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The three‐dimensional structure of the Tropical Cyclone's baroclinic wake is synthesized as an averaged baroclinic‐dominant response of the upper ocean. The resulting persisting sea surface depression can easily be monitored using the present‐day altimeter constellation. Following a semi‐empirical framework, these baroclinic wake signatures are linked to the inner core TC dynamic and the ocean stratification. To collect these fine‐scale parameters, spaceborne SAR instruments and Argo fleet are used, to precisely capture the maximum wind region and the irregularities of the ocean vertical structure. This combination of high‐resolution information is found paramount to fully capture the modulation of sea surface height anomalies, and its mean trend, especially for major hurricanes. Baroclinic signatures mostly range around 10–20 cm and peak at 40 cm. Deeper anomalies correspond to barotropic response, removed from the present analysis. Plain Language Summary: In the wakes of Tropical Cyclones (TCs), sea surface depressions of about 10 cm appear. These TC signatures are persistent enough to be easily monitored by the current fleet of altimeter instruments. A measured sea surface height anomaly integrates and reduces the air/sea interactions during the TC passage into a single observable metric. It mostly encodes the cyclonic wind forcing and the interior ocean state. A broad constellation of remote sensing and in‐situ instruments has been gathered to compile 200 cyclonic episodes, collecting a wide range of TC sizes, intensities, and translation speeds together with oceanic conditions. A synthetic relationship is found to robustly predict most observed sea surface height anomalies. Moreover, when high‐resolution information is available to estimate the ocean interior state and the TC radius of maximum winds. Such a diagnostic thus explains the dominant baroclinic ocean response to a TC passage, and, inversely, can be used to infer ocean stratification or forcing parameters in the absence of high‐resolution observations. Key Points: Residual sea surface height anomalies from the cold wakes of Tropical Cyclones are analyzed using a multi‐modal approach at global scaleA scaling law provides a robust interpretation of the baroclinic response to given ocean stratification and forcing conditionsHigh resolution measurements are found critical to correctly anticipate the SSHA amplitudes with localized pre‐storm ocean stratification [ABSTRACT FROM AUTHOR]