Challenges, unresolved open problems, and next-generation entropy hydrology

Authors

https://doi.org/10.48313/uda.v2i4.92

Abstract

Hydrological systems are naturally complex with great spatial and temporal variation caused by several interacting processes. Often difficult to fully reflect this complexity and related uncertainties are conventional deterministic and stochastic hydrological models. A framework for measuring uncertainty, disorder, and information content inside hydrological processes based in thermodynamics and information theory is given by entropy. This work thoroughly surveys applications of entropy modeling in hydrology, therefore highlighting the unresolved issues and obstacles impeding its broad adoption. Additionally, it investigates the terrain of next-generation entropic hydrology, pointing out potential avenues for future development and research including Machine Learning (ML), multiscale analysis, and sophisticated data-driven techniques. Through the entropy perspective, the goal is to highlight the current state-of-art and plan a route for more strong, educational, and predictive hydrological research.

Keywords:

Entropy, Hydrology, Information theory, Uncertainty, Water resources, Maximum entropy principle, Open problems, Challenges, Next-generation hydrology

References

  1. [1] Dembélé, M., Hrachowitz, M., Savenije, H. H. G., Mariéthoz, G., & Schaefli, B. (2020). Improving the predictive skill of a distributed hydrological model by calibration on spatial patterns with multiple satellite data sets. Water resources research, 56(1), e2019WR026085. https://doi.org/10.1029/2019wr026085
  2. [2] Van Stan II, J. T., & Simmons, J. (2024). Plato’s wonder and hydrology. In Hydrology and its discontents: Contemplations on the innate paradoxes of water research (pp. 131–145). Springer. https://doi.org/10.1007/978-3-031-49768-1_14
  3. [3] Shannon, C. E. (1948). A mathematical theory of communication. The bell system technical journal, 27(3), 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  4. [4] Mageed, I. A. (2024). Entropy-based feature selection with applications to industrial internet of things (IoT) and breast cancer prediction. Big data and computing visions, 4(3), 170–179. https://doi.org/10.22105/bdcv.2024.479315.1203
  5. [5] Mageed, I. A. (2024). Entropic imprints on bioinformatics. Big data and computing visions, 4(4), 245–256. https://doi.org/10.22105/bdcv.2024.479239.1201
  6. [6] Mageed, I. A., & Zhang, Q. (2023). Formalism of the rényian maximum entropy (RMF) of the stable M/G/1 queue with geometric mean (GeoM) and shifted geometric mean (SGeoM) constraints with potential geom applications to wireless sensor networks (WSNs). Electronic journal of computer science and information technology, 9(1), 31–40. https://doi.org/10.52650/ejcsit.v9i1.143
  7. [7] Mageed, I. A., & Zhang, Q. (2022). An introductory survey of entropy applications to information theory, queuing theory, engineering, computer science, and statistical mechanics. 2022 27th international conference on automation and computing (ICAC) (pp. 1–6). IEEE. https://doi.org/10.1109/ICAC55051.2022.9911077
  8. [8] Koutsoyiannis, D., & Montanari, A. (2022). Bluecat: A local uncertainty estimator for deterministic simulations and predictions. Water resources research, 58(1), e2021WR031215. https://doi.org/10.1029/2021WR031215
  9. [9] Li, Z., & Izumida, Y. (2023). Thermodynamic efficiency of atmospheric motion governed by the Lorenz system. Physical review e, 108(4), 44201. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.044201
  10. [10] Jaime Gómez-Hernández, J., Chen, Z., & Zanini, A. (2020). Tracking back the source of contamination. Book of abstracts (pp. 447). Interpore. https://air.unipr.it/handle/11381/2888088
  11. [11] Schroers, S., Eiff, O., Kleidon, A., Scherer, U., Wienhöfer, J., & Zehe, E. (2022). Morphological controls on surface runoff: An interpretation of steady-state energy patterns, maximum power states and dissipation regimes within a thermodynamic framework. Hydrology and earth system sciences, 26(12), 3125–3150. https://doi.org/10.5194/hess-26-3125-2022
  12. [12] Mageed, I. A. (2023). Cosistency axioms of choice for Ismail’s entropy formalism (IEF) Combined with information-theoretic (IT) applications to advance 6G networks. European journal of technique (EJT), 13(2), 207–213. https://doi.org/10.36222/ejt.1299311
  13. [13] Mageed, I. A. (2024). Entropic artificial intelligence and knowledge transfer. Advanced machine learning and artificial intelligence, 5(2), 1–8. https://www.researchgate.net/publication/379899469
  14. [14] Moraffah, R., Sheth, P., Karami, M., Bhattacharya, A., Wang, Q., Tahir, A., … ., & Liu, H. (2021). Causal inference for time series analysis: Problems, methods and evaluation. Knowledge and information systems, 63(12), 3041–3085. https://doi.org/10.1007/s10115-021-01621-0
  15. [15] Eibeck, A., Zhang, S., Lim, M. Q., & Kraft, M. (2024). A simple and efficient approach to unsupervised instance matching and its application to linked data of power plants. Journal of web semantics, 80, 100815. https://doi.org/10.1016/j.websem.2024.100815
  16. [16] Jaynes, E. T. (1957). Information theory and statistical mechanics. II. Physical review, 108(2), 171–190. https://doi.org/10.1103/PhysRev.108.171
  17. [17] Sreeparvathy, V., & Srinivas, V. V. (2020). A fuzzy entropy approach for design of hydrometric monitoring networks. Journal of hydrology, 586, 124797. https://doi.org/10.1016/j.jhydrol.2020.124797
  18. [18] Sharma, A., Kumar, H., & Kumar, B. (2023). One-dimensional velocity distribution in seepage bed open channels using Tsallis entropy. ASCE-asme journal of risk and uncertainty in engineering systems, part A: civil engineering, 9(4), 4023030. https://doi.org/10.1061/AJRUA6.RUENG-1041
  19. [19] Farajpanah, H., Adib, A., Lotfirad, M., Esmaeili-Gisavandani, H., Riyahi, M. M., & Zaerpour, A. (2024). A novel application of waveform matching algorithm for improving monthly runoff forecasting using wavelet--ML models. Journal of hydroinformatics, 26(7), 1771–1789. https://doi.org/10.2166/hydro.2024.128
  20. [20] Prajapati, A., Roshni, T., & Berndtsson, R. (2024). Entropy based approach for precipitation monitoring network in Bihar, India. Journal of hydrology: Regional studies, 51, 101623. https://doi.org/10.1016/j.ejrh.2023.101623
  21. [21] Hermosilla-Albala, N., Silva, F. E., Cuadros-Espinoza, S., Fontsere, C., Valenzuela-Seba, A., Pawar, H., … ., & Boubli, J. P. (2024). Whole genomes of Amazonian uakari monkeys reveal complex connectivity and fast differentiation driven by high environmental dynamism. Communications biology, 7(1), 1283. https://doi.org/10.1038/s42003-024-06901-3
  22. [22] Jeung, M., Her, Y., Baek, S. S., & Yoon, K. (2024). Sensitivity of hydrological machine learning prediction accuracy to information quantity and quality. Hydrology and earth system sciences discussions, 30(4), 1077–1095. https://doi.org/10.5194/hess-30-1077-2026
  23. [23] Saha, S., Sarkar, D., & Mondal, P. (2022). Efficiency exploration of frequency ratio, entropy and weights of evidence-information value models in flood vulnerabilityassessment: A study of raiganj subdivision, Eastern India. Stochastic environmental research and risk assessment, 36(6), 1721–1742. https://doi.org/10.1007/s00477-021-02115-9
  24. [24] Cui, Z., Wang, J., Gao, C., & Dong, S. (2024). Application research on China’s logistics network structure: An overview. International journal of logistics research and applications, 27(8), 1277–1299. https://doi.org/10.1080/13675567.2022.2128094
  25. [25] Shi, L., Li, Y., Han, J., & Yang, X. (2024). Water richness evaluation of coal roof aquifers based on the game theory combination weighting method and the topsis model. Mine water and the environment, 43(4), 691–706. https://doi.org/10.1007/s10230-024-01018-9
  26. [26] Sun, S., Xue, Q., Xing, X., Zhao, H., & Zhang, F. (2024). Remote sensing image interpretation for coastal zones: A review. Remote sensing, 16(24), 1-27. https://doi.org/10.3390/rs16244701
  27. [27] Dehkordi, M. F., Hatefi, S. M., & Tamošaitienė, J. (2025). An integrated fuzzy shannon entropy and fuzzy ARAS model using risk indicators for water resources management under uncertainty. Sustainability, 17(11), 1-22. https://doi.org/10.3390/su17115108
  28. [28] Pei, W., Hao, L., Fu, Q., Ren, Y., & Li, T. (2023). Study on agricultural drought risk assessment based on information entropy and a cluster projection pursuit model. Water resources management, 37(2), 619–638. https://doi.org/10.1007/s11269-022-03391-y
  29. [29] Ju, X., Wang, D., Wang, Y., Singh, V. P., Xu, P., Zhang, A., … ., & Zhang, J. (2023). An entropy and copula-based framework for streamflow prediction and spatio-temporal identification of drought. Stochastic environmental research and risk assessment, 37(6), 2187–2204. https://doi.org/10.1007/s00477-023-02388-2
  30. [30] Tahroudi, M. N., Ramezani, Y., De Michele, C., & Mirabbasi, R. (2023). Development of the entropy theory for wind speed monitoring by using copula-based approach. https://doi.org/10.21203/rs.3.rs-2526048/v1
  31. [31] Guo, Y., Han, H., Nones, M., Xu, W., & Liu, S. (2023). Information entropy theory-based optimizing of gauge networks for hydrological modelling—A case study in the Loess Plateau, China. In International school of hydraulics (pp. 167–181). Springer. https://doi.org/10.1007/978-3-031-56093-4_13
  32. [32] Pizarro, A., Koutsoyiannis, D., & Montanari, A. (2025). Combining uncertainty quantification and entropy-inspired concepts into a single objective function for rainfall-runoff model calibration. Hydrology and earth system sciences discussions, 2025, 1–21. https://doi.org/10.5194/hess-29-4913-2025
  33. [33] Koutsoyiannis, D., Iliopoulou, T., Koukouvinos, A., Malamos, N., Mamassis, N., Dimitriadis, P., … ., & Markantonis, D. (2023). In search of climate crisis in Greece using hydrological data: 404 not found. Water, 15(9), 1-22. https://doi.org/10.3390/w15091711
  34. [34] A Mageed, I. (2024). Towards an info-geometric theory of the analysis of non-time dependent queueing systems. Risk assessment and management decisions, 1(1), 154–197. https://doi.org/10.48314/ramd.v1i1.47
  35. [35] Santos, L., Satolo, L. F., Oyarzabal, R., Escobar-Silva, E., Diniz, M., Negri, R., … ., & Bacelar, L. (2024). Machine learning-based hydrological models for flash floods: A systematic literature review. https://doi.org/10.1007/s44268-025-00071-9
  36. [36] Yan, D., Wang, Y., Qin, D., & Zhang, J. (2025). Hydrological geography: Theoretical framework, research progress, and future development directions. Geographical research bulletin, 4, 186–224. https://doi.org/10.50908/grb.4.0_186
  37. [37] Yaseen, Z. M. (2023). A new benchmark on machine learning methodologies for hydrological processes modelling: A comprehensive review for limitations and future research directions. Knowledge-based engineering and sciences, 4(3), 65–103. https://doi.org/10.51526/kbes.2023.4.3.65-103
  38. [38] A Mageed, I. (2024). On the rényi entropy functional, tsallis distributions and lévy stable distributions with entropic applications to machine learning. Soft computing fusion with applications, 1(2), 91–102. https://doi.org/10.22105/scfa.v1i2.33
  39. [39] Mageed, I. A., & Bhat, A. (2022). Generalized z-entropy (Gze) and fractal dimensions. Applied mathematics & information sciences., 16(5), 829–834. http://dx.doi.org/10.18576/amis/160517
  40. [40] Amigó, J. M., & Rosso, O. A. (2023). Ordinal methods: Concepts, applications, new developments, and challenges—In memory of Karsten Keller (1961-2022). Chaos: An interdisciplinary journal of nonlinear science, 33(8). https://doi.org/10.1063/5.0167263
  41. [41] Kim, Y., Garcia, M., Black, T. A., & Johnson, M. S. (2023). Assessing the complementary role of surface flux equilibrium (SFE) theory and maximum entropy production (MEP) principle in the estimation of actual evapotranspiration. Journal of advances in modeling earth systems, 15(7), e2022MS003224. https://doi.org/10.1029/2022MS003224
  42. [42] Álvarez Chaves, M., Acuña Espinoza, E., Ehret, U., & Guthke, A. (2025). When physics gets in the way: an entropy-based evaluation of conceptual constraints in hybrid hydrological models. EGUsphere. https://doi.org/10.5194/egusphere-2025-1699
  43. [43] Kumari, N., Srivastava, A., Sahoo, B., Raghuwanshi, N. S., & Bretreger, D. (2021). Identification of suitable hydrological models for streamflow assessment in the Kangsabati River Basin, India, by using different model selection scores. Natural resources research, 30(6), 4187–4205. https://doi.org/10.1007/s11053-021-09919-0
  44. [44] Pourmorad, S., Kabolizade, M., & Dimuccio, L. A. (2024). Artificial intelligence advancements for accurate groundwater level modelling: AN updated synthesis and review. Applied sciences, 14(16), 1–26. https://doi.org/10.3390/app14167358
  45. [45] Yu, X., Li, W., Yang, B., Li, X., Chen, J., & Fu, G. (2024). Periodic distribution entropy: Unveiling the complexity of physiological time series through multidimensional dynamics. Information fusion, 108, 102391. https://doi.org/10.1016/j.inffus.2024.102391
  46. [46] Tillman, F. D., Day, N. K., Miller, M. P., Miller, O. L., Rumsey, C. A., Wise, D. R., … ., & McDonnell, M. C. (2022). A review of current capabilities and science gaps in water supply data, modeling, and trends for water availability assessments in the Upper Colorado River Basin. Water, 14(23), 1-35. https://doi.org/10.3390/w14233813
  47. [47] Reichstein, M., Camps-Valls, G., Stevens, B., Jung, M., Denzler, J., Carvalhais, N., & Prabhat, F. (2019). Deep learning and process understanding for data-driven Earth system science. Nature, 566(7743), 195–204. https://doi.org/10.1038/s41586-019-0912-1
  48. [48] Ruddell, B. L., Clark, M., Driscoll, J. M., Gochis, D., Gupta, H., Huntzinger, D., … ., & Xu, Z. (2023). Calling for a national model benchmarking facility. https://doi.org/10.31223/X5195Q
  49. [49] Baumas, C., & Bizic, M. (2023). Did you say marine snow? Zooming into different types of organic matter particles and their importance in the open ocean carbon cycle. https://doi.org/10.31223/X5RM1T
  50. [50] Hu, S., Lou, Z., Yan, X., & Ye, Y. (2024). A survey on information bottleneck. IEEE transactions on pattern analysis and machine intelligence, 46(8), 5325–5344. https://doi.org/10.1109/TPAMI.2024.3366349
  51. [51] Huang, Z., Shao, J., Guo, W., Li, W., Zhu, J., & Fang, D. (2023). Hybrid machine learning-enabled multi-information fusion for indirect measurement of tool flank wear in milling. Measurement, 206, 112255. https://doi.org/10.1016/j.measurement.2022.112255
  52. [52] Allan, R. P., Barlow, M., Byrne, M. P., Cherchi, A., Douville, H., Fowler, H. J., … ., & Zolina, O. (2020). Advances in understanding large-scale responses of the water cycle to climate change. Annals of the new york academy of sciences, 1472(1), 49–75. https://doi.org/10.1111/nyas.14337
  53. [53] Volpi, E., Grimaldi, S., Aghakouchak, A., Castellarin, A., Chebana, F., & Papalexiou, S. M. (2024). The legacy of STAHY: milestones, achievements, challenges, and open problems in statistical hydrology. Hydrological sciences journal, 69(14), 1913–1949. https://doi.org/10.1080/02626667.2024.2385686
  54. [54] Chen, J., Arsenault, R., Brissette, F. P., & Zhang, S. (2021). Climate change impact studies: Should we bias correct climate model outputs or post-process impact model outputs? Water resources research, 57(5), e2020WR028638. https://doi.org/10.1029/2020WR028638

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Published

2025-12-23

Issue

Vol. 2 No. 4 (2025): Uncertainty Discourse and Applications

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Articles

How to Cite

A Mageed, I. (2025). Challenges, unresolved open problems, and next-generation entropy hydrology. Uncertainty Discourse and Applications, 2(4), 331-341. https://doi.org/10.48313/uda.v2i4.92

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