Unravelling the physical and physiological basis for the solar-induced chlorophyll fluorescence and photosynthesis relationship

Estimates of the gross terrestrial carbon uptake exhibit large uncertainties. Sun-induced chlorophyll fluorescence (SIF) has an apparent near-linear relationship with gross primary production (GPP). This relationship will potentially facilitate the monitoring of photosynthesis from space. However, the exact mechanistic connection between SIF and GPP is still not clear. To explore the physical and physiological basis for their relationship, we used a unique dataset comprising continuous 15 field measurements of leaf and canopy fluorescence and photosynthesis of corn over a growing season. We found that, at canopy scale, the positive relationship between SIF and GPP was dominated by absorbed photosynthetically active radiation (APAR), which was equally affected by variations in incoming radiation and changes in canopy structure. After statistically controlling these underlying physical effects, the remaining correlation between far-red SIF and GPP due solely to the functional link between fluorescence and photosynthesis at the photochemical level was much weaker. Active leaf-level 20 fluorescence measurements revealed a moderate correlation between the efficiencies of fluorescence emission and photochemistry for sunlit leaves but a weak correlation for shaded leaves. Differentiating sunlit and shaded leaves in the light use efficiency (LUE) models for SIF and GPP facilitates a better understanding of the SIF-GPP relationship at different environmental and canopy conditions. Leaf-level fluorescence measurements also demonstrated that the sustained thermal dissipation efficiency dominated the seasonal energy partitioning while the reversible heat dissipation dominated the diurnal 25 leaf energy partitioning. These diurnal and seasonal variations in heat dissipation underlie, and are thus responsible for, the observed remote sensing-based link between far-red SIF and GPP. https://doi.org/10.5194/bg-2020-323 Preprint. Discussion started: 8 September 2020 c © Author(s) 2020. CC BY 4.0 License.

within ± 3 times the standard deviation for the mean of seven consecutive measurements. Once all cases with fluctuating atmospheric conditions were identified, the reflectance, GPP and SIF measurements acquired within ±half hour of their occurrence were excluded from the analysis. Finally, the remaining FLoX measurements were re-sampled into the 30-minute temporal resolution of the eddy covariance measurements. 160

Calculation of canopy SIF, fAPAR and APAR
The QEpro spectral measurements were used to compute Top-of-Canopy (TOC) SIF in the O2-A absorption feature at around 760 nm (F760). SIF was retrieved using the spectral fitting method (SFM) described in Cogliati et al. (2015). Canopy iPAR (iPARcanopy) was computed from the irradiance spectra collected with the FLAME-S spectrometer as the integral of irradiance over the spectral region from 400 to 700 nm. Canopy fAPAR was approximated by using the Rededge NDVI (Normalized 165 Difference Vegetation Index) (Viña and Gitelson, 2005): where RededgeNDVI = 750 − 705 where reflectance at specific wavelengths is utilized ( :705 and 750 nm). Rededge NDVI is a widely used index for estimating 170 fAPAR, and Viña and Gitelson (2005) suggest it as an optimal index for fAPAR among various other vegetation indices in corn canopies. We, however, have tested several other indices for estimating fAPAR, including the enhanced vegetation index (EVI) (Huete et al., 2002;Xiao et al., 2004) and the green NDVI (Viña and Gitelson, 2005), and found that the choice among the three indices had little impact on the results in section 3.1.

Quantifying energy partitioning from leaf fluorescence measurements 175
The continuous MoniPAM measurements offered a way for assessing the dynamics of energy partitioning in photosystem II (PSII). The pathways include photochemistry (P), fluorescence emission (F) and heat dissipation (H). H is further categorized as a sustained thermal dissipation (D) and a reversible energy-dependent heat dissipation (N). N is controlled by mechanisms that regulate the electron transport of the photosystems and is related to photo-protection mechanisms and NPQ (Baker, 2008). dissipation (Φ ) of PSII. The usual approach to obtain Φ is to 'switch off' photochemistry by applying a saturating light to leaves, so that the fluorescence measurements in the presence and absence of photochemistry (Fs and Fm), can be estimated (Maxwell and Johnson, 2000). A generic expression of Φ proposed by Genty et al. (1989) was used: 190 Unlike photochemistry, it is difficult to fully inhibit heat dissipation. Nevertheless, long duration dark-adaptation can reduce reversible heat dissipation to zero. Then, fluorescence measurements acquired in the presence and absence of reversible heat dissipation can be estimated. We took the expression proposed by Hendrickson et al. (2004) for Φ : 195 where is the highest (or maximal) value obtained for dark-adapted leaf fluorescence measurements in the absence of reversible heat dissipation; the pre-dawn value of Fm is typically used as an estimate of true maximal dark-adapted fluorescence (Maxwell and Johnson, 2000). Alternative expressions of Φ can be found in the literature, but they are equivalent and convertible to each other. For example, Eq. 5 can be rewritten as Φ = (1 − Φ )(1 − ). Furthermore, it can be expressed 200 as a function of a commonly used fluorescence parameter NPQ, which is defined as − 1 (Baker, 2008). In that The expression of the sum of Φ and Φ (symbolized as Φ + ) is straightforward, because the sum of the efficiencies of the four pathways (Φ , Φ , Φ and Φ ) is always unity and Φ + = 1 − Φ − Φ , and 205 Further separation of Φ and Φ from Φ + is difficult, because neither can be inhibited. However, relative efficiency of the sustained heat dissipation (Φ * ) across the growing season can be inferred from the pre-dawn values of Fm (i.e., ). Because was measured during the night in the absence of both reversible heat dissipation and photochemistry, a change in must 210 be caused by a change in the sustained heat dissipation. Therefore, we can take the maximal pre-dawn Φ * = m fAPAR leaf , (when Φ * is minimal) as a reference and express Φ * across the growing season as: Photosynthetic light use efficiency can be predicted as a function of leaf temperature, ambient radiation levels, intercellular 215 CO2 concentrations Ci, and other leaf physiological parameters (e.g., photosynthetic pathways, maximum carboxylation rate https://doi.org/10.5194/bg-2020-323 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
Vcmo) by using a conventional photosynthesis model of Collatz et al., (1992;. Van der Tol et al., (2014) established empirical relationships between fluorescence emission efficiency and photosynthetic light use efficiency under various environmental conditions by using active fluorescence measurements. With these relationships, the fraction of the absorbed radiation by a leaf emitted as fluorescence and dissipated as heat can be simulated. The MoniPAM system measured leaf 220 temperature and incoming radiation intensity. We reproduced the efficiencies of photochemistry, fluorescence, and reversible and sustained heat dissipation by using the biochemical model of Van der Tol et al., (2014). The field measurements of leaf temperature and incoming radiation intensity were used for the model input. We set Vcmo to 30 μmol m -2 s -1 , which is a recommended value for C4 crops, and the rest of the model parameters (e.g., Ci) to their default values. In this way, we simulated the efficiencies for the temporal resolution of the MONIPAM measurements (i.e., 10 minutes) and examined the 225 relationship among the efficiencies as predicted by the biochemical model.

Statistical analysis
Pearson correlation coefficients ( ) were computed to evaluate the relationships between pairs of observations, such as Φ and Φ * , or GPP and SIF. In addition to the correlation coefficients, partial correlation coefficients were computed to measure the degree of association between GPP and SIF, where the effect of a set of controlling variables was removed, including 230 fAPAR, iPAR and APAR. Partial correlation is a commonly used measure for assessing the bivariate correlation of two quantitative variables after eliminating the influence of one or more other variables (Baba et al., 2004). The partial correlation between x and y given a controlling single variable z was computed as where , is the Pearson correlation coefficient between x and y. 235 Partial correlation can be calculated to any arbitrary order. , ( ) is a first-order partial correlation coefficient, because it is conditioned solely on one variable (z). We used a similar equation to calculate the second-order partial coefficient that accounts for the correlation between the variables x and y after eliminating the effects of two variables z and q (de la Fuente et al., 2004).

Relationship between canopy SIF and GPP observations
Fig. 1a confirms the linear SIF-GPP relationship reported in previous studies and shows that F760 and GPP were strongly correlated with an overall correlation = 0.83. This correlation was slightly stronger than the relationship between APARcanopy 245 https://doi.org/10.5194/bg-2020-323 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. and GPP (an overall = 0.80, Fig. 1b). The APARcanopy-GPP relationship was apparently comprised of parallel groups of responses (colors) with large variation in GPP exhibited for the same levels of APARcanopy (Fig. 1b). This relationship complies with the common understanding of the response of photosynthesis to light showing the well-known saturation with irradiance as photosynthesis of the whole canopy gradually shifts from light limitation to carbon limitation, while the unexplained (by light intensity) variation in GPP can be attributed to stomatal aperture responses and a time-varying carboxylation capacity, 250 especially in the upper sunlit canopy, which experienced larger variations of light intensity. SIF, which is affected by both light and carbon limitations, shows a more linear response to GPP than APARcanopy (Figs. 1a vs. 1b).

[Insert Figure 1 here]
Incoming radiation (i.e., iPARcanopy) had a strong, positive linear relationship with SIF, GPP and APARcanopy (as shown in Figs. 255 1 and 2). We investigated these canopy-scale relationships with partial correlation analysis as diagrammed in Fig. 2, where for simplicity's sake, the subscripts denoting "canopy" variables were omitted in the diagram. Our team (Yang et al., 2020) and others (Miao et al., 2018;Migliavacca et al., 2017) have previously demonstrated that in addition to incoming radiation intensities, the energy available for photochemistry and fluorescence (i.e., APARcanopy) is strongly affected by canopy structure and leaf biochemistry. As a result, there were cases of low SIF, GPP and/or APARcanopy values at high iPARcanopy (

[Insert Figure 2 here]
After removing the effects of this important controlling variable that affects both SIF and GPP, namely APARcanopy, the correlation between GPP and SIF was weak ( SIF,GPP(APAR) = 0.27; refer to results below the triangle's baseline). In contrast, 270 the correlation between SIF and GPP remained significant after controlling for the effects of the components of canopy APAR, either fAPARcanopy or iPARcanopy, i.e., SIF,GPP(fAPAR) = 0.72, SIF,GPP(iPAR) = 0.66 (equations below the triangle, Fig. 2).
We further investigated how the SIF-GPP relationship varied seasonally with growth stage and diurnally with time of the day ( Fig. 3). The SIF-GPP correlation was significantly lower (by 22-27%) for the senescent canopy than for the young and mature 275 canopy. The Pearson correlation coefficient was highest when the canopy was fully developed with the underlying surface covered in the mature stage ( = 0.77, Fig. 3b). As for the different times of a day, we found that their correlations were the https://doi.org/10.5194/bg-2020-323 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. strongest in the afternoon ( = 0.89) while was only 0.76 when the data were acquired in the morning, representing an order of magnitude improvement of 13% from mid-morning to mid-afternoon observations (Figs 3d vs. 3f).

Dynamics of energy partitioning in photosystems
The continuously acquired active fluorescence measurements offered a way to assess the dynamics of energy partitioning in photosystems and facilitated the understanding of the relationship between fluorescence and photosynthesis before aggregation to the canopy, at the photochemical level. We investigated how the partitioning evolved over time. 285 During the nighttime, as can be seen from the responses in the dark-bars in Figs. 4a and 4b, the photosystem energy partitioning was stable for all leaves, whether they were designated as sunlit or shaded during the day. Three efficiencies (Φ , Φ * and Φ * ) showed little overnight change, and the reversible heat dissipation Φ was always close to zero. This null response for Φ agrees with the known status/behavior of the most important driver of reversible heat dissipation, the xanthophyll pigment 290 cycle, which reverts overnight to the energy-neutral form violaxanthin, and then converts during the day to antheraxanthin in moderately high light levels and subsequently to zeaxanthin at high light levels by chemical de-epoxidation (Middleton et al., 2016;Müller et al., 2001).

295
During the daytime, there were dramatic day-to-day changes in energy partitioning to photochemistry, fluorescence and reversible heat dissipation (Figs. 4a and 4b). Generally, both Φ * and Φ increased during mornings to midday and decreased afterwards, except that Φ exhibited unexplained midday dips during the senescent stage. On the other hand, Φ decreased during mornings to midday lows and increased afterwards (i.e., Φ diurnals were bowl-shaped, as shown in many studies).
The changes in Φ and Φ corresponded closely with the changes in incident radiation, while Φ * changes corresponded 300 closely with the dynamics in incident radiation in the morning but not at midday when the radiation level was high.
At the seasonal scale (Fig. 4), however, the nighttime energy partitioning over the three other pathways (Φ , Φ * and Φ * ) displayed substantial variations. The nighttime Φ was about 0.82 on all days during the young and mature stages, which is close to the theoretical maximal value (Zhu et al., 2008), but it was only about 0.64 during the senescent stage. Similarly, the 305 nighttime relative light use efficiency of fluorescence Φ * clearly decreased as the canopy development progressed from the physiologically robust (young and mature) stages to the senescent stage. The seasonal/growth stage decreases during nighttime in both Φ * and Φ were attributed to an increase of sustained heat dissipation Φ * since nighttime Φ was always close to zero. In extrapolating Φ * to daytime, we assumed that the sustained heat dissipation remained unchanged within any full day https://doi.org/10.5194/bg-2020-323 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
It is evident that the contribution to the photosynthetic process by the combined fluorescence and sustained heat dissipation group (Φ + , red color in Fig. 5) increased through the growing season, to competitively reduce photochemical efficiency (Φ , green color), especially during senescence. Additionally, the reversible heat dissipation (Φ , gold color) was generally 315 higher at the senescent stage than at the young and mature stages, which contributed to the reduction in photochemical efficiency as well. In the pie charts, we focus on the energy partitioning in both nighttime and midday since they represent the potential maximal Φ (i.e., the photosynthetic reaction centers in the nighttime are mostly open) and the steady-state Φ at the most common time of day for satellite observations, respectively.

[Insert Figure 5 here] 320
The pie charts (Fig. 5) clearly show how these relative efficiency pathway contributions changed with growth stage. The nighttime Φ was reduced by 17% between the young and senescent stages, while Φ + increased by 16% during senescence.
The pie charts also clearly show the very strong role of reversible heat dissipation in limiting midday photosynthesis throughout the growing season. For example, the per cent contribution for the pathways from the young crop (DOY 196) was 33% for 325 Φ , 22% for Φ , and 45% for Φ + ). The corresponding values for leaves in the mature crop (DOY 232) were 30%, 12%, and 59%. And for the leaves in the senescing crop (DOY 254), the corresponding values were 13%, 26%, and 61%. Combining these together, Fig. 5 further highlights the complexity of energy efficiency dynamics underlying the photosynthetic process.

Relationships among photosynthesis, fluorescence and heat dissipation at leaf level
Next, we examine the leaf-level efficiency terms obtained from in situ measurements, in terms of their combined responses. 330 The first set compares Φ * and Φ , in the context of variable iPARleaf (Figs. 6a, b). This figure clearly shows that the relationship between Φ * and Φ during daylight (9:00 -17:00) was different for the sunlit (sun adapted) vs. shaded (shade adapted) leaves, since the sunlit leaves were more often exposed to iPAR above 1000 μmol m -2 s -1 . The higher Φ values were obtained for relatively low iPARleaf, whether sunlit or shaded. For sunlit leaves, Φ * and Φ were positively correlated overall ( = 0.53, Fig. 6a) and in conditions with moderate to high light intensity (iPARleaf >500 μmol m -2 s -1 , excluding blue and teal 335 colored dots), = 0.60. In contrast, at low light intensity (iPARleaf <500 μmol m -2 s -1 , blue dots), correlation between Φ * and Φ was weak and negative for Φ >0.4. These two efficiency terms were uncorrelated in shaded leaves (Fig. 6b), and Φ * was much lower in the shaded than in sunlit leaves.
[Insert Figure 6 here] At the seasonal scale, the midday Φ * and Φ values (the average of all values acquired between 11:00 and 14:00) had a quasilinear, positive relationship for both the sunlit and shaded leaves when iPARleaf >500 μmol m -2 s -1 (Fig. 6c). In contrast, at low average midday light intensities, the relationships were clearly negative. The Φ values tended to decrease with the increasing light intensities while the relationship between Φ * and iPARleaf was not definite. However, the seasonally averaged ranges for Φ * in sunlit and shaded leaves clearly represent two populations: Φ * shaded was < 110 (Fig. 6b) whereas Φ * sunlit > 100 345 (Fig. 6a). These results could have implications for interpreting canopy-scale measurements.
The relationship obtained between Φ and Φ was considerably stronger for both sunlit and shaded leaves (Figs. 7a, b) than the correlation between Φ * and Φ previously shown for sunlit leaves (Fig. 7a). Here, both sunlit and shaded leaves showed consistent and strong linear decreases in Φ as Φ increased in response to variations in the intensity of incoming light 350 (iPARleaf) (Figs. 7a, b). Furthermore, the Φ and Φ relationships definitely varied in response to the sustained heat dissipation (Φ * , levels represented in the color bar) in a similar fashion for both sunlit and shaded leaves, although higher Φ * values (orange and red dots) were obtained in sunlit leaves. The efficiency of photochemistry obviously declined at higher Φ * , as indicated with the arrows in Fig. 7, especially pronounced in sunlit leaves. When both thermal dissipations were strongly expressed, the Φ was greatly reduced; in sunlit leaves, this reduction was ~40%. 355

[Insert Figure 7 here]
At the seasonal scale, as can be seen from Figs. 4 and 5, Φ decreased while Φ * increased as the canopy progressed through its growth stages. Their seasonal relationship is depicted in Fig. 7c, showing a same-day comparison of the midday Φ value (the average between 11:00 and 14:00), as a function of Φ across the growing season noting that Φ * remained unchanged 360 within any full day. Generally, Φ and Φ exhibited an overall negative correlation, but clearly their relationship was regulated by Φ . This is seen in the different midday Φ responses at high vs. low Φ * values. At the same level of Φ , the magnitudes of midday Φ varied by up to 0.45 (65%) due to variations in the efficiency of the sustained heat dissipation which varied between 0.1 and 0.6.

365
We have shown that Φ was regulated by heat dissipation (Figs. 5 and 7), and was moderately correlated with Φ * for the sunlit leaves (Fig. 6). With the dynamics of energy partitioning within the photosystem now quantified, we interpret the emerging relationship between photochemical and fluorescence efficiencies, namely Φ and Φ * (Table 2), in the context of thermal dissipation efficiencies (Φ , Φ * ). After eliminating the effects of both sustained and reversible heat dissipation, Φ and Φ * were negatively and equally correlated ( = -0.75) for both sunlit and shaded leaves. As surprising as this is, the presence of 370 either sustained or reversible heat dissipations changed this underlying negative relationship (Φ vs. Φ * ) into an observed apparent positive relationship at leaf scale, which contributes to the positive relationship of GPP and SIF at canopy scale. In fact, accounting for the effects of either Φ or Φ * reduced the correlation coefficients between Φ and Φ * . For sunlit leaves, https://doi.org/10.5194/bg-2020-323 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
controlling for only Φ reduced the correlation from 0.53 to 0.05 (by ~0.48 units); after controlling for only Φ * , the correlation dropped by 0.45 units to 0.08. For shaded leaves this reduction was from 0.10 to -0.31 after controlling for Φ , or to -0.35 375 after controlling for Φ * . These results represent trends that include both diurnal and seasonal variations. Table 2 here]

[Insert
Results of model simulations are presented in Figs 8 and 9. In comparison with Figs. 6 and 7 that describe our in situ measurements, these two figures show that the biochemical model outputs were more successful in describing photosynthetic 380 efficiency as a function of reversible heat dissipation (Φ ) than fluorescence efficiency (Φ ). Specifically, for the Φ -Φ relationships, the Fig. 8 simulation shows some similarity to the Fig. 6 measurements, but clearly does not capture the different responses we obtained for sunlit versus shaded leaves. However, Fig. 9 does generally replicate the general responses expected based on in situ measurements (Fig. 7), portraying the strong negative impact of Φ on Φ , but it doesn't convey the variability captured under field conditions. These differences occurred in the simulations because we did not consider the physiological 385 (i.e., enzyme activity) or physical (i.e., thickness, pigment ratios) differences among leaves at different growth stages. Neither did we consider the physical differences or photochemical potential differences (e.g., total chlorophyll content and Chl a/b ratios; rubisco activity) between sunlit and shaded leaves in this modelling experiment. Therefore, it is to be expected that the simulations for sunlit and shaded leaves would be similar, and not displaying the differences observed in field measurements. Furthermore, we did not include changes in leaf display geometry induced by low water stress (i.e., drought), a common 390 phenomenon in corn plants, in either measurements or simulations. Another likely reason contributing to the differences between simulations and observations is that in using the model of Van der Tol et al. (2014) to derive Φ from Φ , Φ is assumed to be a constant and Φ is empirically estimated as a function of Φ /Φ 0 . The observations shown in Figs. 4 and 5 prove that Φ varied over the growing season, and therefore, cannot be considered as a constant. These findings may help improve the modelling of Φ at the biochemical level and thus improve our understanding of the relationship between SIF and 395 GPP at the canopy scale.

Comparison of light use efficiencies at leaf and canopy levels
The responses of the efficiencies to APAR and the relationships between these efficiencies are diagrammed in Fig. 10, showing the Pearson correlation coefficients between pairs of variables, for leaves (Fig. 10a) that were either sunlit or shaded (indicated in bold, blue text), and for canopy (Fig. 10b).
Further efforts on implementing this extended model in canopy radiative transfer models will connect efficiencies of photochemistry and reversible heat dissipation to canopy reflectance observations. This may open new opportunities to estimate photosynthetic light use efficiency and improve GPP estimation using remote sensing methods in situ and from space.

Physically and physiologically joint effects on the SIF-GPP relationship
The canopy equivalent efficiencies (Φ and Φ ) are composed of integrals of the efficiencies of leaves of the 475 sunlit and shaded canopy fractions. The correlation between the canopy effective equivalents of Φ and Φ may be expected to take a value between the equivalent correlation of leaf-level Φ and Φ for sunlit leaves ( = 0.53) and for shaded leaves ( = 0.10). This means that the ability to view the SIF and reflectance hot spots (whether they occur together or not) from sunlit leaves varies with viewing angle and time of day (e.g., illumination angle, diffuse light). We suggest that these factors strongly affect . Therefore, they must, in turn, affect the success of remote sensing relationships for SIF-GPP (Yang and 480 Van der Tol, 2018). Likewise, these factors also affect the variability of the APAR-GPP relationship (Dechant et al., 2020;Qiu et al., 2019), and the LUE-GPP relationship (e.g., Middleton et al., 2019).

The exact correlation between Φ
and Φ at canopy scales depends on both the relative contributions of sunlit and shaded leaves to the canopy equivalents and the native correlation of the efficiencies at leaf level (Köhler et al., 2018;485 Mohammed et al., 2019). Canopy structure dictates the relative abundance and thus the relative weights of these contributing factors to the canopy equivalent Φ and Φ . The weight is not only determined by leaf class abundance, but also by the relative magnitude of the SIF and GPP response of the leaf classes. Sunlit leaves during daytime usually constitute a greater contribution to the effective canopy efficiencies than shaded leaves, simply because sunlit leaves tend to emit a higher SIF signal and, at the same time, produce a higher GPP. This suggests that the correlation between the canopy effective equivalents 490 of Φ and Φ tends to be closer to the correlations of leaf-level Φ and Φ for sunlit leaves ( =0.53) than for shaded leaves.
The LUE models as shown in Eq. 1 are, essentially, one-big-leaf models. The one-big-leaf approach assumes that canopy photosynthesis or SIF have the same relative responses to the environment as any single leaf, and that the scaling from leaf to 495 canopy is therefore linear (Friend, 2001). However, sunlit and shaded leaves clearly showed a different Φ -Φ relationship ( Figs. 6 and 10). In order to better interpret the SIF-GPP relationship, we recommend a revision of the LUE model of SIF and GPP (Eq. 1) by separating the contributions of sunlit and shaded leaves: This approach updates the existing one-big-leaf LUE models into two-big-leaf LUE models. The idea of differentiating sunlit and shaded leaves in vegetation modelling has been applied in predicting canopy temperature and photosynthesis, and was shown for the canopy PRI response when including both sunlit and shaded leaves in model simulations of field results (Dai et al., 2004;Luo et al., 2018;Wang and Leuning, 1998;Zhang et al., 2017), but has not been implemented in the LUE model for 505 SIF. More explicit models, such as SCOPE (Soil-Canopy-Observation of Photosynthesis and Energy fluxes, Van Der Tol et al., 2009), consider more classes of leaves with varying ambient temperature and radiation levels, but they require many parameters as input. The two-big-leaf LUE models consider the major difference of leaves in a canopy, and are relatively simpler compared with SCOPE but more realistic compared with one-big-leaf LUE models in linking SIF and GPP.

510
The fraction of sunlit canopy is determined by canopy structure and the direction of incoming light as well as the fraction of diffuse light. Hence, it is expected that these factors will affect the contribution of sunlit and shaded leaves to the canopy SIF-GPP correlation. Furthermore, the instantaneous sun-view angle geometry affects where the sunlit leaves occur during the day and the likelihood of their being viewed at particular angles (e.g., nadir). This means that the ability to view the SIF hot spot emitted from sunlit leaves varies with viewing angle and time of day. We suggest that these factors strongly affect which 515 must, in turn, affect the SIF-GPP remote sensing relationship .
Intuitively, in fully contiguous vegetation canopies the leaves in the upper layer (which are often sunlit) contribute a major fraction to the whole canopy of APAR, whereas fAPARshaded is small. Therefore, Φ sunlit and Φ sunlit have much larger relative contributions to Φ and Φ , respectively. Hence, a stronger relationship between SIF and GPP for dense canopies 520 is expected since Φ sunlit and Φ sunlit are moderately correlated. This insight can provide some explanation for the seasonally varying results describing canopy SIF and GPP (Fig. 3 a-c), where the SIF-GPP relationship varied with the growth stages: for the Young crop ( = 0.72); Mature crop ( = 0.77); and the Senescent crop ( = 0.50).
Furthermore, the effects of diffuse light (the diffuse/direct iPAR ratio) on the relationship between SIF and GPP can be 525 explained by the revised equation (Eq. 10). When the fraction of diffuse light is higher (e.g., a hazy, or cloudy day), there is greater iPAR penetration into lower canopy layers (the shaded leaves). As a result, fAPARshaded increases while fAPARsunlit decreases. This leads to a higher contribution of shaded leaves to the SIF-GPP relationship at canopy level, and weakens the SIF-GPP correlation. This was indeed observed in earlier field measurements reported in Miao et al. (2018), which showed that both the SIF-GPP correlation and the correlation between the SIF/APAR and GPP/APAR ratios were significantly weaker 530 under cloudy conditions than sunny conditions. The relative fraction of diffuse light is also a possible cause for the diurnally varying correlation between SIF and GPP (Fig. 3 d-f), where the SIF-GPP relationship varied at different times of day: for the data acquired in the morning ( = 0.76); for the data acquired in the midday ( = 0.83); and for the data acquired in the afternoon ( = 0.89). This highlights the unique physiological information of SIF for monitoring GPP, and the joint effects of https://doi.org/10.5194/bg-2020-323 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
incoming radiation, canopy structure and leaf physiology on the SIF-GPP relationship. We suggest that the canopy structure, 535 illumination and viewing conditions, and especially the foliage thermal dissipation must be taken into account to accurately represent the physiological underpinnings of the observed SIF-GPP relationships.
A simple model was used to examine the sensitivity of the fraction of sunlit canopy to LAI, leaf angle distribution function (LIDF) and solar zenith angles ( ). Considering a vegetation canopy as a turbid medium consisting of leaves, the instantaneous 540 sunlit fraction can be estimated as a function of the direction of incoming light, canopy LAI (L) and leaf angle distribution. In stochastic models describing the transfer of radiation in plant canopies, the probability of the leaves being sunlit at a specified vertical height (i.e., x= 0 referring to top of canopy, x= -1 referring to bottom of canopy) can be estimated as = exp( ), where L is canopy LAI and k the extinction coefficient, which is determined by the solar direction and leaf angle distribution (He et al., 2017;Stenberg and Manninen, 2015). The computation of k is explicitly given in Verhoef (1984) by projecting the 545 leaf area into the direction of the sun. In the model SCOPE (Van Der Tol et al., 2009), the total fraction of sunlit canopy LAI is the integral of Ps in the vertical direction given as: The effects of LAI, leaf angle distribution function (LIDF) and solar zenith angles (θs) on the instantaneous sunlit canopy 550 fraction are presented in Fig. 11. In line with our intuitive understanding, the fraction of sunlit canopy decreases with increasing canopy LAI in denser canopies. This fraction also decreases with increasing solar zenith angle, which are also affected by the leaf angle distribution. The important quantity for our purposes is the relative (not absolute) angular difference between the sun and leaf positions.

[Insert Figure 11 here] 555
A limitation of the current SCOPE capability for describing physiological responses is related to capturing the changing light environments that affect estimates of the sunlit/shaded fractions. This is because SCOPE and most radiative transfer models for vegetation assume steady state conditions and lack temporal memory of state variables at different times. SCOPE predicts the sunlit/shaded fractions at one moment while the shaded and sunlit leaves discussed in this paper are a result of long-term 560 adaption to the light conditions (i.e., sun-adapted and shade-adapted leaves). Nevertheless, we can gain insights into relationships under specified conditions, which can serve as new information to be used in updating the models.

Conclusions
We have used a unique dataset to explore the relationship between fluorescence and photosynthesis at leaf and canopy levels over a growing season in a corn canopy. We have quantified the contribution of incoming radiation, canopy structure and plant 565 physiology to the SIF-GPP relationship by using partial correlation analysis.
We demonstrate that the observed positive relationship between SIF and GPP is largely due to the fact that both of them are dependent on APAR (i.e., not on iPAR). Incoming radiation and canopy structure had comparable contributions to the SIF-GPP relationship. After eliminating the effects of variable APAR on the SIF-GPP relationship, the apparent positive 570 relationship between SIF and GPP became much weaker. However, there is still some remaining connection due to the functional link between fluorescence and photosynthesis at the leaf level, which is confirmed by active fluorescence measurements.
We propose to use a two-big-leaf LUE model instead of the commonly used one-big-leaf LUE model for interpreting the SIF-575 GPP relationship. This is because of clearly different relationships between fluorescence emission and photochemical light use efficiencies for sunlit and shaded leaves. The use of the two-big-leaf LUE model leads to a better understanding of the SIF-GPP relationship and its responses to weather conditions, such as clouds and fraction of diffuse light, as well as its responses to canopy structure, such as canopy openness and growth stages.

580
We also confirm that heat dissipation is responsible for the positive relationship between the efficiencies of fluorescence and photochemistry. Sustained (i.e., diurnally stable) heat dissipation increased through the crop's growth into the senescent stage, which caused the late season decrease in photosynthetic light use efficiency. The seasonal variation in sustained heat dissipation contributed to a moderate positive relationship between the efficiencies of fluorescence and photochemistry at the seasonal scale. At the diurnal scale, the reversible heat dissipation is responsible for the change of photosynthetic light use 585 efficiency.
Author contributions: P.Y., E.M., C.vdT and P.C. designed and performed research; P.Y. analyzed the data and prepared the original draft; P.Y., E.M., C.vdT and P.C. reviewed and edited the paper.
Data availability: The data is provided as a supplement.