the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Nov 2023
Development of a plant carbon-nitrogen interface coupling framework in a coupled biophysical-ecosystem-biogeochemical model (SSiB5/Triffid/DayCent-SOM v1.0): Its parameterization, implementation, and evaluation
Abstract. Plant and microbial nitrogen (N) dynamics and N availability regulate the photosynthetic capacity and capture, allocation, and turnover of carbon (C) in terrestrial ecosystems. Studies have shown that a wide divergence in representations of N dynamics in land surface models leads to large uncertainty in the biogeochemical cycle of the terrestrial ecosystems and then in climate simulations as well as the projections of future trajectories. In this study, a plant C-N interface coupling framework is developed and implemented in a coupled biophysical-ecosystem-biogeochemical model (SSiB5/TRIFFID/ DayCent-SOM v1.0). The main concept and structure of this plant C-N framework and its coupling strategy are presented. This framework takes more plant N-related metabolism processes into account. For instance, plant resistance and self-adjustment is represented by a dynamic C/N ratio for each plant functional type (PFT). Furthermore, when available N is less than plant N demand, plant growth is restricted by a lower maximum carboxylation capacity of Rubisco (Vmax) level, reducing gross primary productivity (GPP). In addition, a module for plant respiration rates is introduced by adjusting the respiration with different rates at different plant components for the same N concentration. Since insufficient N can potentially give rise to lags on plant phenology, phenology scheme is also adjusted with a lag factor related to N processes. All these considerations ensure a more comprehensive incorporation of N regulations to plant growth and C cycling. This new approach has been tested systematically to assess the effects of this coupling framework and N limitation on the terrestrial carbon cycle. Long term measurements from both flux tower sites with different PFTs and global satellite-derived products are employed as references to assess these effects. The results show a general improvement with the new plant C-N coupling framework, with more consistent emergent properties, such as GPP and leaf area index (LAI), compared to observations. The main improvements occur in tropical Africa and boreal regions, accompanied by a decrease of the bias in global GPP and LAI by 16.3 % and 27.1 %, respectively.
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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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Status: closed
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RC1: 'Comment on egusphere-2023-2634', Anonymous Referee #1, 11 Jan 2024
General comments:
This study addresses the critical need to improve the representation of nitrogen cycle in land biogeochemical processes which is a crucial aspect of modelling development. The manuscript presents a novel approach by integrating a soil organic matter and nutrient cycling model to advance simulating coupled global carbon-nitrogen cycles in a process-based dynamic vegetation model. The authors demonstrate that the coupled model version show in general improvement of GPP, LAI, and heat fluxes validated against site-level and global observations, compared to the previous model version. It is certainly a timely work with supporting analysis, although only partially reflecting the performance of the revised model. There are several concerns that the authors should address to enhance the manuscript.
Main concerns:
- The framework implemented in the study revolves around processes in terrestrial N cycles, more specifically about plant N demand and stress. However, the relevant processes are overly simplified when describing the necessity to modify current representations in the models.
- Although it is important to evaluate the impacts on C and heat fluxes, more information on how the dynamic representation of the C/N ratios alter the N cycles would be very pertinent and interesting to report, provided the model outputs include relevant variables to describe the processes. Otherwise there would remain a logic gap to make sense of the differences in C and heat variables between the new and old model versions.
- The need to evaluate plant C processes under the modified N processes is well motivated in the introduction. However, the connection between N processes and heat fluxes is absent.
- The introduction made a leap from “C-only models and dynamic vegetation models generally miss the inclusion of N processes” to “this new framework not only consider N processes but also has a more realistic way to represent the processes with dynamic C/N ratios”. Often dynamic vegetations include N cycles since decades, see e.g, Kou-Giesbrecht, S., et al. (2023) 10.5194/esd-14-767-2023. The current state of modelling C-N cycles is therefore misrepresented and the progress in other models is under recognised, although cited Davies-Barnard et al 2020 the authors themselves.
- The manuscript contains erroneous, redundant, or repetitive expressions throughout. Especially in the method section, there is a substantial amount of text either already addressed in the introduction or better suited for the discussion.
Minor points:
- Suggest revising the title to make it more concise.
- The manuscript may benefit from additional analysis relating to the improved representation on N limitation for different PFTs.
- The use of “wood” or “stems/wood” as a plant organ can be misleading. In Table 1 they are then listed as “component” where it is also false to list “wood” under grasses. Please be consistent with the common terms and stick with stem.
- Suggest adding some information on tundra shrub as it is not covered in the validation sites (Table 3).
- The figure qualities are not consistent.
- When dealing with a variable having the unit of per area (e.g., Navail, g N m-2), the soil depth is essential information, however not clearly indicated in the manuscript.
- The authors are strongly suggested to select references carefully instead of piling them up excessively, such as with the 17 citations in L54 to 57 and 12 citations in L40.
- Please clarify several terms in the paragraph of L70-87, including “plant resistance on photosynthesis ...” (as in it does not make sense to call it resistance on photosynthesis but more like resistance on the reduction of photosynthesis capacity or potential photosynthesis rate, not to be confused with photosynthesis rate, under N limitation), “C/N interactions” (as in if it is about the C to N ratio and something else, or the interactions between some C processes and N processes), “self-adjustment” (as in how such behaviours differ from being simply considered as “responses”), and “fertility” (as in if it refers to soil fertility or plant fertility which is not a well-known term).
Line-specific comments:
- L38, suggest changing to only “physical processes” instead of “biophysical processes” as the commonly simplified land representation in ESMs does not include biological processes as the authors listed themselves.
- L47, suggest changing “Those C-only models” to “The C-only models” as in not all those models mentioned prior, i.e., land process models and dynamic vegetation models, are C-only.
- L72 “dynamic plant C/N ratio” is not necessarily a concept. According to the authors, it should be a more realistic representation than fix ratios.
- L73-74, please revise these two sentences. Suggest removing “Due to their relative immobility”. Suggest changing “A deficiency of any type of nutrient” to “Nutrient deficiency”.
- L75-77, suggest changing “have to” to “can” and keeping fewer citations. The usage of self-adjustment is misleading in such context.
- L77-79, please revise this sentence. Lipid is not a polymer. It should be “nutrient-starved”. Unclear if the authors mean C/N ratios are influenced by being exposed to high light or the accumulation of C polymer are greater when exposed to high light. Please revise the term “high light”.
- L82, suggest clarifying what the N is, such as soil N availability or plant N, and whether it is photosynthesis capacity or actual photosynthesis rate.
- L96-99, please add references for the flux data and satellite-derived observational data.
- L116, please clarify what “vegetation conditions” are. It should be “physiological”.
- L119, suggest changing to “C4 grasses” to be precise and consistent with Tables 2 and 3. It is “tundra shrub” in Tables 1 and 2. Please clarify what is “net C availability”.
- L125, consider listing the pools in a table to present the information more clearly.
- L130, please clarify “based on lignin: N ratio of plant material”.
- L134, please either clarity the temperature and moisture effects or remove the word “effects”.
- L140, please revise “plant life activities”.
- L141, L144, please refrain from using “/” excessively. Suggest changing “physical/biological” to “physical and biological” and “temperature/moisture” to “temperature and moisture”. Please check for other “/” as well.
- L145, please revise this sentence and clarify “surface water”, “carbon fluxes” (it is not mentioned in the second half of the sentence), and “plant litter” (e.g., as in fluxes for production and decomposition or pools).
- L148-150, please revise this sentence. It is unclear what the authors mean by “N effects on plant physiology from photosynthesis, ... plus a dynamic C/N ratio”.
- L152-154, please revise this sentence. It reads repetitive with “not only considers N limitation ... but also emphasizes the N limitation effect ...” and “help us obtain more information to understand ...”
- L163-164, please revise the sentence to clarify the potential confusion that GPP follows autotropic respiration. Please revise “in plant life”.
- L166, this might be controversial as in plants can certainly respond and adapt to lower N availability but it would be a stretch to certainly call it “adjust resource requirements”.
- L167-170, please revise this sentence. It reads contradicting with “resorb only 50%” and “cause a major internal nutrient flux”.
- L170-172, please revise this sentence to improve clarity and avoid going in circle, such as what affect plant productivity and litter N content. Now it reads like “plant responses affect plant productivity and litter N content”.
- L173-174, please revise this sentence to clarify “improve plant responses”.
- L179-196, the majority of this paragraph should fit in the introduction or discussion better.
- L197, please revise this sentence to increase clarity. For instance, NPP is part of the terrestrial C cycle.
- L199, please clarify “normal N concentration”.
- L203, please revise the sentence “Because plants need time to turnover, the plant N processes ...” for clarity and accuracy.
- L205, perhaps the authors mean “modulates LAI evolution, e.g., via leaf mortality?” Should it be “supplies” instead of “supplements?”
- L209, since C/N ratios is abbreviated as CNRs from here, why not introducing it from the start?
- Regrettably, similar issues persist throughout the rest of the text. I will refrain from detailing them further until the authors have thoroughly revised the manuscript.
Overall, the general structure, clarity, terminology, as well as accuracy throughout the manuscript need to be substantially improved.
Citation: https://doi.org/10.5194/egusphere-2023-2634-RC1 - AC1: 'Reply on RC1', Zheng Xiang, 14 Apr 2024
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RC2: 'Comment on egusphere-2023-2634', Anonymous Referee #2, 08 Mar 2024
Review comments for egusphere-2023-2634
Title: Development of a plant carbon-nitrogen interface coupling framework in a coupled biophysical-ecosystem-biogeochemical model (SSiB5/Triffid/DayCent-SOM v1.0): Its parameterization, implementation, and evaluation
This study proposed a plant carbon-nitrogen coupling framework to improve a biophysical-ecosystem-biogeochemical model. The author ran the modified model at the site and global levels, and compared the model results with in-situ observations and remote sensing/machine learning estimations . Moreover, the authors conducted a series of experimental experiments at the global level to quantify the major effects of the N process and C-N interface coupling methodology on the C cycle. This study proposes a new approach, and considers the N limitation effects not only on photosynthesis but also on plant respiration and phenology. However, there are several significant drawbacks in this study. The reviewer has the following concerns and suggestions for the authors to consider:
- Does the SSiB5/Triffid/DayCent-SOM v1.0 model consider anthropogenic N inputs (N deposition, fertilizer and manure) into terrestrial ecosystems? I guess no, since there is not no such information mentioned in the manuscript. If the model doesn’t consider anthropogenic N inputs, the reported N limitation effects may be largely exaggerated because anthropogenic N inputs to terrestrial ecosystems are much larger than the vegetation N fixation in recent decades which can relief N limitation. In Figure 8 (f), the effect of N limitation is large in Eastern China and central USA, however, the anthropogenic N inputs were quite large in these regions (Tian et al., 2022), the N limitation shouldn’t be large if anthropogenic N inputs are considered. This is my major concern.
- The SSiB5/Triffid/DayCent-SOM v1.0 model performs poor in modelling the magnitude of LAI although its performance is better than SSiB4. At the global level, SSiB5 estimation is about 100% higher than the remote sensing estimation (Figure 11)! Please elaborate on how is LAIbalance calculated in model and the vegetation carbon allocation scheme. Also, it is necessary to add one paragraph discussing the potential reasons for the overestimation of LAI and the future improvement measures.
- There is no tundra site in site-level validation. I recommend adding at least one tundra site. Please elaborate on the calculation of PFT fractional coverage in model, and add one figure comparing model results with satellite-based land cover product to justify that model can accurately estimate PFT fractional coverage.
- I suggest list equations that calculate key processes and variables in carbon and nitrogen cycles such as GPP, SOC/SON decomposition, plant N fixation, plant N uptake, and N mineralization.
- The manuscript needs modifications on the structure. From my point of view, it is better to move line 164-176 and line 179-191 to the Introduction part, and the order of section 3.3 and 3.2 should be reversed.
- Moreover, more discussions on the limitations of the SSiB5/Triffid/DayCent-SOM v1.0 model and potential future developments are needed.
- Please show some results of NlResp and NlPhen, otherwise, you should delete the descriptions of these experiments.
Line-specific comments and suggestions:
Line 86: Please list these plant N metabolism processes.
Line 104: 1982-2007 rather than 1948-2007.
Line 126: eight types rather than six types?
Line 197: delete “ and terrestrial CX cycles”
Line 268-270: I suggest delete line 268-270 to avoid misinterpretation
Line 284: I didn’t find the paper: Yang et al., 1992
Line 320: temporal resolution of vegetation dynamics is ten-day, is it too coarse for phenology (especially for the boreal forests and tundra)?
Line 395: How do you set up the equilibrium rum at the site level? The same with global run?
Line 405: Four sets of sensitivity experiments rather than six sets?
Figure 7: SSiB5 is higher than in (g) and (k). In these tow sites, SSiB5 has lower GPP than SSiB4, why its evapotranspiration (latent heat) is higher? This doesn't seem to make sense.
Figure 9: IS LAI the mean value of GIMMIS and GLASS?
Line 542-543: Is there any observational evidence for this vegetation transition?
Reference:
Tian H, Bian Z, Shi H, et al. History of anthropogenic Nitrogen inputs (HaNi) to the terrestrial biosphere: a 5 arcmin resolution annual dataset from 1860 to 2019[J]. Earth System Science Data, 2022, 14(10): 4551-4568.
Citation: https://doi.org/10.5194/egusphere-2023-2634-RC2 - AC2: 'Reply on RC2', Zheng Xiang, 14 Apr 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-2634', Anonymous Referee #1, 11 Jan 2024
General comments:
This study addresses the critical need to improve the representation of nitrogen cycle in land biogeochemical processes which is a crucial aspect of modelling development. The manuscript presents a novel approach by integrating a soil organic matter and nutrient cycling model to advance simulating coupled global carbon-nitrogen cycles in a process-based dynamic vegetation model. The authors demonstrate that the coupled model version show in general improvement of GPP, LAI, and heat fluxes validated against site-level and global observations, compared to the previous model version. It is certainly a timely work with supporting analysis, although only partially reflecting the performance of the revised model. There are several concerns that the authors should address to enhance the manuscript.
Main concerns:
- The framework implemented in the study revolves around processes in terrestrial N cycles, more specifically about plant N demand and stress. However, the relevant processes are overly simplified when describing the necessity to modify current representations in the models.
- Although it is important to evaluate the impacts on C and heat fluxes, more information on how the dynamic representation of the C/N ratios alter the N cycles would be very pertinent and interesting to report, provided the model outputs include relevant variables to describe the processes. Otherwise there would remain a logic gap to make sense of the differences in C and heat variables between the new and old model versions.
- The need to evaluate plant C processes under the modified N processes is well motivated in the introduction. However, the connection between N processes and heat fluxes is absent.
- The introduction made a leap from “C-only models and dynamic vegetation models generally miss the inclusion of N processes” to “this new framework not only consider N processes but also has a more realistic way to represent the processes with dynamic C/N ratios”. Often dynamic vegetations include N cycles since decades, see e.g, Kou-Giesbrecht, S., et al. (2023) 10.5194/esd-14-767-2023. The current state of modelling C-N cycles is therefore misrepresented and the progress in other models is under recognised, although cited Davies-Barnard et al 2020 the authors themselves.
- The manuscript contains erroneous, redundant, or repetitive expressions throughout. Especially in the method section, there is a substantial amount of text either already addressed in the introduction or better suited for the discussion.
Minor points:
- Suggest revising the title to make it more concise.
- The manuscript may benefit from additional analysis relating to the improved representation on N limitation for different PFTs.
- The use of “wood” or “stems/wood” as a plant organ can be misleading. In Table 1 they are then listed as “component” where it is also false to list “wood” under grasses. Please be consistent with the common terms and stick with stem.
- Suggest adding some information on tundra shrub as it is not covered in the validation sites (Table 3).
- The figure qualities are not consistent.
- When dealing with a variable having the unit of per area (e.g., Navail, g N m-2), the soil depth is essential information, however not clearly indicated in the manuscript.
- The authors are strongly suggested to select references carefully instead of piling them up excessively, such as with the 17 citations in L54 to 57 and 12 citations in L40.
- Please clarify several terms in the paragraph of L70-87, including “plant resistance on photosynthesis ...” (as in it does not make sense to call it resistance on photosynthesis but more like resistance on the reduction of photosynthesis capacity or potential photosynthesis rate, not to be confused with photosynthesis rate, under N limitation), “C/N interactions” (as in if it is about the C to N ratio and something else, or the interactions between some C processes and N processes), “self-adjustment” (as in how such behaviours differ from being simply considered as “responses”), and “fertility” (as in if it refers to soil fertility or plant fertility which is not a well-known term).
Line-specific comments:
- L38, suggest changing to only “physical processes” instead of “biophysical processes” as the commonly simplified land representation in ESMs does not include biological processes as the authors listed themselves.
- L47, suggest changing “Those C-only models” to “The C-only models” as in not all those models mentioned prior, i.e., land process models and dynamic vegetation models, are C-only.
- L72 “dynamic plant C/N ratio” is not necessarily a concept. According to the authors, it should be a more realistic representation than fix ratios.
- L73-74, please revise these two sentences. Suggest removing “Due to their relative immobility”. Suggest changing “A deficiency of any type of nutrient” to “Nutrient deficiency”.
- L75-77, suggest changing “have to” to “can” and keeping fewer citations. The usage of self-adjustment is misleading in such context.
- L77-79, please revise this sentence. Lipid is not a polymer. It should be “nutrient-starved”. Unclear if the authors mean C/N ratios are influenced by being exposed to high light or the accumulation of C polymer are greater when exposed to high light. Please revise the term “high light”.
- L82, suggest clarifying what the N is, such as soil N availability or plant N, and whether it is photosynthesis capacity or actual photosynthesis rate.
- L96-99, please add references for the flux data and satellite-derived observational data.
- L116, please clarify what “vegetation conditions” are. It should be “physiological”.
- L119, suggest changing to “C4 grasses” to be precise and consistent with Tables 2 and 3. It is “tundra shrub” in Tables 1 and 2. Please clarify what is “net C availability”.
- L125, consider listing the pools in a table to present the information more clearly.
- L130, please clarify “based on lignin: N ratio of plant material”.
- L134, please either clarity the temperature and moisture effects or remove the word “effects”.
- L140, please revise “plant life activities”.
- L141, L144, please refrain from using “/” excessively. Suggest changing “physical/biological” to “physical and biological” and “temperature/moisture” to “temperature and moisture”. Please check for other “/” as well.
- L145, please revise this sentence and clarify “surface water”, “carbon fluxes” (it is not mentioned in the second half of the sentence), and “plant litter” (e.g., as in fluxes for production and decomposition or pools).
- L148-150, please revise this sentence. It is unclear what the authors mean by “N effects on plant physiology from photosynthesis, ... plus a dynamic C/N ratio”.
- L152-154, please revise this sentence. It reads repetitive with “not only considers N limitation ... but also emphasizes the N limitation effect ...” and “help us obtain more information to understand ...”
- L163-164, please revise the sentence to clarify the potential confusion that GPP follows autotropic respiration. Please revise “in plant life”.
- L166, this might be controversial as in plants can certainly respond and adapt to lower N availability but it would be a stretch to certainly call it “adjust resource requirements”.
- L167-170, please revise this sentence. It reads contradicting with “resorb only 50%” and “cause a major internal nutrient flux”.
- L170-172, please revise this sentence to improve clarity and avoid going in circle, such as what affect plant productivity and litter N content. Now it reads like “plant responses affect plant productivity and litter N content”.
- L173-174, please revise this sentence to clarify “improve plant responses”.
- L179-196, the majority of this paragraph should fit in the introduction or discussion better.
- L197, please revise this sentence to increase clarity. For instance, NPP is part of the terrestrial C cycle.
- L199, please clarify “normal N concentration”.
- L203, please revise the sentence “Because plants need time to turnover, the plant N processes ...” for clarity and accuracy.
- L205, perhaps the authors mean “modulates LAI evolution, e.g., via leaf mortality?” Should it be “supplies” instead of “supplements?”
- L209, since C/N ratios is abbreviated as CNRs from here, why not introducing it from the start?
- Regrettably, similar issues persist throughout the rest of the text. I will refrain from detailing them further until the authors have thoroughly revised the manuscript.
Overall, the general structure, clarity, terminology, as well as accuracy throughout the manuscript need to be substantially improved.
Citation: https://doi.org/10.5194/egusphere-2023-2634-RC1 - AC1: 'Reply on RC1', Zheng Xiang, 14 Apr 2024
-
RC2: 'Comment on egusphere-2023-2634', Anonymous Referee #2, 08 Mar 2024
Review comments for egusphere-2023-2634
Title: Development of a plant carbon-nitrogen interface coupling framework in a coupled biophysical-ecosystem-biogeochemical model (SSiB5/Triffid/DayCent-SOM v1.0): Its parameterization, implementation, and evaluation
This study proposed a plant carbon-nitrogen coupling framework to improve a biophysical-ecosystem-biogeochemical model. The author ran the modified model at the site and global levels, and compared the model results with in-situ observations and remote sensing/machine learning estimations . Moreover, the authors conducted a series of experimental experiments at the global level to quantify the major effects of the N process and C-N interface coupling methodology on the C cycle. This study proposes a new approach, and considers the N limitation effects not only on photosynthesis but also on plant respiration and phenology. However, there are several significant drawbacks in this study. The reviewer has the following concerns and suggestions for the authors to consider:
- Does the SSiB5/Triffid/DayCent-SOM v1.0 model consider anthropogenic N inputs (N deposition, fertilizer and manure) into terrestrial ecosystems? I guess no, since there is not no such information mentioned in the manuscript. If the model doesn’t consider anthropogenic N inputs, the reported N limitation effects may be largely exaggerated because anthropogenic N inputs to terrestrial ecosystems are much larger than the vegetation N fixation in recent decades which can relief N limitation. In Figure 8 (f), the effect of N limitation is large in Eastern China and central USA, however, the anthropogenic N inputs were quite large in these regions (Tian et al., 2022), the N limitation shouldn’t be large if anthropogenic N inputs are considered. This is my major concern.
- The SSiB5/Triffid/DayCent-SOM v1.0 model performs poor in modelling the magnitude of LAI although its performance is better than SSiB4. At the global level, SSiB5 estimation is about 100% higher than the remote sensing estimation (Figure 11)! Please elaborate on how is LAIbalance calculated in model and the vegetation carbon allocation scheme. Also, it is necessary to add one paragraph discussing the potential reasons for the overestimation of LAI and the future improvement measures.
- There is no tundra site in site-level validation. I recommend adding at least one tundra site. Please elaborate on the calculation of PFT fractional coverage in model, and add one figure comparing model results with satellite-based land cover product to justify that model can accurately estimate PFT fractional coverage.
- I suggest list equations that calculate key processes and variables in carbon and nitrogen cycles such as GPP, SOC/SON decomposition, plant N fixation, plant N uptake, and N mineralization.
- The manuscript needs modifications on the structure. From my point of view, it is better to move line 164-176 and line 179-191 to the Introduction part, and the order of section 3.3 and 3.2 should be reversed.
- Moreover, more discussions on the limitations of the SSiB5/Triffid/DayCent-SOM v1.0 model and potential future developments are needed.
- Please show some results of NlResp and NlPhen, otherwise, you should delete the descriptions of these experiments.
Line-specific comments and suggestions:
Line 86: Please list these plant N metabolism processes.
Line 104: 1982-2007 rather than 1948-2007.
Line 126: eight types rather than six types?
Line 197: delete “ and terrestrial CX cycles”
Line 268-270: I suggest delete line 268-270 to avoid misinterpretation
Line 284: I didn’t find the paper: Yang et al., 1992
Line 320: temporal resolution of vegetation dynamics is ten-day, is it too coarse for phenology (especially for the boreal forests and tundra)?
Line 395: How do you set up the equilibrium rum at the site level? The same with global run?
Line 405: Four sets of sensitivity experiments rather than six sets?
Figure 7: SSiB5 is higher than in (g) and (k). In these tow sites, SSiB5 has lower GPP than SSiB4, why its evapotranspiration (latent heat) is higher? This doesn't seem to make sense.
Figure 9: IS LAI the mean value of GIMMIS and GLASS?
Line 542-543: Is there any observational evidence for this vegetation transition?
Reference:
Tian H, Bian Z, Shi H, et al. History of anthropogenic Nitrogen inputs (HaNi) to the terrestrial biosphere: a 5 arcmin resolution annual dataset from 1860 to 2019[J]. Earth System Science Data, 2022, 14(10): 4551-4568.
Citation: https://doi.org/10.5194/egusphere-2023-2634-RC2 - AC2: 'Reply on RC2', Zheng Xiang, 14 Apr 2024
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Zheng Xiang
Melannie D. Hartman
William J. Parton
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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