# General comments

In general, I think this manuscript makes a valuable contribution to the literature. It introduces a concept - internal drift uncertainty arising from internal climate variability within model control simulations - that is typically overlooked by authors working with climate model variables that are prone to drift (i.e. those influenced by the deep ocean). The main result - that drift uncertainty can be relatively large in comparison to forced trends in historical simulations - is important and the authors put forward a useful method (Monte Carlo Drift Correction) for quantifying/checking the size of drift uncertainty.

Some other minor results are also interesting and well worth documenting:

1. The results the authors present regarding the how the fraction of excess energy absorbed by the ocean and expansion efficiency of heat behaves in control simulations before and after drift correction also adds a little to the existing literature on energy conservation in CMIP models (Hobbs et al 2016; Irving et al 2021).

2. The authors point out that it is preferable to integrate fluxes before correcting the trend (as opposed to correcting the bias before integrating the flux) which is something other papers do (e.g. Irving et al 2019; https://doi.org/10.1029/2019GL082015) but don't necessarily explain why they make that methodological choice.

# Specific comments

The authors acknowledge in the manuscript (line 415 and elsewhere) that a limitation of their study is that they ignore branch time metadata, which could be used to reduce uncertainty by allowing for higher order polynomials to be fitted. I agree with the authors that in some cases the branch time metadata is either not available or incorrect, but more often than not branch time metadata is available/correct and where it isn't it can usually be estimated. For instance, Irving et al (2019; https://doi.org/10.1029/2019GL082015) analyse an ensemble of CMIP models and say the following: "We obtained a drift estimate by fitting a cubic polynomial to the full control time series... The time period in the control simulation that parallels the forced simulation was then identified using the branch time information provided in the file metadata, so that the correct segment of the cubic polynomial could be subtracted from the forced simulation. For models with erroneous metadata, the branch time was estimated via visual inspection of the globally integrated OHC timeseries."

I strongly encourage the authors to follow the lead of Irving et al (2019) by attempting to verify model branch times by plotting a variable such as globally integrated OHC. Since essentially all models have a fairly large drift in globally integrated OHC, if you plot the control and forced experiment time series (using branch time information to line up the respective time axes) it's usually pretty easy to see if the first value of the forced experiment does in fact branch off the control experiment at the time the metadata says it does. If it doesn't, it's usually pretty easy to approximately esimate where the branch point actually is. Following this procedure I'd be surprised if there were many models for which the branch time couldn't be verified as correct or sufficiently estimated. This would allow the authors to overcome some of the main limitations of their study.

# Technical corrections

Irving et al "2020" is quoted throughout the paper but the actual publication year of that paper is 2021: https://doi.org/10.1175/JCLI-D-20-0281.1  

The authors build on previous papers that considered model drift in coupled climate models, and in particular the potential role of internal variability in affecting drift corrections. To that end they propose a Monte Carlo method of drift estimation, and compare drift estimates using time derivative/flux vs time-integrals/state variables. The paper is quite clearly written (although I found the paragraph structure - with almost each sentence being a separate paragraph - to be quite jarring), and the figures are mostly clear. However, there are some significant technical/methodological issues that the authors will need to either address or justify before i could recommend publication. 

I have attached a marked-up PDF, but my significant comments are;

1) terminology - the authors need to be a little careful claiming that the climate models are not energy conserving, which isn't really true. There are errors in the models' energy budgets - which previous papers have termed 'leaks' - but because the models ARE energy-conserving these leaks are generally absorbed by the ocean. 

2) Method - this is my biggest issue. The authors split a model control into 150-year segments and calculate the spurious trends (ie. drift) for each segment. That's an entirely appropriate way fo looking at century0scale internal variability. However, for thier Monte Carlo method they then create a parametric Gaussian distribution of the drift, based on the statistical error of each 150-year segment. That uncertainty is then included in their estimates of uncertainty in the overall drift, since they extrapolating that 150-year estimate (with statistical error) to the full 1100-year control run. This spuriously magnifies the actual uncertainty, because the statistical error in a trend calculated from the full 1100-year series would be much less than that from a 150-year series. Almost any reasonable analysis would use the whole control run, and not a 10% subset, for drift correct.

3) Justification of Method - the use of 150-year estimates rather than the full control is not adequately justified. The only real justification that's given is related to issues with an unknown branch time in forced model experiments. That argument isn't relevent here where there's an a priori assumption that the drift is a constant, and it's also untrue that branch time is inherently unknowable, It is correct that in CMIP5 some published branch times were incorrect, but the correct ones were able to be inferred and indeed were publicly posted on the CMIP5 errata. I'm not aware of any such issue in CMIP6.

4) as a counterpoint to using time subsets, the authors could still use a Monte Carlo method of dealing with internal variability by calculating the trend across the full control run, and considering the standard error from that estimate.

5) One the authors' main conclusions is that drift estimated from time-intergrals has less uncertainty than from a time-derivative, becuase time-derivatives are inherently more noisy and so have highr standard error. This is certainly true, but since the use of subset periods spuriously elevates the uncertainty, this effect is magnified. Figures 3b and f show that there really isn't any difference when you use the entire control run (beyond that fact that one is estimated using an average, and the other using least squares optimisation).

In summary, I think the authors need to make a much clearer argument for using temporal subsets rather than the full series, and also need to consider very carefully how uncertainty from a subset should be extrapolated to the whole series.