# World Ocean Thermocline Weakening and Isothermal Layer Warming
## 1 Introduction  
The thermocline with a strong vertical gradient is the transition layer between the vertically quasi-uniform layer from the surface, the isothermal layer (ITL), and the deep-water layer [1, 2]. Intense turbulent mixing near the ocean surface causes formation of ITL. The thermocline resists the turbulent mixing from the ITL and limits the ITL deepening and heat exchange between the ITL and deeper layer due to its strong vertical gradient. The mean thermocline gradient (\(G\)) directly affects the ITL warming or cooling [3, 4, 5, 6].  
The oceanic climate change is represented by temporal variation of the upper layer ocean heat content (OHC), which is the integrated heat stored in the layer from the sea surface (\(z=0\)) down to a below-surface depth. Here, \(z\) is the vertical coordinate. The below-surface depth can be either a fixed depth or the ITL depth (\(h\)). With \(h\) as the below-surface depth, the upper layer OHC is called the ITL heat content (\(H_{ITL}\)). Both \(G\) and \(H_{ITL}\) are important in ocean prediction [6].  
However, the oceanographic community uses various fixed depths to define the OHC such as 0-300 m [7; 8], 0-400 m [9], 0-700 m [10; 11], 0-750 m [12], 0-2000 m [13], deep layer OHC such as below 700 m [8], and below 2000 m [14], and the full layer OHC [15]. We apologize for not citing all the work on the ocean OHC due to the huge amount of literature. Interested readers are referred to two excellent review papers [16; 17].  
Such fixed-depth OHC has three weaknesses. First, the layer with the fixed depth range includes ITL, the thermocline, and the layer below the thermocline. The effects of the thermocline gradient on ocean climate change and phytoplankton dynamics are not represented. Phytoplankton growth depends upon water temperature, light, and availability of nutrients. Nutrients are normally brought up from deep waters and into the photic zone where phytoplankton growth can occur [18]. Such nutrient pumping is affected by the thermocline gradient. Second, the fixed-depth OHC leads to the uncertainty in estimating the upper ocean warming trend. For example, the warming trend is estimated as 0.64 \(\pm\) 0.11 W m\({}^{-2}\) for OHC (0-300 m) on 1993-2008 with the significant level \(\alpha\) = 0.10 [8], 0.26 \(\pm\) 0.02 W m\({}^{-2}\) for OHC (0-300 m) on 1975-2009 [14] and 0.20 W m\({}^{-2}\) for OHC (0-700 m) on 1955-2012 [10], among others (see Table 1). Third, there is no simple relationship between the OHC with the fixed depth range and the sea surface temperature, which is the most important oceanic variable for the heat exchange between the ocean and atmosphere.  
Alternatively, we use the ITL OHC (\(H_{\textit{ITL}}\)) to overcome these three weaknesses of the traditional OHC with the fixed depth range. Recently, a global ocean synoptic thermocline gradient (\(G\)) and isothermal layer depth (\(h\)) dataset has been established from the NOAA/NCEI World Ocean Database (WOD) with each (\(G\), \(h\)) pair corresponding to particular CTD (or XBT) temperature profile in WOD [19; 20]. This synoptic dataset is at the NOAA website ([[https://www.ncei.noaa.gov/access/metadata/landing-age/bin/iso?id=gov.noaa.nodc:0173210](https://www.ncei.noaa.gov/access/metadata/landing-age/bin/iso?id=gov.noaa.nodc:0173210)]([https://www.ncei.noaa.gov/access/metadata/landing-age/bin/iso?id=gov.noaa.nodc:0173210](https://www.ncei.noaa.gov/access/metadata/landing-age/bin/iso?id=gov.noaa.nodc:0173210))) for public use. With the given ITL depth \(h\), it is easy to compute ITL heat content (\(H_{\textit{ITL}}\)). After the quality control, we have 1,111,647 (\(G\), \(H_{\textit{ITL}}\)) data pairs for the global oceans. The warming trend can be identified from the \(H_{\textit{ITL}}\) data. A new phenomenon 'thermocline weakening' was explored.