Thank you for your input and constructive comments on the manuscript. We agree to adapt the title of the article by including the recommendation. Lines 177-179 will be modified using the geostrophic velocity instead of the proposed pressure gradient to match the quantities introduced in the paper. A new figure containing the vertical profile of the geostrophic velocity anomalies and of the streamfunctions will be added to the document to help the reader understand the link between Figure 2 and the diagnostic expressed in Figure 1. We agree to split section 3.1 into two subsections to aid readability. Line 271 will be changed according to the mistake that you pointed out. We plan to drop Figure 5 as it does not add much valuable information to the text. However, since this oscillation results in substantial fluctuations in the diagnostic of thermal wind, we think that the brief examination can help some readers. Nevertheless, we will revisit and condense this paragraph at least to match the drop of Figure 5. Figures 4a and b contain only 2 hysteresis simulations each: one dotted and one solid. The ‘additional’ lines correspond to the return path of these simulations when the forcing is inverted. We will indeed add Figures A1 and A2 to the main text. For the final remark, we will provide a diagnostic of the different components of the circulation and discuss them appropriately. 

We are happy you enjoyed the reading.