Barnett, L., Barrett, A. B., and Seth, A. K.: Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables, Phys. Rev. Lett., 103, 238701,
https://doi.org/10.1103/PhysRevLett.103.238701, 2009.
a
Bracken, L. J., Wainwright, J., Ali, G. A., Tetzlaff, D., Smith, M. W., Reaney, S. M., and Roy, A. G.: Concepts of hydrological connectivity: Research approaches, pathways and future agendas, Earth-Sci. Rev., 119, 17–34,
https://doi.org/10.1016/j.earscirev.2013.02.001, 2013.
a,
b,
c
CRA-W: Agrometeorological data for the Jemelle station, Wallonia,
https://agromet.be/, last access: 22 April 2022. a
Delforge, D., Muñoz‐Carpena, R., Van Camp, M., and Vanclooster, M.: A Parsimonious Empirical Approach to Streamflow Recession Analysis and Forecasting, Water Resour. Res., 56, e2019WR025771,
https://doi.org/10.1029/2019WR025771, 2020a.
a,
b,
c,
d,
e
Delforge, D., Watlet, A., Kaufmann, O., Van Camp, M., and Vanclooster, M.: “Data for: Time-series clustering approaches for subsurface zonation and hydrofacies detection using a real time-lapse electrical resistivity dataset”, V2, Mendeley Data [data set],
https://doi.org/10.17632/zh5b88vn78.2, 2020b.
a
Delforge, D., Watlet, A., Kaufmann, O., Van Camp, M., and Vanclooster, M.: Time-series clustering approaches for subsurface zonation and hydrofacies detection using a real time-lapse electrical resistivity dataset, J. Appl. Geophys., 184, 104203,
https://doi.org/10.1016/j.jappgeo.2020.104203, 2020c.
a,
b,
c,
d,
e,
f
Dooge, J.: Linear Theory of Hydrologic Systems, Agricultural Research Service, U.S. Department of Agriculture,
https://books.google.be/books?id=6acoAAAAYAAJ (last access: 14 April 2022), 1973.
a,
b,
c
Goodwell, A. E., Jiang, P., Ruddell, B. L., and Kumar, P.: Debates—Does Information Theory Provide a New Paradigm for Earth Science? Causality, Interaction, and Feedback, Water Resour. Res., 56, e2019WR024940,
https://doi.org/10.1029/2019WR024940, 2020.
a,
b,
c
Granger, C. W. J.: Investigating Causal Relations by Econometric Models and Cross-spectral Methods, Econometrica, 37, 424–438,
https://doi.org/10.2307/1912791, 1969.
a,
b,
c
Hartmann, A., Goldscheider, N., Wagener, T., Lange, J., and Weiler, M.: Karst water resources in a changing world: Review of hydrological modeling approaches, Rev. Geophys., 52, 218–242,
https://doi.org/10.1002/2013RG000443, 2014.
a,
b
Huffaker, R., Bittelli, M., and Rosa, R.: Nonlinear Time Series Analysis with R, vol. 1, Oxford University Press,
https://doi.org/10.1093/oso/9780198782933.001.0001, 2018.
a,
b,
c,
d,
e,
f,
g
Hume, D.: Philosophical Essays Concerning Human Understanding, A. Millar, 1748.
a,
b
Jourde, H., Mazzilli, N., Lecoq, N., Arfib, B., and Bertin, D.: KARSTMOD: A Generic Modular Reservoir Model Dedicated to Spring Discharge Modeling and Hydrodynamic Analysis in Karst, in: Hydrogeological and Environmental Investigations in Karst Systems, edited by: Andreo, B., Carrasco, F., Durán, J. J., Jiménez, P., and LaMoreaux, J. W., Springer Berlin Heidelberg, Environmental Earth Sciences, 1, 339–344,
https://doi.org/10.1007/978-3-642-17435-3_38, 2015.
a
Kadić, A., Denić-Jukić, V., and Jukić, D.: Revealing hydrological relations of adjacent karst springs by partial correlation analysis, Hydrol. Res., 49, 616–633,
https://doi.org/10.2166/nh.2017.064, 2018.
a
Klemeš, V.: Empirical and causal models in hydrology, in: Scientific Basis of Water-Resource Management, Washinton D.C.,
http://www.itia.ntua.gr/en/docinfo/1075/ (last access: 14 April 2022), 1982. a
Labat, D., Ababou, R., and Mangin, A.: Rainfall–runoff relations for karstic springs. Part I: convolution and spectral analyses, J. Hydrol., 238, 123–148,
https://doi.org/10.1016/S0022-1694(00)00321-8, 2000.
a
Larocque, M., Mangin, A., Razack, M., and Banton, O.: Contribution of correlation and spectral analyses to the regional study of a large karst aquifer (Charente, France), J. Hydrol., 205, 217–231,
https://doi.org/10.1016/S0022-1694(97)00155-8, 1998.
a
Mathevet, T., Lepiller, M. I., and Mangin, A.: Application of time-series analyses to the hydrological functioning of an Alpine karstic system: the case of Bange-L'Eau-Morte, Hydrol. Earth Syst. Sci., 8, 1051–1064,
https://doi.org/10.5194/hess-8-1051-2004, 2004.
a
Medina, M., Huffaker, R., Jawitz, J. W., and Muñoz-Carpena, R.: Nonlinear Dynamics in Treatment Wetlands: Identifying Systematic Drivers of Nonequilibrium Outlet Concentrations in Everglades STAs, Water Resour. Res., 55, 11101–11120,
https://doi.org/10.1029/2018WR024427, 2019.
a,
b,
c
Molini, A., Katul, G. G., and Porporato, A.: Causality across rainfall time scales revealed by continuous wavelet transforms, J. Geophys. Res., 115, D14123,
https://doi.org/10.1029/2009JD013016, 2010.
a,
b
Nes, E. H. v., Scheffer, M., Brovkin, V., Lenton, T. M., Ye, H., Deyle, E., and Sugihara, G.: Causal feedbacks in climate change, Nat. Clim. Change, 5, 445–448,
https://doi.org/10.1038/nclimate2568, 2015.
a
Ombadi, M., Nguyen, P., Sorooshian, S., and Hsu, K.: Evaluation of Methods for Causal Discovery in Hydrometeorological Systems, Water Resour. Res., 56, e2020WR027251,
https://doi.org/10.1029/2020WR027251, 2020.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k,
l,
m,
n,
o,
p
Park, J., Smith, C., Sugihara, G., Deyle, E., Saberski, E., Ye, H., and The Regents of the University of California: rEDM: Empirical Dynamic Modeling ('EDM'),
https://CRAN.R-project.org/package=rEDM, last access: 22 April 2022. a
Poulain, A., Watlet, A., Kaufmann, O., Van Camp, M., Jourde, H., Mazzilli, N., Rochez, G., Deleu, R., Quinif, Y., and Hallet, V.: Assessment of groundwater recharge processes through karst vadose zone by cave percolation monitoring, Hydrol. Process., 32, 2069–2083,
https://doi.org/10.1002/hyp.13138, 2018.
a,
b,
c,
d,
e,
f,
g,
h,
i
Reichenbach, H.: The Direction of Time, California library reprint series, University of California Press,
https://books.google.be/books?id=f6kNAQAAIAAJ (last access: 14 April 2022), 1956.
a,
b
Rinderer, M., Ali, G., and Larsen, L. G.: Assessing structural, functional and effective hydrologic connectivity with brain neuroscience methods: State-of-the-art and research directions, Earth-Sci. Rev., 178, 29–47,
https://doi.org/10.1016/j.earscirev.2018.01.009, 2018.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k,
l,
m,
n
Rodriguez‐Iturbe, I., Entekhabi, D., and Bras, R. L.: Nonlinear Dynamics of Soil Moisture at Climate Scales: 1. Stochastic Analysis, Water Resour. Res., 27, 1899–1906,
https://doi.org/10.1029/91WR01035, 1991.
a
Runge, J.: Causal network reconstruction from time series: From theoretical assumptions to practical estimation, Chaos: An Interdisciplinary J. Nonlinear Sci., 28, 075310,
https://doi.org/10.1063/1.5025050, 2018a.
a,
b,
c,
d,
e,
f
Runge, J.: Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information, in: International Conference on Artificial Intelligence and Statistics, Playa Blanca, Lanzarote, Canary Islands, 9–11 April 2018, edited by: Storkey, A. and Perez-Cruz, F., Proceedings of Machine Learning Research, 84, 938–947,
http://proceedings.mlr.press/v84/runge18a.html (last access: 14 April 2022), 2018b.
a,
b,
c,
d,
e,
f
Runge, J.: Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets, in: Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), edited by: Peters, J. and Sontag, D., Proceedings of Machine Learning Research (PMLR), 124, 1388–1397,
https://proceedings.mlr.press/v124/runge20a.html (last access: 14 April 2022), 2020.
a,
b
Runge, J., Bathiany, S., Bollt, E., Camps-Valls, G., Coumou, D., Deyle, E., Glymour, C., Kretschmer, M., Mahecha, M. D., Muñoz-Marí, J., van Nes, E. H., Peters, J., Quax, R., Reichstein, M., Scheffer, M., Schölkopf, B., Spirtes, P., Sugihara, G., Sun, J., Zhang, K., and Zscheischler, J.: Inferring causation from time series in Earth system sciences, Nat. Commun., 10, 2553,
https://doi.org/10.1038/s41467-019-10105-3, 2019a.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k
Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., and Sejdinovic, D.: Detecting and quantifying causal associations in large nonlinear time series datasets, Science Advances, 5, eaau4996,
https://doi.org/10.1126/sciadv.aau4996, 2019b (data available at:
https://jakobrunge.github.io/tigramite/, last access: 22 April 2022).
a,
b,
c,
d,
e,
f,
g,
h
Salvucci, G. D., Saleem, J. A., and Kaufmann, R.: Investigating soil moisture feedbacks on precipitation with tests of Granger causality, Adv. Water Resour., 25, 1305–1312,
https://doi.org/10.1016/S0309-1708(02)00057-X, 2002.
a,
b
Schrödinger, E.: Nature and the Greeks, Shearman lectures, 1948, University Press,
https://books.google.be/books?id=H7sAAAAAMAAJ (last access: 14 April 2022), 1954. a
Slater, L. and Binley, A.: Advancing hydrological process understanding from long-term resistivity monitoring systems, WIREs Water, 8, e1513,
https://doi.org/10.1002/wat2.1513, 2021.
a
Spirtes, P. and Glymour, C.: An Algorithm for Fast Recovery of Sparse Causal Graphs, Soc. Sci. Comput. Rev., 9, 62–72,
https://doi.org/10.1177/089443939100900106, 1991.
a,
b,
c,
d
Spirtes, P., Glymour, C. N., and Scheines, R.: Causation, prediction, and search, Adaptive computation and machine learning, 2nd edn., MIT Press, Cambridge, Mass, ISBN 0-262-19440-6, 2000.
a,
b
Sugihara, G. and May, R. M.: Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature, 344, 734–741,
https://doi.org/10.1038/344734a0, 1990.
a,
b
Sugihara, G., Grenfell, B. T., May, R. M., and Tong, H.: Nonlinear forecasting for the classification of natural time series, Philos. T. Roy. Soc. A, 348, 477–495,
https://doi.org/10.1098/rsta.1994.0106, 1994.
a
Sugihara, G., May, R., Ye, H., Hsieh, C.-H., Deyle, E., Fogarty, M., and Munch, S.: Detecting Causality in Complex Ecosystems, Science, 338, 496–500,
https://doi.org/10.1126/science.1227079, 2012.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j
Sugihara, G., Deyle, E. R., and Ye, H.: Reply to Baskerville and Cobey: Misconceptions about causation with synchrony and seasonal drivers, P. Natl. Acad. Sci. USA, 114, E2272–E2274,
https://doi.org/10.1073/pnas.1700998114, 2017.
a,
b
Theiler, J.: Spurious dimension from correlation algorithms applied to limited time-series data, Phys. Rev. A-Gen. Phys., 34, 2427–2432, 1986.
a,
b,
c
Triantafyllou, A., Watlet, A., Le Mouélic, S., Camelbeeck, T., Civet, F., Kaufmann, O., Quinif, Y., and Vandycke, S.: 3-D digital outcrop model for analysis of brittle deformation and lithological mapping (Lorette cave, Belgium), J. Struct. Geol., 120, 55–66,
https://doi.org/10.1016/j.jsg.2019.01.001, 2019.
a
Tuttle, S. E. and Salvucci, G. D.: Confounding factors in determining causal soil moisture-precipitation feedback, Water Resour. Res., 53, 5531–5544,
https://doi.org/10.1002/2016WR019869, 2017.
a,
b
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, I., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., and SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nat. Methods, 17, 261–272,
https://doi.org/10.1038/s41592-019-0686-2, 2020.
a
Wang, Y., Yang, J., Chen, Y., De Maeyer, P., Li, Z., and Duan, W.: Detecting the Causal Effect of Soil Moisture on Precipitation Using Convergent Cross Mapping, Scientific Reports, 8, 12171,
https://doi.org/10.1038/s41598-018-30669-2, 2018.
a,
b,
c,
d
Watlet, A., Kaufmann, O., Triantafyllou, A., Poulain, A., Chambers, J. E., Meldrum, P. I., Wilkinson, P. B., Hallet, V., Quinif, Y., Van Ruymbeke, M., and Van Camp, M.: Data and results for manuscript “Imaging groundwater infiltration dynamics in karst vadose zone with long-term ERT monitoring”, Version 1, Zenodo [data set],
https://doi.org/10.5281/zenodo.1158631, 2018a.
a
Watlet, A., Kaufmann, O., Triantafyllou, A., Poulain, A., Chambers, J. E., Meldrum, P. I., Wilkinson, P. B., Hallet, V., Quinif, Y., Van Ruymbeke, M., and Van Camp, M.: Imaging groundwater infiltration dynamics in the karst vadose zone with long-term ERT monitoring, Hydrol. Earth Syst. Sci., 22, 1563–1592,
https://doi.org/10.5194/hess-22-1563-2018, 2018b.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j
Wiener, N.: The theory of prediction, in: Modern Mathematics for the Engineer, edited by: Beckenbach, E. F., McGraw-Hill, New York,
https://books.google.be/books?id=OGe4AAAAIAAJ (last access: 14 April 2022), 1956. a
Ye, H., Deyle, E. R., Gilarranz, L. J., and Sugihara, G.: Distinguishing time-delayed causal interactions using convergent cross mapping, Scientific Reports, 5, 14750,
https://doi.org/10.1038/srep14750, 2015.
a,
b,
c,
d,
e
