Response of Canopy Solar-Induced Chlorophyll Fluorescence to the Absorbed Photosynthetically Active Radiation Absorbed by Chlorophyll

Solar-induced chlorophyll fluorescence (SIF), which can be used as a novel proxy for estimating gross primary production (GPP), can be effectively retrieved using ground-based, airborne and satellite measurements. Absorbed photosynthetically active radiation (APAR) is the key bridge linking SIF and GPP. Remotely sensed SIF at the canopy level (SIFcanopy) is only a part of the total SIF emission at the photosystem level. An SIF-based model for GPP estimation would be strongly influenced by the fraction of SIF photons escaping from the canopy ( fesc). Understanding the response of SIFcanopy to the absorbed photosynthetically active radiation absorbed by chlorophyll (APARchl) is a key step in estimating GPP but, as yet, this has not been well explored. In this study, we aim to investigate the relationship between remotely sensed SIFcanopy and APARchl based on simulations made by the Soil Canopy Observation Photosynthesis Energy fluxes (SCOPE) model and field measurements. First, the ratio of the fraction of the absorbed photosynthetically active radiation absorbed by chlorophyll (fPARchl) to the fraction of absorbed photosynthetically active radiation absorbed by green leaves (fPARgreen) is investigated using a dataset simulated by the SCOPE model. The results give a mean value of 0.722 for Cab at 5 μg cm−2, 0.761 for Cab at 10 μg cm−2 and 0.795 for other Cab content (ranging from 0.71 to 0.81). The response of SIFcanopy to APARchl is then explored using simulations corresponding to different biochemical and biophysical conditions and it is found that SIFcanopy is well correlated with APARchl . At the O2-A band, for a given plant type, the relationship between SIFcanopy and APARchl can be approximately expressed by a linear statistical model even for different values of the leaf area index (LAI) and chlorophyll content, whereas the relationship varies with the LAI and chlorophyll content at the O2-B band. Finally, the response of SIFcanopy to APARchl for different leaf angle distribution (LAD) functions is investigated using field observations and simulations; the results show that fesc is larger for a planophile canopy structure. The values of the ratio of SIFcanopy to APARchl are 0.0092 ± 0.0020, 0.0076 ± 0.0036 and 0.0052 ± 0.0004 μm−1 sr−1 for planophile vegetables/crops, planophile grass and spherical winter wheat, respectively, at the O2-A band. At the O2-B band, the ratios are 0.0063± 0.0014, 0.0049± 0.0030 and 0.0033 ± 0.0004 μm−1 sr−1, respectively. The values of this ratio derived from observations agree with simulations, giving values of 0.0055 ± 0.0002 and 0.0068 ± 0.0001 μm−1 sr−1 at the O2-A band and 0.0032 ± 0.0002 and 0.0047 ± 0.0001 μm−1 sr−1 at the O2-B band for spherical and planophile canopies, respectively. Therefore, both the simulations and observations confirm that the relationship between SIFcanopy and APARchl is species-specific and affected by biochemical components and canopy structure, especially at the O2-B band. It is also very important to correct for reabsorption and scattering of the SIF radiative transfer from the photosystem to the canopy level before the remotely sensed SIFcanopy is linked to the GPP. Remote Sens. 2017, 9, 911; doi:10.3390/rs9090911 www.mdpi.com/journal/remotesensing Remote Sens. 2017, 9, 911 2 of 19


Introduction
Accurate estimation of the amount of carbon dioxide fixed by vegetation photosynthesis is a key component of the global carbon cycle and is also important for studies on ecosystem-climate interactions and ecosystem responses to extreme climate events [1,2].There have been many approaches to estimating GPP (gross primary production) including the eddy covariance (EC) technique [3][4][5][6], process-based models [7][8][9] and LUE-models (light use efficiency models)based on the absorbed photosynthetically active radiation (APAR) absorbed by the canopy [10,11] or by green leaves [12,13].However, the solar-induced chlorophyll fluorescence (SIF) emitted from vegetation chloroplasts is a more promising proxy for GPP than vegetation indices derived from reflectance data [14,15].Recent instrumental developments in hyperspectral remote sensing make it possible to measure SIF using field spectrometers at ground level [16], airborne imaging spectrometers [17], and also satellite sensors including the high-spectral-resolution Japanese Greenhouse gases Observing SATellite (GOSAT) [18][19][20][21] and Orbiting Carbon Observatory 2 (OCO-2) [22] as well as the Scanning Imaging Absorption spectrometer for Atmospheric CHartograhY (SCIAMACHY) [23,24] and the Global Ozone Monitoring Experiment 2 (GOME-2) [25,26].
The simple linear response of the SIF to GPP at the large scale has been considered by many researchers.Based on the satellite-based Vegetation Photosynthesis Model (VPM) proposed by Xiao et al. [12], which includes the light use efficiency (LUE, ε P ), the GPP can be calculated using Equation (1): where PAR is the incident irradiance, fPAR chl is the fraction of absorbed photosynthetically active radiation absorbed by chlorophyll, ε P is the light use efficiency and APAR chl is the absorbed photosynthetically active radiation absorbed by chlorophyll [12,27,28].Similarly, the total SIF originally emitted at the photosystem level (SIF PS ), a by-product of photosynthesis, can be expressed as where ε F is defined as the quantum yield for fluorescence (i.e., the fraction of APAR photons that are re-emitted from the photosystems as SIF photons).In this context, based on Equations ( 1) and ( 2), the GPP can be directly estimated using a linear model based on SIF PS .However, the remotely sensed SIF is only part of total SIF emitted from the chloroplasts within the leaves and is also not isotropic due to the upward radiation transfer path.As demonstrated by numerous observations and simulation results, the remotely sensed SIF at the canopy level (SIF canopy ) has a noticeable directional variation similar to that of the canopy reflectance in the solar principal plane [29].In addition, the remotely sensed SIF canopy is strongly influenced by the effects of leaf and canopy structure, which affects the fluorescence reabsorption and the light penetration within the plant canopy [30].Therefore, the remotely sensed SIF canopy can be similarly expressed as [14,28] where f esc is a parameter related to the optical properties of the canopy, which accounts for the fraction of SIF photons escaping from the photosynthesis level to the canopy level.It is determined by the canopy structure, the pigments that are present, the soil background, the illumination and the imaging geometries.
Remote Sens. 2017, 9, 911 Therefore, if the ratio of ε p to ε F is constant, there should be a strong linear relationship between GPP and SIF canopy for a given vegetation type.Nevertheless, this linear relationship differs for different plant types due to the influence of the canopy structure or photochemical pathways [19,[31][32][33][34].
As shown in Equations ( 1) and (3), APAR is the bridge linking SIF and GPP.Schlau-Cohen and Berry [35] found that the discrepancy and variation in the fluorescence quantum yield were both small under a range of illumination and stress conditions.So, the SIF signal may be a better proxy for estimating APAR.Based on diurnal and seasonal measurements made on a temperate deciduous forest [36] and crops [34], previous studies have demonstrated that SIF has a stronger correlation with APAR than with GPP.It is reasonable to assume that APAR is absorbed mainly by chlorophyll and also that the SIF is emitted by chlorophyll, which results in the significant correlation between SIF and APAR [14,37].Therefore, understanding the mechanism underlying the link between directional SIF and APAR chl is the key issue in interpreting the relationship between GPP and SIF.However, so far, this link has not been well explored.
In this paper, based on simulations made using the SCOPE (Soil Canopy Observation Photosynthesis Energy fluxes) model and field observations, we aim: (1) to investigate whether a reliable relationship exists between SIF canopy and APAR chl and how this relationship is controlled by the canopy biochemical components and canopy structure-this includes the effect of the chlorophyll a + b content (Cab), leaf area index (LAI) and leaf angle distribution (LAD); and (2) to explore whether this relationship is different for SIF canopy signals at different bands.We hope this exploration of the relationship between SIF canopy and APAR chl will assist in the estimation of GPP using remotely sensed SIF.

Simulation Data
The SCOPE model (version 1.61) was employed to simulate the SIF emission and APAR of the leaves and canopy with different biochemical and biophysical parameters under different environmental conditions.The inputs to the simulation experiment are listed in Table 1.The SCOPE model is a 1-D vertically integrated radiative transfer and energy balance model linking radiance observations at the top of the canopy with land surface characteristics, thus providing estimation of the amount of photosynthesis, leaf and canopy chlorophyll fluorescence and reflectance [38].A range of values of the vegetation parameters, Cab, LAI, LIDFa (leaf angle distribution function) and LIDFb, as well as the geometrical parameters, solar zenith angle (SZA) and view zenith angle (VZA), were used in the simulation.Values of Cab ranging from 5 µg/cm 2 to 80 µg/cm 2 were used to represent the different chlorophyll levels.The LAI inputs were set from 0.5 to 7, indicating different levels of vegetation coverage.Six different leaf inclinations represented by combinations of LIDFa and LIDFb were used to represent different plant types.Different values of the SZA were set to correspond to different incident light conditions.All other SCOPE parameters were set to their default values.

Field Experiments
Seven independent field experiments were conducted in Beijing and in Sanya, Hainan Province, China.The distribution and location of three experimental sites are shown in Figure 1.The details are described below and also listed in Table 2. Corresponding to the spectral measurements, the auxiliary parameters measured simultaneously are also provided, including Cab, LAI and f c (the fractional cover of green vegetation).

Field Experiments
Seven independent field experiments were conducted in Beijing and in Sanya, Hainan Province, China.The distribution and location of three experimental sites are shown in Figure 1.The details are described below and also listed in Table 2. Corresponding to the spectral measurements, the auxiliary parameters measured simultaneously are also provided, including Cab, LAI and (the fractional cover of green vegetation).Five experiments were carried out on winter wheat at the National Precision Agriculture Demonstration Base located at Xiao Tangshan (XTS) Farm, north of Beijing (40 °11′N, 116 °27′E).These experiments were conducted on two winter wheat varieties during two growth cycles, i.e., the 2015-2016 and 2016-2017 cycles.In the 2015-2016 cycle, the winter wheat (Triticum aestivum L.) was cultivated using conventional fertilizer and irrigation management and had a uniform growth status.Three diurnal experiments were conducted on 8, 9 and 18 April 2016 with the corresponding growth stages being the jointing, jointing, and booting stages, respectively.In each diurnal experiment, the upwelling canopy radiance and incident irradiance spectra were measured approximately every half hour from 8:30 to 17:00.In the 2016-2017 cycle, four fertilization rates were applied to two cultivated  • 10 E) in Sanya City, Hainan Province.The plant types at Nanbin farm included vegetables and crops such as potato, cabbage, cotton, rice and maize; their canopy structures were all planophile except for one observation made on rice.Figure 2 displays three photographs of studied canopies at XTS Farm in November (left, winter wheat), Nanbin Farm (middle, cotton) and Sanya Station (right, gold coin grass).The canopy structure of winter wheat is spherical and the leaves are more erect compared with a planophile canopy.The Nanbin Farm experiment was carried out on a series of planophile crops that had horizontal leaves.The investigation of the diurnal dynamics of SIF canopy and APAR chl at the Sanya Station focused on gold coin grass which had homogeneous, planophile leaves.
Remote Sens. 2017, 9, 911 5 of 18 columns next to each other on each field site.Four nitrogen fertilization treatments, i.e., different amount of carbamide were used: 585 kg ha −1 (N3), 390 kg ha −1 (N2), 195 kg ha −1 (N1), and no fertilization (N0).For each fertilization rate, three duplicates were also designed.Two experiments were conducted-one on 7 November 2016 and another on 8 December 2016-when the winter wheat was at the emergence and tillering stages, respectively.Another diurnal spectral experiment was designed for gold coin grass (Lysimachia christinae Hance) and conducted on 18 December 2016 at Sanya Remote Sensing Satellite Data Receiving Station (18 °18′N, 109 °18′E) located in Sanya City, Hainan Province, China.The upwelling canopy radiance and incident irradiance spectra were measured approximately every 20 min from 8:00 to 17:00.The canopy structure was homogeneous and its coin-like leaves were oriented very close to ground.
A multi−species experiment was conducted on 18 December 2016 at Nanbin Farm (18 °22′N, 109 °10′E) in Sanya City, Hainan Province.The plant types at Nanbin farm included vegetables and crops such as potato, cabbage, cotton, rice and maize; their canopy structures were all planophile except for one observation made on rice.
Figure 2 displays three photographs of studied canopies at XTS Farm in November (left, winter wheat), Nanbin Farm (middle, cotton) and Sanya Station (right, gold coin grass).The canopy structure of winter wheat is spherical and the leaves are more erect compared with a planophile canopy.The Nanbin Farm experiment was carried out on a series of planophile crops that had horizontal leaves.The investigation of the diurnal dynamics of and APAR at the Sanya Station focused on gold coin grass which had homogeneous, planophile leaves.

Details of the Spectral Measurements and SIF Retrieval Method
The canopy spectral measurements were made using a customized Ocean Optics QE Pro spectrometer (Ocean Optic, Inc., Dunedin, FL, USA) fitted with a 25 ° field-of-view fiber optic that functions in the 645-805 nm spectral range with a full-width-at-half-maximum (FWHM, i.e., spectral resolution (SR)) of 0.31 nm, a spectral sampling interval of 0.155 nm and a peak signal-to-noise ratio (peak SNR) >1000.Canopy radiance measurements were taken by averaging 50 scans with an optimized integration time to weaken the influence of noise, and a dark current correction was applied to each spectral measurement.The canopy spectra were measured at a height of about 130 cm above the canopy for nadir observation.A BaSO4 calibration panel was used to measure the incoming solar irradiance.For all measurements, a relatively homogeneous view size of about 1 m × 1 m was selected.The weather was sunny and stable during all of the above experiments.
The SIF is a re-emitted signal corresponding to only a small amount of the reflected radiance and about 1% of the total light absorbed.It has two peaks at 685 nm and 740 nm.The SIF signal overlaps with the reflected light and needs to be separated out at the Fraunhofer lines or strong atmospheric absorption bands as, here, the incident irradiance is comparable to the amount of emitted fluorescence [39].In this study, for the QE Pro spectral measurements, the O2-A (761 nm) and O2-B (688 nm) oxygen absorption bands were used to retrieve the far-red and red SIF, respectively, based on the 3FLD (3 band Fraunhofer Line Depth) method [40].

Details of the Spectral Measurements and SIF Retrieval Method
The canopy spectral measurements were made using a customized Ocean Optics QE Pro spectrometer (Ocean Optic, Inc., Dunedin, FL, USA) fitted with a 25 • field-of-view fiber optic that functions in the 645-805 nm spectral range with a full-width-at-half-maximum (FWHM, i.e., spectral resolution (SR)) of 0.31 nm, a spectral sampling interval of 0.155 nm and a peak signal-to-noise ratio (peak SNR) >1000.Canopy radiance measurements were taken by averaging 50 scans with an optimized integration time to weaken the influence of noise, and a dark current correction was applied to each spectral measurement.The canopy spectra were measured at a height of about 130 cm above the canopy for nadir observation.A BaSO 4 calibration panel was used to measure the incoming solar irradiance.For all measurements, a relatively homogeneous view size of about 1 m × 1 m was selected.
The weather was sunny and stable during all of the above experiments.
The SIF is a re-emitted signal corresponding to only a small amount of the reflected radiance and about 1% of the total light absorbed.It has two peaks at 685 nm and 740 nm.The SIF signal overlaps with the reflected light and needs to be separated out at the Fraunhofer lines or strong atmospheric absorption bands as, here, the incident irradiance is comparable to the amount of emitted fluorescence [39].In this study, for the QE Pro spectral measurements, the O 2 -A (761 nm) and O 2 -B (688 nm) oxygen absorption bands were used to retrieve the far-red and red SIF, respectively, based on the 3FLD (3 band Fraunhofer Line Depth) method [40].
The 3FLD assumes that the variation in the SIF and in the reflectance are linear over the spectral range used.The single reference channel used in the standard FLD method (sFLD) for the incident irradiance and upwelling radiance is replaced by the weighted average of two channels at the left and right shoulders of the absorption band.Liu et al. [16] assessed the FLD-based SIF retrieval methods for different spectral specifications and showed that the 3FLD method was more accurate than the standard FLD method and also more robust than the improved FLD method proposed by Alonso et al. [41].Therefore, we adopted the 3FLD method for SIF canopy retrieval in this study.The shoulder wavebands of the 3FLD method were determined according to Liu et al. [16,42].In the case of the O 2 -A band, this corresponds to wavelengths of 757.92 nm, 760.72 nm and 768.87 nm for the bands corresponding to the left shoulder of the absorption feature, within the absorption feature and right shoulder of the absorption feature, respectively; for the O 2 -B band, it corresponds to wavelengths of 686.44 nm, 687.09 nm and 688.23 nm, respectively.

Measurement of f PAR green and APAR chl
The accurate measurement of the fraction of absorbed photosynthetically active radiation absorbed by green leaves (fPAR green ) is a critical step in the estimation of APAR chl .An in situ fPAR green measurement method for low canopy vegetation based on a digital camera and reference panel was presented by Liu et al. [43] and has proved to be an effective solution for low canopy vegetation.Using this method, fPAR green is given by where PAR i and PAR r are the incident and reflected (including all exposed components) photosynthetically active radiation (PAR) derived from the DN values of the digital photograph.APAR exposed background and APAR covered background are the PAR absorbed by the exposed background (including non-photosynthetic components) and the vegetation-covered background respectively.In green leaves, photosynthesis starts with the absorption of PAR, mainly by chlorophyll [30].
The absorption of APAR by green leaves is mostly due to the chlorophyll content.There is a linear correlation between fPAR chl and fPAR green : where k is the ratio of fPAR chl to fPAR green .Then APAR chl can be calculated based on Equation (6):

The Relationship between f PAR green and f PAR chl
The ratio of fPAR chl to fPAR green was determined for canopies with different LAI and Cab based on the simulation dataset described in Table 1.The results are illustrated in Figure 3 and there are 88 and 66 model runs in the subplot a and b (including 11 variations of SZA in each figure), respectively.The results show a mean value of 0.722 for Cab at 5 µg cm −2 and 0.761 for Cab at 10 µg cm −2 and 0.795 for other Cab content, with a range of 0.71 to 0.81.The ratio increases with increasing chlorophyll content but there is almost no change as LAI increases.Based on these results, the k values (see Equation ( 5)) of 0.722 for Cab at 5 µg cm −2 and 0.761 for Cab at 10 µg cm −2 and 0.795 for other Cab content (ranging from 0.71 to 0.81) were subsequently used for the calculation of APAR chl based on the field observations.Remote Sens. 2017, 9, 911  shows a strong linear relationship with APAR for a values of Cab tested, which means this linear relationship is almost independent of the chloro content.It can be concluded that SIF at the O2-A band is primarily driven by APAR .Fo O2-B band, when the results for different values of Cab are plotted, the relationship between SIF and APAR exhibits a pronounced wing-like shape (Figure 4b).The slope of SIF to AP is sensitive to the Cab content, decreasing when Cab increases and becoming almost saturated w Cab is bigger than 40 μg/cm 2 .These results are similar to those found by Zhang et al. [33].exhibits a pronounced wing-like shape (Figure 4b).The slope of SIF to APAR is sensitive to the Cab content, decreasing when Cab increases and becoming almost saturated when Cab is bigger than 40 μg/cm 2 .These results are similar to those found by Zhang et al. [33].The ratio of SIF to APAR for different Cab levels was also calculated using the simulated dataset, as illustrated in Figure 5, which represents the response of SIF to APAR .The ratio of SIF to APAR is equal to the product of the fluorescence efficiency ( ) and the fraction of SIF photons escaping the canopy ( ).
was fixed in the simulation experiment and hence, in this experiment, this ratio was determined by .At the O2-B band, decreases The ratio of SIF canopy to APAR chl for different Cab levels was also calculated using the simulated dataset, as illustrated in Figure 5, which represents the response of SIF canopy to APAR chl .The ratio of SIF canopy to APAR chl is equal to the product of the fluorescence efficiency (ε F ) and the fraction of SIF photons escaping the canopy ( f esc ).ε F was fixed in the simulation experiment and hence, in this experiment, this ratio was determined by f esc .At the O 2 -B band, f esc decreases markedly from 0.016 to 0.002 µm −1 sr −1 as Cab increases but, at the O 2 -A band, it remains almost constant for a given LAI.Therefore, the ratio of SIF canopy to APAR chl is less influenced by the Cab content at the O 2 -A band than the O 2 -B band, which accounts for the linear relationship between SIF canopy and APAR chl at the O 2 -A band, which exists no matter what the value of Cab is.

Effect of LAI on the Relationship between SIF and APAR
Using the simulated dataset, the response of SIF to APAR at both bands was also investigated for canopies with different values of the LAI (see Figure 6).It can be seen that, at the O2-A band, this relationship varies very little as the LAI changes, especially for dense vegetation (LAI > 3).However, for the O2-B band, plotting the relationship between SIF and APAR produces a very scattered distribution (Figure 6b) because it is dominated by Cab as illustrated in Figure 5b.The ratio of SIF to APAR at the O2-A band increases with LAI (Figure 7a).An opposite trend is observed at the O2-B band (Figure 7b).Except for the low Cab condition at the O2-B band, the

Effect of LAI on the Relationship between SIF canopy and APAR chl
Using the simulated dataset, the response of SIF canopy to APAR chl at both bands was also investigated for canopies with different values of the LAI (see Figure 6).It can be seen that, at the O 2 -A band, this relationship varies very little as the LAI changes, especially for dense vegetation (LAI > 3).However, for the O 2 -B band, plotting the relationship between SIF canopy and APAR chl produces a very scattered distribution (Figure 6b) because it is dominated by Cab as illustrated in Figure 5b.

Effect of LAI on the Relationship between SIF and APAR
Using the simulated dataset, the response of SIF to APAR at both bands was also investigated for canopies with different values of the LAI (see Figure 6).It can be seen that, at the O2-A band, this relationship varies very little as the LAI changes, especially for dense vegetation (LAI > 3).However, for the O2-B band, plotting the relationship between SIF and APAR produces a very scattered distribution (Figure 6b) because it is dominated by Cab as illustrated in Figure 5b.The ratio of SIF to APAR at the O2-A band increases with LAI (Figure 7a).An opposite trend is observed at the O2-B band (Figure 7b).Except for the low Cab condition at the O2-B band, the ratio of SIF to APAR at both bands is almost saturated for values of the LAI greater than 3 and the influence of the LAI decreases as Cab increases.This can be contributed to the effects of The ratio of SIF canopy to APAR chl at the O 2 -A band increases with LAI (Figure 7a).An opposite trend is observed at the O 2 -B band (Figure 7b).Except for the low Cab condition at the O 2 -B band, the ratio of SIF canopy to APAR chl at both bands is almost saturated for values of the LAI greater than 3 and the influence of the LAI decreases as Cab increases.This can be contributed to the effects of reabsorption and scattering at different wavelengths.At the O 2 -B band, the reflectance is very low (<5%) and the reabsorption effect of SIF canopy increases with larger LAI values; therefore, the ratio of SIF canopy to APAR chl decreases with increased LAI.At the O 2 -A band, the leaf reflectance and transmittance is high (40-60%) and the reabsorption effect due to SIF canopy can be neglected.Therefore, the f esc increases with larger LAI and is determined by the scattering mechanism at the near infrared (NIR) band.

Effect of Plant Structure Type on the Relationship between SIF and APAR
To explore whether the relationship between SIF and APAR depends on the plant type, a simulation using different leaf angle distribution functions was carried out to investigate the relationship between SIF and APAR at both the O2-A and O2-B bands.The results are illustrated in Figure 8. Six plant types, described in terms of different values of LIDFa and LIDFb, were used in the simulation.LIDFa determines the leaf inclination whereas LIDFb describes the variation in leaf inclination.At the O2-A band, the slopes for the relationships shown in Figure 8 range from 0.0035 μm −1 sr −1 for erectophile-type plants to 0.0067 μm− 1 sr −1 for planophile-type plants.Similarly, for the O2-B band, the slope values are 0.0017 μm −1 sr −1 and 0.0046 μm −1 sr −1 for erectophiletype plants and planophile-type plants, respectively.This means that the fraction of APAR reemitted by chlorophyll fluorescence and observed at the top of the canopy is higher for planophiletype plants than erectophile-type plants when the same amount of PAR is absorbed by chlorophyll.For planophile plants, the fraction of fluorescence photons that escape from the lower leaves is much lower than from the top leaves.Therefore, the increase in the slope of SIF against APAR as the LAD (leaf angle distribution) becomes more horizontal can be considered due to the different PAR distribution within canopies with different canopy structures.

Effect of Plant Structure Type on the Relationship between SIF canopy and APAR chl
To explore whether the relationship between SIF canopy and APAR chl depends on the plant type, a simulation using different leaf angle distribution functions was carried out to investigate the relationship between SIF canopy and APAR chl at both the O 2 -A and O 2 -B bands.The results are illustrated in Figure 8. Six plant types, described in terms of different values of LIDFa and LIDFb, were used in the simulation.LIDFa determines the leaf inclination whereas LIDFb describes the variation in leaf inclination.At the O 2 -A band, the slopes for the relationships shown in Figure 8 range from 0.0035 µm −1 sr −1 for erectophile-type plants to 0.0067 µm− 1 sr −1 for planophile-type plants.Similarly, for the O 2 -B band, the slope values are 0.0017 µm −1 sr −1 and 0.0046 µm −1 sr −1 for erectophile-type plants and planophile-type plants, respectively.This means that the fraction of APAR chl re-emitted by chlorophyll fluorescence and observed at the top of the canopy is higher for planophile-type plants than erectophile-type plants when the same amount of PAR is absorbed by chlorophyll.For planophile plants, the fraction of fluorescence photons that escape from the lower leaves is much lower than from the top leaves.Therefore, the increase in the slope of SIF canopy against APAR chl as the LAD (leaf angle distribution) becomes more horizontal can be considered due to the different PAR distribution within canopies with different canopy structures.
For planophile plants, the fraction of fluorescence photons that escape from the lower leaves is much lower than from the top leaves.Therefore, the increase in the slope of SIF against APAR as the LAD (leaf angle distribution) becomes more horizontal can be considered due to the different PAR distribution within canopies with different canopy structures.The slope of SIF to APAR was also calculated for different plant types.For a given plant type, remains almost constant when LAI and Cab are constant.However, for planophile plants, the slope is 3.51 times higher than for erectophile plants at the O2-B band and 2.26 times higher at the O2-A band.The results illustrated in Figure 8 indicates, therefore, that the GPP-SIF relationship may be species-specific.The slope of SIF canopy to APAR chl was also calculated for different plant types.For a given plant type, f esc remains almost constant when LAI and Cab are constant.However, for planophile plants, the slope is 3.51 times higher than for erectophile plants at the O 2 -B band and 2.26 times higher at the O 2 -A band.The results illustrated in Figure 8 indicates, therefore, that the GPP-SIF canopy relationship may be species-specific.9, the diurnal variation in the SIF signal at O2-A and O2-B bands are similar to that for the incoming PAR, and the emitted SIF is synchronously responded to the incoming PAR.The effect of different fertilization treatments and varieties on the relationship between APAR and SIF was shown in Figure 10.There was no obvious effect of fertilization treatment on the slope of the relationship so the fertilization treatment only influenced the growth status, which only showed a higher SIF and APAR with the most appropriate fertilization treatment (N2).We can also conclude that the discrepancy of this relationship between different varieties was negligible.

The Influence of Different Fertilization Treatments and Varieties on the Relationship between SIF canopy and APAR chl
The effect of different fertilization treatments and varieties on the relationship between APAR chl and SIF canopy was shown in Figure 10.There was no obvious effect of fertilization treatment on the slope of the relationship so the fertilization treatment only influenced the growth status, which only showed a higher SIF canopy and APAR chl with the most appropriate fertilization treatment (N2).We can also conclude that the discrepancy of this relationship between different varieties was negligible.

and SIF
was shown in Figure 10.There was no obvious effect of fertilization treatment on the slope of the relationship so the fertilization treatment only influenced the growth status, which only showed a higher SIF and APAR with the most appropriate fertilization treatment (N2).We can also conclude that the discrepancy of this relationship between different varieties was negligible.

Effect of Cab and f c on the Relationship between SIF canopy and APAR chl
As illustrated in Figure 11, the relationship between SIF canopy at O 2 -A band and APAR chl is not significantly affected by Cab content based on the experimental measurements conducted on Nanbin and XTS Farm.However, for the O 2 -B band, the plots are more diverse if Cab varies greatly as shown in Figure 11a,b for observations at Nanbin Farm.The diurnal experiments were conducted during two periods in April 2016 at XTS Farm, and the Cab content of the wheat leaves at each period varied little during the period of the experiments, with a Cab value of 55.29 and 53.62 µg/cm 2 .So, the relationship was linear at the O 2 -B band.
The effect of f c on the relationship between SIF canopy at both bands and APAR chl was also analyzed using the experimental measurements (see Figure 12).Similar to the effect of the Cab content, the response of SIF canopy at the O 2 -A band to APAR chl was linear under different f c conditions.But at the O 2 -B band, the relationship varies as the f c changes for Nanbin Farm.The effect of on the relationship between SIF at both bands and APAR was also analyzed using the experimental measurements (see Figure 12).Similar to the effect of the Cab content, the response of SIF at the O2-A band to APAR was linear under different conditions.But at the O2-B band, the relationship varies as the changes for Nanbin Farm.patterns show a more diverse distribution while also presenting approximate linear relationships for experiments at different sites.It clearly shows that the slope of SIF to APAR is higher for experimental observations with planophile canopy structure at Nanbin Farm and Sanya Station than that for winter wheat with spherical canopy structure at XTS Farm.

Uncertainties in the SIF Retrieval and Measurements
The SIF retrieval accuracy is dependent on the spectral characteristics of the sensor, such as the SR (spectral resolution) and SNR (signal-to-noise ratio).In this paper, the spectral data was acquired by a QE Pro spectrometer with an SR of 0.3 nm and a peak SNR >1000.According to the work by Liu et al. [16], using the 3FLD method, the SIF retrieval error should be less than 15%.Therefore, because

Uncertainties in the SIF Retrieval and APAR chl Measurements
The SIF retrieval accuracy is dependent on the spectral characteristics of the sensor, such as the SR (spectral resolution) and SNR (signal-to-noise ratio).In this paper, the spectral data was acquired by a QE Pro spectrometer with an SR of 0.3 nm and a peak SNR >1000.According to the work by Liu et al. [16], using the 3FLD method, the SIF retrieval error should be less than 15%.Therefore, because of the high SR and SNR of the QE Pro spectrometer, it is reasonable to believe that the accuracy of the retrieved SIF is good and, hence, that the results describing the ability of the SIF canopy to estimate the APAR chl described here are reliable.The significant correlation between SIF canopy and APAR chl indicates that the SIF may be a better proxy for APAR chl estimation.
The studies by Fournier et al. [44] and Damn et al. [45] showed that, due to variations in the direct and diffuse radiation and also the bi-directional reflectance distribution function (BRDF) characteristics of the canopy, the illumination conditions also have an influence on the retrieval of SIF.The different absorption depths at the oxygen absorption bands that absorb direct and diffuse radiation can lead to an overestimate or underestimate of the SIF at specific observation geometries.In this study, all the measurements of SIF canopy were carried out at nadir conditions.According to the simulations, the error in the SIF retrieval caused by the nonlinear mixing of direct and diffuse radiation is less than 5% for nadir observations under clear-sky conditions and a solar zenith angle larger than 10 • .It is, therefore, reasonable to neglect the influence of this nonlinear mixing of direct and diffuse radiation.The method proposed by Liu et al.
[43] was adopted to measure the fPAR green .According to the validation carried out by Liu et al. [43], which was based on a comparison of fPAR measurements made by a digital camera and those made by a SunScan instrument (Delta-T, Inc., Cambridge, UK) in the 400-700 nm spectral range with a resolution of 0.30 µmol −1 m −2 s −1 , there was a significant correlation between the two types of measurement-the mean absolute error was 0.031 and the mean relative error 6.037%.Therefore, the accuracy of fPAR measurements can be considered reliable.In the present study, the ratio of fPAR chl to fPAR green was calculated using a simulated dataset with different values of Cab and LAI and a mean value of the ratio of fPAR chl to fPAR green depending on different Cab content level was used.For example, if Cab was 5 and 10 µg cm −2 , the ratio used the simulated value.The range of this ratio was 0.775-0.81for Cab greater than 20 µg cm −2 and so the uncertainty in the calculation of fPAR chl and APAR chl should have been smaller than 3%.

The Link between SIF canopy and APAR chl
In this study, we investigated the relationship between SIF canopy and APAR chl using both simulated and field-measured datasets.APAR chl is a key parameter linking SIF to GPP and so the results of this study may serve as a reference for the estimation of GPP using SIF.It is an important issue in studies of applications using SIF and it is still a matter of debate [46,47].According to Porcar-Castell et al. [29], the emitted SIF contains contributions from both photosystem I (PS I) and photosystem II (PS II).Compared to the SIF in the far-red part of the spectrum, the SIF in the red band is more closely linked to the activity of PS II.The SIF yield of PS II is considered to be more sensitive to variations in illumination and physiological or biochemical parameters [30,48].Therefore, at the photosystem level, it is reasonable to believe that the SIF in the red part of the spectrum is more closely related to the GPP.However, in remote sensing applications at the canopy level, only the SIF signal that escapes from the canopy can be detected; the SIF is reabsorbed by chloroplasts during the radiative transfer process within the leaves and canopy [49][50][51][52] and so the characteristics of SIF canopy are different to those of SIF PS .
In this study, the simulated data showed that the relationship between SIF canopy at O 2 -A band and APAR chl is relatively insensitive to the LAI and Cab content compared to the O 2 -B band and can be expressed by a unique linear relationship at the O 2 -A band.However, at the O 2 -B band, this relationship is significantly influenced by the LAI and Cab content.The effect of the Cab content on the ratio of SIF canopy to APAR chl is larger than that due to the LAI.This can be interpreted as meaning that the fluorescence photons emitted at the photosystem level can be reabsorbed by chlorophyll within the leaf or during the radiative transfer process from the leaf to the canopy.This reabsorption occurs because the fluorescence emission spectrum overlaps the chlorophyll absorption spectrum [30].The absorption of chlorophyll at the red band is much stronger than that at the far-red band and the rate of reabsorption of red fluorescence can reach 90% [53].As a result, SIF canopy at the O 2 -B band is strongly influenced by pigments and the correlation between SIF canopy and APAR chl here is more sensitive to the Cab content than at the O 2 -A band.
As Porcar-Castell et al. [30] stated, at the red band, reabsorption effects dominate the amount of fluorescence escaping from the canopy.As verified by both simulations and field experiments, the ratio of SIF canopy to APAR chl at both the O 2 -A and O 2 -B bands varies with the leaf angle distribution function, with more horizontal canopies having a larger ratio of SIF canopy to APAR chl .This indicates that the large uncertainty in f esc can weaken the relationship between the remotely sensed red SIF and APAR chl or GPP.

The Consistency between Simulations and Experimental Measurements
Figures 8 and 13 illustrate the scatter plots of SIF canopy and APAR chl for both O 2 -A and O 2 -B bands based on the simulated dataset and experimental dataset, respectively.The results clearly show that the regression relationship between SIF canopy and APAR chl is significantly different due to different canopy structures, which results in the discrepancies of the values of the ratio of SIF canopy to APAR chl .Furthermore, both simulated dataset and experimental measurements indicate that the ratio of SIF canopy to APAR chl increases when canopy structure becomes more horizontal.The corresponding statistical models are listed in Table 3.As illustrated in Table 3, at the O 2 -A band, for the linear regression models that have an offset of 0, the ratios of SIF canopy to APAR chl with confidence level of 95% are 0.0092 ± 0.0020, 0.0076 ± 0.0036 and 0.0052 ± 0.0004 µm −1 sr −1 at the O 2 -A band and 0.0063 ± 0.0014, 0.0049 ± 0.0030 and 0.0033 ± 0.0004 µm −1 sr −1 at the O 2 -B band for the Nanbin Farm, Sanya Station and XTS Farm experiments, respectively.The slopes derived from the observations correspond well with the simulations, which give values of 0.0055 ± 0.0002 and 0.0068 ± 0.0001 µm −1 sr −1 at the O 2 -A band and 0.0032 ± 0.0002 and 0.0047 ± 0.0001 µm −1 sr −1 at the O 2 -B band for spherical and planophile canopies, respectively.Especially, the ratios of SIF canopy to APAR chl are almost the same for simulations and observations at the O 2 -B band.Thus, this further indicates that the ratio of SIF canopy to APAR chl is dependent on the canopy structure.
The effect of LAD on the relationship between SIF canopy and APAR chl was also investigated using both simulations and field observations.The relationship between SIF canopy and APAR chl varies for different LAD functions and the slope of the graph of SIF canopy against APAR chl decreases for a more erect canopy.The ratio of SIF canopy to APAR chl is also different for different LAD functions with the highest ratio being for planophile plants and the lowest value for erectophile plants.For a given LAI and Cab content, the ratio ranges from 0.0068 ± 0.0001 µm −1 sr −1 for planophile plants to 0.0031 ± 0.0002 µm −1 sr −1 for erectophile plants at the O 2 -A band and from 0.0047 ± 0.0001 to 0.0014 ± 0.0002 µm −1 sr −1 for both types of plant at the O 2 -B band.Similarly, based on the field observations, at the O 2 -A band, the ratios are 0.0076 ± 0.0036 and 0.0052 ± 0.0004 µm −1 sr −1 for gold coin grass with plain leaves and winter wheat with spherical leaves, respectively; the corresponding values at the O 2 -B band are 0.0049 ± 0.0030 and 0.0033 ± 0.0004 µm −1 sr −1 , which corresponds well to the simulated results.These results show that the relationship between SIF canopy and APAR chl varies according to the plant type, which agrees with the dependence of SIF canopy on GPP for specific plant types.However, the influence of the physiological structure of vegetation on the correlation between SIF canopy and GPP awaits more detailed investigation in future studies.
Therefore, the results of this study clearly show that there is a linear relationship between SIF canopy and APAR chl , but that this relationship varies with the canopy biochemical components and canopy structure.The results also show that the reabsorption and scattering effects that occur during the radiative transfer from the photosystem to the canopy level should be corrected for before the remotely sensed SIF canopy is linked to the GPP.

Figure 1 .
Figure 1.The distribution of the three experimental sites in China.

Figure 1 .
Figure 1.The distribution of the three experimental sites in China.

Figure 2 .
Figure 2. The photographs of studied canopies at XTS Farm in November (left, winter wheat), Nanbin Farm (middle, cotton) and Sanya Station (right, gold coin grass).

Figure 2 .
Figure 2. The photographs of studied canopies at XTS Farm in November (left, winter wheat), Nanbin Farm (middle, cotton) and Sanya Station (right, gold coin grass).

Figure 3 .
Figure 3.The ratio of fPAR to fPAR for canopies with different LAI and Cab based on the simulation carried out by the SCOPE model.

3. 2 .
The Relationship between and Based on the Simulated Data 3.2.1.Effect of Chlorophyll Content on the Relationship between SIF and APAR Simulated data representing canopies with different values of chlorophyll content but the leaf angle distribution function (Spherical: LIDFa = −0.35,LIDFb = −0.15)was selected to invest the relationship between SIF and APAR at the O2-A and O2-B bands, illustrated in Figu For the O2-A band (Figure 4a), SIF

Figure 4 .
Figure 4.The relationship between and APARchl at the O2-A (a) and O2-B (b) bands for

Figure 3 .
Figure 3.The ratio of fPAR chl to fPAR green for canopies with different LAI and Cab based on the simulation carried out by the SCOPE model.

3. 2 .
The Relationship between SIF canopy and APAR chl Based on the Simulated Data 3.2.1.Effect of Chlorophyll Content on the Relationship between SIF canopy and APAR chl Simulated data representing canopies with different values of chlorophyll content but the same leaf angle distribution function (Spherical: LIDFa = −0.35,LIDFb = −0.15)was selected to investigate the relationship between SIF canopy and APAR chl at the O 2 -A and O 2 -B bands, illustrated in Figure 4.For the O 2 -A band (Figure 4a), SIF canopy shows a strong linear relationship with APAR chl for all the values of Cab tested, which means this linear relationship is almost independent of the chlorophyll content.It can be concluded that SIF canopy at the O 2 -A band is primarily driven by APAR chl .For the O 2 -B band, when the results for different values of Cab are plotted, the relationship between SIF canopyand APAR chl exhibits a pronounced wing-like shape (Figure4b).The slope of SIF canopy to APAR chl is sensitive to the Cab content, decreasing when Cab increases and becoming almost saturated when Cab is bigger than 40 µg/cm 2 .These results are similar to those found by Zhang et al.[33].

Figure 3 .
Figure 3.The ratio of fPAR to fPAR for canopies with different LAI and Cab based on the simulation carried out by the SCOPE model.

3. 2 .
The Relationship between and Based on the Simulated Data 3.2.1.Effect of Chlorophyll Content on the Relationship between SIF and APAR Simulated data representing canopies with different values of chlorophyll content but the same leaf angle distribution function (Spherical: LIDFa = −0.35,LIDFb = −0.15)was selected to investigate the relationship between SIF and APAR at the O2-A and O2-B bands, illustrated in Figure 4.For the O2-A band (Figure 4a), SIF shows a strong linear relationship with APAR for all the values of Cab tested, which means this linear relationship is almost independent of the chlorophyll content.It can be concluded that SIF at the O2-A band is primarily driven by APAR .For the O2-B band, when the results for different values of Cab are plotted, the relationship between SIF and APAR

Figure 4 .
Figure 4.The relationship between and APARchl at the O2-A (a) and O2-B (b) bands for different values of the Cab content.These results were obtained using the simulated dataset.

Figure 4 .
Figure 4.The relationship between SIF canopy and APAR chl at the O 2 -A (a) and O 2 -B (b) bands for different values of the Cab content.These results were obtained using the simulated dataset.

Figure 5 .
Figure 5.The ratio of SIF to APAR for canopies with different Cab content at the O2-A (a) and O2-B (b) bands based on the simulated dataset.

Figure 6 .
Figure 6.The relationship between SIF and APAR at the O2-A (a) and O2-B (b) bands for different LAI values, as obtained using the simulated dataset.

Figure 5 .
Figure 5.The ratio of SIF canopy to APAR chl for canopies with different Cab content at the O 2 -A (a) and O 2 -B (b) bands based on the simulated dataset.

Figure 5 .
Figure 5.The ratio of SIF to APAR for canopies with different Cab content at the O2-A (a) and O2-B (b) bands based on the simulated dataset.

Figure 6 .
Figure 6.The relationship between SIF and APAR at the O2-A (a) and O2-B (b) bands for different LAI values, as obtained using the simulated dataset.

Figure 6 .
Figure 6.The relationship between SIF canopy and APAR chl at the O 2 -A (a) and O 2 -B (b) bands for different LAI values, as obtained using the simulated dataset.

Figure 7 .
Figure 7.The ratio of SIF to APAR for canopies with different values of the LAI at the O2-A (a) and O2-B (b) bands, as obtained using the simulated dataset.

Figure 7 .
Figure 7.The ratio of SIF canopy to APAR chl for canopies with different values of the LAI at the O 2 -A (a) and O 2 -B (b) bands, as obtained using the simulated dataset.

Figure 8 .
Figure 8.The relationship between SIF canopy and APAR chl at the O 2 -A (a) and O 2 -B (b) bands for different plant types, as obtained using the simulated dataset (LAI = 3 m 2 m −2 , Cab = 40 µg cm −2 ).

3. 3 . 1 . 18 3. 3 .Figure 9
Figure 9 illustrates the diurnal observations of incoming PAR and SIF at O 2 -A and O 2 -B bands of the diurnal experiments at XTS Farm in April and Sanya Station.As shown in Figure 9, the diurnal variation in the SIF signal at O 2 -A and O 2 -B bands are similar to that for the incoming PAR, and the emitted SIF is synchronously responded to the incoming PAR.

Figure 9 .
Figure 9.The diurnal cycle of incoming PAR (a) and SIF (b,c) at O2-A and O2-B bands for XTSApr and Sanya Station measurements.

Figure 9 .
Figure 9.The diurnal cycle of incoming PAR (a) and SIF (b,c) at O 2 -A and O 2 -B bands for XTS Apr and Sanya Station measurements.

Figure 10 .
Figure 10.The relationship between the APAR and SIF at the O2-A (a,c) and O2-B (b,d) bands for experiment data obtained under different fertilization treatments (a,b) and varieties (c,d) at XTS Farm in November.

Figure 10 .
Figure 10.The relationship between the APAR chl and SIF canopy at the O 2 -A (a,c) and O 2 -B (b,d) bands for experiment data obtained under different fertilization treatments (a,b) and varieties (c,d) at XTS Farm in November.

3. 3 . 4 .Figure 11 .
Figure13shows scatter plots of SIF canopy against APAR chl at the O 2 -A and O 2 -B bands based on all the experimental data.Compared to the simulated data, the measured SIF canopy APAR chl patterns show a more diverse distribution while also presenting approximate linear relationships for experiments at different sites.It clearly shows that the slope of SIF canopy to APAR chl is higher for experimental observations with planophile canopy structure at Nanbin Farm and Sanya Station than that for winter wheat with spherical canopy structure at XTS Farm.

Figure 11 .Figure 12 .
Figure 11.The relationship between SIF canopy and APAR chl at the O 2 -A (upper) and O 2 -B (bottom) bands for different values of the Cab content obtained using the experimental dataset at Nanbin (a) XTS (b,c) Farm.Remote Sens. 2017, 9, 911 12 of 18

3. 3 . 4 .
Figure13shows scatter plots of SIF against APAR at the O2-A and O2-B bands based on all the experimental data.Compared to the simulated data, the measured SIF -APAR patterns show a more diverse distribution while also presenting approximate linear relationships for

Figure 12 .
Figure 12.The relationship between SIF canopy and APAR chl at the O 2 -A (a,c) and O 2 -B (b,d) bands for different values of the f c obtained using the experimental dataset at Nanbin (a,b) and XTS (c,d) Farm in November.

Figure13.
Figure13.The relationship between the APAR and SIF at the O2-A (a) and O2-B (b) bands for different plant types based on the experimental data.

Figure 13 .
Figure 13.The relationship between APAR chl and SIF canopy at the O 2 -A (a) and O 2 -B (b) bands for different plant types based on the experimental data.

Table 1 .
Main parameters of the SCOPE model used for the simulations in this study.

Table 2 .
Details of the field experiments.