General comment:

Modeling irrigation in earth system models is facing different sources of uncertainties and utilizing satellite products via data assimilation could be an effective way to constrain and improve irrigation simulation and its effects on the terrestrial water, carbon, and energy cycles. This study evaluates the irrigation simulation in Noah-MP, identifies the potential of Sentinel-1  observations in containing irrigation signals and discusses the potential of assimilating this observation into Noah-MP in improving irrigation simulation. I found the study interesting and valuable as the exploration of high-resolution remote sensing products in improving model representation of agricultural activities could be valuable in improving modeling of hydrological and carbon cycles under human regulation and in providing info for water management in the future. However, I do think there are some sections need to be improved and clarified, and further discussion is needed regarding revealing the benefits of assimilating the  observations into the model. Please see my specific comments below:

Specific comments:

1. I found the abstract a bit misleading as the study is only exploring the potential of Sentinel-1 sigma-0 observations in containing irrigation signals and providing evaluations in preparation for data assimilation instead of a data assimilation paper. For instance, it is difficult to connect WCM calibration with optimizing Noah-MP by reading only the abstract. I would suggest the authors to reorganize the second paragraph of the abstract to avoid vague statement of the scientific goal and the content of the study.
2. L 49-51: I didn’t get the logistics using “either…or…”. Are the authors trying to say one of the shortcomings of irrigation parameterization in existing studies is not specifying the source water (Ozdogan et al. 2010b, Evans and Zaitchik, 2008), and even if source water partitioning is considered in Nie et. al. (2018), it only includes groundwater irrigation, instead of dividing the source into different parts? Please clarify and rephrase.
3. Why assuming a spatially distributed parameter sets (A, B, C, D) instead of a uniform distribution? I wonder whether the authors analyze the spatial pattern of the parameter distribution and is there any obvious patterns or stratifications of the parameters relating to soil types, climate types, or anything else? Showing this would help audience understand better the meaning of those parameters and relate that to why Natural and Irrigation runs lead to different calibration performance.
4. Irrigation affects SSM and LAI, leading to different parameter distribution in WCM calibration process. However, there are mixed results when evaluating against observed SSM and LAI products. For instance, Irrigation run provides improved estimation of LAI magnitude, while degradation in LAI temporal variability. I wonder whether the authors can calibrate the WCM model using the observed SSM and LAI product, and compare the difference in parameter distribution. How does that look like and what could be the uncertainties in retrieving these parameters purely depending on Noah-MP or depending on observations? In other words, could the authors elaborate the discussion on the uncertainty of the calibrated parameters and for example quantify how capturing the LAI magnitude vs. LAI temporal variation would contribute to the calibration of WCM?
5. L349-352: I didn’t quite understand the rationale of “minimizing the impact of the irrigation signal already contained in sigma-0 observations”. Why activating irrigation can minimize this impact? And if the impact is minimized, how you can utilize the irrigation related info in data assimilation if detectable in sigma-0 observations? Please clarify.
6. The simulation is performed at 0.01 deg while part of the evaluation is conducted at field level, the area of which is much smaller than the model space. Could the authors discuss the uncertainties that might be associated with this evaluation due to the scale mismatch?
7. Figure 7 (a): could the authors elaborate a bit why simulated soil moisture can be directly compared to the  VV and VH data, and what might be the difference between the VV and VH data regarding the detection of soil moisture? What might be the reason for negative correlation between simulated SSM and  VH for both Natural and Irrigation runs?
8. L462-463: It is encouraging to see that the CR has a strong relation to the vegetation signal and could be potentially used to correct the simulated vegetation phenology. However, I was confused how exactly this calibration framework could be introduced to Noah-MP DA? Are you suggesting approximating CR to LAI and directly assimilating CR into the model? Or if you are using calibrated parameter to assimilate  into Noah-MP, how does the CR information is going to be ingested? I would suggest the authors to clarify and provide more in detail how the current study is connected to assimilating sigma-0 observations into Noah-MP as I found it is unclear throughout the text.
9. L486-491: Why a more uniform distributed C and D is more realistic? If so, why the calibrated parameters are designed to be spatially distributed?
10. What is the benefit of assimilating sigma-0 observations instead of directly assimilating LAI or SSM products? I think the authors should discuss and highlight the benefit of assimilating sigma-0 observations in both introduction section and results section.

Technical corrections:

1. L57: remove “to” after “from”.
2. L102: “focussed” -> “focused”.
3. L195: Add a space between and “observations”
4. L528 & L530: “Table 3” should be “Table 2”?

General comments:

Irrigation is the largest human intervention in the water cycle, yet it is poorly represented in the land surface (LSM) and hydrological models. One way to account for irrigation is by assimilating the observations that contain the irrigation signal, such as radar backscatter (σ⁰) or satellite soil moisture retrieval. One important step prior to the assimilation is removing biases between the model and the observation through calibration. In this study, the Noah MP model is coupled with a backscatter observation model (WCM), and Sentinel-1 σ⁰ observations were used to calibrate the model. Furthermore, The impact of activating the irrigation schemes within the Noah MP model, using different backscatter polarization (VV or VH) and cost functions in model calibration, is investigated. I found the study interesting; however, as a calibration study, I expected that the results be more focused on the calibration rather than evaluating the performance of the LSM. I also have some concerns regarding the mixed results obtained regarding the activation of the irrigation module. Please see my comments for detail:

Specific comments:

1. L175: The size of the Budrio test sites is much smaller than the model resolution (almost 1/200 of the model spatial resolution). I do not think it is a good choice for validation purposes.
2. L300-305: It is not indicated which vegetation indicator (VWC, NDVI, or LAI) is finally chosen to represent V1 and V2 in equation 2 and 3. Moreover, it is not clear whether it is assumed that V1=V2 and a unique descriptor is used for both of them or not? According to the rest of the paper, I suppose that LAI is the chosen vegetation indicator, but I think this should be explicitly mentioned here.
3. Section 2.4: As mentioned in L95, assimilating the SSM or VWC retrieval instead of MW brightness temperature or σ⁰ can be problematic due to inconsistent ancillary data used in their production, and σ⁰ is a better choice for assimilation. However, as is explained in section 2.4, assimilation of σ⁰  requires the NOAH MP model to be coupled with a WCM model to simulate σ⁰. In turn, the WCM model has many empirical parameters and simplifying assumptions such as not accounting for scattering interactions between ground and vegetation and assuming a linear relation between soil σ⁰ and the SSM that can increase the uncertainty of the estimated σ⁰. Given this, can the authors clarify why assimilating σ⁰ is a better choice relative to the assimilation of SSM and VWC?
4. L356: Another interesting comparison would be comparing the performance of a third calibration approach which is, deactivating the irrigation scheme and calibrating the model only during the non-irrigated season, with the current approach (activating the irrigation scheme and calibrating for the entire period) during the non-irrigated season. This would also be an interesting comparison for the future study in which σ⁰  will be assimilated to see whether calibrating during the irrigation season with the activated irrigation module is beneficial for the ultimate goal of irrigation quantification or not.
5. L405-416: I am not convinced that the improvement in the simulation of SSM by Noah MP is due to the activation of the irrigation module for two reasons:

• In most of the previous studies, it is shown that coarse-scale MW products are not able to detect irrigation signals at the plot scale (e.g., Brocca et al., 2019, Zaussinger et al., 2018, Dari et al., 2020) unless there is intensive flood irrigation over a large area such as California central valley in which fields are flooded, and the water level is sustained throughout the irrigation season (Lawston et al., 2017). Moreover, to have a fair comparison, other metrics such as RMSE or bias should also be reported alongside the Pearson correlation (R).
• The deterioration in LAI simulation when irrigation is activated makes more sense to me as the spatial resolution of the Proba-V LAI product is 1km, and the possibility of detecting the irrigation signal is higher relative to the coarse-scale SSM products.

        Please comment on this.

6.  L435-446: I think the part of this significant difference between simulated and observed irrigation and missing the irrigation events is related to the spatial mismatch between the model and the test site, as it is mentioned in the first comment. Please comment on this.