Status: this preprint is open for discussion and under review for Earth Surface Dynamics (ESurf).
From XRD signal to erosion rate maps
Fien De Doncker,Frédéric Herman,Bruno Belotti,and Thierry Adatte
Abstract. Understanding the spatio-temporal dynamics of suspended sediment source activation is essential for effective ecological management, risk assessment, and infrastructure planning. Provenance analysis, which traces sediment origins, plays a crucial role in these applications, but is often based on costly fingerprinting methods. In this study, we validate a time- and cost-effective fingerprinting approach based on X-ray diffraction (XRD) data. We implement and compare two non-linear inversion schemes (steepest descent and Quasi-Newtonian) applied to binned XRD data and spatial information on potential source areas, in order to invert detrital mineralogical data into erosion rate maps while quantifying posterior uncertainty and error propagation. Forward-inverse tests with synthetic data demonstrate consistent convergence of the posterior solution. The application to real-world datasets further validates the practical utility and robustness of the model.
Received: 23 Sep 2025 – Discussion started: 06 Oct 2025
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.
DeDonker et al. present a novel and ambitious inverse methodology to infer maps of erosion rates from mineralogical data derived from XRD analysis of suspended sediments. Their method defines a model matrix, which uses bedrock mineralogy data also from XRD analysis and a geological map to characterise the catchment, and then uses a non-linear inversion to infer erosion rates based on the mineralogical data of the suspended sediments. They provide a thorough analysis of the inversion method, including testing two different inverse schemes, as well as testing a wide range of various parameter values to explore their limitations. Having done this, they then apply their method to the Gornergletscher catchment, presenting an erosion rate map for the area. Generally I found the manuscript to be well written, and will likely be suitable for publication following some further exploration/explanation of the limitations of the inversion.
Firstly, I think the authors do an excellent job of acknowledging and testing many of the limitations of the inversion, and so I commend them for this. However, I found some of the presentation of the scatter plots in figures 7-10 to be slightly unintuitive. It would be really helpful, perhaps in a supplement, or alongside these figures, that the resulting erosion rate maps of the synthetic tests are shown. Of course, it would be nice to see all of them, but perhaps 3 for each parameter tested would aid the reader in understanding how different the inversion result can be. For example, what do the three erosion rate maps look like for the three different geological map inputs? Perhaps the results are very similar, but at the moment, it is difficult to infer how much variation is possible for the model results based on different inversion parameters being changed.
On this note, I perhaps would also like to see a more complex synthetic test set up than the one presented. Something akin to a checkerboard test might be ideal, or a scenario where there are more than one peak in erosion rate. From what I can tell, the present synthetic test has high erosion rates across two similar lithologies (Stockhorn-Turftgrat-Gornergrat and ZSF ophiolites?), and low rates elsewhere. This is quite a simple set up. Would the inversion scheme be able to identify two different peaks of erosion that are spatially discrete within these two units? What about three peaks spread out across the catchment? Hence, I would like to see a slightly more complex synthetic erosion rate map tested. Having said this, I did like the testing of two different inversion schemes on the synthetic data to decide which one is more suitable – nice analysis.
Finally, I felt that the XRD data needed explaining a little better and perhaps slightly more exploration of the associated errors. For instance, the number of bedrock XRD analyses is not stated. I wondered whether if only one per lithology were analysed, how different two samples from the same lithology could be, and how much error this could introduce? If only one is used per lithology, is the assumption that each mapped lithology is homogenous fair? From what I can tell from the unit descriptions they can be quite variable. How is this variability accounted for? Hence, I would like to firstly see greater detail given for the acquisition of XRD data and mineralogy data, and perhaps some exploration of inversion results akin the analysis presented in figure 8 for an error introduced when the measured bedrock mineralogy is different from the true bedrock mineralogy. Here you could synthesise a sediment mineralogy based on one set of bedrock mineralogies, and then randomly change each mineralogy in the A matrix by some value of the ‘error’. I am not sure whether this is reasonable or not however, as I am not an expert in XRD, and I am not sure how the bedrock XRD data was collected.
One final comment, the introduction is duplicated. One needs to be removed, and the section numbers redone.
I hope the authors find these help to improve the manuscript. I also outline a few line comments below.
Line 61 – Should be an in-text citation.
Line 270ish Gorner-gletscher then gornergletcher, needs to be consistent throughout the manuscript.
Sediments carried by rivers can damage infrastructure, affect ecosystems, and alter landscapes, yet it is often unclear where these sediments come from, especially in regions hidden beneath ice. We developed a simple way to trace their origins by shining X-rays on crushed rocks and sediments. The resulting X-ray signals act like fingerprints that can be matched to source rocks, revealing where sediments come from and allowing us to map erosion across landscapes.
Sediments carried by rivers can damage infrastructure, affect ecosystems, and alter landscapes,...
DeDonker et al. present a novel and ambitious inverse methodology to infer maps of erosion rates from mineralogical data derived from XRD analysis of suspended sediments. Their method defines a model matrix, which uses bedrock mineralogy data also from XRD analysis and a geological map to characterise the catchment, and then uses a non-linear inversion to infer erosion rates based on the mineralogical data of the suspended sediments. They provide a thorough analysis of the inversion method, including testing two different inverse schemes, as well as testing a wide range of various parameter values to explore their limitations. Having done this, they then apply their method to the Gornergletscher catchment, presenting an erosion rate map for the area. Generally I found the manuscript to be well written, and will likely be suitable for publication following some further exploration/explanation of the limitations of the inversion.
Firstly, I think the authors do an excellent job of acknowledging and testing many of the limitations of the inversion, and so I commend them for this. However, I found some of the presentation of the scatter plots in figures 7-10 to be slightly unintuitive. It would be really helpful, perhaps in a supplement, or alongside these figures, that the resulting erosion rate maps of the synthetic tests are shown. Of course, it would be nice to see all of them, but perhaps 3 for each parameter tested would aid the reader in understanding how different the inversion result can be. For example, what do the three erosion rate maps look like for the three different geological map inputs? Perhaps the results are very similar, but at the moment, it is difficult to infer how much variation is possible for the model results based on different inversion parameters being changed.
On this note, I perhaps would also like to see a more complex synthetic test set up than the one presented. Something akin to a checkerboard test might be ideal, or a scenario where there are more than one peak in erosion rate. From what I can tell, the present synthetic test has high erosion rates across two similar lithologies (Stockhorn-Turftgrat-Gornergrat and ZSF ophiolites?), and low rates elsewhere. This is quite a simple set up. Would the inversion scheme be able to identify two different peaks of erosion that are spatially discrete within these two units? What about three peaks spread out across the catchment? Hence, I would like to see a slightly more complex synthetic erosion rate map tested. Having said this, I did like the testing of two different inversion schemes on the synthetic data to decide which one is more suitable – nice analysis.
Finally, I felt that the XRD data needed explaining a little better and perhaps slightly more exploration of the associated errors. For instance, the number of bedrock XRD analyses is not stated. I wondered whether if only one per lithology were analysed, how different two samples from the same lithology could be, and how much error this could introduce? If only one is used per lithology, is the assumption that each mapped lithology is homogenous fair? From what I can tell from the unit descriptions they can be quite variable. How is this variability accounted for? Hence, I would like to firstly see greater detail given for the acquisition of XRD data and mineralogy data, and perhaps some exploration of inversion results akin the analysis presented in figure 8 for an error introduced when the measured bedrock mineralogy is different from the true bedrock mineralogy. Here you could synthesise a sediment mineralogy based on one set of bedrock mineralogies, and then randomly change each mineralogy in the A matrix by some value of the ‘error’. I am not sure whether this is reasonable or not however, as I am not an expert in XRD, and I am not sure how the bedrock XRD data was collected.
One final comment, the introduction is duplicated. One needs to be removed, and the section numbers redone.
I hope the authors find these help to improve the manuscript. I also outline a few line comments below.
Line 61 – Should be an in-text citation.
Line 270ish Gorner-gletscher then gornergletcher, needs to be consistent throughout the manuscript.
Figure 7. Originial geology – should be original.