many thanks for adressing my comments and for revising the manuscript. However, some of your answers are not really to the point or are not reflected in the revised text.
I previously asked how well the simulated biomass captures observed biomass(e.g. remote sensing estmiates) as any biases in modelled biomass will cause errors in the simulation of fire. The authors responded to this question by comparing a global total estimate of biomass (Figure S6). This comparison is not meaningful because a global total biomass can originate from various regional patterns of biomass. I request to make a proper evaluation of the simulated biomass by e.g. comparing a map of simulated biomass with a map of observed biomass and making a difference map (e.g. Biomass CCI dataset). This will allow assessing if regional biases in simulated biomass (and hence other fuel properties) might cause biases in the simulation of burned area. Ultimately, it is completley unclear how such an differences would affect the simulations in a coupled model.
In the response it is written that "we tuned the DNN-Fire surrogate model towards ensemble mean with standard deviation across 14 GFED regions" which implies that the standard deviation was considered in the tuning. However, the standarad deviation of burned area is not included in the used cost function in equation 8. This needs to be clarified.
Figures 4 and S7: Some of the symbols/colours are used for two regions and hence cannot be distinguished (e.g. BONA and CEAS). The colours, symbols and legends need to be revised.
The analysis of the sensitivity of the results to different forcing data is interesting as it reflects actually a strong influence of the forcing data on the simulation result. In order to identify the most reliable forcing data a comparison with the observed burned area and biomass would be insightful. Which forcing dataset results in model simulation closest to the observations?
Figure S5: To make the plot more clear, it would be usefull to include the 1:1 line each panel.
Lines 360-370 are not clearly written and some sentences are repetitive. Please revise.
Figure 7 looks fuzzy and the colours are difficult to see.
Lines 101-102: "Although explicit processes are simulated, the accuracy of process-based wildfire models
are highly dependent on parameterization, which is computationally expensive" - This statement is mis-leading as indeed most process-based wildfire models like the models within FireMIP actually were never parametrised using computational approaches. Parameters were rather taken from literature sources during model development. A proper calibration of process-oriented models, i.e. by using a cost function and optimization algorithm was rarely done and otherwise the computation time is comparable to the time needed for the building and training of neural network models.
Finally, I'm not really convinced by the study. Although you can nicely demonstrate that the DNN can 1) reproduce the simulated burned area of the Earth system model and 2) it also captures regional total burned area from observations, the study does not contribute to an improved "understanding of human, climate, and
ecosystem controls on fire number, fire size, and burned area" (as motivated in the abstract). As the DNN models are only trained against burned area, no statements about number and size of fires can be done. Furthermore, the ecosystem controls are mostly represented by the input variables tree cover and biomass. As tree cover is always described from an input dataset and biomass is used from the base simulation, the DNN models are actually inconsistent because they have been trained gainst different sources and magntiude of burned area (but always using the same magnitude of tree cover and biomass!). As fire has a clear reducing effect on tree cover and biomass (Lasslop et al. 2020), it is obvious that the relation between fire, biomass and tree cover sis actually inconsitent in some DNN models because the spatial patterns of biomass and tree cover do not correspond to the patterns of fire. Hence the approach cannot give meaningful insights on how ecosystem controls affect fire and I am not convinced that this can be transfered to a coupled model.
The abstract and discussion needs to be revised in order to make this limiation clear.