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Tropospheric Warming Over The Past Two Decades

  • Scientific Reports 7, Article number: 2336 (2017)
  • doi:10.1038/s41598-017-02520-7
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Abstract

Satellite temperature measurements do not support the recent claim of a “leveling off of warming” over the past two decades. Tropospheric warming trends over recent 20-year periods are always significantly larger (at the 10% level or better) than model estimates of 20-year trends arising from natural internal variability. Over the full 38-year period of the satellite record, the separation between observed warming and internal variability estimates is even clearer. In two out of three recent satellite datasets, the tropospheric warming from 1979 to 2016 is unprecedented relative to internally generated temperature trends on the 38-year timescale.

Introduction

After a recent Senate confirmation hearing, Scott Pruitt – the new Administrator of the U.S. Environmental Protection Agency – received a written question regarding observed warming estimates. In response, Mr. Pruitt claimed that “over the past two decades satellite data indicates there has been a leveling off of warming”1. We test this claim here. In the following, we assume the satellite data referred to by Mr. Pruitt are measurements of the temperature of the lowest layer of the atmosphere (the troposphere). These measurements were the focus of recent Congressional testimony2. We update and extend the analysis in ref. 3 using satellite temperature data spanning the period from January 1979 to December 2016.

Since late 1978, satellite microwave sounders have monitored the microwave emissions of oxygen molecules. Emissions are proportional to the temperature of different atmospheric layers, and require adjustments for known problems associated with satellite orbital drift and instrument calibration4,5,6. Satellite estimates of global changes in the temperature of the mid- to upper troposphere (TMT) are currently available from Remote Sensing Systems (RSS), the Center for Satellite Applications and Research (STAR), and the University of Alabama at Huntsville (UAH). All three groups provide older and more recent TMT datasets4, 5, 7. The newer, more reliable datasets are the primary focus here.

Satellite TMT measurements include a contribution from the cooling stratosphere. To study warming of the troposphere, we used a standard regression method8,9,10,11 to remove the stratospheric cooling contribution to TMT (see Methods). The corrected TMT data show pronounced tropospheric warming (Fig. 1A). In the most recent versions of the RSS, STAR, and UAH datasets, the TMT trend over the full 38-year period of the satellite record is 0.199 °C, 0.202 °C, and 0.142 °C per decade (respectively).

Figure 1
Figure 1

Evaluation of claimed “leveling off” of warming in satellite temperature data. Results are for monthly-mean anomalies in the temperature of the mid- to upper troposphere (TMT), corrected for stratospheric cooling8 and spatially averaged over 82.5°N–82.5°S. The average of the latest satellite dataset versions (RSS v4.0, STAR v4.0, and UAH v6.0) has a warming trend of 0.181 °C/decade over the 456-month period from January 1979 to December 2016 (panel A). Maximally overlapping 20-year (240-month) trends in the six individual satellite TMT time series are plotted on the end month of the trend-fitting period (panel B). The p-values for these trends (panel C) are for tests of the null hypothesis that observed tropospheric warming could be due to natural internal variability alone3. The grey shaded box is the rejection region (at a stipulated 10% significance level) for the null hypothesis. The p-value calculations rely on estimates of the multi-decadal internal variability of the climate system from model pre-industrial control runs. These simulations have no year-to-year changes in natural or human external forcings. The sampling distributions of control run TMT trends on 20-year and 38-year timescales (the orange histograms in panels D and E, respectively) are based on results from 36 different models. The symbols (plus signs) in panel D are the final 20-year trends from panel B. Bold vertical lines in panel D are the averages of the overlapping 20-year trends in panel B (see arrows to the right of panel B). Vertical lines in panel E are observed trends over the full 456-month satellite record. Results in D and E are for the latest satellite dataset versions only. Full analysis details are in ref. 3 and the Methods section.

To evaluate the claim that satellite data show “leveling off” of warming over the past two decades, we examine all possible 20-year periods of satellite TMT records. We calculate linear temperature trends for each 20-year period, and then determine whether the observed TMT trends are significantly larger than the 20-year trends arising from natural processes internal to the climate system3. Estimates of natural internal variability are based on results from 36 different climate models (see Methods and Supplementary Information).

Results

In each of the six satellite datasets, all 20-year TMT trends are positive, irrespective of the trend start date (Fig. 1B). The specific period of “the past two decades” yields 20-year TMT trends that have not “leveled off”. As expected, there are multi-decadal changes in trend size12, 13. Recent 20-year trends are smaller than most of the earlier 20-year trend values. This is due to the combined effects of multiple factors: the anomalous warmth at the beginning of the last 20 years (arising from a large El Niño event in 1997/98), the shift from a warm phase to a cold phase of the Interdecadal Pacific Oscillation in the late 1990s14,15,16,17, changes in other modes of internal variability18,19,20, a succession of moderate volcanic eruptions in the early 21st century21,22,23, a long and low minimum in solar output during the last solar cycle24, and an increase in anthropogenic sulphate pollution25, 26.

Figure 1C provides information on whether observed TMT trends show unusually large warming relative to the estimated warming trends caused by natural internal climate variability. Two features are noteworthy. First, we find that significant 20-year tropospheric warming trends are a commonplace occurrence during the satellite era. Second, despite their smaller size, warming trends over the last 20 years (January 1997 to December 2016) are significantly larger, at the 10% level or better, than estimates of 20-year trends arising from natural internal variability (Fig. 1C,D). This holds for all six satellite datasets. In the latest versions of the RSS, STAR, and UAH TMT data, the probability that internal variability could produce warming exceeding that observed over the last 20 years is only 1.6%, 3.1%, and 6.3% (respectively). These probabilities decrease markedly if the averages of all individual 20-year trends are considered (see vertical lines in Fig. 1D).

The unusual size of observed tropospheric warming becomes even clearer for the full 38-year period of TMT measurements. Over 1979 to 2016, global warming of the troposphere far exceeds current estimates of natural internal climate variability (Fig. 1E). TMT trends in the latest versions of the RSS, STAR, and UAH datasets are (respectively) 7.50, 7.64, and 5.35 standard deviations removed from the mean of the distribution of unforced 38-year TMT trends. The probabilities associated with these numbers are miniscule. In fact, the tropospheric warming trends in versions 4.0 of the RSS and STAR data are unprecedented – they are not exceeded by any of the 212,808 unforced TMT trends in the distribution shown in Fig. 1E. In version 6.0 of the UAH data, only 16 of the 212,808 unforced trends are larger than the observed TMT trend. To plausibly explain the observed tropospheric warming by natural internal variability would require that the model results in Fig. 1E underestimate real-world internal variability by a factor of 2.5 or more. There is no evidence of a systematic model error of this size12, 27, 28 (see Methods).

Summary

Satellite temperature measurements do not support the claim of a “leveling off of warming” over the past two decades1. They are also inconsistent with a similar claim2 (see Supplementary Figure S1). Trend assessments over short, 1–2 decade-long periods of time are often sensitive to small changes in the trend start date3. More reliable estimates of underlying temperature changes are obtained by averaging over all possible short-term trends or by considering longer analysis periods.

When examined over the full period of record, long-term tropospheric warming far exceeds current estimates of natural internal climate variability (Fig. 1E). Our results support and strengthen previous findings of a large human-caused contribution to warming29,30,31,32. Studies involving patterns of tropospheric temperature change (rather than the global averages considered here) yield even stronger evidence of a human fingerprint in the thermal structure of the atmosphere27, 33,34,35. The recent focus on satellite temperature data in political discourse1, 2 provides an opportunity to highlight this fingerprint evidence, and underscores the importance of continued satellite-based monitoring of Earth’s climate.

Methods

Satellite atmospheric temperature data

We used satellite estimates of atmospheric temperature produced by RSS4, STAR5, and UAH7. All three groups provide satellite measurements of the temperatures of the mid- to upper troposphere (TMT) and the lower stratosphere (TLS). Our focus here is on assessing the significance of observed trends in TMT. TLS is required for correcting TMT for the influence it receives from stratospheric cooling.

Each group provides the most recent version and the previous version of their datasets. The versions available are: 3.3 and 4.0 (RSS), 3.0 and 4.0 (STAR), and 5.6 and 6.0 (UAH). Satellite datasets are in the form of monthly means on 2.5° × 2.5° latitude/longitude grids. At the time this analysis was performed, temperature data were available for the 456-month period from January 1979 to December 2016.

There are differences in the spatial coverage of the satellite temperature data produced by the three groups. While UAH TLS and TMT datasets have global coverage, areas poleward of 87.5° (82.5°) are excluded from STAR (RSS). To avoid any impact of spatial coverage differences on trend comparisons, we calculated all near-global averages of actual and synthetic satellite temperatures over the area of common coverage in the RSS, UAH, and STAR datasets (82.5°N to 82.5°S).

Method used for correcting TMT data

Trends in TMT estimated from microwave sounders receive a substantial contribution from the cooling of the lower stratosphere8,9,10,11. In ref. 8, a regression-based approach was developed for removing the bulk of this stratospheric cooling component of TMT. This method has been validated with both observed and model atmospheric temperature data9, 36, 37. Correction was performed at each observational and model grid-point. Corrected grid-point data were then spatially averaged over 82.5°N–82.5°S. Further details of the correction method are provided in the Supplementary Information.

Details of model output

We used model output from phase 5 of the Coupled Model Intercomparison Project38 (CMIP5). The simulations analyzed here were contributed by 18 different research groups (see Supplementary Table S1). Our focus was on pre-industrial control runs with no changes in external influences on climate, which provide estimates of the natural internal variability of the climate system (see Supplementary Table S2).

To compare satellite-derived atmospheric temperature trends with model estimates of trends arising from natural internal variability, we calculate synthetic TMT and TLS from CMIP5 control runs. This calculation relies on a local weighting function method developed at RSS. At each model grid-point, simulated temperature profiles were convolved with local weighting functions. Local weights depend on the grid-point surface pressure, the surface type (land or ocean), and the selected layer-average temperature (TMT or TLS).

Statistical analysis

We use model estimates of natural internal variability to evaluate the statistical significance of trends in the observed temperature time series T o (k, t), where k and t are (respectively) indices over the number of satellite TMT datasets and the time in months. Internal variability estimates are obtained from CMIP5 control runs. Rather than focusing on one specific period, we analyze maximally overlapping 20-year trends in T o (k, t). “Maximally overlapping” indicates that an 20-year sliding window is being used for trend calculations. This window advances in increments of one month until the end of the current window reaches the final month of the satellite or control run TMT time series.

Anomalies in the satellite observations are defined relative to climatological monthly means calculated over the 38-year period from January 1979 to December 2016. Control run anomalies are with respect to climatological monthly means over the full length of each model’s control integration.

We assess trend significance using weighted p-values, which account for inter-model differences in control run length3.

The weighted p-value, p c ¯ (i,k ) , is defined as:

p c ¯ (i,k ) = j = 1 N m o d e l p c (i,j,k)/ N m o d e l
(1)
i=1,, N o ;j=1,, N m o d e l ;k=1,, N s a t

where the index i is over N o , the number of maximally overlapping 20-year trends in T o (k, t), and the index j spans N model , the number of model control runs (which is 36 here). The sample size N sat is the total number of satellite datasets. Here, N sat  = 6, and N o  = 217 for 20-year trends.

The individual p c (i, j, k) values for each model pre-industrial control run are calculated as follows:

p c (i,j,k)= K c (i,j,k)/ N c (j)
(2)
i=1,, N o ;j=1,, N m o d e l ;k=1,, N s a t

where the summation variable K c (i, j, k) is the number of 20-year trends in each model control run that are larger than b o (i, k), the current 20-year trend in T o (k, t). The sample size Nc(j) is the number of maximally overlapping 20-year trends in the jth control run. Further information on the statistical notation and analysis is given in the Supplementary Information.

Sensitivity of results to model variability errors

The credibility of our trend significance results rests on the assumption that model control runs yield reliable estimates of internal variability on the timescales considered here (20 years in Fig. 1C and D, 38 years in Fig. 1E, and 18 years in Supplementary Fig. 1C and D). On these multi-decadal timescales, it is not feasible to use the single realization of the observed 38-year satellite TMT record to evaluate how reliably models capture “observed” internal variability. The primary difficulty is that observed temperature records are simultaneously influenced by both internal variability (operating on a wide range of different space and timescales) and multiple external forcings. Unambiguous partitioning of observational temperature records into internally generated and externally forced components is an aspirational goal, but not attainable in practice. All model-versus-observed internal variability comparisons are affected by the uncertainties involved in isolating multi-decadal internal variability from observational climate records27.

Other approaches must therefore be employed to enhance confidence in the reliability of model variability on 18- to 38-year timescales, such as variability comparisons involving longer SST and land + ocean surface temperature records12, 28. The latter work shows no evidence that models systematically underestimate observed variability on multi-decadal timescales – see, e.g., Fig. 4 in ref. 28. The same applies to model-versus-data variability comparisons on shorter timescales of roughly 10 years27.

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References

  1. 1.

    U. S. Senate. Available online at: https://www.epw.senate.gov/public/_cache/files/6d95005c-bd1a-4779-af7e-be831db6866a/scott-pruitt-qfr-responses-01.18.2017.pdf U. S. Senate Environment and Public Works Committee Hearing, “Nomination of Attorney General Scott Pruitt to be Administrator of the U. S. Environmental Protection Agency”, January 18, 2017 (Date of access: 28/03/2017) (2017).

  2. 2.

    U. S. Senate, Available online at: http://www.commerce.senate.gov/public/index.cfm/2015/12/data-or-dogma-promoting-open-inquiry-in-the-debate-over-the-magnitude-of-human-impact-on-earth-s-climate. “Data or Dogma? Promoting open inquiry in the debate over the magnitude of human impact on Earth’s climate”. Archived webcast of Hearing before the U. S. Senate Committee on Commerce, Science, and Transportation, Subcommittee on Space, Science, and Competitiveness, December 8, 2015 (Date of access: 28/03/2017) (2015).

  3. 3.

    Santer, B. D. et al. Comparing tropospheric warming in climate models and satellite data. J. Clim. 30, 373–392, doi:10.1175/JCLI-D-16-0333.1 (2017).

  4. 4.

    Mears, C. & Wentz, F. J. Sensitivity of satellite-derived tropospheric temperature trends to the diurnal cycle adjustment. J. Clim. 29, 3629–3646, doi:10.1175/JCLI-D-15-0744.1 (2016).

  5. 5.

    Zou, C.-Z. & Wang. W. Inter-satellite calibration of AMSU-A observations for weather and climate applications J. Geophys. Res. 116, doi:10.1029/2011JD016205 (2011).

  6. 6.

    Po-Chedley, S., Thorsen, T. J. & Fu, Q. Removing diurnal cycle contamination in satellite-derived tropospheric temperatures: Understanding tropical tropospheric trend discrepancies. J. Clim. 28, 2274–2290, doi:10.1175/JCLI-D-13-00767.1 (2015).

  7. 7.

    Christy, J. R., Norris, W. B., Spencer, R. W. & Hnilo, J. J. Tropospheric temperature change since 1979 from tropical radiosonde and satellite measurements. J. Geophys. Res. 112, D06102, doi:10.1029/2005JD006881 (2007).

  8. 8.

    Fu, Q., Johanson, C. M., Warren, S. G. & Seidel, D. J. Contribution of stratospheric cooling to satellite-inferred tropospheric temperature trends. Nature 429, 55–58, doi:10.1038/nature02524 (2004).

  9. 9.

    Fu, Q. & Johanson, C. M. Stratospheric influences on MSU-derived tropospheric temperature trends: A direct error analysis. J. Clim. 17, 4636–4640, doi:10.1175/JCLI-3267.1 (2004b).

  10. 10.

    Fu, Q. & Johanson, C. M. Satellite-derived vertical dependence of tropical tropospheric temperature trends. Geophys. Res. Lett. 32, doi:10.1029/2004GL022266 22266 (2005).

  11. 11.

    Johanson, C. M. & Fu, Q. Robustness of tropospheric temperature trends from MSU Channels 2 and 4. J. Clim. 19, 4234–4242, doi:10.1175/JCLI3866.1 (2006).

  12. 12.

    Santer, B. D. et al. Separating signal and noise in atmospheric temperature changes: The importance of timescale. J. Geophys. Res. 116, doi:10.1029/2011JD016263 (2011).

  13. 13.

    Easterling, D. R. & Wehner, M. F. Is the climate warming or cooling? Geophys. Res. Lett. 36, doi:10.1029/2009GL037810 (2009).

  14. 14.

    Meehl, G. A., Arblaster, J. M., Fasullo, J. T., Hu, A. & Trenberth, K. E. Model-based evidence of deep-ocean heat uptake during surface-temperature hiatus periods. Nat. Cli. Change 1, 360–364, doi:10.1038/nclimate1229 (2011).

  15. 15.

    Fyfe, J. C. et al. Making sense of the early-2000s warming slowdown. Nat. Clim. Change 6, 224–228, doi:10.1038/nclimate2938 (2016).

  16. 16.

    England, M. H. et al. Recent intensification of wind-driven circulation in the Pacific and the ongoing warming hiatus. Nat. Clim. Change 4, 222–227, doi:10.1038/nclimate2106 (2014).

  17. 17.

    Trenberth, K. E. Has there been a hiatus? Science 349, 791–792, doi:10.1126/science.aac9225 (2015).

  18. 18.

    Kosaka, Y. & Xie, S.-P. Recent global-warming hiatus tied to equatorial Pacific surface cooling. Nature 501, 403–407, doi:10.1038/nature12534 (2013).

  19. 19.

    Risbey, J. S. et al. Well-estimated global surface warming in climate projections selected for ENSO phase. Nat. Clim. Change 4, 835–840, doi:10.1038/nclimate2310 (2014).

  20. 20.

    Steinman, B. A., Mann, M. E. & Miller, S. K. Atlantic and Pacific multidecadal oscillations and Northern Hemisphere temperatures. Science 347, 988–991, doi:10.1126/science.1257856 (2015).

  21. 21.

    Solomon, S. et al. The persistently variable “background” stratospheric aerosol layer and global climate change. Science 333, 866–870, doi:10.1126/science.1206027 (2011).

  22. 22.

    Vernier, J.-P. et al. Major influence of tropical volcanic eruptions on the stratospheric aerosol layer during the last decade. Geophys. Res. Lett. 38, doi:10.1029/2011GL047563 (2011).

  23. 23.

    Ridley, D. A. et al. Total volcanic stratospheric aerosol optical depths and implications for global climate change. Geophys. Res. Lett. 41, 7763–7769, doi:10.1002/2014GL061541 (2014).

  24. 24.

    Kopp, G. & Lean, J. L. A new, lower value of total solar irradiance: Evidence and climate significance. Geophys. Res. Lett. 38, L01706, doi:10.1029/2010GL045777 (2011).

  25. 25.

    Smith, D. M. et al. Role of volcanic and anthropogenic aerosols in the recent global surface warming slowdown. Nat. Clim. Change 6, 936–940, doi:10.1038/nclimate3058 (2016).

  26. 26.

    Schmidt, G. A., Shindell, D. T. & Tsigaridis, K. Reconciling warming trends. Nat. Geosci. 7, 1–3, doi:10.1038/ngeo2105 (2014).

  27. 27.

    Santer, B. D. et al. Identifying human influences on atmospheric temperature. Proc. Nat. Acad. Sci. 110, 26–33, doi:10.1073/pnas.1210514109 (2013a).

  28. 28.

    Imbers, J., Lopez, A., Huntingford, C. & Allen, M. R. Testing the robustness of anthropogenic climate change detection statements using different empirical models. J. Geophys. Res. 118, 3192–3199, doi:10.1002/jgrd.50296 (2013).

  29. 29.

    Summary for Policymakers. In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Solomon, S. et al. (eds.), Cambridge University Press (2007).

  30. 30.

    Hegerl, G. C. et al. Understanding and attributing climate change. In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Solomon, S. et al. (eds), Cambridge University Press, Cambridge, UK (2007).

  31. 31.

    Summary for Policymakers. 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. Stocker, T. F. et al. (eds.), Cambridge University Press (2013).

  32. 32.

    Bindoff, N. et al. 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. Stocker, T. F. et al. (eds.), Cambridge University Press (2013).

  33. 33.

    Santer, B. D. et al. Human and natural influences on the changing thermal structure of the atmosphere. Proc. Nat. Acad. Sci. 110, 17235–17240, doi:10.1073/pnas.1305332110 (2013b).

  34. 34.

    Thorne, P. W. et al. Probable causes of late twentieth century tropospheric temperature trends. Cli. Dyn. 21, 573–591, doi:10.1007/s00382-003-0353-1 (2003).

  35. 35.

    Lott, F. C. et al. Models versus radiosondes in the free atmosphere: A new detection and attribution analysis of temperature. J. Geophys. Res. 118, 2609–2619 (2013).

  36. 36.

    Gillett, N. P., Santer, B. D. & Weaver, A. J. Quantifying the influence of stratospheric cooling on satellite-derived tropospheric temperature trends. Nature 432, doi:10.1038/nature03209 (2004).

  37. 37.

    Kiehl, J. T., Caron, J. & Hack, J. J. On using global climate model simulations to assess the accuracy of MSU retrieval methods for tropospheric warming trends. J. Clim. 18, 2533–2539, doi:10.1175/JCLI3492.1 (2005).

  38. 38.

    Taylor, K. E., Stouffer, R. J. & Meehl, G. A. An overview of CMIP5 and the experiment design. Bull. Amer. Meteor. Soc. 93, 485–498, doi:10.1175/BAMS-D-11-00094.1 (2012).

Download references

Acknowledgements

We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups for producing and making available their model output. For CMIP, the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison (PCMDI) provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We thank Cheng-Zhi Zou (Center for Satellite Applications and Research, NOAA/NESDIS) for kindly providing STAR TMT data, Ivana Cvijanovic (PCMDI) for assistance with processing CMIP5 control run data, and Mike MacCracken (the Climate Institute) for helpful comments. Work by B.D.S., J.F.P., and C.B. was performed under the auspices of the U.S. Department of Energy under contract DE-AC52-07NA27344. Support was also provided by the Ellen Swallow Richards Professorship at MIT (S.S.), NASA Grant NNH12CF05C (F.J.W. and C.M.), NASA Grant NNX13AN49G (Q.F.), and NSF Grant AGS-1624881 (S.P.-C). The views, opinions, and findings contained in this report are those of the authors and should not be construed as a position, policy, or decision of the U.S. Government or the U.S. Department of Energy.

Author information

Affiliations

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

    • Benjamin D. Santer
    • , Stephen Po-Chedley
    • , Jeffrey F. Painter
    •  & Céline Bonfils
  2. Massachusetts Institute of Technology, Earth, Atmospheric, and Planetary Sciences, Cambridge, MA, 02139, USA

    • Susan Solomon
  3. Remote Sensing Systems, Santa Rosa, CA, 95401, USA

    • Frank J. Wentz
    •  & Carl Mears
  4. Dept. of Atmospheric Sciences, University of Washington, Seattle, WA, 98195, USA

    • Qiang Fu

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Contributions

B.D.S. and J.F.P. analyzed model and satellite data. F.J.W. and C.M. contributed satellite data. B.D.S., S.S., F.J.W., Q.F., S.P.-C., C.M., J.F.P., and C.B. wrote and reviewed the manuscript.

Competing Interests

The authors declare that they have no competing interests.

Corresponding author

Correspondence to Benjamin D. Santer.

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