the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 Jan 2024
Introducing ELSA v2.0: an isochronal model for ice-sheet layer tracing
Abstract. We provide a detailed description of the ice-sheet layer age tracer ELSA – a model that uses a straightforward method to simulate the englacial stratification of large ice sheets – as an alternative to Eulerian or Lagrangian tracer schemes. ELSA’s vertical axis is time and individual layers of accumulation are modeled explicitly and are isochronal. ELSA is not a stand-alone ice-sheet model, but requires uni-directional coupling to another model providing ice physics and dynamics (the “host model”). Via ELSA’s layer tracing, the host model’s output can be evaluated throughout the interior using ice core or radiostratigraphy data. We describe the stability and resolution-dependence of this coupled modeling system using simulations of the last glacial cycle of the Greenland ice sheet using one specific host model. Key questions concern ELSA’s design to maximize usability, which includes making it computationally efficient enough for ensemble runs, as well as exploring the requirements for offline forcing of ELSA with output from a range of existing ice-sheet models. ELSA is an open source and collaborative project, and this work provides the foundation for a well-documented, flexible, and easily adaptable model code to effectively force ELSA with (any) existing full ice-sheet model via a clear interface.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
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Status: closed
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CEC1: 'Comment on egusphere-2023-3127', Juan Antonio Añel, 26 Jan 2024
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
You have archived your code on Git repositories. However, Git repositories are not suitable for scientific publication. Therefore, please, publish your code in one of the appropriate repositories, and reply to this comment with the relevant information (links and DOIs) as soon as possible, as it should be available before the Discussions stage. Also, please, include the relevant primary input/output data.In this way, if you do not fix this problem, we will have to reject your manuscript for publication in our journal. I should note that, actually, your manuscript should not have been accepted in Discussions, given this lack of compliance with our policy. Therefore, the current situation with your manuscript is irregular.
Also, you must include in a potentially reviewed version of your manuscript the modified 'Code and Data Availability' section, the DOIs of the new repositories (and DOIs for datasets if necessary).
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2023-3127-CEC1 -
AC1: 'Reply on CEC1', Therese Rieckh, 31 Jan 2024
Dear Juan A. Añel,
we have uploaded all model code and relevant input and output data at zenodo:
https://zenodo.org/records/10590358
I am working on having the manuscript with the updated Data and Code Availability section uploaded for discussion.
Thank you,
Therese Rieckh
Citation: https://doi.org/10.5194/egusphere-2023-3127-AC1 -
AC2: 'Reply on CEC1', Therese Rieckh, 01 Feb 2024
It is not possible to upload the revised manuscript. The Code availability section of the original manuscript has been substituted by the following section in the revised manuscript:
Code and data availability. ELSA’s source code is available at https://git.app.uib.no/melt-team-bergen/elsa under the license GPL-3.0, including instructions for the ELSA and Yelmo coupling. The version for this manuscript is the tagged version v2.0. The source code of Yelmo and Yelmox is available at https://github.com/palma-ice/yelmo and https://github.com/palma-ice/yelmox under the license GPL-3.0. We used version 1.801 (tag v1.801) for both Yelmo and Yelmox for this manuscript.
The exact version of all three models and necessary input data to produce the results presented in this manuscript, as well as the output data themselves, are archived on Zenodo at https://zenodo.org/records/10590358 (Rieckh, 2024).Citation: https://doi.org/10.5194/egusphere-2023-3127-AC2
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AC1: 'Reply on CEC1', Therese Rieckh, 31 Jan 2024
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RC1: 'Comment on egusphere-2023-3127', Anonymous Referee #1, 17 Feb 2024
Authors presented results of a novel modeling approach for simulation of isochronal surfaces in an ice sheet model. General modeling methodology was described in detail in earlier papers of the authors (Born, 2017; Born and Robinson, 2021). The essence of the methodology is the description of an emerging of an isochronous surface and its evolution through time in a host model generated velocity field. In some sense it resembles tracking passive tracers though the body of an ice sheet. Compared to the previous studies (Clarke and Marshall, 2002; Clarke et al., 2005; Lhomme et al., 2005), where semi-Lagrangian approach is implemented for particle tracing, authors use straightforward tracing (so to say, “pure” Lagrangian approach). The novelty compared to (Rybak and Huybrechts, 2003) is that the whole isochronous surface is tracked, not individual particles.
As was mentioned above, the paper is a continuation of the previous studies. From this point of view, it has a more technical focus rather than the research one, though some results concerning evolution of isochronous surfaces through glacial cycles have certain scientific value. Anyway, systematic detailed narration of the method presented in the paper is of course handful and corresponds to the scope of the Geoscientific Model Development.
Though the authors stress (lines 184-185) that their main goal is not to reach as much closer fit to what they call “observations”, but rather to present capabilities of the method, I would suggest to enlarge the section 3.1 and discuss the problem of distortion and overturning of ice layers close to bottom (NEEM community members, 2013; fig. 13 in (MacGregor et al., 2015)). In view of the severe problems close to the bottom of the ice sheet, the choice of the 115 ka isochrone as target one in the model tests looks ret very reliable and must be additionally justified.
For me, it is not clear how authors technically deal with the lateral ice melting and calving in terms of isochronous surfaces propagation, as well as with changes in ice sheet configuration (retreat-advance) and with basal melting. I suggest to discuss this issue in the revised manuscript.
Particular notes
Line 16: I suggest to add a reference to (EPICA community members, 2006).
Line 16: “ice core data are limited to specific locations”. This is not exactly correct. Because of ice flow, ice core data characterize climate change in the past on a relatively big territory – the deeper is the layer in the ice core the more remote is the place of origin of the ice (see eg. (Huybrechts et. al, 2007 in Climate of the Past; EPICA Community members, 2006, in Nature – specifically, Supplementary materials; NEEM community members, 2013, in Nature; Huybrechts et al., 2009, in Annals of Glaciology). I suggest to add a paragraph discussing the problem.
Line 57: The description is somewhat vague – how can the vertical axis be defined in time RATHER than in space? Either in time or in space, I think, and not a little bit here and a little bit there. In the previous papers (Born, 2017; Born and Robinson, 2021) this issue is enlightened rather clear. I suggest to describe vertical discretization in the more clear way as well as propagation of the isochrone surfaces (layers) in the horizontal (in the vertical, too) in the more clear way.
Line 134: Authors use Shapiro and Ritzwoller (2004) geothermal heat flux (GHF) field to calculate basal melting. Though the GHF field in the cited work seems to correctly reproduce the reality in general, I am not sure about the North-Western Greenland around stations NEEM and especially NorthGRIP, where the bottom layers older than 120-124 ka BP disappeared because of relatively high basal melting rate probably caused by locally enhanced GHF.
Caption to Fig. 2. Authors use term “observed” for the OIB data which is comfusing. In lines 151-162 authors describe how the OIB chronology was derived as a combination of radiostratigraphy and ice core dating (which is model derived in deeper layers).
Figure 2, panels a-c: the difference in depth between modelled and the OIB isochrones is confusing, especially if we consider not very “old” ages – 11,7 and 29 ka BB isochrones. These results must be explained and discussed, because the discrepancy in estimates may question the possibility of practical implementation of the method. In this view, I do not agree with the authors (Lines 162-166) that the model reproduces radiostratigraphy “reasonably well”. For instance, in panel b, isochrones 11,7 ka (“observed”) and 29 ka (modelled) merge. Same for 29 ka and 57 ka. I cannot qualify this result as “reasonably well” even taking into account uncertainty in “observed” values.
Citation: https://doi.org/10.5194/egusphere-2023-3127-RC1 -
AC3: 'Reply on RC1', Therese Rieckh, 26 Mar 2024
We thank the reviewer for their input and comments.
It seems like parts of the manuscript could benefit from being more precisely worded, and we are planning to implement changes based on your suggestions.
Furthermore, we will add more specifics regarding the development of individual layers during the simulation with respect to calving, lateral melting, etc. We will also address the 115ka isochrone and overturning of layers at close to the base of the ice sheet in the manuscript revision.
Citation: https://doi.org/10.5194/egusphere-2023-3127-AC3
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AC3: 'Reply on RC1', Therese Rieckh, 26 Mar 2024
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RC2: 'Comment on egusphere-2023-3127', Anonymous Referee #2, 21 Feb 2024
This paper concerns what I’d describe as a performance tradeoff analysis of a presently unique model (ELSA) that cleverly couples offline with a full ice-sheet model (Yelmo) to generate the resulting synthetic age structure of the ice sheet. The model described is appealingly simple and so the number of model parameters is small, but they are all fairly considered in terms of their impact on the output. The result is a compact study that mostly stands on its merits but could use better context with what has preceded it. I have mostly glaciological and non-modeler type concerns about the paper as it stands. I’ve noted one bigger issue on which that I think the paper needs substantially more clarity for its intended audience.
Major concern:
It took a careful reading and checking of references for me to understand (or think I do) how ELSA vertically advects the age structure and thins the layers at each time step. At first, I was surprised not to see any mention of *vertical* velocities in Figure 1. I wondered if ELSA used a Nye sandwich model throughout the ice sheet, which would not be good. Then I realized that the vertical velocities must simply be determined by continuity from the host model’s 3-D horizontal velocity field. That’s fine, but not expressed clearly in the paper. However, I then became curious about the nature of the host model itself and found that it uses a depth-averaged approximation of vertical shear in the ice column (129-130). While substantial and informative work has been done on this model’s properties (Born and Robinson, 2021; Robinson et al., 2022), I find this an odd choice in the context of resolving the 3-D age structure of an ice sheet as it forces a pre-determined vertical velocity pattern (if not magnitude) on the ice sheet, which is a risk considering past observations (Fahnestock et al., 2001, 10.1126/science.1065370). A potential resolution here would be greater clarity in the model description as to what happens to the isochronal layers *inside* the ice sheet at each time step (not just the top and bottom), and later a more robust discussion of better ways to model an age structure generally. The latter part tends more toward the host model physics and other inputs, so maybe a summary of the conclusions of Born and Robinson (2021) is appropriate.
1: Is it correct to describe this paper as “Introducing ELSA v2.0…”, given the verbiage on L41? That suggests that Born and Robinson (2021) “introduced” ELSA v2.0. This paper still stands on its own merits and is certainly a more complete description. I wonder if a different title is more appropriate, e.g., “Design and performance of ELSA v2.0…”.
23: Is the reference to “Standard tools” those for glaciology or a different field? More context here is appropriate before the relevant citations later on in this paragraph.
132: Clarify what a “sigma-coordinate grid” is for non-modelers. Also, how are they different from “zeta levels” mentioned later on (L203)?
144: Which “bed properties”? There are several relevant ones.
148 and elsewhere: For paleoclimate in much more common usage these days is the use of Common Era (CE) instead of AD for historical ages.
151: There is also pre-OIB data used by MacGregor et al. (2015).
178: parameterization
186: If there’s no section 3.2, then there doesn’t need to be a section 3.1. Also, this sub-section may be more appropriate for the Discussion.
191: I’m familiar with BedMachine and haven’t heard of v3.1. It’s not mentioned in Morlighem et al. (2017), which is simply described as v3. Regardless, BedMachine v5 has been out since mid-2022. I realize that big ice-sheet models are strangely slow at updating their boundary conditions, hence the use of Shapiro and Ritzwoller (2004…20 years ago…) for geothermal flux, but some clarity or nomenclature adjustment is needed here.
204: vertical dimension
263: I’m not knowledgeable in these matters or what GMD policy is, but more commonly whenever runtimes are mentioned or compared I’ve also seen the processor / # cores / etc. described.
Figure 2e-l/3/5/7/A1: Could some colors be added other than gray to distinguish between the ocean, land and ice where the isochrones are not mapped? It’s a bit drab as is with just the present-day coastline.
Citation: https://doi.org/10.5194/egusphere-2023-3127-RC2 -
AC4: 'Reply on RC2', Therese Rieckh, 26 Mar 2024
We thank the reviewer for their feedback and comments.
We will be more clear in the model description regarding the advection process and how layers evolve inside the ice sheet. But to summarize it shortly here, layers within the ice sheet only change thickness due to advection (flow towards the margin of the ice sheet). Advection happens within the individual layers exclusively, layers do not ever exchange mass. The vertical velocity from the host model is not used at all. The only layers that change thickness due to accumulation or melt are the bottom and top layer (or few layers, depending on layer resolution and coupling period between ELSA and the host model).
We further thank for the detailed comments where clarification is needed, we will address these in the revision. We will also take the title change into account.
Citation: https://doi.org/10.5194/egusphere-2023-3127-AC4
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AC4: 'Reply on RC2', Therese Rieckh, 26 Mar 2024
Interactive discussion
Status: closed
-
CEC1: 'Comment on egusphere-2023-3127', Juan Antonio Añel, 26 Jan 2024
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
You have archived your code on Git repositories. However, Git repositories are not suitable for scientific publication. Therefore, please, publish your code in one of the appropriate repositories, and reply to this comment with the relevant information (links and DOIs) as soon as possible, as it should be available before the Discussions stage. Also, please, include the relevant primary input/output data.In this way, if you do not fix this problem, we will have to reject your manuscript for publication in our journal. I should note that, actually, your manuscript should not have been accepted in Discussions, given this lack of compliance with our policy. Therefore, the current situation with your manuscript is irregular.
Also, you must include in a potentially reviewed version of your manuscript the modified 'Code and Data Availability' section, the DOIs of the new repositories (and DOIs for datasets if necessary).
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2023-3127-CEC1 -
AC1: 'Reply on CEC1', Therese Rieckh, 31 Jan 2024
Dear Juan A. Añel,
we have uploaded all model code and relevant input and output data at zenodo:
https://zenodo.org/records/10590358
I am working on having the manuscript with the updated Data and Code Availability section uploaded for discussion.
Thank you,
Therese Rieckh
Citation: https://doi.org/10.5194/egusphere-2023-3127-AC1 -
AC2: 'Reply on CEC1', Therese Rieckh, 01 Feb 2024
It is not possible to upload the revised manuscript. The Code availability section of the original manuscript has been substituted by the following section in the revised manuscript:
Code and data availability. ELSA’s source code is available at https://git.app.uib.no/melt-team-bergen/elsa under the license GPL-3.0, including instructions for the ELSA and Yelmo coupling. The version for this manuscript is the tagged version v2.0. The source code of Yelmo and Yelmox is available at https://github.com/palma-ice/yelmo and https://github.com/palma-ice/yelmox under the license GPL-3.0. We used version 1.801 (tag v1.801) for both Yelmo and Yelmox for this manuscript.
The exact version of all three models and necessary input data to produce the results presented in this manuscript, as well as the output data themselves, are archived on Zenodo at https://zenodo.org/records/10590358 (Rieckh, 2024).Citation: https://doi.org/10.5194/egusphere-2023-3127-AC2
-
AC1: 'Reply on CEC1', Therese Rieckh, 31 Jan 2024
-
RC1: 'Comment on egusphere-2023-3127', Anonymous Referee #1, 17 Feb 2024
Authors presented results of a novel modeling approach for simulation of isochronal surfaces in an ice sheet model. General modeling methodology was described in detail in earlier papers of the authors (Born, 2017; Born and Robinson, 2021). The essence of the methodology is the description of an emerging of an isochronous surface and its evolution through time in a host model generated velocity field. In some sense it resembles tracking passive tracers though the body of an ice sheet. Compared to the previous studies (Clarke and Marshall, 2002; Clarke et al., 2005; Lhomme et al., 2005), where semi-Lagrangian approach is implemented for particle tracing, authors use straightforward tracing (so to say, “pure” Lagrangian approach). The novelty compared to (Rybak and Huybrechts, 2003) is that the whole isochronous surface is tracked, not individual particles.
As was mentioned above, the paper is a continuation of the previous studies. From this point of view, it has a more technical focus rather than the research one, though some results concerning evolution of isochronous surfaces through glacial cycles have certain scientific value. Anyway, systematic detailed narration of the method presented in the paper is of course handful and corresponds to the scope of the Geoscientific Model Development.
Though the authors stress (lines 184-185) that their main goal is not to reach as much closer fit to what they call “observations”, but rather to present capabilities of the method, I would suggest to enlarge the section 3.1 and discuss the problem of distortion and overturning of ice layers close to bottom (NEEM community members, 2013; fig. 13 in (MacGregor et al., 2015)). In view of the severe problems close to the bottom of the ice sheet, the choice of the 115 ka isochrone as target one in the model tests looks ret very reliable and must be additionally justified.
For me, it is not clear how authors technically deal with the lateral ice melting and calving in terms of isochronous surfaces propagation, as well as with changes in ice sheet configuration (retreat-advance) and with basal melting. I suggest to discuss this issue in the revised manuscript.
Particular notes
Line 16: I suggest to add a reference to (EPICA community members, 2006).
Line 16: “ice core data are limited to specific locations”. This is not exactly correct. Because of ice flow, ice core data characterize climate change in the past on a relatively big territory – the deeper is the layer in the ice core the more remote is the place of origin of the ice (see eg. (Huybrechts et. al, 2007 in Climate of the Past; EPICA Community members, 2006, in Nature – specifically, Supplementary materials; NEEM community members, 2013, in Nature; Huybrechts et al., 2009, in Annals of Glaciology). I suggest to add a paragraph discussing the problem.
Line 57: The description is somewhat vague – how can the vertical axis be defined in time RATHER than in space? Either in time or in space, I think, and not a little bit here and a little bit there. In the previous papers (Born, 2017; Born and Robinson, 2021) this issue is enlightened rather clear. I suggest to describe vertical discretization in the more clear way as well as propagation of the isochrone surfaces (layers) in the horizontal (in the vertical, too) in the more clear way.
Line 134: Authors use Shapiro and Ritzwoller (2004) geothermal heat flux (GHF) field to calculate basal melting. Though the GHF field in the cited work seems to correctly reproduce the reality in general, I am not sure about the North-Western Greenland around stations NEEM and especially NorthGRIP, where the bottom layers older than 120-124 ka BP disappeared because of relatively high basal melting rate probably caused by locally enhanced GHF.
Caption to Fig. 2. Authors use term “observed” for the OIB data which is comfusing. In lines 151-162 authors describe how the OIB chronology was derived as a combination of radiostratigraphy and ice core dating (which is model derived in deeper layers).
Figure 2, panels a-c: the difference in depth between modelled and the OIB isochrones is confusing, especially if we consider not very “old” ages – 11,7 and 29 ka BB isochrones. These results must be explained and discussed, because the discrepancy in estimates may question the possibility of practical implementation of the method. In this view, I do not agree with the authors (Lines 162-166) that the model reproduces radiostratigraphy “reasonably well”. For instance, in panel b, isochrones 11,7 ka (“observed”) and 29 ka (modelled) merge. Same for 29 ka and 57 ka. I cannot qualify this result as “reasonably well” even taking into account uncertainty in “observed” values.
Citation: https://doi.org/10.5194/egusphere-2023-3127-RC1 -
AC3: 'Reply on RC1', Therese Rieckh, 26 Mar 2024
We thank the reviewer for their input and comments.
It seems like parts of the manuscript could benefit from being more precisely worded, and we are planning to implement changes based on your suggestions.
Furthermore, we will add more specifics regarding the development of individual layers during the simulation with respect to calving, lateral melting, etc. We will also address the 115ka isochrone and overturning of layers at close to the base of the ice sheet in the manuscript revision.
Citation: https://doi.org/10.5194/egusphere-2023-3127-AC3
-
AC3: 'Reply on RC1', Therese Rieckh, 26 Mar 2024
-
RC2: 'Comment on egusphere-2023-3127', Anonymous Referee #2, 21 Feb 2024
This paper concerns what I’d describe as a performance tradeoff analysis of a presently unique model (ELSA) that cleverly couples offline with a full ice-sheet model (Yelmo) to generate the resulting synthetic age structure of the ice sheet. The model described is appealingly simple and so the number of model parameters is small, but they are all fairly considered in terms of their impact on the output. The result is a compact study that mostly stands on its merits but could use better context with what has preceded it. I have mostly glaciological and non-modeler type concerns about the paper as it stands. I’ve noted one bigger issue on which that I think the paper needs substantially more clarity for its intended audience.
Major concern:
It took a careful reading and checking of references for me to understand (or think I do) how ELSA vertically advects the age structure and thins the layers at each time step. At first, I was surprised not to see any mention of *vertical* velocities in Figure 1. I wondered if ELSA used a Nye sandwich model throughout the ice sheet, which would not be good. Then I realized that the vertical velocities must simply be determined by continuity from the host model’s 3-D horizontal velocity field. That’s fine, but not expressed clearly in the paper. However, I then became curious about the nature of the host model itself and found that it uses a depth-averaged approximation of vertical shear in the ice column (129-130). While substantial and informative work has been done on this model’s properties (Born and Robinson, 2021; Robinson et al., 2022), I find this an odd choice in the context of resolving the 3-D age structure of an ice sheet as it forces a pre-determined vertical velocity pattern (if not magnitude) on the ice sheet, which is a risk considering past observations (Fahnestock et al., 2001, 10.1126/science.1065370). A potential resolution here would be greater clarity in the model description as to what happens to the isochronal layers *inside* the ice sheet at each time step (not just the top and bottom), and later a more robust discussion of better ways to model an age structure generally. The latter part tends more toward the host model physics and other inputs, so maybe a summary of the conclusions of Born and Robinson (2021) is appropriate.
1: Is it correct to describe this paper as “Introducing ELSA v2.0…”, given the verbiage on L41? That suggests that Born and Robinson (2021) “introduced” ELSA v2.0. This paper still stands on its own merits and is certainly a more complete description. I wonder if a different title is more appropriate, e.g., “Design and performance of ELSA v2.0…”.
23: Is the reference to “Standard tools” those for glaciology or a different field? More context here is appropriate before the relevant citations later on in this paragraph.
132: Clarify what a “sigma-coordinate grid” is for non-modelers. Also, how are they different from “zeta levels” mentioned later on (L203)?
144: Which “bed properties”? There are several relevant ones.
148 and elsewhere: For paleoclimate in much more common usage these days is the use of Common Era (CE) instead of AD for historical ages.
151: There is also pre-OIB data used by MacGregor et al. (2015).
178: parameterization
186: If there’s no section 3.2, then there doesn’t need to be a section 3.1. Also, this sub-section may be more appropriate for the Discussion.
191: I’m familiar with BedMachine and haven’t heard of v3.1. It’s not mentioned in Morlighem et al. (2017), which is simply described as v3. Regardless, BedMachine v5 has been out since mid-2022. I realize that big ice-sheet models are strangely slow at updating their boundary conditions, hence the use of Shapiro and Ritzwoller (2004…20 years ago…) for geothermal flux, but some clarity or nomenclature adjustment is needed here.
204: vertical dimension
263: I’m not knowledgeable in these matters or what GMD policy is, but more commonly whenever runtimes are mentioned or compared I’ve also seen the processor / # cores / etc. described.
Figure 2e-l/3/5/7/A1: Could some colors be added other than gray to distinguish between the ocean, land and ice where the isochrones are not mapped? It’s a bit drab as is with just the present-day coastline.
Citation: https://doi.org/10.5194/egusphere-2023-3127-RC2 -
AC4: 'Reply on RC2', Therese Rieckh, 26 Mar 2024
We thank the reviewer for their feedback and comments.
We will be more clear in the model description regarding the advection process and how layers evolve inside the ice sheet. But to summarize it shortly here, layers within the ice sheet only change thickness due to advection (flow towards the margin of the ice sheet). Advection happens within the individual layers exclusively, layers do not ever exchange mass. The vertical velocity from the host model is not used at all. The only layers that change thickness due to accumulation or melt are the bottom and top layer (or few layers, depending on layer resolution and coupling period between ELSA and the host model).
We further thank for the detailed comments where clarification is needed, we will address these in the revision. We will also take the title change into account.
Citation: https://doi.org/10.5194/egusphere-2023-3127-AC4
-
AC4: 'Reply on RC2', Therese Rieckh, 26 Mar 2024
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Andreas Born
Alexander Robinson
Robert Law
Gerrit Gülle
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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