General comments:

This study presents an open-source global data assimilation (DA) system for integrating GRACE/GRACE-FO total water storage into Global Hydrological Models. The study achieves a previously unseen high spatial resolution, with the potential to increase the use of GRACE/GRACE-FO data in the hydrological modelling community. The study is well within the scope of GMD and a relevant contribution, particularly as it provides a reproducible and transparent approach. The authors have done a thorough effort to test that their implementation can be used at the targeted levels and with consistency.

The paper could benefit from a proof-reading and more importantly some clarifications – quite a few terms are treated as self-explanatory which they are not for non-GRACE experts, who might still benefit from using the tools and models developed and kindly made available by the authors.

While the data processing and DA setups are quite thorough, the GHM used is still quite fundamental to the DA and clearer details on its limitations and structure could be beneficial both to understanding some of the results, but also to identify where additional experiments and developments are warranted. I think the paper would gain in strength and impact if it were to include some model validation and analysis of the hydrological consistency.

Specific comments:

l. 28-30 I would revise how you classify the models – most of these are rainfall-runoff and conceptual which is also the case of a water balance model. In general we talk more of conceptual versus physically based and whether a model is lumped, distributed or semi-distributed (e.g. SWAT with Hydrological Response Units). The question can also be how many processes are lumped/conceptualized and how simple the model structure is.

l. 71 spelling of project name

2.2 Which up- or down-scaling routine are you using?

2.3 How are the parameters down-scaled? Is there any risk of non-linearities at the boundaries between pixels or basins?

2.4 Please explain more clearly what ITSG-2018 is and who is developing it? In 2.4 you only present the three official data centers, and it would be good with a bit more background information on ITSG-2018 and why you prefer an unofficial provider (and whether that is available to any user). Why is a better quality expected with ITSG-2018?

Figure 1. Several of the subparts are difficult to read even when zooming in on a screen (figure in b, boxes in the ensemble output) – I recommend that you either remove the text or increase the font size.

Would refining the grid size not increase your susceptibility to lateral redistribution? Does W3RA include any kind of routing component?

l.186 spelling of Gaussian

l. 189 verb missing in sentence

Table 1 – please give more details on the corrections which use acronyms or simple symbols, as well as what each correction does.

l. 206 Please clarify – do you mean that if the required number of ensembles is run, each individual ensemble is independent of each other or is that the case no matter the number of ensembles?

l. 214 What would be a recommended number of ensembles?

Figure 3 You are assuming no inter-correlation within the tiles but there is clearly hydrological correlation between several neighboring tiles crossing large river basins – can you clarify how that is not an issue?

3.3.2 How do you determine the width of the transition zone? Are there large differences where the average might not make sense? Have you tested whether your assumption of reasonability of the inverse-distance weight is correct?

l 325 This we would expect – the GW has much longer memory than the surface components.

l. 334 Please clarify “the phase shift has been compromised” – where is it happening in the model?

l. 377 Is the water balance also maintained?

l. 439 Have you considered using GRDC discharge data for validation?

The manuscripts describes a Python-based Global Land Data Assimilation

(PyGLDA) software for integrating the estimates of Terrestrial Water Storage

(TWS) variations from satellite gravimetry data into a Global Hydrological Model

(GHM). The former data are provided by GRACE and GRACE Follow-on (GFO) satellite

missions. As far as the hydrological model is concerned, the authors have

adapted W3RA model (line 84). Technically, the Ensemble Kalman filter

(EnKF) and an Ensemble Kalman Smoother (EnKS) can be used as

data assimilation tools (line 90).

In general, the manuscript provides a sufficiently detailed description

of the developed software. Nevertheless, there are a number of points

which remain unclear. In particular, some statements in the abstract

seem to be inconsistent with the main text. This makes an impression that

the actual status of the developed software is much less advanced

than the abstract claims.

I would like to highlight the following uncertain points:

1. In the abstract, the authors mention that "choice is made ...

to avoid numerical problems, e.g., instabilities related to the

inversion of covariance matrices" (lines 5-6). At the same time,

they admit at the end of the manuscript that "Potential numerical

instability introduced by the inverse of the covariance matrix ...

has not been found yet so far in our study. Therefore, in the current

version, none of the covariance localization techniques has been integrated

into PyGLDA, and consequently, users may face the potential risk of instability

when the gridded DA is configured to run at a smaller scale" (lines 466-470).

These two statements seem to contradict to each other.

2. The abstract claims that W3RA hydrological model

is used just to demonstrate the performance of the developed data

assimilation software (lines 15-16). At the same time, the manuscript

itself does not go beyond W3RA. Moreover, the concluding section mentions

that "PyGLDA is being developed to allow for more candidate GHMs, other

than W3RA" (lines 454-455). Thus, it remain unclear to what extent

the developed software in the present form is suited to assimilate

GRACE/GFO data into other hydrological models.

3. The authors mention that the adopted hydrological model W3RA

ignores lateral water redistribution between grid cells

(lines 174-175). This sounds odd. I cannot imagine a

hydrological model that ignores streams and rivers.

Perhaps, the authors mean the absence of underground

water redistribution?

4. In the description of data assimilation procedure

(Sect. 3.2 and further; also, Fig. 2), the authors seem to use the

term "ensemble" instead of the term "ensemble member".

This makes the description not very clear.

5. At many places in the main text, the authors address correlations

(or covariances), but do not explain whether they mean signal

correlations or error correlations.

6. The authors mention that they use a multiplicative error

to disturb, among other, forcing fields (e.g., lines 312-314).

Furthermore, they mention that the forcing fields

include the daily precipitation, the maximal/minimal temperature

and the surface solar radiation (lines 123-124). On the other hand,

appendix A admits that the only disturbed forcing field is

precipitation: "In PyGLDA, we consider multiplicative errors

for precipitation, thus q = 1" (lines 499-500). This is inconsistent.

7. The statement cited in the previous item implies that no disturbances

are applied when the nominal precipitation is zero and no disturbances

are applied at all to the other forcing fields. This seems to be sub-optimal,

since it may result in an insufficient variability of forcing fields

(and, therefore, of the state vectors) among the ensemble members.

In addition, the manuscript suffers from numerous textual deficiencies.

Among others, there are many very long sentences,

which definitely should be split into 2-3 shorter ones. 

Occasionally, the manuscript makes an impression that

the authors have never taken time to read the text they wrote.

In the enclosed annotated manuscript, I left a number of

specific suggestions concerning an improvement of the text.

Nevertheless, I encourage the authors also to carefully revise

the manuscript themselves.

I recommend to publish the manuscript provided that the authors

update it in line with my remarks.