# World Ocean Thermocline Weakening and Isothermal Layer Warming
## 2 Data  
Three open datasets were used for this study. The first one is the NOAA World Ocean Database 2018 (WOD18) conductivity, temperature, depth (CTD) and expendable bathythermograph (XBT) temperature profiles \(T(t,\textbf{r},\textbf{z})\) 1970-2017 ([[https://www.nodc.noaa.gov/OC5/WOD/pr_wod.html](https://www.nodc.noaa.gov/OC5/WOD/pr_wod.html)]([https://www.nodc.noaa.gov/OC5/WOD/pr_wod.html](https://www.nodc.noaa.gov/OC5/WOD/pr_wod.html))) [19]. \begin{table}
\begin{tabular}{l l c c} \hline \hline
**Source** & **Fixed-Depth Layer** & **Trend (W m\({}^{-2}\))** & **Duration** \\ \hline Lyman and Johnson (2014) [11] & \(H_{\text{0-100 m}}\) & 0.07 & 1956–2011 \\ Lyman and Johnson (2014) [11] & \(H_{\text{0-100 m}}\) & 0.10 & 1967–2011 \\ Lyman and Johnson (2014) [11] & \(H_{\text{0-100 m}}\) & 0.09 & 1983–2011 \\ Lyman and Johnson (2014) [11] & \(H_{\text{0-100 m}}\) & \(-\)0.04 & 2004–2011 \\ [PERSON] et al. (2010) [8] & \(H_{\text{0-300 m}}\) & 0.64 \(\pm\) 0.11 & 1993–2008 \\ Lyman and Johnson (2014) [11] & \(H_{\text{0-300 m}}\) & 0.19 & 1967–2011 \\ Lyman and Johnson (2014) [11] & \(H_{\text{0-300 m}}\) & 0.25 & 1983–2011 \\ Lyman and Johnson (2014) [11] & \(H_{\text{0-300 m}}\) & 0.10 & 2004–2011 \\ [PERSON] et al. (2013) [14] & \(H_{\text{0-300 m}}\) & 0.26 \(\pm\) 0.02 & 1975–2009 \\ [PERSON] et al. (2013) [14] & \(H_{\text{0-700 m}}\) & 0.38 \(\pm\) 0.03 & 1975–2009 \\ [PERSON] et al. (2012) [10] & \(H_{\text{0-700 m}}\) & 0.27 & 1955–2010 \\ Lyman and Johnson (2014) [11] & \(H_{\text{0-700 m}}\) & 0.43 & 1983–2011 \\ Lyman and Johnson (2014) [11] & \(H_{\text{0-700 m}}\) & 0.13 & 2004–2011 \\ [PERSON] et al. (2003) [12] & \(H_{\text{0-750 m}}\) & 0.86 \(\pm\) 0.12 & 1993–2003 \\ [PERSON] and Johnson (2014) [11] & \(H_{\text{0-1800 m}}\) & 0.29 & 2004–2011 \\ [PERSON] et al. (2012) [10] & \(H_{\text{0-2000 m}}\) & 0.39 & 1955–2010 \\ [PERSON] et al. (2019) [13] & \(H_{\text{0-2000 m}}\) & 0.30 \(\pm\) 0.6 & 1955–2017 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Several reported trends (warming rate) of fixed depth ocean heat content anomaly. Here, the Earth coordinate system is used with \(\mathbf{r}=(x,y)\) for the longitudinal and latitudinal and z in the vertical (upward positive). The second one is the 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\) gridded climatological monthly mean temperature fields \(\hat{T}_{c}(t_{c},\mathbf{r}_{c},z_{c})\) of the NOAA World Ocean Atlas 2018 (WOA18) ([[https://www.nodc.noaa.gov/OC5/woa18/](https://www.nodc.noaa.gov/OC5/woa18/)]([https://www.nodc.noaa.gov/OC5/woa18/](https://www.nodc.noaa.gov/OC5/woa18/))) [20] with \(t_{c}\) representing the month, \(\mathbf{r}_{c}\) the horizontal grid point, and \(z_{c}\) the WOA standard depth. The third one is the global ocean thermocline gradient, ITL depth, and other upper ocean parameters calculated from WOD CTD and XBT temperature profiles from 1 January1970 to 31 December 2017 (NCEI Accession 0173210) ([[https://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.nodc:0173210](https://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.nodc:0173210)]([https://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.nodc:0173210](https://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.nodc:0173210))) [21], which was established using the optimal schemes [22; 23; 24]. The third dataset contains 1,202,061 synoptic \(G(t,\mathbf{r})\) and \(h(t,\mathbf{r})\) for the world oceans [25]. Each data pair has a corresponding observed temperature profile \(T(t,\mathbf{r},\mathbf{z})\) in the first dataset. The decadal variations of statistical parameters for the global \((G,h)\) data are depicted in Table 2 (isothermal layer depth \(h\)) and Table 3 (thermocline gradient \(G\)). Both (\(h\), \(G\)) are positively skewed. The isothermal layer depth (\(h\)) monotonically increased its mean (standard deviation) from 38.8 m (41.7 m) during 1970-1980 to 67.5 m (61.7 m) during 2011-2017, and monotonically decreased skewness (kurtosis) from 3.97 (27.3) during 1970-1980 to 2.70 (15.1) during 2011-2017.