Cover, T. M. and Thomas, J. A.: Elements of Information Theory, 2nd ed., John Wiley & Sons, New Jersey, USA, 784 pp., ISBN: 978-0-471-24195-9, 2006.
a,
b,
c,
d,
e,
f
Darscheid, P., Guthke, A., and Ehret, U.: A maximum entropy method to estimate discrete distributions from samples ensuring nonzero probabilities, Entropy, 20, 601,
https://doi.org/10.5445/IR/1000085954, 2018.
a,
b
David, N., Alpert, P., and Messer, H.: Technical Note: Novel method for water vapour monitoring using wireless communication networks measurements, Atmos. Chem. Phys., 9, 2413–2418,
https://doi.org/10.5194/acp-9-2413-2009, 2009.
a
Djibo, M., Chwala, C., Graf, M., Polz, J., Kunstmann, H., and Zougmoré, F.: High-Resolution Rainfall Maps from Commercial Microwave Links for a Data-Scarce Region in West Africa, J. Hydrometeor., 24, 1847–1861,
https://doi.org/10.1175/JHM-D-23-0015.1, 2023.
a
Fencl, M., Dohnal, M., Rieckermann, J., and Bareš, V.: Gauge-adjusted rainfall estimates from commercial microwave links, Hydrol. Earth Syst. Sci., 21, 617–634,
https://doi.org/10.5194/hess-21-617-2017, 2017.
a
Fencl, M., Dohnal, M., Valtr, P., Grabner, M., and Bareš, V.: Atmospheric observations with E-band microwave links – challenges and opportunities, Atmos. Meas. Tech., 13, 6559–6578,
https://doi.org/10.5194/amt-13-6559-2020, 2020.
a
Foroozand, H. and Weijs, S. V.: Objective functions for information-theoretical monitoring network design: what is “optimal”?, Hydrol. Earth Syst. Sci., 25, 831–850,
https://doi.org/10.5194/hess-25-831-2021, 2021.
a
Gong, W., Gupta, H. V., Yang, D., Sricharan, K., and Hero III, A. O.: Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach, Water Resour. Res., 49, 2253–2273,
https://doi.org/10.1002/wrcr.20161, 2013.
a
Graf, M., Chwala, C., Polz, J., and Kunstmann, H.: Rainfall estimation from a German-wide commercial microwave link network: optimized processing and validation for 1 year of data, Hydrol. Earth Syst. Sci., 24, 2931–2950,
https://doi.org/10.5194/hess-24-2931-2020, 2020.
a,
b,
c,
d
Graf, M., Chwala, C., Wenzel, M., Vogel, C., Kunstmann, H., and Winterrath, T.: The new real-time radar-gauge-CML adjustment system pyRADMAN at DWD, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12890,
https://doi.org/10.5194/egusphere-egu24-12890, 2024.
a
Heistermann, M., Jacobi, S., and Pfaff, T.: Technical Note: An open source library for processing weather radar data (wradlib), Hydrol. Earth Syst. Sci., 17, 863–871,
https://doi.org/10.5194/hess-17-863-2013, 2013.
a
Imhoff, R. O., Overeem, A., Brauer, C. C., Leijnse, H., Weerts, A. H., and Uijlenhoet, R.: Rainfall nowcasting using commercial microwave links, Geophys. Res. Lett., 47, e2020GL089365,
https://doi.org/10.1029/2020GL089365, 2020.
a
ITU-R: Radio-frequency channel arrangements for fixed service systems (Recommendation F.746-5), ITU-R, Geneva, Switzerland,
https://www.itu.int/rec/R-REC-F.746-5-200105-S/en (last access: 10 October 2024), 2001. a
ITU-R: Specific attenuation model for rain for use in prediction methods (Recommendation P.838-3), ITU-R, Geneva, Switzerland,
https://www.itu.int/rec/R-REC-P.838-3-200503-I/en (last access: 12 May 2022), 2005.
a,
b
ITU-R: Handbook – Radiowave propagation information for designing terrestrial point-to-point links, ITU, Geneva, Switzerland,
http://handle.itu.int/11.1002/pub/80301443-en, 2009. a
Leijnse, H., Uijlenhoet, R., and Stricker, J.: Microwave link rainfall estimation: Effects of link length and frequency, temporal sampling, power resolution, and wet antenna attenuation, Advances in Water Resources, 31, 1481–1493,
https://doi.org/10.1016/j.advwatres.2008.03.004, 2008.
a
Leijnse, H., Uijlenhoet, R., and Berne, A.: Errors and Uncertainties in Microwave Link Rainfall Estimation Explored Using Drop Size Measurements and High-Resolution Radar Data, Journal of Hydrometeorology, 11, 1330–1344,
https://doi.org/10.1175/2010JHM1243.1, 2010.
a
Liu, D., Wang, D., Wang, Y., Wu, J., Singh, V. P., Zeng, X., Wang, L., Chen, Y., Chen, X., Zhang, L., and Gu, S.: Entropy of hydrological systems under small samples: uncertainty and variability, J. Hydrol., 532, 163–176,
https://doi.org/10.1016/j.jhydrol.2015.11.019, 2016.
a
Loritz, R., Gupta, H., Jackisch, C., Westhoff, M., Kleidon, A., Ehret, U., and Zehe, E.: On the dynamic nature of hydrological similarity, Hydrol. Earth Syst. Sci., 22, 3663–3684,
https://doi.org/10.5194/hess-22-3663-2018, 2018.
a
Mishra, A. K., Özger, M., and Singh, V. P.: An entropy-based investigation into the variability of precipitation, J. Hydrol., 370, 139–154,
https://doi.org/10.1016/j.jhydrol.2009.03.006, 2009.
a
Neuper, M. and Ehret, U.: Quantitative precipitation estimation with weather radar using a data- and information-based approach, Hydrol. Earth Syst. Sci., 23, 3711–3733,
https://doi.org/10.5194/hess-23-3711-2019, 2019.
a,
b
Olsen, R., Rogers, D., and Hodge, D.: The aRb relation in the calculation of rain attenuation, IEEE T. Anten. Propag., 26, 318–329,
https://doi.org/10.1109/TAP.1978.1141845, 1978.
a
Ostrometzky, J. and Messer, H.: Dynamic determination of the baseline level in microwave links for rain monitoring from minimum attenuation values, IEEE J. Sel. Top. Appl., 11, 24–33,
https://doi.org/10.1109/JSTARS.2017.2752902, 2018.
a
Overeem, A., Leijnse, H., and Uijlenhoet, R.: Measuring urban rainfall using microwave links from commercial cellular communication networks, Water Resources Research, 47,
https://doi.org/10.1029/2010WR010350, 2011.
a
Overeem, A., Leijnse, H., and Uijlenhoet, R.: Country-wide rainfall maps from cellular communication networks, Proc. Natl. Acad. Sci., 110, 2741–2745,
https://doi.org/10.1073/pnas.1217961110, 2013.
a
Overeem, A., Leijnse, H., and Uijlenhoet, R.: Retrieval algorithm for rainfall mapping from microwave links in a cellular communication network, Atmos. Meas. Tech., 9, 2425–2444,
https://doi.org/10.5194/amt-9-2425-2016, 2016.
a
Pastorek, J., Fencl, M., and Bareš, V.: Calibrating microwave link rainfall retrieval model using runoff observations, EGU General Assembly 2019, 7-12 April 2019, Geophysical Research Abstracts, 21, EGU2019-10072,
https://meetingorganizer.copernicus.org/EGU2019/EGU2019-10072.pdf (last access: 1 December 2024), 2019. a
Pastorek, J., Fencl, M., Rieckermann, J., and Bareš, V.: Precipitation estimates from commercial microwave links: Practical approaches to wet-antenna correction, IEEE Transactions on Geoscience and Remote Sensing, 60, 1–9,
https://doi.org/10.1109/TGRS.2021.3110004, 2022.
a,
b
Pastorek, J., Fencl, M., and Bareš, V.: Uncertainties in discharge predictions based on microwave link rainfall estimates in a small urban catchment, J. Hydrol., 617, 129051,
https://doi.org/10.1016/j.jhydrol.2022.129051, 2023.
a
Polz, J., Chwala, C., Graf, M., and Kunstmann, H.: Rain event detection in commercial microwave link attenuation data using convolutional neural networks, Atmos. Meas. Tech., 13, 3835–3853,
https://doi.org/10.5194/amt-13-3835-2020, 2020.
a
Rios Gaona, M. F., Overeem, A., Brasjen, A. M., Meirink, J. F., Leijnse, H., and Uijlenhoet, R.: Evaluation of rainfall products derived from satellites and microwave links for the Netherlands, IEEE T. Geosci. Remote, 55, 12, 6849–6859,
https://doi.org/10.1109/TGRS.2017.2735439, 2017.
a
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., and Tarantola, S.: Global Sensitivity Analysis: The Primer, John Wiley and Sons, Hoboken, New Jersey, 292 pp.,
https://doi.org/10.1002/9780470725184, 2008.
a
Schleiss, M., Rieckermann, J., and Berne, A.: Quantification and modeling of wet-antenna attenuation for commercial microwave links, in IEEE Geoscience and Remote Sensing Letters, 10, 5, 1195–1199,
https://doi.org/10.1109/LGRS.2012.2236074, 2013.
a
Schleiss, M., Olsson, J., Berg, P., Niemi, T., Kokkonen, T., Thorndahl, S., Nielsen, R., Ellerbæk Nielsen, J., Bozhinova, D., and Pulkkinen, S.: The accuracy of weather radar in heavy rain: a comparative study for Denmark, the Netherlands, Finland and Sweden, Hydrol. Earth Syst. Sci., 24, 3157–3188,
https://doi.org/10.5194/hess-24-3157-2020, 2020.
a,
b
Schleiss, M., Raupach, T. H., and Berne, A.: The raindrop size distribution – the unknown that holds everything together, in Advances in Weather Radar, Volume 2: Precipitation Science, Scattering and Processing Algorithms, edited by: Bringi, V. N., Mishra, K. V., and Thurai, M., Institution of Engineering and Technology, 247–292,
https://doi.org/10.1049/sbra557g_ch6, 2023.
a
Shannon, C. E.: A mathematical theory of communication, Bell Syst. Tech. J., 27, 379–423, 1948.
a,
b
Singh, V. P.: Entropy theory and its application in environmental and water engineering, John Wiley & Sons, Chichester, West Sussex, UK, ISBN 978-1-119-97656-1, 2013. a
Šlerka, J. and Šisler, V.: Who is shaping your agenda? Social network analysis of anti-Islam and anti-immigration movement audiences on Czech facebook, in: Expressions of radicalization, edited by: Steiner, K. and Önnerfors, A., Palgrave Macmillan, Cham, Germany, 61–85,
https://doi.org/10.1007/978-3-319-65566-6_3, 2018.
a
Špačková, A., Fencl, M., and Bareš, V.: Evaluation of error components in rainfall retrieval from collocated commercial microwave links, Atmos. Meas. Tech., 16, 3865–3879,
https://doi.org/10.5194/amt-16-3865-2023, 2023.
a,
b
Steuer, R., Kurths, J., Daub, C. O., Weise, J., and Selbig, J.: The mutual information: Detecting and evaluating dependencies between variables, Bioinformatics, 18, 2, S231–S240,
https://doi.org/10.1093/bioinformatics/18.suppl_2.S231, 2002.
a
Thiesen, S., Darscheid, P., and Ehret, U.: 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, 2019.
a,
b,
c,
d,
e
Timme, N. M. and Lapish, C.: A tutorial for information theory in neuroscience, eNeuro, 5, 3,
https://doi.org/10.1523/ENEURO.0052-18.2018, 2018.
a,
b,
c,
d,
e
Uijlenhoet, R., Overeem, A., and Leijnse, H.: Opportunistic remote sensing of rainfall using microwave links from cellular communication networks, Wires Water, 5, e1289,
https://doi.org/10.1002/wat2.1289, 2018.
a
van het Schip, T. I., Overeem, A., Leijnse, H., Uijlenhoet, R., Meirink, J. F., and van Delden, A. J.: Rainfall measurement using cell phone links: classification of wet and dry periods using geostationary satellites, Hydrol. Sci. J., 62, 1343–1353,
https://doi.org/10.1080/02626667.2017.1329588, 2017.
a
van Leth, T. C., Leijnse, H., Overeem, A., and Uijlenhoet, R.: Estimating raindrop size distributions using microwave link measurements: potential and limitations, Atmos. Meas. Tech., 13, 1797–1815,
https://doi.org/10.5194/amt-13-1797-2020, 2020.
a
Walraven, B., Overeem, A., Leijnse, H., Coenders, M., Hut, R., van der Valk, L., and Uijlenhoet, R.: Considering local network characteristics and environmental conditions improves rainfall estimates from commercial microwave links in Sri Lanka, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9544,
https://doi.org/10.5194/egusphere-egu22-9544, 2022.
a
Weiss, T., Routtenberg, T., Ostrometzky, J., and Messer, H.: Intensity estimation after detection for accumulated rainfall estimation, Front. Sig. Proc., 4, 1291878,
https://doi.org/10.3389/frsip.2024.1291878, 2024.
a
