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Photosynth Res DOI 10.1007/s11120-017-0388-5

ORIGINAL ARTICLE

Photosynthetic responses to temperature across leaf–canopy–ecosystem scales: a 15-year study in a Californian oak-grass savanna

Siyan Ma1  · Jessica L. Osuna2 · Joseph Verfaillie1 · Dennis D. Baldocchi1  

Received: 9 January 2017 / Accepted: 13 April 2017 © Springer Science+Business Media Dordrecht 2017

At the ecosystem level, photosynthetic responses to tem-perature did follow a quadratic function on average. The optimum value of photosynthesis occurred within a nar-row temperature range (i.e., optimum temperature, Topt): 20.6 ± 0.6, 18.5 ± 0.7, 19.2 ± 0.5, and 19.0 ± 0.6 °C for the oak canopy, understory grassland, entire savanna, and open grassland, respectively. This paradigm confirms that pho-tosynthesis response to ambient temperature changes is a functional relationship consistent across leaf–canopy–eco-system scales. Nevertheless, Topt can shift with variations in light intensity, air dryness, or soil moisture. These find-ings will pave the way to a direct determination of thermal optima and limits of ecosystem photosynthesis, which can in turn provide a rich resource for baseline thresholds and dynamic response functions required for predicting global carbon balance and geographic shifts of vegetative commu-nities in response to climate change.

Keywords Growth temperature · Temperature dependence · Thermal adaptation · Thermal acclimation · Net ecosystem exchange of CO2 · Gross primary productivity

Introduction

Understanding how photosynthesis responds to variations in temperature is critical for predicting terrestrial ecosys-tem carbon balance and geographic vegetation distribution in response to climate change (Lombardozzi et  al. 2015; Chapin III and Starfield 1997; Woodward 1992; Wood-ward and Lomas 2004). Yet, such a relationship has rarely been tested at the ecosystem scale. Hence, models on large spatial scales must rely on leaf-level understandings (Lom-bardozzi et al. 2015; Atkin et al. 2008; Wehr et al. 2016).

Abstract Ecosystem CO2 fluxes measured with eddy-covariance techniques provide a new opportunity to retest functional responses of photosynthesis to abiotic factors at the ecosystem level, but examining the effects of one factor (e.g., temperature) on photosynthesis remains a challenge as other factors may confound under circumstances of natu-ral experiments. In this study, we developed a data mining framework to analyze a set of ecosystem CO2 fluxes meas-ured from three eddy-covariance towers, plus a suite of abi-otic variables (e.g., temperature, solar radiation, air, and soil moisture) measured simultaneously, in a Californian oak-grass savanna from 2000 to 2015. Natural covariations of temperature and other factors caused remarkable confound-ing effects in two particular conditions: lower light inten-sity at lower temperatures and drier air and soil at higher temperatures. But such confounding effects may cancel out.

Electronic supplementary material The online version of this article (doi:10.1007/s11120-017-0388-5) contains supplementary material, which is available to authorized users.

* Siyan Ma syma@berkeley.edu

Jessica L. Osuna osuna2@llnl.gov

Joseph Verfaillie jverfail@berkeley.edu

Dennis D. Baldocchi baldocchi@berkeley.edu

1 Ecosystem Science Division, Department of Environmental Science, Policy and Management, University of California at Berkeley, 137 Mulford Hall # 3114, Berkeley, CA 94720, USA

2 Atmospheric, Earth, and Energy Division, Lawrence Livermore National Laboratory, 7000 East Avenue L-103, Livermore, CA 94550, USA

http://orcid.org/0000-0002-6145-196Xhttp://orcid.org/0000-0003-3496-4919http://crossmark.crossref.org/dialog/?doi=10.1007/s11120-017-0388-5&domain=pdfhttp://dx.doi.org/10.1007/s11120-017-0388-5

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A common assumption is that photosynthesis-related rela-tionships are consistent across biological hierarchical lev-els (e.g., from chloroplast to leaf and from leaf to canopy) (Harley and Tenhunen 1991; Farquhar et  al. 1980; Berry and Bjorkman 1980; Way and Yamori 2014). However, it is not well known whether the assumption fits vegetative communities in natural habitats. Filling this gap in knowl-edge requires a set of variables measurable simultaneously across leaves, canopies, and ecosystems. Fortunately, mod-ern technologies (e.g., portable infrared gas analyzers and eddy-covariance towers) provide new opportunities to cap-ture physiological information not only in controlled envi-ronments but also in natural habitats concurrently with a range of exposures and microclimates (Baldocchi 2008).

Temperature is one of many environmental factors that influence photosynthesis (Farquhar et al. 1980, 2001; Reed et al. 1976; Yamori et al. 2014). Chloroplast-scale studies have shown that photosynthesis depends on the photosyn-thetic carbon reduction cycle and the photo-respiratory carbon oxidation cycle, and these cycles require particu-lar levels of energy (electron transport and ATP synthesis) (Farquhar et  al. 1980, 2001; Berry and Bjorkman 1980). Temperature can directly influence the rate of RuBisco (ribulose-1-5-bisphosphate carboxylase/oxygenase) activ-ity and the rate of photosynthetic electron transport (Leun-ing 2002; Xu and Baldocchi 2003). Temperature variations also influence photosynthetic enzymes availability, mem-brane fluidity, and expressions of related proteins (Yamori et al. 2014). Besides these direct effects of temperature on biochemical cycles, temperature increases can promote photorespiration over photosynthesis by causing the rela-tive solubility of CO2 to O2 and the specificity to Rubisco to decrease (Way and Yamori 2014; Bernacchi et al. 2001).

Leaf-level studies on photosynthetic response to tem-perature rely on manipulative experiments in controllable environments by directly measuring net photosynthetic rate (i.e., the difference between gross photosynthesis and leaf respiration) and leaf or growth temperature. Typically, a temperature response curve is parabolic in shape with a vertex that represents the maximum photosynthetic rate. The position of the vertex along the temperature axis is known as the “optimum temperature” (Reed et  al. 1976; Berry and Bjorkman 1980; Way and Yamori 2014; Yamori et  al. 2014). As a result of thermal adaptation, optimum temperature values can be relatively stable in certain spe-cies or functional types; optimum temperature values can also be quite flexible or plastic through thermal acclima-tion (Way and Yamori 2014; Baldocchi et  al. 2001; Hel-liker and Richter 2008; Yuan et al. 2011). For example, if a plant is moved to a colder environment for a short period, its optimum temperature may shift to a colder temperature after return to its original growth conditions (Ghannoum and Way 2011; Way and Yamori 2014). Besides optimum

temperature, lower and upper thermal limits of photosyn-thesis also indicate the inherent capacities of thermal adap-tation and acclimation of plants (Way and Yamori 2014; Yamori et  al. 2014; Reed et  al. 1976). Large-scale mode-ling efforts demand such baseline information and dynamic response functions for predicting geographic shifts of plant communities in response to climate change (Lombardozzi et al. 2015; Woodward and Lomas 2004).

Assessing thermal adaptation and acclimation on larger scales (e.g., ecosystems) remains a challenge (Lombar-dozzi et al. 2015). One reason is that temperature co-varies with other factors that also influence photosynthesis under conditions of in  situ ecological experiments (Woodward and Lomas 2004; Berry and Bjorkman 1980; Reed et  al. 1976). For example, increases in temperature are associ-ated with increased light intensity (e.g., sunny days or sum-mer). Stomatal conductance is sensitive to air dryness, and air dryness is intensified by high temperature. Either air or soil droughts can suspend photosynthesis either temporar-ily or permanently, while droughts relate to a distribution of precipitation in seasons. Although leaf-level studies intend to manage or reduce confounding effects in con-trolled environmental chambers or greenhouses (Reed et al. 1976), uncertainties in results often arise from confound-ing effects. Technical issues and high costs limit sample sizes. Also, an understanding of individual species cannot precisely match that of multi-species or vegetative com-munities. Eddy-covariance techniques afford an alternative approach on larger spatial scales, allowing us to monitor photosynthetic behaviors of vegetative communities auto-matically in natural habitats. Once a tower is installed and maintained properly, it begins to collect photosynthetic signals during the daytime at fine time-scales (e.g., half hourly) and then continuously over years or decades (Bal-docchi 2008; Ma et  al. 2016). Although problems such as low turbulence, rain, and power or sensor failures may cause missing data, a tower can in general collect more data than a traditional leaf-level experiment can.

Having large sample sizes is a unique feature of tower-base datasets that probably can enhance our under-standing of natural experiments because in statistics the Law of Larger Numbers supports the idea of achieving a “theoretical mean” for large samples. A following-up question would be, “how large is the large?” In the past, common sense may regard three samples as a minimum; 15 or more samples might then already be considered as large. Today, hundreds of thousands of samples are collected by eddy-covariance towers worldwide, chal-lenging statistical methods developed for dealing with experiments with small sample sizes. Modern statisti-cal methods such as artificial neural networks, wavelet analysis, and regression trees take advantage of large datasets and enable more reliable predictive analytics

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(Papale and Valentini 2003; Stoy et al. 2006; Xiao et al. 2008; Moffat et al. 2010). For basic research, investiga-tors are also curious about functional relationships bur-ied in “Big Data” (if we can borrow the popular term in computation science) rather than trying to fit biological or ecological processes into a “black box.” Mining the functional relationships from Big Data requires a suit-able novel data mining framework (Marr 2016; Bahga and Madisetti 2016; Boyd and Crawford 2012).

A set of ecosystem CO2 fluxes and related abiotic var-iables has been measured over 15 years from three eddy-covariance towers in a Californian oak-grass savanna area. Two of the towers were installed, respectively, above and below the oak canopy to capture clear signals of the oak canopy, and the third tower was installed in an open grassland nearby to capture signals only from the annual grassland, as a comparison to the grassland under the tree canopy. The three towers allowed us to tease apart photosynthetic behaviors of four typical vegetative communities in the study area individually, including oak canopy, understory grassland, entire savanna, and open grassland canopy (Ma et al. 2007, 2011).

Our study had four objectives. First, we identify potential confounding effects caused by covariations of temperature and three other abiotic factors (i.e., light intensity, air dryness, and soil moisture) in the field con-ditions. Second, we test whether canopy-level measure-ments were comparable to leaf-level experiments under similar conditions. Third, we examine whether our data mining framework can exact the relationships between photosynthetic flux and temperature in a consistent way, given different experimental scenarios. Finally, we examine average patterns of temperature response curves for four vegetative communities dominating the study area.

We generate four hypotheses based on our leaf-level understandings, but we intend to retest them regard-ing the circumstances of natural experiments over veg-etative communities. Hypothesis I: covariations between temperature and other factors (e.g., light intensity, air dryness, and soil moisture) would determine natural occurrences of confounding effects. Hypothesis II: the canopy- and leaf-level experiments would show a similar trend in photosynthetic responses to variations in tem-perature. Hypothesis III: variations in light intensity, air dryness, or soil moisture influenced the magnitude of ecosystem photosynthesis, but the pattern of temperature response curves would remain similar. Hypothesis IV: an average temperature response curve for each vegetative community would have a parabolic shape, which is simi-lar to the pattern reported in the leaf-level literature.

Methods

Study sites

Oak-grass savanna is a typical ecosystem type in the foothills of the Sierra Nevada Mountains in California, USA. Our two study sites are located in this area, about 2  km apart: an oak-dominated woody land (Tonzi Ranch, 38.438 N, 120.968 W) and an open annual grassland (Vaira Ranch, 38.418  N, 120.958  W). The average elevation is 177 m at the woody savanna site and 129 m at the grassland site.

At the woody savanna site, deciduous blue oaks (Quercus douglasii) cover about 40% of the landscape within a square kilometer of the flux tower and are unevenly distributed in space, with an average tree density of about 144 stem ha−1, an average height of about 14 m, and a basal area of about 0.1 m2. Species of annual grasses and forbs under oak canopy are similar to those in the open grass-land, including Brachypodium distachyon, Bromus hordea‑ceous, Erodium cicutarium, Hypochaeris glabra, Trifo‑lium dubium Sibth., Trifolium hirtum All., Dichelostemma volubile A., and Erodium botrys Cav. These grass species are invasive and originally from the Mediterranean Basin (Jackson 1985).

The sites experience a Mediterranean climate with wet, mild winters, and dry, hot summers. Based on data collected between 1926 and 2016 from a climate station located approximately 26  km from the study site (Camp Pardee, California, 38.258 N, 120.858 W), average annual precipitation was 546  mm; average mean annual tem-perature was 16.6 °C; average maximum temperature was 23.5 °C; and average minimum temperature was 9.7 °C (http://www.wrcc.dri.edu/cgi-bin/cliMAIN.pl?ca1428).

The soil of the oak-grass savanna is an Auburn very rocky silt loam (Lithic haploxerepts), about 0.75  m deep, overlaying fractured rock. Additional details on the site have been reported in previous papers (Tang et al. 2003; Xu and Baldocchi 2003, 2004).

Canopy- and ecosystem-level measurements

Two eddy-covariance towers were installed at the woody savanna site in the spring of 2001. One was 23.5 m high, above the tree canopy of ~10  m; the other was installed below the tree canopy at 2  m high. The open grassland tower was installed in the fall of 2000, also at 2 m in height (Xu and Baldocchi 2004; Ma et al. 2007). On each tower, a sonic anemometer (Model 1352, Gill Instruments Ltd., Lymington, United Kingdom) was installed for collecting three-dimensional wind velocities ten times per second. An open-path infrared CO2 and water vapor analyzer (IRGA, Li-7500, Li-cor, Lincoln, Nebraska, USA) measured CO2

http://www.wrcc.dri.edu/cgi-bin/cliMAIN.pl?ca1428

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and water vapor concentration five times per second. These data were recorded by on-site computers or data loggers (CR1000, Campbell Scientific, Inc., Logan, Utah, USA). We reprocessed the high-frequency data into half-hour average CO2 and water fluxes with lab-made MATLAB® scripts (R2016b, The Mathworks, Inc., Natick, Massachu-setts, USA), including spike removal, coordinate rotation, application of standard gas laws, and corrections for vapor density fluctuations (Webb et al. 1980). We then screened out unreliable flux data due to low turbulence conditions, rain, and other technical issues (e.g., power or sensor failures).

Air temperature (Tair, oC) and relative humidity were measured using a shielded and aspirated sensor (HMP-35 A, Vaisala, Helsinki, Finland). Water vapor deficit pres-sure (VPD, kPa) was calculated based on measurements of Tair and relative humidity. Volumetric soil moisture (θv, cm3  cm−3) was measured near the soil surface (~2  cm in depth) with three frequency-domain reflectometer probes (ML2x, Delta-T Devices, Burwell, Cambridge, UK). Two of the soil moisture probes were installed under the tree canopy and the third in open grassland area. Incoming photosynthetically active radiation (PAR, μmol  m−2  s−1) was measured above the tree canopy with a quantum sen-sor (PAR-Lite, Kipp and Zonen, Delft, Holland), and pre-cipitation (mm) was measured with a rain gauge (Campbell Scientific Inc. Logan, Utah, USA). These sensors were connected to data loggers (CR10X or CR23, Campbell Sci-entific, Inc., Logan, Utah, USA) which automatically sam-pled every 10 s and recorded half-hour averages.

Leaf-chamber experiments

Leaf-level temperature response experiments were con-ducted in the field on the days numbered 100, 116, 123, 128, 137, 152, 158, and 185 starting since Jan. 1, 2008. For each day, measurements started around 9:00 am local time and lasted 2–4 h depending on the number of meas-urements made. Oak trees were around 85 years with either cylindrical or round crowns. We sampled leaves from the same area of the crown each time.

Leaf photosynthesis was measured with a 4  cm2 leaf cuvette (LI-6400, Li-cor Inc., Lincoln, NE, USA). Once a leaf was inserted into the chamber, the machine measured initial leaf temperature and was set to maintain this initial temperature until stabilized (~15  min). Leaf temperature was then reduced as far as set-up and conditions allowed, by fitting the chamber head with a water jacket on each side to remove heat dissipated by sleeves and either an ice-water bath or a hot-water bath. The water was pumped through the closed loop using a bilge pump (Super Sub Pump 500, West Marine, Watsonville, CA, USA) fitted with a volt-age regulator. Once steady-state conditions were again

achieved, the leaf was exposed to a saturating flash, and photosynthesis were recorded. Then leaf temperature was increased by 1 °C. This process was repeated at increasing temperatures until the temperature could not be increased further. Leaf-chamber temperatures were controlled in the range from 16 to 43 °C, approximately ±6 °C below or above ambient air temperature. To avoid condensation on the infrared gas analyzer mirrors, we did not repeat the pro-cedure at lower temperatures, except a single curvet span-ning 12 to 18 °C.

Before clamping on to a leaf, the CO2 concentration in the cuvette was set to 380 ppm, and light intensity was set to saturating, which was determined by photosynthetic light response curves measured on a neighboring leaf the day before measurement of photosynthetic temperature response curves. Control of leaf-to-air vapor pressure dif-ference in the leaf chamber requires the flow rate through the chamber to be adjusted depending on air tempera-ture and transpiration rate. Because the relative humidity of ambient air and transpiration rates at this site are low throughout most of the summer, maintaining a constant water vapor density in the chamber would often lead to low flow rates that might increase chamber leakage, espe-cially in the smaller leaf chamber of the LI-6400-49. Thus, we chose to maintain a constant flow rate to avoid leakage problems rather than hold water vapor density constant during each measurement.

Pheno-stages and LAI measurements

To interpret the tower-based data and match them with leaf-level measurements correctly, we defined four pheno-stages (Pheno I, II, and III) and leaf area index (LAI) of oak trees and annual grasses (Fig. 1).

The dates of grass green-up, oak leaf-out, grass senes-cence, and oak litter-fall were determined to occur when 60–70% of plant communities showed the same phenol-ogy (Ma et  al. 2007). Pheno I was the period between grass green up and oak leaf out, covering the autumn and winter months, while grasses grew slowly and there were no leaves on the oak trees. Pheno II started from the time when oak leaves came out till annual grasses were died out. This pheno-stage was equivalent to spring when oak leaves and grasses grew and developed rapidly. Pheno III was the period of dry summer before rains returned. Dur-ing this period, oak leaves stayed photosynthetically active, but photosynthetic activities gradually decreased. In late summer, oak trees are photosynthetically active in the early morning. Deeper roots enabled oak trees to access ground-water, but the amount of water was just enough to retain vital activities during the summer (Miller et  al. 2010). Thus, the growing season of grasses included Pheno I and

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II; the growing season of oak trees included Pheno II and III.

During the growing season of annual grassland, we clipped grasses within a 20 × 20  cm2 square monthly at three locations selected randomly around the flux towers. Green grass leaves were separated from litter or senescent leaves and run through a leaf area meter (Li-3100, Li-cor, Lincoln, Nebraska, USA) in the lab. Oak LAI was esti-mated from images of three upward-pointing digital cam-eras (Ryu et al. 2012). Sample size, mean, minimum, and maximum values for each month are listed in Supplemental Materials (S1).

A framework of data analysis

In a comparison to manipulative experiments carried out in leaf-level studies, we visualize the surroundings of a tower (within its footprint) as an individual “chamber” of natural experiments. Inside the natural chamber, the state of bio-physical conditions is relatively steady given a short period (e.g., half hourly) when an average behavior of photosyn-thesis can be measured. This new vision may be count-intu-itive because tower-based data are recorded in time series by electrical data loggers. A wavelet study confirms that autocorrelation exists on the time-scale of 24 h (Stoy et al. 2005), supporting the fact that temporal correlation (e.g., autocorrelation) is necessary for subsequent time series analysis. However, the wavelet study also suggests that a single measurement at one moment should not correlate

with measurements a few hours before or after. Thus, we assume that tower-based datasets record a set of depend-ent variables and independent variables. The following is a framework for exploring and verifying the functional relationships between a pair of dependent and independent variables.

Defining the dependent variable—net photosynthetic flux of ecosystems

Daytime CO2 flux (FA) measured from the tower is known as net photosynthetic flux, a difference between photosyn-thesis and ecosystem respiration averaged upon each half hour (Wofsy et al. 1993). This ecosystem-level concept can be a proxy of the leaf-level concept of net photosynthetic rate if LAI is close to 1, which is the case of oak trees in this savanna (Ma et  al. 2011). Because FA also includes respiration of leaves, roots, and soil microbes and may mit-igate photosynthetic signals, only FA  >  0 are used in the rest of our analyses. Daytime and nighttime were separated with a threshold of PAR (i.e., 5 μmol m−2 s−1).

Sorting, binning, and smoothing

A scatter plot of half-hour photosynthetic fluxes versus air temperature did not suggest any visible pattern (Fig.  2a, gray dots, using tree canopy as an example). One might interpret that temperature had no effect on photosynthesis at the ecosystem level. Or, the apparent disorder in the data

Fig. 1 Monthly leaf area index (LAI) of a oak trees and b annual grasses shown with box plots that indicate mean (in diamond), median (bar across the box), 95 and 5% percentiles (upper and lower horizontal bars). Sample size, mean, mini-mum, and maximum values of monthly LAI are also available in Supplemental Material (S1). The bars above the box plots are three main pheno-stages including Pheno I—the period between grass green-up and oak leaf-out, Pheno II—the period between oak leaf-out and annual grass die-off, and Pheno III—the period between annual grass die-out and germination

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might suggest that temperature should not be the only fac-tor determining individual photosynthetic fluxes on this fine time-scale (i.e., half hour).

The former interpretation seemed acceptable after our polynomial regression analyses failed. We then questioned whether the failure occurred simply because the tower-based data had a large sample size. Thus, we examined the data mining methods commonly applied in analyzing Big Data. A key idea was to assign data into discrete categories so that statistical characteristics could be described within each bin but also be compared across bins. A nonparamet-ric statistical approach—binning—is a promising method that has been used successfully for extracting functional patterns in CO2 fluxes and environmental factors (Falge et al. 2001; Barr et al. 2013).

We first tried binning FA with a temperature interval of 1 °C and calculated mean, median, and quartiles within each bin (Fig. 2a). We computed the histogram within each bin and estimated the probability density with the Kernel Density method (SAS 9.4, SAS Institute Inc., Cary, NC, USA). Results of both methods indicated that the data dis-tribution of FA was skewed within each bin, and the major-ity of flux data were located on the positive side, indicating that photosynthetic behaviors contributed to the majority

of signals (an example shown in Fig.  2b). When individ-ual means (or medians) of bins together were connected across the sampling domain of temperature, a peaked curve emerged, similar to the pattern often found in the leaf-level literature.

This initial analysis was interesting, but the bin interval was fixed, perhaps resulting in an uneven number of sam-ples per bin. For example, for the tree canopy, the number of samples per bin was approximately n = 5000, but n < 100 for extreme low or high temperature bins. To avoid possible biases caused by uneven numbers, we sorted the flux data by order of temperature and then binned a pair of FA and Tair with a fixed sample size n (e.g., n = 1000) (Barr et al. 2013). Also, we calculated bin averages of FA weighted with probability density to take skew into account, com-paring with simple arithmetic averages (i.e., unweighted averages) (Fig.  2c). The unweighted averages of FA were slightly lower than the weighted value. After apply-ing a nonparametric local regression method (LOESS), the peaked pattern remained. Thus, the sorting–bin-ning–smoothing process did suggest a significant pattern for the relationships between FA and Tair. Importantly, dif-ferent computing strategies did not alter the peaked shape. Whether the peaked shape was meaningful depended on

Fig. 2 Panel a is a scatter plot of daytime net photosynthetic flux of oak tree canopy (FA) against air temperature (Tair) (in gray dots, n = 108,336), overlaid with means, medians, and quartiles (binned by 1 °C intervals, as shown in each box plot). Panel b is a histogram of half-hourly FA within one of the bins (using the 23rd bin as an example), overlaid by the probability density function estimated with the Kernel density method. Panel c is averaged FA binned by a 1 °C

interval or by a constant number of data points (e.g., n = 1000). In addition, arithmetical bin-averaged FA are compared with weighted bin averages of FA, while the weighting factor for each bin is deter-mined by the probability density function, as in the example shown in b. Smoothing curves for each group are estimated with the LOESS method (see details in “Methods” section)

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our further comparisons with leaf-level measurements, which we present in the “Results” section.

Confounding effects

To identify which abiotic factors might have confounded the temperature effects on photosynthesis, we examined covariations of light intensity, air dryness, and soil moisture with air temperature based on half-hourly measurements over the 15 years. The probability density function of light intensity (PAR), air dryness (VPD), and soil moisture (θv) within the domain of air temperature (Tair) was estimated using the Kernel density method. Higher probability den-sity values indicated greater likelihood of co-occurrence of each confounding factor and temperature.

Experimental scenarios

According to the range of these continuous variables in the field, five discrete levels were designed as five experi-mental scenarios: Low (L), Low-Moderate (LM), Moderate (M), Moderate-High (MH), and High (H).

For the convenience of computation, the entire range of PAR within each pheno-stage was categorized with an interval of 500  μmol  m−2  s−1: L (PAR ≤500); LM (500 < PAR ≤ 1000); M (1000 < PAR ≤ 1500), MH (1500 < PAR ≤ 2000), and H (PAR >2000). To iden-tify degrees of air dryness, we used VPD and divided the dataset with an interval of 1  kPa: L (VPD ≤1); LM (1 < VPD ≤ 2); M (2 < VPD ≤ 3), MH (3 < VPD ≤ 4), and H (VPD >4). Soil moisture was defined by θv with an interval of 0.05 cm3 cm−3 (5%): L (θv ≤ 5%); LM (5% < θv ≤ 10%); M (10% < θv ≤ 15%), MH (15% < θv ≤ 20%), and H (θv > 20%).

Theoretically, the total number of combinations of the three-factor, five-level experimental scenarios is 53 = 125. Not all occurred in natural conditions according to an analysis of frequency. Only 75 out of the 125 combinations were recorded over the 15 years. The frequencies of the 75 combinations varied across the pheno-stages.

Verifying the tower‑derived temperature response curve

The general expression of the quadratic function is y = ax2 + bx + c. If a function is quadratic, its first-order differential

(

dy

dx

)

is a linear function. Thus, we resampled ΔFA

ΔTair along the response curve and applied a regression anal-

ysis to test for linearity. The temperature at the maximum value of photosynthetic flux, the optimum temperature, was (Topt), Topt = −

b

2a.

We used minimum and maximum temperatures (Tmin and Tmax) to describe the lower and upper temperature lim-its, typically when photosynthetic flux was low, such as FA 

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a decreasing trend as air temperature increased from 16 to 43 °C (Fig.  6a). Tower-derived measurements of canopy photosynthesis (FA_canopy) during the 8  days of the leaf-chamber measurements used 129 samples. The smooth-ing curve was peaked, suggesting an increasing trend in photosynthesis as temperature increased approximately from 5 to 18 °C and a decreasing trend with tempera-ture increasing above 18 °C (Fig. 6b). The pattern might be more easily discernible if we had expanded our data to include the towers during Phenos II and III in 2008

since the sample size would increase to 5227, almost 50-fold the number of samples from the leaf-chamber experiments.

Although the magnitudes of photosynthetic fluxes measured at the leaf level were greater than the tower-derived canopy-level measurements, these two data sources were comparable within the overlaid tempera-ture range (Fig.  6c). The regression model fitting for FA_canopy versus FA_leaf was statistically significant (F test, p < 0.001).

Fig. 3 Variations in a light intensity (PAR), b air dryness (VPD), and c soil moisture (θv), while net photosynthetic flux of oak tree canopy (FA_canopy) varies with increases in air temperature (Tair), sug-gesting that these measurable abiotic factors mutually constrain one another in situ

Fig. 4 The probability density function of a light intensity (PAR), b air dryness (VPD), and c soil moisture (θv) within the domain of air temperature (Tair), estimated with the Kernel density methods based on their half-hourly measurements from 2001 to 2015. The color scale on the right side of each panel shows the value of the probabil-ity

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The FA_canopy–Tair relationship under experimental scenarios

To test how variations in light intensity, air dryness, and soil moisture influenced the relationship between can-opy photosynthesis and temperature, we extracted the FA_canopy–Tair relationship under each experimental sce-nario. Unsurprisingly, canopy photosynthesis was greater in conditions of higher light intensity, lesser air dryness, and higher soil moisture. Most of the curves displayed in a

peaked pattern, although the slopes of the two sides differ (Fig. 7a, b, c).

Fig. 5 Variations in light intensity (a, PAR), air dryness (b, VPD), and soil moisture (c, θv) during the daytime hours on days numbered 100, 116, 123, 128, 137, 152, 158, and 185 starting since Jan 1 in 2008, when leaf chamber experiments were carried out. The rectan‑gles indicate the conditions controlled inside the leaf chamber—satu-rated light intensity, relatively no stress due to air dryness, and soil moisture levels

Fig. 6 Panel a the relationship of oak leaf photosynthesis (FA_leaf) to temperature measured with the leaf chamber (Tleaf) (n = 169); Panel b the relationship of tower-based oak canopy photosynthesis (FA_canopy) to in situ air temperature (Tair) when leaf-chamber experiments were performed (n = 129) with saturated light intensity; Panel c FA_canopy is related to FA_leaf positively, and the fitting model is statistically sig-nificant (p < 0.001)

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Among the experimental scenarios, not all of the peaked shape was symmetric, but the one for the mod-erate soil moisture level was (Fig.  7c). Such conditions absent water stress often occurred in the middle of spring, when light intensity was not as low as in earlier seasons (Fig. 4a). The left-side slope excluded effects of low light intensity at lower temperatures, and the right-side slope eliminated effects of water stress at higher temperatures. Interestingly, the curve extracted from the entire sam-pling domain—the average temperature response curve—was similar to the no-water-stress pattern (Fig. 7d–f).

Optimum temperatures

We applied the same method in extracting the average tem-perature response curve for each vegetative community (Fig. 8a). The average curves were all peaked, whereas the maximum FA occurred around 20 °C. The first-order differ-entials

(

ΔFA

ΔTair

)

were linearly related to air temperature (F

test, p < 0.0001) (Fig. 8b), verifying that the average curve was parabolic in shape, while Topt equaled 20.6 ± 0.6, 18.5 ± 0.7, 19.2 ± 0.5, and 19.0 ± 0.6 °C for oak canopy, understory grasses, the entire savanna, and the open

Fig. 7 Panels on the left side show the binned averages of oak canopy photosynthesis (FA_canopy) and air temperature (Tair) under experimental sce-narios by five levels of a light intensity (PAR), b air dryness (VPD), and c soil moisture (θv). For each scenario, the number of data for each bin (n) is 500. Panels on the right side show the FA_canopy–Tair relationship (in dark triangle and solid curve) extracted from the 15-year, tower-based measurements during the growing season of oak trees (including pheno-stages II and III), suggesting that the overall pattern averages out possible confounding effects such as light intensity, air dryness, and soil moisture; the gray triangles are the same as those for data shown on the left side in the same row. Smoothing curves are estimated based on averages of FA (binned by n = 1000) with the LOESS method (see details in “Methods” section)

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grassland, respectively. Differences in these Topt values were not statistically significant according to results of the F test, indicating that these four vegetative communities had similar Topt on average, which should not be surprising given that they all belong to C3 plants and exist in basically the same location.

Besides variations in the positions of optimum tempera-ture, the temperature response curves also showed varia-tions in the positions of the lowest or highest temperatures that would limit regular photosynthesis. For the vegetation types studied here, Tmin was close to 0 °C, approximately.

Oak photosynthesis exhibited Tmax close to 40 °C, about 5 °C higher than that of annual grasslands (Fig. 8a).

We also checked that light intensity, air dryness, or soil moisture could cause significant changes in the values of Topt for each vegetation type (F test, p < 0.0001). As oak canopy showed, Topt were higher with increases in light intensity and air dryness (Fig.  9a, b), but Topt was lower with increases in θv (Fig.  9c). Topt could vary more than 10 °C with variations in light intensity, air dryness, and soil moisture (Fig. 9). The oak canopy exhibited a range larger than the annual grassland, suggesting greater flexibility of oak photosynthesis in response to changes in ambient temperature.

Discussion

The leaf-chamber experiment is a fundamental method that supports the tower-based observations, although the leaf-chamber experiments presented in this study did so partially. We were short of data at temperatures lower than 18 °C due to condensation problems. Also, measurements relied on a few sun-exposed leaves belonging to three indi-vidual oak trees in the summer of 2008. That year alone, the eddy-covariance towers measured almost 50-fold as many samples as the leaf-chamber experiments. Thus, the towers are more likely to capture a large population of sun-exposed and shaded leaves distributed across a footprint several hundred meters along the main axis of the study site (Kim et al. 2006). As a result, the tower-based temperature response curves covered a temperature sampling domain wider that the leaf-level experiments. Although the eddy-covariance flux towers are also expensive and require high-level technical support, we offer timely new methods for analyzing flux tower data to extract information on photo-synthetic temperature responses over ecosystems.

The flux tower is usually set up for natural experiments, but the tower-based datasets provide both physiological and environmental information that is richer than that histori-cally existing. The feature of large sample sizes from the perspectives of experiments opens up the possibility to tease apart potential confounding factors during data analy-sis, instead of during experiment design. Our analyses show how larger sample sizes can average out most of confound-ing effects, whereas sub-samples under each experimental scenarios cannot. Nevertheless, confounding effects should be a major concern if the sample size is small. For exam-ple, confounding effects were associated with the 8-day leaf-chamber measurements if the light intensity inside the chamber was not controlled at the saturated level. When we extracted tower-based temperature response curves under different experimental scenarios, we reduced the sample size for each scenario, resulting in unbalanced slopes on

Fig. 8 Panel a shows the averaged relationship between photosyn-thetic flux (FA) and air temperature (Tair) for oak canopy, understory grassland, savanna, and open grassland, binned by n = 1000. Panel b shows the slopes of the curves shown in Panel a by calculating dFA/dTair along with the axis of Tair; a linear function (statistically signifi-cant) proves that the curves shown in Panel a are parabolic

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the left and right side of the temperature response curves. Thus, caution on confounding effects is always needed, especially when the entire tower-based dataset is catego-rized into groups.

Variations in abiotic variables such as light intensity, air dryness, and soil moisture not only can affect the magni-tude of photosynthesis but also can shift optimum tempera-tures. However, variations in these abiotic variables do not alter the peak shape of the temperature response curves; background climate and seasonality constrain the occur-rences of confounding effects. For example, the savanna area shows two particular confounding scenarios: (1) low light intensity confounds with lower temperatures and (2) air and soil dryness confound with higher temperatures, due to the Mediterranean climate type—wet winters and springs and dry summers. In recent years, dry conditions

occur in the winters and springs more often (Ma et  al. 2016). Yet the probability of occurrences of dry winters and springs is still lower than the probability of wet winters and springs. Thus, confounding factors and their effects on photosynthesis depend greatly on the background climate, and we conclude that many theoretical paradigms rarely occur in situ.

During data analysis, we visualize the tower-based experiments as if we perform a series of manipulative experiments numerically (Jones 1992). This visualization impieties problems caused by applying general climato-logical methods in synthesizing flux and environmental variables, such as integrating flux data over a fixed period (e.g., daily, monthly, or annually). Such a climatologi-cal approach reduces the degree of freedom of original data and causes loss of fine time-scale information, which

Fig. 9 Variations of optimum temperature of photosynthesis (Topt) under experimental scenarios of light intensity (PAR), air dryness (VPD), and soil moisture (θv) for a oak canopy, b understory grass-land, c entire savanna, and d open grassland. Notice that for each box plot, the mean is presented as a diamond; the median is the bar across

the vertical rectangular box; the lower and upper edges of the box are the 25 and 75% percentiles, respectively; the 5% percentile is the lower bar below the box; the 95% percentile is the upper bar above the box; and circles outside percentile bars are outliers

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reflects the fast responses of vegetation to changes in environments (Woodward 1987). For the same reason, a few studies may exaggerate the meaning of mean annual temperature with ignorance of fine time-scale variations in ambient temperature (Helliker and Richter 2008; Yuan et al. 2011; Niu et al. 2012). Thus, it is worth paying more attention to fine time-scale variations in fluxes and ambi-ent variables to test process-based hypotheses regarding dominated vegetative communities of ecosystems.

The temperature response curves extracted from the entire sampling domain have many ecological implica-tions. First, the average position of temperature optima and limits reflects the inherent capacity of thermal adap-tation of vegetative communities. For example, the opti-mum temperatures for the four vegetative communities at our study sites show the thermal characteristics of C3 plants. We may expect differences in temperature optima and limits are significant enough that could distinguish C3, C4, and CAM plants or functional types occupying a variety of natural habitats (Yamori et al. 2014; Berry and Bjorkman 1980). Thus, by using the data mining frame-work that we proposed here, we can further test the sta-bility of temperature response for photosynthesis across different ecosystems or biomes.

Second, our results show that oak canopy started being photosynthetically active in the temperature range from near 0 to 40 °C, whereas photosynthesis is inhibited in the annual grasslands when temperatures are greater than ~35 °C. Such a 5 °C difference in maximum temperature reflects the different thermal tolerances of vegetative communities for performing photosynthesis and produc-ing biomass. These temperature limits may be useful for identifying critical thresholds of ecosystems that deter-mine the direction of primary productivity as the global climate warms up (Woodward 1987; Woodward et  al. 2004). The lower and upper limits of temperature for photosynthesis suggested by the tower-based temperature response curve provide a set of quantified thresholds of ecosystems for defining extreme climatic events.

Third, ecosystems may face serious problems if a majority of fine time-scale ambient temperatures shifts toward the outside of the temperature range favorable to current dominant vegetative communities—even though mean annual temperature may vary insignificantly—per-haps leading to species extinction in sensitive ecosystems or regions (Chapin III and Starfield 1997; Woodward 1987). Such influences may occur gradually along with normal climate fluctuations, but weather extremes or natural disasters may cause sudden impacts on vegetation and ecosystem primary productivity. More research can be carried out to clarify the functional relationships of ecosystems in climate extremes.

Finally, this study paves the way for estimating impor-tant parameters and response functions dynamically to feed photosynthesis models on large spatial scales. A recent remote sensing work reports that a dynamic temperature-related index can improve performances of light-use effi-ciency models (Yuan et al. 2007; Medlyn 1998; Wang et al. 2016). Tower-based temperature response curves provide plenty of information for extracting such indices. Further-more, our data mining framework is suitable for mining different functional relationships, such as light response curve or VPD response curve, and so forth. We also see the potential of the data mining framework suitable for exploring nighttime CO2 fluxes and following temperature response of ecosystem respiration. To retain the focus of our study, we decide not to extend our current efforts into those aspects, but we expect that future research with the data mining framework will turn tower-based datasets into an abundant data resources for determining baseline infor-mation and response functions of vegetative communities in ecosystems in a dynamic way.

Conclusions

This study develops a data mining framework to extract temperature response functions for ecosystem photosyn-thesis from eddy-covariance tower-based natural experi-ments. Our results confirm that the  temperature response of photosynthesis is a functional relationship consistent at the ecosystem level as well. Local background climate and seasonality constrain natural occurrences of confound-ing effects, and most of the confounding effects may cancel out, benefits of the feature of large sample sizes. Thus, the tower-based data are a Big Data of ecosystem science for exploring functional responses of ecosystems to environ-mental factors dynamically. Our methods will turn world-wide tower-based datasets into an abundant resource of a determination of ecosystems thresholds and response func-tions, which are critical for predicting terrestrial ecosystem carbon balance and geographic vegetation distribution in responses to climate change.

Acknowledgements This research is a member of the Ameri-Flux and Fluxnet networks, supported in part by the Office of Sci-ence (BReco), U.S. Department of Energy, Grant No. DE-FG02-03Reco63638 and through the Western Regional Center of the National Institute for Global Environmental Change under Coopera-tive Agreement No. DE-FC02-03Reco63613. Other sources of sup-port included the Kearney Soil Science Foundation, the National Science Foundation, and the Californian Agricultural Experiment Station. We are grateful to Dr. Laurie Kotten and Housen Chu who commented on early versions and Dr. Kenneth Worthy who edited the manuscript and suggested clearer expressions in English and sci-ence. We are grateful for receiving constructive comments from two anonymous reviewers who shared their expertise helping us to make

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a stronger scientific contribution. We also thank the Tonzi and Vaira families for allowing us to access their ranches for research.

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Photosynthetic responses to temperature across leaf–canopy–ecosystem scales: a 15-year study in a Californian oak-grass savannaAbstract IntroductionMethodsStudy sitesCanopy- and ecosystem-level measurementsLeaf-chamber experimentsPheno-stages and LAI measurementsA framework of data analysisDefining the dependent variable—net photosynthetic flux of ecosystems

Sorting, binning, and smoothingConfounding effectsExperimental scenariosVerifying the tower-derived temperature response curve

ResultsBackground climate and confounding effectsCanopy photosynthesis during leaf-chamber experimentsThe FA_canopy–Tair relationship under experimental scenariosOptimum temperatures

DiscussionConclusionsAcknowledgements References