Ding, H., Trajcevski, G., Scheuermann, P., Wang, X. Y., and Keogh, E.: Querying and Mining of Time Series Data: Experimental Comparison of Representations and Distance Measures, Proceedings of the Vldb Endowment, 1, 1542–1552, https://doi.org/10.14778/1454159.1454226, 2008.
Douzas, G. and Bacao, F.: Self-Organizing Map Oversampling (SOMO) for imbalanced data set learning, Expert systems with Applications, 82, 40–52, https://doi.org/10.1016/j.eswa.2017.03.073, 2017.
Dupas, R., Tavenard, R., Fovet, O., Gilliet, N., Grimaldi, C., and Gascuel-Odoux, C.: Identifying seasonal patterns of phosphorus storm dynamics with dynamic time warping, Water Resour. Res., 51, 8868–8882, https://doi.org/10.1002/2015wr017338, 2015.
Evans, C. and Davies, T. D.: Causes of concentration/discharge hysteresis and its potential as a tool for analysis of episode hydrochemistry, Water Resour. Res., 34, 129–137, https://doi.org/10.1029/97wr01881, 1998.
Gellis, A. C.: Factors influencing storm-generated suspended-sediment concentrations and loads in four basins of contrasting land use, humid-tropical Puerto Rico, Catena, 104, 39–57, https://doi.org/10.1016/j.catena.2012.10.018, 2013.
Haddadchi, A. and Hicks, M.: Interpreting event-based suspended sediment concentration and flow hysteresis patterns, Journal of Soils and Sediments, 21, 592–612, https://doi.org/10.1007/s11368-020-02777-y, 2021.
Hamshaw, S. D., Dewoolkar, M. M., Schroth, A. W., Wemple, B. C., and Rizzo, D. M.: A New Machine-Learning Approach for Classifying Hysteresis in Suspended-Sediment Discharge Relationships Using High-Frequency Monitoring Data, Water Resour. Res., 54, 4040–4058, https://doi.org/10.1029/2017wr022238, 2018.
Harris, C. R., Millman, K. J., Van Der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., and Smith, N. J.: Array programming with NumPy, Nature, 585, 357–362, https://doi.org/10.1038/s41586-020-2649-2, 2020.
Heidel, S. G.: The progressive lag of sediment concentration with flood waves, Eos, Transactions American Geophysical Union, 37, 56–66, https://doi.org/10.1029/TR037i001p00056, 1956.
Hodson, T., Hariharan, J., Black, S., and Horsburgh, J.: dataretrieval (Python): a Python package for discovering and retrieving water data, US Federal Hydrologic Web Services [code], https://doi.org/10.5066/P94I5TX3, 2023.
Husic, A., Fox, J. F., Clare, E., Mahoney, T., and Zarnaghsh, A.: Nitrate Hysteresis as a Tool for Revealing Storm-Event Dynamics and Improving Water Quality Model Performance, Water Resour. Res., 59, e2022WR033180, https://doi.org/10.1029/2022WR033180, 2023.
Jing, T. G., Zeng, Y., Fang, N. F., Dai, W., and Shi, Z. H.: A Review of Suspended Sediment Hysteresis, Water Resour. Res., 61, e2024WR037216, https://doi.org/10.1029/2024WR037216, 2025.
Kalteh, A. M., Hiorth, P., and Bemdtsson, R.: Review of the self-organizing map (SOM) approach in water resources: Analysis, modelling and application, Environ. Model. Softw., 23, 835–845, https://doi.org/10.1016/j.envsoft.2007.10.001, 2008.
Kiviluoto, K.: Topology preservation in self-organizing maps, Proceedings of International Conference on Neural Networks (ICNN'96), Washington, DC, USA, 294–299, 1996.
Kohonen, T.: Self-Organized Formation of Topologically Correct Feature Maps, Biological Cybernetics, 43, 59–69, https://doi.org/10.1007/Bf00337288, 1982.
Kohonen, T.: The self-organizing map, Proc. IEEE, 78, 1464–1480, https://doi.org/10.1109/5.58325, 1990.
Kohonen, T.: Essentials of the self-organizing map, Neural Netw., 37, 52–65, https://doi.org/10.1016/j.neunet.2012.09.018, 2013.
Koppa, A., Gebremichael, M., and Yeh, W. W.: Multivariate calibration of large scale hydrologic models: The necessity and value of a Pareto optimal approach, Adv. Water Resour., 130, 129–146, https://doi.org/10.1016/j.advwatres.2019.06.005, 2019.
Lee, S., Kim, J., Hwang, J., Lee, E., Lee, K. J., Oh, J., Park, J., and Heo, T. Y.: Clustering of Time Series Water Quality Data Using Dynamic Time Warping: A Case Study from the Bukhan River Water Quality Monitoring Network, Water, 12, 2411, https://doi.org/10.3390/w12092411, 2020.
Liu, W., Birgand, F., Tian, S., and Chen, C.: Event-scale hysteresis metrics to reveal processes and mechanisms controlling constituent export from watersheds: A review(?), Water Res., 200, 117254, https://doi.org/10.1016/j.watres.2021.117254, 2021.
Lloyd, C. E. M., Freer, J. E., Johnes, P. J., and Collins, A. L.: Using hysteresis analysis of high-resolution water quality monitoring data, including uncertainty, to infer controls on nutrient and sediment transfer in catchments, Sci. Total Environ., 543, 388–404, https://doi.org/10.1016/j.scitotenv.2015.11.028, 2016.
Malutta, S., Kobiyama, M., Chaffe, P. L. B., and Bonuma, N. B.: Hysteresis analysis to quantify and qualify the sediment dynamics: state of the art, Water Sci. Technol., 81, 2471–2487, https://doi.org/10.2166/wst.2020.279, 2020.
Marin-Ramirez, A.: HySOM: A Python library for Self-Organizing Map-based analysis of concentration–discharge hysteresis (v0.4.0), Zenodo [code], https://doi.org/10.5281/zenodo.18553832, 2026.
Marin-Ramirez, A., Mahoney, D. T., Riddle, B., Bettel, L., and Fox, J. F.: Response time of fast flowing hydrologic pathways controls sediment hysteresis in a low-gradient watershed, as evidenced from tracer results and machine learning models, J. Hydrol., 645, 132207, https://doi.org/10.1016/j.jhydrol.2024.132207, 2024.
Mazilamani, L. S., Walsh, R. P. D., Annammala, K. V., Bidin, K., Yusop, Z., Reynolds, G., and Nainar, A.: Concentration-discharge hysteresis: current approaches and future directions for quantifying pollutant dynamics in storm events-with a particular focus on the tropics, Sustainable Water Resources Management, 10, 156, https://doi.org/10.1007/s40899-024-01130-2, 2024.
McGrain, P. and Currens, J. C.: Topography of Kentucky: Kentucky Geological Survey, Series X, Special Publication, 25, 76,
https://kgs.uky.edu/kgsweb/olops/pub/kgs/KGS10SP25reduce.pdf (last access: 5 March 2026), 1978.
Miljković, D.: Brief review of self-organizing maps, 2017 2017 40th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), Opatija, Croatia, 2017, 1061–1066, https://doi.org/10.23919/MIPRO.2017.7973581, 2017.
Molder, B., Cockburn, J., Berg, A., Lindsay, J., and Woodrow, K.: Sediment-assisted nutrient transfer from a small, no-till, tile drained watershed in Southwestern Ontario, Canada, Agric. Water Manage., 152, 31–40, https://doi.org/10.1016/j.agwat.2014.12.010, 2015.
Nainggolan, R., Perangin-angin, R., Simarmata, E., and Tarigan, A. F.: Improved the performance of the K-means cluster using the sum of squared error (SSE) optimized by using the Elbow method, J. Phys. Conf. Ser., 1361, 012015, https://doi.org/10.1088/1742-6596/1361/1/012015, 2019.
Munoz, A. and Muruzábal, J.: Self-organizing maps for outlier detection, Neurocomputing, 18, 33–60, https://doi.org/10.1016/S0925-2312(97)00068-4, 1998.
Pickering, C. and Ford, W. I.: Effect of watershed disturbance and river-tributary confluences on watershed sedimentation dynamics in the Western Allegheny Plateau, J. Hydrol., 602, 126784, https://doi.org/10.1016/j.jhydrol.2021.126784, 2021.
Pölzlbauer, G.: Survey and comparison of quality measures for self-organizing maps, in: Proceedings of the Fifth Workshop on Data Analysis (WDA2004), edited by: Paralič, J., Pölzlbauer, G., and Rauber, A., Elfa Academic Press, 67–82, 2004.
Samarasinghe, S.: Neural networks for applied sciences and engineering: from fundamentals to complex pattern recognition, Auerbach publications, https://doi.org/10.1201/9780849333750, 2016.
Sherriff, S. C., Rowan, J. S., Fenton, O., Jordan, P., Melland, A. R., Mellander, P. E., and hUallachain, D. O.: Storm Event Suspended Sediment-Discharge Hysteresis and Controls in Agricultural Watersheds: Implications for Watershed Scale Sediment Management, Environ. Sci. Technol., 50, 1769–1778, https://doi.org/10.1021/acs.est.5b04573, 2016.
Shokoohi-Yekta, M., Hu, B., Jin, H., Wang, J., and Keogh, E.: Generalizing DTW to the multi-dimensional case requires an adaptive approach, Data Min. Knowl. Discov., 31, 1–31, https://doi.org/10.1007/s10618-016-0455-0, 2017.
Speir, S. L., Rose, L. A., Blaszczak, J. R., Kincaid, D. W., Fazekas, H. M., Webster, A. J., Wolford, M. A., Shogren, A. J., and Wymore, A. S.: Catchment concentration–discharge relationships across temporal scales: A review, Wiley Interdisciplinary Reviews: Water, 11, e1702, https://doi.org/10.1002/wat2.1702, 2024.
Tavenard, R., Faouzi, J., Vandewiele, G., Divo, F., Androz, G., Holtz, C., Payne, M., Yurchak, R., Rußwurm, M., and Kolar, K.: Tslearn, a machine learning toolkit for time series data, J. Mach. Learn. Res., 21, 1–6, 2020.
Vesanto, J.: Neural Network Tool for Data Mining: SOM Toolbox, in: Precedings of symposium on tool environments and developmen methods for intelligent systems (TOOLMET2000), 184–196, Oulun yliopistopain, Oulu, Finland, ISBN 951425595X, 2000.
Williams, G. P.: Sediment Concentration Versus Water Discharge during Single Hydrologic Events in Rivers, J. Hydrol., 111, 89–106, https://doi.org/10.1016/0022-1694(89)90254-0, 1989.
Zarnaghsh, A. and Husic, A.: Degree of Anthropogenic Land Disturbance Controls Fluvial Sediment Hysteresis, Environ. Sci. Technol., 55, 13737–13748, https://doi.org/10.1021/acs.est.1c00740, 2021.
Zuecco, G., Penna, D., Borga, M., and van Meerveld, H. J.: A versatile index to characterize hysteresis between hydrological variables at the runoff event timescale, Hydrol. Process., 30, 1449–1466, https://doi.org/10.1002/hyp.10681, 2016.