I really like this paper.  The authors focus on something that is known but perhaps not as widely appreciated as it could be – observations have errors, and imposing tight constraints on models assuming the observations are “truth” is not appropriate.  I particularly like how the authors have essentially automated this process in a software package.  This is a valuable tool for computing observational constraints.  I particularly appreciate the authors’ careful treatment of statistics, for example Figure 2 and the surrounding discussion.

My perspective is that of someone who is quite familiar with CMIP6, but I will admit that I am not well qualified to provide an in-depth review of the formulas and equations provided.  They seem to be reasonable based on my knowledge of how t-distributions work, but my hope is that these are covered more in depth by another reviewer who spends a lot more time thinking about such things.

My biggest issue with this paper is stated on line 74 and then used throughout the rest of the paper, namely that the assumed underlying distribution of the projected variable is random.  This is not always true (as the authors know), and for some important cases it is demonstrably false.  One example is the hot bias of some of the CMIP6 models that received quite a bit of attention recently.  Another is that this tool is essentially not usable for precipitation, which is known to (more or less) have an extreme value distribution.  I realize that modifying this tool so that one can specify prior distributions rather than assume them would be far too much work for the scope of this paper.  But I would like to see two things in the paper that address this comment:  1)  An acknowledgment of this point and appropriate caveats in the paper, particularly in Section 2.  Line 457 is the only place I saw this explicitly mentioned, and that makes it seem kind of buried.  2)  A brief discussion as to either how one could specify prior distributions (and the information needed) or an express acknowledgment of the limitations of this tool.  There is a hint of this on lines 450-452, but I don’t think that’s sufficient.

I would also appreciate a bit more description of the software aspects of this tool.  For example, what language it’s written in, package dependencies, a clear description of inputs/outputs, etc.  In one example, as I was reading Section 2 (around line 85), I was wondering if alpha is user-specifiable.  Those sorts of things would be good to know.  I did look at the python notebook available, but the readme is rather terse, and the code could be better commented, so it was difficult to discern some of these answers on my own.

My final major comment is that I would like to see a specific example to illustrate the package.  The author does provide synthetic examples (e.g., Figure 8), but I think it would be more powerful and interesting if the authors recompute an example from the literature, showing that previous studies have flaws that are significant enough to warrant revisiting.

Other than that, my only comments are that there are a few typos or improper tense issues that the copyediting office can likely take care of.

The manuscript presents ClimLoco1.0, a statistical model aimed at providing confidence intervals for climate variables using a multivariate linear observational constraint approach. This work is a commendable effort to address the pressing challenge of reducing uncertainty in climate projections. By extending traditional emergent constraint methods to a multivariate framework, the authors offer an innovative tool that leverages multiple observational constraints to enhance the reliability of future climate predictions. The manuscript demonstrates a robust statistical foundation, with detailed derivations of confidence and prediction intervals, making it a valuable contribution to the field.

The strengths of the manuscript include its innovative methodology, relevance to current climate science challenges, and rigorous statistical approach. The use of multivariate regression to constrain climate variables such as equilibrium climate sensitivity (ECS) or gross primary production (GPP) aligns well with the growing need for more sophisticated tools to handle complex climate data. However, the manuscript could benefit from greater clarity in its assumptions, more practical examples, and a thorough discussion of validation and limitations. While the theoretical framework is sound, its accessibility and applicability could be enhanced to broaden its impact within the climate science community. Therefore, I recommend a ‘minor revision’ of this manuscript and let the authors revise the manuscript accordingly to strengthen its scientific rigor and utility for the meteorology community.

Specific comments:

 1. The authors should clarify assumptions and their implications. The manuscript relies on key assumptions, such as linearity between climate variables and Gaussian error distributions (Page 27-28). These assumptions are critical but may not always hold in climate systems, which often exhibit non-linear dynamics (e.g., feedback loops) or non-Gaussian distributions (e.g., extreme events). The authors should add a dedicated subsection in the methods or discussion section to explicitly list these assumptions and discuss their implications. For instance, address how non-linear relationships or heavy-tailed distributions might affect the confidence intervals and suggest potential extensions (non-linear regression) for future work. This will improve transparency and help readers assess the model’s applicability to diverse climate scenarios.

2. The authors need to provide a detailed case study. The manuscript mentions potential applications but lacks a concrete example demonstrating ClimLoco1.0’s implementation. Include a section applying the model to a specific climate variable, such as global mean temperature or precipitation, using real observational data. Present the observational constraints, derived confidence intervals, and a comparison with traditional univariate methods. This would illustrate the model’s practical utility, making it more compelling and easier for potential readers to replicate or adapt.

3. The authors should expand on model validation. While the manuscript provides theoretical derivations in Page 27-29, it does not discuss how ClimLoco1.0’s performance was validated against real-world data or existing methods. It would be better to add a validation section that evaluates the model’s performance, potentially using cross-validation or comparison with established emergent constraint approaches, including metrics like coverage probability or uncertainty reduction to quantify improvements. This would strengthen the manuscript’s credibility and provide evidence of the model’s effectiveness, addressing a key expectation in scientific reviews.

4. The authors should add a discussion to discuss potential biases and uncertainties. The model’s reliance on covariance matrices (in Page26) and observational constraints introduces potential biases, such as errors in covariance estimation or constraint selection, which are not addressed. The authors should include a discussion on sources of uncertainty (e.g., noisy observations in Page 28) and biases, and conduct a sensitivity analysis to show how these factors affect the confidence intervals and suggest mitigation strategies (e.g., robust estimation). Acknowledging and addressing these issues will enhance the model’s robustness and guide users in its application. Also, the authors need to add a subsection in the discussion comparing ClimLoco1.0’s methodology and performance to existing multivariate emergent constraint approaches. Highlight unique features, such as its handling of noisy observations (page 28), and discuss trade-offs.

5. Enhance accessibility for broader readers. The manuscript’s statistical derivations (Page 26-29) are rigorous but may be inaccessible to climate scientists if someone without a strong statistical background. The authors need to include a brief primer or appendix explaining key concepts (e.g., multivariate regression, confidence vs. prediction intervals) in simpler terms. In addition, using visual aids, such as a flowchart of the ClimLoco1.0 workflow, to complement the equations. This will broaden the impact of this study, making the model more usable by meteorologists and policymakers who may not be statisticians.