Campos, G. (2012) ‘Coupling diffusion and maximum entropy models to estimate thermal inertia’, Remote Sensing of Environment, 119, pp. 222-231. Full Nearing reference.

Nearing, G. S., Ruddell, B. L., Bennett, A. R., Prieto, C., & Gupta, H. V. (2020). Does information theory provide a new paradigm for earth science? Hypothesis testing. Water Resources Research, 56, e2019WR024918. https://doi.org/10.1029/2019WR024918

Nearing, G. S., Ruddell, B. L., Clark, M. P., Nijssen, B., & Peters-Lidard, C. (2018). Benchmarking and Process Diagnostics of Land Models. Journal of Hydrometeorology, (2018). https://doi.org/10.1175/JHM-D-17-0209.1.

Nearing, G. S., Ruddell, B., Clark, M. P. and Nissan, B. (2017) “Process-Level Diagnostics of Terrestrial Hydrology Models.” American Meteorological Society 31st conference on Hydrology, Seattle, WA USA.

Nowack, P., Runge, J., Eyring, V. et al. (2020) “Causal networks for climate model evaluation and constrained projections.” Nat Commun 11, 1415. https://doi.org/10.1038/s41467-020-15195-y

Olbrich, E., Bertschinger, N., and Rauh, J. (2015). Information Decomposition and Synergy. Entropy pp. 3501–3517.

Papalexiou, Simon Michael, and Koutsoyiannis, Demetris (2012). “Entropy-based derivation of probability distributions: A case study to daily rainfall.” Advances in Water Resources 45: 51-57. Lessons from the long flow records of the Nile: determinism vs indeterminism and maximum entropy D Koutsoyiannis, A Georgakakos – 2006

Pechlivanidis, I.G., Gupta, H., and Bosshard, T. (2018). “An Information Theory Approach to identifying a representative subset of hydro-climatic simulations for impact modeling studies.” Water Resources Research, doi:10.1029/2017WR022035.

Pechlivanidis, I. G., Jackson, B., McMillan, H. and Gupta, H. V. (2016). Robust informational entropy-based descriptors of flow in catchment hydrology. Hydrological Sciences Journal 61 (1), 1-18. Full Pechlivanidis reference.

Pechlivanidis, I. G., Jackson, B., McMillan, H. K., & Gupta, H. V. (2012). Using an informational entropy-based metric as a diagnostic of flow duration to drive model parameter identification. Global NEST Journal, 14(3), 325–334.

Pechlivanidis, I. G., Jackson, B., McMillan, H., & Gupta, H. (2014). Use of an entropy-based metric in multiobjective calibration to improve model performance. Water Resources Research, 50(10), 8066–8083. https://doi.org/10.1002/2013WR014537

Perdigão, R. A. P., Ehret, U., Knuth, K. H., & Wang, J. ( 2020). Debates: Does information theory provide a new paradigm for Earth science? Emerging concepts and pathways of information physics. Water Resources Research, 56, e2019WR025270. https://doi.org/10.1029/2019WR025270

Pires, C. A. L. and R. A. P. Perdigao (2012). Minimum Mutual Information and Non-Gaussianity Through the Maximum Entropy Method: Theory and Properties. Entropy 2012, 14, 1103-1126; Full Pires reference.

Pompe, Bernd, and Jakob Runge. “Momentary information transfer as a coupling measure of time series.” Physical Review E 83.5 (2011): 051122. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.83.051122

Pothapakula, Praveen Kumar, Cristina Primo, and Bodo Ahrens. “Quantification of Information Exchange in Idealized and Climate System Applications.” Entropy 21.11 (2019): 1094. https://doi.org/10.3390/e21111094

Qiu, J., Crow, W. T., Nearing, G. S., Mo, X. and Liu, S. (2014). The impact of vertical measurement depth on the information content of soil moisture times series data, Geophys. Res. Lett., 41, 4997–5004. Full Qui reference.

Quijano, Juan, and Henry Lin. “Entropy in the critical zone: a comprehensive review.” Entropy 16.6 (2014): 3482-3536. Full Quijano and Lin reference.

Ruddell, B. L., Drewry, D. T., & Nearing, G. S. (2019), Information theory for model diagnostics: structural error is indicated by tradeoffs between functional and predictive performance. Water Resources Research. https://doi.org/10.1029/2018WR023692

Ruddell, B. L. and Kumar, P. (2009a). “Ecohydrologic process networks: 1. Identification,” Water Resources Research, 45(3).

Ruddell, B. L. and Kumar, P. (2009b). “Ecohydrologic process networks: 2. Analysis and characterization,” Water Resources Research, 45(3), pp. W03420.

Ruddell, B. L., Yu, R., Kang, M. and Childers, D. L. (2015). ‘Seasonally varied controls of climate and phenophase on terrestrial carbon dynamics: modeling eco-climate system state using Dynamical Process Networks’, Landscape Ecology, pp. 1-16.

Ruddell, B.L., Drewry, D. and Brunsell, N. (2012). Applications of Information Theory for Ecohydrology Model Diagnostics, Data analysis and modeling in Earth sciences (DAMES), Potsdam Physical Climate Institute (PIK), Potsdam, Germany, October 2012.

Ruddell, B.L., N.A. Brunsell and P. Stoy (2013). Applying information theory to quantify process uncertainty, feedback, and scale in the Earth system. EoS, 94, 56. Full Ruddell reference.

Runge, J., Heitzig, J., Petoukhov, V., and Kurths, J. (2012). Escaping the curse of dimensionality in estimating multivariate transfer entropy. Phys. Rev. Lett. 108.

Runge, Jakob, et al. “Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy.” Physical Review E 86.6 (2012): 061121.

Runge, Jakob, Reik V. Donner, and Jürgen Kurths. “Optimal model-free prediction from multivariate time series.” Physical Review E 91.5 (2015): 052909.

Schreiber, T. (2000). Measuring information transfer. Phys. Rev. Lett. 85, 461.

Sebastiani P. and Wynn H.P. (2000). Maximum entropy sampling and optimal Bayesian experimental design. J. Roy. Stat. Soc. B, 62:145-157, 2000.

Shannon C.E. and Weaver, W. (1949). The Mathematical Theory of Information, University of Illinois Press, Urbana IL.

Singh, V.P. (2014). Introduction to Entropy Theory in Hydraulic Engineering. 784 pp., ASCE Press, Reston, Virginia, 2014.

Smirnov, D.A. (2013). Spurious causalities with transfer entropy. Phys. Rev. E 87.

Stevens, B. (2020). The Perils of Computing Too Much and Thinking Too Little. https://eos.org/editor-highlights/the-perils-of-computing-too-much-and-thinking-too-little.

Thiesen, S. and Ehret, U. (2021). “Assessing local and spatial uncertainty with nonparametric geostatistics.” Stochastic Environmental Research and Risk Assessment (2022) 36:173–199. https://link.springer.com/article/10.1007%2Fs00477-021-02038-5

Thiesen, S., Vieira, D. M., Mälicke, M., Loritz, R., Wellmann, J. F., and Ehret, U.. (2020). “Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics.” Hydrol. Earth Syst. Sci., 24, 4523–4540, https://doi.org/10.5194/hess-24-4523-2020.

Thiesen, S., Darscheid, P., and Ehret, U. (2019). “Identifying rainfall-runoff events in discharge time series: a data-driven method based on information theory.” Hydrol. Earth Syst. Sci., 23, 1015–1034, https://doi.org/10.5194/hess-23-1015-2019.

Tononi, G. (2011). ‘Integrated information theory of consciousness: an updated account’, Archives italiennes de biologie, 150(2-3), pp. 56-90.

Vejmelka, M. and Paluš, M. (2008). Inferring the directionality of coupling with conditional mutual information. Phys. Rev. E 2008, 77.

Wang, J. F. and Bras, R. L. (2011). “A model of evapotranspiration based on the theory of maximum entropy production,” Water Resources Research, 47. Full Wang reference.

Weijs, S. V., Schoups, G. and Giesen, N. (2010). ‘Why hydrological predictions should be evaluated using information theory’, Hydrology and Earth System Sciences, 14(12), pp. 2545-2558.

Weijs, S. V., Ronald Van Nooijen, and Nick Van De Giesen (2011). “Kullback–Leibler divergence as a forecast skill score with classic reliability–resolution–uncertainty decomposition.” Monthly Weather Review 138.9 (2010): 3387-3399. Accounting for observational uncertainty in forecast verification: an information-theoretical view on forecasts, observations, and truth SV Weijs, N Van De Giesen – Monthly Weather Review

Weijs, S. V., & Ruddell, B. L. (2020). Debates: Does information theory provide a new paradigm for earth science? Sharper predictions using Occam’s digital razor. Water Resources Research, 56, e2019WR026471. https://doi.org/10.1029/2019WR026471

Weijs, S. V., van de Giesen, Nick and Parlange, Marc B. (2013). “HydroZIP: how hydrological knowledge can be used to improve compression of hydrological data.” Entropy 15.4 (2013): 1289-1310. Data compression to define information content of hydrological time series SV Weijs, N Van De Giesen, MB Parlange – Hydrology and Earth System Sciences.

Williams, P. L. and Beer, R. D. (2010). Nonnegative decomposition of multivariate information.

Yu, R., Ruddell, B. L., Kang, M., Kim, J., & Childers, D. (2019). Anticipating global terrestrial ecosystem state change using FLUXNET. Global change biology. https://doi.org/10.1111/gcb.14602 Full Yu reference.