Review of “A Systematic Atmospheric Parameter Optimization method to Improve ENSO Simulation in the ICON XPP Earth System Model” by Yu et al.

General comments:

This study presented a linear optimization methodology to improve ENSO fidelity in the ICON XPP Earth System Model. The authors firstly assessed the sensitivity of ENSO metrics to 21 atmospheric parameters in atmosphere-only simulations. Then, six parameters were identified as most impactful and were subsequently tuned in fully coupled simulations, yielding moderate improvements in various ENSO metrics. Overall, the results demonstrated that the newly proposed method can effectively optimize key atmospheric parameters to improve representation of critical ENSO characteristics and feedback processes fidelity within a climate model. However, some aspects related to the optimization methodology should be improved before the paper is suitable for publication.

Major comments:

1. As stated by the authors, one of the novelties of this work is that they provided a newly proposed optimization method. However, the motivation to develop such a new method is unclear to me. Many previous studies focusing on parametric sensitivity or parameter calibration have been conducted in the past two decades. The limitations of the methodologies in previous studies and the advantage of the new method provided here (e.g., linear vs nonlinear; direct tuning vs using surrogate model) should be discussed in more detail.
2. For both atmosphere-only and fully coupled experiments, the cost functions are rescaled by the parameter setting in the control runs. This helps prevent the optimized parameter values from deviating excessively from their control-run settings, thereby ensuring physical plausibility (Line 408). However, the default settings are different in the atmosphere-only and in the fully coupled experiments. One may ask which setting has more physical plausibility?
3. In section 3.4, the ENSO metric is estimated by using Eq. 11, which is based on the pre-calculated parameter sensitivities. However, the lefthand side of Eq. 11 (i.e., delta_m) is expressed as a quadratic function of a physical variable which measures the difference between simulation and observation (according to Line 386), while the righthand side of Eq. 11 is just a linear function with no observation information included (according to Line 323). So it is unclear to me what are the physical meaning and theoretical basis of Eq. 11?

Other comments:

1. Line 267 (i.e., Eq. 3), phi_l or phi_i? Same question for Line 276.
2. Line 352, “the correlation between the pair of sensitivities is shown in the heading of each panel”. It seems it is not given in the figure.
3. Line 372, left X-axis, RMSE?
4. Line 402 (i.e., Eq. 9), np_i or np_k?
5. Line 409, the constraint term delta_limit ensures that parameters remain within physically meaningful bounds. Do the authors mean some values of parameters are out of the prescribed bounds? How does the sampling algorithm work when searching the parameter space?
6. Line 695, the use of the word “although” is a bit strange.

This manuscript presents a linear sensitivity–based optimization approach combined with the Nelder–Mead algorithm to improve ENSO simulation in the ICON XPP Earth System Model. The authors conduct a two-stage tuning: first in atmosphere-only mode (21 parameters) and then in fully coupled mode (6 selected parameters), using the CLIVAR ENSO Metrics Package for evaluation. The atmosphere-only optimization achieves roughly 30% reduction in the cost function; the coupled optimization yields improvements in ENSO amplitude, cold tongue bias, phase-locking, and some feedbacks, comparable in magnitude to gains from doubling resolution. The manuscript frankly discusses the unintended global mean warming induced by ENSO-only tuning and its correction via turbulence parameters, and recommends including global constraints (e.g. GMT, AMOC) in future multi-objective optimization.

The methodology is clearly structured, the two-stage design is well justified, and the comparison with CMIP6 and high-resolution ICON XPP is useful. Overall, I recommend MINOR revision: address the points below so that the manuscript is fully consistent and reproducible.

1. The manuscript contains MANYbasic errors in equation/figure cross-references, spelling, grammar, and section numbering that collectively impair readability and raise concerns about the thoroughness of internal review. The authors are strongly urged to conduct a systematic, end-to-end proofread before resubmission. A non-exhaustive list is given below:
   1. Incorrect equation references: The cost function is defined in Section 3.3 as eq. [6], with Δmetric and Δpara given by eq. [7] and [8]. However, in Section 4.1 and 4.2 the text refers to “eq. 3”, and “eq. 4”.
   2. Missing section heading: Section 5 has subsections 5.1～4 but no parent heading (e.g. “5 Results for fully coupled experiments”) before 5.1.The authors should add a main Section 5 parent heading before 5.1 so that the section hierarchy is consistent and readers can locate the start of the coupled results.
   3. Incorrect figure references: The text (Line 309~310) “By design, the composite RMSE of the control simulation equals 1.0 (Fig. 2b)” refers to Fig. 3b.
   4. Incorrect maplabels: The “180°E” label in Figure 7 is incorrect, it should be labeled as “0°”. In addition, I recommend that the author use the longitude range label 0~360°E here to ensure consistency with the coordinates in other figures and the descriptions in the text.
   5. Spelling errors:
      1. "LIoyd" → "Lloyd" (Line 67 and 95). According to the reference list, the second letter should be a lowercase “l”, not an uppercase “I”.
      2. "fileds" → "fields" (Line 131).

• "regirded" → "regridded" (Line 134).

1. "metrices" → "metrics" (Line 189, 190, 192. The correct plural of "metric" is "metrics").

1. Inconsistent parameter names: Section 3.3 writes "tune_entrog"; Table 1 uses "tune_entrorg".

1. For data grid resolution, Section 2.1 states that the model data and observational data are regridded to the same 1°x1° global grids, while Section 2.2 specifies that the model runs at 160 km atmosphere (~1.4°) and 40 km ocean (~0.36°). This creates confusion. (1) What are the native grid resolutions of each observational dataset and of the ICON model output, respectively? (2) What regridding/interpolation method was used to bring all data onto the 1°×1° grid. (3) Could interpolating the 160 km atmosphere (~1.4°) to a finer 1° grid introduce artificial smoothness in local metrics such as the meridional precipitation structure? (4) Could coarsening the 40 km ocean output to 1° obscure sub-degree small-scale ocean features (e.g. tropical instability waves, sharp SST fronts) that may be relevant to some ENSO feedbacks?
2. For experiment period range, Section 2.1 states that the period for all observational reference data is 1980~2018, while Section 2.3 indicates that the AO experiments cover 1979~1997. The first year of the AO experiments (1979) has no corresponding observational reference. (1) When calculating ENSO metrics, is the AO model output compared with observations using only the 17 years from 1980~1997, or the full 19 years? If the latter, what is the source of observations for 1979? (2) The AO experiments do not cover the 1998~2018 period, which includes several strong ENSO events, does this affect the representativeness of the sensitivity estimates?
3. In Table 1, multiple optimized values fall outside the stated ranges. Eq. [10] and the accompanying text imply that parameter combinations violating physical bounds are penalized and discarded, yet many parameters exceed the stated ranges.
4. [11] approximates the metric bias δm by a linear combination of parameter sensitivities and is central to the computational efficiency of the scheme. However, ENSO is a complex air-sea coupled system with highly nonlinear characteristics. (1) Why is it reasonable to use a linear superposition approximation in such a complex nonlinear system? It seems to lack a physical or dynamical explanation for this basic assumption. (2) Over what range of parameter changes is this approximation expected to hold? (3) What is the impact of neglecting nonlinear and cross-parameter terms (interaction terms) on the optimization results?
5. The “RMS threshold of 0.2” is used to select parameters with “significant” impact on ENSO metrics. The text states it corresponds to roughly 20% of the control-run bias amplitude. (1) Was this value chosen from a break in the sensitivity distribution or from a signal-to-noise criterion? (2) Has this empirical threshold been used in previous studies?
6. The six parameters carried into the FC optimization were selected based on their AO sensitivity ranking. Giventhat AO and FC sensitivities differ substantially in both magnitude and sign, the AO ranking may not reliably reflect parameter importance in the coupled system. (1) Could parameters with weak AO sensitivities nonetheless have significant impacts in the coupled configuration? (2) What are the potential consequences of this selection strategy for the final coupled optimization?
7. The Nelder-Mead method can converge to local minima. Was the optimization run from a single initial point or from multiple starting points?