This manuscript introduces the development and application of a novel LCDA system that utilizes the 4DEnVar method in E3SMv2. Through the assimilation of monthly mean soil moisture and temperature data from a global land reanalysis product, this LCDA system effectively improves the simulation of land-related variables in E3SMv2 and the temporal evolution of the 2012 U.S. Midwest drought. This work not only contributes to understanding the sources of climate predictability provided by land, but also provides the groundwork for future predictive modeling efforts using E3SM. Given the comprehensive and well-described analysis presented in this paper, I believe this manuscript is well-suited for publication in GMD. I am pleased to recommend acceptance.

Although I am favorably impressed by this study, to further improve this paper, I’d like to add additional comments/suggestions below:

(1) Abstract: Please specify the reanalysis data you assimilate and improvements of soil moisture and temperature simulations.

(2) Sub-section 2.2: GLDAS dataset cannot actually be classified as a “observation dataset” since it is generally based on land surface models. Besides, soil moisture derived from different land surface models are systematically different (e.g., different soil moisture range and long-term mean value) which may introduce additional bias into the coupled data assimilation system. How do you handle this problem?

(3) Eq. (5): How to represent the cost function? Please add a string or symbol.

(4) Figure 3: How do you explain the temporal dynamics (maybe some seasonal cycles) of the cost function?

(5) Figure 4: The explanations summarized in sub-section 3.2 are inadequately for demonstrating soil moisture degradation over many regions after the coupled data assimilation. It is suspiciously for me that Figure 4a, i and j show similar degradation spatial patterns while Figure 4b-h perform differently. If these degradations are related to GLDAS data quality, the off-line data assimilation results should be degraded over similar regions. I think more interpretations or experiments are necessary to figure out these issues.

(6) I suggest adding a discussion section and focusing on the preconditions or theory basis for applying coupled data assimilation. For examples, if the land-atmosphere relationship is poorly represented, the improved land surface states may incorrectly influence the atmospheric process; for humid regions, the evaporative regime is typically energy-limited and the assimilation of soil moisture has very limited benefit while soil temperature may more effective. Vice versa for arid regions…

This paper presents experiments assimilating soil moisture and soil temperature from the GLDAS modeling system into the E3SM model using 4DEnVar. The use of Hybrid DA method for the land DA is unusual, and is an interesting development that I am curious to see more work on. Unfortunately, the experimental design is badly flawed, and the information presented in the paper is vague, out-dated, very often incorrect, and difficult to follow.

MAJOR COMMENTS:

1. This work is assimilating model output soil moisture and soil temperature into a different model, with no accounting for the systematic differences between the two models. Data assimilation is not typically applied to assimilate fields from one model into another (unless conducting a synthetic twin experiment to test aspects of the DA, which is not how this is presented). There is also extensive literature discussing the fact that soil moisture cannot be transferred from one model to another without rescaling it, which makes the approach here invalid. For example see:

RD Koster, Z Guo, R Yang, PA Dirmeyer, K Mitchell, MJ Puma, On the nature of soil moisture in land surface models, Journal of Climate 22 (16), 4322-4335

And many references in that paper.

Additionally, the assimilated fields are monthly means, which is not the obvious choice, and this is not adequately discussed.

To be publishable, the authors would need to assimilate actual observations, not model output, and would need to apply adequate bias correction / rescaling to those observations (particularly to soil moisture - see work by Rolf Reichle, Randy Koster, etc).

2. The background information presented in the introduction demonstrates very little understanding of the standard methods used in land DA and coupled land/atmosphere DA, and presents a picture of modern data assimilation practices that is incorrect. Much of the introduction is also rather vague - with references to coupled and uncoupled systems that are unclear.  I recommend completely re-writing the introduction by first identifying the modeling system that you are working with (land /atmosphere?), and introducing examples related to that system. Then, then make sure it is always clear what you are referring to when referencing a coupled model or coupled DA system (with a clear distinction between coupling in the model and coupling in the DA). 

Of greatest concern, the method is presented as ‘coupled data assimilation’ but the experiments assimilate land “observations” into only the land component of their model  (a coupled land/atmosphere model)  - this is not coupled DA! In general, the paper seems confused between coupled modeling, and coupled DA. There’s also no mention of weakly or strongly coupled DA, which is very relevant.

Specific comments (I’ve provided these only up to the end of the methods, since the experimental design will need to be completely redone to be publishable)

Paragraph starting L37. I had a lot of trouble following the argument in this paragraph, largely because the terms used have not been defined (and I suspect are not being applied in their standard usage). The distinction between coupling in the model and in the DA is unclear, and I really don’t know what the “uncoupled” option is. Perhaps using an explanatory example might help.

L38: I’m not sure what is meant by “uncoupled initialization” here or “uncoupled data assimilation”. I suspect you mean weakly coupled data assimilation (as in separate DA systems for each model component, each assimilating obs from that component) - which is still coupled DA.

L39: what is a “stand-alone” model state?

L40: I assume the Prodhomme paper refers to a hydrological system, so it’s a bit misleading to say “some modeling centers …” and then refer to a single product that is not their main product.

L41: again, I don’t know what you mean by “uncoupled methods”. If you’re applying DA to multiple model components in a coupled model, there is some coupling introduced via the model forecasts - at a minimum, this is weakly coupled DA.

L44 “each coupled model individually”. Do you mean each component of the coupled model?

L50: Again, without concrete examples it is hard to follow the argument in the paragraph. I am unclear what the actual application being discussed is, since the text just refers to “modeling centers” or “models”. The references come largely from atmospheric DA, with some coupled atmosphere / other component examples. If this is the case, then the information presented is this paragraph about the usage of different methods is  largely incorrect and very outdated.

L52: Here you are talking about the method used to add the analysis increment to the model states, which is a secondary detail to how the increment is calculated - the discussion is very misleading. For example, the Bloom paper you cite is from NASA GMAO. They currently use 4DEnVar to calculate the increment, and IAU to add it.

You may also be mixing up the “nudging” DA method with nudging methods to add increments. If so, nudging is also a very old DA technique, and has not been standard use for decades.

L54: IAU (and nudging schemes I know of )  do not “recover the observations”. They move the model towards the observations, by some amount determined by the respective observation and background errors.

L59: The information presented here is very outdated. Major NWP / reanalysis all use hybrid DA methods now - 3Dvar was two generations of DA schemes ago. I’m not familiar with the Yao paper, but the Lin paper was conducted at a university, not a “modeling center”.  Likewise the Santonello paper - that’s a research paper, not linked to an operational DA system.

L71: This sentence is wrong (or at least, extremely misleading). If we’re talking about Earth system modeling - so NWP, reanalysis, etc (which the references imply is what we’re talking about) then most centers did use 4DVar, but have now moved on to more sophisticated hybrid methods.

L121: how many soil layers?

L123:  GLDAS does not produce observations! These are modeled output.

Section 2.3

There is not enough information here on the 4DEnVar / DRP-4Dvar technique for the reader to understand how it works.

Also, how is the ensemble created? How do you ensure the ensemble has reasonable spread near the land? How do you estimate the B matrix?

L152: This paragraph implies that there is no atmospheric DA in these experiments? In which case this is not coupled DA. It is land data assimilation into a coupled model.

L157 it’s not clear what “freely coupled” means. Which components are coupled? Likewise “externally forced”, which components are externally forcing used for?

L187:Some discussion here of how you updated the model states from monthly means would have been useful, as this is not straight forward. There has been a lot of work done on this within the context of assimilation GRACE terrestrial water storage.

Also, assimilating monthly means to update instantaneous states is not the obvious way to do it - given that you’re assimilating model output, you had the option of assimilation instantaneous output.

This manuscript presents the implementation of a 4DEnVAR method in the E3SMv2. The authors assimilate monthly mean soil moisture and temperature from a land re-analysis product and evaluate the performance of the new data assimilation system vs a control experiment (no assimilation). 

I find the approach of 4DEnVAR for land data assimilation very interesting. However, there are several shortcomings of the paper that need to be addressed before it is ready to be published in GMD. I recommend the following changes:

Major revisions:

1. The authors need to differentiate between coupled data assimilation and coupled modelling, the study is presented as “land coupled data assimilation” however it is land data assimilation only. Please consider to re-write parts of the introduction to make this clear. 
2. As pointed out by Referee #2, the authors assimilate model derived soil moisture and temperature without taking into account the systematic differences between the two models. I fully agree with Referee #2 that the authors need to do some kind of bias correction before the assimilation step. It is not clear to me why monthly mean values are chosen and also not why you do not assimilate actual observations, please make this clear to the reader. 

In my opinion the authors should consider changing the experiment design and either assimilate (and evaluate) their system against actual observations or create a synthetic twin experiment study.