This work presents a surrogate-assisted framework for calibrating runoff relevant parameters in global-scale Earth System Models (ESMs). The large computation burden arisen from repeated simulations in calibration is alleviated by building fast-to-run PCE-based surrogate models of ESMs. It is concluded that the calibrated model obtains an improved performance compared to the one with default parameter values. In summary, the manuscript is generally well-written and may be eventually accepted after addressing the following comments:

-The title should be revised. In my opinion, uncertain quantification is different from calibration. How can one use a UQ framework to calibrate models? How about “Using a surrogate-assisted Bayesian framework to ...”?

-In table 1, the prior for q_{drai,max} is U(1e-6,1e-1). Why not use a logarithmic transformation for it? Otherwise, much more prior samples will be drawn from, e.g., (1e-2, 1e-1).

-Line 193 and Eq. (17), the authors should clearly present how they determine the values of sigma.

-In section 3.3, which criterion (e.g., the Gelman-Rubin R statistic [Gelman et al., 1995]) is used here to check the convergence of MCMC sampling? From Fig. 6 it can be seen that the posterior ranges are still relatively large, which gives the feeling that the MCMC chain has not totally converged.

-In section 5.2, the poor performance of PCE surrogate models in arid regions probably because of PCE’s inability to approximate highly nonlinear functions (a well-known limitation of PCE) or/and the low signal-to-noise ratio in these regions. The authors should elaborate these to provide more informative results to readers. An alternative surrogate method for approximating highly nonlinear function is the deep neural networks.

-In Figs. 10a and 11, the simulated runoff time series with default parameter values could be even closer to the reference GRUN time series than the calibrated ones, giving the feeling that the calibration is not that satisfactory. Please further explain.

-Line 533, ‘are estimated’, Line 534, ‘are run’?

The manuscript performed a per-grid calibration of the E3SM ELM model against a global monthly runoff dataset. The calibration was enabled by developing surrogate models for each grid of the ELM using Polynomial Chaos Expansion to mimic the response surface, which was chosen to be the root mean square error of monthly runoff for each grid. Subsequent analyses examined the spatial distribution of calibrated parameters with higher sensitivity and parametric uncertainty effects on simulated runoff. The paper is well organized, clearly written, and deals with an important topic of calibrating ELM and similar models. However, I have some concerns regarding the accuracy of surrogate and its effect on calibration, as detailed below.

• Line 15: “The main methodological advance in this work is the construction of surrogates for the error metric between the ELM and the benchmark data”. But this is not entirely new as using surrogate in this manner has been done previously, e.g. Wang et al. (2014); Razavi et al. (2012) and references therein.
• Line 111: what’s the difference between surface runoff and surface water runoff?

• Line 195 - to reduce the log likelihood to least-squares regression, further assumption is needed, which might include constant and known sigma. Please verify.

• Line 197 - I am not sure whether 1,000 samples are sufficient for burn-in, since MCMC often requires a large number (e.g., tens of thousands) of samples to converge. Including some convergence check statistics or plots in supplementary material would be helpful. Also, what is the MCMC algorithm being used here? Please include a reference for reproducibility. 

• Fig. 1& 2 - there’s some discrepancy between RMSE given by the surrogate and by ELM. Studies have shown that even small surrogate error can lead to large deviation of the inferred parameter posterior from the “true” posterior (Laloy and Jacques, 2019). I realize that it is not possible to calibrate ELM at global scale, but it seems possible to perform some quick test to validate the surrogate modeling approach. For example: for a few grids compare the posterior obtained using PCE and using ELM; In Section 3.5, step #4, compare the RMSE of ELM simulation with that of PCE. 
• Line 355: If I understand correctly, 10,000 is the number of runs of the surrogate. It is not necessarily the case if ELM is run, because the convergence rate may be different given the surrogate error (Razavi et al., 2012).

• Fig. 11 - it seems that the same period of 1997-2010 is used to calibrate the model and validate the optimal parameters. Is data available after 2010 for validation, so that validation data is independent from calibration data? 

• Some paragraphs are indented, some are not. 

References

Laloy, E., & Jacques, D. (2019). Emulation of CPU-demanding reactive transport models: a comparison of Gaussian processes, polynomial chaos expansion, and deep neural networks. Computational Geosciences, 23(5), 1193-1215.

Wang, C., Duan, Q., Gong, W., Ye, A., Di, Z., & Miao, C. (2014). An evaluation of adaptive surrogate modeling based optimization with two benchmark problems. Environmental Modelling & Software, 60, 167-179.