Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D.: Weight Uncertainty in Neural Network, in: Proceedings of the 32nd International Conference on Machine Learning, 1613–1622, PMLR, Lille, France,
https://proceedings.mlr.press/v37/blundell15.html (last access: 2 May 2024), 2015.
a,
b,
c,
d
Bouguet, J.-Y.: Pyramidal implementation of the affine lucas kanade feature tracker description of the algorithm, Intel corporation, 5,
http://robots.stanford.edu/cs223b04/algo_tracking.pdf (last access: 2 May 2024), 2001. a
Bowler, N. E., Pierce, C. E., and Seed, A. W.: STEPS: A probabilistic precipitation forecasting scheme which merges an extrapolation nowcast with downscaled NWP, Q. J. Roy. Meteor. Soc., 132, 2127–2155,
https://doi.org/10.1256/qj.04.100, 2006.
a,
b,
c
Caceres, J., Gonzalez, D., Zhou, T., and Droguett, E. L.: A probabilistic Bayesian recurrent neural network for remaining useful life prognostics considering epistemic and aleatory uncertainties, Struct. Contr. Health Monit., 28, e2811,
https://doi.org/10.1002/stc.2811, 2021.
a
Dechesne, C., Lassalle, P., and Lefèvre, S.: Bayesian U-Net: Estimating Uncertainty in Semantic Segmentation of Earth Observation Images, Remote Sens., 13, 3836,
https://doi.org/10.3390/rs13193836, 2021.
a
Espeholt, L., Agrawal, S., Sønderby, C., Kumar, M., Heek, J., Bromberg, C., Gazen, C., Carver, R., Andrychowicz, M., Hickey, J., Bell, A., and Kalchbrenner, N.: Deep learning for twelve hour precipitation forecasts, Nat. Commun., 13, 5145,
https://doi.org/10.1038/s41467-022-32483-x, 2022.
a,
b
Farquhar, S., Osborne, M. A., and Gal, Y.: Radial Bayesian Neural Networks: Beyond Discrete Support In Large-Scale Bayesian Deep Learning, in: Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR, 1352–1362,
https://proceedings.mlr.press/v108/farquhar20a.html (last access: 2 May 2024), 2020. a
Gal, Y. and Ghahramani, Z.: Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning, in: Proceedings of The 33rd International Conference on Machine Learning, PMLR, New York, NY, USA, 1050–1059,
https://proceedings.mlr.press/v48/gal16.html (last access: 2 May 2024), 2016. a
Graves, A.: Practical Variational Inference for Neural Networks, in: Advances in Neural Information Processing Systems, vol. 24, Curran Associates, Inc., Granada, Spain, 2348–2356, ISBN 978-1-61839-599-3,
https://papers.nips.cc/paper_files/paper/2011/hash/7eb3c8be3d411e8ebfab08eba5f49632-Abstract.html (last access: 2 May 2024), 2011. a
Harnist, B.: Probabilistic Precipitation Nowcasting using Bayesian Convolutional Neural Networks, Master's thesis, Aalto University, School of Science,
http://urn.fi/URN:NBN:fi:aalto-202208285227 (last access: 2 May 2024), 2022.
a,
b,
c
Hershey, J. R. and Olsen, P. A.: Approximating the Kullback Leibler Divergence Between Gaussian Mixture Models, in: 2007 IEEE International Conference on Acoustics, Speech and Signal Processing – ICASSP '07, vol. 4, Honolulu, HI, USA, IV–317–IV–320,
https://doi.org/10.1109/ICASSP.2007.366913, 2007.
a
Hogan, R. J., Ferro, C. A. T., Jolliffe, I. T., and Stephenson, D. B.: Equitability Revisited: Why the “Equitable Threat Score” Is Not Equitable, Weather Forecast., 25, 710–726,
https://doi.org/10.1175/2009WAF2222350.1, 2010.
a,
b,
c
Jospin, L. V., Laga, H., Boussaid, F., Buntine, W., and Bennamoun, M.: Hands-On Bayesian Neural Networks – A Tutorial for Deep Learning Users, IEEE Comput. Intell. Mag., 17, 29–48,
https://doi.org/10.1109/MCI.2022.3155327, 2022.
a
Kendall, A. and Gal, Y.: What uncertainties do we need in Bayesian deep learning for computer vision?, in: Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS'17, Curran Associates Inc., Red Hook, NY, USA, 5580–5590, ISBN 978-1-5108-6096-4, 2017.
a,
b,
c,
d
Kingma, D. P. and Ba, J.: Adam: A Method for Stochastic Optimization, in: Proceedings of the 3rd International Conference on Learning Representations (ICLR), San Diego, CA, USA,
https://doi.org/10.48550/arXiv.1412.6980, 2015.
a
Leinonen, J., Moisseev, D., Leskinen, M., and Petersen, W. A.: A Climatology of Disdrometer Measurements of Rainfall in Finland over Five Years with Implications for Global Radar Observations, J. Appl. Meteorol. Clim., 51, 392–404,
https://doi.org/10.1175/JAMC-D-11-056.1, 2012.
a
Liu, G., Reda, F. A., Shih, K. J., Wang, T.-C., Tao, A., and Catanzaro, B.: Image Inpainting for Irregular Holes Using Partial Convolutions, in: Computer Vision – ECCV 2018 Proceedings, Part XI, edited by Ferrari, V., Hebert, M., Sminchisescu, C., and Weiss, Y., Lecture Notes in Computer Science, Springer International Publishing, Munich, Germany, 89–105, ISBN 978-3-030-01252-6,
https://doi.org/10.1007/978-3-030-01252-6_6, 2018.
a
Lucas, B. D. and Kanade, T.: An Iterative Image Registration Technique with an Application to Stereo Vision, in: IJCAI'81: Proceedings of the 7th international joint conference on Artificial intelligence, vol. 2, University of British Columbia Vancouver, B.C., Canada, p. 674,
https://hal.science/hal-03697340 (last access: 2 May 2024), 1981. a
Mason, I.: A model for assessment of weather forecasts, Austr. Meteorol. Mag., 30, 291–303, 1982.
a,
b
Naeini, M. P., Cooper, G., and Hauskrecht, M.: Obtaining Well Calibrated Probabilities Using Bayesian Binning, in: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, vol. 29,
https://doi.org/10.1609/aaai.v29i1.9602, 2015.
a,
b
Pan, X., Lu, Y., Zhao, K., Huang, H., Wang, M., and Chen, H.: Improving Nowcasting of Convective Development by Incorporating Polarimetric Radar Variables Into a Deep-Learning Model, Geophys. Res. Lett., 48, e2021GL095 302,
https://doi.org/10.1029/2021GL095302, 2021.
a
Prudden, R., Adams, S., Kangin, D., Robinson, N., Ravuri, S., Mohamed, S., and Arribas, A.: A review of radar-based nowcasting of precipitation and applicable machine learning techniques, arXiv [preprint],
https://doi.org/10.48550/arXiv.2005.04988, 2020.
a
Pulkkinen, S., Nerini, D., Pérez Hortal, A. A., Velasco-Forero, C., Seed, A., Germann, U., and Foresti, L.: Pysteps: an open-source Python library for probabilistic precipitation nowcasting (v1.0), Geosci. Model Dev., 12, 4185–4219,
https://doi.org/10.5194/gmd-12-4185-2019, 2019.
a,
b,
c
Pulkkinen, S., Chandrasekar, V., and Niemi, T.: Lagrangian Integro-Difference Equation Model for Precipitation Nowcasting, J. Atmos. Ocean. Tech., 38, 2125–2145,
https://doi.org/10.1175/JTECH-D-21-0013.1, 2021.
a,
b,
c
Radhakrishnan, C. and Chandrasekar, V.: CASA Prediction System over Dallas–Fort Worth Urban Network: Blending of Nowcasting and High-Resolution Numerical Weather Prediction Model, J. Atmos. Ocean. Tech., 37, 211–228,
https://doi.org/10.1175/JTECH-D-18-0192.1, 2020.
a
Ravuri, S., Lenc, K., Willson, M., Kangin, D., Lam, R., Mirowski, P., Fitzsimons, M., Athanassiadou, M., Kashem, S., Madge, S., Prudden, R., Mandhane, A., Clark, A., Brock, A., Simonyan, K., Hadsell, R., Robinson, N., Clancy, E., Arribas, A., and Mohamed, S.: Skilful precipitation nowcasting using deep generative models of radar, Nature, 597, 672–677,
https://doi.org/10.1038/s41586-021-03854-z, 2021.
a,
b,
c,
d
Ritvanen, J., Harnist, B., Aldana, M., Mäkinen, T., and Pulkkinen, S.: Advection-Free Convolutional Neural Network for Convective Rainfall Nowcasting, IEEE J. Sel. Top. Appl., 1–16,
https://doi.org/10.1109/JSTARS.2023.3238016, 2023.
a,
b
Ruzanski, E. and Chandrasekar, V.: Scale Filtering for Improved Nowcasting Performance in a High-Resolution X-Band Radar Network, IEEE T. Geosci. Remote, 49, 2296–2307,
https://doi.org/10.1109/TGRS.2010.2103946, 2011.
a,
b
Seed, A. W., Pierce, C. E., and Norman, K.: Formulation and evaluation of a scale decomposition-based stochastic precipitation nowcast scheme, Water Resour. Res., 49, 6624–6641,
https://doi.org/10.1002/wrcr.20536, 2013.
a,
b
Shi, X., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W.-K., and Woo, W.-C.: Convolutional LSTM Network: a machine learning approach for precipitation nowcasting, in: Proceedings of the 28th International Conference on Neural Information Processing Systems – Volume 1, NIPS'15, MIT Press, Cambridge, MA, USA, 802–810, 2015. a
Shi, X., Gao, Z., Lausen, L., Wang, H., Yeung, D.-Y., Wong, W.-K., and Woo, W.-C.: Deep learning for precipitation nowcasting: a benchmark and a new model, in: Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS'17, Curran Associates Inc., Red Hook, NY, USA, 5622–5632, ISBN 978-1-5108-6096-4, 2017. a
Sun, J., Xue, M., Wilson, J. W., Zawadzki, I., Ballard, S. P., Onvlee-Hooimeyer, J., Joe, P., Barker, D. M., Li, P.-W., Golding, B., Xu, M., and Pinto, J.: Use of NWP for Nowcasting Convective Precipitation: Recent Progress and Challenges, B. Am. Meteorol. Soc., 95, 409–426,
https://doi.org/10.1175/BAMS-D-11-00263.1, 2014.
a
Sønderby, C. K., Espeholt, L., Heek, J., Dehghani, M., Oliver, A., Salimans, T., Agrawal, S., Hickey, J., and Kalchbrenner, N.: MetNet: A Neural Weather Model for Precipitation Forecasting, arXiv [preprint],
https://doi.org/10.48550/arXiv.2003.12140, 2020.
a,
b
Valdenegro-Toro, M. and Mori, D. S.: A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement, in: 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), IEEE, New Orleans, LA, USA, ISBN 978-1-66548-739-9, 1508–1516,
https://doi.org/10.1109/CVPRW56347.2022.00157, 2022.
a
Wen, Y., Vicol, P., Ba, J., Tran, D., and Grosse, R. B.: Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches, in: 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, 30 April–3 May 2018, Conference Track Proceedings, OpenReview.net,
https://openreview.net/forum?id=rJNpifWAb (last access: 2 May 2024), 2018. a
Wilks, D. S.: Statistical Methods in the Atmospheric Sciences, Academic Press, 3rd Edn., ISBN 978-0-12-385022-5, 2011.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k
Woo, S., Park, J., Lee, J.-Y., and Kweon, I. S.: Cbam: Convolutional block attention module, in: Proceedings of the European conference on computer vision (ECCV), Munich, Germany, 3–19,
https://doi.org/10.1007/978-3-030-01234-2_1, 2018.
a
Xu, L., Chen, N., Yang, C., Yu, H., and Chen, Z.: Quantifying the uncertainty of precipitation forecasting using probabilistic deep learning, Hydrol. Earth Syst. Sci., 26, 2923–2938,
https://doi.org/10.5194/hess-26-2923-2022, 2022.
a