the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 01 Jul 2022
Lightning Assimilation in the Weather Research and Forecasting (WRF) Model Version 4.1.1: Technique Updates and Assessment of the Applications from Regional to Hemispheric Scales
Abstract. The lightning assimilation (LTA) technique in the Kain-Fritsch convective parameterization in the WRF model has been updated and applied to continental and hemispheric simulations using lightning flash data obtained from the National Lightning Detection Network (NLDN) and the World Wide Lightning Location Network (WWLLN), respectively. The impact of different values for cumulus parameters associated with the Kain-Fritsch scheme on simulations with and without LTA were evaluated for both the continental and the hemispheric simulations. Comparisons to gauge-based rainfall products and near-surface meteorological observations indicated that the LTA improved the model’s performance for most variables. The simulated precipitation with LTA using WWLLN lightning flashes in the hemispheric applications was significantly improved over the simulations without LTA when compared to precipitation from satellite observations in the Equatorial regions. The simulations without LTA showed significant sensitivity to the cumulus parameters (i.e., user-toggled switches) for monthly precipitation that was as large as 40 % during convective seasons for month-mean daily precipitations. With LTA, the differences in simulated precipitation due to the different cumulus parameters were minimized. The horizontal grid spacing of the modeling domain strongly influenced the LTA technique and the predicted total precipitation, especially in the coarser scales used for the hemispheric simulation. The user-definable cumulus parameters and domain resolution manifested the complexity of convective process modeling both with and without LTA. These results revealed sensitivities to domain resolution, geographic heterogeneity, and the source and quality of the lightning dataset.
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RC1: 'Comment on egusphere-2022-348', Lisa Neef, 03 Aug 2022
** General comments
The submitted manuscript describes how a method for convection in the WRF model to observed lightning changes its sensitivity to various namelist parameters, at both local and regional spatial scales. The paper is informative and very well organized, but heavy on details that may not serve the overall message (more on this below). I recommend it for publication following minor revisions, which are outlined below.
** Specific comments
1. I am concerned about the use of the term "data assimilation" to describe the approach used here, which essentially uses the presence of observed lightning to trigger convection in the model, whereas the term "data assimilation" typically refers to complex systems that use some sort of variational or Kalman-filter type method to periodically update prognostic model variables with observations. "Lightning-triggered convection" might be a more apt descriptor, but I leave this up to the authors and editor to decide.
2. The main thrust of the paper outlines how LTA changes the sensitivity of the convection to various namelist parameters in WRF. It's unclear, however, to what extent this result is interesting to users of other models. It looks like there are two major conclusions about the parameters (reading from lines 579-584 here): (1) that regional simulations are sensitive to both a parameters but hemispheric simulations only to the trigger parameter, and (2) that sensitivity to both of these parameters really goes down once LTA is turned on. I can see how the second of these is interesting beyond WRF (more constraint to data means less sensitivity to parameters) but the first is less intuitive. Can you zoom out and draw a more general, non-WRF-specific, conclusion?
3. Lines 95-117: The introduction explains previous successes with LTA and the plan for the current paper, but without explaining what LTA actually is. As stated above, calling it "Lightning Data Assimilation" might imply something different than what is actually done (i.e. the assimilation of lightning data as part of the existing WRF 4D data assimilation), which makes it difficult to see why LTA should be tested in conjunction with two namelist parameters for convection. Paragraph 1 of section 2 has a great, concise summary of what LTA does -- I suggest moving this statement to the introduction.
4. Line 257: How many minutes is the model timestep? (Is cudt=10 more or less frequent?)
5. The abbreviations for the experiment matrix (Table 1) are confusing! For example, since the names of individual WRF namelist parameters are pretty meaningless to people who don't use WRF, there's nothing intuitive about abbreviating which convective trigger is used as "K" or abbreviating the timing of the convective scheme as "C". I can't say what a more effective naming scheme would look like, but I found the abbreviations hard to remember, which made all the subsequent figures hard to understand. For example, the discussion of Figure 1 talks about the effects of trig 1 vs trig2, but in order to understand what is being talked about, the reader needs to connect the xaxis labels in 5 panels to entries in table 1 and figure out what all that means, and all that work is going to muddle the main results of the figure.
6. Line 294: the "ShallowOnly" option is mentioned but not explained. It would be helpful, in Section 3 where the parameters of the convective scheme are described, to briefly explain how the trigger options change then LTA is on/off.
7. Figure 3: I advise against the use of a line plot here, because connecting the dots with lines implies to the reader that they are have a temporal ordering, when really you are showing independent experiments. How about bar graphs? This would clearly show one of the major results of this figure, which is that the experiments with LTA off are much more sensitive to the choice of convection parameters. Also, it really necessary to show 5 different statistical measures? They seem to mostly reflect the same things (correlation goes down, while bias and errors go up, when agreement with obs is poor) so it seems like there is a lot of redundant information in this figure.
8. Figure 3: It's unclear from the text _why_ LTA has the strongest effect on the Ohio Valley -- I assume it would be because there is a lot of lightning in this region in the summer, but the same is true for the Southeast and the Upper Midwest, and those regions have a much smaller effect on LTA. Is there a simple explanation?
9. Figs. 4-5: These figures show a lot of the same things as Fig 3, with the most noticeable difference being (I think?) that the different namelist parameters can really affect the bias in surface variables. However, it's hard to discern a real memorable message from this part -- Section 4.2 lists a lot of detailed results but doesn't really put them into a greater context. It would be great if these figures could be distilled down to the most salient results (perhaps by only showing one type of bias?) and then given more physical explanation rather than listing out the various details of each figure.
10. Fig. 7: Column and row headings would be great here; without them, it's really hard to know which panel shows what (again, the experiment abbreviations aren't really intuitive). For the panels showing differences in rainfall, a divergent colormap (where zero is white) would be helpful (I realize that this can be pain to implement in a small-multiples plots so this is just a tip). More impportantly, the only result discussed for Figure 7 is that LTA brings the simulated precipitation closer to the observations. If that's all this figure shows, are 9 panels really necessary? Again, it's a lot of information to confront the reader with, when the actual take home message of the figure is probably more simple.
11. I'm not sure how Figure 8 fits into the larger premise of the paper. The main result seems to be that the different parameters produce subtle differences in the daily precipitation. Since you don't go into detail about these differences, it's maybe not necessary to include this figure. (Figure 9 seems far more informative and maybe covers your bases sufficiently?)
12. Line 450: FDDA is mentioned for the first time here; are all the simulations described here run with data assimilation? If yes, that should be made clear much earlier, i.e. when the experiments are described. Also, since most of the runs have significant biases in precipitation, it would be good to know roughly what types of data were assimilated in the FDDA framework.
13. Figure 11: If I understood correctly, the authors are arguing that mean bias changes more drastically with different parameters settings for regions that are less constrained by observations and/or to which the model is less well tuned than the United States. But does this really bear out? Looking at the figure, I see MB for the USA vacillate wildly between the different experiments, even flipping sign. Also, why does MB change so drastically between experiments but RMSE doesn't? Since you show both, it would be good tp explain what each of these measures reflects.
14. Line 468: On the hemispheric scale, LTA means triggering convection over a huge area by something as local and small scale as lightning -- it actually seems quite surprising that you have any success at all with LTA at these scales. It would be helpful to mention much earlier on what a stretch it is to try to apply LTA at these scales, and then emphasize what about it works (if I understand correctly, it's that LTA improves the correlation to rain gauge data, i.e. Fig. 9?).
** Technical corrections1. Line 103: Does the lower cost of WWLLN data mean a lower cost to users (i.e. it costs less to obtain the data) or a lower cost of the actual measurements? Is there a simple reason why this is the case?
2. Line 133: If lightning is present the Updraft Source Layer changes relative to the default value of what? Also you don't really need to abbreviate updraft source layer since it doesn't come up again. There are already a lot of acronyms in this paper!
3. Lines 138-151: This paragraph explains why Heath et al changed the criteria for deep convection. The previous paragraph explains that the scheme adds moisture and heat to meet the criteria, but it's a bit confusing since at that point we don't get know what the criteria are and what they have to do with lightning. I suggest switching the paragraph that starts at line 138 with the one that starts at 126 (with other edits to make it flow).Citation: https://doi.org/10.5194/egusphere-2022-348-RC1 - AC2: 'Reply on RC1', Daiwen Kang, 16 Sep 2022
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CEC1: 'Comment on egusphere-2022-348', Juan Antonio Añel, 15 Aug 2022
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.htmlYou state in the "Code and data availability" section of your manuscript that "The LTA code is not publicly available yet but interested users can
620 contact the corresponding author to acquire the source code". The LTA code is a core part of your manuscript and must be published with it. Admittedly, this has been an oversight of the Topical Editor, and indeed, the manuscript should have never been accepted for the Discussions stage without including the LTA code.Therefore, according to our policy, please publish your code in one of the appropriate repositories. In this way, you must reply to this comment with the link to the repository used in your manuscript, with its DOI. The reply and the repository should be available as soon as possible and before the Discussions stage is closed to be sure that anyone has access to it for review purposes. Also, in a potential reviewed version of your manuscript, you must include the modified 'Code and Data Availability' section and the DOI of the code.
When publishing the LTA code, note that if you do not include a license, the code continues to be your property and can not be used by others, despite any statement on being free to use. Therefore, when uploading the model's code to the repository, you could want to choose a free software/open-source (FLOSS) license. We recommend the GPLv3. You only need to include the file 'https://www.gnu.org/licenses/gpl-3.0.txt' as LICENSE.txt with your code. Also, you can choose other options that Zenodo provides: GPLv2, Apache License, MIT License, etc.
Be aware that failing to comply with this request could result in the rejection of your manuscript for publication.
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2022-348-CEC1 -
AC1: 'Reply on CEC1', Daiwen Kang, 15 Aug 2022
Dear Dr. Juan A. Anel
Thank you for catching our negligence of the code availability. We have now uploaded the related code to Zenodo (https://zenodo.org/record/6993223#.YvpwDXbMKUk, doi: 10.5281/zenodo.6993223). To include lightning assimilation in WRFv4.1.1 (the model version used in this study), users can simply replace the files from WRFv4.1.1 release with the files in the same name provided at the link under the normal WRF directories: Registry, phys, and dyn_em, respectively, and compile WRF as usual. We will update the "Code and data availability" section with correct information in our next revised manuscript.
Thank you again,
Daiwen Kang
On behalf of all the co-authors
Citation: https://doi.org/10.5194/egusphere-2022-348-AC1
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AC1: 'Reply on CEC1', Daiwen Kang, 15 Aug 2022
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RC2: 'Comment on egusphere-2022-348', Anonymous Referee #2, 21 Aug 2022
This manuscript convincingly demonstrates the benefits of lightning data assimilation in the WRF model when run regionally over CONUS and when run over the Northern Hemisphere at courser resolution. The benefits over CONUS were the greatest when high detection efficiency National Lightning Detection Network data are used, but model performance improvement was noted even when the lower detection efficiency World Wide Lightning Location Network (WWLLN) data are used. The authors considered the effects of two of the Kain-Fritsch convective scheme parameters (trigger function and convective time step) in association with the lightning assimilation. These parameters have major effects on precipitation in the base case without lightning assimilation, but the effects of variation of these parametes is diminished when the assimilation is used. The paper presents comprehensive statistics on the performance of the simulations with the two lightning data sets and with the variation of convective parameters. The results suggest possible future improvement of the lightning assimilation scheme to take into account horizontal grid resolution by using the observed flash densities to determine when to trigger convection. The paper certainly fits in the scope of GMD, and I recommend publication after some minor revisions outlined below.
line 32-33: monthly mean daily precipitation
line 64: add some more references: Allen et al. (2012); Kang et al. (2019a,b)
line 90: Even though there are some....
lnes 93-94: ...there is no literature evaluating how these parameter....
line 104: efficiency is much lower than the >95% of NLDN for cloud-to-ground (CG) flashes
line 109: ...with NLDN lightning flashes over CONUS
line 212: and snow.
line 218: move URL to after the word "dataset" in the previous line
line 298: ...present the more dramatic fluctuations...
line 376: ...errors were noticable (Figure 6).
line 436: ...among the BASE cases were noted in all the....
line 462: In the analysis in Figure 3b....
line 503: ...12-km LTA cases (both K2C10W and K2C10N)
line 507: ...in that the precipitation from Trig2 was....
line 574: ...directions are to use criteria values of lightning flash density dependent on grid resolution to trigger deep convection...
line 586: "updates" Please remind the reader here what the updates were
line 603: ...the convective processes (e.g., convective transport of air pollutants matching the times and locations of lightning NOx production) to have....
line 610: I'm not sure what is meant by "scope" here. Please add "strokes per flash" to this list of new data from GLM.
lines 640-647: should these items be moved to the "Code and Data Availability" section?
Citation: https://doi.org/10.5194/egusphere-2022-348-RC2 - AC3: 'Reply on RC2', Daiwen Kang, 16 Sep 2022
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-348', Lisa Neef, 03 Aug 2022
** General comments
The submitted manuscript describes how a method for convection in the WRF model to observed lightning changes its sensitivity to various namelist parameters, at both local and regional spatial scales. The paper is informative and very well organized, but heavy on details that may not serve the overall message (more on this below). I recommend it for publication following minor revisions, which are outlined below.
** Specific comments
1. I am concerned about the use of the term "data assimilation" to describe the approach used here, which essentially uses the presence of observed lightning to trigger convection in the model, whereas the term "data assimilation" typically refers to complex systems that use some sort of variational or Kalman-filter type method to periodically update prognostic model variables with observations. "Lightning-triggered convection" might be a more apt descriptor, but I leave this up to the authors and editor to decide.
2. The main thrust of the paper outlines how LTA changes the sensitivity of the convection to various namelist parameters in WRF. It's unclear, however, to what extent this result is interesting to users of other models. It looks like there are two major conclusions about the parameters (reading from lines 579-584 here): (1) that regional simulations are sensitive to both a parameters but hemispheric simulations only to the trigger parameter, and (2) that sensitivity to both of these parameters really goes down once LTA is turned on. I can see how the second of these is interesting beyond WRF (more constraint to data means less sensitivity to parameters) but the first is less intuitive. Can you zoom out and draw a more general, non-WRF-specific, conclusion?
3. Lines 95-117: The introduction explains previous successes with LTA and the plan for the current paper, but without explaining what LTA actually is. As stated above, calling it "Lightning Data Assimilation" might imply something different than what is actually done (i.e. the assimilation of lightning data as part of the existing WRF 4D data assimilation), which makes it difficult to see why LTA should be tested in conjunction with two namelist parameters for convection. Paragraph 1 of section 2 has a great, concise summary of what LTA does -- I suggest moving this statement to the introduction.
4. Line 257: How many minutes is the model timestep? (Is cudt=10 more or less frequent?)
5. The abbreviations for the experiment matrix (Table 1) are confusing! For example, since the names of individual WRF namelist parameters are pretty meaningless to people who don't use WRF, there's nothing intuitive about abbreviating which convective trigger is used as "K" or abbreviating the timing of the convective scheme as "C". I can't say what a more effective naming scheme would look like, but I found the abbreviations hard to remember, which made all the subsequent figures hard to understand. For example, the discussion of Figure 1 talks about the effects of trig 1 vs trig2, but in order to understand what is being talked about, the reader needs to connect the xaxis labels in 5 panels to entries in table 1 and figure out what all that means, and all that work is going to muddle the main results of the figure.
6. Line 294: the "ShallowOnly" option is mentioned but not explained. It would be helpful, in Section 3 where the parameters of the convective scheme are described, to briefly explain how the trigger options change then LTA is on/off.
7. Figure 3: I advise against the use of a line plot here, because connecting the dots with lines implies to the reader that they are have a temporal ordering, when really you are showing independent experiments. How about bar graphs? This would clearly show one of the major results of this figure, which is that the experiments with LTA off are much more sensitive to the choice of convection parameters. Also, it really necessary to show 5 different statistical measures? They seem to mostly reflect the same things (correlation goes down, while bias and errors go up, when agreement with obs is poor) so it seems like there is a lot of redundant information in this figure.
8. Figure 3: It's unclear from the text _why_ LTA has the strongest effect on the Ohio Valley -- I assume it would be because there is a lot of lightning in this region in the summer, but the same is true for the Southeast and the Upper Midwest, and those regions have a much smaller effect on LTA. Is there a simple explanation?
9. Figs. 4-5: These figures show a lot of the same things as Fig 3, with the most noticeable difference being (I think?) that the different namelist parameters can really affect the bias in surface variables. However, it's hard to discern a real memorable message from this part -- Section 4.2 lists a lot of detailed results but doesn't really put them into a greater context. It would be great if these figures could be distilled down to the most salient results (perhaps by only showing one type of bias?) and then given more physical explanation rather than listing out the various details of each figure.
10. Fig. 7: Column and row headings would be great here; without them, it's really hard to know which panel shows what (again, the experiment abbreviations aren't really intuitive). For the panels showing differences in rainfall, a divergent colormap (where zero is white) would be helpful (I realize that this can be pain to implement in a small-multiples plots so this is just a tip). More impportantly, the only result discussed for Figure 7 is that LTA brings the simulated precipitation closer to the observations. If that's all this figure shows, are 9 panels really necessary? Again, it's a lot of information to confront the reader with, when the actual take home message of the figure is probably more simple.
11. I'm not sure how Figure 8 fits into the larger premise of the paper. The main result seems to be that the different parameters produce subtle differences in the daily precipitation. Since you don't go into detail about these differences, it's maybe not necessary to include this figure. (Figure 9 seems far more informative and maybe covers your bases sufficiently?)
12. Line 450: FDDA is mentioned for the first time here; are all the simulations described here run with data assimilation? If yes, that should be made clear much earlier, i.e. when the experiments are described. Also, since most of the runs have significant biases in precipitation, it would be good to know roughly what types of data were assimilated in the FDDA framework.
13. Figure 11: If I understood correctly, the authors are arguing that mean bias changes more drastically with different parameters settings for regions that are less constrained by observations and/or to which the model is less well tuned than the United States. But does this really bear out? Looking at the figure, I see MB for the USA vacillate wildly between the different experiments, even flipping sign. Also, why does MB change so drastically between experiments but RMSE doesn't? Since you show both, it would be good tp explain what each of these measures reflects.
14. Line 468: On the hemispheric scale, LTA means triggering convection over a huge area by something as local and small scale as lightning -- it actually seems quite surprising that you have any success at all with LTA at these scales. It would be helpful to mention much earlier on what a stretch it is to try to apply LTA at these scales, and then emphasize what about it works (if I understand correctly, it's that LTA improves the correlation to rain gauge data, i.e. Fig. 9?).
** Technical corrections1. Line 103: Does the lower cost of WWLLN data mean a lower cost to users (i.e. it costs less to obtain the data) or a lower cost of the actual measurements? Is there a simple reason why this is the case?
2. Line 133: If lightning is present the Updraft Source Layer changes relative to the default value of what? Also you don't really need to abbreviate updraft source layer since it doesn't come up again. There are already a lot of acronyms in this paper!
3. Lines 138-151: This paragraph explains why Heath et al changed the criteria for deep convection. The previous paragraph explains that the scheme adds moisture and heat to meet the criteria, but it's a bit confusing since at that point we don't get know what the criteria are and what they have to do with lightning. I suggest switching the paragraph that starts at line 138 with the one that starts at 126 (with other edits to make it flow).Citation: https://doi.org/10.5194/egusphere-2022-348-RC1 - AC2: 'Reply on RC1', Daiwen Kang, 16 Sep 2022
-
CEC1: 'Comment on egusphere-2022-348', Juan Antonio Añel, 15 Aug 2022
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.htmlYou state in the "Code and data availability" section of your manuscript that "The LTA code is not publicly available yet but interested users can
620 contact the corresponding author to acquire the source code". The LTA code is a core part of your manuscript and must be published with it. Admittedly, this has been an oversight of the Topical Editor, and indeed, the manuscript should have never been accepted for the Discussions stage without including the LTA code.Therefore, according to our policy, please publish your code in one of the appropriate repositories. In this way, you must reply to this comment with the link to the repository used in your manuscript, with its DOI. The reply and the repository should be available as soon as possible and before the Discussions stage is closed to be sure that anyone has access to it for review purposes. Also, in a potential reviewed version of your manuscript, you must include the modified 'Code and Data Availability' section and the DOI of the code.
When publishing the LTA code, note that if you do not include a license, the code continues to be your property and can not be used by others, despite any statement on being free to use. Therefore, when uploading the model's code to the repository, you could want to choose a free software/open-source (FLOSS) license. We recommend the GPLv3. You only need to include the file 'https://www.gnu.org/licenses/gpl-3.0.txt' as LICENSE.txt with your code. Also, you can choose other options that Zenodo provides: GPLv2, Apache License, MIT License, etc.
Be aware that failing to comply with this request could result in the rejection of your manuscript for publication.
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2022-348-CEC1 -
AC1: 'Reply on CEC1', Daiwen Kang, 15 Aug 2022
Dear Dr. Juan A. Anel
Thank you for catching our negligence of the code availability. We have now uploaded the related code to Zenodo (https://zenodo.org/record/6993223#.YvpwDXbMKUk, doi: 10.5281/zenodo.6993223). To include lightning assimilation in WRFv4.1.1 (the model version used in this study), users can simply replace the files from WRFv4.1.1 release with the files in the same name provided at the link under the normal WRF directories: Registry, phys, and dyn_em, respectively, and compile WRF as usual. We will update the "Code and data availability" section with correct information in our next revised manuscript.
Thank you again,
Daiwen Kang
On behalf of all the co-authors
Citation: https://doi.org/10.5194/egusphere-2022-348-AC1
-
AC1: 'Reply on CEC1', Daiwen Kang, 15 Aug 2022
-
RC2: 'Comment on egusphere-2022-348', Anonymous Referee #2, 21 Aug 2022
This manuscript convincingly demonstrates the benefits of lightning data assimilation in the WRF model when run regionally over CONUS and when run over the Northern Hemisphere at courser resolution. The benefits over CONUS were the greatest when high detection efficiency National Lightning Detection Network data are used, but model performance improvement was noted even when the lower detection efficiency World Wide Lightning Location Network (WWLLN) data are used. The authors considered the effects of two of the Kain-Fritsch convective scheme parameters (trigger function and convective time step) in association with the lightning assimilation. These parameters have major effects on precipitation in the base case without lightning assimilation, but the effects of variation of these parametes is diminished when the assimilation is used. The paper presents comprehensive statistics on the performance of the simulations with the two lightning data sets and with the variation of convective parameters. The results suggest possible future improvement of the lightning assimilation scheme to take into account horizontal grid resolution by using the observed flash densities to determine when to trigger convection. The paper certainly fits in the scope of GMD, and I recommend publication after some minor revisions outlined below.
line 32-33: monthly mean daily precipitation
line 64: add some more references: Allen et al. (2012); Kang et al. (2019a,b)
line 90: Even though there are some....
lnes 93-94: ...there is no literature evaluating how these parameter....
line 104: efficiency is much lower than the >95% of NLDN for cloud-to-ground (CG) flashes
line 109: ...with NLDN lightning flashes over CONUS
line 212: and snow.
line 218: move URL to after the word "dataset" in the previous line
line 298: ...present the more dramatic fluctuations...
line 376: ...errors were noticable (Figure 6).
line 436: ...among the BASE cases were noted in all the....
line 462: In the analysis in Figure 3b....
line 503: ...12-km LTA cases (both K2C10W and K2C10N)
line 507: ...in that the precipitation from Trig2 was....
line 574: ...directions are to use criteria values of lightning flash density dependent on grid resolution to trigger deep convection...
line 586: "updates" Please remind the reader here what the updates were
line 603: ...the convective processes (e.g., convective transport of air pollutants matching the times and locations of lightning NOx production) to have....
line 610: I'm not sure what is meant by "scope" here. Please add "strokes per flash" to this list of new data from GLM.
lines 640-647: should these items be moved to the "Code and Data Availability" section?
Citation: https://doi.org/10.5194/egusphere-2022-348-RC2 - AC3: 'Reply on RC2', Daiwen Kang, 16 Sep 2022
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Nicholas Heath
Robert Gilliam
Tanya Spero
Jonathan Pleim
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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