Causes of differences in model and satellite tropospheric warming rates

Journal name:
Nature Geoscience
Year published:
Published online


In the early twenty-first century, satellite-derived tropospheric warming trends were generally smaller than trends estimated from a large multi-model ensemble. Because observations and coupled model simulations do not have the same phasing of natural internal variability, such decadal differences in simulated and observed warming rates invariably occur. Here we analyse global-mean tropospheric temperatures from satellites and climate model simulations to examine whether warming rate differences over the satellite era can be explained by internal climate variability alone. We find that in the last two decades of the twentieth century, differences between modelled and observed tropospheric temperature trends are broadly consistent with internal variability. Over most of the early twenty-first century, however, model tropospheric warming is substantially larger than observed; warming rate differences are generally outside the range of trends arising from internal variability. The probability that multi-decadal internal variability fully explains the asymmetry between the late twentieth and early twenty-first century results is low (between zero and about 9%). It is also unlikely that this asymmetry is due to the combined effects of internal variability and a model error in climate sensitivity. We conclude that model overestimation of tropospheric warming in the early twenty-first century is partly due to systematic deficiencies in some of the post-2000 external forcings used in the model simulations.

At a glance


  1. Time series and difference series of simulated and observed tropospheric temperature.
    Figure 1: Time series and difference series of simulated and observed tropospheric temperature.

    a, Monthly mean TMT anomalies for the 456-month period from January 1979 to December 2016, spatially averaged over 82.5°N–82.5°S and corrected for lower stratospheric cooling 40. Multi-model average (MMA) temperature data are from HIST + 8.5 simulations performed with 37 different CMIP5 models; satellite TMT data are for RSS version 4.0 (ref. 29). Model TMT data were computed using vertical weighting functions that approximate the satellite-based vertical sampling of the atmosphere54. b, Time series of differences between the MMA and the RSS data shown in both raw form and smoothed with a 12-month running mean. All anomalies are relative to climatological monthly means calculated over January 1979 to December 2016. The vertical purple line is plotted at the time of the maximum global-mean tropospheric warming during the 1997/98 El Niño. The vertical green lines denote the eruption dates of El Chichón and Pinatubo. Trends in the MMA and RSS over the full 456 months (the grey and pink lines in a) are 0.291 and 0.199°C per decade, respectively. The corresponding trends over the early twenty-first century (January 2000 to December 2016) are 0.286 and 0.191°C per decade.

  2. Trends (left column) and trend significance (right column) for TMT difference series.
    Figure 2: Trends (left column) and trend significance (right column) for TMT difference series.

    The six difference series are for near-global averages of corrected TMT, and were computed by subtracting each of the six individual satellite TMT records from the HIST + 8.5 multi-model average TMT time series (see Fig. 1). Maximally overlapping trends were fitted to each 456-month difference series. Results are for trend lengths of L = 10,12,14,16, and 18 years; the overlap between successive L-year trends is by all but one month. The p values associated with each L-year difference series trend were obtained by testing against multi-model distributions of unforced L-year TMT trends from 36 different CMIP5 control runs. Results are plotted on the last month of the trend-fitting period. Grey shading denotes the rejection region (at a stipulated 10% significance level) for the null hypothesis that the difference between modelled and observed TMT trends is due to internal variability alone. Each panel in the right-hand column has a lower (upper) rejection region for large positive (large negative) trends in the model-minus-observed difference series. The lower (upper) rejection region spans the p value range 0 to 0.1 (0.9 to 1.0). The y-axis range was extended to − 0.06 to facilitate visual display of p values at or close to zero. To calculate the actual values of the γ2 and γ3 statistics in Fig. 3d and f, the maximally overlapping L-year trends were divided into two sets of approximately equal size (‘SET 1 and ‘SET 2; see Methods). The dashed vertical lines in the panels of the right-hand column denote the final month of the last L-year trend in SET 1.

  3. Asymmetries in the statistical significance of differences between modelled and observed tropospheric temperature trends.
    Figure 3: Asymmetries in the statistical significance of differences between modelled and observed tropospheric temperature trends.

    Results are for maximally overlapping 10-year trends in near-global averages of corrected TMT. a-c, We calculate three asymmetry statistics. The first compares the numbers of significant positive and negative trends in the ΔTfo(k, t) difference time series (a). Subtracting the number of significant negative trends from the number of significant positive trends yields the γ1 statistic (b). The second statistic gauges asymmetry in the temporal distribution of positive trends in the difference series (c). d-f, To quantify this asymmetry, we split the number of maximally overlapping 10-year trends into two sets of approximately equal size. Trends sampling earlier (later) portions of the difference series are in SET1 (SET 2). The difference in the number of positive trends (SET1 minus SET2) is the γ2 statistic (d). The third asymmetry statistic relies on the average p values of the individual trends in SET1 and SET2 (e). The difference between these set-average p values is γ3 (f). The vertical lines in b,d and f are the actual values of γ1, γ2 and γ3. The grey histograms in b,d and f are null distributions of the asymmetry statistics, which were generated using 5,000 realizations of surrogate observations (see Methods).

  4. Overall statistical significance of the [gamma]1, [gamma]2 and [gamma]3 asymmetry statistics as a function of the analysis timescale and the satellite data used to compute the /`MMA minus observed[rsquor] difference time series.
    Figure 4: Overall statistical significance of the γ1, γ2 and γ3 asymmetry statistics as a function of the analysis timescale and the satellite data used to compute the ‘MMA minus observed difference time series.

    ac, Results are estimates of pγ1 (a), pγ2 (b) and pγ3 (c), the probabilities that the actual value of the asymmetry statistic could have been obtained by natural internal variability alone. The magenta lines are the averages (over the three recent observational data sets and the five analysis timescales) of pγ1, pγ2 and pγ3. Zero values of the probabilities are indicated by coloured arrows. The y-axis range in a and b is substantially smaller than in c. For further details refer to the caption of Fig. 3 and the Methods.


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Author information


  1. Program for Climate Model Diagnosis and Intercomparison (PCMDI), Lawrence Livermore National Laboratory, Livermore, California 94550, USA

    • Benjamin D. Santer,
    • Giuliana Pallotta,
    • Jeffrey F. Painter,
    • Céline Bonfils,
    • Ivana Cvijanovic &
    • Stephen Po-Chedley
  2. Canadian Centre for Climate Modelling and Analysis (CCCma), Environment and Climate Change Canada, Victoria, British Columbia V8W 2Y2, Canada

    • John C. Fyfe &
    • Gregory M. Flato
  3. National Center for Atmospheric Research, Boulder, Colorado 80307, USA

    • Gerald A. Meehl
  4. ARC Centre of Excellence for Climate System Science, University of New South Wales, New South Wales 2052, Australia

    • Matthew H. England
  5. National Centre for Atmospheric Science, Department of Meteorology, University of Reading, Reading RG6 6BB, UK

    • Ed Hawkins
  6. Department of Meteorology and Earth and Environmental Systems Institute, Pennsylvania State University, University Park, Pennsylvania 16802, USA

    • Michael E. Mann
  7. Remote Sensing Systems, Santa Rosa, California 95401, USA

    • Carl Mears &
    • Frank J. Wentz
  8. Department of Atmospheric Sciences, University of Washington, Seattle, Washington 98195, USA

    • Qiang Fu
  9. Center for Satellite Applications and Research, NOAA/NESDIS, College Park, Maryland 20740, USA

    • Cheng-Zhi Zou


B.D.S., J.C.F., G.P., G.M.F. and E.H. designed the analysis. B.D.S. performed all statistical analyses. J.F.P. calculated synthetic satellite temperatures from model simulation output and provided assistance with processing of observed temperature data. C.M., F.J.W., S.P.-C., Q.F. and C.-Z.Z. provided satellite temperature data. I.C., C.B. and J.F.P. assisted with the processing of the CMIP5 simulations analysed here. All authors contributed to the writing and review of the manuscript.

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