ПОТОЧЕЧНЫЕ И КОМПЛЕКСНЫЕ МЕРЫ КАЧЕСТВА В ИССЛЕДОВАНИЯХ АТМОСФЕРЫ И ОКЕАНА: ОБЗОР МЕТОДОВ И ПОДХОДОВ

  • В. Ю. Резвов Институт океанологии им. П. П. Ширшова РАН; Московский физико-технический институт (национальный исследовательский университет)
  • М. А. Криницкий Институт океанологии им. П. П. Ширшова РАН; Московский физико-технический институт (национальный исследовательский университет)
  • Н. Д. Тилинина Институт океанологии им. П.П. Ширшова РАН
DOI: 10.29006/1564-2291.JOR-2024.52(4).10
Ключевые слова: метрики качества, сеточные данные, масштабирование, верификация, поточечные метрики, комплексные метрики, ансамблевый прогноз, феноменологические метрики

Аннотация

В науках об океане и атмосфере для описания качества результатов моделирования различного рода, включая численный прогноз погоды, статистическую коррекцию, повышение пространственного разрешения данных, используются различные обобщающие количественные показатели, называемые метриками, или мерами качества. Метрики дают представление о точности воспроизведения процессов моделями и позволяют сравнивать модели путем оценки неопределенности их результатов. В настоящей статье представлена наиболее общая классификация встречающихся в научной литературе метрик качества. Для каждой группы мер качества приведены примеры их использования в научных задачах. Помимо оценки традиционных поточечных метрик исследуются комплексные меры, рассматривающие различные аспекты сеточных данных. Среди таких специфических метрик выделяются меры с акцентом на пространственной структуре, внутренних корреляциях и неоднородностях прогнозируемых полей переменных, вероятностные методы проверки ансамблевых прогнозов. Отдельное внимание в данной работе также посвящено описанию феноменологических метрик и мер, основанных на редких и экстремальных явлениях.

Литература


  1. Бундель А. Ю., Муравьев А. В., Ольховая Е. Д. Обзор методов пространственной верификации и их применение для ансамблевых прогнозов // Гидрометеорологические исследования и прогнозы. 2021. № 4 (382). С. 30. https://doi.org/10.37162/2618-9631-2021-4-30-49.

  2. Калмыкова О. В. Методика оценки смерчеопасности вблизи Черноморского побережья России и результаты ее испытаний // Результаты испытания новых и усовершенствованных технологий, моделей и методов гидрометеорологических прогнозов. 2021. №. 48. С. 42–61.

  3. РД 52.27.284-91. Методические указания. Проведение производственных (оперативных) испытаний новых и усовершенствованных методов гидрометеорологических и гелиофизических прогнозов. Л.: Гидрометеоиздат, 1991. 150 с.

  4. Alessi M. J., DeGaetano A. T. A comparison of statistical and dynamical downscaling methods for short‐term weather forecasts in the US Northeast // Meteorological Applications. 2021. Vol. 28. No. 1. https://doi.org/10.1002/met.1976.

  5. Baño-Medina J., Manzanas R., Gutiérrez J. M. On the suitability of deep convolutional neural networks for continental-wide downscaling of climate change projections // Climate Dynamics. 2021. Vol. 57. No. 11. P. 2941–2951. https://doi.org/10.1007/s00382-021-05847-0.

  6. Barnston A. G., Thomas J. L. Rainfall measurement accuracy in FACE: A comparison of gage and radar rainfalls // Journal of Applied Meteorology and Climatology. 1983. Vol. 22. No. 12. P. 2038–2052. https://doi.org/10.1175/1520-0450(1983)022%3C2038:RMAIFA%3E2.0.CO;2.

  7. Barnston A. G. Correspondence among the correlation, RMSE, and Heidke forecast verification measures; refinement of the Heidke score // Weather and Forecasting. 1992. Vol. 7. No. 4. P. 699–709. https://doi.org/10.1175/1520-0434(1992)007%3C0699:CATCRA%3E2.0.CO;2.

  8. Barsugli J. J., Guentchev G., Horton R. M., Wood A., Mearns L. O., Liang X. Z., Winkler J. A., Dixon K., Hayhoe K., Rood R. B., Goddard L., Ray A., Buja L., Ammann C. The practitioner’s dilemma: How to assess the credibility of downscaled climate projections // Eos, Transactions American Geophysical Union. 2013. Vol. 94. No. 46. P. 424–425. https://doi.org/10.1002/2013EO460005.

  9. Böker B., Laux P., Olschewski P., Kunstmann H. Added value of an atmospheric circulation pattern‐based statistical downscaling approach for daily precipitation distributions in complex terrain // International Journal of Climatology. 2023. Vol. 43. No. 11. P. 5130–5153. https://doi.org/10.1002/joc.8136.

  10. Briley L., Kelly R., Blackmer E. D., Troncoso A. V., Rood R. B., Andresen, J., Lemos M. C. Increasing the usability of climate models through the use of consumer-report-style resources for decision-making // Bulletin of the American Meteorological Society. 2020. Vol. 101. No. 10. P. E1709–E1717. https://doi.org/10.1175/BAMS-D-19-0099.1.

  11. Bröcker J. Evaluating raw ensembles with the continuous ranked probability score // Quarterly Journal of the Royal Meteorological Society. 2012. Vol. 138. No. 667. P. 1611–1617. https://doi.org/10.1002/qj.1891.

  12. Buizza R., Palmer T. N. Impact of ensemble size on ensemble prediction // Monthly Weather Review. 1998. Vol. 126. No. 9. P. 2503–2518. https://doi.org/10.1175/1520-0493(1998)126%3C2503:IOESOE%3E2.0.CO;2.

  13. Buschow S., Pidstrigach J., Friederichs P. Assessment of wavelet-based spatial verification by means of a stochastic precipitation model (wv_verif v0. 1.0) // Geoscientific Model Development. 2019. Vol. 12. No. 8. P. 3401–3418. https://doi.org/10.5194/gmd-12-3401-2019.

  14. Carroll R. J., Ruppert D., Stefanski L. A., Crainiceanu C. M. Measurement error in nonlinear models: a modern perspective. Chapman and Hall/CRC, 2006.

  15. Casati B., Wilson L. J., Stephenson D. B., Nurmi P., Ghelli A., Pocernich M., Damrath U., Ebert E. E., Brown B. G., Mason S. Forecast verification: current status and future directions // Meteorological Applications: A journal of forecasting, practical applications, training techniques and modelling. 2008. Vol. 15. No. 1. P. 3–18. https://doi.org/10.1002/met.52.

  16. Chai T., Draxler R. R. Root mean square error (RMSE) or mean absolute error (MAE)? –Arguments against avoiding RMSE in the literature // Geoscientific model development. 2014. Vol. 7. No. 3. P. 1247–1250. https://doi.org/10.5194/gmd-7-1247-2014.

  17. Cho D., Im J., Jung S. A new statistical downscaling approach for short‐term forecasting of summer air temperatures through a fusion of deep learning and spatial interpolation // Quarterly Journal of the Royal Meteorological Society. 2024. Vol. 150. No. 760. P. 1222–1242. https://doi.org/10.1002/qj.4643.

  18. Collier N., Hoffman F. M., Lawrence D. M., Keppel-Aleks G., Koven C. D., Riley W. J., Mu M., Randerson J. T. The international land model benchmarking (ILAMB) system: Design, theory, and implementation // Journal of Advances in Modeling Earth Systems. 2018. Vol. 10. No. 11. P. 2731–2754. https://doi.org/10.1029/2018MS001354.

  19. Davis C., Brown B., Bullock R. Object-based verification of precipitation forecasts. Part I: Methodology and application to mesoscale rain areas // Monthly Weather Review. 2006. Vol. 134. No. 7. P. 1772–1784. https://doi.org/10.1175/MWR3145.1.

  20. De Haan L. L., Kanamitsu M., De Sales F., Sun, L. An evaluation of the seasonal added value of downscaling over the United States using new verification measures // Theoretical and applied climatology. 2015. Vol. 122. P. 47–57. https://doi.org/10.1007/s00704-014-1278-9.

  21. Dosselmann R., Yang X. D. A comprehensive assessment of the structural similarity index // Signal, Image and Video Processing. 2011. Vol. 5. P. 81–91. https://doi.org/10.1007/s11760-009-0144-1.

  22. Ebert E. E., McBride J. L. Verification of precipitation in weather systems: Determination of systematic errors // Journal of hydrology. 2000. Vol. 239. No. 1–4. P. 179–202. https://doi.org/10.1016/S0022-1694(00)00343-7.

  23. Ebert E. E. Fuzzy verification of high‐resolution gridded forecasts: a review and proposed framework // Meteorological Applications: A journal of forecasting, practical applications, training techniques and modelling. 2008. Vol. 15. No. 1. P. 51–64. https://doi.org/10.1002/met.25.

  24. Ebert E., Wilson L., Weigel A., Mittermaier M., Nurmi P., Gill P., Göber M., Joslyn S., Brown B., Fowler T., Watkins A. Progress and challenges in forecast verification // Meteorological Applications. 2013. Vol. 20. No. 2. P. 130–139. https://doi.org/10.1002/met.1392.

  25. Ebert P., Milne P. Methodological and conceptual challenges in rare and severe event forecast-verification // Natural Hazards and Earth System Sciences Discussions. 2022. Vol. 20. P. 539–557. https://doi.org/10.5194/nhess-22-539-2022.

  26. Ebtehaj A. M., Foufoula‐Georgiou E., Lerman G. Sparse regularization for precipitation downscaling // Journal of Geophysical Research: Atmospheres. 2012. Vol. 117. No. D8. https://doi.org/10.1029/2011JD017057.

  27. Entekhabi D., Reichle R. H., Koster R. D., Crow W. T. Performance metrics for soil moisture retrievals and application requirements // Journal of Hydrometeorology. 2010. Vol. 11. No. 3. P. 832–840. https://doi.org/10.1175/2010JHM1223.1.

  28. Faggian N., Roux B., Steinle P., Ebert B. Fast calculation of the fractions skill score // Mausam. 2015. Vol. 66. No. 3. P. 457–466. http://dx.doi.org/10.54302/mausam.v66i3.555.

  29. Fisher S. R. A. Statistical Methods for Research Workers. 13th ed. Hafner Publishing Co., 1958. 356 p.

  30. Geiss A., Silva S. J., Hardin J. C. Downscaling atmospheric chemistry simulations with physically consistent deep learning // Geoscientific Model Development. 2022. Vol. 15. No. 17. P. 6677–6694. https://doi.org/10.5194/gmd-15-6677-2022.

  31. Gentile E. S., Gray S. L., Lewis H. W. The sensitivity of probabilistic convective‐scale forecasts of an extratropical cyclone to atmosphere–ocean–wave coupling // Quarterly Journal of the Royal Meteorological Society. 2022. Vol. 148. No. 743. P. 685–710. https://doi.org/10.1002/qj.4225.

  32. Gilabert M. A., Moreno A., Maselli F., Martinez B., Chiesi M., Sanchez-Ruiz S., Garcia-Haro F. J., Perez-Hoyos A., Campos-Taberner M., Perez-Priego O., Serrano-Ortiz P., Carrara A. Daily GPP estimates in Mediterranean ecosystems by combining remote sensing and meteorological data // ISPRS Journal of Photogrammetry and Remote Sensing. 2015. Vol. 102. P. 184–197. https://doi.org/10.1016/j.isprsjprs.2015.01.017.

  33. Gilleland E., Ahijevych D., Brown B. G., Casati B., Ebert E. E. Intercomparison of Spatial Forecast Verification Methods // Weather Forecasting. 2009. Vol. 24. P. 1416–1430. https://doi.org/10.1175/2009WAF2222269.1.

  34. Glawion L., Polz J., Kunstmann H., Fersch B., Chwala C. spateGAN: spatio‐temporal downscaling of rainfall fields using a cGAN approach // Earth and Space Science. 2023. Vol. 10. No. 10. https://doi.org/10.1029/2023EA002906.

  35. Gong W., Gupta H. V., Yang D., Sricharan K., Hero III A. O. Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach // Water resources research. 2013. Vol. 49. No. 4. P. 2253–2273. https://doi.org/10.1002/wrcr.20161.

  36. Gupta H. V., Kling H., Yilmaz K. K., Martinez G. F. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling // Journal of hydrology. 2009. Vol. 377. No. 1–2. P. 80–91. https://doi.org/10.1016/j.jhydrol.2009.08.003.

  37. Habib E., Krajewski W. F., Ciach G. J. Estimation of rainfall interstation correlation // Journal of Hydrometeorology. 2001. Vol. 2. No. 6. P. 621–629. https://doi.org/10.1175/1525-7541(2001)002%3C0621:EORIC%3E2.0.CO;2.

  38. Harris L., McRae A. T., Chantry M., Dueben P. D., Palmer T. N. A generative deep learning approach to stochastic downscaling of precipitation forecasts // Journal of Advances in Modeling Earth Systems. 2022. Vol. 14. No. 10. https://doi.org/10.1029/2022MS003120.

  39. Hersbach H. Decomposition of the continuous ranked probability score for ensemble prediction systems // Weather and Forecasting. 2000. Vol. 15. No. 5. P. 559–570. https://doi.org/10.1175/1520-0434(2000)015%3C0559:DOTCRP%3E2.0.CO;2.

  40. Hertig E., Maraun D., Bartholy J., Pongracz R., Vrac M., Mares I., Gutiérrez J. M., Wibig J., Casanueva A., Soares P. M. M. Comparison of statistical downscaling methods with respect to extreme events over Europe: Validation results from the perfect predictor experiment of the COST Action VALUE // International Journal of Climatology. 2019. Vol. 39. No. 9. P. 3846–3867. https://doi.org/10.1002/joc.5469.

  41. Hewitson B. C., Crane R. G. Climate downscaling: techniques and application // Climate Research. 1996. Vol. 7. No. 2. P. 85–95. https://doi.org/10.3354/cr007085.

  42. Hodson T. O. Root mean square error (RMSE) or mean absolute error (MAE): When to use them or not // Geoscientific Model Development Discussions. 2022. Vol. 15. No. 14. P. 5481–5487. https://doi.org/10.5194/gmd-15-5481-2022.

  43. Jagannathan K., Jones A. D., Ray I. The making of a metric: Coproducing decision-relevant climate science // Bulletin of the American Meteorological Society. 2020. Vol. 102. No. 8. P. 1–33. https://doi.org/10.1175/BAMS-D-19-0296.1.

  44. Jin H., Jiang W., Chen M., Li M., Bakar K. S., Shao Q. Downscaling long lead time daily rainfall ensemble forecasts through deep learning // Stochastic Environmental Research and Risk Assessment. 2023. Vol. 37. No. 8. P. 3185–3203. https://doi.org/10.1007/s00477-023-02444-x.

  45. Jolliffe I. T., Stephenson D. B. Forecast verification: a practitioner’s guide in atmospheric science. John Wiley & Sons, 2012.

  46. Kharin V. V., Zwiers F. W. On the ROC score of probability forecasts // Journal of Climate. 2003. Vol. 16. No. 24. P. 4145–4150. https://doi.org/10.1175/1520-0442(2003)016%3C4145:OTRSOP%3E2.0.CO;2.

  47. Kikumoto H., Ooka R., Arima Y., Yamanaka T. Study on the future weather data considering the global and local climate change for building energy simulation // Sustainable Cities and Society. 2015. Vol. 14. P. 404–413. https://doi.org/10.1016/j.scs.2014.08.007.

  48. Kling H., Fuchs M., Paulin M. Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios // Journal of hydrology. 2012. Vol. 424. P. 264–277. https://doi.org/10.1016/j.jhydrol.2012.01.011.

  49. Knoben W. J. M., Freer J. E., Woods R. A. Inherent benchmark or not? Comparing Nash–Sutcliffe and Kling–Gupta efficiency scores // Hydrology and Earth System Sciences. 2019. Vol. 23. No. 10. P. 4323–4331. https://doi.org/10.5194/hess-23-4323-2019.

  50. Lerch S., Thorarinsdottir T. L., Ravazzolo F., Gneiting T. Forecaster’s dilemma: extreme events and forecast evaluation // Statistical Science. 2017. Vol. 32. No. 1. P. 106–127. https://www.jstor.org/stable/26408123.

  51. Manzanas R., Frías M. D., Cofiño A. S., Gutiérrez J. M. Validation of 40 year multimodel seasonal precipitation forecasts: The role of ENSO on the global skill // Journal of Geophysical Research: Atmospheres. 2014. Vol. 119. No. 4. P. 1708–1719. https://doi.org/10.1002/2013JD020680.

  52. Maina F. Z., Siirila-Woodburn E. R., Vahmani P. Sensitivity of meteorological-forcing resolution on hydrologic variables // Hydrology and Earth System Sciences. 2020. Vol. 24. No. 7. P. 3451–3474. https://doi.org/10.5194/hess-24-3451-2020.

  53. Mason S. J., Graham N. E. Conditional probabilities, relative operating characteristics, and relative operating levels // Weather and Forecasting. 1999. Vol. 14. No. 5. P. 713–725. https://doi.org/10.1175/1520-0434(1999)014%3C0713:CPROCA%3E2.0.CO;2.

  54. McKeen S. A., Wilczak J., Grell G., Djalalova I., Peckham S., Hsie E., Gong W., Bouchet V., Menard S., Moffet R., McHenry J., McQueen J., Tang Y., Carmichael G. R., Pagowski M., Chan A., Dye T., Frost G., Lee P., Mathur R. Assessment of an ensemble of seven real‐time ozone forecasts over eastern North America during the summer of 2004 // Journal of Geophysical Research: Atmospheres. 2005. Vol. 110. No. D21. https://doi.org/10.1029/2005JD005858.

  55. Mittermaier M., Roberts N., Thompson S. A. A long‐term assessment of precipitation forecast skill using the fractions skill score // Meteorological Applications. 2013. Vol. 20. No. 2. P. 176–186. https://doi.org/10.1002/met.296.

  56. Moss R. H., Avery S., Baja K., Burkett M., Chischilly A. M., Dell J., Fleming P. A., Geil K., Jacobs K., Jones A., Knowlton K., Koh J., Lemos M. C., Melillo J., Pandya R., Richmond T. C., Scarlett L., Snyder J., Stults M., Waple A. M., Whitehead J., Zarrilli D., Ayyub B. M., Fox J., Ganguly A., Joppa L., Julius S., Kirshen P., Kreutter R., McGovern A., Meyer R., Neumann J., Solecki W., Smith J., Tissot P., Yohe G., Zimmerman R. Evaluating knowledge to support climate action: A framework for sustained assessment. Report of an independent advisory committee on applied climate assessment // Weather, Climate, and Society. 2019. Vol. 11. No. 3. P. 465–487. https://doi.org/10.1175/WCAS-D-18-0134.1.

  57. Murphy A. H. Skill scores based on the mean square error and their relationships to the correlation coefficient // Monthly weather review. 1988. Vol. 116. No. 12. P. 2417–2424. https://doi.org/10.1175/1520-0493(1988)116%3C2417:SSBOTM%3E2.0.CO;2.

  58. Murphy A. H., Brown B. G., Chen Y. S. Diagnostic verification of temperature forecasts // Weather and Forecasting. 1989. Vol. 4. No. 4. P. 485–501. https://doi.org/10.1175/1520-0434(1989)004%3C0485:DVOTF%3E2.0.CO;2.

  59. Murphy A. H. Probabilities, odds, and forecasts of rare events // Weather and forecasting. 1991. Vol. 6. No. 2. P. 302–307. https://doi.org/10.1175/1520-0434(1991)006%3C0302:POAFOR%3E2.0.CO;2.

  60. Murphy A. H. What Is a Good Forecast? An Essay on the Nature of Goodness in Weather Forecasting // Weather Forecasting. 1993. Vol. 8. No. 2. P. 281–293. https://doi.org/10.1175/1520-0434(1993)008<0281:WIAGFA>2.0.CO;2.

  61. Nearing G. S., Gupta H. V. The quantity and quality of information in hydrologic models // Water Resources Research. 2015. Vol. 51. No. 1. P. 524–538. https://doi.org/10.1002/2014WR015895.

  62. O’Neill A. C., Erikson L. H., Barnard P. L. Downscaling wind and wavefields for 21st century coastal flood hazard projections in a region of complex terrain // Earth and Space Science. 2017. Vol. 4. No. 5. P. 314–334. https://doi.org/10.1002/2016EA000193.

  63. Pool S., Vis M., Seibert J. Evaluating model performance: towards a non-parametric variant of the Kling-Gupta efficiency // Hydrological Sciences Journal. 2018. Vol. 63. No. 13–14. P. 1941–1953. https://doi.org/10.1080/02626667.2018.1552002.

  64. Reed K. A., Goldenson N., Grotjahn R., Gutowski W. J., Jagannathan K., Jones A. D., Leung L. R., McGinnis S. A., Pryor S. C., Srivastava A. K., Ullrich P. A., Zarzycki C. M. Metrics as tools for bridging climate science and applications // Wiley Interdisciplinary Reviews: Climate Change. 2022. Vol. 13. No. 6. P. e799. https://doi.org/10.1002/wcc.799.

  65. Roberts N. M. Assessing the spatial and temporal variation in the skill of precipitation forecasts from an NWP model // Meteorological Applications: A journal of forecasting, practical applications, training techniques and modelling. 2008. Vol. 15. No. 1. P. 163–169. https://doi.org/10.1002/met.57.

  66. Roberts N. M., Lean H. W. Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events // Monthly Weather Review. 2008. Vol. 136. No. 1. P. 78–97. https://doi.org/10.1175/2007MWR2123.1.

  67. Robertson C., Long J. A., Nathoo F. S., Nelson T. A., Plouffe C. C. Assessing quality of spatial models using the structural similarity index and posterior predictive checks // Geographical Analysis. 2014. Vol. 46. No. 1. P. 53–74. https://doi.org/10.1111/gean.12028.

  68. Savage N. H., Agnew P., Davis L. S., Ordóñez C., Thorpe R., Johnson C. E., O’Connor F. M., Dalvi M. Air quality modelling using the Met Office Unified Model (AQUM OS24-26): model description and initial evaluation // Geoscientific Model Development. 2013. Vol. 6. No. 2. P. 353–372. https://doi.org/10.5194/gmd-6-353-2013.

  69. Schoof J. T. Statistical downscaling in climatology // Geography Compass. 2013. Vol. 7. No. 4. P. 249–265. https://doi.org/10.1111/gec3.12036.

  70. Schultz M. G., Betancourt C., Gong B., Kleinert F., Langguth M., Leufen L. H., Mozaffari A., Stadtler S. Can deep learning beat numerical weather prediction? // Philosophical Transactions of the Royal Society A. 2021. Vol. 379. No. 2194. https://doi.org/10.1098/rsta.2020.0097.

  71. Shahriar S. A., Siddique M. A. M., Rahman S. M. A. Climate change projection using statistical downscaling model over Chittagong Division, Bangladesh // Meteorology and Atmospheric Physics. 2021. Vol. 133. No. 4. P. 1409–1427. https://doi.org/10.1007/s00703-021-00817-x.

  72. Skok G. Analysis of fraction skill score properties for a displaced rainband in a rectangular domain // Meteorological Applications. 2015. Vol. 22. No. 3. P. 477–484. https://doi.org/10.1002/met.1478.

  73. Skok G., Roberts N. Estimating the displacement in precipitation forecasts using the Fractions Skill Score // Quarterly Journal of the Royal Meteorological Society. 2018. Vol. 144. No. 711. P. 414–425. https://doi.org/10.1002/qj.3212.

  74. Song L., Xu C., Long Y., Lei X., Suo N., Cao L. Performance of seven gridded precipitation products over arid central Asia and subregions // Remote Sensing. 2022. Vol. 14. No. 23. P. 6039. https://doi.org/10.3390/rs14236039.

  75. Stephenson D. B., Casati B., Ferro C. A. T., Wilson C. A. The extreme dependency score: A non‐vanishing measure for forecasts of rare events // Meteorological Applications: A journal of forecasting, practical applications, training techniques and modelling. 2008. Vol. 15. No. 1. P. 41–50. https://doi.org/10.1002/met.53.

  76. Sun Y., Deng K., Ren K., Liu J., Deng C., Jin Y. Deep learning in statistical downscaling for deriving high spatial resolution gridded meteorological data: A systematic review // ISPRS Journal of Photogrammetry and Remote Sensing. 2024. Vol. 208. P. 14–38. https://doi.org/10.1016/j.isprsjprs.2023.12.011.

  77. Taylor K. E. Summarizing multiple aspects of model performance in a single diagram // Journal of Geophysical Research: Atmospheres. 2001. Vol. 106. P. 7183–7192. https://doi.org/10.1029/2000JD900719.

  78. Tian Y., Nearing G. S., Peters-Lidard C. D., Harrison K. W., Tang L. Performance metrics, error modeling, and uncertainty quantification // Monthly Weather Review. 2016. Vol. 144. No. 2. P. 607–613. https://doi.org/10.1175/MWR-D-15-0087.1.

  79. Vaughan A., Tebbutt W., Hosking J. S., Turner R. E. Convolutional conditional neural processes for local climate downscaling // Geoscientific Model Development. 2022. Vol. 15. No. 1. P. 251–268. https://doi.org/10.5194/gmd-15-251-2022.

  80. Vrugt J. A., Sadegh M. Toward diagnostic model calibration and evaluation: Approximate Bayesian computation // Water Resources Research. 2013. Vol. 49. No. 7. P. 4335–4345. https://doi.org/10.1002/wrcr.20354.

  81. Wang Z., Bovik A. C., Sheikh H. R., Simoncelli E. P. Image quality assessment: from error visibility to structural similarity // IEEE transactions on image processing. 2004. Vol. 13. No. 4. P. 600–612. https://doi.org/10.1109/TIP.2003.819861.

  82. Wehner M. F. Very extreme seasonal precipitation in the NARCCAP ensemble: Model performance and projections // Climate Dynamics. 2013. Vol. 40. P. 59–80. https://doi.org/10.1007/s00382-012-1393-1.

  83. Weijs S. V., Schoups G., Van De Giesen N. Why hydrological predictions should be evaluated using information theory // Hydrology and Earth System Sciences. 2010. Vol. 14. No. 12. P. 2545–2558. https://doi.org/10.5194/hess-14-2545-2010.

  84. Weniger M., Kapp F., Friederichs P. Spatial verification using wavelet transforms: a review // Quarterly Journal of the Royal Meteorological Society. 2017. Vol. 143. No. 702. P. 120–136. https://doi.org/10.1002/qj.2881.

  85. Wilby R. L., Wigley T. M. L. Downscaling general circulation model output: a review of methods and limitations // Progress in physical geography. 1997. Vol. 21. No. 4. P. 530–548. https://doi.org/10.1177/030913339702100403.

  86. Wilks D. S. Statistical methods in the atmospheric sciences. Academic press, 2011. 676 p.

  87. Willmott C. J., Matsuura K. Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance // Climate research. 2005. Vol. 30. No. 1. P. 79–82. https://doi.org/10.3354/cr030079.

  88. Willmott C. J., Matsuura K., Robeson S. M. Ambiguities inherent in sums-of-squares-based error statistics // Atmospheric Environment. 2009. Vol. 43. No. 3. P. 749–752. https://doi.org/10.1016/j.atmosenv.2008.10.005.

  89. Yeggina S., Teegavarapu R. S. V., Muddu S. Evaluation and bias corrections of gridded precipitation data for hydrologic modelling support in Kabini River basin, India // Theoretical and Applied Climatology. 2020. Vol. 140. P. 1495–1513. https://doi.org/10.1007/s00704-020-03175-7.

  90. Zandler H., Senftl T., Vanselow K. A. Reanalysis datasets outperform other gridded climate products in vegetation change analysis in peripheral conservation areas of Central Asia // Scientific Reports. 2020. Vol. 10. No. 1. https://doi.org/10.1038/s41598-020-79480-y.

  91. Zhong X., Du F., Chen L., Wang Z., Li H. Investigating transformer‐based models for spatial downscaling and correcting biases of near‐surface temperature and wind‐speed forecasts // Quarterly Journal of the Royal Meteorological Society. 2024. Vol. 150. No. 758. P. 275–289. https://doi.org/10.1002/qj.4596.

Опубликован
2024-12-29
Выпуск
Том 52 № 4 (2024): Океанологические исследования
Раздел
Физика океана и климат

Передача авторских прав происходит на основании лицензионного договора между Автором и Федеральным государственным бюджетным учреждением науки Институт океанологии им. П.П. Ширшова Российской академии наук (ИО РАН)

Наиболее читаемые статьи этого автора (авторов)