The authors are thankful to the reviewer for their assessment of our paper. Really appreciated!

The correct DOI for STREAM model is: 10.5281/zenodo.4588304. This DOI represents all versions, and will always resolve to the latest one.

RC2: This paper presents a simple data-driven model, call STREAM, to estimate global runoff using satellite observations of precipitation, soil moisture, and total water storage anomalies (TWSA). The structure of the model is simple but clear — precipitation and soil moisture are used to estimate surface quick flow while TWSA is used to compute underground slow flow. It is shown that the model can be used to estimate runoff at a basin scale after careful calibrations, which is evidenced by the validation over five calibrated sections in Figure 4.

AC: The authors are thankful to the reviewer for their assessment of our paper. We have provided a point-by-point reply to each of the comments in the sequel.

RC2: However, I doubt very much whether the model can be used for the global runoff estimation since 8 parameters need to be well calibrated based on observed river discharge, which will, to a large extent, limit its application on a global scale.

AC: The intent of the paper is to describe a model that could be used for the estimation of river flow (and runoff) worldwide. However, as correctly stated by the reviewer, the model results are only shown for the Mississippi River basin and the "Global" in the title may not be appropriate. Consistent with the reviewer's assertion, the article and model should be evaluated for their ability to estimate river flow and runoff in the Mississippi River Basin, not globally. In the revised version of the manuscript, the term “Global” from the title will be removed.

The possibility to regionalize the model parameters for the estimation of river discharge at global scale is a topic beyond the scope of this article. However, the authors are working on the regionalization of the model parameters. Preliminary results, which will be shown at the next EGU 2021 conference, demonstrate the possibility to link model parameter values to the basin characteristics, still obtaining satisfactory results.

RC2: For example, the validation results over the gauged sections not used in the calibration phase do not show very good performance of the model as the difference between simulations and observed river discharge may go beyond 1000 m3/s in most sections. The authors attribute this difference to the presence of dams, but this may also happen in sections without dams such as sections 3 and 7.

AC: As any hydrological model calibrated against observed data, it is expected that the best performances of STREAM model can be obtained over the calibrated gauging sections whereas the performances will decrease over the gauging sections not used for the calibration. However, gauging section 3 and section 7 cannot be taken as reference to understand if the STREAM model is suitable for reproducing river discharge over not calibrated sections as they are affected by local characteristics (section 7 is located over the Rock river (near Joslin), a tributary of Mississippi river) and by the presence of an important dam (section 3).

Moreover, we underline that a decrease in the model performance is obtained for all hydrological models. We are preparing a second paper showing the comparison between STREAM and other global hydrological model performances, and STREAM model is working similarly (and even better) than other models (much more complex and with a much larger number of parameters). Preliminary results have been shown at EGU conference in 2020 (https://doi.org/10.5194/egusphere-egu2020-13718).

RC2: On the other hand, this paper highlights the use of three satellite observations of precipitation, soil moisture, and TWSA. However, these three components are highly correlated with each other. For example, soil moisture can be used to estimate rainfall through the SM2RAIN algorithm [1]. Another example is that, on a regional scale, TWSA is very synchronous with soil moisture [2]. Accordingly, the synergy between precipitation, soil moisture, and TWSA, to me, shall be very limited.

AC: The reviewer is right that precipitation, soil moisture and TWSA are in some way correlated but this does not represent a problem for our approach. The proposed STREAM model is a conceptual hydrological model where the inputs contribute to the different runoff components according to specific laws. Specifically, soil moisture and precipitation contribute to the quick component of runoff (daily time scale) while TWSA contributes to the slow component (monthly scale). The differences in the temporal (and spatial) scale of the input data allow us to use the different input consistently and to optimize their synergy for runoff estimation.

Likely, the misunderstanding could have been generated as in the text the STREAM model is defined as a “data-driven model” to indicate that the model is mainly based on the contribution of the input data rather than of complex equations and processes.

RC2: For these reasons, I suggest rejecting this paper as is.

AC: We hope that with these new explanations the reviewer might reconsider their decision.

RC2: [1] Luca Brocca et al (2015). Rainfall estimation from in situ soil moisture observations at several sites in Europe: an evaluation of the SM2RAIN algorithm. HESS. [2] A Geruo et al (2017). Satellite-observed changes in vegetation sensitivities to surface soil moisture and total water storage variations since the 2011 Texas drought. ERL.

Minor comments:

• As the experiments are only conducted over the Mississippi river basin, the word “GLOBAL” used in the title may not be suitable.
• In line 122, please add necessary references regarding SMAP and GPM.
• Please add some necessary references to Eqs. 1 and 4.
• The statements in lines 295-296 are slightly in conflict with the statements in lines 306-308. As I know, TWSA can partly include information on soil moisture.
• In line 303, what are the ranges of beta and m values?
• In line 344, the meaning of the Horton-Strahler order is not clear.
• In lines 444-445, the authors mention that the performance of model in section 3 is not bad. However, as I checked from Figure 5, the difference between simulated and observed discharge can go beyond 8000 m3/s.

AC: The minor comments will be addressed in the revised version of the manuscript.

RC3: The authors present a model ‘STREAM’ that is used to derive river discharge and runoff. The STREAM model is conceptually and computationally simple, and uses inputs of precipitation, total water storage, soil moisture as well as air temperature to provide estimates of global runoff. The results are tested for the Mississippi River basin in the United States and indicate good agreement. Enhancing the ability to model distributed runoff has important applications for hydrology. However, further justification of the methods used and applicability to other climate regimes and regions is needed.

AC: The authors are thankful to the reviewer for their assessment of our paper. We have provided a point-by-point reply to each of the comments in the sequel. Additional details and justifications of the method used will be added in the revised version of the manuscript.

RC3: For example, the authors should comment on the sensitivity of the model to the hydrological inputs of precipitation, soil moisture and total water storage anomaly. The authors should comment on the contribution of using these inputs, and whether results are improved or not by using all three. Otherwise it is not immediately clear to the reader the contribution of each to the estimation of runoff.

AC: In a preliminary analysis, we have tested the sensitivity of STREAM model to the different hydrological inputs of precipitation, soil moisture and total water storage anomaly (not shown for brevity). In particular, by running the STREAM model with different input configurations (e.g., by using TRMM3B42 or CPC data for precipitation, ESA CCI or ASCAT data for soil moisture, GRACE or soil moisture data to simulate the slow-flow river discharge component), we found that STREAM results are more sensitive to soil moisture data rather than to precipitation input. In addition, by running STREAM model with soil moisture data as input to simulate the slow-flow river discharge component (i.e. without using GRACE data) we found a deterioration of the model results.

A sentence to explain the contribution of the hydrological inputs to the STREAM results will be added in the revised version of the manuscript

RC3: The authors also only test their model in the Mississippi River basin, however it would be interesting and informative to address the performance of this model in different regions including more arid basins, snow-dominated, lots of topography, heavily managed, etc. The study indicates it is a ‘global’ model so more discussion of its applicability worldwide is needed.

AC: The intent of the paper is to describe a model that could be used for the estimation of river flow (and runoff) worldwide. However, as correctly stated by the reviewer, the model results are only shown for the Mississippi River basin and even if the model could be applied at global scale, the "Global" in the title may not be appropriate for this manuscript. For that, in the revised version of the manuscript, “Global” in the title will be removed.

Concerning the applicability of the model to other climate regimes and regions, the authors are preparing a new manuscript where STREAM model has been tested on 5 pilot basins (Mississippi, Amazon, Niger, Danube and Murray-Darling) across the world with good model performances. Preliminary results have been shown at EGU conference in 2020 (https://meetingorganizer.copernicus.org/EGU2020/EGU2020-13718.html) and 2021 (https://meetingorganizer.copernicus.org/EGU21/EGU21-14175.html).

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Specific comments:

RC3: Line 208 - Can the authors provide the depth of the soil moisture used in this study. 

AC: Satellite soil moisture observations obtained by the ESA CCI soil moisture product refer to first centimeters of soil (2-3 cm). However, in the STREAM formulation we used a root-zone soil moisture product derived by the surface ESA CCI satellite soil moisture product, by applying the exponential filtering approach in its recursive formulation as in Albergel et al. (2009). For that, the root zone soil moisture used in the STREAM model is referred to the first layer of the model, whose depth varies approximatively from 5 to 20 cm.

RC3: Line 262 - Given that the authors only validate in the Mississippi basin, can they comment on how different climate regimes could impact the accuracy of the modeled runoff in particular more snow-dominated basins. Can the authors comment on the validation of the snow module.

AC: The Mississippi basin contains different climatic regimes, particularly if we consider the differences between the eastern and western parts of the basin. As anticipated before, the authors are preparing a new manuscript where STREAM model has been tested on 4 additional basins (Amazon, Niger, Danube and Murray-Darling) thus exploring a larger variability of climatic regimes, as well as soil and land use characteristics.

In the revised paper we will add specific comments about the model performances in snow-dominated basins. The detailed testing of the snow module is also under investigation, but it is beyond the purpose of this paper.

RC3: Line 300 - Can the authors provide additional information on how they resolve the differences in spatial and temporal scale between the various input data sets provided. In particular, the coarser scale of the GRACE data.

AC: Concerning the spatial scale, air temperature, soil moisture, precipitation and GRACE data have been resampled over the precipitation spatial grid at 0.25° resolution through a bilinear interpolation. For the temporal scale, air temperature soil moisture and precipitation data are available at daily time step, while monthly GRACE data have been linearly interpolated at daily time step. Major details on how the differences in spatial and temporal scale between the various input data sets is resolved will be added in the revised version of the manuscript.

RC3: Line 462 - can the model be run with same input precipitation as GRUN for the validation purposes? Or can the authors comment on precipitation differences between either product .

AC: The STREAM model could be run with the same input precipitation as GRUN to compare the runoff maps obtained by the two approaches. However, as it is beyond the purpose of the paper, the authors will add only comment in the revised version of the manuscript to underline the differences between the two precipitation products and the related runoff estimates.

RC3: Line 520 - Does using GRACE data for water storage (which captures both human and natural processes) address this? GRACE can indicate human activity and water extraction practices, which I think could help improve purely ‘natural’ estimates of runoff.

AC: The added value of satellite observations in the STREAM model is the possibility to capture processes and human activities not modelled but directly observed by satellite. However, we think that GRACE could not be appropriate for capturing reservoir management and for that, in the current development of STREAM model, we are including additional modules for simulating the presence of reservoirs and diversions along the river that can be relevant in several basins/regions.