Radiative transfer modelling reveals why canopy reflectance follows function

Optical remote sensing is potentially highly informative to track Earth’s plant functional diversity. Yet, causal explanations of how and why plant functioning is expressed in canopy reflectance remain limited. Variation in canopy reflectance can be described by radiative transfer models (here PROSAIL) that incorporate plant traits affecting light transmission in canopies. To establish causal links between canopy reflectance and plant functioning, we investigate how two plant functional schemes, i.e. the Leaf Economic Spectrum (LES) and CSR plant strategies, are related to traits with relevance to reflectance. These traits indeed related to both functional schemes, whereas only traits describing leaf properties correlated with the LES. In contrast, traits related to canopy structure showed no correlation to the LES, but to CSR strategies, as the latter integrates both plant economics and size traits, rather than solely leaf economics. Multiple optically relevant traits featured comparable or higher correspondence to the CSR space than those traits originally used to allocate CSR scores. This evidences that plant functions and strategies are directly expressed in reflectance and entails that canopy ‘reflectance follows function’. This opens up new possibilities to understand differences in plant functioning and to harness optical remote sensing data for monitoring Earth´s functional diversity.

Through natural selection plants have diversified in various functions in order to adapt to environmental conditions, including abiotic factors (e.g. precipitation or nutrient gradients) and biotic interactions (e.g. competition or herbivory). Assessing patterns of plant functioning in space and time is a prerequisite to understand biosphere-atmosphere interactions and ecosystem dynamics such as community assembly or nutrient cycles [1][2][3][4][5] . With accelerated global change the data demand on patterns of plant functioning has increased, as the latter is heavily affected by anthropogenic impacts [6][7][8][9] . However, due to vast temporal and spatial variation in plant functions, and the complexity to retrieve the latter in an explicit, consistent and spatially exhaustive way, data of Earth's plant functional diversity remain limited 5,10 . To close this gap optical Earth observation data is potentially highly informative 11,12 . During recent years, various studies have demonstrated that optical Earth observation data allows mapping variation in plant functioning, functional types and strategies [13][14][15][16][17][18][19][20] . However, it often remains unclear why we can remotely sense differences in plant functioning 11,21,22 . To fully harness the potential of Earth observation data and to improve available algorithms, it is crucial to understand the underlying processes that enable us to monitor plant functioning. The key to such understanding are the traits that contribute to canopy reflectance.
The mechanics of solar radiation in plant canopies, including light emitted from plant canopies and thus retrievable from Earth observation sensors, is already well understood and formulated in process-oriented models, i.e. canopy radiative transfer models (RTMs). Although radiative transfer is determined by traits with relevance for plant functioning, few studies have explicitly linked RTMs and plant functioning 19,23,24 . Such RTMs are particularly determined by canopy characteristics defining the amount of light being intercepted or scattered by the foliage as well as foliage properties (e.g. leaf constituents or structure) defining leaf internal scattering, absorption and transmission rates. Here, we assess the distribution of these traits along plant functional gradients, because knowing more about the links between optically relevant traits and plant functioning allows for mapping and monitoring plant functions in a more mechanistic way. This could dramatically improve the robustness and transferability of our models. Furthermore, it can be assumed that bridging plant functioning and canopy reflectance with radiative transfer theory can increase our understanding of how environmental factors and biotic interactions shape plant functional diversity 11 (Fig. 1).

Results
Optically relevant traits versus Leaf Economic Spectrum. Which role do optically relevant traits play in relation to the LES? The set of optically relevant plant traits (compare Table 1) can be summarised using a three-dimensional feature space (Fig. 3), built by a principal component analysis, with component 1, 2 and 3 explaining 28%, 26% and 16% of the total variation, respectively. The LES was projected to this three-dimensional trait space to visualise relationships with optically relevant traits. As expected, LMA, as one of the original constituents of the LES, showed the highest correlation with the LES (−0.68 Pearson's r). A lower yet positive correlation (p < 0.05) existed with pigment contents measured on a mass basis, i.e. Cab mass (r = 0.42), Car mass (r = 0.53), Ant mass (r = 0.52), indicating decreasing pigment concentrations with increasing resource investments. Pigments measured on an area-basis also correlated significantly but negatively with the LES, i.e. Cab area (r = −0.45), Car area (r = −0.44), so that pigment contents predominantly increased with slow and conservative growth. Mesophyll thickness N meso correlated negatively with the LES (r = −0.40), reflecting higher mesophyll thickness with increasing resource investments. Traits linked to leaf water content (EWT, EWT canopy , LDMC) and canopy structure (LAI, ALA, fAPAR, APAR cum ) were not significantly correlated to the LES. A table with all correlations is provided in S5.
Optically relevant traits versus CSR plant strategies. The distribution of optically relevant traits within the three-dimensional CSR scheme of plant strategies was assessed using thin plate regression splines 32 and Generalized Additive Models (GAM) 33 . Neither EWT nor EWT canopy correlated to plant strategies among forbs or graminoids. In contrast LAI, LMA, LMA canopy , LDMC, pigment mass , fAPAR and APAR cum showed significant and consistent relationships across forbs and graminoids (Fig. 4). Pigment area , N meso , Cbrown and ALA exhibited no consistent relationship to CSR plant strategies across growth forms and thus related differently among forb and graminoid strategies (Figs 4-6). A table summarising the results for all traits is given in S6.

Discussion
Vegetation canopies can be considered as solar power plants and various functions and traits are coordinated to ensure an efficient energy assimilation by adapting to environmental factors (e.g. nutrient availability, temperature) and biotic interactions (e.g. competition) 11,34 . Indeed, our results confirmed that plant functions and strategies are expressed through traits that directly affect or are directly related to optical processes in plant canopies and thus determine their reflectance. This relationship of 'reflectance follows function' firstly provides the physical basis for retrieving differences in plant functions by means of optical Earth observation data, and underlines the potential to track Earth's functional diversity. Secondly, linking plant functions and strategies with radiative transfer provides a different and additional perspective on how environmental factors and biotic interactions shape plant functional diversity.
Why does reflectance of plant canopies follow function? Our results showed strong links between optically relevant plant traits and the two schemes used as baselines for plant functioning, i.e. the Leaf Economic Spectrum (LES) and CSR plant strategies. Originally the LES has been captured through leaf lifespan, LMA, photosynthetic capacity, dark respiration rate, nitrogen and phosphorus content 3 . Indeed, variation of observed LMA showed an strong correspondence to the LES, whereas we also found significant correlations with pigment mass, and pigment area , both of which are directly linked to photosynthetic capacity and nitrogen content 35 . Our results further suggest that pigment content (pigment area ) generally increases with leaf lifespan, whereas the concentration of pigments (pigment mass ) decreases. Thus, plant investment in leaf tissue proportionally outweigh investment in leaf pigment, which can be explained as with increasing chlorophyll content light absorption follows a saturating curve, since chloroplasts become increasingly stacked in the palisade cells resulting in intraleaf shading [36][37][38] . Accordingly, plants with short leaf lifespan invest fewer pigment to optimise energy revenue. However, the LES reflects only one primary dimension of plant functioning, ranging from a quick to slow return on leaf resource investments. Accordingly, the canopy-structure-related traits (LAI, LMA canopy , ALA, fAPAR or APAR cum ) showed no significant correspondence to the LES, suggestingthat these traits are indeed related to other functional axes (Fig. 3). With the 'global spectrum of plant form and function' Diaz et al. have identified two major axes of plant functional convergence, with one axis reflecting leaf resource investments (LES) and the other axis reflecting plant and organ size-related traits. Accordingly, we expected that optically relevant traits integrating canopy properties are associated with the size-related axis. We actually observed such association between canopy-structure-related traits and the multidimensional CSR space, which characterises plant functioning in terms of competitive, stress tolerant and ruderal abilities at the whole plant level 31 . Accordingly, multiple traits that did not exhibit an association with the LES (e.g. LAI, LMA canopy , or fAPAR), in turn showed a notable correspondence to the CSR space. Our results confirmed previous relationships between traits and the CSR space and exhibited gradients that have not been assessed before.
In agreement with pivotal formulations of the CSR scheme 29 and the allocation by Hodgson et al. 39 , LMA was lowest for ruderal species and highest for stress tolerators, closely followed by competitors (Fig. 4). Leaf mass per canopy area, i.e. LMA canopy (LMA • LAI), which was to our knowledge not compared to CSR strategies before, www.nature.com/scientificreports www.nature.com/scientificreports/ reflects total leaf carbon assimilation per canopy area. We found highest LMA canopy for competitive species, followed by intermediate LMA canopy for stress tolerators and intermediates and lowest values for ruderals. This gradient reflects the primary principles of the plant strategies 29 ; stress tolerators feature a conservative growth with a long leaf lifespan resulting in a steady accumulation of dry matter in the canopy, whereas ruderals are adapted to disturbance events and thus have short lifecycles in which they accumulate few resources. Competitors feature both high productivity and a relatively long lifespan and therefore highest resource accumulation (LMA canopy ).
Both leaf and canopy water content, i.e. EWT [g/cm²] and EWT canopy , did not show a clear relationship with plant strategies. In contrast LDMC, which is the ratio of leaf mass and leaf water content (LDMC = LMA/ (LMA + EWT)), showed a clear coherence towards plant strategies and was therefore already used by Hodgson et al. 39  www.nature.com/scientificreports www.nature.com/scientificreports/ to allocate CSR scores. This suggests that functional characteristics are expressed through the relative water concentration in leaf tissue, rather than the absolute leaf water content.
A more complex pattern was found for LAI, where intermediate species (CSR) have highest LAI values followed by competitors, and lowest LAI values correspond to high S and R scores. We thus expect that intermediate species (CSR) invest a large share of resources in foliage area, whereas competitors, ruderals and stress tolerators invest more resources towards their strategy-specific trait-expressions and functions. Competitors occur primarily in nutrient rich sites, where competition for sunlight is most pronounced and triggers increased height growth to overtop neighbouring individuals. Increased canopy height in turn requires additional resource investments in support tissues, e.g. in the stem for vertical plant growth itself as well as in enhanced leaf robustness (higher LMA), to compensate for increased exposure to wind (compare LMA gradient, Fig. 4) 40 . An increased LMA was also found for plants adapted to high light intensities (competitors) through increased palisade parenchyma to maximise photosynthetic capacity and thus quantum yield per unit leaf area and reduce potential light saturation 41,42 . This suggests that relative to intermediate strategies, competitors invest fewer resources in the development of total foliage area (LAI). Therefore, competition for sunlight might enforce a trade-off between the maximisation of height growth and light interception. This agrees with Porter et al. 43 , who have reported higher accumulation of leaves for shade tolerant species leaves with smaller canopy heights among tropical tree species.
Leaf inclination (ALA) did not show a trivial correspondence to the CSR spectrum, but differed between growth forms, reflecting generic differences in the canopy architecture of graminoids and forbs. Variation in leaf angles across graminoid strategies showed no explicit pattern. For forb strategies ALA increased from competitive forbs to stress tolerant and ruderal forbs (Fig. 5). This agrees with Hikosaka & Hirose 44 , who have simulated leaf angle distributions for plant canopies and found lower leaf angles with increasing competition. Competitive forbs, which aim to overtop and shade out the surrounding and competing plants, develop rather flat leaf angles to deplete or scatter most of the light before it is available for rivals. However, a horizontal leaf position requires increased support costs for petioles and branches, and is generally less efficient for light absorption as self-shading and light saturation increases 44,45 . Leaf angles hence increase with decreasing competition to scatter light between leaves and hence distribute light into the lower canopy 44,46 .
Similar to the LES-based analysis, the derived distributions of chlorophylls, carotenoids and anthocyanins across the CSR space are very alike (Figs 4, S6), since pigments are usually highly correlated in mature leaves 27 . Yet, the relationships differed greatly among pigments measured on an area basis (pigment mass ) and measured on a mass basis (pigment area , Figs 6, S6). The relationship between pigment area and CSR strategies further differed between forbs and graminoids (Fig. 6), which agrees with Tjoelker et al. 47 , who has found differences in leaf photosynthetic activity between grasses and forbs. For forbs ruderals and intermediates feature highest pigment area . Among graminoid strategies pigment area showed a low and inconclusive variation across the CSR space apart from a strong increase for extremely stress tolerant graminoids (Festuca ovina and Nardus stricta).
Pigments normalised by mass (pigments mass ) showed a very consistent gradient across growth forms (S8), which however almost exclusively mirrors the LMA gradient (r² of 0.74, 0.80, 0.85 for Cab mass , Car mass , Ant mass , respectively). This is further confirmed as the modelled pigment mass values across the CSR-space were highly www.nature.com/scientificreports www.nature.com/scientificreports/ correlated with pigment mass values based on a null-model, in which we sampled random pigments area values that were subsequently divided by LMA and thus mass normalised (r² of 0.80, 0.91, 0.64 for Cab mass , Car mass , Ant mass , respectively). Accordingly, we found that pigments mass indeed do not reflect pigment variation per se, but rather the LMA gradient, which varies in higher magnitudes than traits with photosynthetic function 48,49 . Likewise the strong correspondence between pigments mass and the LES can largely be attributed by the high variation in LMA, as indicated by the null-model (S9). This indicates that the characterisation of plant canopies through pigments on a mass basis is greatly redundant with LMA and therefore appears to be not expedient, despite its frequent use in the remote sensing community 50,51 .
The distribution of simulated fAPAR across the CSR space showed a strong correspondence to LAI (Fig. 4), suggesting that variation in light harvesting is particularly determined by LAI (in line with 44,46,52 ) and therefore highest for intermediate strategies followed by competitors. Yet, fAPAR solely represents the potential energy gain at a point in time and thereby does not consider phenological differences between plant strategies. Accordingly we modelled the accumulated photosynthetic active radiation APAR cum . This measure integrates fAPAR and the course of absorbed direct and diffuse radiation (assessed from HelioClim-3 archives 53 ) during a plants phenological season (recorded for the cultivated plants). APAR cum thus reflects the accumulated photosynthetic and carbon assimilation during a plant´s growth period 54 . APAR cum showed a very consistent and clear pattern across growth forms. Corresponding to their short growth period ruderals featured the lowest APAR cum . Intermediate APAR cum was found for stress tolerators, as these can compensate conditions that limit productivity through robustness and persistence, resulting in a comparably low but prolonged light harvesting. Highest APAR cum was found for competitors, as competitive abilities require long-term investments (e.g., height growth) that are rewarded with long-term returns. These results thus showed that the phenology-dependent variation in energy acquisition directly reflects established plant strategies and functions. Moreover, the comparable strong relationship with APAR cum emphasised that gradients in plant productivity are not fully reflected by a single biochemical or structural trait, but relate to the integrated response of pigments, LAI, ALA as well as phenology 22 . This particularly highlights the potential of multi-temporal Earth observation data to map functional gradients. The overall strong correlation between gradients derived from APAR cum and LMA canopy (r² = 0.88) underlines the plausibility of the models, as a large share of the absorbed energy is used for carbon assimilation in leaves 35 . The minor discrepancy between APAR cum and LMA canopy existed for competitors, where photosynthetic assimilation (APAR cum ) is highest, but LMA canopy showed a slight bias towards C-CSR, which could result from competitors investing a considerable part of their resources in height growth rather than total leaf tissue.
According to our results Cbrown and N meso did not show a consistent relation with the CSR strategies across growth forms. Both traits only corresponded to CSR strategies among graminoids (S7). In agreement with Jacquemoud & Baret 55 N meso correlates with LMA. The distribution of Cbrown could not be explained in an  www.nature.com/scientificreports www.nature.com/scientificreports/ ecological context. Overall, Cbrown and N meso have a relatively low impact on canopy reflectance 56 and do not greatly contribute to the spectral differentiation of variations in plant functioning 57 .
All trait measurements used in this study were retrieved from plants cultivated under optimal growth conditions. It can be expected that some traits more explicitly express their functional role under non-optimal environmental conditions. For instance, increased leaf anthocyanin content has been observed during pathogen infections 58 . Furthermore, a plant's ability to cope with excess incident radiation can be expressed through developing ample leaf carotenoid content 27 .
A limitation of our study was the initial definition and selection of plant traits. Plant traits such as Leaf Area Index and the Average Leaf Angle are abstractions of complex canopy structural properties, and may not fully reflect subtle differences in plant functioning. Further errors are introduced by the trait measurementsand the analysis, such as GAM extrapolations, and the abstraction of plant functioning in the CSR model 29 and the LES 3 . Yet, given that plant functioning and the radiative transfer in plant canopies are two complex fields on its own, empirically testing the links between these two realms requires a certain level of abstraction. Despite these uncertainties, our results showed unprecedented links between functioning and reflectance, hopefully triggering further advances towards this field using more sophisticated methods.

Conclusion and Outlook
Optical remote sensing data is potentially highly informative to track Earth's functional diversity. Yet, causal explanations on why plant functioning can be differentiated using canopy reflectance sensed by optical Earth observation data remain limited. Our findings demonstrate that bridging ecological theory and canopy reflectance through radiative transfer modelling enables us to identify causal links between canopy reflectance and plant functioning. These links suggest that canopy 'reflectance follows function' , meaning that adaptations of plants to their environment are directly 'reflected' in their optical properties across the visible, near and short wave infrared wavelengths. More specifically plant functions and strategies are considerably expressed through multiple structural, physiological and phenological traits with relevance for canopy reflectance and thus optical Earth observation data. This opens up new opportunities for understanding plant functional changes in space and time. Increasing the dimension of relevant traits for an ecological system allows us to more precisely and completely understand and predict ecosystem dynamics and ecological processes such as community assembly 59 . Furthermore, trait ecology may lack a sufficient variety of traits to capture dissimilarities and explain competition among species 60 . As shown here optically relevant traits depict variations in multiple plant functions and can thus complement the suite of determinable proxies to describe spatial variation in plant functioning and community assembly. This is particularly emphasised as several optically relevant traits show comparable or even stronger correlations with CSR plant strategies (LAI, LMA canopy , APAR cum ) than traits used originally to allocate the CSR space (e.g. LMA or LDMC 39 ). Upcoming hyperspectral satellite missions such as EnMAP 61 or HyspIRI 62 will provide optical reflectance products that are sensitive to the traits considered in this study. Our results therefore encourage further research to deepen our understanding how plant functioning is expressed through optically relevant traits using more extensive trait data and further traits incorporated in more complex radiative transfer models (e.g., crown architecture), such as INFORM 63 or FLIGHT 64 .

Material and Methods
Retrieval of the traits space implemented in PROSAIL. We derived the PROSAIL trait space from outdoor cultivated plants, including 45 forb and graminoid species covering the full range of the CSR spectrum ( Table 2). We performed seed propagation in greenhouses and moved the plants outdoor for a week of acclimatisation once they were grown to an adequate size. Afterwards the plants were planted out in four repetitions in separate pots with a size of 0.4 m • 0.4 m and 30 l volume filled with a standardised substrate. Fewer repetitions had to be planted for species where seedling propagation was less successful. All pots were regularly fertilised, weeded and irrigated.
For each species we measured the considered traits on a weekly basis for each pot. We determined the species-specific trait expressions by averaging the measurements among pots and subsequently calculating the median for the whole season. We only considered measurements that were performed in non-senescent canopies of adult plants (here defined as plants with closed canopy).
In view of the envisaged amount of measurements per species traditional approaches for pigment retrieval such as the spectrophotometer method by Lichtenthaler 65 was not feasible. Furthermore, N meso and Cbrown are specific parameters of PROSPECT. We measured leaf chlorophyll content (Cab area ), carotenoid content (Car area ), anthocyanin content (Ant area ), mesophyll structure coefficient (N meso ) and brown pigment content (Cbrown) using leaf reflectance spectra and their inversion using the leaf radiative transfer model PROSPECT-D 27 . We acquired leaf spectra of 5 individual leaves per cultivated pot using an ASD FieldSpec III (ASD, Inc. Boulder, CO, USA) attached with a plant probe and leaf clip. If the area of a leaf was smaller than the opening of the plant probe (3.14 cm²) we seamlessly, and without overlap, placed the leaves side by side on an adhesive tape. The inversion of PROSPECT-D was based on a look-up-table approach and wavelets [66][67][68] . Further details on the inversion procedure and its validation are given in S1.
We estimated LAI using an Accu-PAR LP-80 ceptometer equipped with an external reference sensor to account for the current photosynthetic active radiation (PAR). For each pot we recorded and subsequently averaged 18 individual measurements.
To limited the destructice impact over time, we measured leaf mass per area (LMA) and equivalent water thickness (EWT) per species rather than per pot. Samples consistend of leaflets only without petioles and rachis. Fresh leaf mass of around 10 g of whole leaves per species was measured on site. Total leaf area of these leaf samples was retrieved using a flatbed scanner. The LMA [g/cm²] was derived by drying the sample material at 70 °C for at least 72 h. EWT [mg/cm²] was derived by subtracting LMA from leaf fresh mass per area.
www.nature.com/scientificreports www.nature.com/scientificreports/ The ALA was retrieved from leaf inclination distributions that we determined using levelled digital photograph and the procedure described by Ryu et al. 69 . For each species we measured not less than 50 angles of leaves parallel to the viewing direction. Leaf angle distributions and ALA were only retrieved once due to logistic constrains.
We deduced additional traits from the PROSAIL traits space to further exploit its information content: leaf dry matter content (LDMC = LMA/(LMA + EWT)); canopy leaf mass per area (LMA canopy = LMA • LAI); canopy pigment content (pigment canopy = pigment area • LAI); fraction of absorbed photosynthetic active radiation (fAPAR) simulated using PROSAIL (details in S3) 25 ; cumulative absorbed photosynthetic active radiation (APAR cum in kWh/m²), which corresponds to the total absorbed energy within the growing season of each species. The APARcum was calculated as the product of fAPAR, direct and diffuse irradiance averaged for April-October (data assessed from HelioClim-3 data 53 , details in S3) and the length of the growing season, (here defined as the observed number of weeks between maturity and senescence). A statistical summary of the trait space is given in S2. Wright et al. 3 determined the LES using the first component of a principal component transformation of six leaf traits, i.e. LMA, photosynthetic assimilation rate mass , leaf nitrogen mass , leaf phosphorus mass , dark respiration rate mass , and leaf lifespan. From those traits we only measured LMA (or SLA respectively) within the above described plant experiment. We therefore requested the remaining traits from the TRY-database, where sufficient data was available for 26 of the 45 species (see S4 for a list of the 26 species) and two further traits, leaf nitrogen mass , leaf phosphorus mass . We determined the LES for the 26 species using the log10 transformed expressions of these three traits and the loadings reported by Wright et al. 3 . The LES retrieved this way was compared to each of the optically relevant traits using Pearson´s correlation coefficient. Additionally, the relationship among the different optically relevant traits and their relation to the LES was visualised by means of a principal component analysis (PCA). Therefore, we built a PCA of the PROSAIL trait space on which the LES was projected using the function ('envfit' of the vegan package). Prior to the PCA the PROSAIL traits were centered and scaled.

Linking the Leaf Economic Spectrum and optically relevant plant traits.
Linking CSR plant strategies and optically relevant plant traits. The position of a species in the CSR space is defined by three axes expressing competitive, stress tolerant and ruderal abilities (scores). We used the CSR scores provided by Hodgson et al. 39 , who allocated CSR strategies for a multitude of European plant species using trait expressions of canopy height, LDMC, flowering period, flowering start, lateral spread, LMA and specific leaf area (Table 2). For some species we adopted the allocation from the BiolFlor database 70 and expert knowledge.
We assessed the relationship between each PROSAIL trait and the CSR space using Generalized Additive Models (GAM) 33 and thin plate regression splines 32 . As input for the GAM we used the first two PCA components (cumulative variance 97%) instead of the raw CSR scores to facilitate the interpretability of the results. The results were visualised in ternary plots (R-package 'ggtern') 71 .