The use of the uncertainty quantification approach through the Last-Layer Laplace Approximation (LLLA) is a novel and much-needed addition to Digital Soil Mapping (DSM). Artificial Neural Networks (ANNs) are often overconfident, but this approach appears to mitigate that risk. The importance of uncertainty quantification in DSM is increasingly recognized. Nowadays, many people use machine learning algorithms without fully considering the risks of overfitting or overconfidence, which highlights the need for accurate uncertainty measurement, whether in interpolation or extrapolation purposes. Overall, I find the general concept of the paper to be quite interesting. However, it could be improved by providing more clarity and adding further details to the methodology section. The results and discussion sections are well written, but the readability would be enhanced if the authors more frequently referenced specific figures. I would recommend this paper for publication in EGU Sphere, pending minor adjustments.

The manuscript by Rau and co-authors addresses an important issue for the use of machine learning (ML) models for digital soil mapping, namely the problem of spatial uncertainty. They propose an approach based on a previously published approach combining neural networks (ANN), Bayesian learning and Laplace approximation. The advantage is that this approach informs on spatial uncertainty. The proposed approach is applied to soil classification in central Baden Württemberg in Germany.

The manuscript is well organized, and the presentation of the methods and results are clear. Yet, many aspects (listed below) remain unclear and even unjustified. They should be clarified and further elaborated before publication. Therefore, I recommend major corrections by incorporating, if possible, the following recommendations.

Main comments

1.    Position of the study

In several places in the main text, the authors refer to their previous work published in 2024. It is difficult to see the differences because in that work the authors also address the problem of uncertainty with ANN by combining it with techniques similar to those described in this new study.

Could the authors elaborate more on the differences with this study and on the originality of this new work?

2.    Definition of uncertainty

My second comment may be related to my first one. I am really confused about the type of uncertainty that the authors aim to tackle:

-    The authors underline that the proposed method addresses the problem of spatial uncertainty,

-    At line 155, the authors speak about model parameters and structural uncertainty similarly as the problem of tuning of machine learning models (e.g. Probst et al., 2019). 

-    The title suggests more a problem of data scarcity. 

-    The application case with two separate regions seems more related to a problem of transferability (e.g. Ludwig et al., 2023).

Could the authors clarify the notion of uncertainty that they intend to address? The introduction should be expanded on this aspect, and a discussion of the wide range of uncertainties is also welcome.

References:

Ludwig, Marvin, et al. "Assessing and improving the transferability of current global spatial prediction models." Global Ecology and Biogeography 32.3 (2023): 356-368.

Probst, P., Boulesteix, A. L., & Bischl, B. (2019). Tunability: Importance of hyperparameters of machine learning algorithms. Journal of Machine Learning Research, 20(53), 1-32.

3.    Protocol to address spatial uncertainty

If the main objective is to address the problem of spatial uncertainty, I would encourage the authors to carry out more experiments by varying the key factors of the problem: number of training samples, level of similarity between training and test regions, etc. Could the authors propose and carry out a more extensive series of experiments in order to demonstrate the robustness and effectiveness of their approach in a larger number of situations? 

Could the authors propose and carry out a more extensive series of experiments in order to demonstrate the robustness and effectiveness of their approach in a larger number of situations?

4.    Comparison to existing methods

From what I understand of the method proposed by the authors, the ANN is equipped with a final layer for predicting the probability of classification. This is a feature shared by many other techniques, i.e. logistic regression, decision trees, random forest, xgboost, neural networks with Monte Carlo dropout, neural networks combined with a deep set, generative models, and so on.

 

Could the authors elaborate more on the state of the art and discuss the benefits of their method compared to alternative methods?

Minor comments:

Line 55: the authors underline that the ANNs make predictions through complex internal processes that are difficult to understand and interpret. Here references to recent studies improving the interpretability of such methods for digital soil mapping should be added. 

Suggested references

Padarian, J., McBratney, A. B., and Minasny, B.: Game theory interpretation of digital soil mapping convolutional neural networks, Soil, 6,389–397, 2020.

Wadoux, A. M. J.-C. and Molnar, C.: Beyond prediction: methods for interpreting complex models of soil variation, Geoderma, 422, 115 953, 2022.

The results in Fig. 5 are very convincing. Despite the efficiency of LLMA, a long tail in the probability distribution still remains. I wonder whether this could be further alleviated with an extra calibration of the probability. See for instance Niculescu-Mizil & Caruana (2005).

Suggested reference

Niculescu-Mizil, A., & Caruana, R. (2005). Predicting good probabilities with supervised learning. In Proceedings of the 22nd international conference on Machine learning (pp. 625-632).