Response to reviewer comments

In the manuscript “On the impact of canopy model complexity on simulated carbon, water, and solar-induced chlorophyll fluorescence fluxes”, Wang and Frankenberg examined how different representations of canopy structure in models influence the estimates of carbon, water and SIF fluxes. They used a recent version of Land model in Climate Modelling Alliance to design 5 different representations of canopies – from simple to complex, and compared their estimated fluxes at one example site. I think this work is a valuable theoretical contribution to both model and remote sensing communities. It delivers a key message that the underlying assumptions of models and remote sensing on canopy structure are often not compatible with each other, and integrating them without proper consideration canopy structural can lead to biases. I am happy to support the paper, however, there is one major concern that I hope the authors could address first.

canopy model that regards canopy as a single big leaf was typically used with Penman-Monteith equation (Penman, 1948;Monteith, 1965) to compute land surface evaporation in early LSMs. Sellers et al. (1992) updated the one-big-leaf model by adding an exponentially diminishing photosynthetic rate within the canopy depth to upscale photosynthesis for the carbon-water coupled LSMs. Yet, this scheme often underestimated canopy assimilation rate as the exponential function cannot properly represent the vertical light and photosynthesis profiles. (2) Two-leaf radiation scheme that separates the canopy into a group of sunlit leaves and a group of shaded leaves (Norman, 1982;De Pury and Farquhar, 1997;Campbell and Norman, 1998;Chen et al., 1999) was used to account for the horizontal and vertical light heterogeneity in the canopy.
(3) Two-big-leaf canopy model combines one-big-leaf canopy model and twoleaf radiation scheme to upscale carbon and water fluxes, and treats each of the sunlit and shaded fractions as a single big leaf where leaf biochemical parameters and radiation are upscaled to canopy level (De Pury and Farquhar, 1997;Wang and Leuning, 1998). (4) Two-leaf canopy model uses two-leaf radiation scheme, and treats each of the sunlit and shaded fractions as a leaf with average traits for its representation (not integrated value as in a big leaf) Chen et al. (1999Chen et al. ( , 2012. Therefore, the use of term"big leaf model" needs to be cautious as it may refer to (i) two-leaf radiation scheme which is a canopy radiative transfer model or (ii) upscaling schemes which differ in the way leaf biochemical parameters are integrated (such as one-big-leaf and two-big-leaf models) or averaged (such as two-leaf canopy model).
-the author suggested that big-leaf model overestimated carbon and water fluxes, but that seems to contrast with previous studies (Sprintsin et al., 2012)(Luo et al., 2018 sorry for self-citation -where these studies suggested that big-leaf underestimated GPP and ET. I think that's partly relevant to the different definitions of big-leaf used in the current study. One characteristic of big-leaf is that they often do not use leaf-level Vcmax. Instead they use canopy-level Vcmax (such as those introduced in Sellers and De Pury papers, or CLM4.5) -just imagine a really big-leaf with a Vcmax of up to 500 umol/m2/s (LAI X leaf-level Vcmax) and how it will never be light saturated! In this case, the Jenson's inequity is working in the opposite way that reduce GPP and ET through lower Ci/Ca and the problematic upscaling from gs to canopy conductance.

RESPONSE:
We now clarify in our method section that our 1X model differs from the onebig-leaf model in that we did not integrate leaf parameters and light but used average values. So it is a one-leaf canopy model compared to the two-leaf canopy model. Because the models are different between one-leaf model and one-big leaf model, the results were not directly comparable. See the following changes made related to this comment Lines 145-148: Also, we note here that leaf biochemical parameters and APAR were not integrated within a canopy layer or sunlit/shaded fractions; instead, we used average APAR and leaf traits in our simulations. Thus, our "1X" model is a one-leaf model rather than a one-big-leaf model, and our "2X" model resembles the two-leaf model rather than two-big-leaf model.
-I think the authors have done a great modelling experiment, and I agree with that multilayer and sunlit/shaded separation is the way to go. But perhaps it is helpful to describe your different structure representations in the context of previous studies, or I concern that it may bring more confusions to the community -admittedly the perceptions of bigleaf have been already quite different between scholars.

RESPONSE:
We have now added a paragraph to highlight the difference among canopy models, following the naming/definition in Luo et al. (2018). Changes related to this comment: Lines 23-39: It should be noted that "big leaf model" may refer to different models within the last decades given their interchangeable uses (Luo et al., 2018). According to Luo et al. (2018), the "big leaf model" can be categorized as least as the following types given the purposes they were developed. (1) One-big-leaf canopy model that regards canopy as a single big leaf was typically used with Penman-Monteith equation (Penman, 1948;Monteith, 1965) to compute land surface evaporation in early LSMs. Sellers et al. (1992) updated the one-big-leaf model by adding an exponentially diminishing photosynthetic rate within the canopy depth to upscale photosynthesis for the carbon-water coupled LSMs. Yet, this scheme often underestimated canopy assimilation rate as the exponential function cannot properly represent the vertical light and photosynthesis profiles. (2) Two-leaf radiation scheme that separates the canopy into a group of sunlit leaves and a group of shaded leaves (Norman, 1982;De Pury and Farquhar, 1997;Campbell and Norman, 1998;Chen et al., 1999) was used to account for the horizontal and vertical light heterogeneity in the canopy. (3) Two-big-leaf canopy model combines one-big-leaf canopy model and two-leaf radiation scheme to upscale carbon and water fluxes, and treats each of the sunlit and shaded fractions as a single big leaf where leaf biochemical parameters and radiation are upscaled to canopy level (De Pury and Farquhar, 1997;Wang and Leuning, 1998). (4) Two-leaf canopy model uses two-leaf radiation scheme, and treats each of the sunlit and shaded fractions as a leaf with average traits for its representation (not integrated value as in a big leaf) Chen et al. (1999,2012). Therefore, the use of term"big leaf model" needs to be cautious as it may refer to (i) two-leaf radiation scheme which is a canopy radiative transfer model or (ii) upscaling schemes which differ in the way leaf biochemical parameters are integrated (such as one-big-leaf and two-big-leaf models) or averaged (such as two-leaf canopy model)." Other minor comments: 1. Considering the importance IJKX in this study and how other representations of canopy are based on it, maybe there is a need to show the equations on how to separate sunlit and shaded leaves in IJKX RESPONSE: It is a really good point. We have now included three new equations to show what we did with the sunlit/shaded partitioning. Changes related to this comment: Lines 115-124: (screenshot pasted below for equation display).
2. FQE was not defined, so it was not easy to grasp the key points from the heavy discussion in L240-260. Adding a few summary statements at the beginning of these paragraphs might help readers to follow.

RESPONSE:
We have defined FQE already as φF in the method section, to be more consistent, we changed the FQE to φF throughout the manuscript. To help readers know better what PSII and fluorescence quantum yields are, we have added a brief description of them along with the discussion of the two. Changes related to this comment: Lines 299-302: These contrasting patterns of the simpler models resulted from the different photosynthesis system II (PSII) quantum yield and fluorescence quantum yield (namely φF ) responses to APAR and CO2 (Figure 11a,b). PSII quantum yield measures efficiency of converting absorbed photons to electrons by PSII; and φF measures the efficiency of converting absorbed photons to fluorescence photons.
3. Figure 2b. Just curious about the environmental conditions for leaves described in this plot. Not very clear why Anet increases with Vcmax while gs becomes saturated.

RESPONSE:
We set a maximum stomatal conductance limit to the leaf, so that gsw cannot go beyond the maximum. This is why gsw peaks but Anet still increases with higher APAR and Vcmax. We have clarified this in the caption of Figure 2. Changes related to this comment:

RC2
The authors show the impact of using radiative transfer schemes of increasing complexity on the SIF simulated by a land model. The different options include a big leaf versus a multilayer canopy, having sun and shaded leaves, considering the leaf angle distribution and a vertically varying Vcmax. The paper is very didactic with nice illustrative figures. It demonstrates in a very elegant way the consequences of using an average APAR when lots of the relationships are non-linear. The results are as expected, differences between models are quantified, and specific behaviors of the simpler models are explained in detail to the readers (e.g. Figure 10). The authors draw important conclusions, while using a simple formalism.

RESPONSE:
We thank reviewer 2 for the support and valuable suggestions. We have now addressed all the main and minor comments, and believe the revision has improved significantly. Please see our point-to-point responses below for the detailed changes.

Main comments
The authors should clarify what they consider a land surface model. Indeed, they cite models such as CLM and ORCHIDEE that can run at global scales over centuries, such models simply cannot integrate the large number of operations performed by a model such as CliMA Land.

RESPONSE:
We consider land surface models as the models that can be used to simulate terrestrial biosphere processes at regional and global scales. We have now included sentences to highlight the importance of LSM in earth system modeling at the beginning of the Introduction. Actually, we can perform the large number of operations in the CliMA Land at the global scale such as the hyperspectral radiative transfer scheme. In the CliMA Land, a single evaluation of the basic biophysics only takes a few ms. For example, it takes less than 3 minutes to perform an hourly simulation of a site for a year (8760 values). It takes about 2 hours when we perform the global scale land surface simulations on a 1x1 degree resolution using 200 cores. We will show the result of the global simulation in a future publication. Changes related to this comment (clarification of what we consider a LSM): Lines 17-19 clean revision, hereafter): Land surface models (LSMs) simulate the carbon, water, and energy fluxes at the land-atmosphere interface at regional and global scales, and are key component for Earth system models (ESMs). The ability of LSMs to accurately model the carbon, water, and energy fluxes within vegetation canopy largely determines the predictive skills of the ESMs.
Do the authors precise somewhere how many layers they used (K)? Same for the leaf angle distribution?

RESPONSE:
We have now included the default settings for I, J, and K in the revision. Changes related to this comment: Lines 125-126: We used a default I = 9 inclination angles, J = 36 azimuth angles, K = 20 vertical layers for "IJKX" (K = 20 for for "2KX" and "KX" as well).
Page 4, Figure 2: "The black dotted vertical lines indicate two leaves at low and high light conditions.": Are they representative of shaded and sun leaves? Do sun and shaded leaves have different characteristics/parameter values? Or do they just differ by the level of light they receive? The authors should maybe show values/curves of APARsun, APARshaded and APAR for 1X/KX to clarify this point (e.g. Figure 6c in Bonan et al., 2021).

RESPONSE:
Thanks for pointing out the points that need clarification. We did not use the term sunlit or shaded leaves here in the diagram as we classify leaves by the level of light they receive. For example, in 2KX or IJKX, APAR for sunlit and shaded fractions may be above 500 umol m-2 s-1 for the top canopy layer. In this case, averaging APAR would not result in any difference. However, averaging APAR could be problematic if two APARs are on different sides of the turning point, say 150-250 umol m-2 s-1 as in Figure 2a. For example, the two leaves can be both from shaded fraction, but one is from the upper canopy layer and one is from the lower canopy layer (such as when we move from 2KX to 2X). Changes related to this comment: Lines 97-100: Note that averaging APAR values that are beyond the turning point, say 350 μmol m−2 s−1 , may not result in any bias in modeled gsw and Anet (such as for sunlit and shaded leaves in the top canopy layer); however, averaging APAR for leaves with high APAR and low APAR, say 300 and 50 μmol m−2 s−1 would result in overestimated gsw and Anet (such as for shaded leaves in upper and lower canopy as typically done in the two-leaf radiation scheme).
Regarding the difference between sunlit and shaded leaves, as the sunlit and shaded fraction change throughout the day as a function of solar zenith angle, it is not realistic to use different characteristics for the leaves based on whether they are sunlit or shaded. Yet, it is more reasonable to use different parameters for leaves at different canopy height, for example, leaves in the top canopy layer have higher Vcmax25. And we had this mentioned along with equation 8 (old equation 5). We also have revised the text to clarify this. Changes related to this comment: Lines 160-163: Note that as leaves are experiencing dynamically changing light environment throughout the day, it is unrealistic to assume the sunlit and shaded leaves have different traits; thus, we only accounted for the vertical heterogeneity but neglected the horizontal heterogeneity in each canopy layer, namely using the same characteristics for leaves within the same canopy layer. Equation 8: As to the figure, we had a similar figure as that from Bonan et al. (2021) in an earlier model description paper (Wang et al., 2021), and Figure 4b of the paper showed the magnitude of APAR for sunlit and shaded leaves. To better inform readers of the difference among APARs at different canopy complexity levels, we have included a new figure to highlight the differences. Changes related to this comment: Page 4, lines 86-90: It is nice to show the correspondence with other land surface models.

RESPONSE:
Thanks for the suggestion. We have now classified more LSMs to each canopy complexity type in a new table. Changes related to this comment: Table 1 in page 6 (pasted below) Lines 108-110: "IJKX" further modifies "2KX" by accounting for leaf inclination and azimuth angle distributions per layer (Figure 1). See Table 1 for the canopy model complexity adopted by other vegetation models (see https://yujiew.github.io/PAGES/dev/methods/#Vegetation-canopy-model-complexity for a growing list).
Equations page 5: The authors should precise that not all models compute the APAR and fractions this way. I understand Bonan et al. (2011) describe in their section 2.3 "Radiative Transfer" different ways to address the 2X problem for CLM, with different results shown in their Figure 1. RESPONSE: This is a good point, and thanks for bringing it up. We have now included a paragraph to highlight the difference between the equations and why we performed the calculation differently. Changes related to this comment: Lines 137-148: We emphasize here that to derive canopy fluorescence spectrum and its sun-sensor geometry, we need to simulate the canopy radiative transfer using hyperspectral reflectance, transmittance, and fluorescence. Due to the high spectral resolution and multiple layers required, radiative transfer and canopy fractions in complex models such as SCOPE are computed numerically. In comparison, radiative transfer and sunlit/shaded fractions are computed analytically in the two-leaf radiation scheme as the model is single layered and uses broadband reflectance and transmittance (Campbell and Norman, 1998;Bonan et al., 2021). Yet, the two-leaf radiation scheme that use broadband radiative transfer are not adequate for accurate fluorescence modeling. Crucially, the difference in the analytic and numerical solutions could result in biases in the simulated APAR and fraction.To avoid such bias, we computed the APAR and sunlit/shaded fractions for the simpler canopy setups numerically using the algorithm in "IJKX". See Figure 3 for the APAR profiles for "2KX", "KX", "2X", and "1X" derived from "IJKX". Also, we note here that leaf biochemical parameters and APAR were not integrated within a canopy layer or sunlit/shaded fractions; instead, we used average APAR and leaf traits in our simulations. Thus, our "1X" model is a one-leaf model rather than a one-big-leaf model, and our "2X" model resembles the two-leaf model rather than two-big-leaf model.
Page 6, equation 8: What is p? Is the summation over i? Same questions for equation 9 on Page 7. RESPONSE: p need to be iterated through all sunlit and shaded fractions (if any) and all canopy layers. Now we have included the two suites of equations. Changes related to this comment: Equations 11 (pasted below) Equations 12 (pasted below)