Review of the paper “Computing time-dependent activity rate using non-declustered and declustered catalogues. A first step towards time dependent seismic hazard calculations for operational earthquake forecasting” by David Montiel-Lopez et al. (egusphere 2023-2819).

In this paper the authors propose a methodology that includes a spatially-gridded time-dependent bvalue and activity rate in PSHA calculations. They apply this methodology to central Italy  and to south-eastern Spain, comparing three different models based on different choices of the parameters considered in the calculations (distance from spatial cells to faults and epicentral distance uncertainty), and calculated the changes of the annual probability of exceedance for a given background PGA value. The results show variations of the annual probability of exceedance related to the occurrence of moderate-large magnitude events. The paper includes also an analysis of the relevance of using declustered or non-declustered catalogues in the PSHA calculations. The authors claim, but they don’t justify in reliable way, the relevance of their study in the context of Orerational Earthquake Forecasting.

Among a number of points that need clarification, as described in the annotated manuscript, this paper needs a detailed discussion of the results concerning the changes of the probability of exceedance. Are these changes due to the occurrence of foreshock activity before the mainshocks or are they simply consequences of aftershock activity, without any relevance for OEF? Moreover, why the occurrence of mainshocks sometimes produces increase and sometimes decrease in the probability of exceedance?

I recommend the publication of this paper after a careful revision of the text, including the English language.

The manuscript, entitled ' Computing time-dependent activity rate using non-declustered and declustered catalogues. A first step towards time dependent seismic hazard calculations for operational earthquake forecasting,' introduces various models for earthquake forecasting and seismic hazard assessment. After reviewing the manuscript, I have several concerns and suggestions to share concerning its content. Below are my detailed comments:

Major concerns:

The Italy case not discussed: The abstract and various sections of the manuscript mention the application of this approach to the L’Aquila, Italy, case. However, I am unable to find any corresponding results or discussion.

Definition of smoothing kernel: In this study, the smoothing kernel is determined by the average distance between all events surrounding an earthquake and the precision of the epicenter's location (Lines 68-70). When defining the second moment of the distribution (Sec. 2.1.2), this parameter is solely attributed to the precision of the earthquake epicenter measurement. However, I anticipate that the distance between all events is equally important for this parameter.

Completeness magnitude: Based on my interpretation of Table 7, it appears that the magnitude range indicated in the top column has been complete from the year specified in the bottom column. Therefore, it should be that magnitudes of 3.0 and above are complete since 1978, rather than starting from magnitude 3.25 as stated in Lines 277-280. Additionally, the completeness magnitude typically decreases with upgrades to the seismic network, as such improvements generally enhance detection capabilities. It is customary for the completeness magnitude to remain stable for approximately a decade before decreasing sharply with a network upgrade. The gradual increase in the average completeness magnitude observed in Table 8 is unexpected. An explanation for the trend of decreasing completeness magnitude would be beneficial.

Model validation: Based on the results presented for the three models concerning both annual and monthly variations in the change of exceedance probability (as seen in Figures 12 and 13 and discussed in Lines 335-337), the authors assert that Model 1t outperforms the others. However, discerning significant differences is challenging, whether in the monthly variations of the relative change in annual probability of exceedance (Figure 12) or in the annual variations of the same (Figure 13). Moreover, I question the approach of basing model validation solely on 'greater changes before and after selected earthquakes' without incorporating statistical analyses. I believe that a more rigorous statistical evaluation is necessary to substantiate the claimed superiority of Model 1t.

Minor Comments:

- Figure 1 caption: Please provide clear definitions for each symbol and color used.

- Lines 159: I am not quite sure if equation (7) is essential.

- Line 182: Revise ‘time-dependent’ as ‘stability’.

- Figure 3 caption: Is the tectonic b-value obtained by EHSM20 or by this study?

- Figure 4 caption: Please provide clear definitions for the dashed line.

- Table 6: The effectiveness of the declustering approaches can be assessed with a confusion matrix, which provides not only the number of events but also the counts of true positives, true negatives, false positives, and false negatives.

- Figures 14 and A1, Lines 370-372: Why is there an increase in the expected hazard and rate in Vera? Does this suggest that a large earthquake is anticipated in the future? An explanation based on the data and/or methodology used would be helpful.

Chung-Han Chan, National Central University, Taiwan, February, 2024.