Summary: the study estimates the land heat uptake since the start of the industrialisation period based on borehole temperature profiles and surface temperature data and compares them with the magnitude derived from climate simulations. Climate models with a shallow soil model tend to understatement the heat uptake, whereas new model versions with a deep soil model produce heat uptakes much more in agreement with observational estimates.  Another important conclusion is that the deeper soil model does not necessarily produce different surface temperature histories.

Recommendation: Although the land heat uptake is only a relatively small fraction of the heat taken up by the global ocean, this study is interesting since it points to deficiencies of soil models in Earth System Models that can be easily amended. Heat uptake can also be more relevant regionally, for instance, in eras of permafrost, where a more accurate estimation of the land-heat uptake can be critical to estimate permafrost melting in the future.

I have a few comments that the authors may want to consider, but in general terms, the manuscript can be published after some revisions.

Main point

1) I was slightly surprised by how the simulated heat uptake was calculated. The authors took an indirect detour by using the simulated surface temperature history and passing this history through a simple forward model. This forward model needs to include some assumptions about the thermal conductivity and capacity of the soil. Why not just use the simulated surface heat flux? Is there a hidden reason not to do so? 

Minor points

2) ' The land contribution ranks second with the latest observational estimates based on borehole temperature profiles, which quantify the terrestrial energy surplus to be 6 % in the last five decades, whereas studies based on state-of-the-art climate models scale it down to 2 %. '

The reader might be interested in the range of uncertainty of the observational estimates. Could those cover the model value of 2%?

3)' This approach yields values of 10.5-16.0 ZJ for 1971-2018,'

Comparing this number with the ocean heat uptake can be informative for the reader

4) 'State-of-the-art climate models estimate land contribution to be 2 %, misrepresenting observational results.'

Misrepresenting is perhaps not the right word here, as the models’ goal is not to represent the heat uptake but to simulate it.

5) 'Temperature anomalies are calculated by subtracting the temperature value at t1 from the  temperature values of the trimmed series to depart from equilibrium initial conditions.'

There is something strange in this sentence that makes it hard to understand

Summary

In this work the authors aim to quantify the energy absorbed by the land surface globally using model simulations. They start with an evaluation of sub-surface terrestrial heat storage in one model that has its lower soil thermal boundary at a conventional shallow depth and in a version where this is extended to much deeper. They use the findings from this to correctly forward model the outputs from other Earth System models with shallow bottom soil thermal depths and produce an ensemble of estimates across these.

The paper is well written, is very thorough and provides useful insights into the problem. I have only a small number of recommendations.

Main comment:

There are far too many acronyms in this text for a easy reading. For example FTP, P2k, STP, FTP, BBCP, 30ENS, GST, SAT, ST5, BTP, FM, LSM, etc.

Please consider reducing the number of acronyms in order to make this work more accessible.

Minor comments:

Abstract: The last sentence states that “This approach yields values of 10.5-16.0 ZJ for 1971-2018, slightly smaller than the latest borehole-based estimates (18.2 ZJ).”

I would be more specific and say this is 12-42% smaller than the latest borehole estimate (18.2 ZJ).

However, looking at figure 4, I can’t see where the range of 10.5-16.0 is derived from. The corrected CMIP6 models are in the range from ~0 to 25?

Figure 4: for clarity I would recommend you move the BBCP depth (m) grey arrow to outside the figure as otherwise I was at first trying to interpret it in terms of the y-axis.