Articles | Volume 7, issue 2
https://doi.org/10.5194/ascmo-7-73-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/ascmo-7-73-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Comparing climate time series – Part 2: A multivariate test
Department of Atmospheric, Oceanic, and Earth Sciences, George Mason University, Fairfax, VA 22030, USA
Michael K. Tippett
Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
Related authors
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 10, 1–27, https://doi.org/10.5194/ascmo-10-1-2024, https://doi.org/10.5194/ascmo-10-1-2024, 2024
Short summary
Short summary
This paper introduces a method to assess whether two data sets come from the same source. Current methods do not adequately consider spatial and temporal correlations and their annual cycles in a comprehensive test. This method addresses that gap, thereby providing a new and rigorous tool for evaluating the realism of climate simulations and measuring changes in variability over time.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 187–203, https://doi.org/10.5194/ascmo-8-187-2022, https://doi.org/10.5194/ascmo-8-187-2022, 2022
Short summary
Short summary
Most climate time series contain annual and diurnal cycles. However, an objective criterion for deciding whether two time series have statistically equivalent annual and diurnal cycles is lacking, particularly if the residual variability is serially correlated. Such a criterion would be helpful in deciding whether a new version of a climate model better simulates such cycles. This paper derives an objective rule for such decisions based on a rigorous statistical framework.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 97–115, https://doi.org/10.5194/ascmo-8-97-2022, https://doi.org/10.5194/ascmo-8-97-2022, 2022
Short summary
Short summary
A common problem in climate studies is to decide whether a climate model is realistic. Such decisions are not straightforward because the time series are serially correlated and multivariate. Part II derived a test for deciding wether a simulation is statistically distinguishable from observations. However, the test itself provides no information about the nature of those differences. This paper develops a systematic and optimal approach to diagnosing differences between stochastic processes.
Kelsey Malloy and Michael K. Tippett
EGUsphere, https://doi.org/10.5194/egusphere-2025-3145, https://doi.org/10.5194/egusphere-2025-3145, 2025
Short summary
Short summary
Tornado outbreaks—many tornadoes in short succession—have major impacts, but it is hard to accurately assess their risk because they are rare. We used weather model data to create hundreds of thousands of realistic but unseen tornado outbreak scenarios. With this event set, we estimated U.S. and local outbreak risk and detected clear links to La Niña and upward outbreak activity in recent years.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 10, 1–27, https://doi.org/10.5194/ascmo-10-1-2024, https://doi.org/10.5194/ascmo-10-1-2024, 2024
Short summary
Short summary
This paper introduces a method to assess whether two data sets come from the same source. Current methods do not adequately consider spatial and temporal correlations and their annual cycles in a comprehensive test. This method addresses that gap, thereby providing a new and rigorous tool for evaluating the realism of climate simulations and measuring changes in variability over time.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 187–203, https://doi.org/10.5194/ascmo-8-187-2022, https://doi.org/10.5194/ascmo-8-187-2022, 2022
Short summary
Short summary
Most climate time series contain annual and diurnal cycles. However, an objective criterion for deciding whether two time series have statistically equivalent annual and diurnal cycles is lacking, particularly if the residual variability is serially correlated. Such a criterion would be helpful in deciding whether a new version of a climate model better simulates such cycles. This paper derives an objective rule for such decisions based on a rigorous statistical framework.
Michael K. Tippett, Chiara Lepore, and Michelle L. L’Heureux
Weather Clim. Dynam., 3, 1063–1075, https://doi.org/10.5194/wcd-3-1063-2022, https://doi.org/10.5194/wcd-3-1063-2022, 2022
Short summary
Short summary
The El Niño–Southern Oscillation (ENSO) and Arctic Oscillation (AO) are phenomena that affect the weather and climate of North America. Although ENSO hails from from the tropical Pacific and the AO high above the North Pole, the spatial patterns of their influence on a North American tornado environment index are remarkably similar in computer models. We find that when ENSO and the AO act in concert, their impact is large, and when they oppose each other, their impact is small.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 97–115, https://doi.org/10.5194/ascmo-8-97-2022, https://doi.org/10.5194/ascmo-8-97-2022, 2022
Short summary
Short summary
A common problem in climate studies is to decide whether a climate model is realistic. Such decisions are not straightforward because the time series are serially correlated and multivariate. Part II derived a test for deciding wether a simulation is statistically distinguishable from observations. However, the test itself provides no information about the nature of those differences. This paper develops a systematic and optimal approach to diagnosing differences between stochastic processes.
Cited articles
Alexander, M. A., Matrosova, L., Penland, C., Scott, J. D., and Chang, P.:
Forecasting Pacific SSTs: Linear Inverse Model Predictions of the PDO,
J. Climate, 21, 385–402, https://doi.org/10.1175/2007JCLI1849.1,
2008. a
Allen, M. R. and Tett, S. F. B.: Checking for model consistency in optimal
fingerprinting, Clim. Dynam., 15, 419–434, 1999. a
Bindoff, N. L., Stott, P. A., AchutaRao, K. M., Allen, M. R., Gillett, N.,
Gutzler, D., Hansingo, K., Hegerl, G., Hu, Y., Jain, S., Mokhov, I. I.,
Overland, J., Perlwitz, J., Webbari, R., and Zhang, X.: Detection and
Attribution of Climate Change: From Global to Regional, in: Climate Change
2013: The Physical Science Basis. Contribution of Working Group I to the
Fifth Assessment Report of the Intergovernmental Panel on Climate
Change, edited by Stocker, T., Qin, D., Plattner, G.-K., Tignor, M., Allen,
S., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P., chap. 10,
867–952, Cambridge University Press, New York, 2013. a, b
Booth, B. B. B., Dunstone, N. J., Halloran, P. R., Andrews, T., and Bellouin,
N.: Aerosols implicated as a prime driver of twentieth-century North
Atlantic climate variability, Nature, 484, 228–232,
https://doi.org/10.1038/nature10946, 2012. a, b
Branstator, G., Teng, H., Meehl, G. A., Kimoto, M., Knight, J. R., Latif, M.,
and Rosati, A.: Systematic estimates of initial value decadal predictability
for six AOGCMs, J. Climate, 25, 1827–1846, 2012. a
DelSole, T. and Tippett, M. K.: Laplacian Eigenfunctions for Climate
Analysis, J. Climate, 28, 7420–7436, https://doi.org/10.1175/JCLI-D-15-0049.1,
2015. a, b, c
DelSole, T. and Tippett, M. K.: Comparing climate time series – Part 1: Univariate test, Adv. Stat. Clim. Meteorol. Oceanogr., 6, 159–175, https://doi.org/10.5194/ascmo-6-159-2020, 2020. a
DelSole, T. and Tippett, M. K.: A Mutual Information Criterion with
Applications to Canonical Correlation Analysis and Graphical Models, Stat,
10, e385, https://doi.org/10.1002/sta4.385, 2021a. a
DelSole, T. and Tippett, M. K.: Software for comparing time series, available at: https://github.com/tdelsole/Comparing-Time-Series, GitHub [code], last access: 29 November 2021b. a
DelSole, T., Tippett, M. K., and Shukla, J.: A significant component of
unforced multidecadal variability in the recent acceleration of global
warming, J. Climate, 24, 909–926, 2011. a
Dias, D. F., Subramanian, A., Zanna, L., and Miller, A. J.: Remote and local
influences in forecasting Pacific SST: a linear inverse model and a
multimodel ensemble study, Clim. Dynam., 55, 1–19, 2018. a
Flato, G., Marotzke, J., Abiodun, B., Braconnot, P., Chou, S., Collins, W.,
Cox, P., Driouech, F., Emori, S., Eyring, V., Forest, C., Gleckler, P.,
Guilyardi, E., Jakob, C., Kattsov, V., Reason, C., and Rummukainen, M.:
Evaluation of Climate Models, in: Climate Change 2013: The Physical Science
Basis. Contribution of Working Group I to the Fifth Assessment Report of the
Intergovernmental Panel on Climate Change, edited by: Stocker, T.,
Qin, D., Plattner, G.-K., Tignor, M., Allen, S., Boschung, J., Nauels, A.,
Xia, Y., Bex, V., and Midgley, P., 741–866, Cambridge University Press, New York,
2013. a
Griffies, S. M. and Bryan, K.: A predictability study of simulated North
Atlantic multidecal variability, Clim. Dynam., 13, 459–487, 1997. a
Hourdin, F., Mauritsen, T., Gettelman, A., Golaz, J.-C., Balaji, V., Duan, Q.,
Folini, D., Ji, D., Klocke, D., Qian, Y., Rauser, F., Rio, C., Tomassini, L.,
Watanabe, M., and Williamson, D.: The Art and Science of Climate Model
Tuning, B. Am. Meteorol. Soc., 98, 589–602,
https://doi.org/10.1175/BAMS-D-15-00135.1, 2016. a
Huang, B., Thorne, P. W., Banzon, V. F., Boyer, T., Chepurin, G., Lawrimore,
J. H., Menne, M. J., Smith, T. M., Vose, R. S., and Zhang, H.-M.: Extended
Reconstructed Sea Surface Temperature, Version 5 (ERSSTv5): Upgrades,
Validations, and Intercomparisons, J. Climate, 30, 8179–8205,
https://doi.org/10.1175/JCLI-D-16-0836.1, 2017. a
Huddart, B., Subramanian, A., Zanna, L., and Palmer, T.: Seasonal and decadal
forecasts of Atlantic Sea surface temperatures using a linear inverse model,
Clim. Dynam., 49, 1833–184, https://doi.org/10.1007/s00382-016-3375-1, 2016. a
Izenman, A. J.: Modern Mutivariate Statistical Techniques: Regression,
Classification, and Manifold Learning, corrected 2nd Edn., Springer, New York,
2013. a
Keenlyside, N. S., Latif, M., Jungclaus, J., Kornblueh, L., and Roeckner, E.:
Advancing decadal-scale climate prediction in the North Atlantic sector,
Nature, 453, 84–88, 2008. a
Kushnir, Y.: Interdecadal variations in the North Atlantic sea surface
temperature and associated atmospheric conditions, J. Climate, 7, 141–157,
1994. a
Latif, M., Roeckner, E., Botzet, M., Esch, M., Haak, H., Hagemann, S.,
Jungclaus, J., Legutke, S., Marsland, S., Mikolajewicz, U., and Mitchell, J.:
Reconstrucing, Monitoring, and Predicting Multidecadal-Scale Changes in the
North Atlantic Thermohaline Circulation with Sea Surface Temperature, J.
Climate, 17, 1605–1614,
https://doi.org/10.1175/1520-0442(2004)017<1605:RMAPMC>2.0.CO;2,
2004. a
Latif, M., Collins, M., Pohlmann, H., and Keenlyside, N.: A review of
predictability studies of Atlantic sector climate on decadal time scales,
J. Climate, 19, 5971–5987, 2006. a
Mann, M. E., Steinman, B. A., Brouillette, D. J., and Miller, S. K.:
Multidecadal climate oscillations during the past millennium driven by
volcanic forcing, Science, 371, 1014–1019, https://doi.org/10.1126/science.abc5810,
2021. a
Marshall, J., Kushnir, Y., Battisti, D., Chang, P., Czaja, A., Dickson, R.,
Hurrell, J., McCartney, M., Saravanan, R., and Visbeck, M.: North
Atlantic Climate Variability: Phenomena, Impacts, and Mechanisms, Int. J.
Climatol., 21, 1863–1898, 2001. a
Newman, M.: An Empirical benchmark for decadal forecasts of global surface
temperature anomalies, J. Climate, 26, 5260–5269, 2013. a
Pennell, C. and Reichler, T.: On the Effective Number of Climate Models,
J. Climate, 24, 2358–2367, https://doi.org/10.1175/2010JCLI3814.1,
2011. a
Schmidt, G. A., Bader, D., Donner, L. J., Elsaesser, G. S., Golaz, J.-C., Hannay, C., Molod, A., Neale, R. B., and Saha, S.: Practice and philosophy of climate model tuning across six US modeling centers, Geosci. Model Dev., 10, 3207–3223, https://doi.org/10.5194/gmd-10-3207-2017, 2017. a
Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An Overview of CMIP5 and
the Experimental Design, B. Am. Meteorol. Soc., 93, 485–498, 2012. a
Trenberth, K. E. and Shea, D. J.: Atlantic Hurricanes and Natural Variablity
in 2005, Geophys. Res. Lett., 33, L12704, https://doi.org/10.1029/2006GL026894, 2006. a
Tung, K.-K. and Zhou, J.: Using data to attribute episodes of warming and
cooling in instrumental records, P. Natl. Acad.
Sci. USA, 110, 2058–2063, 2013. a
Vimont, D. J.: Analysis of the Atlantic Meridional Mode Using Linear Inverse
Modeling: Seasonality and Regional Influences, J. Climate, 25, 1194–1212, https://doi.org/10.1175/JCLI-D-11-00012.1,
2012. a
Washington, B., Seymour, L., Lund, R., and Willett, K.: Simulation of
temperature series and small networks from data, Int. J.
Climatol., 39, 5104–5123, https://doi.org/10.1002/joc.6129,
2019. a
WCRP: Coupled Model Intercomparison Project 5 (CMIP5), World Climate Research Programme [data set], available at: https://esgf-node.llnl.gov/projects/cmip5/, last access: 1 December 2021. a
Wittenberg, A. T.: Are historical records sufficient to constraint ENSO
simulations?, Geophys. Res. Lett., 36, L12702, https://doi.org/10.1029/2009GL038710, 2009.
a
Zanna, L.: Forecast skill and predictability of observed North Atlantic sea
surface temperatures, J. Climate, 25, 5047–5056, 2012. a
Zhang, R., Delworth, T. L., Sutton, R., Hodson, D. L. R., Dixon, K. W., Held,
I. M., Kushnir, Y., Marshall, J., Ming, Y., Msadek, R., Robson, J., Rosati,
A. J., Ting, M., and Vecchi, G. A.: Have Aerosols Caused the Observed
Atlantic Multidecadal Variability?, J. Atmos. Sci., 70, 1135–1144,
https://doi.org/10.1175/JAS-D-12-0331.1,
2013. a, b, c
Download
- Article
(4936 KB) - Full-text XML
Short summary
After a new climate model is constructed, a natural question is whether it generates realistic simulations. Here,
realisticdoes not mean that the detailed patterns on a particular day are correct, but rather that the statistics over many years are realistic. Past approaches to answering this question often neglect correlations in space and time. This paper proposes a method for answering this question that accounts for correlations in space and time.
After a new climate model is constructed, a natural question is whether it generates realistic...