Review:

The study uses different statistical metrics (referred as hydrologic signatures) like annual median, coefficient of variations (at different timescales) and use them to compare evapotranspiration derived using two remotely sensed products (MODIS and CMRSET) with observations from 17 flux tower sites across Australia.

While this study reports important biases in remote sensing products with observations, it severely lacks in the interpretation of the comparisons and the application of different metrics. As a result, I would recommend a major revision for the manuscript to be publishable in HESS.

Comments (below) are provided in sequential order.

Comments: 

C1: Line 44 – 45: I would disagree with this statement. Understanding changes in AET is a well-researched (and ongoing) subject. I don’t think the right motivation for this paper is that statistical metrics like (annual median, coefficient of variations) have not been used to study AET before. Rather I suggest authors motivation should be on comparing and interpreting the remotely sensed evaporation estimates with Flux tower data, the reasons which can lead to discrepancy between them and the use of hydrologic signatures in understanding those biases.

C2: Line 170-174: It will be useful to also have Morton’s equation to estimate potential evaporation written here.

C3: Figure 3b: There should be some discussion/explanation about why coefficient of variation (interannual variability) is high in dry regions irrespective of dataset. Does it relate to the interannual variability in rainfall/net radiation/PET over these sites?

C4: In addition to coefficient of variation at inter-annual scale, maybe it will be helpful to also compare absolute deviations at annual scale, report it and keep it in supplement.

C5: Line 213: I am confused about what is meant by CMRSET shows minimal bias? Do you mean spatial variability in lag-12 auto-correlations are low? 

C6: Figure 4: This is an important figure which depicts the difference in seasonality and phase lags in season peaks between remotely sensed data and flux tower observations. But there is no interpretation about what does this imply? My intuition is that this may likely relate to the vegetation parameterizations and surface water stress in remote-sensing derived AET products. However, it is clear that aridity index (defined at long timescales) does not explain these variations either with flux-towers or the remotely sensed data. I suggest authors to look at periodicity and phase lags in surface water-stress if they explain these effects.

C7: Similar to C3, there shall be some discussion/explanation of why coefficient of variation (at monthly scale) shows a variation with aridity.

C8: I don’t think signature 8 (Index of AET responsiveness to a rainfall event) is a robust metrics. The results presented in figure 6 don’t support it either. The response of AET to rainfall will be affected by many confounding factors like water availability, energy availability, land-cover type and seasonality. For e.g, a summer time or winter time rainfall can have very different effects on AET due to differences in net radiation (energy availability). The cloud radiative effects associated with rainfall will also be different across seasons. The presence/absence of vegetation can also significantly alter surface water-stress conditions through water-channelling mechanisms like root systems. A better way to diagnose this effect could perhaps be to first link changes in rainfall to antecedent hydrologic condition like surface water-stress and then look at their response to AET.

C9: For each figure, there should be some quantitative measure of consistency like Rsquared or RMSE with respect to observations for both MODIS and CMRSET. This would help assess which dataset performs better for each hydrologic signature.

C10: It may be useful to analyse if the biases between flux tower observations and remote sensing derived estimates shows a variation with vegetation type for different hydrologic signatures.

C11: Section 4.2: This section is more of a repetition/summary of results rather than insights.

C12: Line 334 – 335: This is not demonstrated in the manuscript rather argued qualitatively. Refer to comment C9.

C13: Line 351: The current version of the study compares hydrological signatures but does not provide comprehensive insights into AET dynamics.

Minor:

Line 19: AET_Rs instead of RS_AET to be consistent.

Line 213: suggest to change “minimal” to “reduced”

Figure 7: Legend missing for MODIS AET

For all the figures it may be helpful to have a legend depicting color scale of aridity index (humid – blue, arid – red) or an arrow beside the colormap.

General comments

The paper introduces actual evapotranspiration signatures at different temporal scales (annual, seasonal, monthly, and event-based), similar to hydrological signatures, for example. The signatures include among others interannual variability, the timing of seasonal peaks, water stress, and responsiveness to rainfall events. The authors use them to compare actual evapotranspiration data from 17 Australian flux towers with data from two different remote sensing products. They conclude that CMRSET performed better than MODIS 16A2GFv061 in matching flux tower data and highlight the utility of signatures in selecting appropriate remote sensing products.

The manuscript is generally well-written, facilitating the clear understanding of the authors' main points. The authors present an existing approach of defining specific signatures in a new context (actual evapotranspiration). The signatures are similar to those used in the hydrological context. Three applications of these signatures are mentioned, and the authors test one of them (comparing flux tower data with remote sensing products) to demonstrate applicability. While the idea is promising and the application useful, the study lacks depth in presenting the results, especially in the discussion section. There is more potential in the comparison of the signatures of flux tower with those of remote sensing products that should be explored further.

Two three points I would like to point out:

• The results section frequently contains interpretations, which should be moved to the discussion section This would allow for a more detailed and in-depth exploration of the signatures in the discussion.
• The discussion section lacks depth and further evaluation of the results. Additionally, it would benefit from better contextualization within the existing literature, as there are very few references cited. Some of the points mentioned in the introduction could be expanded upon. I elaborate on this in the main comments.
• The title reflects one of the three potential applications of AET signatures mentioned in the manuscript, however, it does not really align with the application being tested (comparison of remote sensing and flux tower data). I suggest removing “for improved behavioral insights” from the title and including the comparison aspect instead.

Specific comments

• L. 32: Add the literature reference.
• L. 36: Araki et al., 2022 is not a modelling study. They apply signatures to observed time series. McMillan, 2021 is a review paper including both modelling and observed data.
• Figure 1: Do the colors of the locations indicate the aridity index as in figure 2? It should be explained here, too, and a legend included.
• L. 40: “hydrological processes” should be replaced with “hydrological variables” or similar, because streamflow, soil moisture and groundwater are not processes.
• L. 44: I wonder if “surprising” is appropriate here. In general, signatures are simply one of many methods to analyze data. Some of the suggested signatures have been previously used (e.g. median) to analyze data, though they were not refer to by that term. While I think it’s valuable that you introduce and test AET signatures, I would suggest placing less emphasis on the “surprising” aspect.
• L. 78: Refer to table 1.
• L. 96: I suggest removing “these” for better readability.
• L. 102: The asynchronicity signature is not completely clear to me. Since you are working with monthly timeseries here, you are looking at differences in the yearly cycles of AET, aren’t you? Since you normalize the curves you are not interested in the “height/amplitude” of the signal but are looking at the timing? What is the advantage of this signature over something like lagged correlation? Wouln’t it be helpful to use a signature, where you receive for example also the magnitude of the shift, i.e. the phase shift between two signals?
• Table 1: You could name signature 8 only “AET responsiveness to rainfall event” without the “index of”.
• L. 200: I agree that the spatial footprint plays a role in AET signatures. However, does a sensitivity of a flux tower to the position within the landscape relate to the deviation between AET_Fluxtower and AET_RS with aridity? You mentioned that RS understimate AET_annual for less aridity. If I understand this correctly, this would imply that all flux towers in dry areas were placed in locations that lead to an underestimation and wetter areas in locations that lead to an overestimation. Or is it that in dry regions the landscape is often less heterogeneous as in wet regions? If would be interesting if you could expand on this a bit more in the discussion.
• L. 203: The remaining sentence after “implying” is interpretation and should be moved to discussion.
• Figure 2: x-axis is years not months. The legend is very small and CMRSET and MODIS are hard to differentiate in the plots. I miss some sentences on figure 2 except for the introduction at the beginning of the results section. Maybe you can point out some things you want to demonstrate with these plots.
• Figure 3 and 4 (and others): I suggest adding an R² or similar to give some quantification of the correlation between signatures of flux towers and remote sensing. A legend for the aridity index is missing. It is a bit cumbersome to look it up in table 1.
• L. 219: “This results…” interpretation -> discussion
• L. 241: “…perhaps suggesting…” interpretation -> discussion
• L. 250: “…perhaps suggesting…” interpretation -> discussion
• L. 283: In this section, I would expect a more thorough discussion of the method introduced. Table 3 is a nice summary comparing visual dynamics with signature results, but it is barely touched upon in the text. If evaluating a new method or an existing method in a new context, I would expect some comparisons of how this method is performing as opposed to other methods from your own results but also how it compares to literature. For example, you mention in the introduction that signatures are being used in other disciplines or with other variables. Are there studies that show how this improved over using NSE/KGE? Are there studies that do a similar comparison as you did with visual inspection vs. signatures? What is the advantage/disadvantage of the signatures over other methods? What are the strengths/weaknesses? …
• L. 297: This is a nice introduction to pick out one or two concrete examples from above to illustrate how NSE/KGE do not deliver as much detail as the signatures. It would help in supporting the drawn conclusions later on.
• L. 303: This section sounds more like a listing of the results. From the header I would expect more on the AET behavior. What do you learn from the signatures on AET behavior? How do your results compare to other studies that looked at AET in Australia? How reliable are the flux tower data? Were they tested for energy balance closure? …
• L. 360: MODIS and CMRSET miss units (probably mm) and a short readme as in the flux tower data would help.
• L. 338: You conclude that both MODIS AET and CMRSET have issues with seasonality, right (offset in MODIS AET and scatter in CMRSET)? What could be reasons for this?

Technical corrections

• L. 18: AET_RS?
• L. 28: “across space AND TIME”
• L. 84: Parentheses and “&” should be “…such as Clausen and Biggs (2000)”
• L. 134: “measurements” or “measurement device”/”measurement equipment”
• L. 155: The abbreviations are not used anywhere in the manuscript again, so no need to introduce them here.
• L. 195: “m” instead of “meters”
• L. 208: Here it is “autocorrelation” and in figure 4a “auto-correlation”.
• L. 356: “before they are adopted”