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Artificial intelligence reconstructs missing climate information

Abstract

Historical temperature measurements are the basis of global climate datasets like HadCRUT4. This dataset contains many missing values, particularly for periods before the mid-twentieth century, although recent years are also incomplete. Here we demonstrate that artificial intelligence can skilfully fill these observational gaps when combined with numerical climate model data. We show that recently developed image inpainting techniques perform accurate monthly reconstructions via transfer learning using either 20CR (Twentieth-Century Reanalysis) or the CMIP5 (Coupled Model Intercomparison Project Phase 5) experiments. The resulting global annual mean temperature time series exhibit high Pearson correlation coefficients (≥0.9941) and low root mean squared errors (≤0.0547 °C) as compared with the original data. These techniques also provide advantages relative to state-of-the-art kriging interpolation and principal component analysis-based infilling. When applied to HadCRUT4, our method restores a missing spatial pattern of the documented El Niño from July 1877. With respect to the global mean temperature time series, a HadCRUT4 reconstruction by our method points to a cooler nineteenth century, a less apparent hiatus in the twenty-first century, an even warmer 2016 being the warmest year on record and a stronger global trend between 1850 and 2018 relative to previous estimates. We propose image inpainting as an approach to reconstruct missing climate information and thereby reduce uncertainties and biases in climate records.

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Fig. 1: AI models reconstruct two exemplary monthly show cases with many missing values.
Fig. 2: Evaluation of AI models with different methods for annual global mean temperature reconstructions.
Fig. 3: AI model spatial reconstruction of an observed El Niño with many missing values in HadCRUT4.
Fig. 4: AI model reconstruction of HadCRUT4 for the full time series between 1850 and 2018.

Data availability

A software snapshot, trained AI models (checkpoints), missing value masks and the HadCRUT4 reconstructions by the AI models can be downloaded at https://doi.org/10.5281/zenodo.3766741. Training data from 20CR and CMIP5 cannot be hosted due to copyrights, but are available at National Oceanic and Atmospheric Administration and ESGF (Methods). Contact kadow@dkrz.de for further information. Source Data are provided with this paper.

Code availability

All the code utilized in this project can be downloaded here or cloned here at https://github.com/FREVA-CLINT/climatereconstructionAI. This code will be updated and changed over time.

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Acknowledgements

We thank the HPC-Service of ZEDAT, Freie Universität Berlin and the German Climate Computing Center (DKRZ) for the computation resources; the Climatic Research Unit (CRU) of the University East Anglia (UEA) and the MetOffice UK for providing the HadCRUT4 and HadSST4 datasets; the Earth System Grid Federation (ESGF) for providing the CMIP5 experiments; J. Marotzke (MPI-M), M. Schuster (FUB), E. Barnes (CSU), K. Buscher (UKM) for discussions; N. Inoue (University of Tokyo) for providing the applicable code for image inpainting; A. Richling (FUB) for reproducing the Intergovernmental Panel on Climate Change trend, uncertainty and confidence values; K. Cowtan, R. Way, and the University of York for not just providing the reconstructed HadCRUT4 data (used in Fig. 3b), but also software to apply the kriging scheme (used in Fig. 2). Support for the 20CR Project dataset is provided by the US Department of Energy, Office of Science Innovative and Novel Computational Impact on Theory and Experiment (DOE INCITE) programme, by the Office of Biological and Environmental Research (BER) and by the National Oceanic and Atmospheric Administration Climate Program Office.

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Authors

Contributions

C.K. initiated the study design, coded the AI technology for climate research, performed the analysis and drafted the paper. D.M.H. supervised the NVIDIA AI technology and U.U. supervised the climate research results. All the authors discussed the results and edited the manuscript.

Corresponding author

Correspondence to Christopher Kadow.

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The authors declare no competing interests.

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Peer review information Primary Handling Editors: Stefan Lachowycz; Heike Langenberg.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Scheme for the study setup including training set.

Input for the AI models, training of the models, and their output. HadCRUT4 data in black, CMIP data or AI in red, 20CR data or AI in blue. Numbers on the bottom of the boxes represent the number of ‘images’ / months / time steps, which are used as input or result as output (see Method section).

Extended Data Fig. 2 Detailed grid space evaluation of 20CR reconstruction.

Correlation (left) and root mean squared error in centigrade (right) comparing the reconstructed 20CR 56th member by the 20crAI model with the original 20CR 56th member. Comparison of all grid points in an annual (row 1) and monthly (row 2) analysis. The respective analysis for the reconstructed grid points only, without (w/o) grid points which were evident during reconstruction below (row 3/4). Grey grid points indicate points that exist for the whole time series.

Source data

Extended Data Fig. 3 Detailed grid space evaluation of CMIP reconstruction.

Correlation (left) and root mean squared error in centigrade (right) comparing the reconstructed CMIP 145th member by the cmipAI model with the original CMIP 145th member. Comparison of all grid points in an annual (row 1) and monthly (row 2) analysis. The respective analysis for the reconstructed grid points only, without (w/o) grid points which were evident during reconstruction below (row 3/4). Grey grid points indicate points that exist for the whole time series.

Source data

Extended Data Fig. 4 Time-series analysis and evaluation of AI model reconstruction.

As Fig. 2, but the annual global mean anomaly temperature reconstructions in centigrade of 20CR (a, b) / CMIP (c, d) test-suite of monthly grid reconstructions of the held-out 56th / 145th member using the HadCRUT4 missing value mask (1870-2005). In black the original held-out member, in black-dashed the original but masked held-out member to see the effect of the missing values. In blue/red the reconstructed grid time-series of the 20crAI/cmipAI. Tables show anomaly correlation (r) and root mean squared error (rmse) compared to the original dataset on four selected time ranges. (see also Fig. 2).

Source data

Extended Data Fig. 5 Spatial evaluation of AI models over time.

Fieldcorrelation of the annual (a) and monthly (b) mean reconstruction of the 20CR 56th / CMIP 145th member by the 20crAI / cmipAI models with the original 20CR 56th / CMIP 145th member in blue / red. Solid line compares the full grid space, while the dashed line respective analysis for the reconstructed grid points only, without (w/o) grid points which were evident during reconstruction.

Source data

Extended Data Fig. 6 Evaluation on reconstructed grid points only.

Annual global mean anomaly temperature reconstruction in centigrade of 20CR (a) and CMIP (b) of monthly grid reconstructions applying only reconstructed missing values the extra 56th / 145th member using the HadCRUT4 missing value mask between 1870 and 2005. In black the extra member without (w/o) existing grid points, in black-dashed the original full left-out member to see the effect of the missing values. In blue/red the reconstructed grid time-series of the 20crAI/cmipAI models without (w/o) existing grid points.

Source data

Extended Data Fig. 7 Reconstruction analysis of additional Hadley Centre products.

Annual global mean anomaly temperature time series between 1850 and 2018. (a) HadCRUT4 original (masked) 100 member data in black (median, 95th, 5th percentile). The HadCRUT4 reconstruction of the 20crAI/cmipAI models in blue/red (median, 95th, 5th percentile). (b) HadCRUT4 original (masked) data in black, HadSST4 original (masked) data in pink, HadMIX original (masked) data in orange. The originals are dashed, the reconstructions have straight lines. HadMIX has all grid points available of HadSST4, if not available (usually over land) HadCRUT4 grid points are used.

Source data

Extended Data Fig. 8 HadCRUT4 trends of AI models in grid space.

Trends in surface temperature from Fig. 4 for 1901–2012. White areas indicate incomplete or missing data. Trends have been calculated only for those grid boxes with greater than 70% complete records and more than 20% data availability in first and last decile of the period. Black plus signs (+) indicate grid boxes where trends are significant (i.e., a trend of zero lies outside the 90% confidence interval). Graphics are constructed, to be compared with IPCC AR5 Chapter 2 Figure 2.21. Here HadCRUT4 Version 4.6.0.0 is used, IPCC report used Version 4.1.1.

Source data

Extended Data Fig. 9 Spatial reconstruction of an observed El Niño.

As Fig. 3 but with additional datasets. Recently, the HadSST4 (b) data set was released as an update to HadSST3 (ocean component of HadCRUT4 (a)). Kriging analysis of Cowtan&Way (c) is set next to Berkley Earth (d). In July 1877 HadSST4 has three new grid points, which show very high (warm) temperature anomalies in a region (further south than usual) where the the PCA reconstruction of 20crPCA (e) and cmipPCA (f) show some weak signal. Neural network reconstructions of 20crAI (g) and cmipAI (h) show some strong signal of an El Niño like temperature pattern.

Source data

Extended Data Fig. 10 CMIP numerical models to train the neural network.

CMIP5 Historical monthly experiments between 1850 and 2005 applied to train the cmipAI. Data from refs. 42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61.

Supplementary information

Supplementary Information

Supplementary Figs. 1–5.

Source data

Source Data Fig. 1

Temperature anomaly maps in NetCDF format.

Source Data Fig. 2

Temperature anomaly time series in NetCDF format.

Source Data Fig. 3

Temperature anomaly maps in NetCDF format.

Source Data Fig. 4

Temperature anomaly time series in NetCDF format.

Source Data Extended Data Fig. 2

Statistical Source Data on maps in NetCDF format.

Source Data Extended Data Fig. 3

Statistical Source Data on maps in NetCDF format.

Source Data Extended Data Fig. 4

Temperature anomaly time series in NetCDF format.

Source Data Extended Data Fig. 5

Statistical measure time series in NetCDF format.

Source Data Extended Data Fig. 6

Temperature anomaly time series in NetCDF format.

Source Data Extended Data Fig. 7

Temperature anomaly time series in NetCDF format.

Source Data Extended Data Fig. 8

Temperature trend maps in NetCDF format.

Source Data Extended Data Fig. 9

Temperature anomaly maps in NetCDF format.

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Kadow, C., Hall, D.M. & Ulbrich, U. Artificial intelligence reconstructs missing climate information. Nat. Geosci. 13, 408–413 (2020). https://doi.org/10.1038/s41561-020-0582-5

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