We thank the anonymous referee for the interesting and insightful comments about our work. We would like to post a few comments on some of the points, in order to have better clarifications as long as the interactive discussion is available.

1 In the Introduction section, it is unnecessary to elaborate extensively on tide gauges because they do not have much significance in tsunami detection. Instead, the focus should be on offshore observations. For instance, I suggest categorizing OBPG systems; those use cable for signal transmission, while others use sonar (DARTs). Additionally, the author could discuss GPS buoys.

Although we do think that tide gauges can be important for detection, e.g. in the case of late arrivals or to alert further away coastal areas, they do not have any role in the present work, thus we will modify the text, following your suggestions

2 In the application of real-time tsunami detection, the computational speed of algorithms is also crucial. I suggest the authors discuss the computational efficiency of these methods and whether they can rapidly produce results.

All the algorithms are already fast enough to be used in real time, i.e. the computational costs for each time step is shorter than the sampling time of the instruments. Nonetheless, we understand the need for a more detailed analysis which we will add to the paper.

3 When DART records sea surface elevation data, significant deviations can sometimes occur. I would like the authors to discuss how to address such situations.

What is asked in this point is not clear to the authors. Thus, we kindly ask for further clarifications.

4 In Line 105, I disagree with this viewpoint; even within the same bay, due to tsunami resonance, long-period signals can exhibit significant differences at different locations.

This is in fact not a general statement, but it is experimentally valid for the EOF detiding as claimed by Tolkova (2009, 2010). We will specify more clearly the origin and scope of validity of the statement.

5 Regarding FTF-based decomposition, what causes significant false signals to appear before the arrival of a tsunami (Figure 2c)? How can this be avoided?

The appearances of this oscillations before the real disturbance in the decomposition is related to the loss of causality intrinsic in signal decomposition techniques. This is not exclusive to IMF decompositions, since it can be observed also in the case of classical Fourier trigonometric series and it can be observed in Fig. 18 and 19 of the work by Tolkova (2009).In the specific case, the presence of a "spike" at the end of the signal is the specific cause of these oscillations. By summingthe components within a not too narrow frequency band, their effect is cancelled out, as shown in Fig. 3c.

6 In Line 274, how is the post-processed waveform obtained? Please provide a detailed explanation.

The post-processed waveforms are taken directly from the material provided by Davies (2019). An explanation of how they are obtained will be added to the paper.

We thank the anonymous referee for the interesting and insightful comments about our work. 

In the following, we would like to answer the comments and suggestions from the referee.

With respect to the previous reply, here we addressed all points raised by the referee, while some minor ones were not addressed in the previous reply.

1 In the Introduction section, it is unnecessary to elaborate extensively on tide gauges because they do not have much significance in tsunami detection. Instead, the focus should be on offshore observations. For instance, I suggest categorizing OBPG systems; those use cable for signal transmission, while others use sonar (DARTs). Additionally, the author could discuss GPS buoys.

- Although we do think that tide gauges can be important for detection, e.g. in the case of late arrivals or to alert further away coastal areas, they do not have a specific role in the present work, thus we will modify the text, following your suggestions

2 In the application of real-time tsunami detection, the computational speed of algorithms is also crucial. I suggest the authors discuss the computational efficiency of these methods and whether they can rapidly produce results.

- All the algorithms are already fast enough to be used in real time, i.e. the computational costs for each time step is shorter than the sampling time of the instruments. Nonetheless, we understand the need for a more detailed analysis which we will add to the paper.

3 When DART records sea surface elevation data, significant deviations can sometimes occur. I would like the authors to discuss how to address such situations.

- The point is not clear to the authors. If the referee is referring to deviations of the pressure record from the shallow water

regime, a topic which is gaining more attention after the 2022 Tonga tsunami, we point out that we do not address the problem.

Our analysis is based on the application of the four techniques to detect anomalies in the pressure records, as if the technique

was in real-time on the instrument. Each pressure value is expressed in meters through the hydrostatic equivalence for easier 

interpretability of the results. However, since the present paper has applications only to tsunamis of tectonic origin, we can 

assume the hydrostatic approximation to hold.

Nonetheless, further clarification on the point would be appreciated.

4 In Line 105, I disagree with this viewpoint; even within the same bay, due to tsunami resonance, long-period signals can exhibit significant differences at different locations.

- This is in fact not a general statement, but it is experimentally valid for the EOF detiding as claimed by Tolkova (2009, 2010). We will specify more clearly the origin and scope of validity of the statement.

5 Regarding FTF-based decomposition, what causes significant false signals to appear before the arrival of a tsunami (Figure 2c)? How can this be avoided?

- The appearances of this oscillations before the real disturbance in the decomposition is related to the loss of causality intrinsic in signal decomposition techniques. This is not exclusive to IMF decompositions, since it can be observed also in the case of classical Fourier trigonometric series and it can be observed in Fig. 18 and 19 of the work by Tolkova (2009).In the specific case, the presence of a "spike" at the end of the signal is the specific cause of these oscillations. By summing the components within a not too narrow frequency band, their effect is cancelled out, as shown in Fig. 3c. We will add a comment in this regard in the revised manuscript.

6 In Line 274, how is the post-processed waveform obtained? Please provide a detailed explanation.

- The post-processed waveforms are taken directly from the material provided by Davies (2019). To remove the tidal component a LOWESS filter was applied. An explanation of how they are obtained will be added to the paper.

Other minor comments:

1 Figure 1: Please add the unit to y-axis

- Being a basis set, the computations do not change if the vectors are multiplied by an arbitrary constant. For this reason, a unit of measurement is not strictly necessary. The same holds for the plot ranges.

Nonetheless, we see that in the present state, the text and this figure may be disorienting. So the suggestions about the plot will be implemented and an explanation about the arbitrariness of amplitude of these vectors will be added to the text.

2 Line 190: Do you refer to ‚“exclude detiding procedures”? Any typo?

-  Here, we refer to the tsunami detection tecniques described along the manuscript. We will rephrase for improved clarity.

3 Line 322: ‚“much better then” -> “much better than”

- The text will be corrected. 

We thank the anonymous referee for the thorough and insightful comments about our work. In the following, we would like to briefly respond to some selected points, in order to receive further feedback, if the referee deems it appropriate. It is implied that any other comment is accepted and all corrections will be implemented in the final version of the paper.

Major comments:

2 The work will benefit greatly by comparing computational costs of each of the four algorithms. A robust method that takes up too much time defeats the purpose of real-time detection. The authors say the algorithms are efficient, but it should also be shown. This addition would make the paper more impactful.

Each technique is fast enough to be used in real time, i.e. the computational costs for each time step is shorter than the sampling time of the instruments. Nonetheless, we understand the need for a more detailed a quantitative analysis which we will add to the paper.

3 Background noise should be done for the same time periods rather than at differing times. This leaves the DART stations open to misrepresented background values that may be influenced by meteorological and oceanographic phenomena. All 5 DARTs studied here have overlapping data at the same times with multiple tsunami detections in those times. Without accounting for these features, it makes the research less impactful, as it remains unclear if differing conditions favor different detection algorithms.

1 The manuscript should add the New Zealand DARTs, as they provide a good dataset for the Southern Pacific.

The major difficulty for the analysis of overlapping time series in different DART is finding portions of data as close to "ideal" as possible to reduce the influence of other factors. In particular, as specified in the paper, we want weeks long time series with no seismic shaking, no tsunami signal, no discontinuity, no holes in the data and enough preceding data to compute accurate tidal coefficients for TDA. This last point is the most critical. Nonetheless, the suggestion is very interesting and on point. We will find overlapping signals in conditions as close as possible to the criteria explained above and we will add the analysis to the paper.

Minor comments

17 Line 361: Authors should consider posting FIR filter coefficients and EOF scripts as they were calculated using MATLAB with examples to ensure correct application. I was able to check everything else; however, good scientific coding practices dictate that even if native functions are used that they be viewable to ensure correct application of them.

The codes for both of them are very simple and only use basic MATLAB functions. All the informations needed for the implementation are present in the paper. Nonetheless, the codes will be added either as Supplementary Material or as listings in a dedicated appendix.