Comment on nhess-2021-119

The paper by Kanai et al. 2022 ‘Robust uncertainty quantification of the volume of tsunami ionospheric holes for the 2011 Tohoku-Oki Earthquake: towards low-cost satellitebased tsunami warning systems’ presents a new interesting statistical method to estimate the surface of the Tsunami Ionospheric Hole (TIH). The manuscript is well structured and described, and their method could help better understand the relation between the initial tsunami and the produced TIH. I recommend publishing the manuscript after considering the following general and minor comments.

The paper by Kanai et al. 2022 'Robust uncertainty quantification of the volume of tsunami ionospheric holes for the 2011 Tohoku-Oki Earthquake: towards low-cost satellitebased tsunami warning systems' presents a new interesting statistical method to estimate the surface of the Tsunami Ionospheric Hole (TIH). The manuscript is well structured and described, and their method could help better understand the relation between the initial tsunami and the produced TIH. I recommend publishing the manuscript after considering the following general and minor comments.

General comments:
It makes sense to show the results of the surface fitting in 3D in Figure 5. However, the uncertainty (confidence interval) is not illustrative in 3D. I suggest showing the uncertainty estimates for the fitted surface in 2D instead of 3D, like the visualization in panels (g) and (h).
The authors claim that their surface fitting method reproduces the shape of the TIH in the same region, almost like the initial tsunami source by Saito et al. (2011b). The authors should better specify to what extent (area, wave height) the shape is reproduced. Do uplift or subsidence areas of the initial tsunami match the TIH? In how far are TECu and vertical displacement in meters comparable? Does the TIH mimic the initial tsunami shape? Here the authors could visualize better by comparing the initial tsunami source by Saito et al. (2011b) directly with their results. How does it compare to the initial tsunami source presented by other authors?
The authors should show a couple of other random cases with sparse data for the surface fitting. It will be visually beneficial for their work to demonstrate that their method could enhance future warning systems. Since other randomly chosen datasets should deliver similar results, the authors should demonstrate it in a figure.

TIH overlapping the initial tsunami:
The representation of the initial tsunami is problematic. It is not clear how the authors have chosen the sea-level threshold value to define the area of the initial tsunami. The authors should represent the initial tsunami wave in m concerning the sea level of the event. Tsunamis may contain depression and elevation features in the wave field, which must be shown in the figure. There are many published source inversions for the 2011 Tohoku-Oki tsunami source, and the authors should compare the TIH to other published source inversions (e.g. Ammon et al. 2011, Wei et al. 2012, Yue and Lay 2013; otherwise, it seems they have chosen Saito et al. (2011b) that fits best to their results.
Moreover, it is essential to explore how the TIH overlaps the initial tsunami. The initial tsunami wavefield values should be compared directly to the TEC values.
On page 18, line 359, the authors claim that their method can estimate the tsunami region but the authors only use the Tohoku-Oki event. Before they can draw this conclusion, their method needs verification with other real cases. Moreover, it is not clear to the reader which TECu value (-2, -3) should be used to define the area of the initial tsunami. Is the same TECu value applicable for other tsunami cases?

Minor comments:
Page 3, line 56: Please define TECu the first time it appears in the text.