Reply on AC2

: Confusing mix of LPJ-something used here. First LPJ-Vegetation, then LPJ-DGVM, then LPJ-PM. Also LPJ-VSJA, but I appreciate that is the DA system (although the VSJA acronym is not explained). Then in line the introduction the authors talk about LSMs, not DGVMs and at line 66 terrestrial biosphere models are mentioned. Please be clear and consistent throughout the manuscript.

GLASS LAI products are designed by combining ground observation with MODIS and CYCLOPES LAI information, and MODIS reflectance was used to train and generate fused LAI using General Regression Neural Networks (GRNNs). It has been verified that this method can improve the LAI inversion accuracy of long time series Xiao et al. 2016). GLASS LAI product has been verified to be more accurate than MODIS and CYCLOPES, with stronger temporal continuity and spatial integrity . Considering the temporal and spatial continuity and accuracy, GLASS LAI products were selected as observation data, and the error of LAI products was analyzed in the Discussion section (L720-726)。 Line 88: Do the authors mean more accurate SM data assimilated into models can improve accuracy? And if the authors are not talking about assimilating SM data here, then how was SM data used to improve accuracy of models and is that relevant to a DA study? Same comment for the references used on Line 85. From the sentence they're referencing I assume these references demonstrate how LAI has been used to improve models, but I am not sure that is the case. If instead these references are to demonstrate uncertainty in these variables in models then that should be better specified.
Response: Yes, the concept is that more accurate SM data assimilated into models can improve accuracy. Similarly, more accurate LAI can improve model accuracy. We have deleted these references above to avoid ambiguity.
Line 104: Maybe the authors could explain why microwave RS instruments are used to detect soil moisture, and how that differs to the type of RS instruments that are used to derive LAI data, for the purposes of consistency.

Response:
Microwave satellite data have a strong correlation with soil dielectric constant, and therefore microwave remote sensing is considered as an effective tool to measure soil water content (Petropoulos et al. 2015). Because atmospheric effects can be minimized and less energy is absorbed or reflected by vegetation at L-band, the L-band (12 GHz) is considered the best band for soil moisture retrieval. SMAP and SMOS (Jacquette et al. 2010) are the only two soil moisture specific satellites that are currently in orbit and are equipped with L-band microwave instruments. A verification analysis based on soil moisture measurements from 231 sites across the globe (Cui et al. 2018;Kim et al. 2018) showed that SMAP and SMOS products are superior to other soil moisture products (e.g., Advanced Scatterometer (ASCAT) and Advanced Microwave Scanning Radiometer 2 (AMSR2)). We chose the SMOS-L2 product and the SMAP-L3-Enhanced product, which both provide global coverage every three days for soil depth of 5 cm. By contrast, the GLASS LAI product used in this paper is generated from the optical reflectance data derived from the Advanced Very High Resolution Radiometer (AVHRR) and moderate resolution imaging spectrometer (MODIS)  Points could be added to discussion too. This will help the modeling and DA community more widely discern the best practices and possible pitfalls for assimilation of these two datasets. If it is purely a technical advance (e.g. sheer scale of obs etc), then those advances and lessons learned should be highlighted more in this manuscript. The authors could add specific questions that they are trying to answer to the final paragraph of the introduction.
Response: No, they did not assimilate global data. Bonan et al. (2020) assimilated LAI and SM regionally, not on a global scale. A description of this history was added to the introduction (L 127-140) and we summarized how this study differs from previous studies and the progress made in this study (e.g., the use of datasets, assimilation methods, and regional analyses).

Methods:
Table 1: Is LPJ-VSJA used for assimilating data into LPJ-DGVM or LPJ-PM? I would have thought the latter?
Response: Yes, it is LPJ-PM. The relevant part of the manuscript has been revised (Line195).
Lines: 147-149: Not sure I understand here. There is or is not soil stratification in LPJ?
And please could the authors explain how that connects to simulating water limited regions? I also think this sentence might be better after the authors have explained LPJ more generally.
Response: Due to the characteristics of water limitation in semi-arid regions, many studies have shown that surface soil moisture is the main factor controlling vegetation productivity (Liu et al. 2020), introducing surface soil moisture (SSM) into the model can significantly improve the simulation accuracy of GPP and ET in arid and semi-arid regions (He et al. 2017;).
There is soil stratification in LPJ. In the LPJ model, the soil is assumed to be barrelshaped. The soil is vertically divided into two layers with a thickness of 0.5 m (upper layer) and 1m (lower layer).
In this module, it is assumed that the soil layer above 20 cm produces water through evaporation, and Wr 20 is the relative water content of the soil above 20 cm, which is used as the only soil water limit for calculating vegetation transpiration and soil evaporation. In the evapotranspiration estimation, the over-simplification of soil structure and soil water limitation can lead to a large error (Sitch et al. 2003), while LPJ-DGVM cannot directly assimilate surface soil water due to the limitation of soil layer stratification. In addition, the model is driven by monthly data. The simulated daily soil moisture could not accurately reflect its diurnal variation, thus causing propagation errors for the simulated daily GPP and ET.
The above description of soil stratification in the LPJ model and the limitation of soil moisture are explained in Line 163-172.
Line 152: Need much more information than this: "the GPP is calculated by implementing coupled photosynthesis and water balance" with references.

Response:
The canopy GPP is updated daily: where J C is the Rubisco limiting rate of photosynthesis, J E is the light limiting rate of photosynthesis, and the empirical parameter θ represents the common limiting effect between the two terms. J E is related to APAR (absorbed photosynthetic radiation, product of FPAR and PAR), while J C is related to Vcmax (canopy maximum carboxylation capacity, μ mol CO 2 /m 2 /s) : where C 1 and C 2 are determined by a variety of photosynthetic parameters and the intercellular partial pressure of CO 2 , which is related to atmospheric CO 2 content and further altered by leaf stomatal conductance (Sitch et al. 2003). APAR and FPAR are directly related to LAI.
More detailed explanations and related formulae have been added to L153-155. In the LPJ-PM model, the LAI, canopy height, Maximum annual photosynthetically active radiation and soil texture were inherited by LPJ model. ET PM was calculated by PT-JPL SM . A relationship between the assimilated ET and soil moisture in process models is required to construct the connection between the assimilated system and model. The soil water content was calculated from the nonlinear soil water availability function using the assimilated ET and soil parameters. The soil moisture modeled by LPJ-DGVM in the next time step is replaced by the soil water content.
A basic description of the LPJ and PT-JPL models including the important formulas involved in the coupled models was added to section 2.1.
18.Line 167: What do the authors mean when they say "The SMAP SM was applied to model global ET using PT-JPLSM"? Do they mean the data was assimilated? 19.Line 170: The authors talk about "scheme 2" here before talking about scheme 1? This is confusing. Please resolve.
Response: This paragraph mainly describes how SM is assimilated into the LPJ-PM model, that is scheme 2. This paragraph that describe the SM assimilation was removed to the section 2.2.2 in L244-253 . 20.Line 169-176: I am a bit confused by what is going on in this paragraph. Please make it more clear for the reader.
Response: This paragraph mainly describes how the SMAP SM was assimilated into the model in the SM assimilation scheme. The assimilated ET SM is superior to the ET PM and ET LPJ through site-level evaluation. This paragraph was revised and moved to Section 2.2.2 (L241-250). 21.Line 185: Earlier you say "PODEN4DVAR".

Response:
The acronym has been standardized as "PODEN4DVAR".

Response:
The paragraph has been reorganized in accordance with your suggestion.
Lines 201-202: which dataset did the authors use to define humid, semi-arid etc?

Response:
The basis for distinguishing arid and humid regions is the classification system of global arid and humid regions in Middleton and Thomas (1997) that uses the "drought index" to classify different arid and wet regions. The drought index is defined as the ratio of precipitation to potential evapotranspiration. Regions with aridity index between 0.2 and 0.65 are defined as semi-arid regions, regions between 0.05 and 0.2 are arid regions, and regions below 0.05 are severely arid regions, that is, desert areas. The drought index of humid area and sub-dry humid area is about 0.65-3. In this paper, arid zone, semi-arid zone, humid zone and sub-dry humid zones are selected to evaluate the assimilation results in different regions. 27.Section 2.2.3: this is really a step-wise assimilation, rather than a true "simultaneous" joint assimilation. There are advantages and disadvantages to that should be discussed, and assumptions explained. See MacBean et al. (2016) for discussion.
Response: Yes, this is really a step-wise joint assimilation. We adopted step-wise assimilation because of technical constraints. As a nonlinear dynamic processed-model, LPJ-DGVM was simulated according to numerous physiological processes of vegetation; when it is running, SM and LAI could only be assimilated step by step inevitably. In the discussion section, the influence of assimilation sequences on assimilation results, the importance of error correlation between parameters, the density of spatio-temporal information of observations, and the deviation between model and observations to the step-wise joint assimilation performance have been added in Lines738-750.
28.Line 244-245: "Finally, GPPCO and ETCO were output by joint assimilation based on the POD-En4DVar method." I am confused here. This sentence reads like a separate joint assimilation is done when from earlier in the section/paragraph it seems like the LAI and SM/ET have already been assimilated?
Response: Yes, this sentence summarized the results of joint assimilation, which has been explained step by step in the previous paragraph. This sentence was deleted to avoid confusion.
Response: This reference was revised to Tian and Feng 2015.

Response:
The POD decomposition technique is adopted to transform the original ensemble coordinate system into an optimal one in the L 2 norm (Ly and Tran, 2001), which contributes greatly to its enhanced assimilation performance. The POD base is the Transformed OP (Observing Perturbation) and MP (Model Perturbation. This was explained in L274-278.
. 31.Line 254: "flow-dependent error estimates" please explain what this is for the non DA specialist.
Response: By forecasting statistical characteristics, the EnKF through ensemble method can provide flow-dependent estimates of the background error covariance. The flowdependent is the ensembles of forecasting statistical characteristics in the t time, which is also explained in Lines 282.
32.In general the number of subtext acronyms is difficult to parse. I suggest the authors find a slightly different way to refer to all the variables. For example, GPP_prior, GPP_scheme1, GPP_scheme2 etc.

Response:
We feel that the subscript of assimilated observation data can make the result comparison more intuitive for readers in the result analysis, while the scheme serial number may cause confusion for readers.

Results:
32. Figure   34. Figure 8: would be useful to put the labels "semi-arid" etc inside the actual subplots.

Response:
We have added a label at the bottom right corner of each figure.
35.Lines 468-476: this is nice but it would be great to see the prior model-data comparison to see how the "CO" optimization has improved things. Otherwise, the authors' claim at line 476 that SM data are needed for water-limited areas is an overreach. Actually, without comparing to schemes 1 and 2 it is hard to say whether it is SM or LAI data that have achieved a good result in water-limited areas. The authors do seem to discuss the prior in the paragraph lines 485-490 but I am having trouble seeing where this fits into the bigger picture.

Response:
The assimilation results of the LPJ-DGVM and the three schemes in wet and dry regions are analyzed in Tables S2 and S3 of the Supplementary Material. For ET, the R 2 and ubRMSE implied that the SM assimilation alone had a better performance than the LAI assimilation alone, especially for sites in arid areas. and the bias showed that the ET LAI improved better than ET SM for sites in humid and sub-dry humid areas.
For GPP, the R 2 and bias implied that the LAI assimilation alone had a better performance than the SM assimilation alone. However, for sites in arid and semi-arid areas, the RMSE and ubRMSE showed that the GPP SM improved better than GPP LAI , which both demonstrated SM data are essential in water-limited regions. These analyses were added to section 4.2. 38. Figure 10: the color coded grid is helpful here.
Response: Thanks for your comment. We thereby retain the color coded grid in the figure.

Discussion:
Generally a well-rounded discussion of the advantages and caveats of the approach. I would appreciate more discussion on the inconsistency between LAI products in Section 5.3, and implications of the fact the assimilated products (LAI and SM) may be biased. What impact do the authors think that would have on the results? Also issues related to temporal sampling interval could be discussed somewhere in the discussion, as well as assumptions/caveats of the DA method that may affect the results.

Response:
In the discussion section, the inconsistency of LAI products and analysis of the assimilation results (reasons of bias) and the influence of ensemble size, error setting and temporal sampling interval on assimilation performance have been discussed in L700-740.