Different determinants of radiation use efficiency in cold and temperate forests

Aim: To verify which vegetation and environmental factors are the most important in determining the spatial and temporal variability of average and maximum values of radiation use efficiency (RUE ann and RUE max , respectively)


| INTRODUC TI ON
Radiation use efficiency (RUE; gC/MJ) has emerged in recent decades as a key parameter to determine photosynthetic carbon uptake by vegetation, and thus the carbon exchange between the atmosphere and biosphere (Monteith, 1972).RUE represents the efficiency of vegetation to transform absorbed light energy into organic compounds; it is the ratio between gross primary production (GPP; gC/m 2 /year) and the absorbed photosynthetically active radiation (APAR; MJ/m 2 /year), with APAR being the product of the incident photosynthetically active radiation (PAR; MJ/m 2 /year) and its fraction absorbed by vegetation (fAPAR) (Monteith, 1972): The global ecological modelling and the remote sensing communities are particularly interested in the RUE concept (e.g., Cheng, Zhang, Lyapustin, Wang, & Middleton, 2014;Grace et al., 2007;King, Turner, & Ritts, 2011;McCallum et al., 2009;Running et al., 2004;Stocker et al., 2018;Wang, Prentice, & Davis, 2014;Wang et al., 2017;Yuan et al., 2014;).Nevertheless, to date, no consensus has been reached regarding the most suitable algorithm for RUE (Gitelson & Gamon, 2015) and scientists still need to fully understand if (and how) models should simulate the impact of environmental factors on RUE (Baldocchi, 2018).To do this, first we need to find suitable proxies that capture well RUE variability in space (from local to global) and in time (from daily to annual).RUE changes over time because GPP is affected by the current environmental conditions and because the absorbed radiation is affected by changes in incident PAR and leaf properties (e.g., leaf and chloroplast movement), which can occur over short time periods.On the other hand, the impact of respiration variability on RUE is expected to be low in the short term (when plant respiration is thought to be independent of photosynthesis) but it can be greater over longer, annual timescales (when plant respiration is thought to be proportional to photosynthesis) (Ryan, Linder, Vose, & Hubbard, 1994).
First, RUE was used as a constant parameter (e.g., Myneni, Los, & Asrar, 1995).Subsequently, interannual variability has been recognized.The ratio between the accumulated GPP over the year and the total solar radiation absorbed by the canopy was then defined as annual RUE (RUE ann ).This definition has been widely used in simple crop growth models, based on in situ observations (McCallum et al., 2009), as well as in meta-analyses seeking general ecological elucidations (Fernández-Martínez et al., 2014).Finally, the intra-annual variability of RUE, due to its dependency on seasonal environmental factors, was recognized (e. g., Grace et al., 2007).Production efficiency models define the light conversion factor as the product of an optimum RUE value (RUE potential or maximum, RUE max ) and other factors that relate to the environmental variables that regulate photosynthesis and APAR.For example, in the moderate resolution imaging spectroradiometer (MODIS) algorithm, RUE is implicitly calculated (to determine GPP) based on temperature, light, vapour pressure deficit and the biome-specific RUE max derived from a look-up table (Zhao, Running, & Nemani, 2006).However, many studies considering different biomes (Garbulsky et al., 2010;Runyon, Waring, Goward, & Welles, 1994) have shown that RUE might be influenced not only by environmental factors, but also by a range of biophysical and structural factors related to plant properties, sometimes affected by ecosystem management (e.g., irrigation, fertilization).Both environmental and vegetation factors that affect RUE are reported in Table 1 with the aim of summarizing the current state of the art.
In detail, factors that have been reported to date as determinants of RUE are: (a) temperature-related variables [air and soil temperature, length of the warm period (i.e., the number of months with mean temperature above 5 °C), thermal amplitude (i.(a) Temperature-related variables.The impact of air temperature on RUE has been tested the most, but contrasting results have been found, ranging from significant (Chasmer et al., 2008;Kergoat, Lafont, Arneth, Dantec, & Saugier, 2008;Mäkelä et al., 2008;Schwalm et al., 2006) to non-significant (Jenkins et al., 2007;Turner et al., 2003), or with impact limited to periods during the warm season (see above definition; Fernández-Martínez et al., 2014) or only at cold sites (Garbulsky et al., 2010).The latter evidence is the most anticipated, as the positive effect of temperature on photosynthesis is larger in cold environments and APAR is not expected to depend significantly on temperature. Furthermore, Fernández-Martínez et al. (2014)  TA B L E 1 (Continued) in stomatal conductance or stomata closure.VPD has frequently been tested as a potential driver of RUE.As can be seen in Table 1, both significant (Bracho et al., 2012;Chasmer et al., 2008;Mäkelä et al., 2008;Runyon et al., 1994) and non-significant (Garbulsky et al., 2010;Jenkins et al., 2007;Turner et al., 2003) impacts of VPD on RUE have been found.Also annual precipitation was identified both as a significant (Garbulsky et al., 2010) and a non-significant driver of RUE (Fernández-Martínez et al., 2014).In the latter work, the water deficit was tested as potential driver of RUE (i.e., an indicator of the intensity of water stress that the vegetation must tolerate) but with a negative response.Soil water content was reported as a significant driver of RUE in one study on temperate forests (Bracho et al., 2012) and one on cold forests (Chasmer et al., 2008), while it was not relevant in the study of Mäkelä et al. (2008) (Bracho et al., 2012;Chasmer et al., 2008) and non-significant driver of RUE (Fernández-Martínez et al., 2014), whereas leaf habitat and type were found to be non-significant (Fernández-Martínez et al., 2014).It has been reported by several authors that RUE varies with vegetation type (Field, Randerson, & Malmstrom, 1995, Garbulsky et al., 2010;Prince & Goward 1995;Schwalm et al., 2006;Turner et al., 2003) because of the different ratio of respiration to photosynthesis.RUE was found to be around 2 gC/MJ for annual crops, for which the ratio of respiration to photosynthesis is assumed to be low, whereas for woody plants the value of RUE varies from 0.2 to 1.5 gC/MJ because the ratio of respiration to photosynthesis is assumed to increase with plant size (Hunt, 1994;Waring & Running, 1998).
(e) Fertility-related variables.The impact of fertility on RUE has been tested in two experiments on temperate forests but contrasting results were found [significant in Campoe et al. (2013), non-significant in Allen et al. (2005)].Bracho et al. (2012) identified fertility as not influential for RUE in drought conditions.Leaf nitrogen content affects RUE directly (mainly through its impact on photosynthesis) but also indirectly (through its impact on leaf and plant structure, which influence light absorption).Leaf N has been therefore considered as a potential driver of RUE in manifold studies on forest ecosystems (Kergoat et al., 2008;Ollinger et al., 2008;Peltoniemi et al., 2012) but has not been found to be consistently significant (Mäkelä et al., 2008;Schwalm et al., 2006).In a recent study, Fernández-

| Forest categories and sites
It appears clear that most of the variables (e.g., related to temperature, water status, fertility) potentially affecting RUE differ between the two main climate zones where the majority of the northern forests are situated, that is, the temperate and cold zones.As for most of the previous studies on RUE variability (see Table 1), we therefore separated the two forest types in our analysis.This categorization is also important to generalize our findings and match the forest land classification used in global vegetation modelling.
The categorization of cold and temperate is based on the Köppen-Geiger classification (Peel, Finlayson, & McMahon, 2007), using monthly temperature data from the European Commission-Joint Research Centre-Monitoring Agricultural ResourceS (EC-JRC-MARS, https ://ec.europa.eu/jrc/en/mars)portal.The Köppen-Geiger classification defines a particular site as "cold" when the temperature of the hottest month is > 10°C, while the temperature of the coldest month is below or equal to 0°C.On the other hand, sites are classified as "temperate" when the temperature of the hottest month is > 10°C and the temperature of the coldest month is between 0 and 18°C.
For the analysis on spatial variability of RUE ann we used 26 cold and 22 temperate forests in the Northern Hemisphere (Figure 1).
These sites were selected because they had both GPP derived from eddy covariance flux measurements and the associated satellite value of fAPAR available (see below for fAPAR determination).
Multiple years were considered when available.Total site-year combinations were 114 for cold and 102 for temperate forests (see Supporting Information Appendix S1).For the analysis of the spatial variability of RUE max, only the sites with seasonal data for GPP and fAPAR were selected.A subset of 20 cold forests and 20 temperate forests was thus used (see Supporting Information Appendix S1).
The temporal analyses (interannual variability of RUE ann and RUE max and short-term RUE variability, RUE 8days ) were conducted by considering 11 sites that had at least 8 years of seasonal data for GPP and fAPAR.or sites (leaf N concentration was available only at about half of the sites and only those sites were considered in the data analysis for leaf N).

| Analyses of temporal variability
For the analysis of short-term variability of RUE 8days the available (meteorological) variables were: mean 8-day temperature, 8-day minimum and maximum temperature, 8-day mean potential evapotranspiration, 8-day mean VPD and 8-day mean CO 2 concentration.For the analysis of the interannual variability of both RUE ann and RUE max , we considered the same meteorological explanatory variables used for the analysis of short-term variability of RUE 8days .

(a) Meteo-variables
Mean annual temperature, mean monthly minimum and maximum temperature, annual precipitation and potential evapotranspiration, yearly number of days with mean daily temperature below zero and the duration of the longest period without rain (expressed in number of days), mean 8-day temperature, 8-day minimum and maximum temperature, 8-day mean potential evapotranspiration and 8-day mean VPD were calculated using the EC-JRC-MARS data set.
The evaporation data that we used are derived from Penman (1948) and they represented the annual potential evapotranspiration.We

(c) Leaf type and habit
We collected the description of each site from the database of Luyssaert et al. (2007).The two leaf type categories are needleleaved and broadleaved, while the categories deciduous and evergreen represent the leaf habit of the forest tree species.

(d) N deposition
In our analysis, N deposition was considered as the sum of dry and wet deposition.We extracted these data from the global N deposition data set simulated with goddard earth observing system-Chem (GEOS; http://acmg.seas.harvard.edu/geos/index.html)for years from 2004 to 2006, at 2°×2.5° grid resolution (Ackerman, Chen, & Millet, 2018).

(e) LAI and leaf N concentration
We extracted LAI data from the forest database of Luyssaert et al. (2007) and the literature (see Supporting Information Appendix S2).Leaf N was obtained from the ancillary files of the Fluxnet and European Fluxes Database Cluster and the literature (see Supporting Information Appendix S3).For both LAI and leaf N concentration, we used the maximum annual value.

(f) CO 2 concentration
For 81% of the sites, we used CO 2 concentration data from the Fluxnet database.For the remaining sites, we used values provided

| Spatial variability of RUE ann and RUE max
The analyses of RUE ann and RUE max were conducted separately for cold forests and temperate forests (see Tables 2 and 3), with the analysis on the entire data set reported only in the Supporting Information (see Appendices S4 and S5).

| Temporal analysis of short-term RUE variability
For this test, we performed univariate analyses considering as dependent variable the time series of RUE 8days and as independent variables the 8-day time series of the predictors (see above).The analyses were done for each of the 11 selected sites, separately, and averages were done across years.First, the analyses were done for all 8-day periods within the growing season.Second, the analyses were run separately for three periods representing the main seasons: spring (considering 8-day windows from 15 April to 15 June), summer (from 16 June to 15 August) and autumn (from 16 August to 15 October).

| Temporal analysis of interannual variability of RUE ann and RUE max
This analysis was done separately on the selected 11 sites (see above).We conducted a univariate analysis to evaluate the goodness of the linear correlation between RUE (RUE ann and RUE max ) of each year and the value of each predictor variable (see above for the variables list).For RUE ann , we used annual values of the predictor variables.For predictors of RUE max , we used the values of the 8-day window corresponding to the 8-day period associated with RUE max .
All the statistical analyses were done using R (R Core Team, 2015).

| RE SULTS
Mean RUE ann for cold and temperate forests was very similar: 1.10  3).
In general, there was a good agreement between the univariate analysis and random forest analysis and the variables that were significant in the univariate analysis also showed high importance in the random forest analysis (Figures 2 and 3).However, there were exceptions.First, for temperate forests, the relation between RUE ann and maximum air temperature was not significant according to the Stepwise backwards regression model univariate analysis but was highly ranked in random forest analysis (see Figure 2 and Table 2).This is probably due to the hyperbolic relationship between maximum temperature and RUE ann which was likely detected by the random forest but not by the univariate analysis (Supporting Information Appendix S6).However, we believe this relationship to be spurious as it is driven by only three sites with exceptionally high maximum temperatures (Supporting Information Appendix S6).Second, similarly to the previous case, RUE max of cold forests was not significantly correlated with Tmean in the univariate analysis but Tmean was highly ranked in the random forest analysis, likely because of a few exceptional sites (Supporting Information Appendix S7).Third, for RUE ann and RUE max of cold forests, LAI was significant according to the univariate analysis but of very low importance in the random forest analysis.This suggests that for RUE ann and RUE max of cold forests, nonlinear relationships might dominate and overshadow the linear dependencies.
Tables 2 and 3   Stepwise backwards regression model Abbreviations and symbols: LAI = leaf area index; Tmin and Tmax = mean monthly minimum and maximum air temperature, respectively; Number days under 0°C = the number of days in a year with mean daily temperature below zero.RUE ann for cold and temperate forests, respectively, and 44 and 88% of the spatial variability of RUE max for cold and temperate forests, respectively.However, note that a high number of variables were retained in the best models (see Tables 2 and 3).
As mentioned above, we also carried out an analysis on the entire data set, without separating forests into the cold and temperate categories.For RUE ann , both temperature-related variables (important for cold forests) and drought-related variables (important for  RUE max was weakly related to the examined variables (Table 5).
For RUE ann , for five (out of six) cold forests and three (out of five) temperate forests, interannual variability was not related to any variable.Moreover, the other sites only showed significant relationships with one or two variables per site (variables involved: mainly evapotranspiration and precipitation but also Tmax; see Table 5).For RUE max , significant relationships were found only for three cold forests and one temperate forest.The interannual variability of RUE max was explained mainly by evapotranspiration and precipitation, with some weak relationships (.05 < p < .10)with temperature-related variables (see Table 5).
Table 6 and Supporting Information Appendix S8 report the results of the short-term variability analysis of RUE 8days for the whole season and for each season separately (i.e., spring, summer, autumn).The variables selected were generally correlated with RUE 8days , particularly for cold forests.In fact, for cold forests, RUE 8days was significantly correlated with (a) potential evapotranspiration at five sites (out of six), (b) Tmean and Tmin at four sites, and with (c) VPD, annual precipitation and Tmax at about half of the sites.For temperate forests, only three of the five sites presented significant correlations between RUE 8days and the examined variables (Table 6).SBRA showed in general R 2 between .21 and .61(Supporting Information Appendix S9).The low R 2 of some of the SBRAs may be related to the fact that important variables were not considered and/or because of nonlinear relationships.
When analysed for the three seasons, cold forests presented two main results.First, cold forests showed the strongest relationships between RUE 8days and the environmental factors in summer, for both temperature-and drought-related variables and for all sites.Second, the drivers of RUE 8days in spring (mainly VPD, Tmean and Tmin) were different to the drivers of RUE 8days in autumn (mainly evapotranspiration, Tmax and precipitation) and in any case less relevant (e.g., significant at about half of the sites).
For temperate forests, RUE 8days appeared to be related to environmental factors mainly in summer and autumn (with dependencies for both temperature-and drought-related variables at most sites) but to be conservative in spring (with only one variable important at one site).The fact that (low) temperature plays an important role in the eco-physiology of trees in the cold zone is not surprising.Subfreezing temperatures stop photosynthesis, because leaf stomata are forced to close (Waring & Running, 1998).Moreover, negative effects of freezing on RUE could be related to direct frost damage to the leaves (Marchand, 1996) or to indirect, freezing-induced damage to the hydraulic system that supplies leaves with water and nutrients (e.g., freezing-induced xylem cavitation) (Jackson, Sperry, & Dawson, 2000;Sperry, Nichols, Sullivan, & Eastlack, 1994;Sperry & Sullivan, 1992).Our temporal analysis showed that drought-related variables (e.g., VPD) were also important to determine RUE of cold forests but mainly in summer.Thus, they should not be neglected for seasonal Furthermore, more leaves (i.e., higher LAI) correspond to a higher fAPAR.

| D ISCUSS I ON
The key role of nutrient availability in affecting plant and ecosystem processes is well known.In particular, high N availability allows the maintenance of high Rubisco concentration in the leaves, which contributes to a high photosynthetic capacity (Field, Merino, & Mooney, 1983).However, the role of nutrient availability in determining RUE was unclear (Table 1).Our study shows no impact of leaf N or site fertility but a positive impact of N deposition.This indicates the relevance of a fertilization effect, which might be more important than actual N pools (leaf and soil N) and more important in colder (typically nutrient limited) high latitude areas.The past uncertainty in understanding the effect of N deposition on RUE might also have been related to the quality and representativeness of N deposition data.In this work, we used very recent global simulations for N deposition for the period 2004-2006(Ackerman et al., 2018)).
The effect of CO 2 concentration was found to be of some significance but not a key driver of RUE as found by De Kauwe et al. (2016).
This might be due to the fact that we analysed natural variability Our study is difficult to compare to the one of Wang et al. (2017) on a universal mechanism driving RUE across biomes, as the studies are methodologically very different.For instance, our seasonal short-term analysis of RUE variability could have not taken into account factors found to be important by Wang et al. (2017), such as the ratio of internal leaf CO 2 to external CO 2 , or elevation.On the other hand, both studies found that temperature and a droughtrelated variable [Wang et al. (2017) considered VPD, we potential evapotranspiration; Table 6] are crucial determinants of the shortterm variability of RUE.
Two general remarks should also be made concerning our study.
First, the short-term temporal analysis clearly revealed differences among sites, with some sites showing stronger relationships between RUE and the environment than others.This might be the reason why so many contrasting results have been found about the environmental drivers of RUE dynamics in the past (Table 1).Second, one general difficulty in understanding the effects of environmental variables on RUE is finding a good surrogate of each environmental factor at the global scale and their availability at daily to annual time-scales.The accuracy of available meteorological data is of particular importance for modelling the RUE dynamics of ecosystems under stress conditions such as drought.Moreover, note that under drought conditions other specific factors might also play a role as determinants of RUE (Garbulsky et al., 2010;Goerner et al., 2009;Stocker et al., 2018).
In summary, our study synthesized existing knowledge on the determinants of the variability of RUE in cold and temperate forests and tested their potential roles as predictor variables considering a high number of sites in the Northern Hemisphere.We found that, on average, RUE ann and RUE max do not differ markedly between equations parameterized for one index cannot be used for the other index.Our analysis showed also that RUE max is less related to environmental conditions than RUE ann .This helps modelling and remote sensing applications.In detail, while RUE max for cold forests depends on two variables (LAI and N deposition), RUE max of temperate forests is not related to any variables.So, the latter might be used as a constant.Finally, concerning the temporal variability, our analysis at a short-term scale (i.e.8-day), indicated that the relationships between RUE and predictors differ when the whole growing season or spring, summer and autumn are considered separately.On the other hand, interannual variability of RUE ann and RUE max was less related to the environment.
e., mean maximum minus mean minimum temperature)]; (b) water status variables [vapour pressure deficit (VPD), precipitation, intensity and duration of drought, evaporative fraction, actual and potential evapotranspiration, soil water content and deficit, irrigation]; (c) radiation-related variables [diffuse light and leaf area index (LAI)]; (d) variables related to leaf and vegetation characteristics [stand age, leaf habit and type and biome type] and (e) fertility-related variables [nitrogen (N) deposition, leaf N, management and CO 2 concentration].The relevance of these factors is reviewed below based on the literature.
tested the thermal amplitude and the length of the warm season, finding them not relevant to RUE variability.(b) Water status variables.Water limitation is generally expected to reduce RUE because of reduced photosynthesis following reduction should be considered in the formulation of climate zone-specific tools for remote sensing and global models.K E Y W O R D S meteorological and vegetation influences, forest ecosystems, gross primary production, light use efficiency, meta-analysis, short-term variability, spatial and temporal variabilities TA B L E 1 List of the vegetation and environmental drivers tested in the literature as potential drivers of radiation use efficiency (RUE) in forests = significant impact; 0 = no significant impact.Abbreviations: Potential drivers: LAI = leaf area index; AET = actual evapotranspiration; PET = potential evapotranspiration.Variables used to calculate RUE: GPP = gross primary production (measurement methods of GPP: EC = eddy covariance; ANPP = measurements based on aboveground net primary productivity; P = simulated by processed based models); APAR: absorbed photosynthetically active radiation; fAPAR: fraction of APAR; (measurement methods of fAPAR: I = derived from in situ optical LAI or radiation measurements; P = simulated by processed based models; RS = derived from satellite data).
photosynthesis and radiation absorption vary daily over the growing season and, potentially, among years.Therefore, here, we aim to elucidate the spatial (across the Northern Hemisphere) and temporal (short-term, annual and interannual) variability of RUE in temperate and cold forests by comparing the impact on RUE and RUE max of several potential drivers.The short-term variability refers to the variability of RUE among 8-day time windows (RUE 8days ), as 8 days is a common time reference for remote sensing.The focus on RUE 8days, RUE ann and RUE max offers the most comprehensive insight into RUE dynamics and their possible implementation in global monitoring tools.
PAR.The cumulative annual value of PAR (PAR ann ) and 8-day PAR (PAR 8days ) were calculated, for every site-year combination, from seasonal daily data for PAR using (a) free fair-use data files from the Fluxnet and European Fluxes Database Cluster (69% of the sites) and (b) the EC-JRC-MARS data set for the remaining sites.(a) In the Fluxnet and European Fluxes Database Cluster files the measurement of the incoming radiation in the PAR region (400-700 nm) is reported.(b)EC-JRC-MARS reports only total shortwave incoming radiation.We therefore multiplied the radiation by a factor of 0.45, assuming that about 45% of the total incoming shortwave radiation is in the PAR region(Campbell & Norman, 1998).The physical unit of the total shortwave radiation reported in the EC-JRC-MARS database is MJ/m 2 /day.
calculated the annual aridity index as the ratio of annual precipitation to annual evapotranspiration.VPD (in kPa) is the difference between the saturation vapour pressure (e s , kPa) at air temperature and actual vapour pressure (e a , kPa) (Allen, Pereira, Raes, & Smith, 1998): where T is the air temperature (°C) and RH is the relative humidity (%).Mean daily values of VPD over an 8-day time window and the annual mean of daily values were used in our analyses.RH data were available from the Fluxnet and European Fluxes Database Cluster for 89% of the sites, while for the other sites we used data from the public online Global Weather Data for soil & water assessment tool (SWAT) (Dile & Srinivasan, 2014; Fuka et al., 2014) that provides interpolated RH from local meteorological stations.Cloud cover was used as a proxy of diffuse light, as the latter is a parameter that is not generally measured by meteorological stations and flux towers.We extracted cloud cover data (mean annual value as percentage) from Climatic Research Unit (CRU) Time-Series Version 3.22 (Harris & Jones, 2014).(b)Soil fertilityThe soil type of each site was derived from the food and agriculture organization (FAO) digital Soil Map of the World Version3.6(FAO,   2007).Subsequently, soil types were classified into three levels (H: high, M: medium, L: low) of nutrient availability (see Supporting Information Appendix S1), based on fertility information reported in Creutzberg (1987).
data set compiled by the Institute for Atmospheric and Climate Science at the Eidgenössische Technische Hochschule in Zürich (Switzerland) for the Northern Hemisphere (https ://www.co2.earth/ histo rical-co2-datasets).
Abbreviations and symbols: LAI = leaf area index; Tmin and Tmax = mean monthly minimum and maximum air temperature, respectively; Number days under 0°C = the number of days in a year with mean daily temperature below zero.○ = .05< p < .10;* = .01< p < .05;** = .001< p < .01;*** = p < .001;(+) = positive linear regression; (-) = negative linear regression.a Variable type: "con." when continuous; "cat." when categorical.b For continuous variables, the significance level of the linear regression (p) and adjusted R 2 are reported, with "sign" as the sign of the linear regression.For categorical variables, we report results of one-way ANOVA (p value) and post hoc Tukey's honestly significant difference (HSD) test (absolute difference for two significantly different factors and p value of the difference).c For SBRA, we report the variables of the final model, representing the key predictors of RUE, and (in the last row) the coefficient of determination (R 2 ) of the final model; d Soil fertility was classified as H = high; M = medium; L = low.e Leaf habit was classified as N = needleleaved; B = broadleaved; BN = mixed habit.f Leaf type was classified as D = deciduous; E = evergreen.g Leaf N: variable tested only for univariate analysis as with fewer sites than other variables (cold: n = 11; temperate: n = 12).
also show linear models combining multiple predictors.The models explained 57 and 38% of the spatial variability of TA B L E 3 The impact of vegetation and environmental drivers on maximum radiation use efficiency (RUE max ) for cold (n = 20) and temperate forests (n = 20), from univariate analysis and stepwise backwards regression analysis (SBRA) Abbreviations and symbols: LAI = leaf area index; Tmin and Tmax = mean monthly minimum and maximum air temperature, respectively; Number days under 0°C = the number of days in a year with mean daily temperature below zero.○ = .05< p < .10;* = .01< p < .05;** = .001< p < .01;*** = p < .001.(+): positive linear regression; (-): negative linear regression.a Variable type: "con." when continuous; "cat." when categorical.b For continuous variables, the significance level of the linear regression (p) and adjusted R 2 are reported, with "sign" as the sign of the linear regression.For categorical variables, we report results of one-way ANOVA (p value) and post hoc Tukey's honestly significant difference (HSD) test (absolute difference for two significantly different factors and p value of the difference).c For SBRA, we report the variables of the final model, representing the key predictors of RUE, and (in the last row) the coefficient of determination (R 2 ) of the final model.d Soil fertility was classified as H = high; M = medium; L = low.e Leaf habit was classified as N = needleleaved; B = broadleaved; BN = mixed habit.f Leaf type was classified as D = deciduous; E = evergreen.g Leaf N = variable tested only for univariate analysis as with fewer sites than other variables (cold: n = 11; temperate: n = 12).
Relative importance of vegetation and environmental drivers for annual radiation use efficiency (RUE ann ) for cold forests (n = 26) and temperate forests (n = 22).Data are from (a) random forest analysis (cold forests: light grey bars, temperate forests: black bars) with variable importance positively related to accuracy of model prediction (%IncMSE), and negative %IncMSE indicating lack of importance and (b) univariate analysis, with significant (p < .10)drivers marked with "*" symbol (see text and Table 2 for details).Abbreviations: Tmin and Tmax = mean monthly minimum and maximum air temperature, respectively; N. days under 0°C = the number of days in a year with mean daily temperature below 0°C F I G U R E 3 Relative importance of vegetation and environmental drivers for maximum radiation use efficiency (RUE max ) for cold forests (n = 20) and temperate forests (n = 20).Data are from (a) random forest analysis (cold forests: light grey bars, temperate forests: black bars) with variable importance positively related to accuracy of model prediction (%IncMSE), and negative %IncMSE indicating lack of importance and (b) univariate analysis, with significant (p < .10)drivers marked with "*" symbol (see text and Table3for details).Abbreviations: Tmin and Tmax = mean monthly minimum and maximum air temperature, respectively; N. days under 0°C = the number of days in a year with mean daily temperature below 0°C temperate forests) were significant.Moreover, other variables, significant for at least one of the two forest types, retained their importance (e.g., cloud cover, LAI, N deposition) (Supporting Information Appendix S4).SBRA on the whole data set produced for RUE ann a model with an R 2 (.38, Supporting Information Appendix S4) similar to that for temperate forests (see above).For RUE max , analyses on the entire data set showed only N deposition and LAI having a significant correlation with it (but aridity index presented p = .08;Supporting Information Appendix S5) with a clear similarity to the behaviour of cold forests (see

of CO 2
concentration (overall 380 ± 8 ppm) whereas De Kauwe et al. (2016) analysed long-term FACE forest sites with CO 2 concentrations ranging from 370 to 550 ppm.A high CO 2 concentration may increase the effect of CO 2 on RUE.
cold and temperate forests, but the influence of different vegetation and environment drivers on RUE does differ significantly between the two climatic zones.These findings primarily indicate that global tools using RUE should differentiate their algorithms between climate zones.For instance, MODIS GPP might improve if current RUE max modulators (temperature, light and VPD) become region-dependent.Also, our study suggests that the use of environmental variables only does not suffice to describe the variability of RUE, and therefore that ecological models based on Monteith's approach should include new parameters that describe plant characteristics such as LAI.N deposition should also be accounted for in modelling RUE of cold forests.Moreover, our results show that, within each climatic zone, RUE ann and RUE max have different relationships with environmental and vegetation variables.Therefore, APAR ann .To calculate RUE max for a year we computed 8-day RUE (RUE 8days ) values for the whole growing season from the ratio between GPP 8days and APAR 8days values.RUE max was defined as the maximum value of the RUE 8days time series.
The physical unit of incoming PAR in the Fluxnet and European Flux Database Cluster is μmol/photons/m 2 /s.We converted PAR from μmol/photons/m 2 /s to J/m 2 /s using a conversion factor of 4.55 μmol/J as proposed byGoudriaan and Van Laar (1994).Finally, we obtained daily values in MJ/m 2 /day by multiplying by 0.0864.For sites with the highest quality based on the Quality Assurance/Quality Control flags provided by MODIS (e.g., clear conditions without snow) were selected and retained for computing fAPAR values.For each year, annual fAPAR (fAPAR annW ) was calculated from weighted fAPAR 8days data where the weighting was provided by PAR 8days data.APAR.Annual APAR (APAR ann ) was computed as fAPAR annW multiplied by the cumulative PAR (PAR ann ).To derive APAR 8days, we multiplied fAPAR 8days by the PAR 8days .GPP.GPP data (annual comulative GPP) and 8-day GPP (GPP 8days ) were derived from publicly available databases of forest ecosystem carbon fluxes (Luyssaert et al., 2007, Fluxnet, European Flux Database Cluster).F I G U R E 1 Map with distribution of sites: cold forests and temperate forests are represented with red and blue circles, respectively [Colour figure can be viewed at wileyonlinelibrary.com]RUE ann , RUE max and RUE 8days .According to Monteith's equation (Equation1), we calculated RUE ann as the ratio between GPP ann and to complete the group of determinants with the addition of some new variables related to soil fertility, number of days with mean daily temperature below zero (i.e., freezing period) and duration of the longest period without rain.These variables were determined for each site and year for which RUE ann was available, except for LAI and leaf N concentration, for which data were not consistently available for all years (averages were made with the available data) Three main analyses were performed: univariate analysis, random forest and linear models with multiple predictors.Analyses on leaf N were limited to the univariate analysis (see below), because we did not have leaf N available for all sites (see above).(a) To describe the correlation between each predictor and RUE ann and RUE max , we conducted univariate analysis for each variable.We used single linear regression for continuous variables and one-way ANOVAs with post hoc Tukey's honestly significant difference (HSD) test for categorical variables.
(Breiman, 2001)normality test and Levene's test for homoscedasticity were always passed.(b)We used random forest analysis(Breiman, 2001)to estimate the relative importance of the different variables.This analysis ranks the factors from the one with the strongest impact to the one with the lowest impact, while not exclusively considering linearity but also other, nonlinear, types of relationships.The ranking is based on the mean decrease in accuracy of model prediction (%IncMSE) when the variable is randomly permuted.We used a standard random forest algorithm(Liaw &moving the least important ones.The original model was compared with the new model, with one variable removed, by using the likelihood ratio and Akaike information criterion (AIC).The new model was not accepted if the likelihood ratio was significant (p < .05)or the AIC increased (i.e., we considered as the final model the one that respected those assumptions).

Potential predictor Cold forest (n = 26) Temperate forest (n = 22) Variable type a Univariate analysis b SBRA c Univariate analysis b SBRA c p value Adj. R 2 (sign) Post hoc p value Adj. R 2 (sign) Post hoc
TA B L E 2 The impact of vegetation and environmental drivers on annual radiation use efficiency (RUE ann ) for cold (n = 26) and temperate forests (n = 22), from univariate analysis and stepwise backwards regression analysis (SBRA)

. years RUE ann RUE max Mean SD Mean SD
One of the main findings of this study is that, on average, cold and temperate forests exhibit very similar RUE ann (c.1.1 gC/MJ) and RUE max (c.0.8 gC/MJ) but their relationships with vegetation and environmental drivers differ significantly.Also, the drivers of RUE ann differ from the drivers of RUE max within each forest type.More in detail, RUE ann of cold forests is influenced by mainly variables related Statistics (mean and SD) for interannual variability in annual (RUE ann ) and maximum radiation use efficiency (RUE max ) in cold and temperate forests.Sites' full names can be found in Supporting Information Appendix S1 RUE is strongly related to the environmental conditions, particularly in summer.This evidence was valid for both cold-and temperate forests.TA B L E 4 10 B L E 6 Results of univariate analysis for short-term variability in radiation use efficiency (RUE 8days ) of cold and temperate forests, for the whole growing season and spring, summer and autumn separately.Cells in orange are for correlations with p ≤ .05 and in yellow for correlations with .05<p≤ .10.All detailed data (p and adjusted R 2 ) are reported in Supporting Information Appendix S8.Data are reported for six cold and five temperate forest sites.Sites' full names and descriptions can be found in Supporting Information Appendix S1 Our results support previous findings that identified droughtrelated variables (e.g., annual precipitation, aridity index, longest period without rain, VPD) as highly significant determinants of RUE for temperate forests.The negative relationship between drought and RUE in temperate forests is related to the fact that drought impacts on stomatal conductance and restricts the photosynthe- modelling of RUE but it is also clear that they did not emerge in the annual analyses of either RUE ann or RUE max .greatercloud cover improves the photosynthetic efficiency by decreasing the denominator of Equation 1 at similar values of GPP.