Reply on general comments: 

We would like to thank the reviewer for their comments. We undestand that our methodology section (as is) does not describe how data and modelling were used in a clear manner; and this concern is shared among the three reviewers.

We will revise the methodology section by adding new text, by including flow charts of how data are used and by describing how the DALEC-Grass model works in more detail. We will also add a section in materials and methods that clarifies the C accounting terminology and what every related abbreviation refers to. We will also ensure that the reader is always reminded the sign convention i.e. that "-" before an NEE/NBE value shows a C sink and "+" a C source . In this context, three new figures that we propose to include in the revised manuscript are attached here (figures.zip). Moreover, we will expand the text on limitations and possible solutions and discuss some options such as the this reviewer's suggestion on coupling (or incorporating) soil water models with DALEC-Grass.

Replies on specific comments: 

Comment : The same was for manure. Where did Manure come from and how Cardamom accounted for Manure (C/and N) ?  EDINA database? (see L368) 

Reply : Manure production is estimated on the basis of simulated grazed biomass. 32% of the simulated grazed biomass is converted to manure and added to the litter pool. As it is impossible to infer the type/age/weight of animals grazing a field  using satellite imagery this conversion factor is an average for dairy/beef cattle and sheep based on UK and northwest european data. We will clarify this part in the revised document and provide references for the conversion factors for the grazed biomass. Conversion factors (shown as % of grazed biomass) are presented in the attached DALEC-Grass schematic. 

Comment (L 134ff) : “At each time step the algorithm reads the vegetation reduction information and decides whether to simulate the corresponding … “ this is not quite clear and I wonder of a flowchart will help? What is the time step? Do you mean management practices comeing from Edina AgCenesus . If yes please refer to section 2.1.5

Reply : We understand that this part is not clear. The process of deciding whether a vegetation reduction value (vegetation reduction is model input driver) will be simulated as grazing, cutting or not simulated at all is described in Myrgiotis et al (2021). Inferring management and predicting sub-field scale C dynamics in UK grasslands using biogeochemical modelling and satellite-derived leaf area data. Agricultural and Forest Meteorology, 307, 108466. https://doi.org/10.1016/j.agrformet.2021.108466. We will expand the model-description text to explain the way this is done.

Comment (L212ff) :  “To assess the effectiveness of the LAI assimilation process we quantify the level of fit between MDF-predicted and EO-based time-series using …” Until now I did not get that Cardamom estimates LAI (see L 141 and L241) put is used this as an input. Seems I have missed a point. Can authors please clarify. (eg in a scheme?)

Reply : We understand that the lack of clear description of the use of data in the materials and methods section has caused problems. We believe that new text and figures will help the readers understand better what the model-data fusion (MDF) framework does and how DALEC-Grass is used as part of the framework. The framework is used to implement the model and provide the predictions for the presented variables we, therefore, refer to "MDF-predictions" and not "model-predictions" to reflect this fact.

Comment (L235  and L 331ff ) : RCR is equal to the size of the MDF-predicted 95% confidence interval divided by the corresponding…”  please help the reader to get the number in the right way. eg RCR is 42 ± 9% for LAI, means the uncertainty of LAI is 43% so very high? Or very low? With respect to which best value?

Reply :  The relative confidence range (RCR) presents the uncertainty around the MDF-predicted variables (e.g. LAI) as a %. It shows how wide the 95% confidence intervals (i.e. 2 standard deviations, assuming normality) are relative to the mean value. The cartogram shows the distribution or RCR across Great Britain and the violin plots the distribution or RCR grouped according to whether grazing or cutting was the main removal method (i.e. most biomass was removed via grazing or via cutting). The assimilated LAI data come from processing Sentinel-2-based images (20m resolution) and have an uncertainty attached to them. This means that every 400m2 of a field has an uncertainty that is attributed to "instrument error" (remote sensor). This uncertainty is not always examined in the relevant literature but studies suggest a value 15%; the standard deviation around each LAI data point per 400m2 is 15% of the value which converted to RCR is 30%. We use a  field-mean LAI for each simulated field which means that uncertainty is amplified when we calculate a field-average LAI. Taking this fact  into account and considering that MDF predictions incorporate model parametric uncertainty a mean LAI RCR = ~40-50% is proportional to the observational uncertainty. This is not discussed in sufficient detail in the manuscript and we will revise accordingly. 

Comment on suggested references to include. Reply : These are interesting and very relevant studies that we will include as references in the revised manuscript.

Response to general comments : 

We would like to thank the reviewer for their comments. We would also like to apologise for the presence of many “?” in the submitted manuscript. These are not unresolved comments. They are certain references to the literature (and manuscript figs/tables) that the LaTex-based software, which was used to produce the manuscript, failed to print in the submitted pdf file. 

This reviewer shares the concern of the other two reviewers regarding the clarity of the materials and methods section. We propose to revise the entire materials and methods section by adding new text and figs. We have attached here 2 figures that will be used to show (1) how the data and the model are used in the study and (2) a schematic of the DALEC-Grass model. 

Comment 1 : It is not clear why and how the two sets of remote-sensed LAI were used in the study…

Response : The ESA sentinel-2 mission provides optical imagery every 5-10 days at high resolution (10/20/60m). This means in-field vegetation management can be inferred from satellite data and can be simulated using the inferred information. DALEC-Grass is implemented in this study on a weekly time step. This means that an estimate of standing vegetation (or a proxy of it) at the beginning and at the end of every simulated week is needed in order for the model to simulate : either (1) no vegetation removal or (2) vegetation removal via grazing or (3) vegetation removal via cutting. In places with frequent cloud coverage, such as the UK, there is no guarantee of weekly cloud-free Sentinel-2-based data; and therefore of weekly LAI and vegetation reduction estimates. Interpolating between the available Sentinel-2 data is one way to deal with gaps in the required weekly time series. We argue that in the CGLS LAI time series : (1) this interpolation is done in a robust way i.e. machine learning-based filling of no-data (cloud, haze, shadow-covered) pixels using information from past years and/or neighbouring pixels; and (2) provides information on vegetation biomass obtained from a different satellite mission (Proba-V) in addition to Sentinel-2. Also, we argue that the “predictive accuracy cost” caused by low spatial resolution (300m) of the CGLS vegetation reduction data is smaller than the respective cost of applying interpolation methods (eg linear interpolation) on the Sentinel-2 time series. This is because for many UK locations and certain key periods like spring and summer (when cutting typically takes place) there could be very few cloud-free images available from Sentinel-2. 

Comment 2 : After going through the Materials and methods section, it is still not clear e.g., how the different models/frameworks were connected; how and where the EO-based data were used; how the model parameters were optimized; how the C fluxes were estimated. 

Response : Our proposal to revise the materials and methods using new text and schematics will include the provision of details on these aspects.

Comment 3 : It is not clear how grazed/cut events (as a critical result of this study and an important component of the C budget) were identified, and grazed/cut biomass was simulated.

Reponse: Indeed, we do not describe this process in detail. A recent paper (https://doi.org/10.1016/j.agrformet.2021.108466), that we refer to in the manuscript (L132),  presents the process but we propose to revise the manuscript by adding a paragraph that will describe how the grazing-vs-cutting inference works.

Vegetation reduction model inputs tell the model how much LAI should be removed during every simulated week. Through the model-data fusion algorithm the Sentinel-2-based LAI value at the beginning of every simulated week (before any vegetation removals) is assimilated i.e. the satellite-observed LAI should fit with the simulated LAI as closely as possible. The model decides whether to simulate each weekly vegetation reduction input as grazing or cutting based on the facts that : 1) cutting should remove at least 1.5 t.DM.ha-1 to be worth implementing in grassland farming; 2) cutting can only occur between May and October; and 3) whatever the model simulates should lead to a “good” fit with the Sentinel-2-based LAI data not only for the examined week but for the preceding and following weeks (since the entire observed LAI time series is assimilated). This mechanism of vegetation removal-type inference allows us to detect and simulate cutting by relying on observations and biophysical modelling rather than on statistical analyses of observational data alone. For this reason every predicted cutting date/intensity per simulated field has probability/uncertainty attached to it. This uncertainty reflects the lack of continuous EO-based data since neither the CGLS nor the Sentinel-2 LAI data products are frequent enough i.e obtained every 2-3 days. Our long term aim is to produce such continuous EO data as the only way to drastically reduce the uncertainty around cutting timing and intensity. 

Comment 4 : The components of C budget were only very briefly mentioned. It is not clear how each component was estimated. Especially for manure, I cannot find how it was estimated (or derived from another dataset).

Response : We propose the addition of a materials and methods section (and a schematic) that will clarify all C-balance terms so that that the reader understands what each term means before reaching the results section. On the manure inputs issue, manure-C  is estimated based on grazed biomass (see attached DALEC-Grass schematic). We do not simulate/consider external manure transport/addition as this cannot be inferred from EO data and doing so will require us to use spatially/temporally uncertain data on manure use e.g. national-scale estimates of manure application per ha. All the manure that is simulated as being added to the soil is produced by the simulated grazing livestock using conversion factors from the relevant literature (see attached DALEC-Grass schematic). This mechanism will be clarified in “Materials and Methods / DALEC-Grass”.

Response to specific comments 

Comment : How the sampling of grassland fields can result in only 1-5 simulated fields per cell? Response : Each cell varies in size depending on the number of simulated fields within it. Larger cells include more fields. The smallest cells in the presented cartograms include just 1 simulated field. 

Comment : What are the Metropolis-Hastings (MH) method and the Simulated Annealing (SA) algorithm? What is the difference between them. Response : Considering this issue in the manuscript will require significant text space. We propose adding a brief description of the simulated annealing technique and removing any reference to Metropolis-Hastings since readers interested in MCMC algorithms can find details in 10.1016/j.agsy.2020.102907 (which is among our references)

Comment : How the mean C fluxes across the GB were calculated? Area weighted? If so, how? Whether the selected points are representative for all grassland grid cells? Response : GB-average C fluxes show the mean cumulative annual values across all simulated fields. We argue that the ~2000 simulated fields are representative as they are randomly sampled from a geo-database (UK land cover map) of grassland fields (polygons). The process used for sampling the fields (section 2.2.1) ensures that areas with large managed grassland coverage are more represented than areas with small managed grassland coverage. Strictly speaking, we would have to (1) draw a much larger sample (>10000) of fields from the geo-database, (2) examine how predicted GB-average C fluxes (e.g. GPP, NEE,NBE) change relative to the number of fields included in the calculation of the GB-average and (3) identify the best number of sampled fields. This is fasible but  computationally very expensive. We argue that the comparison of MDF predictions with the census-based livestock maps and the literature-based GB-average yield data is a fair assessment of the representativeness of our sample of grassland fields.

Comment : It would be necessary to provide the maps of rough grazing, permanent and temporary grassland, and the maps of resulted management type (e.g., grazed only field or grazed + cut field), grazed, and cut biomass for users to understand the management intensity. Response : Such maps would have been a great validation dataset but maps of UK grasslands classified by management intensity type are not available (to our knowledge). Our methodology has the potential to produce such maps if sufficient ground data are available for validation of the MDF predictions; i.e. using predicted yields to infer if each field is rough grazing, permanent or temporary grassland.. 

Comment :  It is strange that NEE/NBE were negatively related to both GPP and REco. Response : We use the micrometeorological convention in which fluxes from the biosphere to the atmosphere are positive i.e. negative NEE/NBE shows a C sink and positive NEE/NBE shows a C source. A negative relation suggests that more photosynthetically productive grasslands tend to be stronger C sinks (i.e. higher GPP -> lower NEE ). REco = heterotrophic respiration + autotrophic respiration. Autotrophic respiration is ~45% of GPP and, therefore, REco and GPP have very similar correlation coefficients 

Comment : As the uncertainty for LAI is nearly half of mean LAI, the robustness of the prediction should be further discussed. Response : This issue has been raised by reviewer CC1 as well. We propose to discuss it further in the revised manuscript and we would like to clarify, here, what our uncertainty estimates present (Fig.8). The relative confidence range (RCR) presents the uncertainty around the MDF-predicted variables (e.g. LAI) as a %. It shows how wide the 95% confidence intervals (i.e. 2 standard deviations, assuming normality) are relative to the mean value. The cartogram shows the distribution or RCR across Great Britain and the violin plots the distribution or RCR grouped according to whether grazing or cutting was the main removal method (i.e. most biomass was removed via grazing or via cutting). The assimilated LAI data come from processing Sentinel-2-based images (20m resolution) and have an uncertainty attached to them. This means that every 400m2 of a field has an uncertainty that is attributed to "instrument error" (remote sensor). This uncertainty is not always examined in the relevant literature but studies suggest a value 15%; the standard deviation around each LAI data point per 400m2 is 15% of the value which converted to RCR is 30%. We use a  field-mean LAI for each simulated field which means that uncertainty is amplified when we calculate a field-average LAI. Taking this fact  into account and considering that MDF predictions incorporate model parametric uncertainty a mean LAI RCR = ~40-50% is proportional to the observational uncertainty.

Reply on general comments 

We would like to thank the reviewer for his comments. We would also like to apologise for some "?" seen in the document. These were caused by the LaTex-based software used to produce the submitted pdf but failing to find certain references and links to tables/figures.

Indeed the identification of grazing and (particualrly) cutting instances is not definite. Identifying grazing and cutting timing and intensity from EO data is an outstanding issue. However, this does not reduce the value of the presented reserach. In this respect, we arue that : (1) the use of earth observation (EO) data to identify these events and use them as drivers of model-based predictions is superior to e.g. using generic dates and biomass removal intensities based on agricultural calendars or data from a limited number of monitored fields, which is what most large-scale model-based studies depend on; and (2) the use of an approach that mixes process-level understanding of grass growing, and grazing and cutting patterns (i.e. a biogeochemical model) and EO data is more robust than relying solely on applying machine learning and time series-decomposition analyses on the EO-based time series. 

The concern about the unclear description of how data and modelling is used in this study is shared among the three reviewers. We propose to incude three new figures/schematics that explain the methodology more clearly (figs attached here) and revise the relevant text. 

Replies on specific comments :

Comment (1) : it may be more proper to replace the “constrained” used in the title “The carbon budget of the managed grasslands of Great Britain constrained by earth observations” with “adjusted” or “estimated”.

Reply : We understand the point of view of the reviewer on this issue. The world "constrained" is more widely used in studies that involve observational data assimilation. We believe it is more appropriate than adjusted/estimated mainly because it conveys the message in a way that will be familiar to many readers.

Comment (2) What were included in the managed grasslands? Did they include rough-grazing grasslands in the context of three UK grassland types – temporary, permanent and rough-grazing ?

Reply : When we refer to managed grasslands we refer to all of these three types of grasslads : rough grazing, temporary and permanent. To our knowledge there is no geo-dataset that shows the type of specific fields across the UK. The Land Cover Map that was used to sample the fields that were simulated does not discriminate between these three types which it collectively refers to as "improved grasslands". It is not possible to know the type of grassland of a simulated field before simulating it but we can infer the type based on the annual yield (cut + grazed biomass) since we know the UK-average yield for each of these three types of grasslands.

Comment (3) : It was said that there were 1855 fields selected for simulations across GB in 2017 and 2018. How many fields were selected in 2017 and 2018, respectively? How many fields were grazed only, how many fields were cut only and how many fields were both grazed and cut? What were the total areas for 1855 fields and in each management grassland type? It would be good to make a box plot showing the size distribution of selected 1855 fields.

Reply : The the same 1855 were simulated for 2017 and 2018. There were no cut-only fields among the simulated fields.  This is probably an artefact of the sampling process because only fields 6-13ha in size were included in the sample (see section 2.2.1 in the manuscript and line 356>).  75% of the simulated fields were grazed-only and 25% were both cut and grazed (Line 259). We will provide information on the total simulated area and the distribution of field sizes in the revised manuscript. 

Comment (4) : When selecting fields to be included, the passing criterion was 50% overlap limit. What did the overlap measure specifically? It was also necessary to know how many fields were ignored when simulations were compared with LAI from EO data.

Reply : The overlap shows the percentage of simulated leaf area index (LAI) data points (mean predicted LAI) that are within the the uncertainty limits of the corresponding obsrevational data points (i.e. satellite based LAI at 20m resolution -- mean value across the simulated field). For 12% of the initial dataset of 2108 simulated fields, our analysis failed to generate a simulated-vs-observed LAI overlap > 50% (Line 242). As we do not have a dataset of ground-measured LAI time-series across a range of fields we cannot use a data-based method to determine the overlap % that should be used as a limit. Based on our experience with visually examining the fit between observational and simulated LAI time series we argue that 50% is a fair limit.

Comment (5) The manuscript was not cleanly finalised before it was submitted to the journal website because there were many places that had unanswered question marks in the manuscript.

Reply : We would like to apologise again for this and clarify that these "?" are not unanswered questions but references that for some reason the software used to produce the submitted pdf was unable to find as/where it should. 

Comment (6) :  Flow of information between models used in the coupled MDF algorithm framework was not clearly presented. So, an added diagram may be helpful.

Reply : As stated in our reply to general comments we understand that the materials and methods section was not as clear as it could hav ebeen and we will revise accordingly. 

Comment (7) : The “Removed biomass” item in Table 1 was 220 in 2017 and 280 in 2018. If 2018 was extremely hot and dry summer, why was there more biomass for removal because of limited pasture herbage yields? What was included in the “Removed biomass”?

Reply : This is a very interesting question that we do not discuss in the manuscript. We will include discussion text on this issue in the revised manuscript. Briefly, the 2018 summer heat wave affected all areas of GB but not with the same severity. The southern 1/3 of GB was significantly affected but it is also an area with smaller grassland coverage than e.g. Wales, southwest Endland, northwest England and Scotland. Also, climatic conditions in winter, spring and autumn 2018 were more conducive to higher seasonal (non-summer) yields in areas outwith that southern third of GB. This explains the increased GB-average yield but the possible role of drying on the assimilated satellite based LAI data should also be considered. A drying grassland turning yellow in colour results in a decreasing EO-based LAI. It is possible that as the drought started affecting GB and its grassland fields this reduction in LAI (caused by colour/reflectance change) was simulated by DALEC-Grass as biomass removals and not as leaf drying. However, the model has simulated the impact of drought on leaf production and LAI, and, therefore, the afforementioned process could not have had but a minor impact on the predicted yields

Reply to specific points 

We will ensure references to tables and literature will not appear as "?" in the revised document 

On the issue of livestock units. As it not possible to infer the type/age/weight of grazing animals using EO data we use generic literature-based values for beef/dairy cattle and sheep when : (1) converting simulated grazed biomass-C to manure-C, CO2-C and CH4-C (see DALEC-Grass schematic in attachments)  and (2) calculating livestock units from MDF-predicted grazed biomass (line 217).

On comparing predicted livestock units with census data. We refer to the issues arising from the fact that census data for England are from 2010 while the study examines 2017-2018  (Line 256). Livestock density (total numbers ÷ total area) has been decreasing (albeit slightly) in England and the UK in general. We argue that the negative bias between predicted and census-based data reflects that fact (fig 3). Also, significant changes in the spatial distribution of livestock across the UK has not been reported in the relevant literature. We argue that it is also not possible due to the fact that the zone of naturally highly-productive grasslands has not changed (i.e. western third of GB) .Therefore, the comparison of MDF-predicted and census-based data (Figs 3 and 4)  is -- despite its discussed limiations -- a good way to assess if the MDF framework   "translated" the EO-based LAI time-series into biomass utilisation in a way that (generally) reflects what is known to be happening on the ground (i.e. relative livestock denisty at  local/regional scale).