References

[BC02]

R. T. Baillie and S. K. Chung. Modeling and forecasting from trend-stationary long memory models with applications to climatology. International Journal of Forecasting, 18(2):215–226, 2002. doi:10.1016/S0169-2070(01)00154-6.

[BNA+25]

Anubhab Biswas, Lorenzo Nespoli, Dario Azzimonti, Lorenzo Zambon, Nicolò Rubattu, and Giorgio Corani. Bayesreconpy: a python package for forecast reconciliation. Journal of Open Source Software, 10(111):8336, 2025. URL: https://doi.org/10.21105/joss.08336, doi:10.21105/joss.08336.

[BS21]

Riley X. Brady and Aaron Spring. Climpred: verification of weather and climate forecasts. Journal of Open Source Software, 6(59):2781, 2021. URL: https://doi.org/10.21105/joss.02781, doi:10.21105/joss.02781.

[CTV+22]

Robert A. Caulk, Elin Törnquist, Matthias Voppichler, Andrew R. Lawless, Ryan McMullan, Wagner Costa Santos, Timothy C. Pogue, Johan van der Vlugt, Stefan P. Gehring, and Pascal Schmidt. Freqai: generalizing adaptive modeling for chaotic time-series market forecasts. Journal of Open Source Software, 7(80):4864, 2022. URL: https://doi.org/10.21105/joss.04864, doi:10.21105/joss.04864.

[GBR07]

T. Gneiting, F. Balabdaoui, and A. E. Raftery. Probabilistic forecasts, calibration and sharpness. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 69(2):243–268, 2007. doi:10.1111/j.1467-9868.2007.00587.x.

[HMvdW+20]

Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Stephan Memmesheimer, Tom Backx, and others. Array programming with NumPy. Nature, 585(7825):357–362, 2020. doi:10.1038/s41586-020-2649-2.

[HN98]

Jerry L. Hintze and Ray D. Nelson. Violin plots: a box plot-density trace synergism. The American Statistician, 52(2):181–184, 1998. doi:10.2307/2685478.

[HCJ25]

S. Hong, Y. Choi, and J. J. Jeon. Interpretable water level forecaster with spatiotemporal causal attention mechanisms. International Journal of Forecasting, 41(3):1037–1054, 2025. doi:10.1016/j.ijforecast.2024.10.003.

[Hun07]

J. D. Hunter. Matplotlib: a 2d graphics environment. Computing in Science & Engineering, 9(3):90–95, 2007. doi:10.1109/MCSE.2007.55.

[JS12]

Ian T. Jolliffe and David B. Stephenson. Forecast Verification: A Practitioner's Guide in Atmospheric Science. Wiley, 2012. ISBN 9781119960003. doi:10.1002/9781119960003.

[Kou25]

Kouao Laurent Kouadio. k-diagram: technical report — derivations and details. Technical Report, School of Geosciences and Info-physics, Central South University, Sep 2025. Software technical report accompanying the k-diagram package. URL: https://doi.org/10.5281/zenodo.17051183, doi:10.5281/zenodo.17051183.

[KL25]

Kouao Laurent Kouadio and Rong Liu. Cas: cluster-aware scoring for probabilistic forecasts. Manuscript submitted to the Expert Systems With Applications, 2025.

[KLL+26a]

Kouao Laurent Kouadio, Rong Liu, Zhuo Liu, Shiyu Jiang, Serge Kouamelan Kouamelan, Wenxiang Liu, Zhanhui Qing, and Zhiwen Zheng. Physics-informed deep learning reveals divergent urban land subsidence regimes. Under review in IEEE Transactions on Geoscience and Remote Sensing, 2026.

[KLL+26b]

Kouao Laurent Kouadio, Rong Liu, Kouamé Gbèlè Hermann Loukou, Wenxiang Liu, Zhanhui Qing, and Zhuo Liu. A diagnostic framework for interpreting spatiotemporal probabilistic forecasts. Environmental Modelling & Software, pages 107052, 2026. URL: https://www.sciencedirect.com/science/article/pii/S1364815226001994, doi:10.1016/j.envsoft.2026.107052.

[KLL+25]

Kouao Laurent Kouadio, Zhuo Liu, Rong Liu, Pierre Claver Bizimana, Gaofeng Yang, and Wenxiang Liu. XTFT: A Next-Generation Temporal Fusion Transformer for Uncertainty-Rich Time Series Forecasting. 2025. Preprint. doi:10.22541/au.175390529.91420978/v1.

[LArikLP21]

B. Lim, S. O. Arík, N. Loeff, and T. Pfister. Temporal fusion transformers for interpretable multi-horizon time series forecasting. International Journal of Forecasting, 37(4):1748–1764, 2021. doi:10.1016/j.ijforecast.2021.03.012.

[LLA+24]

Jianxin Liu, Wenxiang Liu, Fabrice Blanchard Allechy, Zhiwen Zheng, Rong Liu, and Kouao Laurent Kouadio. Machine learning-based techniques for land subsidence simulation in an urban area. Journal of Environmental Management, 352(2024):17, 2024. doi:10.1016/j.jenvman.2024.120078.

[LDTC21]

Y. Liu, S. Davanloo Tajbakhsh, and A. J. Conejo. Spatiotemporal wind forecasting by learning a hierarchically sparse inverse covariance matrix using wind directions. International Journal of Forecasting, 37(2):812–824, 2021. doi:10.1016/j.ijforecast.2020.09.009.

[McK10]

Wes McKinney. Data Structures for Statistical Computing in Python. In Stéfan van der Walt and Jarrod Millman, editors, Proceedings of the 9th Python in Science Conference, 56 – 61. SciPy, 2010. doi:10.25080/majora-92bf1922-00a.

[Mur93]

Allan H. Murphy. What is a good forecast? an essay on the nature of goodness in weather forecasting. Weather and Forecasting, 8(3):287–303, 1993. URL: https://journals.ametsoc.org/view/journals/wefo/8/2/1520-0434_1993_008_0281_wiagfa_2_0_co_2.xml, doi:10.1175/1520-0434(1993)008<0281:WIAGFA>2.0.CO;2.

[PVG+11]

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Olsczewski, M. Blondel, F. Prejbal, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay. Scikit-learn: machine learning in Python. Journal of Machine Learning Research, 12:2825–2830, 2011.

[Pow11]

David M. W. Powers. Evaluation: from precision, recall and f-measure to roc, informedness, markedness and correlation. International Journal of Machine Learning Technology, 2(1):37–63, 2011. URL: https://arxiv.org/abs/2010.16061, doi:10.48550/arXiv.2010.16061.

[RMdB+20]

Jeff Reback, Wes McKinney, Joris Van den Bossche, Tom Augspurger, Phillip Cloud, Sinhrks, and others. pandas: a foundational Python library for data analysis and manipulation. Proceedings of the 19th Python in Science Conference, pages 1–9, 2020. doi:10.25080/majora-342d178e-001.

[RH21]

A. Rummens and W. Hardyns. The effect of spatiotemporal resolution on predictive policing model performance. International Journal of Forecasting, 37(1):125–133, 2021. doi:10.1016/j.ijforecast.2020.03.006.

[Sil86]

B. W. Silverman. Density Estimation for Statistics and Data Analysis. Chapman and Hall/CRC, 1986. ISBN 9780412246203.

[Sok25]

A. Sokol. Fan charts 2.0: flexible forecast distributions with expert judgement. International Journal of Forecasting, 41(3):1148–1164, 2025. doi:10.1016/j.ijforecast.2024.11.009.

[Tay01]

Karl E. Taylor. Summarizing quantitative measures of model performance in a single diagram. Journal of Geophysical Research: Atmospheres, 106(D7):7183–7192, 2001. doi:10.1029/2000JD900719.

[VRD09]

Guido Van Rossum and Fred L. Drake. Python 3 Reference Manual. CreateSpace, Scotts Valley, CA, 2009. ISBN 1441412697. URL: https://dl.acm.org/doi/10.5555/1593511.

[Was21]

Michael L. Waskom. Seaborn: statistical data visualization. Journal of Open Source Software, 6(60):3021, 2021. doi:10.21105/joss.03021.

[Wic14]

Hadley Wickham. Tidy data. Journal of Statistical Software, 59(10):1–23, 2014. URL: https://www.jstatsoft.org/index.php/jss/article/view/v059i10, doi:10.18637/jss.v059.i10.

[PythonSFoundation08]

Python Software Foundation. Python language reference, version 3.x. 2008. Accessed: 2025-04-10. URL: https://www.python.org.

[VirtanenGommersOliphant+20]

P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Wehrer, J. Huttunen, T. Håcklin, S. Straub, J. Pike, A. Petroff, K. Conti, R. Lieberman, J. Pollard, B. Nichols, J. Raimi, E. Hoydu, K. B. Kerkwijk, M. Brett, A. Haldane, J. del Río, G. Manolopoulos, A. Ivanov, K. J. Millman, M. C. Wehner, S. J. Briggs, N. Yurkewycz, R. Knothe, J. Butterworth, N. Goodman, S. J. de la Vega, O. Routchenko, A. Perron, Z. Rothberg, E. Ryaboy, N. Williams, P. Turrell, S. Behnel, L. Sieber, R. Blake, B. R. Kern, R. Larson, C. A. Edwards, E. Fazio, I. Juric, T. Pitkanen, S. Cijesek, B. E. Taylor, R. T. Miller, E. Jessen, D. Derksen, C. J. Carey, S. Wejchert, S. Olenín, A. Petrov, A. Jachalsky, V. Slavov, O. Bokhove, J. Jung, M. Aivazis, M. D. Hendriksen, K. A. Halderman, A. de Miranda Cardoso, D. Levy, and Y. Vázquez-Baeza. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature Methods, 17(3):261–272, 2020. doi:10.1038/s41592-019-0686-2.