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: final response (author comments only)

RC1: 'Comment on bg2022172', Anonymous Referee #1, 05 Sep 2022
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On balance, I think it should NOT be published in its current form.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
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.

AC3: 'Reply on RC1', Yujie Wang, 02 Feb 2023
Following our previous response, we have made more changes to the text, including adding two new figures (one for the spartial and temporal patterns of f_APAR * f_PPAR; one for how GPP and SIF may be biased if one neglect the chlorophyll content patterns).
[New Author response]
As mentioned in the last response, we added a new figure to show how global simulations of GPP and SIF may be impacted. We emulated the typical settings of high leaf absorption coefficient of 0.86 compared to using gridded chlorophyll content. We ran the emulation by setting chlorophyll content to 50 ug cm2, and f_PSII = 0.592 so that f_APAR * f_PPAR * f_PSII = 0.86 * 0.5 = 0.43.
Related changes are listed here:
 We emulated how global simulations of the gross primary productivity (GPP; integrated gross photosynthetic rate of the canopy) and solarinduced chlorophyll fluorescence are impacted if one uses the average CLM setting of leaf absorption coefficients (0.86). We ran the emulation of constant fAPAR · fPPAR · fPSII = 0.86 · 0.5 using the Land model developed within the Climate Modeling Alliance (CliMA Land) (Wang et al., 2021, 2022). Because of the higher modeled JPAR, gross photosynthetic rate and thus GPP are always overestimated compared to the reference where spatial variations of chlorophyll content are accounted for (Fig. 7a,c). Annually mean GPP is overestimated by up to 1.5 μmol m−2 s−1 in the tropical regions (Fig. 7a). In comparison, SIF at 740 nm (SIF740) is overestimated in the high latitude regions, but slightly underestimated in the low latitude regions (Fig. 7b,d).

AC1: 'Reply on RC1', Yujie Wang, 08 Sep 2022

RC2: 'Comment on bg2022172', Anonymous Referee #2, 13 Jan 2023
The manuscript presented by Wang and Frankenberg presents a leaf photosynthesis modeling simulation to evaluate light absorption features and smoothing curvature (theta) to impact the maximum electron transport rate and photosynthetic rate. The manuscript is clearly written and well presented, the descriptions for the modeling assumptions and the bias are appropriate, and the reasoning that is given for the interpretation of model results is largely sound. Many Earth system modeling studies have shown the importance of the photosynthetic capacity for vegetation carbon assimilation, due to the availability of the photosynthetic capacity estimation from various data sources (e.g., solarinduced chlorophyll fluorescence). The topic in this manuscript is interesting for both leaf and canopylevel photosynthetic modeling study.
I appreciate the effort of the authors and it is a very interesting and relevant topic for the photosynthesis model, but this manuscript provides the information that the modeler’s community may already be familiar with. I would expect to see some analysis and results that show a clear improvement to resolve the bias in alpha and beta. For example, figure 2b demonstrates that the difference between artificial (red and blue light sources form LICOR) and natural light remains relatively stable for fAPAR*fPPAR when chlorophyll contents > 10 ug cm2, and it suggests that this bias may be corrected by using a constant value for most of the chlorophyll conditions. In addition, I think the presentation of the manuscript and the description of some parts should be improved before publishing. Some comments may be taken into account to improve the manuscript (see more detailed comments on these main concerns below).
1. First, it is better to clarify "JPAR" and "J". In this work, the authors define the JPAR as "potential electron transport in photosystem II" in Lines 1718, and also define the J as "the potential electron transport rate" in Line 61. In my understanding, these two items are the same, considering no mention of photosystem I in this study. But they are totally different in context.
2. The alpha contains information about fAPAR, fPPAR, fPSII, and phiPSIImax. The authors investigate the bias in fAPAR*fPPAR but neglect the variation in fPSII and phiPSIImax. It is worth noting that significant seasonal dynamics of phiPSIImax can be observed in evergreen forests (Mangey 2019, DOI: 10.1073/pnas.1900278116). PorcarCastell (2021, DOI: 10.1038/s41477021009804) also mentioned fPSII did not remain constant over time.
3. Since the manuscript aims to be a type of technical note, the results in this work should provide direct information to help researchers to correct the bias in fAPAR and fPPAR, which is caused by the difference between artificial and natural light conditions. A similar study can be found in McClain et al. 2020 (DOI: 10.1111/nph.16255).
4. A ∼ Ci curve is generally measured under lightsaturated conditions. Thus, it is not appropriate to say: “Jmax25 is fitted from the lightlimited part of A ∼ Ci curve” in Line 59. “RuBPregeneration limited part” may be suitable.

AC2: 'Reply on RC2', Yujie Wang, 02 Feb 2023
The manuscript presented by Wang and Frankenberg presents a leaf photosynthesis modeling simulation to evaluate light absorption features and smoothing curvature (theta) to impact the maximum electron transport rate and photosynthetic rate. The manuscript is clearly written and well presented, the descriptions for the modeling assumptions and the bias are appropriate, and the reasoning that is given for the interpretation of model results is largely sound. Many Earth system modeling studies have shown the importance of the photosynthetic capacity for vegetation carbon assimilation, due to the availability of the photosynthetic capacity estimation from various data sources (e.g., solarinduced chlorophyll fluorescence). The topic in this manuscript is interesting for both leaf and canopylevel photosynthetic modeling study.
I appreciate the effort of the authors and it is a very interesting and relevant topic for the photosynthesis model, but this manuscript provides the information that the modeler’s community may already be familiar with. I would expect to see some analysis and results that show a clear improvement to resolve the bias in alpha and beta. For example, figure 2b demonstrates that the difference between artificial (red and blue light sources form LICOR) and natural light remains relatively stable for fAPAR*fPPAR when chlorophyll contents > 10 ug cm2, and it suggests that this bias may be corrected by using a constant value for most of the chlorophyll conditions. In addition, I think the presentation of the manuscript and the description of some parts should be improved before publishing. Some comments may be taken into account to improve the manuscript (see more detailed comments on these main concerns below).
[Author response]
Thanks for the positive feedback and suggestions. We have revised the manuscript carefully to address the comments. Please find our pointtopoint responses below.
1. First, it is better to clarify "JPAR" and "J". In this work, the authors define the JPAR as "potential electron transport in photosystem II" in Lines 1718, and also define the J as "the potential electron transport rate" in Line 61. In my understanding, these two items are the same, considering no mention of photosystem I in this study. But they are totally different in context.
[Author response]
Thanks for the clarification. We have clarified the definitions of JPAR and J in the revision that both are for PSII (JPAR is the PPAR that potentially excites electrons in photosystem II, and J is the potential electron rate in photosystem II limited by JPAR and Jmax).
2. The alpha contains information about fAPAR, fPPAR, fPSII, and phiPSIImax. The authors investigate the bias in fAPAR*fPPAR but neglect the variation in fPSII and phiPSIImax. It is worth noting that significant seasonal dynamics of phiPSIImax can be observed in evergreen forests (Mangey 2019, DOI: 10.1073/pnas.1900278116). PorcarCastell (2021, DOI: 10.1038/s41477021009804) also mentioned fPSII did not remain constant over time.
[Author response]
Thanks for bringing it up, and it is indeed important to implement these in future land modeling. We have added two paragraphs to discuss how f_PSII and Psi_PSIImax may vary.
Changes
 Besides fAPAR and fPPAR, assumptions of constant fPSII and ΦPSII,max may also introduce errors in computed JPAR. The fPSII is rarely measured but often assumed to be 0.5, given that plants are presumed to equally partition the energy between photosystem I and II to mostly efficiently utilize the absorbed photons when plants are not stressed. It should be aware that the partition of photons between photosystems varies with their wavelength, as shorter wavelength photons (below 680 nm) tend to excite photosystem II whereas longer wavelength photons overexcite photosystem I (Hogewoning et al., 2012; Laisk et al., 2014). Generally, as the light harvest complex on photosystem II may detach and reattach to photosystem I to avoid excessive light into photosystem II (Allen et al., 1981), it makes sense to assume fAPAR = 0.5 when PSII takes more photons when shorter wavelength light (below 680 nm) is abundant. However, if the incoming radiation is mostly longwave light (above 680 nm), the assumption of fAPAR = 0.5 and the photosynthesis models which fail to account for photosystem I electron transport will be problematic (PorcarCastell et al., 2021).
 When not being assumed to be constant, ΦPSII,max is typically computed from the rate coefficients of photochemical yield (KP), fluorescence (KF), and heat dissipation (KD); and in recently years, and rate coefficient of sustained nonphotochemical quenching (KS) at low temperatures also comes into play (PorcarCastell, 2011; Magney et al., 2019; Raczka et al., 2019) [EQ 4 PLACEHOLDER]. However, these rate coefficients are likely temperature dependent. For example, van der Tol et al. (2014) suggested to add a temperature dependency to KD to account for the temperature responses of minimum fluorescence after dark adaptation (Fo) and maximum fluorescence after dark adaptation (Fm); Raczka et al. (2019) found that implementing a dynamic KS term at low temperatures improved the modeled solar induced chlorophyll fluorescence at a subalpine forest during winter time. As a result, it is more reasonable to use a temperature dependent ΦPSII,max by accounting for KD and KS as variables in vegetation modeling, e.g., [EQS 5 and 6 PLACEHOLDER], where Tleaf is leaf temperature in ◦C, [KS,max, b, Ts] are fitting parameters, S is a dynamic acclimation state based on temperature (see Raczka et al. (2019) for more details).
3. Since the manuscript aims to be a type of technical note, the results in this work should provide direct information to help researchers to correct the bias in fAPAR and fPPAR, which is caused by the difference between artificial and natural light conditions. A similar study can be found in McClain et al. 2020 (DOI: 10.1111/nph.16255).
[Author response]
We agree that making corrections over the absorption coefficient could help reduce the model bias in photosynthetic rates. Based on the global scale inversion of chlorophyll contents, we will add a new figure (and data product) showing the spatial and temporal variation of the coefficient (fAPAR*fPPAR), which can be ported to other LSMs. The new figure (pasted below) shows how fAPAR*fPPAR varies spatially based on annually mean chlorophyll contents. The dataset based on annually and weekly mean chlorophyll contents, which can be found at Zenodo, would help improve the model parameterizations for other LSMs.
Changes:
 At the global scale, fAPAR · fPPAR ranges from 0.1 to 0.75 based on the annually mean chlorophyll content derived from Croft et al. (2020) (Fig. 3a–c). Corresponding bias ranges from 0.11 to 0.76, and is highest in the high latitude regions (Fig. 3d). The fAPAR · fPPAR and thus the bias also show seasonal variations because of the seasonality of chlorophyll content (Wang, 2023). The annually and weekly mean fAPAR·fPPAR dataset that can be used as prescribed inputs for other land surface models can be found at Wang (2023).
4. A ∼ Ci curve is generally measured under lightsaturated conditions. Thus, it is not appropriate to say: “Jmax25 is fitted from the lightlimited part of A ∼ Ci curve” in Line 59. “RuBPregeneration limited part” may be suitable.
[Author response]
Thanks for clarifying it. We have fixed it in our revision.

AC2: 'Reply on RC2', Yujie Wang, 02 Feb 2023
Yujie Wang and Christian Frankenberg
Yujie Wang and Christian Frankenberg
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