Diurnal and Seasonal Variations in Chlorophyll Fluorescence Associated with Photosynthesis at Leaf and Canopy Scales

There is a critical need for sensitive remote sensing approaches to monitor the parameters governing photosynthesis, at the temporal scales relevant to their natural dynamics. The photochemical reflectance index (PRI) and chlorophyll fluorescence (F) offer a strong potential for monitoring photosynthesis at local, regional, and global scales, however the relationships between photosynthesis and solar induced F (SIF) on diurnal and seasonal scales are not fully understood. This study examines how the fine spatial and temporal scale SIF observations relate to leaf level chlorophyll fluorescence metrics (i.e., PSII yield, YII and electron transport rate, ETR), canopy gross primary productivity (GPP), and PRI. The results contribute to enhancing the understanding of how SIF can be used to monitor canopy photosynthesis. This effort captured the seasonal and diurnal variation in GPP, reflectance, F, and SIF in the O2A (SIFA) and O2B (SIFB) atmospheric bands for corn (Zea mays L.) at a study site in Greenbelt, MD. Positive linear relationships of SIF to canopy GPP and to leaf ETR were documented, corroborating published reports. Our findings demonstrate that canopy SIF metrics are able to capture the dynamics in photosynthesis at both leaf and canopy levels, and show that the relationship between GPP and SIF metrics differs depending on the light conditions (i.e., above or below saturation level for photosynthesis). The sum of SIFA and SIFB (SIFA+B), as well as the SIFA+B yield, captured the dynamics in GPP and light use efficiency, suggesting the importance of including SIFB in monitoring photosynthetic function. Further efforts are required to determine if these findings will scale successfully to airborne and satellite levels, and to document the effects of data uncertainties on the scaling.


Introduction
Climate change and anthropogenic activities have significantly affected agricultural and forest production by imposing novel combinations of multiple stresses, which act to alter plant function and productivity. Under favorable conditions, solar light absorbed by leaf chlorophyll (Chl) is used to drive photosynthesis through photochemistry [1]. Plant photosynthesis is a fundamental biochemical process for carbon fixation that occurs within chloroplasts, primarily in the cells of the leaf mesophyll tissue [2]. Chl is arguably the key component enabling vegetation photosynthesis, and is therefore an important indicator of plant function and productivity [3][4][5]. Chl levels vary with foliage maturity, nutrient levels, environmental conditions, light availability, and also seasonally. Thus, plants continuously regulate their photosynthetic processes in response to the changing environmental conditions on diurnal and seasonal timescales. To capture the diurnal responses and seasonal changes in plant photosynthesis, there is a critical need for temporally dense remote sensing time series to accurately monitor the key parameters governing vegetation function. Moreover, observations at relevant time scales would enable the detection of diurnal and seasonal changes in plant condition that may otherwise be overlooked.
Remote sensing approaches used to assess vegetation function over larger scales (e.g., regional to global) are commonly based on reflectance vegetation indices (VIs), and only recently on solar induced fluorescence (SIF). The normalized difference vegetation index [6] (NDVI, Table 1) is often used in agriculture and forestry to track changes in vegetation "greenness," capturing the seasonal phenology of green biomass, from leaf unfolding to senescence. NDVI uses reflectance bands from the red and near-infrared spectral regions to detect structural changes, such as the variations in canopy closure and leaf area index (LAI) that occur with leaf growth and senescence, providing an indicator of the absorbed photosynthetically active radiation (APAR) [7]. However, NDVI is more sensitive to changes in canopy biomass or LAI and less sensitive to the changes in Chl content, and therefore less sensitive to the variations in photosynthetic function. The photochemical reflectance index (PRI), in contrast to NDVI, is able to detect subtle changes in the photosynthetic activity, primarily documented in evergreen species [7][8][9][10][11]. PRI is typically calculated as a normalized difference VI, utilizing reflectance at the 531 nm wavelength, as compared to a reference band at 570 nm. Diurnal dynamics in PRI are driven by changes in the xanthophyll cycle, associated with changing light levels and the pH of the thylakoid lumen [9,10], while responses over seasonal timescales reflect the changes in photosynthetic pigment contents (e.g., chlorophyll and carotenoids). PRI is also affected by the changes in canopy structure, leaf pigments, and the background signal [12,13], which vary significantly with season. Frequently, the VIs saturate and provide an inconsistent sensitivity to GPP across the phenology. Table 1. Complementary measurements of corn (Zea mays L.), collected across the 2017 growing season at OPE3, Greenbelt, MD.

Measurement Approach Location Frequency Parameters (units)
PAM F light-adapted and the canopy SIF methodologies, and, therefore, leaf and canopy level studies are needed that relate SIF measurements to photosynthetic performance, to characterize relationships between SIF and PAM F metrics [24,47]. Further research is needed to characterize the effects of the diurnal and seasonal dynamics in environmental conditions on vegetation photosynthesis and the associated F and SIF properties, and to evaluate the ability of SIF metrics to characterize the diurnal and seasonal dynamics in photosynthesis. Further understanding of the mechanisms underlying the relationships of vegetation function and F, SIF, and reflectance VIs in different vegetation canopies and environments is essential for advancing their use in remote sensing, and will also contribute important understanding for ESA's forthcoming Fluorescence EXplorer (FLEX), Earth Explorer 8, which will measure reflectance and SIF together to assess seasonal photosynthetic patterns globally [29,45,52].
To advance the understanding of the utility of SIF metrics to monitor photosynthesis, our goal is to understand how the fine spatial and temporal scale red and far-red SIF (SIF B and SIF A ) measurements relate to leaf-level F signals as well as to canopy VIs and GPP, or the carbon used by photosynthesis as measured by a flux tower, and therefore can be used for monitoring vegetation photosynthetic function. The objectives of this study are: to characterize the dynamic diurnal and seasonal relationships between canopy photosynthetic function and vegetation chlorophyll fluorescence and reflectance properties, at both leaf and canopy scales, and to evaluate the potential of SIF to scale leaf level F parameters to the canopy level for estimating GPP. Some of the driving questions motivating this research are: (1) Does canopy SIF capture the variation in leaf-level light-adapted fluorescence metrics indicative of photosynthetic function (i.e., YII and ETR obtained by the PAM approach)? (2) Can SIF contribute to evaluating canopy photosynthetic function (i.e., GPP and LUE) by providing more accurate or additional information as compared to the current approaches? (3) Do the relationships between leaf F and canopy SIF and between canopy GPP and SIF differ significantly during the day and with growth stage?

Study Site and Crop Condition
The data for this study were collected in 2017 at the Optimizing Production Inputs for Economic and Environmental Enhancement (OPE3) site at the Beltsville Agricultural Research Center in Beltsville (BARC), MD, USA (lat/lon 39.030686/−76.84546, 50 m asl), operated by the US Department of Agriculture (USDA) Agricultural Research Service (ARS). At the OPE3 site, corn (Zea mays L.) is planted annually in predominately loamy sand soils, which are rain fed and augmented with optimal nitrogen fertilizer rates. The site is instrumented with a 10 m eddy covariance tower. The local climate is warm and temperate, with hot, humid summers, and typically mild winters with occasional freezes.
Corn has distinct growth stages, divided into vegetative and reproductive. The first and last vegetative stages are designated as emergence and tussling, while the reproductive stages start with the development of the corn silk and are based on the development of the kernels, which accumulate plant resources, leading to a decline in leaf photosynthesis and the onset of canopy senescence. In 2017 the crop emerged around June 20-22 (DOY 171-173) based on a site visit, Pheno-cam records [53], and the operational flux tower measurements ( Figure 1) [54]. A 3 m tall portable tower supporting the optical fibers of the fluorescence box (FLoX) instrument [55] and a set of monitoring-PAM (MoniPAM) probes were installed on July 6/7, when the corn was sufficiently developed. The collection of measurements started the following week on July 11 (DOY 192, Figure 1 bright green). The FLoX and MoniPAM collections occurred within the footprint of the flux tower, separated by approximately 120 m.
Day of year (DOY, 2017) Figure 1. Eddy covariance measurements collected at OPE3, Greenbelt, MD in 2017, including incident photosynthetically active radiation (PAR, µmol/m 2 /s) and gross primary production (GPP, mg/m 2 /s)). The Y axes indicate the measured parameters. The days with corresponding MoniPAM and FLoX measurements are depicted in bright green. Days 192-209 demonstrate the dynamics in GPP during the corn young (Yn) growth stage, days 220-235 during the mature (M), and days 236-272 (S) during the senescing (S1 early and S2 advanced) growth stages.

Measurements
At the OPE3 site, a 10 m tall eddy covariance tower measured canopy level CO2 assimilation at 30 min intervals continuously throughout the growing season [56] (Figure 1). The measured net CO2 flux (i.e., net ecosystem productivity) is partitioned into GPP (the carbon used by photosynthesis) and ecosystem respiration [28,56,57].
During the summer of 2017 we collected complementary leaf and canopy measurements ( Table  1) for C4 corn canopy (Zea mays L.) to capture the dynamics in photosynthesis, reflectance, and chlorophyll fluorescence (F and SIF) through the growing season.
Leaf-level fluorescence and photosynthetic efficiency were characterized using an automated MoniPAM Data Acquisition system (MONI-DA, Heinz Walz GmbH, Effeltrich, Germany) outfitted with emitter-detector probes. The system continuously measured chlorophyll fluorescence in the presence of ambient sunlight (i.e., light-adapted), from several leaf samples simultaneously [24,38,47]. By DOY 190, when the corn canopy was established, canopy closure was approximately 85%, and no additional agricultural treatments were planned, the MoniPAM emitter-detector probes were mounted on fully developed leaves (i.e., on the 4th leaf from the top of the plant). Measurements were collected during the growing season, continuously re-locating the probes as new leaves emerged. Five emitter-detector probes were operated, measuring in parallel light-adapted steady state F (Fs), a broadband measurement of chlorophyll fluorescence in the 710-800 nm range, and the associated PAR. Three probes were positioned to measure fully sunlit leaves from the upper canopy, while the remaining two probes collected measurements on shaded leaves at varying illumination levels and positions in the canopy. Since the leaf signal available for remote sensing of the canopy is primarily associated with the illuminated leaf surfaces, we further analyzed the measurements collected on sunlit leaves. With each measurement, the following parameters were collected: steady state and maximum F (Fs, relative units), operating photosynthetic efficiency of PSII electron transport under sunlight or yield of photosystem II (YII, right axis), relative electron transport rate (ETR, left axis), and incident PAR (Table 1, Figure 2). Eddy covariance measurements collected at OPE3, Greenbelt, MD in 2017, including incident photosynthetically active radiation (PAR, µmol/m 2 /s) and gross primary production (GPP, mg/m 2 /s)). The Y axes indicate the measured parameters. The days with corresponding MoniPAM and FLoX measurements are depicted in bright green. Days 192-209 demonstrate the dynamics in GPP during the corn young (Yn) growth stage, days 220-235 during the mature (M), and days 236-272 (S) during the senescing (S1 early and S2 advanced) growth stages.

Measurements
At the OPE3 site, a 10 m tall eddy covariance tower measured canopy level CO 2 assimilation at 30 min intervals continuously throughout the growing season [56] (Figure 1). The measured net CO 2 flux (i.e., net ecosystem productivity) is partitioned into GPP (the carbon used by photosynthesis) and ecosystem respiration [28,56,57].
During the summer of 2017 we collected complementary leaf and canopy measurements (Table 1) for C4 corn canopy (Zea mays L.) to capture the dynamics in photosynthesis, reflectance, and chlorophyll fluorescence (F and SIF) through the growing season.
Leaf-level fluorescence and photosynthetic efficiency were characterized using an automated MoniPAM Data Acquisition system (MONI-DA, Heinz Walz GmbH, Effeltrich, Germany) outfitted with emitter-detector probes. The system continuously measured chlorophyll fluorescence in the presence of ambient sunlight (i.e., light-adapted), from several leaf samples simultaneously [24,38,47]. By DOY 190, when the corn canopy was established, canopy closure was approximately 85%, and no additional agricultural treatments were planned, the MoniPAM emitter-detector probes were mounted on fully developed leaves (i.e., on the 4th leaf from the top of the plant). Measurements were collected during the growing season, continuously re-locating the probes as new leaves emerged. Five emitter-detector probes were operated, measuring in parallel light-adapted steady state F (F s ), a broadband measurement of chlorophyll fluorescence in the 710-800 nm range, and the associated PAR. Three probes were positioned to measure fully sunlit leaves from the upper canopy, while the remaining two probes collected measurements on shaded leaves at varying illumination levels and positions in the canopy. Since the leaf signal available for remote sensing of the canopy is primarily associated with the illuminated leaf surfaces, we further analyzed the measurements collected on sunlit leaves. With each measurement, the following parameters were collected: steady state and maximum F (F s , relative units), operating photosynthetic efficiency of PSII electron transport under sunlight or yield of photosystem II (YII, right axis), relative electron transport rate (ETR, left axis), and incident PAR (Table 1, Figure 2).

Figure 2.
Diurnal and seasonal variations in canopy gross primary production (GPP, A), incident and absorbed photosynthetically active radiation (PAR and APAR, B), reflectance indices (NDVI and Clred, C; and PRI, E), leaf-level photosynthetic parameters (YII and ETR, D), and canopy solar induced fluorescence (SIF, F). The Y axes of each panel indicate the measured parameters. The data were collected contemporaneously at time intervals ranging from 1-30 minutes, they were filtered, smoothed and interpolated to the GPP observations (i.e., 30 minutes), resulting in a set of corresponding measurements for 58 days, depicting the diurnal dynamics across the growing season.  Figure 2. Diurnal and seasonal variations in canopy gross primary production (GPP, A), incident and absorbed photosynthetically active radiation (PAR and APAR, B), reflectance indices (NDVI and Cl red , C; and PRI, E), leaf-level photosynthetic parameters (YII and ETR, D), and canopy solar induced fluorescence (SIF, F). The Y axes of each panel indicate the measured parameters. The data were collected contemporaneously at time intervals ranging from 1-30 minutes, they were filtered, smoothed and interpolated to the GPP observations (i.e., 30 minutes), resulting in a set of corresponding measurements for 58 days, depicting the diurnal dynamics across the growing season.
Canopy diurnal measurements including reflectance and SIF (mW/m 2 /nm/sr)-both SIF B in the O 2 B and SIF A in the O 2 A bands, were collected using a field spectroscopy system FLoX (Dual FLuorescence boX; JB Hyperspectral Devices UG, Dusseldorf, Germany) [55]. The FLoX optical cables for measurements of down-welling radiance were mounted on at the top of a tower at approximately 3 m height. The optical cables measuring upwelling radiance were pointed at nadir, and were positioned at 1.5 m above the canopy throughout the measurement period, viewing a 25 • field of view (2.6 m diameter at ground level). The FLoX is designed for high temporal frequency (at approximately 1 min time interval) acquisition of continuous top of canopy (TOC) optical properties with a focus on measurements of SIF, using an Ocean Optics FLAME S, which covers the full range of visible and near-infrared wavelengths (VNIR, 400-900 nm) and an Ocean Optics QEPro, with high spectral resolution (full width at half maximum, FWHM of 0.3 nm) in the range of the fluorescence emissions (i.e., 650-800 nm). Each spectrometer's optical input was split between two fiber optics, one leading to a cosine receptor measuring the incoming solar irradiance, and a bare fiber measuring the vegetation reflected and emitted radiances. Both spectrometers were housed in a Peltier thermally regulated box, keeping the internal temperature lower than 25 • C in order to reduce dark current drift. The thermoelectric cooler of the QEPro was set to 20 • C in order to provide stable measurements. The signal was automatically optimized for each channel at the beginning of each measurement cycle, and two dark current spectra were collected.
The key settings, such as the interval between measurement cycle and the maximum integration time, were saved in configuration files. The data and metadata (e.g., spectrometer temperature, detector temperature and humidity, GPS position and time) were also stored. The system was designed for long-term fully automatic field measurements, requiring only minimal user input.

Data Processing and Analysis
The eddy covariance flux measurements were processed to 30 min time steps during the full 2017 growing season ( Figure 1). The flux measurements obtained on days with corresponding MoniPAM and FLoX collections were selected for further use. Ecosystem respiration (Re) was calculated as an exponential function of air temperature using a relationship developed from nighttime net ecosystem production, measured by the flux tower and corresponding temperature observations [56,57]. The difference between the CO 2 flux and Re provided the GPP (Figure 1, mg/m 2 /s, shown in green on the right axis). This calculation was supported by the tower's micro-meteorology measurements, including PAR (µmol/m 2 /s, Figure 1 in gray on the left axis). Incident PAR was used to estimate the photosynthetic light use efficiency (LUE) [58,59] of the canopy in the tower footprint, which was calculated as: Leaf-level light-adapted PAM fluorescence metrics representative of the canopy were derived by calculating the mean of the values from three MoniPAM emitter-detector probes maintained on fully sunlit leaves, using the simultaneously acquired measurements at 10 min intervals. Large outlier values from a single probe (mean ± three standard deviations) were removed, resulting in averaged light-adapted observations of incoming PAR; steady state F (F s ), measured shortly before a saturating pulse is applied; and maximum F level (F m '), induced by applying a saturating light pulse which temporarily closes all PS II reactions centers. F s and F m ' (relative units) [18,21,24], were used to calculate the electron transport rate (ETR, µmol/m 2 /s 1 , Figure 2 in red on the left axis scaled by 10), and the effective photochemical quantum yield of PSII (YII, Figure 2 in blue on the right axis), as: The FLoX system [55] collects upwelling and down-welling measurements, which were processed to reflectance and solar induced fluorescence (SIF) using two open-source R packages [60,61]. The outputs of the processing are: incoming radiance to the surface, top of canopy reflected radiance, apparent reflectance, and SIF estimates at spectral wavelengths associated with both atmospheric oxygen absorption features centered at 683 (SIF B ) and 760 nm (SIF A ). Canopy reflectance from the FLoX was used to calculate indices indicative of vegetation green biomass, chlorophyll content, and photosynthetic function (i.e., NDVI, Cl red and PRI; Figure 3 and Table 2). SIF A and SIF B were retrieved by applying the spectral fitting method (SFM) [62] at the original acquisition time-steps (i.e., 1 min). Total SIF A+B was calculated as the sum of SIF A and SIF B . Each fluorescence estimate was assigned a quality flag, reporting information related to the illumination stability during the measurement cycle and the internal noise of the instrument at the moment of the data acquisition, which were used for filtering the dataset for saturated data points and anomalous readings [48,62]. Additional screening was done to remove sensor artefacts due to low light levels (i.e., in the early morning and late afternoon, SZA > 75 • ), so that only data collected between 8:00 and 17:00 local time were used in the analyses. from the FLoX was used to calculate indices indicative of vegetation green biomass, chlorophyll content, and photosynthetic function (i.e., NDVI, Clred and PRI; Figure 3 and Table 2). SIFA and SIFB were retrieved by applying the spectral fitting method (SFM) [62] at the original acquisition timesteps (i.e., 1 min). Total SIFA+B was calculated as the sum of SIFA and SIFB. Each fluorescence estimate was assigned a quality flag, reporting information related to the illumination stability during the measurement cycle and the internal noise of the instrument at the moment of the data acquisition, which were used for filtering the dataset for saturated data points and anomalous readings [48,62]. Additional screening was done to remove sensor artefacts due to low light levels (i.e., in the early morning and late afternoon, SZA > 75°), so that only data collected between 8:00 and 17:00 local time were used in the analyses.
Day of year (DOY, 2017). Error bars denote ±SD of the mean. The corn growth stages are depicted with colored lines (blue-young/Yn, green-mature/M, red-early senescence/S1, yellow-late senescence/S2). Refer to Table 1 for measurement units. The corn growth stages are depicted with colored lines (blue-young/Yn, green-mature/M, red-early senescence/S1, yellow-late senescence/S2). Refer to Table 1 for measurement units. The set of complementary leaf and canopy measurements at OPE3 occurred at different time intervals: 30 min (flux tower); 10 min (MoniPam); and approximately 1 min (FLoX). Incident PAR was measured by the OPE3 flux tower and at leaf level by the MoniPAM. The FLoX-measured incoming radiance at 750 nm and the MoniPAM PAR measurements were collected at closer time intervals, and over the study period they display a strong linear relationship, which was used to derive PAR estimates for the FLoX footprint. Outliers (i.e., values greater than three median absolute deviations) from this daily linear trend were removed from both data sets. The absorbed in the footprint of the FLoX canopy PAR (APAR, µmol/m 2 /s), required for computation of the FLoX fluorescence yields, was calculated as: where PAR is the estimate for the FLoX footprint. The fraction of APAR (f APAR) was calculated as a linear function of NDVI [63], experimentally established for corn: where NDVI was derived using the FLoX reflectance measurements. The empirical function was derived based on light bar (Accu-PAR ceptometer, METER (formerly Decagon), Pullman, WA) measurements of incident and transmitted PAR collected near solar noon on five different clear days covering the growing season, measuring every meter along a 100 m transect through the OPE3 corn field, in conjunction with above canopy spectral reflectance measurements collected using an ASD FieldSpec spectrometer (Malvern Panalytical, Longmont, CO). Using the field observations, f APAR field was calculated using the equation: where PARin is the incident PAR and PARtrans is the PAR transmitted through the canopy measured at ground level [64]. NDVI was calculated from the ASD spectral reflectance using the 670 and 800 nm bands. The NDVI and fAPAR were averaged to five meter intervals, and data from all dates were combined into the regression along with measurements of bare ground (where fAPAR = 0) for each day (R 2 = 0.93, standard error of regression 0.056). Canopy SIF yield was calculated as: for both SIF A (SIF Ay ) and SIF B (SIF By ) bands, with the assumption that APAR was equally available to both PSII and PSI.
To compare all three data sets effectively, the most frequently acquired FLoX data set, screened for outliers as described above and including APAR, was smoothed using a moving Savitzky-Golay filter function to reduce the random noise and enhance the measured steady state signal [65] (MATLAB 2018b), which was linearly interpolated to 10 min intervals and resampled at congruent time steps with the Moni-PAM data. The combined MoniPAM and FLoX data sets were then linearly interpolated to extract values at the same 30 min intervals used by the flux data. The PAR values for numerous days across the season were evaluated statistically for significant differences associated with the three sensors, and plotted to confirm that the patterns, variations, and magnitudes of PAR from the MoniPAM, Flux, and FLoX closely matched. As result of the processing, the three data sets ( Figure 2) were merged into one, containing measurements covering the period from 8:15-17:45 (≤20 per day), at consistent 30 min time intervals and with matching PAR levels. To avoid artifacts in the data due to lower solar illumination angels at the site, the measurements collected at 8:15, 17:15, and 17:45 were excluded from the analysis, living the time period of 8:45-16:45 (i.e., 17 observations per day).
The time period for which we have data from all three instruments in 2017 covers from day of year (DOY) 192 to DOY 273 (i.e., July 11 to September 29, 2017, Figure 2). During DOYs 210-220, the FLoX system was deployed for tower measurements of diurnal SIF, in support of the 2017 NASA airborne SIF acquisitions at the Smithsonian Research Center (SERC) in Edgewater, MD. Nevertheless, the 2017 dataset includes measurements representative of the major corn growth stages (58 days total). We identified the distinct growth stages based on Phenocam records [53], the variation in canopy GPP, leaf quantum yield of photosystem two (i.e., YII), and the reflectance VIs (FLoX), as indicated in Figures 1-3. The young (Yn) growth stage was identified by the pattern of increase in the reflectance indices NDVI and Cl red , as seen in early July (Figures 2 and 3), and covers the corn vegetative period. Upon reaching maximal YII, NDVI, and Cl red values (DOY 192-209, July 11-28), we defined the mature corn stage (M, DOY 220-235, August 8-22), which includes the corn initial reproductive phases. Finally, the early and late senescence stages (S1 and S2) displayed a sharp decrease in GPP, YII, and Cl red from August 23 through September 30 (DOY 236-273).
To compare the diurnal and seasonal variation in the observations and statistically evaluate the strength of the relationships of the optical metrics to photosynthetic activity, and their dependence upon the time of collection and growth stage, we selected three representative days free of clouds within each growth stage (12 days, 17 observations/day), as follows: young (Yn , DOY 192-194), mature (M, DOY 222-224), early senescence (S1, DOY 245-247), and advanced senescence (S2, DOY 255-257). Frequently, remote sensing parameters saturate and underperform, and are not transferable across a phenology. To allow for scaling using remote sensing metrics (i.e., SIF), a linear relationship with the parameter of interest (i.e., GPP and LUE) is desired. The relationships between GPP, LUE, and the fluorescence and reflectance metrics were investigated using linear regression analysis, and the established correlations are shown in Figures 6 and 7. The strength of the relationships is indicated by listing the coefficients of determination (i.e., R 2 , percentage of explained variation in the dependent variable) in corresponding colors according to growth stage. The overall coefficient of determination is listed in black when the relationship was statistically significant (p < 0.01).
The diurnal measurements were sub-selected further to form categorical variables representative of the three distinct periods during the day: morning ( representative of each growth stage, as indicated by different colors (blue-young, green-mature, red-early senescence, yellow-late senescence). The trends in the data are depicted using best fit lines (i.e., linear or polynomial). The statistical significance of the differences in the data (p < 0.01), associated with the time of observation (i.e., am/noon/pm) and growth stage (i.e., Yn/M/S1/S2), were determined based on an ANOVA general linear model (GLM) analysis (SYSTAT 12.3, SYSTAT Software Inc., 2017), suggested as optimal for use with data with unbalanced design and uneven number of samples, which occurred due to outliers and missing values. The coefficients of determination (R 2 ) are used to describe the level of variation in the measurements attributed to the ANOVA independent variables: (1) observation time (i.e., morning, midday, afternoon); (2) growth stage (i.e., young, mature, senescent); and (3) the interactions of the first two ( Table 3). The ANOVA GLM least square means of the dependent variables (e.g., GPP, VIs, F, and SIF metrics, etc.) are reported, indicating the significance of the differences among the means with a different letter (Table 3).
We anticipated that SIF observations at high PAR (i.e., saturating light level for photosynthesis) were likely to have stronger correlations with the leaf level F metrics and canopy GPP. To depict the relationship of fluorescence metrics (i.e., F and SIF) with CO 2 assimilation (GPP) not limited/controlled by PAR, we separately analyzed the measurements collected in periods of the day where PAR is known to be below saturation (am and pm) from the period where PAR commonly is at levels saturating for photosynthesis and electron transport (i.e., 12:30 noon ± 1 h, Table 4), therefore providing a more consistent comparison of the relationships between photosynthetic performance and F metrics across the growth stages. To provide context for interpretation and relevance of the results to the satellite observations of SIF, the measurements collected under varying lower light levels were included in the analysis (Tables 3 and 4), and are identified in Figures 4 and 5 (i.e., am, noon and pm). The overpass time of the satellites measuring SIF over Greenbelt, MD is for MetOp GOME-2 9:30 equatorial local time (ELT), Envisat SCIAMACHY and FLEX 10:00 ELT (http://www.ceos-cove.org/en/), ranging during the growing season by more than an hour, and is approximated by the morning (am) observations.

Diurnal and Seasonal Variations in Photosynthesis and the Associated Reflectance and Fluorescence Metrics
The diurnal profiles in vegetation canopy and leaf functional and spectral properties changed gradually throughout the growing season ( Figure 2), and significant differences associated with the different growth stages were established. In general, the diurnal variations in photosynthetic activity, reflectance and SIF metrics exhibited a similar pattern of increase in magnitude in the morning to reach maximum close to midday, declining in the afternoon. However, the phenology-related changes in diurnal variation in the observed parameters were more complex, demonstrating diurnal dynamics which gradually changed in a different manner with phenology. The highest diurnal variability in all metrics was observed in the early morning during the young growth stage (Yn, Figures 2 and 3).  (Figures 2A and 4D). During the mature stage GPP reached highest value on DOY 222, when the canopy was still developing and new leaves were being produced ( Figure 2A). The diurnal patterns of GPP through the entire growing season were consistent, with the highest GPP values always measured near midday ( Figure 2A). Midday average GPP was highest during the young stage ( Figure 3A, Figure 4C, Table 3), declining thereafter.
The diurnal variations in PAR, f APAR, and APAR are compared across the growth stages ( Figure 2B, Figure 3B, Figure 4A-C). PAR ( Figure 4A) consistently increased in the morning to a maximum around midday, and declined in the afternoon at different rates. Mean midday PAR reached a highest value of 1275 µmol/m 2 /s ( Table 3) during early senescence (S1, Figures 1, 2B and 3A). The largest diurnal change in PAR was observed during the early senescent stage (i.e., increase until midday of~600 µmol/m 2 /s, Figure 4A).
During the young and early senescent stages ( Figure 3B, 4B), f APAR declined in the morning to reach minimum in the early afternoon at approximately 14:15, increasing in the afternoon close to the levels measured in the morning. During the mature stage, the behavior of f APAR did not change significantly throughout the day ( Figure 3B, green), indicating that, only during this stage, the use of either PAR or APAR could yield similar results and derivative parameters.
The magnitude of midday average APAR was highest during the early senescence stage ( Figure 3B, Table 3, S1), which coincided with the maximal PAR levels observed during this stage and the high canopy chlorophyll content of the established canopy, as captured by the Cl red and NDVI values ( Figure 3E). Comparing the diurnal profiles of APAR across the growth stages, APAR was significantly lower during the S2 stage ( Figure 4C). During the young stage, ANOVA did not identify statistically significant changes in APAR associated with the diurnal time periods (Table 3, am/noon/pm). However, during the young stage, the diurnal profile of APAR exhibited a complex dynamic behavior ( Figure 4C) similarly to PAR, increasing quickly in the morning to reach highest magnitude in the late morning, and afterward declining by midday approximately in half to a level maintained until the end of the day. During the S1 stage, APAR remained relatively high in the late afternoon ( Figure 4C), which was attributed to the high PAR observed at this time ( Figure 4A). During late senescence (i.e., S2) when chlorophyll levels were significantly lower, APAR remained low during most of the day ( Figure 4C, points in yellow), while PAR exhibited a distinct midday maximum ( Figure 4A).
LUE declined in the morning to reach minimum in the early afternoon during all stages ( Figure 4E). Similarly to GPP, the highest LUE throughout the day was observed in the morning during the young stage. While the late morning LUE values separated the four growth stages, the midday and afternoon values grouped together the S1 and S2 stages, separating them from the young and mature stages ( Figure 4E). The diurnal variation in LUE significantly differed with growth stage (Table 3, significant interaction between 'time of day' and 'growth stage'). During the young stage, LUE did not change significantly throughout the day (Table 3), while significant diurnal changes were observed during the remaining growth stages.
Remote Sens. 2018, 10, x FOR PEER REVIEW 12 of 27 significantly lower during the S2 stage ( Figure 4C). During the young stage, ANOVA did not identify statistically significant changes in APAR associated with the diurnal time periods (Table 3, am/noon/pm). However, during the young stage, the diurnal profile of APAR exhibited a complex dynamic behavior ( Figure 4C) similarly to PAR, increasing quickly in the morning to reach highest magnitude in the late morning, and afterward declining by midday approximately in half to a level maintained until the end of the day. During the S1 stage, APAR remained relatively high in the late afternoon ( Figure 4C), which was attributed to the high PAR observed at this time ( Figure 4A). During late senescence (i.e., S2) when chlorophyll levels were significantly lower, APAR remained low during most of the day ( Figure 4C, points in yellow), while PAR exhibited a distinct midday maximum ( Figure 4A). LUE declined in the morning to reach minimum in the early afternoon during all stages ( Figure  4E). Similarly to GPP, the highest LUE throughout the day was observed in the morning during the young stage. While the late morning LUE values separated the four growth stages, the midday and afternoon values grouped together the S1 and S2 stages, separating them from the young and mature stages ( Figure 4E). The diurnal variation in LUE significantly differed with growth stage (Table 3, significant interaction between 'time of day' and 'growth stage'). During the young stage, LUE did not change significantly throughout the day (Table 3), while significant diurnal changes were observed during the remaining growth stages.

Variation in reflectance VIs
The reflectance indices NDVI and Clred ( Figure 2C) were calculated to evaluate the changes in canopy biomass and chlorophyll content, respectively. The diurnal variation in NDVI and Clred exhibited similar patterns, with lowest values measured at midday.
The diurnal variation in NDVI significantly differed with growth stage (Table 3, ANOVA significant interaction between 'time of day' and 'growth stage'). The largest diurnal range in NDVI was measured on young corn (i.e., diurnal range from 0.6-0.9, Figure 2 Figure 4. Diurnal and seasonal variations in photosynthetically active radiation (PAR, µmol/m 2 /s), absorbed PAR (APAR), fraction of APAR (f APAR), gross primary production (GPP), light use efficiency (LUE), and photochemical reflectance index (PRI). Each value represents a mean (±SE of the mean, n = 12) of the measurements collected at this time on three consecutive clear days, representative of key growth sages for corn. The growth stages are indicated in different colors (blue-young, green-mature, red-early senescence, yellow-late senescence).

Variation in Reflectance VIs
The reflectance indices NDVI and Cl red ( Figure 2C) were calculated to evaluate the changes in canopy biomass and chlorophyll content, respectively. The diurnal variation in NDVI and Cl red exhibited similar patterns, with lowest values measured at midday.
The diurnal variation in NDVI significantly differed with growth stage (Table 3, ANOVA significant interaction between 'time of day' and 'growth stage'). The largest diurnal range in NDVI was measured on young corn (i.e., diurnal range from 0.6-0.9, Figure 2). The low midday values and larger diurnal variation during the young stage contributed to influence of the soil background at higher sun elevations, which was most apparent when the canopy LAI was lower. With an increase in foliage and canopy closure, the NDVI diurnal variation decreased and remained steady until the S2 stage. There were no statistically significant diurnal changes in NDVI during the mature stage, however, during this growth stage, significant differences were observed in GPP, Cl red , PRI, and SIF (Figures 4 and 5, Table 3). Midday NDVI decreased from 0.9 to 0.4 by DOY 262 (Figure 3C, S2).
As compared to NDVI, Cl red exhibited very different seasonal dynamics, gradually increasing during the young stage to reach maximum during the mature stage, declining gradually during the S1 and S2 stages ( Figure 2C). The diurnal variation in Cl red was also largest during the early stage ( Figure 2C, Yn), with a minimum observed at noon in all growth stages. The absolute daily maximum of Clred was measured during the mature stage (Figure 2), after which Cl red declined during senescence, and during S2, the diurnal variations were not statistically significant ( Table 3).
The diurnal variation in PRI significantly differed with growth stage (Table 3, ANOVA significant interaction between 'time of day' and 'growth stage'). During the young and mature stages, daily minimum PRI was measured at noon (i.e., a 'v' pattern), while during senescence the pattern gradually changed, and during advanced senescence, the daily maximum PRI values occurred at noon (i.e., 'Λ' pattern). Similarly to NDVI and Cl red , the highest magnitude of diurnal variation was also observed for the young canopy, when lower PRI values were measured at midday. In contrast, during S2 stage, PRI increased during the middle of the day (Figures 2E and 4F). Only in the early morning during the young stage did PRI have positive mean values (Table 3, Figure 4F). Highest midday values were measured during the young ( Figure 4F, Table 3), followed by the mature and senescent stages. PRI reached lowest values during the senescent stage, which occurred in the early morning (−0.106, Table 3).

Variation in Leaf-level Chlorophyll Fluorescence
The steady state fluorescence (F s ) magnitude was distinctly higher during the young and mature stages, as compared to the S1 and S2 ( Figure 5A). During the young stage, F s reached a daily maximum in the morning (Table 3), while during the mature, S1, and S2 stages, highest daily F s was observed at midday. During the young and mature stages, similar F s amounts were emitted at noon and in the afternoon. The magnitude of afternoon F s was lower than the in the morning only during the young stage ( Figure 5A). F s has been suggested as a leaf proxy for SIF A [51], however it is especially difficult to compare directly the variation in F s to the variation in SIF, since F s does not translate to radiance units and the incident and absorbed PAR varied diurnally and during the season.
During the young stage YII did not significantly change during the day (Table 3). During the mature stage, midday YII was lower, but the morning and afternoon levels were not significantly different (Table 3, Figure 5B). The mean midday YII values declined in the mature as compared to the young stage ( Figure 3C), and YII was significantly lower during the S1 and S2 stages ( Figure 3C, 5B, Table 3). During the S1 and S2 stages, YII was highest in the morning, declined gradually until the early afternoon, and recovered later to magnitudes similar to those observed in the morning ( Figure 5B). The patterns of the diurnal variation in YII resembled these observed in LUE and PRI ( Figure 4E-F).
The highest ETR was observed during the young stage, which was reached in the late morning and maintained during the day ( Figure 5C). During the young and mature stages midday ETR had distinctly higher magnitude as compared to S1 and S2 ( Figure 3D). During the mature stage, ETR had a pronounced midday maximum. The diurnal variation in ETR resembled the trends observed in GPP during the young and mature stages. Only during the mature growth stage did ETR vary significantly when comparing the three observation periods (am/noon/pm, Table 3). ETR magnitudes and dynamics were almost identical during both S1 and S2 stages ( Figure 5C). The growth stages are indicated in different colors (blue-young, green-mature, red-early senescence, yellow-late senescence). Each value represents a mean (±SE of the mean) of the measurements collected at this time on three consecutive clear days representing each growth sage.

Variation in Canopy SIF Metrics
SIFA, SIFB, and SIFA+B exhibited a pronounced diurnal pattern, with highest average values measured close to midday ( Figures 5D-F, Table 3). During the young stage, in the morning, SIFA and SIFA+B increased relatively quickly, reaching a highest value at approximately 10:45 ( Figure 5D). In comparison, SIFB also increased fast until approximately 10:45, but afterwards it continued to rise more gradually until the early afternoon, declining afterward. During the young stage, the diurnal patterns of SIFA and SIFA+B ( Figure 5D, F) closely followed the patterns of the PAR and GPP diurnals ( Figure 4A, D). The highest SIFB was measured during the young stage, while higher levels of SIFA and SIFA+B were measured during the mature stage ( Figure 5, Table 3).
During senescence, SIF yields (SIFBy, SIFAy and SIFA+By) were significantly higher in the morning, declining until midday, and remained relatively unchanged during the remainder of the day ( Table  3). The highest SIFAy average was observed during the mature stage, when Clred also reached significantly higher levels (Table 3). During the mature stage, the magnitude of SIFAy increased in the morning, reaching a daily maximum at noon, and declined in the afternoon ( Figure 5G). SIFAy separated the young and mature from the senescent growth stages during most of the day ( Figure  5G, Table 3).   The growth stages are indicated in different colors (blue-young, green-mature, red-early senescence, yellow-late senescence). Each value represents a mean (±SE of the mean) of the measurements collected at this time on three consecutive clear days representing each growth sage.

Variation in Canopy SIF Metrics
SIF A , SIF B , and SIF A+B exhibited a pronounced diurnal pattern, with highest average values measured close to midday ( Figure 5D-F, Table 3). During the young stage, in the morning, SIF A and SIF A+B increased relatively quickly, reaching a highest value at approximately 10:45 ( Figure 5D). In comparison, SIF B also increased fast until approximately 10:45, but afterwards it continued to rise more gradually until the early afternoon, declining afterward. During the young stage, the diurnal patterns of SIF A and SIF A+B ( Figure 5D, F) closely followed the patterns of the PAR and GPP diurnals ( Figure 4A, D). The highest SIF B was measured during the young stage, while higher levels of SIF A and SIF A+B were measured during the mature stage ( Figure 5, Table 3).
During senescence, SIF yields (SIF By , SIF Ay and SIF A+By ) were significantly higher in the morning, declining until midday, and remained relatively unchanged during the remainder of the day ( Table 3). The highest SIF Ay average was observed during the mature stage, when Cl red also reached significantly higher levels (Table 3). During the mature stage, the magnitude of SIF Ay increased in the morning, reaching a daily maximum at noon, and declined in the afternoon ( Figure 5G). SIF Ay separated the young and mature from the senescent growth stages during most of the day ( Figure 5G, Table 3). Table 3. Diurnal and seasonal variation in canopy GPP, LUE, and the associated leaf and canopy reflectance and fluorescence properties for corn (ANOVA GLM: least square means (n = 12) and regression coefficients (R 2 )). To evaluate the seasonal changes in the diurnal observations, the data were organized into four stages: young (Yn, DOY 192-194), mature (M, DOY 222-224), early senescence (S1, DOY 245-247), and advanced senescence (S2, DOY 255-257). The diurnal measurements were sub-selected further to form three categories: morning ( The diurnal profiles of SIF By significantly differed with growth stage ( Figure 5H, Table 3 AVOVA GLM). During the young stage, the magnitude of SIF By was distinctly higher, as compared to the remaining growth stages, and the dynamics of the diurnal variations were more complex ( Figure 5H). During the young stage, SIF By decreased until mid-morning ( Figure 5H, 9:45), which corresponds inversely with the increase in APAR ( Figure 4C) at the same time. SIF By increased to a mean maximum at midday (Figure 5H), and gradually declined afterwards. The diurnal profile of SIF By depicted a clear separation between the observations of the young and the observations of the mature and senescent stages at midday ( Figure 5H, Table 3), which resembled the pattern established for LUE ( Figure 4E). The diurnal variations in SIF A+By during the young and mature stages did not significantly differ ( Figure 5I), with highest mean SIF A+By values observed at midday for both (Table 3). During the senescent stages, the SIF yield metrics were higher in the morning, steadily declined throughout the day, and reached lowest mean values in the late afternoon, which distinctly differed from the patterns observed during the young and mature stages.
Analysis of variance (ANOVA GLM) established that the diurnal variations in LUE, NDVI, PRI, SIF By , and SIF A+B significantly differed on a seasonal timescale ( Table 3, ‡ significant interaction term between time of day and growth stage). Normalizing the SIF metrics, using parameters that change in a similar manner with time of day and growth stage, could be beneficial for comparison and deriving models for estimating GPP and LUE (e.g., normalizing by PAR, APAR, Cl red ).

Correlations between Diurnal Sets of Observations across Corn Growth Stages
The linear relationships between canopy photosynthetic activity (i.e., GPP) and the optical metrics are shown in Figures 6 and 7, where the strength of relationships is indicated by the coefficients of determination (R 2 , percentage of explained variation in the dependent variable) in colors corresponding to the growth stage. The overall coefficient of determination is listed in black only when the relationship was statistically significant (p < 0.01). The correlation between GPP and YII was negative ( Figure 6A), while positive linear relationships with GPP were established for ETR ( Figure 6B), APAR ( Figure 6C), and the SIF metrics ( Figure 6D-F). Stronger correlations emerged between GPP and the observations collected during the young and mature stages. The relationships between observations from the S1 and S2 stages maintained linearity, however, the relationships were not statistically significant (p > 0.01). The correlation between GPP and YII ( Figure 6A) grouped the observations from the young and mature stages, separating them from those from both S1 and S2 stages.
Strong overall correlations with GPP were established for SIF A , SIF B , and SIF A+B ( Figure 6D-F), grouping the observations from all growth stages together, thus providing the potential for estimating GPP using a generalized (i.e., common) relationship across all growth stages. Overall, the highest correlation emerged between GPP and SIF A+B (R 2 = 0.78, Figure 6F), with the strongest association identified between observations from the mature growth stage (R 2 = 0.80, Figure 6F), followed by the correlation between the observations from the young stage (R 2 = 0.78). Using observations from the young stages, the strongest correlations were established between GPP and SIF A (R 2 = 0.79, Figure 6E). Comparing the correlations between observations from the mature stage, GPP was strongly correlated with SIF B , followed by SIF A+B , SIF A , YII, and ETR (i.e., R 2 = 0.82, Figure 6D; R 2 = 0.80, Figure 6F; R 2 = 0.78, Figure 6E; R 2 = 0.77, Figure 6A; R 2 = 0.71, Figure 6B; respectively). During the young stage, the correlation between GPP and SIF B explained a slightly larger proportion of the variation in GPP as compared to APAR (R 2 = 0.79 vs. R 2 = 0.77, respectively). During the young and mature stages, SIF A and SIF A+B explained a larger percent of the variation as compared to APAR, with SIF A+B providing the stronger correlations ( Figure 6F). To compare the relationships across growth stages, measurements collected on three consecutive clear days in each growth stage were used (young in blue (n = 51), mature in green (n = 50), senescence in red/initial (n = 51) and yellow/advanced (n = 51)). The linear coefficients of determination (R 2 ) are listed in colors according to growth stage. The overall coefficient of determination for the data from all stages (n = 203) is provided in black when the relationships were statistically significant (p < 0.01). Refer for units to Table 1. Negative linear relationships were established between YII and the SIF metrics ( Figure 7A-C), explaining an equally large amount of the variation in SIFA and SIFA+B during the young and mature stages ( Figure 7C, R 2 = 0.63 and R 2 = 0.84, respectively). The strength of these correlations was most pronounced for the observations from the mature stage (green points in Figure 7A-C). The linear regressions between YII and SIFA and SIFA+B clearly separated the observations collected during the senescent stages from those collected during the young and mature stages. The strength of the correlations between YII and SIFB and the slopes of the relationships differed with growth stage ( Figure 7B).
Positive linear relationships were established between ETR and SIF ( Figures 7D-E), with the highest amount of the variation in the data explained for the SIFB observations from the mature stage ( Figure 7E, green, R 2 = 0.77). The relationships between ETR and the SIF metrics grouped the observations from all growth stages closer to a linear relationships, however, the overall coefficients of determination identified a moderate overall association strength (i.e., overall R 2 = 0.54-0.65).
Using the complete diurnal sets (i.e., 8:45-16:15 data), the correlations between the SIF yield metrics (i.e., SIFAy, SIFBy, SIFA+By) and leaf YII and ETR produced weaker relationships of low statistical significance (p > 0.01), and, similarly, no statistically significant correlations were established between GPP diurnal observations and SIF yields. To compare the relationships across growth stages, measurements collected on three consecutive clear days in each growth stage were used (young in blue (n = 51), mature in green (n = 50), senescence in red/initial (n = 51) and yellow/advanced (n = 51)). The linear coefficients of determination (R 2 ) are listed in colors according to growth stage. The overall coefficient of determination for the data from all stages (n = 203) is provided in black when the relationships were statistically significant (p < 0.01). Refer for units to Table 1.
Negative linear relationships were established between YII and the SIF metrics ( Figure 7A-C), explaining an equally large amount of the variation in SIF A and SIF A+B during the young and mature stages ( Figure 7C, R 2 = 0.63 and R 2 = 0.84, respectively). The strength of these correlations was most pronounced for the observations from the mature stage (green points in Figure 7A-C). The linear regressions between YII and SIF A and SIF A+B clearly separated the observations collected during the senescent stages from those collected during the young and mature stages. The strength of the correlations between YII and SIF B and the slopes of the relationships differed with growth stage ( Figure 7B).
Positive linear relationships were established between ETR and SIF ( Figure 7D-E), with the highest amount of the variation in the data explained for the SIF B observations from the mature stage ( Figure 7E, green, R 2 = 0.77). The relationships between ETR and the SIF metrics grouped the observations from all growth stages closer to a linear relationships, however, the overall coefficients of determination identified a moderate overall association strength (i.e., overall R 2 = 0.54-0.65).
Using the complete diurnal sets (i.e., 8:45-16:15 data), the correlations between the SIF yield metrics (i.e., SIF Ay , SIF By , SIF A+By ) and leaf YII and ETR produced weaker relationships of low statistical significance (p > 0.01), and, similarly, no statistically significant correlations were established between GPP diurnal observations and SIF yields.  D-F). The relationships are evaluated using measurements from three consecutive clear days selected in each growth stage (i.e., young (n = 51, blue), mature (n = 49, green), senescing: initial (n = 51, red), and advanced (n = 52, yellow). The linear coefficients of determination (R 2 ) are listed in colors according to growth stage. The overall coefficient of determination (R 2 , n = 203) of the relationship using data from all stages is listed in black, only when the trends were statistically significant (p < 0.01). Refer for units to Table 1.

Correlations between Observations Collected under Different Conditions for Photosynthesis
The relationships between GPP, LUE, and the remote sensing metrics (i.e., APAR, VIs, SIF, and SIFy) were investigated using linear regression analysis. It was anticipated that the midday SIF observations collected under high PAR levels, when the process of photosynthesis is fully activated, would provide stronger correlations and a more unbiased comparison of photosynthetic function across the corn growth stages. The strength of the relationships are compared in Table 4, independently evaluating the relationships for measurements collected at low PAR levels in the morning, afternoon, and at midday from the midday observations when PAR is at saturating levels for photosynthesis, YII, and ETR (i.e., PAR ≥ 1150 µmol/m 2 /s). PAR < 1150 was observed at middays on the days with partial cloud cover, when the FLoX was able to maintain consistent measurements.

Low PAR Conditions Including the Morning, Midday, and Afternoon Time Periods
Correlations to GPP Strong correlations were established during the morning period between GPP and both PAR and APAR (Table 4, R 2 = 0.60, R 2 = 0.79, respectively), at midday with APAR (R 2 = 0.75, Table 4), and in the afternoon only weakly with PAR. This finding indicates that, during the morning period, the variations in GPP at the corn site are mostly driven by the variations in PAR and APAR. and between SIF and electron transport rate (ETR, D-F). The relationships are evaluated using measurements from three consecutive clear days selected in each growth stage (i.e., young (n = 51, blue), mature (n = 49, green), senescing: initial (n = 51, red), and advanced (n = 52, yellow). The linear coefficients of determination (R 2 ) are listed in colors according to growth stage. The overall coefficient of determination (R 2 , n = 203) of the relationship using data from all stages is listed in black, only when the trends were statistically significant (p < 0.01). Refer for units to Table 1.

Correlations between Observations Collected under Different Conditions for Photosynthesis
The relationships between GPP, LUE, and the remote sensing metrics (i.e., APAR, VIs, SIF, and SIF y ) were investigated using linear regression analysis. It was anticipated that the midday SIF observations collected under high PAR levels, when the process of photosynthesis is fully activated, would provide stronger correlations and a more unbiased comparison of photosynthetic function across the corn growth stages. The strength of the relationships are compared in Table 4, independently evaluating the relationships for measurements collected at low PAR levels in the morning, afternoon, and at midday from the midday observations when PAR is at saturating levels for photosynthesis, YII, and ETR (i.e., PAR ≥ 1150 µmol/m 2 /s). PAR < 1150 was observed at middays on the days with partial cloud cover, when the FLoX was able to maintain consistent measurements.

Low PAR Conditions Including the Morning, Midday, and Afternoon Time Periods
Correlations to GPP Strong correlations were established during the morning period between GPP and both PAR and APAR (Table 4, R 2 = 0.60, R 2 = 0.79, respectively), at midday with APAR (R 2 = 0.75, Table 4), and in the afternoon only weakly with PAR. This finding indicates that, during the morning period, the variations in GPP at the corn site are mostly driven by the variations in PAR and APAR. Table 4. Relationships to gross primary production (GPP) and to light use efficiency (LUE) of leaf-level PAM fluorescence metrics (i.e., operating efficiency of PSII or YII and electron transport rate, ETR), canopy-level reflectance indices (i.e., normalized difference vegetation index, NDVI; photochemical reflectance index, PRI; chlorophyll index, CI red ), and solar induced fluorescence (SIF) in the O 2 A (SIF A ) and O 2 B (SIF B ) bands and their total (SIF A+B ). The strength of the relationships was evaluated considering the time of observation and light level (i.e., below or above saturating for photosynthesis PAR, µmol/m 2 /s), and the linear coefficients of determination (R 2 ) were reported. At the leaf level, strong correlations were established between GPP and ETR (Table 4, morning R 2 = 0.75, midday R 2 = 0.70, afternoon R 2 = 0.66). At the canopy level, the strongest correlation was established with the morning observations of GPP for SIF A+B (R 2 = 0.88), followed by the correlation for SIF A (R 2 = 0.86). Considering only the midday timeframe, at low PAR, strong correlations were observed between GPP and SIF A+B (R 2 = 0.83), followed by SIF A (R 2 = 0.80), PRI (R 2 = 0.73), and SIF Ay (R 2 = 0.74).

Correlations to LUE
Under low PAR, there was no significant association between LUE and APAR. Leaf-level ETR and YII were correlated with LUE only weakly during the morning, and YII moderately during midday and the afternoon (Table 4). PRI was strongly correlated to LUE (R 2 = 0.71), using only the afternoon observations. At midday, under low PAR, both SIF Ay and NDVI were similarly correlated with LUE (R 2 = 0.71 for both).

High Light Conditions (i.e., High PAR) at Midday
Correlations to GPP Under saturating PAR levels, no significant relationship was established between APAR and GPP, which was anticipated. At the leaf level, YII exhibited the strongest correlation to GPP (Table 4, R 2 = 0.81). At the canopy level, strong correlations were established between GPP and SIF A+By (R 2 = 0.79), followed by PRI, SIF Ay , and SIF A+B (R 2 = 0.78, R 2 = 0.75, and R 2 = 0.75, respectively).

Correlations to LUE
Under saturating PAR levels, no significant relationship existed between APAR and LUE. As anticipated, at the leaf level under high PAR YII provided the strongest relationship to LUE (Table 4, R 2 = 0.79). At the canopy scale, SIF A+By provided the strongest relationship to LUE (R 2 = 0.71), followed by SIF By (R 2 = 0.70) and PRI (R 2 = 0.67).
Tables summarizing the parameters of the linear correlations between GPP and the F metrics (i.e., listing slope, intercept, and coefficient of determination) for observations collected in the morning, midday, and afternoon, and under high and low PAR, are made available for completeness as Supplementary Materials.

Discussion
This study assembled a set of complementary observations for corn across the crop growth stages, including canopy GPP and leaf and canopy fluorescence metrics, to investigate their complex dynamic behavior at both diurnal and seasonal scales. During the analysis, we noted minimal effect of clouds and light variability on the FLoX VIs and SIF metrics, which is attributed to the innovative design of the FLoX system, the strategy for automated optimization of the acquisitions, and the data processing routines in which the set of quality flags identified the values acquired during unstable light conditions, generating a set of measurements obtained under a consistent sensor optimization, tailored for the incident light levels.
To our knowledge, very few studies have evaluated the correlation between the diurnal (i.e., 8:45-16:15 timeframe) dynamics in photosynthetic function in SIF A and SIF B across seasonality or multiple crop growth stages [42,[49][50][51][52]66]. Most investigations have focused on the relationship of SIF A to GPP, since SIF A can be obtained globally from satellites, and evaluated either the SIF diurnal patterns or phenological changes. Comparing diurnals, prior research have demonstrated that LUE and SIF Ay co-vary, and that their ratio tends to be constant under high light [27,50,51,66]. This study established stronger correlations of LUE to SIF A+By and to SIF By under high PAR, and less so to SIF Ay (Table 4). Recent studies [45,51] similarly report significant linear correlations between midday leaf-level chlorophyll fluorescence parameters (i.e., F s ), canopy PRI, and chlorophyll VIs for C3 coniferous and deciduous forests. These studies have reported a strong association of SIF A with NDVI and chlorophyll content, which our findings corroborate for a C4 crop, and, in addition, demonstrate that SIF B and SIF A+B were also strongly correlated with NDVI and Cl red .
Recently, similar diurnal patterns and positive linear relationships between GPP and SIF A were reported using field and satellite observations for C3 and C4 canopies [36,37,[42][43][44][45]50]. Based on the established correlations between diurnal observations (i.e., 8:45-16:45), we also report strong positive correlations to GPP for SIF A and SIF B . Our results for SIF A concur with the results from these investigations, and show that the relationships between diurnal GPP and SIF A varied with PAR condition (i.e., high vs. low) and growth stage for C4 canopy.
Our results report linear relationships between the SIF metrics (i.e., SIF A , SIF B , and SIF A+B ) and YII, and between SIF and ETR, primarily during the mature stage ( Figure 6), when canopy chlorophyll levels and Cl red were highest. Prior investigations [42,44] have reported that YII correlates well with SIF Ay for C3 canopies, which our findings did not support for corn, a C4 crop.
Using the complete diurnal sets of observations (i.e., 8:45-16:15), no strong linear relationships were established between the SIF yield metrics (i.e., SIF Ay , SIF By , SIF A+By ) and either GPP or LUE, which could be indicative of the complex and nonlinear behavior of their association across the diurnal profile. Deriving consistent diurnal and seasonal estimates of canopy SIF yield remains challenging, due to the difficulties in estimation of the absorbed energy [31,59]. Some of the variations observed in the morning and afternoon estimates of APAR and the associated SIF Ay , SIF By , and SIF A+By could be attributed to the field data used for deriving the linear function between f APAR and NDVI, which were collected near solar noon. While the implemented equation for deriving f APAR describes the seasonal change in NDVI/f APAR, it may underperform under low PAR early in the morning and in the late afternoon.
Prior studies characterizing the diurnal cycle in chlorophyll fluorescence during several consecutive days [38] reported that SIF (i.e., SIF A and SIF B ) was mainly driven by PAR variation, but that fluorescence yield was severely reduced during the central hours of the day in association with stress factors (e.g., high light and temperature). Our results corroborate the importance of PAR as a driving factor for both GPP and SIF, as their yields (LUE and SIF y ) co-varied closely (Table 4).
Under low PAR, SIF A+B and SIF A were correlated strongly with GPP, demonstrating higher sensitivity to GPP as compared to the sensitivity of APAR to GPP (Table 3). Under high PAR levels, SIF A+By and SIF Ay captured the variation in GPP optimally. Under a saturating PAR leaf level YII was also strongly correlated with GPP and indicative of canopy photosynthetic function. SIF A+By and SIF By offered sensitive capabilities for assessment of LUE under saturating PAR, which outperformed PRI, but were inferior as compared to the utility of YII, which explained the highest percentage of the variation in LUE. Under low PAR, the sensitivity of YII to LUE was significantly lower, and the correlations using SIF metrics varied strongly according to time of observation during the day. The use of multiple SIF metrics, depending on PAR condition, offers the potential to improve the sensitivity of statistical models for estimating GPP and LUE, and therefore needs to be considered. Our findings demonstrate that, at midday, under higher PAR levels (e.g., saturating for photosynthesis) YII was correlated more accurately with GPP and LUE (Table 3). Under lower PAR levels, ETR exhibited strong correlations to GPP (Table 3), and also to the canopy SIF metrics, which are strongly influenced by the changing PAR levels, and therefore may suffer inaccuracies.
Further research, investigating the capability of SIF metrics for scaling and spatially extrapolating leaf YII and ETR under varying PAR conditions, is warranted for both C3 and C4 canopies. Recent studies [42,44,47] measuring C3 vegetation used supplemental dark-adapted measurements to augment PAM light-adapted observations and successfully estimate non-photochemical quenching during the day (NPQ) in a modeling framework, and thus enabled the partitioning of leaf PAR into YII, NPQ, and heat dissipation. Future efforts enhancing the current dataset with estimates of NPQ would yield a long term dataset for partitioning of APAR for C4 vegetation, which is not currently available.
Currently SIF observations are available from field, airborne, and space-borne platforms, which are collected at different light levels and times during the day. Their sensitivity for evaluation of photosynthetic function and scaling between leaf and canopy levels would likely benefit from a separate consideration depending on PAR condition (i.e., PAR below or above saturation level for photosynthesis), which would likely improve their applicability for monitoring of GPP and LUE.
GPP, APAR, NDVI, CL red and SIF maintained similar diurnal patterns across the growing season, while the diurnal pattern of PRI changed during the early senescence stage (Figures 2E and 4F). To our knowledge, the change (i.e., inversion) in the PRI diurnal profiles has not been reported previously for corn canopies, and further research is warranted to investigate if it also applies to other species.
In addition to the metabolic changes advancing with phenology, major drivers of the seasonal dynamics in photosynthesis and the associated fluorescence and reflectance properties include variation in light and the seasonal dynamics in canopy chlorophyll. The seasonal changes in midday values for PRI appeared driven mostly by the changes in canopy chlorophyll, as indicated by their strong correlations with CI red (Figure 8). Similar relationships were also observed for both SIF A and SIF B in relation to CI red . These findings are corroborated by previous research evaluating the relationship of canopy PRI and a chlorophyll index (e.g., MTCI) for loblolly stands of various ages [30]. Our findings confirm the capability of SIF A , SIF B , SIF A+B , and their yields to enable more consistent interpretation and estimation of GPP and LUE, and strongly suggest that their diurnal and seasonal dynamics should be considered for scaling of photosynthetic function from leaf to canopy levels. In addition to the metabolic changes advancing with phenology, major drivers of the seasonal dynamics in photosynthesis and the associated fluorescence and reflectance properties include variation in light and the seasonal dynamics in canopy chlorophyll. The seasonal changes in midday values for PRI appeared driven mostly by the changes in canopy chlorophyll, as indicated by their strong correlations with CIred ( Figure 8). Similar relationships were also observed for both SIFA and SIFB in relation to CIred. These findings are corroborated by previous research evaluating the relationship of canopy PRI and a chlorophyll index (e.g., MTCI) for loblolly stands of various ages [30]. Our findings confirm the capability of SIFA, SIFB, SIFA+B, and their yields to enable more consistent interpretation and estimation of GPP and LUE, and strongly suggest that their diurnal and seasonal dynamics should be considered for scaling of photosynthetic function from leaf to canopy levels. Although the spectral data used in this study were acquired from a nadir orientation, it is widely documented that the reflectance measured from vegetation canopies varies with solar illumination angle due to variations in shadows, understory background, and canopy parameters such as biomass and leaf area index, which contribute to the variation in the results to a different degree [12,13,58,59]. A full analysis of the sensitivity of the relationships between GPP and the SIF metrics, focusing on these effects, is warranted. An improved understanding of the drivers of variation with phenology, and the implementation of a strategy for normalisation of their effects, would be a logical follow up research effort. Since the present dataset was collected at a close proximity to the canopy, future efforts would be warranted, using modeling scenarios [67][68][69] to determine whether our present findings can scale successfully to airborne and satellite levels.
Incorporating the consistently collected spectral and field datasets into the Automated Radiative Transfer Models Operator (ARTMO) framework will facilitate the data interpretation, comparisons, and scaling from the leaf to the canopy and above [69] of vegetation function and the associated biophysical variables, which is of importance for the forthcoming spectroscopy missions such as NASAs SBG [70], EnMAP [71], and ESA FLEX [52,72].
Ultimately, we would like to trace the changes in photosynthetic function with phenology and not chlorophyll content or canopy biomass, the effects of which can be domineering and can obscure the relationships of PRI and SIF to GPP. Although the spectral data used in this study were acquired from a nadir orientation, it is widely documented that the reflectance measured from vegetation canopies varies with solar illumination angle due to variations in shadows, understory background, and canopy parameters such as biomass and leaf area index, which contribute to the variation in the results to a different degree [12,13,58,59]. A full analysis of the sensitivity of the relationships between GPP and the SIF metrics, focusing on these effects, is warranted. An improved understanding of the drivers of variation with phenology, and the implementation of a strategy for normalisation of their effects, would be a logical follow up research effort. Since the present dataset was collected at a close proximity to the canopy, future efforts would be warranted, using modeling scenarios [67][68][69] to determine whether our present findings can scale successfully to airborne and satellite levels.

Conclusions
Incorporating the consistently collected spectral and field datasets into the Automated Radiative Transfer Models Operator (ARTMO) framework will facilitate the data interpretation, comparisons, and scaling from the leaf to the canopy and above [69] of vegetation function and the associated biophysical variables, which is of importance for the forthcoming spectroscopy missions such as NASAs SBG [70], EnMAP [71], and ESA FLEX [52,72].
Ultimately, we would like to trace the changes in photosynthetic function with phenology and not chlorophyll content or canopy biomass, the effects of which can be domineering and can obscure the relationships of PRI and SIF to GPP.

Conclusions
Using automated systems, this research effort assembled a set of corresponding leaf and canopy chlorophyll fluorescence and reflectance measurements, representative of the diurnal dynamics in the major growth stages for corn, which is supported by canopy GPP collected by an eddy co-variance tower. Statistical analyses of the observations demonstrated that: (1) Canopy SIF was able capture the dynamics in leaf level light-adapted YII and ETR, and SIF A+B exhibited the strongest correlation.
(2) As compared to APAR and PRI, SIF metrics provided stronger relationships to GPP and LUE, which differed depending on PAR levels: strongest correlations to GPP under low PAR were provided by SIF A+B and SIF A , under high PAR by SIF A+By and SIF Ay ; PRI had the strongest correlation to LUE under low PAR, while under high PAR, SIF A+By and SIF By provided stronger correlations. (3) The relationships of canopy SIF to leaf F and to canopy GPP differed during the day in association with the diurnal variation in PAR and GPP and with growth stage.
This study demonstrated that canopy SIF metrics co-varied with leaf ETR and YII, both indicative of photosynthetic function at leaf level, and therefore show high potential for scaling photosynthetic processes from leaf to canopy level. Using diurnals from the different growth stages, single linear relationships between LUE and SIF A+By , and LUE and SIF By described approximately seventy percent of the variation in data associated with both time of observation and growth stage. Diurnal observations of SIF (both SIF A and SIF B ) and SIF yield (i.e., SIF Ay, SIF By , and SIF A+By ), spanning the growing season can provide an important capability for remote sensing of canopy GPP and LUE, however, additional research and analysis are warranted to corroborate the applicability of these findings for other species. The change in the PRI diurnal pattern established with corn senescence requires further investigation using other species. Future research is needed to evaluate the driving factors for the established relationships between canopy GPP and the associated reflectance and fluorescence properties, in the context of varying climate and environmental conditions, and using independent field bio-physical measurements.
The results contribute to enhancing the ability to relate the commonly measured leaf-level photosynthetic parameters to the canopy level, based on SIF A , SIF B , SIF A+B , and their yields. SIF A is currently measured by satellites (e.g., GOME-2, GOSAT, OCO-2) and the measurement of SIF A , and both SIF A and SIF B are targeted by the future NASA GeoCarb and ESA FLEX missions, respectively.