Review of “Brief communication: A magma depletion alternative for vent distribution in volcanic fields”

The authors present novel kernel density estimation approaches which adopt volume-dependent annular-shaped kernel functions and inverse-volume weights. The methods are tested on the Auckland Volcanic Field (AVF) vent opening dataset, of which the authors are worldwide experts. Fitting performances of the new methods are compared to a more classical isotropic Gaussian kernel estimation method in terms of log-likelihood and AIC. The authors claim that only one of the three new methods produces a better fitting that an isotropic Gaussian kernel in terms of AIC.

The manuscript is well written, Maths is correct and clear, and the topic is interesting and new. However, results are not yet convincing. Additional testing on other datasets and against other kernel approaches would be advised to complete the study.

MAIN COMMENTS

1. ERUPTED VOLUME UNCERTAINTY
   
   The authors should acknowledge that in the majority of volcanic fields a great percentage of erupted volumes are uncertain (or unknown). In fact, all the presented methods depend on past erupted volume and therefore depend on the quality of volume estimates, and cannot be applied when the volumes are not available. The effects of the uncertainty on the volume estimates at AVF should be evaluated and, if possible, considered in the likelihood estimates.
2. ANISOTROPIC GAUSSIAN KERNELS AND OTHER PRE-EXISTING METHODS
   
   New methods performance should be tested against other well-performing kernel methods, and not only an isotropic Gaussian. Many other approaches have been already tested on the AVF and can be found in references. It would be interesting to compare the volume-depletion family against a broader list of pre-existing methods.
3. VENT CLUSTERS AND POLYGENETIC ERUPTIVE CENTERS
   
   The idea of volume depletion is interesting but conflicts with commonly observed clustering trends and polygenetic centers. Therefore, the method may behave badly for calderas and volcanic fields that are not monogenetic. Testing the methods on other published vent opening dataset could be useful to understand its robustness.
4. DISCONTINUOUS KERNEL FUNCTIONS
   
   The disk-based depletion method is based on kernel functions that are not continuous. Their jumps appear in the convolution results in Figure 2, and create an unrealistic “bubbly” appearance, regardless of its better AIC score. Could you make it smoother without decreasing performance?
5. WHY INCLUDING A BAD PERFORMING METHOD
   
   The distance-multiplied method behaved poorly and I am not convinced of its usefulness in the manuscript.
6. MISSING REFERENCES
   
   I acknowledge the limitation to 20 references, but I suggest to improve the reference list.
7. MISSING COORDINATES
   
   Please indicate the coordinates and projection of the vent opening data in S3 and clarify their literature source(s) in the caption.

This paper provides a valuable conceptual and methodological contribution by proposing a magma depletion-based alternative to standard kernel density estimation (KDE) for vent forecasting in volcanic fields. It is especially commendable for challenging the entrenched assumption that “more vents = higher likelihood,” and it offers an implementable framework with code and validation using the Auckland Volcanic Field.

Such contributions are essential for fostering open-mindedness in the scientific community, particularly in probabilistic volcanic hazard modeling, where epistemic uncertainties remain high.

To strengthen the study, it is important to acknowledge and address several key limitations:

1. Dimensionality Oversimplification

The models are inherently two-dimensional, whereas magma ascent and storage processes are fundamentally three-dimensional and evolve over time. This affects how spatial depletion is conceptualized and operationalized. Realistic modeling should account for vertical magma propagation, source region geometry, and the temporal dynamics of recharge and depletion.

2. Geochemical and Structural Constraints

Previous work (e.g., Le Corvec et al., 2013 https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/ggge.20223) has shown that closely spaced vents in monogenetic fields often share geochemical signatures, suggesting overlapping or connected magma sources rather than isolated zones subject to simple local depletion.

Additionally, Rangitoto’s complex and polygenetic eruptive history (e.g., McGee et al., 2011 https://link.springer.com/article/10.1007/s00410-011-0611-x) challenges the assumption that each eruption entirely depletes a discrete source.

3. Vent Clustering and Eruption Grouping

The treatment of each vent as an independent event may misrepresent eruptive behavior in cases where multi-vent eruptions or spatial clustering occur. Grouping vents into eruption events prior to modeling may be necessary to avoid overestimating spatial depletion.

Conclusion

This work is a welcome methodological advance that opens new avenues for spatial vent forecasting. It is suitable for publication pending minor revisions that acknowledge the dimensionality of the magmatic system and the temporal dynamics of source replenishment.



Nicolas Le Corvec