Review of Observed multi-decadal trends in subsurface temperature adjacent to the East Australian Current by Hamming et al. 

The present work investigates the depth-structure of multi-decadal ocean warming along the southeastern Australian shelf and assesses how these rates have changed over time. The authors employ several trend detection methods to two long-term in-situ temperature (T) time series, and three shorter-term T time series, that sit inshore of a global “hotspot” for long-term ocean warming along the East Australian Current (EAC).

Whilst previous work has investigated surface T trends inshore of the EAC, this new work investigates the subsurface T trends over the inner- to mid-continental shelf, and here it makes a nice contributrion. I was not previously familiar with the EMMD method, and the authors also provide a great recipe for others to employ the technique, with a particularly thorough methodology section. In these respects, the work is likely to be of broad interest to the oceanographic community.

Overall, the manuscript is of high quality, is well-written and does not have any structural problems. An aspect that I struggle with, however, is the acceleration of warming that the authors refer to throughout. In particular, I question whether there is sufficient statistical support for an acceleration of warming trends, given what seem to be quite large uncertainties in these trends. Revision of the manuscript, focusing on the acceleration aspect(s), is therefore recommended before the work is considered for publication. The issues that need to be clarified by the authors are given below.  

Major 

1. Section 3.2 presents decadal temperature trends computed from the in-situ T timeseries. The methods used to assess the uncertainties and statistical significance of the trends, calculated from EEMD (L380-402) and TSSE (L122-129), seem appropriate. Multiple reference is also made in this section to finding accelerating warming trends using EMMD (e.g. L156-157, L159, L160-161), and again later in Section 4 (e.g. L215, 243).  

The inference that warming is accelerating seems to be (?) based on the magnitude of decadal trends, given in Figure 4, getting larger when computed for more recent decades. However, I struggle to see what statistical evidence there is for acceleration, since you’ve not explicitly tested for a change in the rate of warming. 

At the very least, uncertainties are needed on the EEMD decadal trends shown in Figure 4, and some evaluation of these is needed so that the reader can understand whether the trend magnitude during one period (e.g. 2010s) is statistically distinguishable from that during another (e.g. 1950s). After all, you go on to state that there is “high uncertainty” that the warming rate at 2 m at Port Hacking and Maria Island has accelerated over time (L215), but it’s not particularly clear to the reader how large these uncertainties are, or how you’ve reached that conclusion. I note that an uncertainty as large as 0.5 °C decade-1 is given later (L263) for the EMMD trends. Can acceleration of warming between decades actually be distinguished from these in-situ T timeseries, given such large uncertainties in the warming trends themselves? 

Minor 

2. L145-147. I think (?) you mean that the decadal trend is estimated by taking “…the mean of the first order temporal monthly derivative of the EMMD R(t) for each decade…”, rather than “…the mean of the first order temporal monthly derivative of the EMMD temperature trend for each decade…”. 

3. L152. It’s really hard to see the white dashed lines in Figure 3. 

4. L160-161. Can you please clarify how you are “detecting” acceleration here? Presumably based on the trend magnitude increasing between decades? This sentence also implies that the acceleration is not statistically significant until the 1990s, but it’s unclear in the manuscript what method you are using to assess this? 

5. L247. I’m not sure that Shears and Bowen (2017) “emphasize acceleration”. The decadal trends at Maria Island they present during 1982-2016 are larger than between 1946-2016, but the uncertainties on these trends are large and they overlap with one another. Therefore, it's questionable whether any acceleration is present and/or statistically supported. 

6. L355-364. Based on the text in Appendix B, I was confused as to how you extract a final value (e.g. °C decade-1) for the “monotonic trend” of x(t) using EMMD. I think this information is given in the main text on L145-147: it is the mean of the first order temporal monthly derivative of R(t). Please clarify how you end up with trends in °C decade-1 in Appendix B.