Evaluating Multi-Angle Photochemical Reﬂectance Index and Solar-Induced Fluorescence for the Estimation of Gross Primary Production in Maize

: The photochemical reﬂectance index (PRI) has been suggested as an indicator of light use e ﬃ ciency (LUE), and for use in the improvement of estimating gross primary production (GPP) in LUE models. Over the last two decades, solar-induced ﬂuorescence (SIF) observations from remote sensing have been used to evaluate the distribution of GPP over a range of spatial and temporal scales. However, both PRI and SIF observations have been decoupled from photosynthesis under a variety of non-physiological factors, i.e., sun-view geometry and environmental variables. These observations are important for estimating GPP but rarely reported in the literature. In our study, multi-angle PRI and SIF observations were obtained during the 2018 growing season in a maize ﬁeld. We evaluated a PRI-based LUE model for estimating GPP, and compared it with the direct estimation of GPP using concurrent SIF measurements. Our results showed that the observed PRI varied with view angles and that the averaged PRI from the multi-angle observations exhibited better performance than the single-angle observed PRI for estimating LUE. The PRI-based LUE model when compared to SIF, demonstrated a higher ability to capture the diurnal dynamics of GPP (the coe ﬃ cient of determination (R 2 ) = 0.71) than the seasonal changes (R 2 = 0.44), while the seasonal GPP variations were better estimated by SIF (R 2 = 0.50). Based on random forest analyses, relative humidity (RH) was the most important driver a ﬀ ecting diurnal GPP estimation using the PRI-based LUE model. The SIF-based linear model was most inﬂuenced by photosynthetically active radiation (PAR). The SIF-based linear model did not perform as well as the PRI-based LUE model under most environmental conditions, the exception being clear days (the ratio of direct and di ﬀ use sky radiance > 2). Our study conﬁrms the utility of multi-angle PRI observations in the estimation of GPP in LUE models and suggests that the e ﬀ ects of changing environmental conditions should be taken into account for accurately estimating GPP with PRI and SIF observations. (GPP)

quantitatively with continuous and long-term observations [46]. Thus, a comparison of PRI-based LUE model and SIF-based linear model could be helpful to better estimate GPP under varying environmental conditions.
In this study, we assessed the performance of a PRI-based LUE model in estimating GPP under various environmental conditions in a maize field, and compare it with SIF-based linear model. We integrated a set of field observation data, including multi-angle spectral observations, eddy flux measurements, environmental variables, and canopy structural parameters. The objectives of our study are: (1) to explore the angular variations of observed PRI and evaluate the performance of single-angle and multi-angle spectral observations of PRI in estimating LUE for a maize canopy, respectively; (2) to evaluate and compare the performance of PRI-based LUE model and SIF-based linear model for the estimation of GPP in the maize field; and (3) to explore the model preferences under different environmental conditions.

Study Site
The study was conducted at the Shangqiu Farmland Ecosystem National Field Scientific Observation and Research Station (34.52°N, 115.59°E, elevation 55 m), located in Shangqiu, Henan Province, from June to September in 2018 ( Figure 1). The site has a warm temperate climate with a mean annual air temperature of 13.9 °C, mean annual precipitation of 708 mm, and mean annual solar radiation of 4823 MJ·m −2 . The soil is fluvo-aquic, which is the main soil type in the North China Plain and annually produces almost 60-80% of wheat and 35-40% of maize in China. The study site is a traditionally managed cropland with a typical crop rotation system, which consists of one season of winter wheat and another season of summer maize. During the 2018 study period, summer maize (Zea mays L.) was planted in the agricultural field. The entire growing season lasted for four months, from sowing in early June (Day of Year (DOY), 155) to harvest in late September (DOY, 267). The phenology of maize is usually divided into two main growth stages: the vegetative (V) stages (emergence to DOY 207) and the ripening (R) stages (DOY 208 to harvest). The V stages included emergence on DOY 160, 5th leaf stage on DOY 170, elongation stage on DOY 183, and tasseling stage on DOY 206. The R stages were characterized by the silking stage on DOY 208, and the physiological maturity stage on DOY 256, until harvest on DOY 267. The crop was fertilized (40.5 kg·N·ha −1 and 103.5 kg·P·ha −1 ) at the time of sowing and was topdressed (225 kg·N·ha −1 , 37.5 kg·P·ha −1 , and 37.5 kg·K·ha −1 ) prior to the elongation stage. The soil was irrigated (45 mm) before the emergence of maize plants (DOY 158). The field measurements began on June 16 (DOY 167) when the maize was emerging and ended on September 24 (DOY 267) when the maize was at the mature grain stage prior to harvest.

Measurements of CO 2 Fluxes and Environmental Data
The flux measurement system was fixed to a flux tower situated in the maize field ( Figure 1a) to derive GPP. The tower included a eddy covariance (EC) system to measure the net ecosystem exchange of CO 2 (NEE) [47]. The EC system consists of an open-path infrared gas analyzer (Model LI-7500, LI-COR Inc., Lincoln, NE, USA) for measuring CO 2 concentrations, a three-dimensional sonic anemometer (Model CSAT3, Campbell Scientific Inc., Logan, UT, USA) for measuring wind components, and data logger (CR3000, Campbell Scientific, Logan, UT, USA) for recording all EC data at 10 Hz. The EddyPro software (LI-COR Inc., Lincoln, NE, USA) was employed for data calculation and quality assurance to produce half-hourly flux estimates of NEE. A flux partitioning algorithm [48] was applied to estimate EC measured GPP (GPP EC ) through net ecosystem exchange of CO 2 (NEE) and daytime ecosystem respiration (R e ).
Half-hourly EC-based light use efficiency (LUE EC ) was estimated as: where FPAR was calculated by leaf area index (LAI) and solar zenith angle as Chen [14]: and, where ρ 1 is the PAR reflectance above the canopy and specified as 0.05; ρ 2 is the PAR reflectance below the canopy and specified as 0.06. LAI e is the effective LAI, obtained from field measurements. θ s is the solar zenith angle calculated using site location and time.
Environmental variables were continuously measured in synchronization with EC flux measurements and integrated over 30 min time periods. The environmental variations included total incident PAR above the canopy, total sky radiation (R g ), diffuse sky radiation (R d ), air temperature (T a ), relative humidity (RH), soil temperature (T s , 10 cm depth), and volumetric soil water content (SWC, 10 cm depth). The ratio of direct and diffuse sky radiation was also calculated to represent the sky condition (Q) using R g and R d [49]. Q varies with real-time cloudiness of sky, with a less cloudy sky having greater Q.

Measurements of Leaf Area Index
We used a plant canopy analyzer (LAI-2200, LI-COR, Lincoln, NE, USA) to measure the effective leaf area index (LAI e ). Measurements of one A value (above the canopy) and four B values (below the canopy) were taken for each sampling point for calculating LAI e . At least five LAI e values were averaged for field measurements. LAI measurements were taken during twilight and overcast conditions to reduce the bias caused by direct sun radiance. The in-situ measurements of LAI e were conducted on several separate days over the season (DOY 200,213,222,236,252,and 267), and combined with the germination date (set as LAI e = 0.1). Linear interpolation was used to calculate LAI e values for every day during entire growing season.

Multi-Angle Observations of Canopy PRI and SIF
A multi-angle spectra system was mounted at 4 m above the ground on an adjacent tower in a paired maize field (details in Li et al. [50]). The system consisted of two spectrometers (HR2000+ and QEPro, Ocean Optics, Dunedin, FL, USA) for measuring high-resolution spectra, which can be used for retrieving PRI and SIF, respectively. The single optical path of each spectrometer was separated into two paths and switched via a 2 × 2 shutter and a Y-shaped splitter fiber (Ocean Optics, Dunedin, FL, USA), pointing towards the sky (up-looking) and the canopy (down-looking) directions to measure Remote Sens. 2020, 12, 2812 5 of 16 irradiance and radiance signals, respectively. In the up-looking direction, cosine-corrected optics (CC3-UV-S, Ocean Optics, Dunedin, FL, USA) were used to collect the hemispherical irradiance signals with a large field of view (FOV) of 180 • ; while the canopy radiance in the down-looking direction was measured using a bare fiber with a small FOV of 25 • . The down-looking fiber optics were installed on a rotating device PTU-D46 (FLIR Motion Systems Inc., Burlingame, CA, USA) to collect canopy radiance from different view angles. In each half-hour observation cycle, the two spectrometers synchronously measured the canopy radiance at varying view azimuth angle (VAA) moving from 60 • to 300 • at a 10 • step. The view zenith angle (VZA) was dynamically set as the solar zenith angle (SZA) and was set as 40 • when SZA > 40 • to avoid the measurements at large VZA [51]. Radiometric calibration was conducted before the growing season using an integrated sphere (Labsphere, North Sutton, NH, USA) and a tungsten halogen light source (HL-CAL-2000, Ocean Optics, Dunedin, FL, USA) [52].
While utilizing the irradiance and radiance signals, the observed PRI (PRI obs ) was estimated by the reflectance of 531 nm (R 531 ) and 570 nm (R 570 ) as follows: R 531 was calculated using the average reflectance of three wavebands centered on 530.87 nm, 531.33 nm, and 531.79 nm; R 570 was calculated using the average reflectance of three wavebands centered on 570.07 nm, 570.53 nm, and 570.98 nm.
In comparison with the estimation of GPP, SIF was estimated from incident irradiance (I) and canopy radiance (L) around the O 2 -A absorption using Spectral fitting methods (SFM). The methods assume that suitable mathematical function (e.g., polynomial) fitted by wavelength (λ) can be used to describe the spectral characteristics of reflectance (R) and fluorescence (F) [53][54][55]. Here, we assumed the linear function of λ could represent R and F [50]. The measured canopy radiance (L(λ)) was expressed as follows, the observed SIF (SIF obs ) was calculated using the function F(λ): where ε(λ) was the bias of observed and modeled radiance. λ 1 and λ 2 were specified as 757 and 768 nm, respectively. λ m represented the wavelength with the minimum irradiance in the O 2 -A absorption band around 760 nm. The highly frequent (around 1 min) multi-angle observed PRI and SIF at each view angle were used to calculate the canopy PRI and SIF. The half-hourly canopy PRI (PRI can ) was calculated as a simple arithmetic average using all available multi-angle PRI obs within 30 min intervals to match half-hourly EC flux data. SIF obs were also averaged every half an hour to obtain the canopy SIF (SIF can ) for half-hourly comparison with GPP.

Statistical Analysis
Our analyses were based on the measurement data from 6:00 to 18:00 local time each day during the entire maize growing season in 2018 (101 days). Negative GPP, APAR, and SIF data were excluded. Days with less than 50% of available data were excluded from the analysis. The GPP EC was fitted with a PRI-based LUE model as: where LUE PRI = a × PRI + b. The GPP EC was also fitted with SIF for comparison with empirical linear SIF-GPP relationship. We used the coefficient of determination (R 2 ), significant level (p), and root mean square error (RMSE) for evaluating the performance of the two models. Both models were applied at "daily mean", "30 min", and "day-by-day" scales. At the "daily mean" scale, we used the daily means of half-hourly values of GPP, APAR, PRI, and SIF from 6:00 to 18:00 of all individual days during the entire growing Remote Sens. 2020, 12, 2812 6 of 16 season in 2018. At the "30 min" scale, we used all the half-hourly values from 6:00 to 18:00 during the growing season. At "day-to-day" scale, we applied two models for each day during the growing season using the half-hourly values from 6:00 to 18:00.
We also conducted a random forest regression analysis to identify the most important environmental variables affecting the performance of the SIF-based model and the PRI-based LUE model for GPP estimation. We calculated the daily mean values of the environmental variables and used them as the predictor variables. The interplays and nonlinear relationships of predictor variables were considered in the random forest analysis, while alleviating multicollinearity problems in the multivariate regression [56,57].The increase in the percentage of mean square error (%IncMSE) of observations and predictions was applied to quantify the importance of predictor variables. Higher values of %IncMSE denoted higher the importance of the variables. We calculated the importance of each tree and averaged it over the forest of 1000 trees. R Studio was used to perform random forest regression analysis.

Estimation of LUE Using Multi-Angle Observed PRI
The observed PRI (PRI obs ) changed with the viewing azimuth angles and its angular pattern differed with the solar position at a varied time on DOY 204 (a sunny day) ( Figure 2). Within 30 min, solar radiation and solar position were near constant and the variations of PRI were a result of the different parts of the maize canopy viewed at different angles. We found that PRI obs obtained from 14:30 to 15:00 were much higher than that obtained closer to noon (11:30 to 12:00). PRI obs values in hotspot directions appeared lower than those when observer and the sun were far apart. These differences were more obvious in the afternoon hours than that at noon. The hotspot direction was in the same direction as the sun, resulting in more sunlit leaves being observed in the hotspot direction.
Remote Sens. 2020, 12, x FOR PEER REVIEW 6 of 16 "30 min", and "day-by-day" scales. At the "daily mean" scale, we used the daily means of half-hourly values of GPP, APAR, PRI, and SIF from 6:00 to 18:00 of all individual days during the entire growing season in 2018. At the "30 min" scale, we used all the half-hourly values from 6:00 to 18:00 during the growing season. At "day-to-day" scale, we applied two models for each day during the growing season using the half-hourly values from 6:00 to 18:00. We also conducted a random forest regression analysis to identify the most important environmental variables affecting the performance of the SIF-based model and the PRI-based LUE model for GPP estimation. We calculated the daily mean values of the environmental variables and used them as the predictor variables. The interplays and nonlinear relationships of predictor variables were considered in the random forest analysis, while alleviating multicollinearity problems in the multivariate regression [56,57].The increase in the percentage of mean square error (%IncMSE) of observations and predictions was applied to quantify the importance of predictor variables. Higher values of %IncMSE denoted higher the importance of the variables. We calculated the importance of each tree and averaged it over the forest of 1000 trees. R Studio was used to perform random forest regression analysis.

Estimation of LUE Using Multi-Angle Observed PRI
The observed PRI (PRIobs) changed with the viewing azimuth angles and its angular pattern differed with the solar position at a varied time on DOY 204 (a sunny day) ( Figure 2). Within 30 min, solar radiation and solar position were near constant and the variations of PRI were a result of the different parts of the maize canopy viewed at different angles. We found that PRIobs obtained from 14:30 to 15:00 were much higher than that obtained closer to noon (11:30 to 12:00). PRIobs values in hotspot directions appeared lower than those when observer and the sun were far apart. These differences were more obvious in the afternoon hours than that at noon. The hotspot direction was in the same direction as the sun, resulting in more sunlit leaves being observed in the hotspot direction. Using the multi-angle observations, we compared the observed PRI in the single view angle (PRIs, VAA = 180°) and the canopy PRI with multi-angle mean values (PRIcan) with LUEEC ( Figure 3). Both PRIs and PRIcan showed similar diurnal variations to LUEEC. LUEEC, PRIs, and PRIcan decreased from sunrise and reached their minimum at noon than increased until the sunset. PRIcan (R 2 = 0.49, p Using the multi-angle observations, we compared the observed PRI in the single view angle (PRI s , VAA = 180 • ) and the canopy PRI with multi-angle mean values (PRI can ) with LUE EC (Figure 3). Both PRI s and PRI can showed similar diurnal variations to LUE EC . LUE EC , PRI s , and PRI can decreased from sunrise and reached their minimum at noon than increased until the sunset. PRI can (R 2 = 0.49, p < 0.01) had a stronger correlation with LUE EC than PRI s (R 2 = 0.41, p < 0.01). The PRI can , which was the mean value of the multi-angle PRI obs , performed better in estimating LUE with tens of measurements evenly distributed at different view angles. < 0.01) had a stronger correlation with LUEEC than PRIs (R 2 = 0.41, p < 0.01). The PRIcan, which was the mean value of the multi-angle PRIobs, performed better in estimating LUE with tens of measurements evenly distributed at different view angles.

Performance of the PRI-Based LUE Model and SIF-Based Linear Model for GPP Estimation
The PRI-based LUE model and SIF-based linear model for GPP estimation were compared at different time scales. The summary statistics of both models are shown in Table 1. Significant relationships were found between LUEPRI × APAR and GPPEC at these three-time scales. The R 2 between LUEPRI×APAR and GPPEC at the "daily mean" scale and the "30 min" scale was lower than that at the "day-by-day" scale (R 2 = 0.71 ± 0.22, p < 0.01). This indicated that LUEPRI × APAR tracked the diurnal variations of GPPEC better than the seasonal variations of GPPEC. Compared to SIFcan, the LUEPRI×APAR was higher R 2 with GPPEC at the short-term time scale, especially at the "day-by-day" scale. However, the R 2 between SIFcan and GPPEC at the "daily mean" scale (R 2 = 0.50, p < 0.001) was highest among the three time scales and higher than the R 2 between LUEPRI×APAR and GPPEC (R 2 = 0.44, p < 0.001) at the same time scale. * LUEPRI = a × PRIcan + b, where a and b were fitted linearly using LUEEC and PRIcan over the half-hourly values from 6:00 to 18:00 each day during the entire growing season in 2018. GPPEC represented the EC measured GPP. ** SIFcan represented the canopy SIF. *** The results of "day-by-day" were the averages ± standard deviations of the statistical variables (coefficient of determination (R 2 ), significant level (p), and root mean square error (RMSE)). Figure 4 showed the day-by-day variation of R 2 between LUEPRI × APAR and GPPEC (R 2 PRI), and between SIFcan and GPPEC (R 2 SIF) and their relative frequency. There was some data loss (Figure 4) because of instrument failure. Significant correlations (p < 0.05) between LUEPRI×APAR and GPPEC occurred on all 51 available days with an R 2 ranging from 0.23-0.96. SIFcan showed significant relationships with GPPEC on 81% of the 79 available days (R 2 : 0.18-0.85). The highest frequency of R 2 PRI was 0.8-0.9, much higher than that of R 2 SIF (0.2-0.5). In summary, LUEPRI×APAR tracked the diurnal variations of GPPEC better than SIFcan for individual days.

Performance of the PRI-Based LUE Model and SIF-Based Linear Model for GPP Estimation
The PRI-based LUE model and SIF-based linear model for GPP estimation were compared at different time scales. The summary statistics of both models are shown in Table 1. Significant relationships were found between LUE PRI × APAR and GPP EC at these three-time scales. The R 2 between LUE PRI ×APAR and GPP EC at the "daily mean" scale and the "30 min" scale was lower than that at the "day-by-day" scale (R 2 = 0.71 ± 0.22, p < 0.01). This indicated that LUE PRI × APAR tracked the diurnal variations of GPP EC better than the seasonal variations of GPP EC . Compared to SIF can , the LUE PRI ×APAR was higher R 2 with GPP EC at the short-term time scale, especially at the "day-by-day" scale. However, the R 2 between SIF can and GPP EC at the "daily mean" scale (R 2 = 0.50, p < 0.001) was highest among the three time scales and higher than the R 2 between LUE PRI ×APAR and GPP EC (R 2 = 0.44, p < 0.001) at the same time scale. * LUE PRI = a × PRI can + b, where a and b were fitted linearly using LUE EC and PRI can over the half-hourly values from 6:00 to 18:00 each day during the entire growing season in 2018. GPP EC represented the EC measured GPP. ** SIF can represented the canopy SIF. *** The results of "day-by-day" were the averages ± standard deviations of the statistical variables (coefficient of determination (R 2 ), significant level (p), and root mean square error (RMSE)). Figure 4 showed the day-by-day variation of R 2 between LUE PRI × APAR and GPP EC (R 2 PRI ), and between SIF can and GPP EC (R 2 SIF ) and their relative frequency. There was some data loss ( Figure 4) because of instrument failure. Significant correlations (p < 0.05) between LUE PRI ×APAR and GPP EC occurred on all 51 available days with an R 2 ranging from 0.23-0.96. SIF can showed significant relationships with GPP EC on 81% of the 79 available days (R 2 : 0.18-0.85). The highest frequency of R 2 PRI was 0.8-0.9, much higher than that of R 2 SIF (0.2-0.5). In summary, LUE PRI ×APAR tracked the diurnal variations of GPP EC better than SIF can for individual days.  represented the R 2 PRI and its relative frequency respectively, while (c) and (d) represented the R 2 SIF and its relative frequency respectively. Figure 5 illustrates the seasonal variations of the environmental variables, GPPEC and LUEEC. PAR and Q exhibited the largest day-to-day variations and high Q usually occurred with high PAR (Figure 5a). The day-to-day variation of RH appeared opposite those of PAR, while the several abrupt changes of SWC depended on irrigation and precipitation (Figure 5b). Both Ta and Ts remained around 30 °C during DOY 180-220, and then slowly decreased to around 22 °C at the end of the growing season (Figure 5c). The day-to-day fluctuation of Ta was larger than that of Ts (Figure 5c). The maize canopy showed pronounced seasonal variations in GPPEC and LUEEC (Figure 5d). The onset of GPPEC occurred on DOY 167, several days after emergence. GPPEC increased with maize development and reached its peak of 60 μmol CO2 m −2 ·s −1 on around DOY 215. During the early reproductive stage, GPPEC had high and stable values, sometimes dropped to low values due to low PAR. GPPEC decreased with leaf senescence at the end of the growing season. LUEEC increased from the start of the growing season, reaching the maximum on around DOY 190, and remaining until the early reproductive stage, and then decreasing.

Effects of Different Environmental Variables on the Abilities of the PRI-Based and SIF-Based Models in
Tracking Diurnal Variations of GPP Figure 5 illustrates the seasonal variations of the environmental variables, GPP EC and LUE EC . PAR and Q exhibited the largest day-to-day variations and high Q usually occurred with high PAR (Figure 5a). The day-to-day variation of RH appeared opposite those of PAR, while the several abrupt changes of SWC depended on irrigation and precipitation (Figure 5b). Both T a and T s remained around 30 • C during DOY 180-220, and then slowly decreased to around 22 • C at the end of the growing season (Figure 5c). The day-to-day fluctuation of T a was larger than that of T s (Figure 5c). The maize canopy showed pronounced seasonal variations in GPP EC and LUE EC (Figure 5d). The onset of GPP EC occurred on DOY 167, several days after emergence. GPP EC increased with maize development and reached its peak of 60 µmol CO 2 m −2 ·s −1 on around DOY 215. During the early reproductive stage, GPP EC had high and stable values, sometimes dropped to low values due to low PAR. GPP EC decreased with leaf senescence at the end of the growing season. LUE EC increased from the start of the growing season, reaching the maximum on around DOY 190, and remaining until the early reproductive stage, and then decreasing.  Figure 5 illustrates the seasonal variations of the environmental variables, GPPEC and LUEEC. PAR and Q exhibited the largest day-to-day variations and high Q usually occurred with high PAR (Figure 5a). The day-to-day variation of RH appeared opposite those of PAR, while the several abrupt changes of SWC depended on irrigation and precipitation (Figure 5b). Both Ta and Ts remained around 30 °C during DOY 180-220, and then slowly decreased to around 22 °C at the end of the growing season (Figure 5c). The day-to-day fluctuation of Ta was larger than that of Ts (Figure 5c). The maize canopy showed pronounced seasonal variations in GPPEC and LUEEC (Figure 5d). The onset of GPPEC occurred on DOY 167, several days after emergence. GPPEC increased with maize development and reached its peak of 60 μmol CO2 m −2 ·s −1 on around DOY 215. During the early reproductive stage, GPPEC had high and stable values, sometimes dropped to low values due to low PAR. GPPEC decreased with leaf senescence at the end of the growing season. LUEEC increased from the start of the growing season, reaching the maximum on around DOY 190, and remaining until the early reproductive stage, and then decreasing.  To avoid the interactions between environmental variables, a random forest regression analysis was used to assess the effects of environmental variables on R 2 PRI and R 2 SIF . Among the environmental variables, the most important one affecting R 2 PRI was RH, with the percentages increase in mean square error (%IncMSE) of 25.6%. T s (%IncMSE = 22.0%) was the second most important environmental variable affecting R 2 PRI followed by SWC (%IncMSE = 13.9%). PAR and Q were the least important variables (Figure 6a). Obvious differences were found between R 2 SIF and those of R 2 PRI . PAR appeared to be the most important driver for R 2 SIF (%IncMSE = 22.3%). Q was of secondary importance to R 2 SIF (%IncMSE = 11.5%) (Figure 6b).

Effects of Different Environmental Variables on the Abilities of the PRI-Based and SIF-Based Models in Tracking Diurnal Variations of GPP
Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 16 soil temperature (Ts), and (d) GPPEC and LUEEC. Daily means were calculated from half-hourly values from 6:00 to 18:00 in the day. Small dot indicates half-hourly GPPEC.
To avoid the interactions between environmental variables, a random forest regression analysis was used to assess the effects of environmental variables on R 2 PRI and R 2 SIF. Among the environmental variables, the most important one affecting R 2 PRI was RH, with the percentages increase in mean square error (%IncMSE) of 25.6%. Ts (%IncMSE = 22.0%) was the second most important environmental variable affecting R 2 PRI followed by SWC (%IncMSE = 13.9%). PAR and Q were the least important variables (Figure 6a). Obvious differences were found between R 2 SIF and those of R 2 PRI. PAR appeared to be the most important driver for R 2 SIF (%IncMSE = 22.3%). Q was of secondary importance to R 2 SIF (%IncMSE = 11.5%) (Figure 6b).

Figure 6.
Relative contributions of the environmental variables for explaining (a) R 2 PRI, the correlation between LUEPRI×APAR and GPPEC, (b) R 2 SIF, the correlation between SIFcan and GPPEC.

Comparison between the Abilities of the PRI-Based and SIF-Based Models under Different Environmental Variables
R 2 PRI and R 2 SIF were compared under classified ranges of the environmental variables (Figure 7). R 2 PRI remained constant (>0.6) with the increase of PAR and Q (Figure 7a). R 2 SIF increased with the increase of the light-related variables (i.e., PAR and Q) and reached the highest values of 0.56 and 0.85 for the PAR range of 800-1000 μmol·m −2 ·s −1 and the Q range of >2, respectively (Figure 7a,b). R 2 SIF was higher than R 2 PRI for the Q range of >2 (Figure 7b).

Comparison between the Abilities of the PRI-Based and SIF-Based Models under Different Environmental Variables
R 2 PRI and R 2 SIF were compared under classified ranges of the environmental variables (Figure 7). R 2 PRI remained constant (>0.6) with the increase of PAR and Q (Figure 7a). R 2 SIF increased with the increase of the light-related variables (i.e., PAR and Q) and reached the highest values of 0.56 and 0.85 for the PAR range of 800-1000 µmol·m −2 ·s −1 and the Q range of >2, respectively (Figure 7a,b). R 2 SIF was higher than R 2 PRI for the Q range of >2 (Figure 7b).
Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 16 soil temperature (Ts), and (d) GPPEC and LUEEC. Daily means were calculated from half-hourly values from 6:00 to 18:00 in the day. Small dot indicates half-hourly GPPEC.
To avoid the interactions between environmental variables, a random forest regression analysis was used to assess the effects of environmental variables on R 2 PRI and R 2 SIF. Among the environmental variables, the most important one affecting R 2 PRI was RH, with the percentages increase in mean square error (%IncMSE) of 25.6%. Ts (%IncMSE = 22.0%) was the second most important environmental variable affecting R 2 PRI followed by SWC (%IncMSE = 13.9%). PAR and Q were the least important variables (Figure 6a). Obvious differences were found between R 2 SIF and those of R 2 PRI. PAR appeared to be the most important driver for R 2 SIF (%IncMSE = 22.3%). Q was of secondary importance to R 2 SIF (%IncMSE = 11.5%) (Figure 6b).

Figure 6.
Relative contributions of the environmental variables for explaining (a) R 2 PRI, the correlation between LUEPRI×APAR and GPPEC, (b) R 2 SIF, the correlation between SIFcan and GPPEC.

Comparison between the Abilities of the PRI-Based and SIF-Based Models under Different Environmental Variables
R 2 PRI and R 2 SIF were compared under classified ranges of the environmental variables (Figure 7). R 2 PRI remained constant (>0.6) with the increase of PAR and Q (Figure 7a). R 2 SIF increased with the increase of the light-related variables (i.e., PAR and Q) and reached the highest values of 0.56 and 0.85 for the PAR range of 800-1000 μmol·m −2 ·s −1 and the Q range of >2, respectively (Figure 7a,b). R 2 SIF was higher than R 2 PRI for the Q range of >2 (Figure 7b).  The distributions of R 2 PRI and R 2 SIF were different for the two water-related variables (i.e., RH and SWC) (Figure 7c,d). R 2 PRI was conspicuously lower in RH < 60% than that in RH > 60%. It reached the highest value of 0.83 for the RH range of 70-80%. R 2 PRI had high values at low and high ends of SWC with a high value of 0.88 for the SWC range of 0.2-0.25 m 3 m −3 and a high value of 0.81 for the SWC range of 0.4-0.5 m 3 m −3 . However, R 2 SIF fluctuated with the increase of RH and SWC. For the temperature-related variables (T a and T s ), the distributions of R 2 PRI and R 2 SIF also differed (Figure 7e,f). The higher soil temperature showed the higher R 2 PRI . The highest R 2 PRI was at the temperature range of 31-34 • C, while the highest R 2 SIF was at the temperature range of 25-28 • C. Overall, R 2 PRI was higher at high RH or under soil water stress (i.e., SWC too low or too high) or high temperature, while the higher R 2 SIF occurred under high solar radiation or clear sky. The PRI-based LUE model exhibited better performance than the SIF-based linear model in estimating GPP in most of the classified ranges of the environmental variables, with the SIF-based linear model performed slightly better under clear sky (Q > 2).

Evaluation of Multi-Angle Observed PRI
This study found that the averages of the multi-angle observed PRI within short time intervals better represented the condition of the entire canopy in estimating LUE than the single angle observed PRI ( Figure 3). This relationship indicates that the utilization of multi-angle observations with tens of measurements evenly distributed at different angles could diminish the angular effects to some extent. Crop canopies are non-Lambertian characterized by bidirectional reflection. Their reflectance changes because of the varied fraction of sunlit/shaded elements of the canopy with the changing angles. The reflectance at 531 nm differed significantly over sunlit and shaded elements of the canopy. The canopy elements whose reflectance differed as a function of illumination intensity lead to the variation in the PRI signal viewed at varied angles [25]. The sunlit elements are more likely to be exposed to excess light levels, causing a conversion of violaxanthin to zeaxanthin and resulting in a lowering of PRI. The angular effects of the observed PRI were also reported by Hilker et al. [49] and Zhang et al. [18], which was consistent with our observations (Figure 2). We used the simple arithmetic averages of the multi-angle observed PRI to represent the whole canopy with assuming the canopy as a big leaf in this study. There are also two-leaf approaches that interpreted the variations of the observed PRI with the sun-view geometry and canopy structure as their sensitivity to the fractions of sunlit/shaded leaves. Zhang et al. [58] used a two-leaf model to derive canopy PRI with multi-angle observations and found the two-leaf PRI could effectively improve the ability for indicating LUE over the big-leaf PRI in a subtropical evergreen coniferous forest. However, the canopy of maize was relatively homogeneous compared to the coniferous forest with more species. Different from the previous observation methods, the view zenith angle in this study was assigned to be consistent with the SZA, while the VAAs within half an hour were evenly distributed ( Figure 2). Therefore, the arithmetic average was chosen as a more simple approach to reduce the angular effect in this study.

Comparison of the PRI-Based and the SIF-Based Models in Estimating Diurnal and Seasonal GPP Variations
Among different time scales, we found that the PRI-based LUE model exhibited better performance than the SIF-based linear model in estimating the diurnal variations of GPP EC , while the SIF-based linear model performed better at estimating the seasonal variations of GPP EC (Table 1, Figure 4). PRI may be a good indicator of LUE because of the link between PRI and xanthophyll cycle activity. The rapid xanthophyll cycle activity represented physiological regulations of photosynthesis on short-term changes in general environmental conditions and thus PRI was regarded as an optical indicator of LUE at diurnal time scales. Several studies have confirmed that the long-term (seasonal) PRI responses were primarily driven by constitutive changes in pigment pools (i.e., the ratio of carotenoid and chlorophyll) instead of facultative xanthophyll cycle activity [27][28][29]59,60]. Although the slower or seasonal pigment pool size adjustments of photosynthesis were also shown to correlate with LUE, the mechanistic explanations of the relationships differed [31]. Thus, the PRI-based LUE model showed a high advantage in the estimation of the diurnal photosynthesis variations, but a lower advantage in estimating the seasonal photosynthesis variations. Maize is a C4 plant, which does not have the photosynthetic "lunch break" phenomenon under high light at noon. Thus, the distribution of absorbed light energy relies on non-photochemical quenching (NPQ), i.e., heat energy dissipation through the xanthophyll cycle, which may be more conducive to the expression of the diurnal LUE variations by PRI. In contrast, it has been found that the relationship between SIF and GPP appears to be linear under stress conditions precisely due to the reduced SIF values around midday [45]. At the seasonal scale, considerable evidence based on retrievals from satellite [32,33,37,41,42] and ground-based measurements [43,44,61,62] has been showing strong empirical linear SIF-GPP relationships. In contrast, the studies conducted at short time scales (e.g., sub-daily) found insignificant relationship (R 2 ≤ 0.3) than that in seasonal scale studies [63], which may be nonlinear [64]. Yang et al. [46] demonstrated that SIF primarily responded to changes in APAR rather than GPP and emphasized the needs of LUE information when estimating GPP at a short-term scale.

Environmental Effects on the Abilities of the PRI-Based and SIF-Based Models in Estimating GPP
In our study, RH was the most limiting factor for the PRI-based LUE model in estimating GPP of maize ( Figure 6). Previous studies have reported that PRI has the highest and most common correlation with LUE under cloudless or slightly cloudy conditions, rather than water-limited conditions [19,58]. Our study demonstrated that the incident radiation (PAR) and sky condition (Q) were not influenced the performance of the PRI-based LUE model in estimating GPP (Figure 7a,b) because the APAR included in the model partly account for the sky radiation. The relationship between LUE PRI ×APAR and GPP EC had a lower correlation when RH was lower than 60% (Figure 7c), which was consistent with the VPD-limited conditions in Zhang et al. [58]. However, in the cropland with irrigation, SWC was not a limitation. We infer that the PRI-based LUE model was more sensitive to the atmospheric water deficit (low RH) than the soil water deficit (low SWC) because the former had a direct effect on opening and closing of the leaf stomata and then the photosynthesis, not the reflectance of the leaf and canopy. Soil temperature also had a positive effect on the PRI-based LUE model (Figures 6a and 7f). The high T s occurred at the late V stages (DOY 195 to 207) with synchronously high RH ( Figure 5). Thus, the maize rapid grown at this stage had a higher photosynthetic rate and linear energy distribution, leading to the good performance of the PRI-based LUE model. Different from the PRI-based LUE model, the relationship between SIF can and GPP EC was influenced by the light-related factors, i.e., PAR and Q. It was found that incident radiation played dominant roles in SIF changes among environmental variables by sensitivity tests on simulated SIF data by Soil Canopy Observation Photosynthesis Energy (SCOPE) model [65]. Photosynthesis and chlorophyll fluorescence were highly correlated when vegetation was exposed to excess incident radiation [38]. The incident radiation absorbed by chlorophyll was a key driver of both GPP and SIF, but limited or saturated light conditions could result in different coupling patterns between the efficiency of photosynthesis and fluorescence [66,67]. Due to the effect of diffuse radiation, the clearer the sky showed the stronger correlation between SIF and GPP for maize canopy in our study (Figure 7). This finding was in agreement with Miao et al. [66], but differed from Yang et al. [46], Goulas et al. [68], and Li et al. [50].

Combination of PRI and SIF for GPP Estimation
Photosynthesis, fluorescence, and NPQ are three pathways to dissipate the absorbed light energy, which interrelate and compete with each other. The relationship between photochemical yield (ΦP) and fluorescence yield (ΦF) is divided into two distinct phases: under high light, NPQ dominates the variations of ΦP, with constant photochemical quenching (PQ); under low light, the variations of ΦP are mainly driven by PQ, with constantly low NPQ [67]. ΦP is in proportion to ΦF under the NPQ stage and becomes inversely proportional under the PQ stage because of the opposite effects on ΦF with decreasing PQ and increasing NPQ. PRI has been proven to be a representative of the temporal dynamics of NPQ [69]. The combination of PRI and SIF observations could be a solution for a better estimation of photosynthesis. Cheng et al. [63]) and Schickling et al. [70] combined the PRI and SIF data in simple linear regression models and found that their combinations improved the estimation of GPP. However, their models were more mathematical than mechanistic. Atherton et al. [71] combined PRI and SIF via NPQ model and ΦF to predict the dynamics of photosynthetic efficiency at leaf scale and short-time scale from a theoretical perspective. Different from their direct combination of PRI and SIF, we treated SIF and PRI as alternatives for the estimation of GPP and pointed out the better performance of the PRI-based LUE model under most environmental conditions for the maize field in our study. Additional studies on the theoretical combination of PRI and SIF at various temporal and spatial scales would be helpful for a more accurate estimation of GPP.

Conclusions
In this study, we measured multi-angular canopy spectra continuously during the whole 2018 growing season of a maize field. We compared the ability of the single-angle and multi-angle PRI observations at canopy level in estimating LUE. Then, the PRI-based LUE model was evaluated and compared to the SIF-based linear model for their performance in the estimation of GPP during the maize growing season in 2018. The major results are as follows: (1) the observed PRI varied with sun-view angles and the averaged PRI using the multi-angle observations within a short time exhibited better performance than single-angle observed PRI in the estimation of LUE in the maize field;