Leaf physiological responses to light are highly non-linear, such as stomatal conductance to water vapor (gsw) and net photosynthetic rate (Anet). Typically, when absorbed photosynthetically active radiation (APAR) is low, gsw and Anet increase with higher APAR (Fig. a); when APAR is high, gsw and Anet saturate. If one has a leaf with low APAR and a leaf with high APAR (e.g., closed circles on the solid curves of Fig. a), the mean behavior of the two leaves ought to be the average gsw and Anet values (closed circles on the colored dashed lines of Fig. a). However, if one uses the mean APAR of the two leaves and calculates gsw and Anet based on the mean APAR, gsw and Anet would be overestimated (open circles on the colored solid curves of Fig. a). Note that averaging APAR values that are beyond the turning point, say 350 µmolm-2s-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 µmolm-2s-1, would result in overestimated gsw and Anet (such as for shaded leaves in an upper and lower canopy as typically done in the two-leaf radiation scheme). Thus, an overly simplified canopy model may overestimate canopy-level carbon and water fluxes, because of the inappropriately averaged APAR, as f(x‾)≠f(x)‾ when averaging non-linear functions (Anet(APAR‾)>Anet(APAR)‾ in leaf photosynthesis).

To evaluate how much canopy model complexity matters, we modeled the canopy using five different levels of complexity, and they are denoted as “1X”, “2X”, “KX”, “2KX”, and “IJKX” (Fig. ). 1X represents the scenario in which the canopy is treated as a single average leaf without sunlit or shaded fractions, and leaf radiation is averaged for the entire canopy. 2X complicates 1X by partitioning the average leaf to sunlit and shaded fractions. KX enhances 1X by partitioning the canopy to multiple layers (but no sunlit or shaded fractions per layer). 2KX partitions each canopy layer of KX to sunlit and shaded fractions. IJKX further modifies 2KX by accounting for leaf inclination and azimuth angle distributions per layer (Fig. ). See Table  for the canopy model complexity adopted by other vegetation models (see https://yujie-w.github.io/PAGES/dev/methods/#Vegetation-canopy-model-complexity for a growing list).

For IJKX, we simulated the canopy radiative transfer using the CliMA Land-adapted SCOPE model Soil Canopy Observation, Photochemistry and Energy fluxes; SCOPE v1.7;. The adaptations included that carotenoid absorption was accounted for as APAR and that canopy clumping was addressed using a clumping index . At layer i, the shaded-leaf fraction (relative to total leaf area in the canopy) is psh,i, and the sunlit-leaf fraction (relative to total leaf area in the canopy) is psl,i(incl, azi) (“incl” is the inclination angle, and “azi” is the azimuth angle). The fraction of sunlit leaves relative to total canopy leaf area in a given canopy layer is computed as 1∑incl,azipsl,i(incl,azi)=LAI(i+1)-LAI(i)LAI ⋅∫LAI(i)LAI(i+1)exp⁡(-kΩx)⋅dx, where LAI is total leaf area index, LAI(i) is the leaf area index above the ith canopy layer, LAI(i+1) is the leaf area index in and above the ith canopy layer, k is the extinction coefficient as a function of leaf inclination angle distribution, and Ω is the clumping index. Then psl,i(incl,azi) is computed using 2psl,i(incl,azi)=∑incl,azipsl,i(incl,azi)⋅1I⋅1J, where I is the number of inclination angles and J is the number of azimuth angles. The fraction of shaded leaves relative to total canopy leaf area in a given canopy layer is computed as 3psh,i=LAI(i+1)-LAI(i)LAI⋅1-∫LAI(i)LAI(i+1)exp⁡(-kΩx)⋅dx.

Corresponding APAR values for the shaded and sunlit leaves are APARsh and APARsl,i(incl, azi), respectively. We used default values of I = 9 inclination angles, J = 36 azimuth angles, and K = 20 vertical layers for IJKX (K = 20 for 2KX and KX as well).

The 2KX fraction and APAR were derived from IJKX by weighing APAR for sunlit leaves per canopy layer: 42KXpsl,i=∑incl,azipsl,i(incl,azi),2KXpsh,i=psh,i,2KXAPARsl,i=∑incl,aziAPARsl,i(incl,azi)⋅psl,i(incl,azi)∑incl,azipsl,i(incl,azi),2KXAPARsh,i=APARsh,i.

The KX fraction and APAR were derived from 2KX by weighing APAR for all sunlit and shaded leaves per canopy layer: 5KXpi=2KXpsl,i+2KXpsh,i,KXAPARi=2KXAPARsl,i⋅2KXpsl,i+2KXAPARsh,i⋅2KXpsh,iKXpi.

The 2X fraction and APAR were derived from 2KX by weighing APAR for sunlit and shaded leaves for all canopy layers, respectively, the following: 62Xpsl=∑ipsl,i,2Xpsh=∑ipsh,i,2XAPARsl=∑i2KXAPARsl,i⋅2KXpsl,i∑i2KXpsl,i,2XAPARsh=∑i2KXAPARsh,i⋅2KXpsh,i∑i2KXpsh,i.

1X APAR was derived from KX by weighing APAR for all layers: 71XAPAR=∑iKXAPARi⋅KXpi.

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 . Yet, the two-leaf radiation schemes 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 APAR and sunlit/shaded fractions for the simpler canopy setups numerically using the algorithm in IJKX. See Fig.  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 the two-big-leaf model.

Leaf traits in the canopy are not uniform among the canopy layers. Typically, leaf photosynthetic capacity (usually represented by the maximum carboxylation rate at 25 ∘C, Vcmax) is higher in upper canopy because of the better light environment. Further, leaf physiological responses to Vcmax are also highly non-linear, and using average Vcmax may also result in overestimated gsw and Anet and thus carbon and water fluxes (e.g., shift from solid circles to open circles in Fig. b).

To examine how much the vertical Vcmax profile impacts modeled canopy flux simulations, we ran the model simulation in two scenarios, one using uniform Vcmax in the canopy and one using decreasing Vcmax towards the lower canopy. For the latter scenario, Vcmax at layer i was tuned using an exponential function following and : 8Vcmax,i=Vcmax,top⋅exp⁡-0.15⋅LAI(i), where Vcmax,top is Vcmax at the top of the canopy and 0.15 is the shape factor that describes the decreasing Vcmax with canopy depth. 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.

The Vcmax profile was applied to IJKX, 2KX, and KX directly, whereas weighed mean Vcmax=∑iVcmax,i⋅KXpi was used in 1X. The Vcmax profile or value stayed constant in these four scenarios throughout the simulation, as sunlit/shaded fractions did not impact them. We note here that mean Vcmax changed with sunlit/shaded fractions in 2X and particular averages of Vcmax for sunlit and shaded fractions (2XVcmax,sl and 2XVcmax,sh, respectively) need to be updated with sunlit and shaded fractions: 92XVcmax,sl=∑i2KXVcmax,i⋅2KXpsl,i∑i2KXpsl,i,2XVcmax,sh=∑i2KXVcmax,i⋅2KXpsh,i∑i2KXpsh,i.

Note that we tuned the maximum electron transport rate and leaf respiration rate in the same manner as Vcmax.

We simulated the canopy carbon and water fluxes using a stomatal optimization model developed in given the good model performance and scalability . The stomatal optimization model posits that stomatal opening is optimized when the difference between carbon gain and risk is maximum: 10max⁡Anet︸gain-Anet⋅EEcrit︸risk, where E is the leaf transpiration rate and Ecrit is the critical transpiration rate of the leaf beyond which leaf hydraulic conductance drops below 0.1 % of the maximum (see , and , for more details of Ecrit).

At each canopy complexity level, for a given environmental condition set, we were able to obtain the steady-state stomatal conductance for each APAR, from which we computed steady-state Anet using the classic C3 photosynthesis model and E as well as leaf fluorescence quantum yield (ϕF) using the model developed in . Stand-level carbon flux, namely net ecosystem exchange (NEE; normalized per ground area), was computed using NEE=LAI⋅∑Anet⋅p-Rremain: 11IJKXNEE=LAI⋅∑i,incl,aziAnetAPARsl,i(incl,azi)⋅psl,i(incl,azi)+LAI⋅∑iAnetAPARsh,i⋅psh,i-Rremain,2KXNEE=LAI⋅∑iAnet2KXAPARsl,i⋅2KXpsl,i+Anet2KXAPARsh,i⋅2KXpsh,i-Rremain,KXNEE=LAI⋅∑iAnetKXAPAR⋅KXpi-Rremain,2XNEE=LAI⋅Anet2XAPARsl⋅2Xpsl+LAI⋅Anet2XAPARsh⋅2Xpsh-Rremain,1XNEE=LAI⋅Anet1XAPAR-Rremain, where LAI is the leaf area index and Rremain is the ecosystem respiration rate per ground area excluding the leaves. The transpiration rate from the canopy is computed and used as a proxy for estimating the difference in model ecosystem evapotranspiration (ET; normalized per ground area) using ET≈LAI⋅∑(E⋅p): 12IJKXET≈LAI⋅∑i,incl,aziEAPARsl,i(incl,azi)⋅psl,i(incl,azi)+LAI⋅∑iEAPARsh,i⋅psh,i,2KXET≈LAI⋅∑iE2KXAPARsl,i⋅2KXpsl,i+E2KXAPARsh,i⋅2KXpsh,i,KXET≈LAI⋅∑iEKXAPAR⋅KXpi,2XET≈LAI⋅E2XAPARsl⋅2Xpsl+LAI⋅E2XAPARsh⋅2Xpsh,1XET≈LAI⋅E1XAPAR.

We remind the reader here that soil evaporation is a function of soil water content, soil surface temperature, and atmospheric-vapor-pressure deficit and that soil evaporation should be the same for all tested canopy complexity models; this is also the case for evaporation from intercepted water on plant surface. Therefore, the modeled ET difference is 100 % caused by canopy transpiration, and using transpiration would not result in any biases in the relative difference of modeled ET.

For IJKX, we used ϕF computed for each sunlit and shaded leaf at each layer to compute the canopy-level SIF spectrum. For 2KX, we plugged the ϕF calculated for sunlit fraction into all the sunlit leaves of the corresponding layer of IJKX and the shaded ϕF into the shaded leaf of the corresponding layer of IJKX. Then we re-simulated the SIF spectrum at IJKX and used it as that of 2KX. For KX, we plugged the ϕF calculated for the whole layer into all the leaves of the corresponding layer of IJKX and recalculated the SIF spectrum. For 2X, we plugged the ϕF of the sunlit fraction into all the sunlit leaves in IJKX and shaded ϕF into all the shaded leaves in IJKX and recalculated the SIF spectrum. For 1X, we plugged the ϕF into all the leaves in IJKX and recalculated the SIF spectrum. We compared SIF at 740 nm (SIF740) among different complexity levels.

Despite the importance of vertical microclimate heterogeneity in modeled canopy energy fluxes e.g.,, we held environmental conditions constant among vertical canopy layers for all tested canopy complexities. Doing this allowed us to tease apart the impact of APAR distribution in the canopy (due to canopy complexity) on simulated carbon, water, and SIF fluxes.

We ran a sensitivity analysis to environmental cues for all five complexity levels to examine how much they differ in predicted carbon, water, and SIF fluxes. The tested cues included solar radiation, atmospheric-vapor-pressure deficit (VPD), temperature, soil water potential (Ψsoil), and atmospheric CO2 partial pressure (PCO2). When we altered temperature, we changed the air and leaf temperature at the same time and held air relative humidity (RH) constant at 0.47 (fraction; unitless). Saturated water vapor pressure was computed using the Clausius–Clapeyron equation: 13Psat=Ptriple⋅TTtripleΔcpRv⋅exp⁡LHv0-Δcp⋅TtripleRv⋅1Ttriple-1T, where Ptriple is the vapor pressure at the triple point (in Pa), T is the temperature (in K), Ttriple is the temperature at the triple point (in K), Δcp is the difference in isobaric specific heat of vapor and liquid (in JKg-1K-1), Rv is the gas constant of water vapor (in JKg-1K-1), and LHv0 is the latent heat of vaporization at the triple point. Atmospheric vapor pressure was computed using Psat⋅RH. For each tested environmental cue, we changed only the tested cue while holding all other environmental conditions constant. We ran the sensitivity test in two scenarios: (a) Vcmax was uniform throughout the canopy, and (b) Vcmax decreased exponentially in the lower canopy. For the two scenarios, we let the entire-canopy mean Vcmax be the same (namely mean Vcmax at 1X). We compared the modeled site-level NEE, ET, and SIF740 among canopy complexity levels.

To evaluate how much the canopy complexity models differ in real-world simulations, we ran the model using weather data from a flux tower located at Ozark, Missouri, USA US-MOz;. We used the weather and soil moisture data from day 177 to 179 in the year 2019 and prescribed leaf temperature and soil water potential to maximally reduce uncertainty among model setups. Briefly, we used outgoing longwave radiation from flux tower measurements to invert canopy temperature and used it as leaf temperature; we also used soil water content to estimate soil water potential and used it as a boundary condition for the soil–plant–air continuum. Prescribing leaf temperature and soil water potential allowed us to tease apart the difference caused by canopy complexity from that caused by environmental and physiological differences. See for the model setup details for US-MOz. In addition to the observations that were used to set up the CliMA Land model , we further applied vertical Vcmax profiles in the simulations (note that Vcmax changed in the sunlit and shaded fractions with time for 2X and stayed constant for the other four complexity levels). We tuned Vcmax and the whole-plant hydraulic conductance to let IJKX predict reasonable NEE and ET values and used these tuned parameters in all the tested canopy complexity levels. We note here that we were not trying to argue one complexity was better than others but to examine how much the complexity levels differ when we used exactly the same model input parameters.

We compared the model-predicted carbon, water, and SIF fluxes. Note here that observed SIF depends on the sun-sensor geometry and that SIF retrievals often have different sun-sensor geometries e.g., the TROPOMI satellite;. Thus, it is necessary to examine how the sun-sensor geometry may impact the SIF flux across canopy complexity levels. We ran the test using the weather data from (a) 12:00–12:30 and (b) 16:00–16:30 of day 177 in the year 2019. At each tested time window, we computed the theoretical SIF at 740 nm for a series of viewing zenith angles from 0 to 85∘ and relative azimuth angles (angle between the sensor and sun) from 0 to 360∘. We compared how much 2KX, KX, 2X, and 1X differed from IJKX.

Given that averaging APAR theoretically results in overestimated carbon and water fluxes, we expected that the difference among different canopy complexity levels meets the following trends: (a) 1X > 2X > 2KX and (b) 1X > KX > 2KX. Further, as Vcmax also theoretically results in overestimated carbon and water fluxes, we expected that adding a vertical Vcmax profile further increases the difference in fluxes across canopy complexity levels.

When a uniform Vcmax profile was applied, all tested five canopy complexity levels exhibited similar carbon and water flux responses to changing environmental cues (Fig. ). The responses included increasing canopy photosynthesis and transpiration with higher radiation (Fig. a), increasing and then decreasing photosynthesis and increasing transpiration with a higher temperature (Fig. b), decreasing photosynthesis and increasing transpiration with a higher VPD (Fig. c), decreasing photosynthesis and transpiration with drier soil (Fig. d), and increasing photosynthesis and decreasing transpiration with higher atmospheric CO2 partial pressure (Fig. e). Further, as expected, 1X, 2X, KX, and 2KX all overestimated canopy photosynthesis and transpiration compared to the IJKX mode; and the overestimation ratios met 1X > 2X > 2KX and 1X > KX > 2KX.

The SIF responses to changing environmental cues in general agreed in trends among tested complexity levels (Fig. ). However, SIF responses to radiation, temperature, and atmospheric CO2 differed dramatically among the five canopy complexity levels given the different response magnitudes (Fig. b and e). 1X and KX often resulted in different trends compared to IJKX (Fig. ). 2X and 2KX overall tracked the SIF responses though slightly overestimated SIF of IJKX well. Notably, we found high disagreement between 2X and IJKX at intermediate radiation and increasing disagreement at higher atmospheric CO2 (Fig. a and e).

When an exponential vertical Vcmax profile (lower Vcmax in the lower canopy) was applied when simulating canopy fluxes, we found similar trends compared to the scenario with constant Vcmax (Fig. ). The differences, however, were that all carbon, water, and SIF fluxes were lower when we applied a vertical Vcmax profile (Fig. ). Again, like the scenario of a uniform Vcmax, we also found divergent SIF responses to radiation and increasing disagreements among 2X, 2KX, and IJKX for elevated CO2 (Fig. a and e). The divergent flux responses to PCO2 underlined the importance of adopting a more complex canopy in future land modeling given that (i) CO2 concentration within the canopy airspace may change dramatically within a diurnal cycle due to plant carbon fixation and (ii) atmospheric mean CO2 is increasing rapidly due to anthropogenic emissions.

2KX and 2X had a lower difference from IJKX compared to KX and 1X, and 2KX had the lowest error given the better-resolved APAR fractions (Figs.  and ). Combining all response curves together from Fig. , we found that when Vcmax was evenly distributed in the canopy, relative differences between 2KX and IJKX for carbon, water, and SIF fluxes were 2.4 %, 1.2 %, and 2.8 %, respectively (Fig. ). In comparison, the differences between 2X and IJKX were all higher at 5.4 %, 3.8 %, and 4.2 %, respectively (Fig. ). Overall, 2KX had a relative error lower than 5 % (Fig. ).

When accounting for a vertically heterogeneous Vcmax profile, we still found a lower difference between 2KX and IJKX, and the relative differences were 11.1 %, 3.7 %, and 7.9 % (the differences for 2X were 23.4 %, 8.2 %, and 13.2 %; Fig. ). Overall, 2KX had a relative error lower than 10 %. Further, the higher error when adopting a vertical Vcmax profile agreed with our expectation as the impacts from APAR and Vcmax added up (canopy fluorescence was lower for the simpler canopy model at low radiations; Fig. ).

Our model simulations suggest that all tested canopy complexity levels can qualitatively capture the trends of carbon and water fluxes at the tested flux tower site (Fig. ). However, the tested complexity levels differed dramatically in the magnitudes of carbon and water fluxes. In general, 1X had the highest fluxes for both carbon and water fluxes (represented by NEE and ET), followed by KX, 2X, 2KX, and IJKX (Figs.  and ). Though 2KX and 2X, in general, had relatively small differences from IJKX, we were still able to distinguish the difference (Figs.  and ). We note here again that Figs.  and  were meant to highlight the difference between canopy complexity levels in model simulations but not to say that some models were better than others.

Using less complicated canopy complexity (namely 2KX, KX, 2X, and 1X) impacted the observed SIF depending on the sun-sensor geometry (Figs.  and ). For the tested time window at 12:00–12:30, 2KX has the least difference from IJKX, followed by 2X, KX, and 1X. In general, 2KX had a difference lower than 11 % at any viewing zenith angle or relative azimuth angle for the tested time window (Figs. ). The impact of sun-sensor geometry changed with time because of changes in solar zenith angle and total radiation (e.g., at 16:00–16:30 in the afternoon; Fig. ). While 2KX still had lower overestimated SIF compared to 2X, KX had better agreement with IJKX, and 1X even underestimated SIF. The dramatic changes in SIF from KX and 1X were due to lower incident radiation from 16:00 to 16:30 (Fig. a).

While simpler canopy models in general predicted higher carbon, water, and SIF fluxes, there were some scenarios that the simpler models predict contrasting SIF responses compared to IJKX: (a) when total radiation increased, SIF of the simpler canopy models was lower than that of IJKX at low radiation but were higher than that of IJKX at high radiation (Figs.  and ); (b) 1X model SIF increased and then decreased and stayed unchanged with higher atmospheric CO2 (Figs.  and ); and (c) KX model SIF increased marginally with higher atmospheric CO2 for a canopy without a vertical Vcmax gradient but decreased with higher CO2 for a canopy with a vertical Vcmax profile (Figs.  and ). 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 (Fig. a, b). The PSII quantum yield measures the efficiency of converting absorbed photons to electrons by PSII; and ϕF measures the efficiency of converting absorbed photons to fluorescence photons. The PSII yield increases and then saturates with higher leaf internal CO2 and lower APAR. In our model, ϕF follows the parameterization of but fitted on leaves measured by , as first used in . Typically, the PSII-to-ϕF relationship depends on the state of non-photochemical quenching NPQ;. ϕF has a maximum at intermediate PSII levels (around 0.6) but decreases at lower PSII yields (increased NPQ) as well as higher PSII yields (increased competition with photochemical quenching). This general behavior explains what we see the following: ϕF (a) stays unchanged at low radiation with higher leaf internal CO2, (b) increases and then decreases and stays unchanged with higher leaf internal CO2 at intermediate APAR, (c) increases with higher CO2 at high CO2, and (d) increases and then decreases with higher APAR (Fig. a, b). Though ϕF in general agrees with the PSII yield patterns at high APAR (typical experimental and top-of-canopy scenarios), the disagreements at low APAR could result in problems when APAR is inappropriately averaged. In our case, the turnover from APAR regions in which PSII and ϕF are anticorrelated (light-limited) to the region in which they are correlated (increase in NPQ) happens at around 200 µmolm2s-1.

When total radiation was higher, the product of ϕF and APAR (leaf-level SIF) increased (Fig. c). When ϕF stayed unchanged at low APAR, leaf-level SIF increases linearly with higher APAR, and SIF increases faster when ϕF starts to increase after a certain threshold (the threshold increased with higher leaf internal CO2; Fig. b). Then leaf-level SIF slowed down with higher APAR due to decreasing ϕF at higher APAR and was higher when leaf internal CO2 was higher (Fig. b, c). As leaf internal CO2 was theoretically lowest for 1X, then followed by KX, 2X, and 2KX given the way APAR was averaged, it was expected that 2KX increased earliest with higher APAR and that 1X had the highest SIF value at high radiation (Figs. a and a). Therefore, in the diurnal-cycle simulations, 1X SIF overestimated SIF at noon when radiation was high (Fig. ) but underestimated SIF in the late afternoon as a result of lower radiation (Fig. ). The inconsistent SIF patterns at low and high radiation from simpler canopy models may potentially result in biases in modeled diurnal and seasonal SIF, and thus we suggest using a complex canopy model when possible to minimize the impact from heterogeneous canopy radiation and leaf physiology.

The 1X model SIF response to atmospheric CO2 ought to depend on the mean canopy APAR (Fig. b): (a) if mean APAR was low, 1X SIF should stay constant with higher CO2; (b) if mean APAR was moderate, 1X SIF ought to increase and then decrease and stay constant with higher CO2; and (c) if mean APAR was high, 1X SIF would increase with higher CO2 (Fig. b, d). For the simulations in Figs.  and , mean APAR was 156 µmolm-2s-1, and thus 1X SIF increased and then decreased with higher CO2.

The KX model SIF response to atmospheric CO2 was impacted by both leaf internal CO2 and the vertical APAR profile given the heterogeneous APAR. As ϕF was higher in the middle layers at lower atmospheric CO2 when there is no vertical Vcmax gradient, modeled SIF showed marginal increase with higher CO2 (Figs.  and e). However, when there was a vertical Vcmax gradient, ϕF was much higher in the lower canopy at lower CO2, potentially resulting in higher SIF at low atmospheric CO2, which was contrary to the IJKX prediction. The erroneous predicted SIF patterns of 1X and KX highlighted the importance of appropriately averaged leaf APAR, particularly the partitioning of sunlit and shaded leaves.

Our model simulations showed that different canopy complexity levels predicted divergent carbon, water, and SIF fluxes. 1X and KX without partitioning the canopy to sunlit and shaded fractions, in particular, showed very high biases compared to the other three levels of complexity, namely 2X, 2KX, and IJKX. Further, as we expected, IJKX, which has the most complex canopy, had the lowest predicted carbon and water fluxes, followed by 2KX and 2X and then KX and 1X. Moreover, when we accounted for a profile of vertical canopy photosynthetic capacity, the difference among canopy complexity levels increased. Though 2KX and 2X were, in general, close to IJKX in predicted canopy fluxes, the disagreements may range up to > 20 % (maximum) for 2KX and up to > 40 % (maximum) for 2X. Given the differences in predicted fluxes using different canopy complexity levels and the varying difference (not a constant ratio), we do not recommend using photosynthetic parameters inverted from different canopy complexity models; i.e., parameter fitting has to be performed with the same underlying model as for the full forward modeling. Given the higher realism of the enhanced complexity models, however, leaf-level fits of photosynthetic parameters could be employed in models of higher complexity but would result in high biases when used in simple big-leaf models.

The disagreements among canopy complexity levels make it difficult to parameterize a land model using a complex canopy setup and thus hamper the fusion of large-scale remote-sensing-based datasets with land models at a global scale. Thus, it is necessary to revisit the flux and plant trait inversions using more applicable land model setups to make sure the inverted datasets and land models are consistent in their assumptions. This is the only way to ensure that inverted parameters are quantitatively useful in future land surface modeling. Moreover, it is also possible for land models to go without the inverted fluxes or traits if the land model runs using a complex canopy such as IJKX. This way, the model can be directly compared against satellite observations without an intermediate step that performs the inversion from radiation observation canopy properties and thus surface water and carbon fluxes.

As suggested by , modelers need to move to a multi-layered canopy modeling to account for the vertical profiles and microclimates in the canopy. Further, to better utilize the broadly available remote sensing data, modelers need to move from broadband radiation to hyperspectral radiation and from sun/shade fractions to leaf angular distribution. One may ask whether it is necessary to implement a way more complex and inefficient multi-layered canopy with leaf angular distributions to account for an average 5 %–22 % difference, while the difference can be compensated by tuning plant traits such as photosynthetic capacity and hydraulic conductance. The answer varies depending on what types of data are used in the model. If one uses parameters meant to use with 2X (namely a two-leaf canopy), using a multi-layered canopy such as 2KX and IJKX would not improve the model performance but instead could result in higher biases. In this case, we suggest keeping the same canopy complexity as used to derive plant traits. However, if one wants to bridge plant physiology to both leaf-level measurements as well as remotely sensed data such as the reflection and fluorescence spectra, we would suggest using IJKX or using an even more complicated canopy model to be as accurate as possible. We note here that 2KX approximates IJKX well with an average 3 %–12 % difference, and 2KX would be useful to speed the calculations for more qualitatively oriented research as the trends generally agree between 2KX and IJKX.

We recognize that increasing model complexity can make it (a) less user-friendly for researchers to use (e.g., when implementing the model into their research projects) and (b) slower to run the model, particularly using less efficient programming languages such as Python and R (compared to C). In our highly modularized CliMA Land model, we use Julia, a just-in-time compiled programming language that allows for the versatility of a scripting language like Python but with the speed of fully compiled languages such as C and Fortran (see https://julialang.org/benchmarks/, last accedss: 22 December 2021). The CliMA Land model can simulate canopy radiation using either the mSCOPE-based radiative transfer scheme or the traditional sunlit- and shaded-fraction scheme e.g.,. Further, CliMA Land supports both stomatal optimization models including those from and empirical stomatal models including those from. For the empirical stomatal models, CliMA Land supports using an ad hoc tuning factor to account for stomatal responses to soil moisture through tuning either the empirical fitting parameter (such as g1 in the , and , models) or the leaf photosynthetic capacity as done in. Users may freely customize the model setup by choosing among the provided alternatives. We believe the practice of making land models more open and modular will benefit the land model and plant physiology communities in future research.