Technical note: Photosynthetic capacity estimation is dependent on model assumptions
 ^{1}Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, USA
 ^{2}Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA
 ^{1}Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, USA
 ^{2}Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA
Abstract. Modeling leaf photosynthesis is crucial for Earth system modeling. However, as photosystem light absorption and gas exchange are not typically simultaneously measured, photosynthetic capacity estimation and thus photosynthesis modeling are subject to inaccurate light absorption representation in photosynthesis models. We analyzed how leaf absorption features and light source may impact photosynthesis modeling at various settings. We found that (1) estimated photosynthetic capacity can be over or underestimated depending on model assumption, and the bias increases with higher mismatch in leaf light absorption parameters and higher true capacity; and (2) modeled photosynthetic rate can also be over or underestimated depending on model assumption, and the bias increases with higher leaf internal CO_{2}, and increases and then decreases with increasing light intensity. We recommend researchers not to mix and match results or models with inconsistent assumptions when modeling photosynthesis.
Yujie Wang and Christian Frankenberg
Status: open (until 14 Oct 2022)

RC1: 'Comment on bg2022172', Anonymous Referee #1, 05 Sep 2022
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It was difficult to make a recommendation on this paper. On the one hand, the information appears to be correct and is well presented. On the other hand, I ask myself whether the information is sufficiently new and necessary for practicing modellers. I would generally think that most modellers are wellaware of the stated issues. So, would it be worth publishing something that the relevant audience is already familiar with? Or would it still be worth publishing it for the small number of modellers that might still be unaware of these potential problems?
On balance, I think it should NOT be published in its current form. The message is just too mundane. The real question is also not really whether one models the correct parameter values but whether one models the correct ultimate fluxes or other variables that are of ultimate interest. For instance, it is not surprising that the ratio of Jmax:Vcmax inferred from leaf measurements depends on theta. That connection is sufficiently obvious that it does not have to be restated. But to what extent would the modelled assimilation rate depend on theta (provided that empirical Jmax:Vcmax ratios and ultimate simulations of assimilation rates consistently all use the same theta)?
Or, alternatively, one might ask to what extent modelled assimilation rates could vary if one combined random choices of theta and derived Jmax:Vcmax ratios. That would emulate the effective situation where empiricists derive Jmax:Vcmax ratios based on some chosen theta, but where those theta values are not communicated or not used in the application of the derived ratios for calculating resultant assimilation rates.
So, the work could be become much more valuable if it could be refocused on illustrating the quantitative importance of the issue of model assumptions for the ultimately required fluxes or other quantities that matter in the real world. It might then reach the threshold of work that provides useful quantitative information even for those readers that might be conceptually sufficiently aware of these issues.

AC1: 'Reply on RC1', Yujie Wang, 08 Sep 2022
reply
NOTE: Author reponses are BOLD.
[Author response]
We thank reviewer 1 for such a quick review and helpful suggestions. Before responding to the comments one by one, we would like to clarify a few general things the reviewer discussed.
The assumptions that may impact photosynthesis modeling include
 The leaf PAR absorption ratio (α = f_{APAR} * f_{PPAR} * f_{PSII} * Φ_{PSII,max})
 Electron transport smoothing curvature (θ)
Therefore, there are four scenarios when modeling photosynthesis
 Both model α and θ are correct
 Only model α is correct
 Only Model θ is correct
 None of α or θ is correct
Accordingly, there are four results
 Estimated J_{max25} and modeled A are correct at any conditions
 Modeled PPAR and J_{PAR} are correct, but modeled J is biased, and thus estimated J_{max25} and modeled A
 Modeled PPAR and J_{PAR} are biased, and thus J, estimated J_{max25}, and modeled A
 All of PPAR, JPAR, and J are biased, and thus estimated J_{max25} and modeled A
In the paper we submitted, we covered the following
 How α can be biased by light source and chlorophyll concentration (our section 1). This is actually the key part of our paper, which was not touched upon by the reviewer. As far as we know, this part itself has not yet been discussed in the scientific literature as we do here. It has several implications: Most land surface models don’t have chlorophyll content as state variable, hence the fraction of absorbed light going into photosynthesis remains constant, usually much more than we see in nature. This not only impacts leaf energy budget and photosynthesis computations but also modeling of spectral reflectance as well as solar induced chlorophyll fluorescence. Maybe we need to emphasize this part more and deemphasize the θ discussion, which might be more well known to the modeling community.
 How a biased α and/or θ may impact fitted J_{max25} (our section 2)
 How a biased α and/or θ may impact modeled A (our section 3)
In section 3, we clarified that in our text that the impact of α or θ only is very straight forward, namely if model α is overestimated, modeled A will be overestimated, and if model θ is overestimated, modeled A will be overestimated. Thus, we showed an example when both α and θ are biased for C3 photosynthesis, and an example when α is biased for C4 photosynthesis (θ not available in C4 photosynthesis model).
Thus, we think the reviewer had focused too much on the θ aspect of our work, which we can partially understand. We are considering changing our title to “Technical note: Leaf light absorption and electron transport assumptions bias photosynthesis modeling” to be more comprehensive and descriptive.
It was difficult to make a recommendation on this paper. On the one hand, the information appears to be correct and is well presented. On the other hand, I ask myself whether the information is sufficiently new and necessary for practicing modellers. I would generally think that most modellers are wellaware of the stated issues. So, would it be worth publishing something that the relevant audience is already familiar with? Or would it still be worth publishing it for the small number of modellers that might still be unaware of these potential problems?
[Author response]
The story of θ (curvature of the electron transport rate [J] smoothing) indeed dates back to a few decades ago. However, although researchers are now using a smoothing algorithm for J, most modelers are using a constant θ and assume the value does not matter much (according to our model, this assumption is incorrect). This assumption would result in little bias if the light condition is the same as that when the ACi curve is measured (typically saturated light environment). However, the error in modeled A can not be neglected if the light conditions differ (we show this in Figures 4 and 5). We agree with the reviewer that most modelers are (or should be) aware of the importance of accurate parameterizations and consistency of assumptions (such as leaf absorption and θ), but this is often not the case when researchers use the models, and specifically not for leaf absorption, which can only be computed correctly if chlorophyll (and Carotenoids) is explicitly taken into account. For example, it is important to calibrate leaf absorption per light source when computing PAR/APAR/PPAR and fit θ, but researchers typically use constants (for simplicity). Further, the fitted V_{cmax25} and J_{max25} may be used in other scenarios, such as to parameterize land surface models. Because of the lack of direct measurements for large scale model simulations, this kind of “biased” results are often used directly in regional and global scale research, and the biases are inherited. Furthermore, it is typically not possible to recalibrate these parameters from raw data (typically not measured or provided). Therefore, it is very important to make sure researchers use consistent model assumptions when they make leaf level measurements and run models at different scales.
As we mentioned above, besides the potential mismatch in θ, a key focus is the leaf PSII electron quantum yield (α). For example, α may differ by 0.2 between artificial and natural lights. Are land surface and vegetation models accounting for this? The answer is no for most models (the hyperspectral light based models do, if they account for Chl. variations). Thus, it is important to highlight these inconsistencies and inform modelers why we need to make changes and where we should improve existing models. In addition, α also impacts leaf energy budget, A and solar induced chlorophyll fluorescence. Thus, models who don’t take this into account might not represent the relation between GPP and chlorophyll fluorescence correctly. We can expand this discussion a bit in the revised version.
On balance, I think it should NOT be published in its current form. The message is just too mundane. The real question is also not really whether one models the correct parameter values but whether one models the correct ultimate fluxes or other variables that are of ultimate interest. For instance, it is not surprising that the ratio of Jmax:Vcmax inferred from leaf measurements depends on theta. That connection is sufficiently obvious that it does not have to be restated. But to what extent would the modelled assimilation rate depend on theta (provided that empirical Jmax:Vcmax ratios and ultimate simulations of assimilation rates consistently all use the same theta)?
[Author response]
We agree with the reviewer that “The real question is also not really whether one models the correct parameter values but whether one models the correct ultimate fluxes or other variables that are of ultimate interest”, and this is indeed what we did in the presented study. However, the question is can we model correct fluxes if the model assumptions and parameters are wrong? The answer is no if we want to model the correct fluxes at scenarios that have different environmental conditions from the reference one. An example is that ACi curve is constructed at saturated light, but the inverted parameters may be used at low light conditions, and the error in modeled fluxes will be biased.
As we mentioned above, modeled A may be biased if model α and/or θ differ from the true values. In the presented study, we showed scenario 4 for C3 photosynthesis and scenario 3 for C4 photosynthesis in our manuscript. As for the scenarios that only α or θ is biased, we covered this in lines 8991 (screenshot pasted below).
Or, alternatively, one might ask to what extent modelled assimilation rates could vary if one combined random choices of theta and derived Jmax:Vcmax ratios. That would emulate the effective situation where empiricists derive Jmax:Vcmax ratios based on some chosen theta, but where those theta values are not communicated or not used in the application of the derived ratios for calculating resultant assimilation rates.
[Author response]
We investigated this using the example of mismatched α and θ for C3 photosynthesis (see our Figure 4).
So, the work could be become much more valuable if it could be refocused on illustrating the quantitative importance of the issue of model assumptions for the ultimately required fluxes or other quantities that matter in the real world. It might then reach the threshold of work that provides useful quantitative information even for those readers that might be conceptually sufficiently aware of these issues.
[Author response]
We thank the reviewer for the constructive suggestions. We were indeed focusing on the modeled fluxes in the main text (Figure 4 and 5). The misunderstanding might arise from our title, which focused only on photosynthetic capacity estimation. We are thinking of changing the title to “Technical note: Leaf light absorption and electron transport assumptions bias photosynthesis modeling” to be more comprehensive. We will emphasize the model implications for α (and the impact on GPP and SIF) in particular, which might not be that well known (mundane) in the global modeling community.
Given that we are still very early in the review process (which is much appreciated), we hope we can still iterate this thread.

AC1: 'Reply on RC1', Yujie Wang, 08 Sep 2022
reply
Yujie Wang and Christian Frankenberg
Yujie Wang and Christian Frankenberg
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