Supplementary material to "The Weddell Gyre heat budget associated with the Warm Deep Water circulation derived from Argo Floats"

S1. Vertical boundary conditions for heat budget integralsSince we are unable to integrate for the full ocean depth (Argo floats profile the upper 2000 dbar), and most importantly, to the surface of the ocean, due to the high seasonal variability at the surface (Section 2.2), we need to decide on suitable vertical 10 boundaries for the heat budget integrals.However, if we simply select uniform depths for the vertical boundaries, we may include certain features in the TS-profile (e.g., such as the temperature minimum) in some areas of the Weddell Gyre, while excluding them in other regions.Hence, we need to ensure the upper boundary is defined such that Θmax (i.e., the core of WDW) is always fully included in the vertical layer, given that the core of WDW is the primary source of heat to the Weddell Gyre.We also need to avoid incorporating seasonally variable Surface Water and Winter Water (a surface water mass