the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Feb 2024
A numerical model for duricrust formation by water table fluctuations
Abstract. Duricrusts are hard elemental layers forming in climatically contrasted environments. Ferricretes (or iron duricrusts) are a type of duricrust, made of indurated iron layers. They form in tropical to semi-arid environments, but can be currently observed all around the world, in areas such as Africa, South America, India, and Australia. In most cases, they cap hills and appear to protect softer layers beneath. Two hypotheses have been proposed for the formation of duricrusts, i.e., the hydrological or horizontal model where the enrichment in the hardening element (iron for ferricretes) is the product of leaching and precipitation through the beating of the water table during contrasted seasonal cycles, and the laterisation or vertical model, where the formation of iron duricrusts is the final stage of laterisation.
In this article, we present the first numerical model for the formation of iron duricrusts based on the hydrological hypothesis. The model is an extension to an existing regolith formation model where the position of the water table is used to predict the formation of a hardened layer at a rate set by a characteristic time scale τ and over a depth set by the beating range of the water table, λ. Hardening causes a decrease in surface erodibility, which we introduce in the model as a dimensionless factor κ that multiplies the surface transport coefficient of the model.
Using the model we show under which circumstances duricrusts form by introducing two dimensionless numbers that combine the model parameters (λ and τ) as well as parameters representing external forcing like precipitation rate and uplift rate. We demonstrate that by using model parameter values obtained by independent constraints from field observations, hydrology and geochronology, the model predictions reproduce the observed conditions for duricrust formation. We also show that there exists a strong feedback from duricrust formation on the shape of the regolith and the position of the water table. Finally we demonstrate that the commonly accepted view that, because they are commonly found at the top of hills, duricrusts protect elements of the landscape is most likely an over-interpretation and that caution must be taken before using duricrusts as markers of uplift and/or base level falls.
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RC1: 'Comment on egusphere-2024-160', John Webb, 19 Apr 2024
This paper showcases a newly developed model for ferricrete formation and uses the outputs of the model to comment on the role of ferricretes in landscape evolution. The paper is clearly written and illustrated, and as a result generally easy to follow. The conclusions are generally well-argued. There are, however, some points that need additional thought, and the terminology requires modification.
- The most important point concerns how iron is transported and precipitated; the authors have not correctly described this, and it affects the model concept.
For the transport of iron in groundwater with more or less neutral pH (true for the vast majority of groundwater), conditions must be reducing; the iron is present as the reduced species Fe2+. For this to precipitate and form a ferricrete, the groundwater must be exposed to oxygen so it becomes oxidising; the Fe2+ converts to Fe3+ and automatically precipitates as poorly crystalline ferric hydroxide, which will crystallise as goethite or haematite over time. This is clearly explained in references like Drever (1997 The Geochemistry of Natural Waters: Surface and Groundwater Environments).
What this means is that ferricrete formation is not uniform; most ferricrete precipitates where the watertable intersects the surface and groundwater seeps occur, allowing maximum contact between the Fe2+-containing groundwater and the oxygen in the atmosphere. Thus the situation shown in Fig. 5 is an oversimplification of the true situation.
Ferricrete precipitation extends to the right beneath the hill because the groundwater is exposed to oxidising conditions at the watertable. This will be enhanced if the watertable fluctuates substantially; as the watertable falls, the groundwater retained as a meniscus around soil particles will be exposed to the air that now fills the pore spaces and the Fe2+ in solution will be oxidised and precipitate ferric hydroxide. The greater the watertable fluctuation, the greater the ferricrete precipitation.
The authors need to explain this more clearly in the text. Note that Fe2+ cannot accumulate (line 73) if it is dissolved in groundwater.
- An additional oversimplification in Fig. 5 is that the watertable is virtually never flat as shown; it is almost always a reflection of the topography with a gentler gradient. Thus, in Fig 5 it should slope gently to the left. This provides a hydraulic gradient that causes groundwater to flow to the left, helping to cause greater ferricrete precipitation where the watertable intersects the ground surface.
The model needs to be modified to take into account points 1 and 2.
- The two different hypotheses of ferricrete formation are more-or-less correctly differentiated, but need to be more carefully described. The difference is between iron that has been concentrated in situ as other elements have been removed, and iron that has been transported in groundwater and precipitated at some distance from its origin. The transport for the latter ferricretes is both lateral and vertical (the presence of vertical transport is evident from Fig 5; the ferricrete beneath the crest of the hill must have received iron transported vertically downwards). The first category of ferricretes is often called residual; the second category can be characterised as transported. Using these terms makes the distinction much clearer. Thus the word ‘lateral’ should be deleted in lines 76 and 413.
- The definition of laterite (lines 84-85) is incorrect because it excludes the abundance of iron oxy-hydroxides as a distinguishing feature. The term ‘laterite’ was originally applied to Fe-rich material in Kerala (India) by Buchanan (1807, A Journey from Madras through the countries of Mysore, Canara and Malabar. East India Company, London). Therefore it is also not correct to say that “All rock types can weather into laterites under the right conditions”, because there has to be enough Fe in the rock originally to form a laterite.
- Lines 4-5, 64-65, 486 – “In most cases today, ferricretes are observed capping and protecting hills, at the top of landscapes” – this is not true of Western Australia, where ferricretes are abundant and largely occur in valleys (e.g. Anand & M. Paine 2002 Australian Journal of Earth Sciences, 49, 3-162; Bourman et al 2020 Geomorphology 354 107017). And it is probably not true generally; this would help to confirm that ferricrete-capped hills commonly occur on only a small scale (line 487).
- The term ‘beating’ needs to be replaced by ‘fluctuation’. Beating has a different meaning: pulsation or throbbing, especially of the heart.
- The word ‘difficultly’ is extremely rarely used. It is better replaced by ‘difficult to’. So ‘difficultly measurable rates’ would become ‘difficult-to-measure rates’ and ‘difficultly soluble elements’ would become ‘difficult-to-dissolve elements’, although the latter would be better as ‘slightly soluble elements’.
Minor comments
“silcretes and calcretes form in arid environments” (line 38). Silcretes can also form in humid environments (Rozefelds et al. 2024 Gondwana Research 130, 234–249; Webb and Golding 1998; Journal of Sedimentary Research A, 68, 981-993).
Line 50 – ‘iron’ should be ‘iron oxides / oxy-hydroxides’
Line 58 – should be 1450 mm.yr-1 ?
Line 103 – new subheading needed
Line 482 – should be ‘result’
Citation: https://doi.org/10.5194/egusphere-2024-160-RC1 -
AC1: 'Reply on RC1', Caroline Fenske, 30 Apr 2024
We thank the reviewer for his thorough and insightful review.
Regarding the two main mentioned points:
1. Iron transport and precipitation:
Indeed, reducing conditions are favourable for the transport of Fe2+ and oxidising conditions for precipitation of Fe3+. The explanation of the water table hypothesis will be adjusted accordingly, to give more details about the processes in place.
According to literature, e.g. Taylor et Eggleton 2001 or Tardy 1993, oxidising environments, in contact with oxygen is not necessarily at the surface. “The upper part of this saturated zone because it is moving and renewed, is generally aerobic and it is in this part of the zone that weathering is most effective. The soluble products of weathering are readily removed by its flow allowing weathering to proceed readily. Because the upper part is oxidizing, particularly near the water-table, Fe-oxyhydroxides mark the position of the water-table” (Taylor et Eggleton 2001).
2. Oversimplification of the water table geometry:
The geometry of the water table in the model is directly linked to the work done by Braun et al. (2016) “A simple model for regolith formation”. In this model, 3 equations describe the behaviour and formation of the regolith. The geometry of the water table and its behaviour enabling regolith formation is described at length in the paper. The water table can take many shapes and geometry and be very close to the surface when the system is saturated, for example. A fully saturated regolith would not be deep, when precipitation is high or regolith is thin, which is not always the case during the formation of duricrusts.
In Braun et al, 2016, it is also shown that the situation where the water table is at the surface has a short time span compared to the time scale we are looking at: equation 27 in Braun et al. 2016 gives the time it takes to go from saturated to undersaturated conditions. This would mean that ferricretes would form only during that short time span and specific case or when a system is undergoing a fast exhumation rate and where the water table is at the surface, which is not only what is described in literature. It is a case in which ferricretes form, but not the only one.
The fact that ferricretes are mostly found capping hills is based on literature (e.g. Taylor et Eggleton 2001 and others) but we will try to be more general in expressing this evidence.
The other points concerning precisions about definitions and descriptions will be considered, and adjustments will be made accordingly.
We hope our answers make the model more understandable. We will explain those points in detail in our revision. We thank the reviewer again for the time invested and throughout reading.
Best regards,
Caroline Fenske
Citation: https://doi.org/10.5194/egusphere-2024-160-AC1
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RC2: 'Comment on egusphere-2024-160', Paulo Marcos Vasconcelos, 24 May 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-160/egusphere-2024-160-RC2-supplement.pdf
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AC2: 'Reply on RC2', Caroline Fenske, 03 Jun 2024
We thank the reviewer for his review and thought-provoking comments.
- General comment:
We agree with the reviewer that the model we develop for duricrust formation by fluctuations of the water table might adequately represent other types of duricrusts than just ferricretes. We will modify the manuscript to ensure that our model is presented such that the ferricretes appear as one of the types of duricrusts that can form in this way.
- Regarding the four general aspects mentioned by the reviewer:
- The model is based on sound depiction of physical processes, but it does not have any chemical component:
From this reviewer’s comment, it appears that our main objective, stated at the end of the introduction, i.e., “to present a simple, yet predictive numerical model to simulate the geometry and timing of duricrust formation on geological time scales, to predict their effect on surface processes and to compare them to observations”, was not explicit enough. We will improve this paragraph and move it to the start of the introduction. We will also add a short paragraph justifying this approach and comparing it to more sophisticated models (as those mentioned by the reviewer) that are based on complex chemical processes but that require numerous parameters that are difficult to constrain and, most importantly, to know state variables characterizing the system (water chemistry, source rock and adjacent rock lithologies, etc.) that are very difficult to track over large temporal and spatial time scales.
As the reviewer states it, our model is based on sound (yet simplified) physics that represent chemical weathering processes, which, as in many other models operating on similar temporal and spatial scales, do not contain explicit chemical process description. For example, the most-widely used model for soil (and regolith formation) assumes a simple exponential rate of propagation of the weathering as a function of the overlying regolith thickness (see Carretier et al, Geomorphology, 2014 for a nice review of this type of approximation, for example). Braun et al (2016)’s model is an attempt to improve on this simple relationship and is based on a well established relationship between water flow and weathering rate (Maher, 2010 and many others). As explained in Braun et al (2016), the constant of proportionality can be made a function of rock type or temperature, for example, but, for a more “generic” use of the model, i.e., over long temporal and spatial scales or to investigate its behavior under varying tectonic forcings and climates, it is adequate to consider this factor as representing a time and space averaged or integrated value.
The duricrust formation model that we present in the current manuscript is another improvement of this representation of the weathering process, in which we include the fact that the product of the weathering can undergo hardening and in doing so affect its resistance to erosion, modify the landscape response and, as we show in our discussion, potentially lead to a feedback into the weathering process. This is the main justification for characterizing the duricrust by a single parameter, kappa, that we call the hardening parameter. As stated earlier, we will improve the introduction to cover these points more clearly.
- It is based on a misunderstanding of the mechanisms underlying the formation of iron duricrusts:
As discussed at length in our manuscript, it is well known that there exists much debate around various hypotheses for the formation of duricrusts. We agree on this point with the reviewer. The model we propose in this manuscript is based on the hypothesis that the formation of duricrusts relates to lateral transport of an element/ion that precipitates during fluctuations of the water table height, most likely in topographic lows, and thus, is similar to the lateral ferricrete hypothesis described by Bourman (1996) and Bourman et al. (2020) and other authors. Other proposed mechanisms include the in-situ hypothesis, as named by Bourman (1996), that we will test in another manuscript that is in preparation and the other type of lateral transport hypothesis of Bourman (1996) that duricrust form from the fragments of an older, dismantled duricrust (to quote Bournam (1996) describing his lateral ferricrete mechanism: “… lateral transport of physical particles or chemical precipitates derived from lateral sources.”).
Consequently, we will improve the section of the manuscript describing the various hypotheses, using the elements brought by the reviewer. We will also make clear that these different hypotheses are not restricted to the formation of ferricretes. We will also improve the section that describes the most commonly accepted theories for each type of duricrust. In this way we think we will respond to the reviewer’s concern on this matter.
- Literature review on the topic ignores relevant information demonstrating that iron duricrusts are indeed long-lived and slowly eroding components of cratonal landscapes:
According to literature, duricrusts can become very old and this aspect has been mentioned in the article (section 2.3). The suggested literature about duricrust dating will be incorporated to improve the data. The suggestion to better differentiate between dating data according to different measuring categories is noted and modifications will be made accordingly.
We fully agree that model results should not be taken at face value but confronted with observational constraints. The point we made about duricrusts being less efficient than stated in many studies in “protecting” landscapes is not at all dependent on the details of the model but is a simple result that can be derived from any hillslope/diffusion erosion model: introducing a thin hard layer is not an efficient way to significantly increase the time it takes for hillslope transport to erode a hill, regardless of the process that created the hardened layer. It does not mean that duricrust are not hard, but that even if they are hard (100 or more times than the rest of the hill) and thick (20% of the height of the hill) they can only retard the erosion of the hill by a factor 2. This conclusion is not inconsistent with the fact that duricrust can be very old: a duricrust can be billions of years old, until it is brought to the surface. And even when it is brought to the surface, it can resist erosion for billions of years until it is subjected to a noticeable base level fall driving erosion. We will make this point clearer in the revised version of the manuscript.
- When the model is applied it produces results that are not substantiated by other models or by observations and measurements of physical reality:
We assume that the reviewer makes a reference here to our simple computation showing that hard layers are inefficient at reducing the erosional timescale of a hill (see our point above) and to his criticism of the weathering model by Braun et al (2016). Regarding this last point, we do not believe that we should “defend” the physical soundness of the model that has been previously published. Furthermore, Braun et al (2016) addresses the concerns raised by the reviewer concerning the relationship between predicted regolith thickness and surface topography. As explained in Braun et al (2016), their model reproduces the observations of Rempe and Dietrich (2014) of a thicker regolith beneath hill tops in actively uplifting/eroding landscapes. It also predicts that in these situations, the water table must be very close to the regolith-bedrock interface, which is not a prediction but an assumption of Rempe and Dietrich (2014), which regard the bedrock as fractured and thus having a finite hydraulic conductivity. It is also worth noting that Rempe and Dietrich (2014) cannot predict any regolith thickness beneath the base level because, contrary to Braun et al (2016), their model assumes that it is nil there. It is also well accepted - see for example concerns expressed in Pelletier et al (2016) global model for regolith thickness – that Rempe and Dietrich (2014)’s model only applies to “uplands”, i.e., tectonically active areas. In non-actively uplifting/eroding areas, Braun et al (2016)’s model predicts indeed thinner regolith thickness beneath ridge tops. As argued in Braun et al (2016) this is true at many sites in Africa and India, where geophysical sounding evidenced that regolith thickness is thinner under hilltops or is relatively uniform beneath the topography (see data from Beauvais et al (1999) in Southern Senegal and Braun et al (2009) in India; see exact references in Braun et al (2016)). We recognize, however, that it is difficult to correlate regolith thickness and surface features in low relief slowly eroding terrains, where the position of channels may have evolved since or during the time of formation of the regolith.
- The model is based on sound depiction of physical processes, but it does not have any chemical component:
- Regarding the line-by-line and section-by-section review:
Precisions and modifications in descriptions and possible confusions due to the chosen vocabulary will be addressed and adjustments will be made accordingly.
- Summary:
We thank the reviewer again for his thorough review. In summary, we believe that all of his concerns can be addressed (1) by improving the introduction of our manuscript to indicate more clearly what the objectives of the models are, (2) by not focusing its range of applicability to the formation of ferricretes, (3) by including a wider range of observations concerning the age and rate of formation of duricrusts as suggested by the reviewer, and (4) by better describing the implications of our findings for duricrust longevity and age, so that they do not appear to conflict with basic observational constraints.
We will therefore proceed with the preparation of a revised version.
Citation: https://doi.org/10.5194/egusphere-2024-160-AC2
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AC2: 'Reply on RC2', Caroline Fenske, 03 Jun 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-160', John Webb, 19 Apr 2024
This paper showcases a newly developed model for ferricrete formation and uses the outputs of the model to comment on the role of ferricretes in landscape evolution. The paper is clearly written and illustrated, and as a result generally easy to follow. The conclusions are generally well-argued. There are, however, some points that need additional thought, and the terminology requires modification.
- The most important point concerns how iron is transported and precipitated; the authors have not correctly described this, and it affects the model concept.
For the transport of iron in groundwater with more or less neutral pH (true for the vast majority of groundwater), conditions must be reducing; the iron is present as the reduced species Fe2+. For this to precipitate and form a ferricrete, the groundwater must be exposed to oxygen so it becomes oxidising; the Fe2+ converts to Fe3+ and automatically precipitates as poorly crystalline ferric hydroxide, which will crystallise as goethite or haematite over time. This is clearly explained in references like Drever (1997 The Geochemistry of Natural Waters: Surface and Groundwater Environments).
What this means is that ferricrete formation is not uniform; most ferricrete precipitates where the watertable intersects the surface and groundwater seeps occur, allowing maximum contact between the Fe2+-containing groundwater and the oxygen in the atmosphere. Thus the situation shown in Fig. 5 is an oversimplification of the true situation.
Ferricrete precipitation extends to the right beneath the hill because the groundwater is exposed to oxidising conditions at the watertable. This will be enhanced if the watertable fluctuates substantially; as the watertable falls, the groundwater retained as a meniscus around soil particles will be exposed to the air that now fills the pore spaces and the Fe2+ in solution will be oxidised and precipitate ferric hydroxide. The greater the watertable fluctuation, the greater the ferricrete precipitation.
The authors need to explain this more clearly in the text. Note that Fe2+ cannot accumulate (line 73) if it is dissolved in groundwater.
- An additional oversimplification in Fig. 5 is that the watertable is virtually never flat as shown; it is almost always a reflection of the topography with a gentler gradient. Thus, in Fig 5 it should slope gently to the left. This provides a hydraulic gradient that causes groundwater to flow to the left, helping to cause greater ferricrete precipitation where the watertable intersects the ground surface.
The model needs to be modified to take into account points 1 and 2.
- The two different hypotheses of ferricrete formation are more-or-less correctly differentiated, but need to be more carefully described. The difference is between iron that has been concentrated in situ as other elements have been removed, and iron that has been transported in groundwater and precipitated at some distance from its origin. The transport for the latter ferricretes is both lateral and vertical (the presence of vertical transport is evident from Fig 5; the ferricrete beneath the crest of the hill must have received iron transported vertically downwards). The first category of ferricretes is often called residual; the second category can be characterised as transported. Using these terms makes the distinction much clearer. Thus the word ‘lateral’ should be deleted in lines 76 and 413.
- The definition of laterite (lines 84-85) is incorrect because it excludes the abundance of iron oxy-hydroxides as a distinguishing feature. The term ‘laterite’ was originally applied to Fe-rich material in Kerala (India) by Buchanan (1807, A Journey from Madras through the countries of Mysore, Canara and Malabar. East India Company, London). Therefore it is also not correct to say that “All rock types can weather into laterites under the right conditions”, because there has to be enough Fe in the rock originally to form a laterite.
- Lines 4-5, 64-65, 486 – “In most cases today, ferricretes are observed capping and protecting hills, at the top of landscapes” – this is not true of Western Australia, where ferricretes are abundant and largely occur in valleys (e.g. Anand & M. Paine 2002 Australian Journal of Earth Sciences, 49, 3-162; Bourman et al 2020 Geomorphology 354 107017). And it is probably not true generally; this would help to confirm that ferricrete-capped hills commonly occur on only a small scale (line 487).
- The term ‘beating’ needs to be replaced by ‘fluctuation’. Beating has a different meaning: pulsation or throbbing, especially of the heart.
- The word ‘difficultly’ is extremely rarely used. It is better replaced by ‘difficult to’. So ‘difficultly measurable rates’ would become ‘difficult-to-measure rates’ and ‘difficultly soluble elements’ would become ‘difficult-to-dissolve elements’, although the latter would be better as ‘slightly soluble elements’.
Minor comments
“silcretes and calcretes form in arid environments” (line 38). Silcretes can also form in humid environments (Rozefelds et al. 2024 Gondwana Research 130, 234–249; Webb and Golding 1998; Journal of Sedimentary Research A, 68, 981-993).
Line 50 – ‘iron’ should be ‘iron oxides / oxy-hydroxides’
Line 58 – should be 1450 mm.yr-1 ?
Line 103 – new subheading needed
Line 482 – should be ‘result’
Citation: https://doi.org/10.5194/egusphere-2024-160-RC1 -
AC1: 'Reply on RC1', Caroline Fenske, 30 Apr 2024
We thank the reviewer for his thorough and insightful review.
Regarding the two main mentioned points:
1. Iron transport and precipitation:
Indeed, reducing conditions are favourable for the transport of Fe2+ and oxidising conditions for precipitation of Fe3+. The explanation of the water table hypothesis will be adjusted accordingly, to give more details about the processes in place.
According to literature, e.g. Taylor et Eggleton 2001 or Tardy 1993, oxidising environments, in contact with oxygen is not necessarily at the surface. “The upper part of this saturated zone because it is moving and renewed, is generally aerobic and it is in this part of the zone that weathering is most effective. The soluble products of weathering are readily removed by its flow allowing weathering to proceed readily. Because the upper part is oxidizing, particularly near the water-table, Fe-oxyhydroxides mark the position of the water-table” (Taylor et Eggleton 2001).
2. Oversimplification of the water table geometry:
The geometry of the water table in the model is directly linked to the work done by Braun et al. (2016) “A simple model for regolith formation”. In this model, 3 equations describe the behaviour and formation of the regolith. The geometry of the water table and its behaviour enabling regolith formation is described at length in the paper. The water table can take many shapes and geometry and be very close to the surface when the system is saturated, for example. A fully saturated regolith would not be deep, when precipitation is high or regolith is thin, which is not always the case during the formation of duricrusts.
In Braun et al, 2016, it is also shown that the situation where the water table is at the surface has a short time span compared to the time scale we are looking at: equation 27 in Braun et al. 2016 gives the time it takes to go from saturated to undersaturated conditions. This would mean that ferricretes would form only during that short time span and specific case or when a system is undergoing a fast exhumation rate and where the water table is at the surface, which is not only what is described in literature. It is a case in which ferricretes form, but not the only one.
The fact that ferricretes are mostly found capping hills is based on literature (e.g. Taylor et Eggleton 2001 and others) but we will try to be more general in expressing this evidence.
The other points concerning precisions about definitions and descriptions will be considered, and adjustments will be made accordingly.
We hope our answers make the model more understandable. We will explain those points in detail in our revision. We thank the reviewer again for the time invested and throughout reading.
Best regards,
Caroline Fenske
Citation: https://doi.org/10.5194/egusphere-2024-160-AC1
-
RC2: 'Comment on egusphere-2024-160', Paulo Marcos Vasconcelos, 24 May 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-160/egusphere-2024-160-RC2-supplement.pdf
-
AC2: 'Reply on RC2', Caroline Fenske, 03 Jun 2024
We thank the reviewer for his review and thought-provoking comments.
- General comment:
We agree with the reviewer that the model we develop for duricrust formation by fluctuations of the water table might adequately represent other types of duricrusts than just ferricretes. We will modify the manuscript to ensure that our model is presented such that the ferricretes appear as one of the types of duricrusts that can form in this way.
- Regarding the four general aspects mentioned by the reviewer:
- The model is based on sound depiction of physical processes, but it does not have any chemical component:
From this reviewer’s comment, it appears that our main objective, stated at the end of the introduction, i.e., “to present a simple, yet predictive numerical model to simulate the geometry and timing of duricrust formation on geological time scales, to predict their effect on surface processes and to compare them to observations”, was not explicit enough. We will improve this paragraph and move it to the start of the introduction. We will also add a short paragraph justifying this approach and comparing it to more sophisticated models (as those mentioned by the reviewer) that are based on complex chemical processes but that require numerous parameters that are difficult to constrain and, most importantly, to know state variables characterizing the system (water chemistry, source rock and adjacent rock lithologies, etc.) that are very difficult to track over large temporal and spatial time scales.
As the reviewer states it, our model is based on sound (yet simplified) physics that represent chemical weathering processes, which, as in many other models operating on similar temporal and spatial scales, do not contain explicit chemical process description. For example, the most-widely used model for soil (and regolith formation) assumes a simple exponential rate of propagation of the weathering as a function of the overlying regolith thickness (see Carretier et al, Geomorphology, 2014 for a nice review of this type of approximation, for example). Braun et al (2016)’s model is an attempt to improve on this simple relationship and is based on a well established relationship between water flow and weathering rate (Maher, 2010 and many others). As explained in Braun et al (2016), the constant of proportionality can be made a function of rock type or temperature, for example, but, for a more “generic” use of the model, i.e., over long temporal and spatial scales or to investigate its behavior under varying tectonic forcings and climates, it is adequate to consider this factor as representing a time and space averaged or integrated value.
The duricrust formation model that we present in the current manuscript is another improvement of this representation of the weathering process, in which we include the fact that the product of the weathering can undergo hardening and in doing so affect its resistance to erosion, modify the landscape response and, as we show in our discussion, potentially lead to a feedback into the weathering process. This is the main justification for characterizing the duricrust by a single parameter, kappa, that we call the hardening parameter. As stated earlier, we will improve the introduction to cover these points more clearly.
- It is based on a misunderstanding of the mechanisms underlying the formation of iron duricrusts:
As discussed at length in our manuscript, it is well known that there exists much debate around various hypotheses for the formation of duricrusts. We agree on this point with the reviewer. The model we propose in this manuscript is based on the hypothesis that the formation of duricrusts relates to lateral transport of an element/ion that precipitates during fluctuations of the water table height, most likely in topographic lows, and thus, is similar to the lateral ferricrete hypothesis described by Bourman (1996) and Bourman et al. (2020) and other authors. Other proposed mechanisms include the in-situ hypothesis, as named by Bourman (1996), that we will test in another manuscript that is in preparation and the other type of lateral transport hypothesis of Bourman (1996) that duricrust form from the fragments of an older, dismantled duricrust (to quote Bournam (1996) describing his lateral ferricrete mechanism: “… lateral transport of physical particles or chemical precipitates derived from lateral sources.”).
Consequently, we will improve the section of the manuscript describing the various hypotheses, using the elements brought by the reviewer. We will also make clear that these different hypotheses are not restricted to the formation of ferricretes. We will also improve the section that describes the most commonly accepted theories for each type of duricrust. In this way we think we will respond to the reviewer’s concern on this matter.
- Literature review on the topic ignores relevant information demonstrating that iron duricrusts are indeed long-lived and slowly eroding components of cratonal landscapes:
According to literature, duricrusts can become very old and this aspect has been mentioned in the article (section 2.3). The suggested literature about duricrust dating will be incorporated to improve the data. The suggestion to better differentiate between dating data according to different measuring categories is noted and modifications will be made accordingly.
We fully agree that model results should not be taken at face value but confronted with observational constraints. The point we made about duricrusts being less efficient than stated in many studies in “protecting” landscapes is not at all dependent on the details of the model but is a simple result that can be derived from any hillslope/diffusion erosion model: introducing a thin hard layer is not an efficient way to significantly increase the time it takes for hillslope transport to erode a hill, regardless of the process that created the hardened layer. It does not mean that duricrust are not hard, but that even if they are hard (100 or more times than the rest of the hill) and thick (20% of the height of the hill) they can only retard the erosion of the hill by a factor 2. This conclusion is not inconsistent with the fact that duricrust can be very old: a duricrust can be billions of years old, until it is brought to the surface. And even when it is brought to the surface, it can resist erosion for billions of years until it is subjected to a noticeable base level fall driving erosion. We will make this point clearer in the revised version of the manuscript.
- When the model is applied it produces results that are not substantiated by other models or by observations and measurements of physical reality:
We assume that the reviewer makes a reference here to our simple computation showing that hard layers are inefficient at reducing the erosional timescale of a hill (see our point above) and to his criticism of the weathering model by Braun et al (2016). Regarding this last point, we do not believe that we should “defend” the physical soundness of the model that has been previously published. Furthermore, Braun et al (2016) addresses the concerns raised by the reviewer concerning the relationship between predicted regolith thickness and surface topography. As explained in Braun et al (2016), their model reproduces the observations of Rempe and Dietrich (2014) of a thicker regolith beneath hill tops in actively uplifting/eroding landscapes. It also predicts that in these situations, the water table must be very close to the regolith-bedrock interface, which is not a prediction but an assumption of Rempe and Dietrich (2014), which regard the bedrock as fractured and thus having a finite hydraulic conductivity. It is also worth noting that Rempe and Dietrich (2014) cannot predict any regolith thickness beneath the base level because, contrary to Braun et al (2016), their model assumes that it is nil there. It is also well accepted - see for example concerns expressed in Pelletier et al (2016) global model for regolith thickness – that Rempe and Dietrich (2014)’s model only applies to “uplands”, i.e., tectonically active areas. In non-actively uplifting/eroding areas, Braun et al (2016)’s model predicts indeed thinner regolith thickness beneath ridge tops. As argued in Braun et al (2016) this is true at many sites in Africa and India, where geophysical sounding evidenced that regolith thickness is thinner under hilltops or is relatively uniform beneath the topography (see data from Beauvais et al (1999) in Southern Senegal and Braun et al (2009) in India; see exact references in Braun et al (2016)). We recognize, however, that it is difficult to correlate regolith thickness and surface features in low relief slowly eroding terrains, where the position of channels may have evolved since or during the time of formation of the regolith.
- The model is based on sound depiction of physical processes, but it does not have any chemical component:
- Regarding the line-by-line and section-by-section review:
Precisions and modifications in descriptions and possible confusions due to the chosen vocabulary will be addressed and adjustments will be made accordingly.
- Summary:
We thank the reviewer again for his thorough review. In summary, we believe that all of his concerns can be addressed (1) by improving the introduction of our manuscript to indicate more clearly what the objectives of the models are, (2) by not focusing its range of applicability to the formation of ferricretes, (3) by including a wider range of observations concerning the age and rate of formation of duricrusts as suggested by the reviewer, and (4) by better describing the implications of our findings for duricrust longevity and age, so that they do not appear to conflict with basic observational constraints.
We will therefore proceed with the preparation of a revised version.
Citation: https://doi.org/10.5194/egusphere-2024-160-AC2
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AC2: 'Reply on RC2', Caroline Fenske, 03 Jun 2024
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Jean Braun
François Guillocheau
Cécile Robin
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