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Increasing ocean stratification over the past half-century


Seawater generally forms stratified layers with lighter waters near the surface and denser waters at greater depth. This stable configuration acts as a barrier to water mixing that impacts the efficiency of vertical exchanges of heat, carbon, oxygen and other constituents. Previous quantification of stratification change has been limited to simple differencing of surface and 200-m depth changes and has neglected the spatial complexity of ocean density change. Here, we quantify changes in ocean stratification down to depths of 2,000 m using the squared buoyancy frequency N2 and newly available ocean temperature/salinity observations. We find that stratification globally has increased by a substantial 5.3% [5.0%, 5.8%] in recent decades (1960–2018) (the confidence interval is 5–95%); a rate of 0.90% per decade. Most of the increase (~71%) occurred in the upper 200 m of the ocean and resulted largely (>90%) from temperature changes, although salinity changes play an important role locally.

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Fig. 1: Climatological mean and long-term trends for global mean ocean density and squared buoyancy frequency (N2) over 1960–2018.
Fig. 2: Trends of N2 over depth and the percent change.
Fig. 3: Time evolution of the 0–2,000 m ocean stratification changes.
Fig. 4: Spatial patterns of the 0–2,000 m stratification (N2) trends and the contributions from temperature and salinity.

Data availability

The data are available in the following links. IAP (; NCEI (; EN4 (; Ishii (; and ORAS4 ( For SST: ERSSTv.5 (; COBE2 (; and HadSST3 ( Also, data are available from the corresponding author on reasonable request. Raw figures and data are available from and Source data are provided with this paper.

Code availability

The source codes used to make the calculations and plots in this paper are available at and from the corresponding author on request.


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This study is supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB42040402), National Key R&D Program of China (grant no. 2017YFA0603202) and Key Deployment Project of Centre for Ocean Mega-Research of Science, CAS (grant no. COMS2019Q01). The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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Authors and Affiliations



L.C. initiated and conceptualized this study and performed the subsample test. G.L. performed all the stratification analyses. All authors contributed to the figure generation, interpretation of results and the preparation of the manuscript.

Corresponding authors

Correspondence to Lijing Cheng or Jiang Zhu.

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Extended data

Extended Data Fig. 1 Climatological means and long-term linear trends of ocean temperature and salinity.

a, Climatological mean and b, linear trend of zonal mean potential temperature. c, Climatological mean and d, linear trend of zonal mean absolute salinity. The stippled areas in b and d denote the signals significant at 90% confidence level.

Extended Data Fig. 2 Temperature anomaly time series and linear trends at surface and 200 m from 1960 to 2018 based on multiple datasets.

a, Time series and b, linear trends of sea surface temperature change. c, Time series and d, linear trends of 200 m temperature change. All time series are relative to a 1981–2010 baseline. Error bar in b and d denotes the 90% confidence interval of linear trend.

Extended Data Fig. 3 Spatial patterns of linear trend in the annual SST for different datasets from the 1971 to 2010.

a is the observational mean based on three independent SST products, including ERSST, COBE2, and HadSST3, b is IAP, c is EN4, and d is NCEI data. The stippled areas in ad denote the signals significant at 90% confidence level.

Extended Data Fig. 4 Annual mean vertical resolution at depths for all in situ temperature and salinity observations within 0–2000 m from 1960 to 2018.

Annual mean vertical resolution at depths for all in situ temperature a and salinity b observations within 0–2000 m from 1960 to 2018.

Extended Data Fig. 5 A schematic of the “vertical subsample test”.

This test is used to quantify the impacts of vertical resolution in ocean profile observation and vertical interpolation methods on the gridded product (IAP gap-filling method). Temperature and salinity data are processed with the same method.

Extended Data Fig. 6 Trends and per cent changes in global mean N2 vertical sampling errors from 1960 to 2018 for three interpolation methods.

a, Linear trends of N2 bias at each depth from surface to 2000m with an interval of 20 m at upper 500 m (100 m below 500 m) (same as Fig. 2a); b is same as a but for percentages of long-term changes relative to the 1981–2010 average of global mean N2. Three interpolation methods are included: Reiniger-Ross, Spline, and Linear interpolation. The dotted lines denote the observed N2 estimates. The shadings are 90% confidence intervals from 5000 realizations.

Extended Data Fig. 7 Global 0–2000 m mean N2 vertical sampling errors (VSE) associated with different vertical interpolation methods.

a for Reiniger-Ross (RR) method, b for spline interpolation and c for linear interpolation. d, Relative error in N2 changes with three different interpolation methods based on 5000 realizations. The VSE for different T/S high-resolution climatology fields subsampled by historical observation locations are shown as dots, with the solid line and the error bar for the median and 90% confidence interval (CI), respectively. The sticks in (d) denote the [5%, 95%] CI of the linear trends based on all realizations using Monte Carlo approach. The fitted Gaussian distribution is included for comparison in (d).

Extended Data Fig. 8 Annual mean 0–2000 N2 anomaly compared with the Niño 3.4 index.

a for the Global (Glb) and Pacific (Pac) Ocean, b for Atlantic (Atl), Indian (Ind) and Southern (So) oceans. For N2 time series, a high-pass filter with cut-off frequency of 1/102 (period of 8.5 years) is applied. To gain better illustration of interannual variability, all the time series are smoothed by a 13-month running smoother17 weighted by (1, 6, 19, 42, 71, 96, 106, 96, 71, 42, 19, 6, 1)/576. The correlation between Niño 3.4 index (shading) and N2 time series (solid lines) are provided at zero lag and * sign means it is statistically significant at the 90% confidence level. Niño3.4 index is obtained from the National Oceanic and Atmospheric Administration Climate Prediction Center (NOAA/CPC) (

Extended Data Fig. 9 Results of decomposing analysis of 0–2000 m mean Ν2 change.

a, Spatial pattern of residual term (Res). b, Basin-mean linear trends of the observed change and its contributors (caused by the temperature, salinity and Res changes). The Res is calculated by the difference between the observed linear trends in N2 (see in Fig. 4a) and the sum of temperature and salinity contributions (see Fig. 4b, c). The dot and the error bar in panel (b) denote the median and 90% confidence interval, respectively.

Extended Data Fig. 10 Ensemble members of 0–2000 m mean Ν2 time series and frequency distribution of their trends.

a, 5000 realizations of global mean N2 time series and its ensemble median. b, Distribution of the estimated per cent changes of N2 from these 5000 realizations, with their ensemble median and 90% confidence interval (CI) shown in dashed red line and pink shading, respectively. The per cent changes are relative to 1981–2010 climatological N2. The fitted Gaussian distribution is included for comparison. The blue bar indicates the estimate (median and 90% CI) when only VES are taken into account in creating 5000 realizations; the green bar indicates the results when only horizonal and instrumental errors are taken into account.

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Supplementary discussion, Figs. 1–3 and Tables 1–4.

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Li, G., Cheng, L., Zhu, J. et al. Increasing ocean stratification over the past half-century. Nat. Clim. Chang. 10, 1116–1123 (2020).

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