I have now finished reviewing the work by Mingo et al. The authors have combined Replica-Exchange Hamiltonian Monte Carlo (HMC) with Thermodynamic Integration in order to do Bayesian inference for the parameters of a conceptual hydrologic model, while simultaneously they compute the marginal likelihood of the model; the latter, facilitates model inter-comparison via the Bayes Factor (BF). In general, the manuscript is well written and has novelty in the sense that the proposed algorithm has never been applied before to hydrological modeling. As a result, I am overall positive! However, I think the manuscript would benefit from a more in-depth discussion (possibly toward the end of the article) about the scientific problem that the authors address, the limitations, and what are some possible alternatives. 

In light of the extensive comments (major and editorial) of Reviewer #1 with which I completely agree, I would like to raise some concerns about the usefulness of BF as a hydrologic model inter-comparison metric. Please see my comments below:

1. For the synthetic experiments, Tables 4 and 5 show that both DIC and WAIC could correctly indicate the data-generating model, i.e., M2 and M3, respectively. For the average reader, this might practically mean that we do not need BF as an additional metric to "tell" us which model to choose. Please provide an explanation to show why employing BF matters. If you cannot demonstrate that the BF can capture the true underlying model while the other, simpler metrics, cannot, then it is hard to justify your analysis. 

2. Although I am not a Hydrologist myself, I have a hard time understanding the usefulness of BF within the context of hydrologic model comparison. Traditional hydrologists calibrate models using algorithms like Shuffled Complex Evolution (SCE) based on optimization of a deterministic metric, e.g., NSE. I do understand that Bayesian inference of hydrologic model parameters, on the other hand, is appealing because it naturally provides a measure of uncertainty, which is always important. But the BF provides no pragmatic information to the modeler as per which model is performing better. For example, one would still have to compute NSE or KGE for all models M2, M3, and M4 for the real-world data (Table 8) to get an idea of what's happening. On the contrary, I would argue that for conceptual hydrologic models, which are not  computationally demanding and time-intensive, likelihood-free methods like Approximate Bayesian Computing (ABC) might be more suitable for model comparison, as the posterior distributions of parameters for different models are obtained on the basis of an actually useful (to the modeler) distance metric, e.g., NSE, KGE, or even a metric tailored only to river discharge peaks!!!

Again, I am positive about your article and I believe it should be considered for publication, but please provide a better discussion about the practical use of BF as a hydrologic model comparison metric...