Accelerated photosynthesis routine in LPJmL4
 ^{1}RICAM, Altenbergerstr. 69, 4040 Linz, Austria
 ^{2}Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14412 Potsdam, Germany
 ^{1}RICAM, Altenbergerstr. 69, 4040 Linz, Austria
 ^{2}Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14412 Potsdam, Germany
Abstract. The increasing impacts of climate change require strategies for climate adaptation. Dynamic Global Vegetation Models (DGVMs) are one type of multisectorial impact models with which the effects of multiple interacting processes in the terrestrial biosphere under climate change can be studied. The complexity of DGVMs is increasing as more and more processes, especially for plant physiology, are implemented. Therefore, there is a growing demand for increasing the computational performance of the underlying algorithms as well as ensuring their numerical accuracy. One way to approach this issue is to analyse the routines which have the potential for improved computational efficiency and/or increased accuracy when applying sophisticated mathematical methods.
In this paper, the FarquharCollatz photosynthesis model under water stress as implemented in the LundPotsdamJena managed Land DGVM (4.0.002) was examined. We found that the numerical solution of a nonlinear equation, so far solved with the Bisection method, could be significantly improved by using Newton's method instead. The latter requires the computation of the derivative of the underlying function which is presented. Model simulations show a significant lower number of iterations to solve the equation numerically and an overall run time reduction of the model of about 16 % depending on the chosen accuracy. The FarquharCollatz photosynthesis model forms the core component in many DGVMs and landsurface models. An update in the numerical solution of the nonlinear equation can therefore be applied to similar photosynthesis models. Furthermore, this exercise can serve as an example for improving computationally costly routines while improving their mathematical accuracy.
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Jenny Niebsch et al.
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RC1: 'Comment on gmd2022126', Anonymous Referee #1, 12 Jul 2022
In their paper "Accelerated photosynthesis routine in LPJmL4" the authors show that using a different algorithm in a subroutine of the photosyntheis computation leads to model speed up and higher numerical accuracy of the DGVM LPJmL.
I very much agree with the authors that DGVMs need improvements in their numerical methods to decrease their computing time. Therefore, I see the proposed methodology as an important step towards this goal.
However, I find that replacing the bisection method with the Newton method to find the root of a continuous function does not suffice for a technical paper. A short technical comment could be appropriate, but quite frankly I believe that this (nonetheless important) improvement of LPJmL should simply be mentioned in the release notes of a new release of LPJmL.I also find that important things are not sufficiently discussed, namely:
1. There are only two citations when mentioning that this representation of photosynthesis is used in the majority of DGVMs. There are also other representations of PS and more citations will underline the point that FarquharCollatz is really the most used one.
2. It should at least be mentioned that the function f suffices all criteria for the Newtonmethod
3. Actually also a plot of f would be interesting to see, at least for one particular set of parameters, to let the reader get an impression of how this function looks like.
4. The Newtonmethod may fail when the starting value is chosen too far away from the root, it is not discussed whether this could become a problem.
5. Some outputs had much higher changes when the new method was applied. There is no discussion why that could be.To conclude, I unfortunately cannot recommend this manuscript for publication as I evaluate its impact as too low for a paper in GMD.
 AC1: 'Reply on RC1', Jenny Niebsch, 07 Nov 2022

RC2: 'Comment on gmd2022126', Anonymous Referee #2, 25 Sep 2022
General comments:
This manuscript describes an implementation of Newton’s method to speed up the computation of the solution to the photosynthesis scheme in the LPJ DGVM. This topic is generally appropriate for a report in Geoscientific Model Development, but as currently written the manuscript is likely to be relatively low impact. Primary concerns are: (1) the application of Newton’s method to this problem while logical is not novel; (2) while it speeds the solution, the marginal improvement is modest (only on the order of ~16%); (3) the focus on the acceleration of the photosynthesis scheme overlooks substantial underlying problems with calibration and evaluation of this scheme. To increase the impact of this manuscript, I would suggest: (a) including a concise review of the numeric methods used to implement the FarquharCollatz style photosynthesis schemes in land surface models; (b) better contextualizing the importance of computational efficiency relative to other priorities for the development of the photosynthesis scheme; (c) condensing the figures down to one or two key visuals, summarizing the magnitude of the impact of Newton’s method.
Specific comments:
Line 30, The current text should be updated to accurately describe the pathway that the Farquharstyle model took into largescale applications. The Farquhar et al. (1980) photosynthesis model was originally coupled to a stomatal model by Collatz et al. (1991; 1992). The coupled photosynthesisconductance scheme was then integrated into the Simple Biosphere Model developed by Sellers et al. (1992; 1996a, b, c, d). These initial applications were then built on by Haxeltine and Prentince.
Farquhar, G.D., von Caemmerer, S.V. and Berry, J.A., 1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta, 149(1), pp.7890.
Collatz, G.J., Ball, J.T., Grivet, C. and Berry, J.A., 1991. Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer. Agricultural and Forest meteorology, 54(24), pp.107136.
Collatz, G.J., RibasCarbo, M. and Berry, J.A., 1992. Coupled photosynthesisstomatal conductance model for leaves of C4 plants. Functional Plant Biology, 19(5), pp.519538.
Sellers, P.J., Berry, J.A., Collatz, G.J., Field, C.B. and Hall, F.G., 1992. Canopy reflectance, photosynthesis, and transpiration. III. A reanalysis using improved leaf models and a new canopy integration scheme. Remote sensing of environment, 42(3), pp.187216.
Sellers, P.J., Randall, D.A., Collatz, G.J., Berry, J.A., Field, C.B., Dazlich, D.A., Zhang, C., Collelo, G.D. and Bounoua, L., 1996. A revised land surface parameterization (SiB2) for atmospheric GCMs. Part I: Model formulation. Journal of climate, 9(4), pp.676705.
Sellers, P.J., Tucker, C.J., Collatz, G.J., Los, S.O., Justice, C.O., Dazlich, D.A. and Randall, D.A., 1996. A revised land surface parameterization (SiB2) for atmospheric GCMs. Part II: The generation of global fields of terrestrial biophysical parameters from satellite data. Journal of climate, 9(4), pp.706737.
Randall, D.A., Dazlich, D.A., Zhang, C., Denning, A.S., Sellers, P.J., Tucker, C.J., Bounoua, L., Berry, J.A., Collatz, G.J., Field, C.B. and Los, S.O., 1996. A revised land surface parameterization (SiB2) for GCMs. Part III: the greening of the Colorado State University general circulation model. Journal of Climate, 9(4), pp.738763.
Lines 3738, I recognize that some of this will be presented later, but it would help to set up the manuscript to summarize the runtime analysis here and state what fraction of the total time was originally required by the photosynthesis routine.
Lines 4245, Suggest to review and summarize here the literature on the numeric methods that have been used to implement the FarquharCollatz style photosynthesis schemes within land surface models. Newton’s method has been implemented in many different modeling frameworks to solve the coupled photosynthesisconductanceenergy balance schemes, but I am not aware of a review that provides a concise overview of these applications.
Lines 99129, Section is difficult to follow without having the mathematical symbols defined at first use and the flow of the equations explained in narrative form. To improve readability, suggest defining each mathematical symbol in text at first use and also explaining what each equation represents in physical terms rather than just presenting the mathematical derivation.
Lines 174184, The argument developed here is a bit confusing. The lack of an impact of Newton’s method on modeled pools and fluxes does not imply anything about the accuracy of the pool/flux calculations. The “accuracy of the photosynthesis scheme” must be defined relative to skill at explaining observations. Recent work by Walker et al. (2021) has highlighted the challenges in rigorously confronting the FarquharCollatz style schemes with observations due to the empirical coefficients that have been used as tuning knobs. One path forward is updating the current FarquharCollatz schemes with the Johnson and Berry (2021) scheme which eliminates empirical coefficients, reduces the total number of free variables, and permits calculation of both gasexchange and chlorophyll fluorescence.
Walker, A.P., Johnson, A.L., Rogers, A., Anderson, J., Bridges, R.A., Fisher, R.A., Lu, D., Ricciuto, D.M., Serbin, S.P. and Ye, M., 2021. Multiâhypothesis comparison of Farquhar and Collatz photosynthesis models reveals the unexpected influence of empirical assumptions at leaf and global scales. Global change biology, 27(4), pp.804822.
Johnson, J.E. and Berry, J.A., 2021. The role of cytochrome b6f in the control of steadystate photosynthesis: a conceptual and quantitative model. Photosynthesis Research, 148(3), pp.101136.
Figures D1D12, The current figures simply summarize differences in model output across a variety of metrics; they add relatively little to the impact of the paper and it would be useful to distill them down to a smaller number of key visuals.
Technical corrections:
Line 38, ‘fracture’ should probably be ‘fraction’

AC2: 'Reply on RC2', Jenny Niebsch, 07 Nov 2022
We want to thank referee 2 for the many useful suggestions and comments which we hope improved our paper significantly.
Now we included a review of the numeric methods used in the implementation of the FarquharCollatz photosynthesis scheme in land surface models in our manuscript.
Also, we have tested the most sensitive parameters in the photosynthesis routine and describe the outcome in comparison to the effect of improving computation efficiency in the manuscript.We condensed the figures to the key visuals, summarizing the magnitude of the impact of Newton's method.
The readabilty of the mathemaical part was improved, too.
Kind regards
corresponding author (Jenny Niebsch)

AC2: 'Reply on RC2', Jenny Niebsch, 07 Nov 2022
Status: closed

RC1: 'Comment on gmd2022126', Anonymous Referee #1, 12 Jul 2022
In their paper "Accelerated photosynthesis routine in LPJmL4" the authors show that using a different algorithm in a subroutine of the photosyntheis computation leads to model speed up and higher numerical accuracy of the DGVM LPJmL.
I very much agree with the authors that DGVMs need improvements in their numerical methods to decrease their computing time. Therefore, I see the proposed methodology as an important step towards this goal.
However, I find that replacing the bisection method with the Newton method to find the root of a continuous function does not suffice for a technical paper. A short technical comment could be appropriate, but quite frankly I believe that this (nonetheless important) improvement of LPJmL should simply be mentioned in the release notes of a new release of LPJmL.I also find that important things are not sufficiently discussed, namely:
1. There are only two citations when mentioning that this representation of photosynthesis is used in the majority of DGVMs. There are also other representations of PS and more citations will underline the point that FarquharCollatz is really the most used one.
2. It should at least be mentioned that the function f suffices all criteria for the Newtonmethod
3. Actually also a plot of f would be interesting to see, at least for one particular set of parameters, to let the reader get an impression of how this function looks like.
4. The Newtonmethod may fail when the starting value is chosen too far away from the root, it is not discussed whether this could become a problem.
5. Some outputs had much higher changes when the new method was applied. There is no discussion why that could be.To conclude, I unfortunately cannot recommend this manuscript for publication as I evaluate its impact as too low for a paper in GMD.
 AC1: 'Reply on RC1', Jenny Niebsch, 07 Nov 2022

RC2: 'Comment on gmd2022126', Anonymous Referee #2, 25 Sep 2022
General comments:
This manuscript describes an implementation of Newton’s method to speed up the computation of the solution to the photosynthesis scheme in the LPJ DGVM. This topic is generally appropriate for a report in Geoscientific Model Development, but as currently written the manuscript is likely to be relatively low impact. Primary concerns are: (1) the application of Newton’s method to this problem while logical is not novel; (2) while it speeds the solution, the marginal improvement is modest (only on the order of ~16%); (3) the focus on the acceleration of the photosynthesis scheme overlooks substantial underlying problems with calibration and evaluation of this scheme. To increase the impact of this manuscript, I would suggest: (a) including a concise review of the numeric methods used to implement the FarquharCollatz style photosynthesis schemes in land surface models; (b) better contextualizing the importance of computational efficiency relative to other priorities for the development of the photosynthesis scheme; (c) condensing the figures down to one or two key visuals, summarizing the magnitude of the impact of Newton’s method.
Specific comments:
Line 30, The current text should be updated to accurately describe the pathway that the Farquharstyle model took into largescale applications. The Farquhar et al. (1980) photosynthesis model was originally coupled to a stomatal model by Collatz et al. (1991; 1992). The coupled photosynthesisconductance scheme was then integrated into the Simple Biosphere Model developed by Sellers et al. (1992; 1996a, b, c, d). These initial applications were then built on by Haxeltine and Prentince.
Farquhar, G.D., von Caemmerer, S.V. and Berry, J.A., 1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta, 149(1), pp.7890.
Collatz, G.J., Ball, J.T., Grivet, C. and Berry, J.A., 1991. Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer. Agricultural and Forest meteorology, 54(24), pp.107136.
Collatz, G.J., RibasCarbo, M. and Berry, J.A., 1992. Coupled photosynthesisstomatal conductance model for leaves of C4 plants. Functional Plant Biology, 19(5), pp.519538.
Sellers, P.J., Berry, J.A., Collatz, G.J., Field, C.B. and Hall, F.G., 1992. Canopy reflectance, photosynthesis, and transpiration. III. A reanalysis using improved leaf models and a new canopy integration scheme. Remote sensing of environment, 42(3), pp.187216.
Sellers, P.J., Randall, D.A., Collatz, G.J., Berry, J.A., Field, C.B., Dazlich, D.A., Zhang, C., Collelo, G.D. and Bounoua, L., 1996. A revised land surface parameterization (SiB2) for atmospheric GCMs. Part I: Model formulation. Journal of climate, 9(4), pp.676705.
Sellers, P.J., Tucker, C.J., Collatz, G.J., Los, S.O., Justice, C.O., Dazlich, D.A. and Randall, D.A., 1996. A revised land surface parameterization (SiB2) for atmospheric GCMs. Part II: The generation of global fields of terrestrial biophysical parameters from satellite data. Journal of climate, 9(4), pp.706737.
Randall, D.A., Dazlich, D.A., Zhang, C., Denning, A.S., Sellers, P.J., Tucker, C.J., Bounoua, L., Berry, J.A., Collatz, G.J., Field, C.B. and Los, S.O., 1996. A revised land surface parameterization (SiB2) for GCMs. Part III: the greening of the Colorado State University general circulation model. Journal of Climate, 9(4), pp.738763.
Lines 3738, I recognize that some of this will be presented later, but it would help to set up the manuscript to summarize the runtime analysis here and state what fraction of the total time was originally required by the photosynthesis routine.
Lines 4245, Suggest to review and summarize here the literature on the numeric methods that have been used to implement the FarquharCollatz style photosynthesis schemes within land surface models. Newton’s method has been implemented in many different modeling frameworks to solve the coupled photosynthesisconductanceenergy balance schemes, but I am not aware of a review that provides a concise overview of these applications.
Lines 99129, Section is difficult to follow without having the mathematical symbols defined at first use and the flow of the equations explained in narrative form. To improve readability, suggest defining each mathematical symbol in text at first use and also explaining what each equation represents in physical terms rather than just presenting the mathematical derivation.
Lines 174184, The argument developed here is a bit confusing. The lack of an impact of Newton’s method on modeled pools and fluxes does not imply anything about the accuracy of the pool/flux calculations. The “accuracy of the photosynthesis scheme” must be defined relative to skill at explaining observations. Recent work by Walker et al. (2021) has highlighted the challenges in rigorously confronting the FarquharCollatz style schemes with observations due to the empirical coefficients that have been used as tuning knobs. One path forward is updating the current FarquharCollatz schemes with the Johnson and Berry (2021) scheme which eliminates empirical coefficients, reduces the total number of free variables, and permits calculation of both gasexchange and chlorophyll fluorescence.
Walker, A.P., Johnson, A.L., Rogers, A., Anderson, J., Bridges, R.A., Fisher, R.A., Lu, D., Ricciuto, D.M., Serbin, S.P. and Ye, M., 2021. Multiâhypothesis comparison of Farquhar and Collatz photosynthesis models reveals the unexpected influence of empirical assumptions at leaf and global scales. Global change biology, 27(4), pp.804822.
Johnson, J.E. and Berry, J.A., 2021. The role of cytochrome b6f in the control of steadystate photosynthesis: a conceptual and quantitative model. Photosynthesis Research, 148(3), pp.101136.
Figures D1D12, The current figures simply summarize differences in model output across a variety of metrics; they add relatively little to the impact of the paper and it would be useful to distill them down to a smaller number of key visuals.
Technical corrections:
Line 38, ‘fracture’ should probably be ‘fraction’

AC2: 'Reply on RC2', Jenny Niebsch, 07 Nov 2022
We want to thank referee 2 for the many useful suggestions and comments which we hope improved our paper significantly.
Now we included a review of the numeric methods used in the implementation of the FarquharCollatz photosynthesis scheme in land surface models in our manuscript.
Also, we have tested the most sensitive parameters in the photosynthesis routine and describe the outcome in comparison to the effect of improving computation efficiency in the manuscript.We condensed the figures to the key visuals, summarizing the magnitude of the impact of Newton's method.
The readabilty of the mathemaical part was improved, too.
Kind regards
corresponding author (Jenny Niebsch)

AC2: 'Reply on RC2', Jenny Niebsch, 07 Nov 2022
Jenny Niebsch et al.
Jenny Niebsch et al.
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