We collected replicated hyperspectral ground reflectance measurements of plant canopies at two sites in northern California with similarly structured, yet phenologically different, plant canopies. The first site was a drained peatland pasture (hereafter referred to as “Pasture”) located on Sherman Island in the Sacramento–San Joaquin Delta (lat: 38.0373; long: -121.7536; elevation: -4 m) with annual grasses growing during the winter and spring, and the invasive perennial pepperweed plant (Lepidium latifolium) active from spring through autumn (Fig. 3). Pepperweed produces a dense canopy of white flowers each year from about the beginning of June through the end of August, creating increased complexity in canopy reflectance during this time (Sonnentag et al., 2011a, b). The second site was a rice paddy (hereafter referred to as “Rice”) located on Twitchell Island in the Sacramento–San Joaquin Delta (lat: 38.1055, long: -121.6521, elevation: -5 m) with an active growing season from May through October and maintained as a fallow and flooded field for the remainder of the year (Fig. 3).

The two sites were located within 10 km of each other in the Sacramento–San Joaquin Delta, and as such, they experienced the same Mediterranean climate with hot and dry summer months and rainy, cool winters. The 30-year mean annual air temperature (1981–2010) recorded at a nearby climate station in Antioch, CA was 16.4 ∘C, and mean annual precipitation was 335 mm. Despite their similar climatology, the difference in hydrological and agricultural management between the two sites results in ecosystems with plant canopies that are phenologically different (Hatala et al., 2012; Knox et al., 2015). The water table at the Pasture was maintained at a level always below the soil surface at around 50–80 cm throughout the year. While the phenology of grasses at the Pasture peaked during the springtime, the pepperweed plants at the site remained relatively active throughout the summer because their roots can tap the shallow water table, creating a biologically active canopy almost year-round (Sonnentag et al., 2011a). The Rice was planted and flooded through irrigation management during the summer growing season only, and the plant canopy sustained high rates of productivity during the precipitation-free summer months. The field remained fallow and flooded during the remainder of the year. Differences in the canopy phenology at both sites propagated into differences in the peak periods of photosynthesis, where peak GPP at the Pasture occurs April–May and peak GPP at the rice occurs August–September (Hatala et al., 2012; Knox et al., 2015).

At both the Pasture and Rice, hyperspectral canopy reflectance was collected with a fiber optic spectrometer (USB 2000; Ocean Optics, Dunedin, FL) with a detector range from 200 to 1100 nm at a height of 1 m above the mean canopy surface. The fiber optic sensor was filtered through a cosine corrector (CC-3-UV-S Spectralon) to ensure that the bi-hemispherical reflectance from the ground surface was measured at an angle normal to the sensor surface (Nicodemus et al., 1977; Schaepman-Strub et al., 2006). We measured bi-hemispherical reflectance to minimize the contribution of background soil surfaces to the spectral signal, and we ensured that our reflectance signal was not comprised by low Sun zenith angles by sampling near midday (Meroni et al., 2011). For this analysis we constrained our data to 400–900 nm due to large levels of noise at the detection edges of this instrument. The spectrometer was mounted on a tripod approximately one meter above the canopy and was connected via USB cable to a laptop computer running the OOBase32 software (USB 2000; Ocean Optics, Dunedin, FL) to capture spectra, which internally corrected for instrument-specific calibration parameters. Each field spectrum was collected and saved by OOBase32. At the start of each site visit, the integration time within OOBase32 was adjusted to the ambient light conditions and a reference dark spectrum measurement was collected by covering the fiber optic head with two layers of black electrical tape and orienting the sensor downward.

After this initial setup, we collected a reflectance spectrum for each site replicate by first pointing the spectrometer directly skyward to record the spectrum of incoming energy, and then within seconds pointing the spectrometer directly at the ground surface to record the spectrum of reflected energy. Thus, we calculated the canopy reflectance for each replicate as the reflected spectrum normalized by the incoming spectrum. For each collection date at each site, we averaged the replicate spectra for this analysis to compute a single mean spectral reflectance. The spectrometer records data at approximately 0.28 nm intervals, and we smoothed each reflectance spectrum using a spline fit to 1 nm intervals between 400 and 900 nm in order to reduce instrumental noise in the data.

We measured canopy hyperspectral reflectance from July 2010 through September 2014 at both sites, collecting measurements during the entire year at the Pasture and during the growing season at the Rice, which amounted to 100 total sampling dates at the Pasture and 71 total sampling dates at the Rice (Fig. 1). On each sampling date, hyperspectral reflectance measurements were collected at each site with a spatial and temporal replicate frequency suited to the individual site heterogeneity. At the Pasture, where the canopy was spatially and temporally heterogeneous, we measured hyperspectral reflectance approximately weekly, every other week, or monthly, with nine replicate canopy reflectances randomly sampled per visit. At the Rice, which had lower spatial variability, hyperspectral reflectance was collected weekly or every other week during the growing season, with five replicate canopy reflectance spectra collected per visit. We occasionally collected up to ten additional replicates at each of the sites, in order to ensure that our smaller sampling sizes were capturing broad landscape-scale patterns in spatial heterogeneity. At each site we randomly sampled canopy reflectance at locations within approximately 10–20 m of the flux tower footprint, the area most representative of the half-hourly flux measurements. For PLSR analysis, we averaged across the hyperspectral canopy reflectance replicates for each site and day. Because leaf geometry and clumping can critically impact the interpretation of canopy reflectance measurements (Colwell, 1974), these two sites provide a useful first-case study for directly connecting hyperspectral canopy reflectance measurements to CO2 flux because both ecosystems have an erectophile in leaf angle distribution for the majority of the year, minimizing shadow effects when field spectra are collected near solar noon.

Both sites are active AmeriFlux and FLUXNET sites (Baldocchi et al., 2001a) measuring fluxes of energy, water vapor, and CO2 using standard eddy covariance methods and processing procedures described elsewhere in detail (Ameriflux site codes: US-Snd and US-Twt; Hatala et al., 2012; Knox et al., 2015; Sonnentag et al., 2011a). The eddy covariance technique was used to measure the fluxes of CO2 at each site by collecting simultaneous 10 Hz measurements of vertical turbulence (w, m s-1), measured with a sonic anemometer (Gill WindMaster Pro; Gill Instruments Ltd, Lymington, Hampshire, England), and CO2 density (c, µmol m-3), measured with an infrared gas analyzer (LI-7500; Li-Cor Biosciences, Lincoln, NE). From these measurements we calculated the net half-hourly mean flux of CO2 (NEE, µmol m-2 s-1) between the surface and atmosphere by averaging the covariance between w and c over a half-hourly time period after applying a coordinate rotation and a set of standard air density and temperature corrections (Detto et al., 2010; Schotanus et al., 1983; Webb et al., 1980). To partition NEE into gross primary photosynthesis (GPP, µmol m-2 s-1) and ecosystem respiration (ER, µmol m-2 s-1), net CO2 fluxes were first gap-filled using artificial neural network (ANN) techniques outlined in detail within Knox et al. (2015), driven by meteorological variables (Moffat et al., 2007; Papale et al., 2006). After the net CO2 fluxes were gap-filled using the ANN technique, we separated the net flux into GPP and ER by modeling nighttime NEE measurements as ER, since GPP is assumed to be zero at night (Reichstein et al., 2005). We prescribed the nighttime temperature dependence of ER with an Arrhenius-type model (Lloyd and Taylor, 1994), and extrapolated this model to the daytime, calculating GPP as the difference between NEE and modeled ER. Net CO2 flux data within this analysis are presented from the atmospheric convention, where a negative flux indicates ecosystem uptake, and a positive flux indicates release from the ecosystem to the atmosphere.

Within this analysis we examined the predictive power of hyperspectral canopy reflectance to explain patterns in instantaneous and daily, weekly, and monthly integrated NEE and GPP flux. We tested these variables separately in order to determine whether the canopy reflectance better predicted an instantaneous flux measurement at the time of collection, or a flux signal integrated over the previous day, week, or month. For instantaneous NEE and GPP flux, we matched the time of spectral collection with the nearest mean half-hourly flux measurement, where these values are presented in units of µmol m-2 s-1. For the daily, weekly, and monthly integrated NEE and GPP fluxes, we integrated the net CO2 and GPP flux over the course of the previous day, week, or month for the date of spectral reflectance collection, where these values are presented in units of g C m-2 time-1. The instantaneous GPP flux and daily NEE flux for both sites are plotted as Fig. 2.

Partial least-squares regression is a standard method in chemometrics for modeling the ability of a set of quasi-continuous spectral variables to predict a single response (Wold et al., 2001). In this analysis we used PLSR methods with the hyperspectral canopy reflectance data set to model the response of instantaneous or integrated NEE or GPP. PLSR is similar to principle components analysis (PCA), in that the modeling algorithm reduces a large predictor matrix of spectral reflectance data to a reduced set of latent variables. In our study, the large predictor matrix is the measured hyperspectral reflectance at each wavelength between 400 and 900 nm during each sampling event, which in this analysis was reduced to a maximum of 10 latent variables that contained the most significant sets of variables from the larger matrix for predicting instantaneous or integrated NEE or GPP. PLSR typically outperforms PCA or standard step-wise linear regression for situations where there is high co-linearity within the predictor matrix, such as within narrow-band spectral reflectance and chemometrics (Wold et al., 2001). For this analysis we used the PLS package (Mevik et al., 2013) within the R statistical environment (R Core Team, 2014). All of the R code used to conduct this analysis is freely available on GitHub at http://github.com/jhmatthes/canreflectance_flux_plsr.

For PLSR model fitting and validation, our methods followed those of Serbin et al. (2014), which used PLSR modeling to determine the ability of hyperspectral reflectance data to predict a suite of leaf traits. However, in this analysis, we used repeated measurements to examine how well the repeated hyperspectral reflectance measurements could directly predict landscape-scale fluxes of NEE and GPP. We conducted one set of PLSR modeling for the entire spectral reflectance data set that combined both the Pasture and Rice data, and then two additional PLSR modeling exercises with the only the Pasture data and only the Rice data, to examine whether there were significant differences between the two sites in the resulting PLSR models. For each of the three PLSR modeling exercises, we split the data into model calibration (80 % of the data) and independent validation (20 % of the data; hereafter referred to as “Independent Validation”), where the model calibration data were used to fit the model, and the Independent Validation data were used to evaluate the ability of the model to predict landscape-scale NEE and GPP outside of the PLSR model fitting exercise. As in Serbin et al. (2014), we randomly split the model calibration data into 70 % for model fitting (hereafter referred to as “Calibration”) and 30 % for model uncertainty evaluation (hereafter referred to as “Evaluation”) over 1000 iterations to evaluate the uncertainty in PLSR model development. Thus overall, we used 56 % of the total data for Calibration, 24 % of the data for Evaluation, and an unchanging 20 % of the data for Independent Validation to test the predictive power of the final mean models. We conducted an initial optimization with a single set of Calibration data and Evaluation data to determine the total number of PLSR latent variables to include in each model by minimizing the prediction residual sum of squares, calculated through leave-one-out cross-validation (Chen et al., 2004). We used the entire 400–900 nm spectrum range with these PLSR methods to fit the instantaneous and daily, weekly, and monthly integrated NEE and GPP flux data.

To quantify the performance of each PLSR model, we calculated the coefficient of determination (R2), the root mean square error (RMSE), and the model bias. We used the 1000-iteration bootstrapping approach for each PLSR model to quantify the model calibration performance as in Serbin et al. (2014). From the random 70 to 30 % split of the Calibration and Evaluation data, we generated new estimates for each iteratively removed sample. This allowed us to test the stability and generality of the models using different sets of calibration data and to estimate robust errors for the prediction of flux measurements by representing the uncertainty across measurements, spectral data, and the PLSR modeling approach. For each set of 1000 model iterations over the random calibration/validation fit data set split, we calculated the resulting mean PLSR model coefficients and the variable importance of projection (VIP) score associated with the reflectance measured at each wavelength. The VIP score represents the statistical contribution of each individual wavelength to the overall fitted PLSR model across all latent model components. In this way, the VIP score can be used to identify the wavelengths that contribute the most information for predicting the variable at hand (in this case, either NEE or GPP). Using the mean of the bootstrapped PLSR models, we tested each final mean model against the 20 % of original data left aside for Independent Validation by linear regression.

We analyzed the skill of standardized vegetation indices (SVIs) in predicting NEE and GPP flux at the Pasture and Rice, and compared the utility of these models to our PLSR modeling results. Due to their wide use in other studies, we tested the normalized difference vegetation index (NDVI; [R800-R680] / [R800+R680]; Rouse et al., 1974), NDVI calculated with the wavelengths from the Moderate Resolution Imaging Spectroradiometer satellite (NDVIMOD; [R841-876-R620-670] / [R841-876+R620-670]), green NDVI (NDVIg; [R800-R550] / [R800+R550]; Gitelson et al., 1996), red-edge NDVI (NDVIre; [R800-R700] / [R800+R700]; Gitelson and Merzlyak, 1994), and the photochemical reflectance index (PRI; [R531-R570] / [R531+R570]; Gamon et al., 1992), where R indicates reflectance in the subscripted wavelengths in nanometers. For all SVIs except NDVIMOD, we averaged the measured reflectance for a 10 nm window centered on the reflectance value to reduce measurement noise.

We assessed the ability of SVIs to predict NEE and GPP fluxes for all data, the Rice only, and the Pasture only by randomly selecting 80 % of the reflectance spectra for calibration, leaving 20 % of the data for validation. For GPP fluxes, we assessed the fit and predictive power of SVIs with a log-linear model as this model best fit the data, and for NEE we used a simple linear model, which fit the data better than a log-linear model. To assess the ability of the SVIs to predict GPP and NEE, we performed an iterative calibration/prediction analysis where we randomly parsed the data into 80 % calibration and 20 % validation for 100 iterations, and present the mean R2 fit for comparative analysis with the PLSR modeling results.

There was significant seasonal, interannual, and site-level variability among the hyperspectral canopy reflectance measurements collected over the course of 5 years at both sites. Intra-site variability within canopy reflectance changed due to the phenological stage of the ecosystem, whereas interannual variability was driven by changes in the timing of these phenological events. The Pasture tended to be more spatially heterogeneous than the Rice, observed through the higher intra-site variability during an individual sampling event, particularly in the infrared reflectance (Fig. 3). This intra-site variability at the Pasture is caused by higher spatial heterogeneity in canopy structure compared with the Rice, which is a monoculture with a simpler crop phenological cycle. During the green leaf-out stage at both the Pasture and Rice, the patterns of hyperspectral reflectance were quite similar, with a peak at the green wavelengths, absorption in the red wavelengths, and high reflectance in the near-infrared wavelengths (Fig. 3a, b). Intra-site variability across the spectrum was high across at the Pasture during periods of white pepperweed flowering that produced a much higher albedo than the green canopy and obscured reflectance patterns in the green and red wavelengths, despite relatively high plant productivity during this time (Fig. 3c). The closest analogous phenological stage to this period at the Rice was the time at which the rice was seeded and the plants dried in preparation for harvest, when the Rice experienced similar trends in increased albedo through the visible wavelengths (Fig. 3d). However, the magnitude of the senescing Rice reflectance was not as large as the white pepperweed canopy at the Pasture, and in addition the reflectance spectra were not obfuscated during this time since the rice productivity was quite low at this point in the growing season.

The seasonal and interannual patterns in narrow-band reflectance in the green (550 ± 5 nm), red (640 ± 5 nm), and near-infrared (NIR; 800 ± 5 nm) wavelengths also highlighted intra-site and interannual variability. At the Pasture, there was low intra-site variability and interannual variability in green reflectance from January through the end of May, when the grass canopy was present at the site (Fig. 4a). However, when pepperweed became the dominant canopy plant at the Pasture during the summer growing season, both replicate and interannual variability increased as the pepperweed created a more heterogeneous cover than the grass due to its white flowers and more spatially variable structure than the winter grass canopy. The same pattern was evident in the red reflectance at the Pasture, with low variability in the second half of winter and spring, and a large increase in variability during the summer growing season and autumn (Fig. 4c). At the Rice, there was also large interannual variability in the timing of the seasonal pattern of green and red reflectance; however, there was a more discernible seasonal pattern of reflectance that tracks within years across the entire growing season (Fig. 4b, d). For example, each year green reflectance and red reflectance started high, decreased as the growing season progressed, then eventually increased again as the rice straw dried before harvest. The NIR reflectance at the Pasture had a stable mean through the year with little interannual variability but large intra-site variability across the year (Fig. 4e). The Rice NIR reflectance had a consistent seasonal pattern between years, with low reflectance in the early growing season and increasing NIR reflectance as the canopy developed due to the change in the rice canopy closure as the growing season progressed (Fig. 4f). Although there was a consistent phenological trend in NIR reflectance at the Rice each year, there remained interannual variability in the timing of the NIR minimum and larger intra-site variability compared with reflectance in the visible wavelengths.

We fit PLSR models to the hyperspectral data to predict landscape-scale NEE and GPP at four integrated flux timescales: instantaneous flux measurements, and daily, weekly, and monthly integrated flux measurements for the period preceding the time of hyperspectral canopy reflectance collection. In this analysis we determined the optimal number of latent variables to include for each model by minimizing the predictive residual sum of squares. The number of optimal latent variables included in the PLSR models ranged from 2 to 8, which indicated that some models achieved the best predictive statistical fit for NEE and GPP with a much lower number of components than other models (Table 1). For the PLSR models that included the entire canopy reflectance data set for both sites, the optimal number of latent variables was stable at six components, except for the instantaneous GPP model, which included seven components. The number of optimal components was more variable across the PLSR models for the Pasture reflectance data (2–8 components) compared with those from the Rice reflectance data (4–6 components).

As expected, across all models, the R2 for the PLSR Calibration was higher than the R2 for the PLSR Evaluation fit, and the RMSE was lower for the Calibration and higher for the Evaluation during the model calibration step (Table 1). The fit statistics presented within Table 1 show the mean fit statistics for the 1000 iterations of random 70 % Calibration, 30 % Validation data selection from the 80 % total data used during the model development fitting process. For each PLSR model, the 1000 iterated fit statistics followed a normal distribution with low variance, which indicated only a low bias to selecting the Calibration and Evaluation data so only the mean results are presented within Table 1. Across almost all of the CO2 flux prediction variables, the PLSR models for the Rice data set achieved the highest fit for both the Calibration (R2= 0.77–0.92) and Evaluation (R2= 0.58–0.68) exercises, the PLSR models with the data set including both sites achieved a slightly lower overall fit for Calibration (R2= 0.63–0.87) and Evaluation (R2= 0.24–0.69), and the PLSR models for the Pasture had the lowest overall fit for Calibration (R2= 0.38–0.97) and Evaluation (R2= 0.29–0.56) (Table 1).

For each set of 1000 model iterations over the random calibration/validation fit data set split, we calculated the resulting mean PLSR model coefficients and the variable importance of projection (VIP) statistic associated with each wavelength. Across all fitted PLSR models, as the timescale of the fitted integrated flux increased from instantaneous to daily, weekly, and monthly integrated values, the VIP statistic in the visible wavelengths (400–700 nm) decreased and the VIP statistic in the near-infrared wavelengths (700–900 nm) increased (Fig. 5). This indicated that for flux measurements on short timescales, the reflectance in the visible wavelengths contributed the highest explanatory power to the PLSR model components, but at longer timescales structural changes in the canopy that are correlated with the NIR range became more important for predicting GPP and NEE flux. This pattern was especially apparent for the VIP scores of the GPP model using the data set with both sites (Fig. 5a), where there was a dramatic shift in VIP scores between the weekly and monthly integrated flux models. For the weekly integrated GPP flux model and those at shorter timescales, the highest VIP scores were contributed by the visible wavelengths, with a peak in the red wavelengths near 700 nm. However, for the monthly integrated GPP flux model, there was a dramatic difference where the highest VIP scores shifted from the visible to the NIR range, indicating that the structural components of the plant canopy correlated with NIR reflectance contributed higher predictive power than reflectance in the visible part of the spectrum. There was a lower shift in VIP scores across integrated flux timescales in the models developed with only the Rice data set (Fig. 5e–f) compared against the models developed with only the Pasture data set (Fig. 5c–d), likely responding to the increased spatial and phenological complexity of the Pasture ecosystem compared with the relatively homogeneous Rice.

Across all models, the visible wavelengths that contributed the most information to the PLSR models, as determined by the magnitude of the VIP score, were within the red portion of the visible spectrum (Fig. 5). Most PLSR models had VIP scores above 1.0 that correlated with reflectance at 642 and 662 nm, the wavelengths of chlorophyll absorption. Across most PLSR models there was also a peak in the VIP score near 673 nm, the wavelength of chlorophyll fluorescence. However, the second band of chlorophyll fluorescence at 726 nm exhibited low VIP scores across all models. For both of the PLSR models developed using only the Pasture data set, there were also high VIP scores within the violet and blue range of the visible spectrum, from 400 to 450 nm. These high VIP scores in the violet–blue portion of the spectrum could be partly explained by the chlorophyll a and b absorption peaks at 430 and 460 nm, because slightly higher VIP scores were also observed at the Rice site for these wavelengths (Fig. 5e–f). However, this part of the spectrum at the Pasture site was particularly significant compared with the other models, and this could correspond to white reflectance of the pepperweed flowers at the site. When the pepperweed canopy was blooming, the bright white flowers reflected light across the entire visible spectrum, a unique characteristic to this site, where the high visible albedo in this spectral range might also have contributed to the high VIP scores within this portion of the spectrum (Fig. 5c–d).

After we fit the PLSR models to 80 % of the entire data set through 1000 iterations of different random sets of Calibration and Evaluation data, we tested the mean fitted models against the Independent Validation data (the 20 % of the original data set left out of the PLSR model fitting process). In general, the fitted PLSR models achieved a good fit with the measurements for this Independent Validation data set, where the R2 fit between the predicted and actual NEE and GPP ranged from 0.26 to 0.69 (Table 2). As was the case for the calibration and validation R2 fits during the PLSR calibration process, the Rice data set achieved the highest R2 values (0.40–0.69), the data set with both sites achieved the second-highest set of R2 (0.27–0.62), and the Pasture data set had the lowest R2 (0.27–0.54). As in the previous discussion for the Calibration and Evaluation fits to these three sets of data, we believe that the lower level of predictability at the Pasture is due to the higher level of spatial heterogeneity and phenological complexity compared with the Rice.

Although all models achieved a statistically significant fit between the predicted and measured CO2 fluxes with the Independent Validation data set with relatively high R2 values, the uncertainty in the prediction was significantly lower for the models that included all the data compared with the models that included only either the Pasture or Rice data. This pattern is clearly observed within the Independent Validation fit for the daily GPP and NEE data (Fig. 6). For the daily prediction of both GPP and NEE, the data set that included all the data had a smaller range for both the 95 % confidence interval and 95 % prediction interval for the relationship between predicted and actual GPP and NEE. This trend likely represented an increase in predictive power achieved by including a larger data set with a wider range of values both for NEE and GPP and for the measured hyperspectral reflectance. As the data sets that included either the Pasture and Rice data only had a lower amount of data overall as well as a narrower range of values, the confidence in the ability to predict NEE and GPP at these individual sites was lower compared with the power of using the entire combined data set.

We compared the ability of a suite of commonly used SVIs to predict GPP and NEE with the skill of the mean PLSR models developed within this study. Overall, the NDVI SVIs performed reasonably well at predicting both GPP and NEE, and models tested with all the reflectance data for both sites achieved predictive R2 values that ranged from 0.18 to 0.59 (Table 3; Supplement Table S1), where red-edge NDVI achieved the highest skill for predicting GPP and NEE for the sites in this study. PRI was not well suited to predicting CO2 fluxes at these sites, and models for this SVI achieved predictive R2 fits that ranged from 0.02 to 0.22.

For models that fit all the data from both sites, the predictive fit from PLSR modeling outperformed the red-edge NDVI (the best-fit SVI) at the instantaneous and weekly timescales, the two models were not significantly different at the daily timescale, and red-edge NDVI outperformed PLSR modeling at the monthly timescale (Table 3). PLSR modeling outperformed SVIs across all timescales for models that fit the Pasture data only. The performance of red-edge NDVI and PLSR models were not significantly different at instantaneous, daily, and weekly timescales when fit with the Rice data only; however, red-edge NDVI was a better predictor of monthly CO2 fluxes than the PLSR models (Table 3).

We investigated the ability of PLSR modeling with the hyperspectral canopy reflectance measurements to predict instantaneous GPP and NEE fluxes from the same half hour of spectral measurement, in addition to fluxes integrated over the previous day, week, and month. Previous work determined that sampling errors in eddy covariance flux measurements diminished when the fluxes were integrated over the course of many days (Moncrieff et al., 1996). We expected that the instantaneous flux would achieve the lowest correlation with the measured canopy reflectance since reflectance changes more slowly compared with CO2 flux, and that the fluxes integrated over longer timescales would provide a stronger signal with a higher predictive capacity. For the Calibration and Evaluation during the initial PLSR model fitting, there was no strong evidence that one timescale (instantaneous, daily, weekly, or monthly flux) was better fit with the hyperspectral canopy reflectance than the other timescales (Table 1). However, during the evaluation of the predictive power of the PLSR models with the Independent Validation data, most models achieved the highest predictive R2 with GPP flux at the weekly integrated timescale, and we found no clear optimal timescale for predicting NEE with measured hyperspectral reflectance data (Table 2; Fig. 7).

Variation across the measured hyperspectral canopy reflectance was dominated by interannual variability in the timing of canopy phenology (Figs. 3, 4). At the Rice, transitions were typical for an agricultural crop, where canopy reflectance incorporated portions of the background flooded soil in conjunction with the emerging green plants early the in growing season, with canopy closure achieved by early July (Beget and Di Bella, 2007). After flooding when the Rice canopy closed, there was less intra-site variability in measured reflectance, until the end of the growing season when the rice plants started to senesce and dry before harvest (Fig. 4). At the Pasture, canopy phenology was more complicated, marked by a transition from a green grass canopy to a green pepperweed canopy in April, followed by the white flowering of the pepperweed canopy from June through August, which increased intra-site variability in measured reflectance (Fig. 4). Both the Rice and Pasture experienced significant interannual variability in the start and end dates of these phenological patterns, but despite this variability the sites experienced relatively low variability in the overall CO2 flux (Fig. 2). The primary driver of interannual variability at the Pasture was the timing of summer drought in the Mediterranean climate, and canopy management (Sonnentag et al., 2011a). These primary controls agreed with the results from European syntheses of FLUXNET sites where water was a key driver of interannual variability in NEE (Reichstein et al., 2007). At the Rice, interannual variability was driven by changes in the start and end dates of canopy phenology that were driven by agricultural management changes of the planting and harvesting dates each year and smaller changes in fertilizer management (Hatala et al., 2012; Knox et al., 2015). The timing of the planting and harvest at the Rice is controlled by environmental management, as the field must be dry enough to drive farm equipment through the soil, and warm enough to ensure seedling survival. Differences in these variables from year to year created variability in the planting dates, and subsequent variability in the seasonal trajectory of hyperspectral canopy reflectance (Figs. 3, 4). There are also important differences between PLSR methods using the complete spectrum and standardized vegetation indices (SVIs) that may lead to differences in interpreting which bands are best suited for correlation with CO2 fluxes. Because SVIs are normalized by a reference band, they may be better suited to reducing noise within temporal trends in reflectance time series, particularly at sites that experience a wide range of illumination conditions. While the PLSR methods used in this analysis benefit from the large information content that results from using the entire reflectance spectrum, the measurements represent relative reflectance values rather than normalized reflectance ratios, and thus likely include more noise in the measurement time series than SVIs. This is an important trade-off when considering whether to use the entire reflectance spectrum or SVIs to understand how canopy reflectance tracks CO2 fluxes, but the simple canopy structure at the sites in this analysis and the collection of measurements during ideal illumination conditions limits the overall noise within the reflectance time series.

Along with the interannual variability experienced at both sites, there were also differences in the intra-site variability of measured reflectance within the two flux tower footprints. The Pasture site was more spatially heterogeneous than the Rice, driving increased variability among replicate hyperspectral reflectance spectra at the site (Fig. 4). The increased spatial variability at the Pasture was reflected in the lower predictive power of the PLSR models in predicting GPP and NEE with only the Pasture data set (Tables 1, 2). The lower overall fit between the hyperspectral measurements and CO2 flux at the Pasture can be explained through three possible mechanisms: (1) the hyperspectral canopy reflectance measurements at the Pasture are less representative of the entire flux footprint than the Rice data, (2) white pepperweed flowers in the Pasture canopy during summertime create an obstruction for reflectance that degrades the representativeness of measured spectra (Hestir et al., 2008; Sonnentag et al., 2011b), (3) the lack of irrigation at the Pasture compared with the Rice could create conditions of water stress during which reflectance becomes temporally decoupled from CO2 flux. It is likely that all of these factors contributed to the lower PLSR predictive power at the Pasture, and in particular the obstruction by white canopy flowers presented a challenge that is somewhat unavoidable for canopy reflectance studies in complex ecosystems. Changes to future sampling efforts that address the footprint representativeness, for example increasing the number and spatial distribution of hyperspectral reflectance collected at the Pasture or flying an unmanned aerial vehicle (UAV) with a mounted hyperspectral sensor, might help to further improve the future PLSR predictive power.

The most important wavelengths for the PLSR modeling with the GPP and NEE flux data in this study fell in line with previous work that has examined correlations between reflectance and traits of photosynthetic uptake (Main et al., 2011). However, we were initially surprised to find that the green wavelengths were not dominant components for prediction of either NEE or GPP across the suite of calibrated PLSR models (Fig. 5). These results parallel recent work in oak forests that demonstrated a temporal mismatch between peak greenness and peak leaf chlorophyll content (Yang et al., 2014). This temporal mismatch could be the cause for the insignificant correlation in narrow-band green reflectance, because at both sites vegetation is a lighter green color early in the growing season and develops into a darker green as the season progresses. There were particularly high VIP scores in the blue visible wavelength range, from 400 to 450 nm, at the Pasture site (Fig. 5c, d), which could be partly explained by the chlorophyll a and b absorption peaks at 430 and 460 nm since the Rice also experienced slightly higher VIP scores in this region (Fig. 5e–f). However, the magnitude of the VIP scores in this region at the Pasture far exceeded those at the Rice. There are two possible explanations for this marked increase in the importance of the blue visible wavelengths at the Pasture: (1) white reflectance of the pepperweed flowers at the site could be increasing the albedo within this portion of the spectrum; (2) the more complex phenology at the site with annual grass and pepperweed senescence is periodically driving reflectance near 420 nm in response to these periods of stress (Carter and Miller, 1994). While the Pasture shifted toward much higher reflectivity across the visible wavelengths during the brief period of white flowering in late spring (Fig. 3a), this site also experienced more dynamic phenology overall, with browning of the grass in early summer and of the pepperweed in late summer.

Almost all of the PLSR models predicting instantaneous and daily and weekly integrated NEE and GPP had a peak in the VIP score at red wavelengths (Fig. 5). Reflectance features within this portion of the spectrum include absorption in the red wavelengths at 642 and 662 nm correlated with chlorophyll absorption, and reflectance in the chlorophyll a fluorescence wavelengths that occurs near 673 nm. The maximum VIP score in the visible wavelengths across nearly all of the PLSR models occurred near the end of the red portion of the spectrum between 670 and 680 nm, indicating that these wavelengths provided critical information to the latent variables that comprised most of the PLSR models (Fig. 5). This result paralleled previous work that demonstrated the importance of narrow-band reflectance at 670–680 nm for predicting chlorophyll absorption features across a diverse suite of plant canopies (Carter and Miller, 1994; Dawson et al., 1999; Gitelson and Merzlyak, 1997; Main et al., 2011).

The differences among the predictive power of the PLSR models that included all the data compared with the models developed at individual sites highlighted important considerations for future work in this area. The predictive models with the smallest 95 % prediction intervals originated from the models that included all of the data from both sites (Table 2), demonstrating the power of using larger data sets, with a wider range of values, to develop the predictive capacity of PLSR models. Further improvements in PLSR predictive power might be achieved by building upon this data to include paired hyperspectral eddy flux data sets from additional sites that can expand and refine the connection between reflectance and CO2 flux. This approach has particular promise for sites with automated hyperspectral sensing systems in conjunction with eddy covariance measurements (Balzarolo et al., 2011; Hilker et al., 2007; Leuning et al., 2006; Rossini et al., 2010). However, we emphasize that changes in the canopy complexity and clumping are important consideration for such work at other sites, compared with the short-statured canopies with low clumping indices (Ryu et al., 2010b) included in this study. In canopies with more complex leaf and branch clumping, hyperspectral canopy reflectance measurements will need to be combined with radiative transfer modeling in order to accurately model the energy reflectance spectrum (Knyazikhin et al., 2013; Verhoef and Bach, 2007).

In testing the ability of common SVIs used in the literature to predict GPP and NEE, the skill of some NDVI models was on par with that of the PLSR models when developed using all the data from both sites or the Rice data only (Table 3). We believe that SVIs well predicted GPP and NEE at the Rice due to its simple annual phenology and corresponding seasonal pattern in CO2 flux. However, PLSR modeling significantly outperformed SVI models for predicting GPP and NEE flux when developed using only the Pasture data, due to the increased canopy complexity at the Pasture site. At the Pasture, the PLSR approach captured more variance within the data set through its ability to model more complex relationships across the entire spectrum compared with SVIs, which focus only on two spectral areas. This highlights the improved utility for PLSR modeling compared with the use of SVIs to predict ecosystem CO2 fluxes from canopies with complex phenology.

Across all sets of PLSR models, there was an interesting shift in VIP scores from the visible wavelengths to the NIR wavelengths as the timescale of NEE and GPP integration increased (Fig. 5). An increase in structural complexity drives higher NIR reflectivity (Main et al., 2011), and the VIP scores across the suite of PLSR models showed that this structural components of the canopy driving NIR reflectance became increasingly important to predicting both NEE and GPP as the integrated timescale increased. This demonstrated that reflectance in visible wavelengths correlated with chlorophyll content was most important for short-term flux prediction, but canopy structural changes in the NIR wavelengths were most important for longer-term flux prediction. These results are analogous with those from a modeling study across a network of European grassland sites that found a strong correlation between GPP and NIR reflectance indicative of phenological shifts in structural canopy components independent of changes in chlorophyll reflectance (Balzarolo et al., 2015). An important constraint of our analysis is that the field spectrometer used only measured wavelengths up to 900 nm reliably, making analysis at longer wavelengths in the infrared area correlated with leaf structural components such as fiber, lignin, and cellulose content impossible (Serbin et al., 2014). However, this same approach of canopy-level PLSR modeling could be used in conjunction with a spectrometer capable of making wider spectral reflectance measurements at eddy covariance sites to evaluate longer wavelength areas of the short-wave IR (SWIR) spectrum, for example, with the newly developed WhiteRef automated sensor for quasi-continuous SWIR hyperspectral measurements (Sakowska et al., 2015).

Comparing the predictive fit achieved with the PLSR models across different CO2 flux timescales with the Independent Validation data set provided important insights into the temporal scale of CO2 flux integration represented by the hyperspectral canopy reflectance collection at a moment in time. Almost all of the final PLSR models achieved the highest predictive fit with the weekly integrated GPP fluxes (Fig. 7). The changes in the PLSR predictive power for NEE and GPP at different timescales provided important information for considering what exactly is represented by measured hyperspectral reflectance in the field, as canopy biochemistry is in fact an emergent response to biological and environmental drivers that are integrated through time. The fact that all three models achieved the best predictive fit with the Independent Validation data for GPP at the weekly timescale yielded support for modeling efforts that determine carbon fluxes from MODIS satellite reflectance, which is aggregated into an 8-day timescale. The results of this flux timescale analysis are congruous with those from previous work, which found a good correlation between gross CO2 flux and the 8-day MODIS data timescale (Sims et al., 2005). While there was a clear signal in the higher predictive power for estimating the weekly integrated GPP flux compared with other timescales, there was less consistency within the best predictive timescale for estimating NEE (Fig. 7). This is likely due to the fact that NEE is a combination of both GPP and ER, which change on different timescales in response to different environmental drivers and are more highly coupled at the Rice than they are at the Pasture (Hatala et al., 2012; Knox et al., 2015). The fact that NEE achieved a good fit with canopy hyperspectral reflectance through the monthly timescale for the models developed with all the data (Fig. 7a) could indicate that the system memory of carbon flux at these sites is integrated over a longer timescale than was tested in this analysis, and that canopy biochemistry collected at one moment reflects at least the previous month of integrated NEE flux.