Overview

The manuscript provides a welcomed intercomparison of approaches and frameworks to quantify irrigation from remotely sensed soil moisture and ET data. Overall, the results improve understanding of the shortcomings and pitfalls of various approaches designed for this task. I recommend publishing the manuscript after addressing the below comments. This study is likely to inform future irrigation quantification analyses.

Primary concern

Eq. 3: This study calculates irrigation as the sum of SM and ET residuals (satellite – model). This seems like irrigation will often be double counted, because surface soil biases propagate to ET biases. There is a time lag, such that a wetter soil surface (from the satellite) that is attributed to irrigation from a previous time step will be accounted for as irrigation again in a later time step when the water returns to the atmosphere. Is it possible that this could be compensating for other sources of error that favor underestimated irrigation?

If I am missing something about this method that is implemented to avoid double counting, please elaborate on this; if not, please discuss this source of error in the manuscript and how it may be data-specific.

Specific comments

Lines 109, 115: the semicolon should be a colon.

Line 120: Please add an additional sentence that explains the reasoning/logic for the assumed losses.

Section 3.1: Can you please provide justification of why MODIS ET is used instead of other products?

Section 3.1: Was a downscaled SMOS product used instead of other high-spatial-res produces (e.g., SMAP-S1) to maintain high temporal resolution? Has there been validation to ensure the SMOS SM product maintains irrigation signals (e.g., similar to Lawston et al., 2017 or Jalilvand et al., 2021)? I believe this is important because the Kumar et al. (2015) analysis seems to suggest the SMOS product fails to detect a significant portion of irrigation signals (which is also related to my concern above regarding Eq. 3).

Lawston, P.M., Santanello, J.A., Kumar, S.V., 2017. Irrigation Signals Detected From SMAP Soil Moisture Retrievals: Irrigation Signals Detected From SMAP. Geophys. Res. Lett. 44, 11,860-11,867. https://doi.org/10.1002/2017GL075733

Jalilvand, E., Abolafia-Rosenzweig, R., Tajrishy, M., Das, N.N., 2021. Evaluation of SMAP-Sentinel1 High-Resolution Soil Moisture Data to Detect Irrigation over Agricultural Domain. IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing 1–1. https://doi.org/10.1109/JSTARS.2021.3119228

Kumar, S.V., Peters-Lidard, C.D., Santanello, J.A., Reichle, R.H., Draper, C.S., Koster, R.D., Nearing, G., Jasinski, M.F., 2015. Evaluating the utility of satellite soil moisture retrievals over irrigated areas and the ability of land data assimilation methods to correct for unmodeled processes. Hydrol. Earth Syst. Sci. 19, 4463–4478. https://doi.org/10.5194/hess-19-4463-2015

In Section 4, abbreviations for the approaches are introduced. It would be useful if in the former section, a table is created that summarizes all evaluated approaches and defines the abbreviations for readers to reference. This would be particularly helpful because the abbreviations are used in Figure legends.

Table 1: Can a figure be added either to main text or supplementary that shows comparisons of the model and observed SM and ET throughout the period? This can be useful to visualize bias characteristic (e.g., random vs. systematic)

Figure 3:

please use different colors to differentiate between NS-SM_bf and RS-SM_bf. Please add the benchmark to the legend. Is there a reason the benchmark is shaded instead of a line (like the predictions)?  (Similar sentiments for Figures 4 & 5 aesthetics)

Section 4.2 can benefit from more attention to writing to report results in a more clear and concise manner

Paragraph starting in line 333: Is this bias characteristic model specific to the mHM? If calibration considered other metrics (e.g., NSE) could this error source be reduced?

Line 392: comma after “Figure 6” should be removed

Section 4.3: It would be extremely helpful to the community if this paper summarizes the insights from analyses and comparisons in this section. Namely, a table which summarizes the strengths and weakness (e.g., uncertainty sources) of the approaches, and which approaches are more robust to various uncertainty sources (e.g., precipitation, satellite temporal and spatial resolution, noise, etc.). This table would likely be the primary take-away of the study.

General comment:

This study focuses on comparing different methods for estimating irrigation water use. The topic is important for understanding the human impact on the hydrological water cycle, and there are various methods available with their own advantages and disadvantages. The authors conducted a comparison between a baseline model representing rainfed agriculture and a satellite-based model that captures irrigation. The difference between the two models represents the unmodeled process, which in this case is irrigation. To ensure accuracy, the authors calibrated the model using rainfed pixels to remove biases between the model and satellite observations before calculating the difference. Other irrigation estimation methods, such as the water inversion method using satellite soil moisture and evapotranspiration (ET), are also used and discussed. The paper provides a comprehensive comparison of different methods, but some details are skipped, possibly assuming that readers are familiar with previous related papers. One concern raised is the possibility of double-counting water when estimating irrigation using both soil moisture and ET residuals, as these variables are interconnected. Overall, the paper is recommended for acceptance after addressing the mentioned comment and the below detailed comments.

Major comments:

1. It appears to me that author assumed the reader has already read their previous papers so they did not explain some terminologies or hypotheses that they had in the abstract, for instance in L15-17 it is not clear what are the satellite or the rainfed framework and what they meant by the baseline framework. Later in the introduction at L43-44, the study hypothesis is explained, I think something to this effect can be added to the abstract.
2. I do not understand lines 236-244 regarding how the water is not counted twice. The ET and soil moisture are interconnected, such that an increase in ET results from an increase in soil moisture. Technically some of the water that enters the soil and increased the soil moisture will later be consumed by the plant with a delay and transpired into the atmosphere. Moreover, it is not necessarily from the rootzone, some studies showed that plants' roots get most of the water from topsoil rather than deeper layers. Thus, the water that is once accounted as residual soil moisture will be later extracted by the plant root and then accounted for twice in the calculations.
3. L235-236 & L304-305: If the soil is over-irrigated then the surface soil will become saturated and SM will stay at a constant level. Consequently, it would not be able to reflect both soil moisture storage and ET fluxes change. Please comment on this. 

Minor:

1. Figure 2) There are some positive and negative residuals after calibration for the rainfed cropland that can propagate to the residual estimated over the irrigated pixels, how are these errors treated in your approach?
2. L193: Could you add a figure with 4 maps to the manuscript? Firstly add two maps derived from ET and soil moisture temporal stability analysis. Secondly, create an overlap map that combines ET and SM maps. Then compare it with an independent land use map that shows the rainfed and irrigated cropland and report how accurate was the rainfed cropland mapping. This step is crucial as the bias removal process is conducted based on the selected pixels from these maps.
3. L197: By calculating the MAE spatially at each time step, you won't have individual values for each pixel. Instead, there would be only 10 or 14 values for the calibrating parameters after optimization. However, wouldn't it have been more beneficial to have separate values for each pixel by calibrating for all the pixels during the non-irrigated period?
4. In equation 1, how time is considered in the calculation of BAE are you again averaging MAE for all time steps? If yes, please show that in the equation and also mention this in the text.
5. L205-210: I am having trouble understanding the steps described in L205-210. Are you implementing both model calibration through optimizing an objective function and rescaling by adjusting the model mean SM to match the satellite SM mean? Is rescaling necessary or has it already been accounted for in the calibration process?
6. L236: replace “it” with water
7. L270: what is the rootzone soil moisture data you used for calibration?, mention it here for RZ_SM_bf
8. Figure 4) I find it a little bit confusing to interpret the legend in Figure 4 legend. To enhance the legend clarity I suggest putting the ET and SM of each approach in individual boxes and labeling them with the corresponding approach names. This adjustment would make it easier to comprehend the legend. Additionally, the solid blue line is not explained in the figure caption.
9. L315-316: How can we ensure that storage of the water from the previous season is the primary reason for estimating a higher irrigation value compared to the benchmark and not an overestimation of irrigation by the model?
10. L325: Perhaps the reservoir is operating based on a relatively fixed plan, regardless of how much precipitation is received. Have you explored this possibility?