Using structure to model function: incorporating canopy structure improves estimates of ecosystem carbon flux in arctic dry heath tundra

Most tundra carbon flux modeling relies on leaf area index (LAI), generally estimated from measurements of canopy greenness using the normalized difference vegetation index (NDVI), to estimate the direction and magnitude of fluxes. However, due to the relative sparseness and low stature of tundra canopies, such models do not explicitly consider the influence of variation in tundra canopy structure on carbon flux estimates. Structure from motion (SFM), a photogrammetric method for deriving three-dimensional (3D) structure from digital imagery, is a non-destructive method for estimating both fine-scale canopy structure and LAI. To understand how variation in 3D canopy structure affects ecosystem carbon fluxes in Arctic tundra, we adapted an existing NDVI-based tundra carbon flux model to include variation in SFM-derived canopy structure and its interaction with incoming sunlight to cast shadows on canopies. Our study system consisted of replicate plots of dry heath tundra that had been subjected to three herbivore exclosure treatments (an exclosure-free control [CT], large mammals exclosure), and a large and small mammal exclosure [ExLS]), providing the range of 3D canopy structures employed in our study. We found that foliage within the more structurally complex surface of CT canopies received significantly less light over the course of the day than canopies within both exclosure treatments. This was especially during morning and evening hours, and was reflected in modeled rates of net ecosystem exchange (NEE) and gross primary productivity (GPP). We found that in the ExLS treatment, SFM-derived estimates of GPP were significantly lower and NEE significantly higher than those based on LAI alone. Our results demonstrate that the structure of even simple tundra vegetation canopies can have significant impacts on tundra carbon fluxes and thus need to be accounted for.


Introduction
Variation in canopy structure can significantly influence the light environment experienced by leaves within the canopy (Monsi et al 2005) and consequently photosynthetic activity (Brunner 1998).
As such, canopy structure can play a major role in controlling the net exchange of carbon between an ecosystem and the atmosphere (i.e.net ecosystem exchange (NEE)), and thus in determining ecosystem C sink strength (Kramer et al 2002).Due to the relatively low stature of Arctic tundra, it may be tempting to assume that canopy structure plays an insignificant role in controlling tundra carbon fluxes, yet this © 2023 The Author(s).Published by IOP Publishing Ltd assumption is rarely tested (n.b. Williams et al 2014).To date, carbon dioxide (CO 2 ) flux chamber studies (Virkkala et al 2018), larger scale eddy flux studies (Rastetter et al 2010, Stoy et al 2013) and regional scale aircraft and satellite studies (Stow et al 1998, Zulueta et al 2011) have typically relied on estimations of leaf area index (LAI) derived from normalized difference vegetation index (NDVI) (Street et al 2007) to incorporate how variation in vegetation canopies influence NEE.Similarly, current tundra carbon exchange models use LAI (in conjunction with air temperature and light) to predict NEE (Shaver et al 2007).However, recent evidence of significant photosynthetic partitioning within low statured tundra canopies (Magney et al 2016) suggests that shadows cast within tundra canopies have a significant impact on the amount of light reaching foliage.As such, canopy structure will need to be taken into account in tundra carbon models as overreliance on LAI alone likely introduces error in estimates of canopy photosynthetic rates and net carbon flux (Sprintsin et al 2012).Lending further motivation to explicitly account for tundra canopy structure, the low sun angles that typify arctic ecosystems cause dramatic, diurnal dynamics in shadow patterns and light quality that interact with spatial variation in tundra canopy structure to have an outsized impact on light available within tundra canopies for photosynthesis (Stow et al 2004, Buchhorn et al 2016).
While NDVI has been shown to identify small spatial differences in maximum woody shrub height before peak leaf out, once leaves are fully expanded during peak growing season, NDVI and thus LAI more closely tracks variation in canopy cover rather than structure (Boelman et al 2011).Traditional methods for quantifying canopy structure are time consuming, prone to substantial error, and have relatively low spatial resolution (Wall et al 1991, Bréda 2003, Weiss et al 2004).Fortunately, recent advances in remote sensing have enabled rapid, fine-scale, and three-dimensional (3D) quantification of canopy structure (Zellweger et al 2019).For example, many studies make use of light detection and ranging (LiDAR) technology to quantify the structure of plant canopies, including tundra canopies, from either spaceborne, airborne and terrestrial sensors (Omasa et al 2007, Greaves et al 2015, Friedli et al 2016, Magney et al 2016).In addition, structure from motion (SFM) techniques that use twodimensional photographs captured in sequence from a suite of view angles, are being increasingly used as an alternative to LiDAR (Ighaut et al 2019).Using SFM specific software, the photographs are converted to point cloud reconstructions of fine-scale plant canopy structure products similar to those generated using LiDAR (Mathews and Jensen 2013, Zellweger et al 2019, Alonzo et al 2020, Mesas-Carrascosa et al 2020).Importantly however, a major advantage of using SFM over LiDAR technology is that consumer grade RGB cameras can be used instead of specialized LiDAR instruments (Westoby et al 2012, Cunliffe et al 2016, Shafian et al 2018), making SFM a more affordable and widely accessible means of assessing vegetation structure and height.In addition, this method produces a point cloud with color information per point that allows for color based classification methods.Although SFM has been used to map tall shrub biomass in arctic tundra ecosystems (Alonzo et al 2020, Cunliffe et al 2020), it is a relatively new technique that has yet to be widely adopted.
Our overall goal is to understand how variation in 3D canopy structure interacts with diurnal dynamics in sun angle to determine ecosystem carbon uptake in arctic tundra during the period of peak leaf out.To achieve this goal, our objective was to use a SFM-based approach, combined with color vegetation indices and hourly data on ambient light levels and sun angle, to estimate the amount of carbon fixed over the course of a single day by dry heath tundra canopies that differ in 3D structure.We hypothesized that periods of substantial surface canopy shading occur, primarily in more structurally complex canopies and during early morning and late evening hours when both the sun altitude and ambient light levels are low.In turn, this may result in lower estimated rates of CO 2 uptake than those previously estimated by Min et al (2021) for the same dry heath canopies.

Study site
Our study was conducted at the Arctic long term ecological research (LTER) site at Toolik Lake in northern Alaska (68.2 • N, 149.6 • W, 760 m a.s.l.) where a long-term study of mammalian herbivory provided for a range of canopy structures.Briefly, a longterm herbivory experiment was established in 1996 in a dry heath tundra community, which is largely composed of lichen and dwarf deciduous and evergreen shrubs.The experimental design consists of three replicate blocks of 5 m × 20 m plots.Each block had one plot with a 5 m × 10 m exclosurefree portion [CT] that was accessible to herbivores, and a 5 m × 10 m fenced portion surrounded by a large-mesh (15.2 cm × 15.2 cm mesh) fence to exclude only large herbivores such as caribou (Rangifer tarandus).This fenced area was divided in half, with one 5 × 5 m half further surround by a smallmesh fence (1.3 cm × 1.3 cm mesh) to additionally exclude small mammals, such as singing voles (Microtus miurus).This resulted in two different herbivore exclosure treatments per block, with one excluding only large herbivores [ExL], and the other excluding both large and small herbivores [ExLS] (Gough et al 2007).The experimental set up and local environmental conditions are fully described elsewhere (Min et al 2021 and references there in).In each The standard approach used by Min et al (2021) combines carbon flux measurements (Fc ; mmol CO2 m −2 ground s −1 ) made by Min et al (2021), with environmental data (PPFD, photosynthetic proton flux density; mmol photons m −2 ground s −1 ) and T, air temperature; • C) and the Leaf Area Index (LAI, m 2 leaf m −2 ground) estimated from measurements of spectral reflectance (i.e.NDVI) to fit the PLIRTLE model of Shaver et al (2007) and partition the observed NEE to the component fluxes of photosynthesis and respiration (GPP and RE, both in mmol CO2 m −2 ground s −1 ).The current approach incorporates canopy structure (using Structure From Motion (SFM)), and solar ray tracing to determine the fully illuminated and green (i.e.photosynthetically effective) leaf area index (LAIeff), thus accounting for shade within the canopy.LAIeff is substituted for LAI when fitting the GPP portion of PLIRTLE.Finally, carbon flux partitioning between GPP and RE from these two modeling approaches can be compared to the measured fluxes (see Min et al 2021) to assess strength of the model fits.
treatment plot, the measurements described below were made within three circular subplots (75.5 cm diameter) that were selected arbitrarily but at least 0.5 m away from the fences to avoid significant shading and artifacts due to slight changes in snow accumulation immediately next to the fences.As the fences were constructed of thin posts and wire mesh, we do not expect the fences to cast significant amounts of shadow on the subplots aside from when the sun angle and light is lowest, minimizing their impact on our results.All measurements were made between 14 July and 28 July 2017, when the tundra's leaf out was at its characteristic annual peak (Shaver andChapin 1991, Johnson et al 2000).We stress, this current study is not focused on the cause of the observed differences in canopy structure among treatment plots (i.e.herbivory) but instead takes advantage of the resulting variation in canopy structure of the plots.

Overview of study approach
We assess the impact of spatial variation in canopy structure (from SFM) on estimates of NEE by comparing them to previous estimates of NEE that were based only on spatial variation in LAI (from NDVI) (Min et al 2021).By quantifying 3D canopy structure and using light ray tracing, we consider only the surface area of green (i.e.photosynthetically active) portions of the canopy that were illuminated as the sun progressed through the ecliptic plane during a 24 h period in late July.The flow chart shown in figure 1 summarizes the main steps taken in the SFM-based approach used to accomplish this, and compares it to an NDVI-based approach previously used by Min et al (2021) on the same tundra canopies.Details on each of the main steps used in the current approach are described in the sections below.

SFM: canopy surface roughness and 3D structure
Photographs were taken of each subplot using five consumer grade red, green and blue (RGB) wavelength cameras (HERO5, GoPro, San Mateo, CA, USA).The cameras were mounted on the vertical arc of a custom hemispherical and rotatable rig attached to a circular base with an inner diameter of 75.5 cm (i.e.slightly larger than subplots) (figure 2).The rig and base were centered over each subplot with cameras facing inward.To ensure sufficient overlap between images for subsequent processing, the rig was systematically rotated a total of 360 • , with a photograph taken from all five cameras every 3 • -5 • of rotation (Forlani et al 2018).This resulted in hundreds of overlapping photographs per subplot.An external marker was placed directly adjacent to the subplot to indicate north in each photograph.
An image processing software (PhotoScan Professional Edition, Agisoft LLC, St. Petersburg, Russia) was used to convert the combination of photographs taken of each individual subplot into a 3D point cloud.A free 3D point cloud processing software (CloudCompare (version 2.10.2),GPL, retrieved from www.cloudcompare.org/) was used to digitally level, center at the origin, orient north and scale each point cloud, using the camera rig as a reference.In order to exclude areas of each subplot that were in shadow cast by the rig and/or those distorted around the edges of the subplot photograph, a rectangular area representing 26% of the total subplot area was clipped from the center of each point cloud.
A digital surface map (DSM) of the canopy was generated from each subplot's point cloud using the point to raster method as implemented in the 'lidR' package (Roussel et al 2020) in R (Team R C 2013).This 3D representation of canopy surface structure is made up of 'voxels' that define each point in threedimensional space.To estimate canopy surface roughness, subplot level terrain ruggedness index (TRI) was calculated from each DSM, as implemented in the 'raster' package (Hijmans et al 2015) in R (Team R C 2013).TRI values range from 0 (smooth surface) to 1 (rough surface).

Effective LAI (LAI eff )
To estimate the average hourly 'effective LAI' (LAI eff , defined as the LAI of only illuminated (i.e.not in shadow), green (i.e.photosynthetically active) vegetation in each subplot), we overlaid the voxels representing the 3D canopy surface structure from the DSM (see section 2.2) with color information from the point cloud to determine whether each voxel was dominated by green vs. non-green points, as well as hourly dynamics in ambient light levels (i.e.photosynthetic photon flux density (PPFD) and solar position (figure 1).The paragraphs below provide details on each of these steps.
The average hourly rate of PPFD (µmol photons m −2 ground s −1 )-hereafter referred to as photosynthetically active radiation (PAR)-was calculated from continuous measurements made on a single cloudless day (28 July 2017) (Toolik Field Station Environmental Data Center).To determine incident sun angles, the NOAA Solar Calculator (US Department of Commerce et al 2005) was used to determine solar position for each hour of the day.The average hourly rate of PAR that reached each voxel (PAR veg ) was determined using the 'rayshader' package (Morgan-Wall 2020) in R (Team R C 2013) which combined information on ambient PAR, incident sun angle and 3D canopy surface structure.The path of individual rays of PAR were traced through the subplot's DSM, generating 25 hourly shade maps showing shade depth per voxel.Average hourly ambient PAR values were then scaled as a function of average hourly shade depth.This yielded 25 hourly estimates of PAR veg per voxel for each subplot on 28 July 2017.The rayshader model incorporates Lambertian reflectance (Morgan-Wall 2020) and assumes a diffusely reflecting matte surface (Koppal 2014), providing an approximation of reflection for the canopy (Verhoef 1984).Light transmission through the leaf is not taken into account but typically less than 5% of radiation in the photosynthetically active range is transmitted (Massa et al 2015) and is thus unlikely to significantly influence our conclusions.Future modeling efforts could test this assumption directly.
In order to distinguish between voxels dominated by green or non-green vegetation in each subplot, we used color vegetation indices (CVI).Prior to calculating CVI values, RGB reflectance values (r, g and b) from the point clouds (see section 2.2) were normalized according to equations (1) and (2): where R, G and B are normalized values of RGB for each point calculated as: where µ and σ are the mean and standard deviation of both classes, respectively.Values of M lower than 1 indicate poor class discrimination, while values of M higher than 1 indicate adequate class discrimination.The excess of green was the only CVI with an M-value greater than 1 and thus was the only CVI able to classify voxels as either green vegetation or non-green vegetation.Each subplot was then randomly sampled for 100 000 points and associated excess of green values were calculated.Otsu's method, an algorithm commonly applied to perform automatic image thresholding (Goh et al 2018), was used to identify a threshold value of excess of green that separates the two classes.This method was applied 100 times per subplot and the resulting 100 threshold values were averaged to calculate the final threshold value used to classify each voxel as either green or non-green vegetation.
We then used element-wise multiplication of each subplot's green vegetation and average hourly PAR veg matrices to calculate the average hourly PAR levels incident on green vegetation voxels (PAR Gveg ) for each subplot.Daily sums of PAR Gveg per subplot were calculated by integrating the 25 average hourly values for each voxel.Finally, LAI eff was calculated by dividing the number of illuminated, green vegetation voxels (in the PAR Gveg matrix) for a given hour, divided by the total number of voxels per subplot.These subplot level LAI eff values were used in the calculation of GPPLAI eff (see equation ( 9)).

LAI
Since the process of foliar respiration does not require light, in addition to LAI eff , we calculated LAI per subplot by dividing the number of all green vegetated voxels by the total number of voxels in each subplot.These LAI values were used in the calculation of RE LAI (see equation ( 8)), as well as in GPP LAI which was compared with GPP LAI eff (see section 2.5).

Modeled canopy carbon fluxes
The same widely used NEE (µmol CO 2 m −2 ground s −1 ) model (PLIRTLE, Shaver et al 2007) (equations ( 4)-( 6)) and model parameters were used as in our previous study (Min et al 2021) to estimate carbon fluxes for each hour of 28 July 2017, in each subplot (figure 1), where RE is ecosystem respiration (µmol CO 2 m −2 ground s −1 ), GPP is gross primary productivity (µmol CO 2 m −2 ground s −1 ), each of R 0 (µmol m −2 leaf s −1 ), R x (µmol m −2 ground s −1 ) and β ( • C −1 ) are empirically derived respiration parameters, T is air temperature inside the chamber ( • C), P maxL is the theoretical light saturated photosynthesis rate (µmol m −2 leaf s −1 ), LAI is canopy LAI (m 2 leaf m −2 ground), E 0 is the light use efficiency (µmol CO 2 µmol −1 photons), and PAR is the PAR at the top of the canopy (µmol photons m −2 ground s −1 ).R 0 , R x and β values were restricted to values ⩾0.However, to take into account shade cast by canopy structure as determined by our SFMbased approach, the following modifications to the LAI and PAR terms used to calculate fluxes were made (equations ( 7)-( 9)).First, to estimate hourly rates of gross primary productivity (GPP LAI eff ) we used average hourly LAI eff and PAR Gveg values (equation ( 9)).Second, to estimate hourly rates of ecosystem respiration (RE LAI ) we used LAI (equation ( 8)).Daily flux values were calculated by integrating hourly flux estimates over the entire 24 h period,

Statistical analysis
Data were analyzed using linear mixed effects models with block as a random effect and either treatment or method as a fixed effect depending on the data being compared.Maximum likelihood estimation was used to obtain p-values for fixed effects.The Kenward-Roger method was used to obtain p-values for differences among treatments when applicable.P-values less than 0.05 were considered significant.Model residuals were checked for normality.In cases where the residuals were non-normal, data were log transformed before performing statistical tests.In the rare case that the transformed data remained nonnormal, outliers, defined as data points beyond 1.5 times the interquartile range, were removed.Unless otherwise noted, statistical analyses were done in R v. 3.5.1 (Team R C 2013), and the following packages were used to calculate statistics: lme4 (Bates et al 2015), lmerTest (Kuznetsova et al 2017), and lsmeans (Lenth 2016).

Canopy surface roughness
There was a statistically significant difference in the canopy surface roughness, estimated via TRI, between the CT and each of the long-term treatments (figure 3).Relative to CT, the mean TRI for ExL was 37% lower, and ExLS was 22% lower, indicating that the canopy surface of the CT subplots has more variation in canopy heights.

Light received by green vegetation throughout the day
Over the course of the day, the hourly mean PAR Gveg of each treatment changed dramatically, ranging from 0 µmol photons m −2 s −1 at midnight to a maximum of ∼1100 µmol photons m −2 s −1 at 2 pm (i.e.solar noon) (figure 4).Throughout the day there were statistically significant differences in PAR Gveg between CT and each of the exclosure treatments.Relative to CT, PAR Gveg for ExL was higher in nearly all hours of the day between 5 am and midnight (except for 9 am and 10 am), while PAR Gveg for ExLS was higher during only late afternoon through evening hours (i.e. from 4 pm through 10 pm) (figure 5).
No statistically significant differences in PAR Gveg were found between ExL and ExLS at any hour of the day.

LAI and LAI eff
There were no statistically significant differences among treatments in either LAI or daily integrated LAI eff .The same trend was observed in LAI and LAI eff among treatments, where values were highest in ExLS and lowest in CT (supp.figure 1).Although there were no statistically significant differences between LAI and mean daily integrated LAI eff within treatments, the variance of LAI eff values was between 150% (ExL and ExLS) and 300% (CT) higher than that of LAI.

Ecosystem carbon fluxes
Daily.Treatment had a statistically significant effect for both the LAI-and LAI eff -derived daily integrated carbon fluxes (figure 5).While GPP LAI eff was significantly higher in ExL relative to both CT and ExLS, there were no statistically significant differences in GPP LAI among treatments (figure 5(a)).There  were statistically significant differences in NEELAI eff among CT (highest; net loss of CO 2 from canopy to atmosphere), ExL (lowest; net gain of CO 2 by canopy from atmosphere) and ExLS (net loss of CO 2 from canopy to atmosphere), while NEE LAI was higher in CT (net loss of CO 2 from canopy to atmosphere) relative to both exclosure treatments (figure 5(b)).There were statistically significant differences between GPPLAI eff and GPP LAI in only ExLS where GPPLAI eff was lower than GPP LAI (figure 5(a)), and between NEELAI eff and NEE LAI where NEELAI eff was both higher and positive (net loss of CO 2 from canopy to atmosphere) relative to NEE LAI which was negative (net gain of CO 2 from atmosphere to canopy) (figure 5(b)).There was little variation in RE fluxes among treatments as the R 0 parameter was near 0 (data not shown).
Hourly.In contrast to daily integrated carbon flux estimates in which only ExLS showed statistically significant differences in LAI eff -compared to LAI-derived values, hourly carbon flux estimates showed strong differences in each of CT, ExL and ExLS (figure 6).In general, GPP LAI eff was lower than GPP LAI during the early morning (∼4 am to 7 am) and late evening (∼9 pm to 11 pm) hours (figures 6(a), (c) and (e)), and NEE LAI eff values were higher than NEE LAI during those same time periods (figures 6(b), (d) and (f)).There was little variation in RE fluxes among treatments as the R 0 parameter was near 0 (data not shown).

Discussion
Daily rates of canopy CO 2 uptake (i.e.GPP) of dry heath tundra canopies during mid-summer are likely significantly lower compared to those estimated by the majority of tundra studies to date that use LAI and assume uniform light distribution over vegetation canopies throughout the day.By explicitly accounting for canopy positions of green vegetation and the amount of light that reaches that vegetation over the course of a single day, our results support our hypothesis by demonstrating that the uniquely low sun angles of arctic summers interact with even the low stature of dry heath ecosystems to create long shadows over canopies for large portions of the day.In turn, the reduction of light reaching green vegetation of dry heath canopies limits rates of canopy carbon uptake via photosynthesis, and since shadows do not impose an equivalent limitation in ecosystem respiration, rates of net carbon loss to the atmosphere are likely greater in this tundra type than previously estimated.
Lack of information on 3D canopy structure has been cited as a cause for both over-and underestimations of GPP in a range of ecosystems due to the contribution of shaded foliage to photosynthesis being improperly accounted for (Chen et al 2012, Sprintsin et al 2012).Although the importance of canopy structure on carbon flux in taller, woody deciduous shrub dominated tundra communities has been previously recognized (Williams et al 2014, Magney et al 2016), the impact of canopy structure in lower stature and partially vegetated (i.e.LAI < 1 m 2 m −2 ) tundra communities, such as dry heath tundra studied herein, has not been considered.Our findings are important as they strongly suggest that even in tundra canopies as simple as dry heath, disregarding the effects of shading introduces inaccuracies into estimates of ecosystem carbon fluxes.In fact, by incorporating canopy structure the current findings can further explain our own previous work in the same dry heath tundra communities and experimental plots (Min et al 2021).Previously we used only NDVI-derived estimates of LAI which do not explicitly account for 3D canopy structure and found that despite having lower LAI, the ExL treatment had higher light saturated rates of photosynthesis in mid-summer than the ExLS treatment (Min et al 2021).Relative to plots with a higher terrain ruggedness (i.e.CT and ExLS), the smoother ExL treatment not only had lower LAI, but there was little difference in its vegetation composition that would help explain the higher light saturated photosynthetic rates observed by Min et al (2021).Instead, our current findings reveal that due to differences in the 3D structure of their canopies, dry heath canopies of the smoother ExL treatment consistently receive higher levels of light due to less shading compared to CT.This suggests that the green vegetation of ExL canopies is well-adapted to high light conditions that support the high rates of light saturated photosynthesis (Laisk et al 2005).
Although not the primary purpose of this study, our findings also provide new insight into how herbivores can alter the form and function of tundra communities.Not only do our results show that mammalian herbivores directly alter the 3D canopy structure of dry heath tundra communities, they also suggest that these alterations can result in significant differences in ecosystem carbon fluxes.Moreover, our findings highlight the fact that in these characteristically low productivity ecosystems, even small inaccuracies in estimates of carbon fluxes can affect the prediction of whether tundra communities are net carbon sinks or sources.When variation in 3D canopy structure was not explicitly accounted for in estimating NEE, the exclusion of both large and small herbivores (ExLS) was predicted to render dry heath communities net sinks for carbon during mid-summer (Min et al 2021).In contrast, our current, explicit inclusion of information on 3D canopy structure in estimating NEE reveals that dry heath tundra is predicted to be a net source of carbon in the absence of both large and small herbivores (ExLS).In this way, our study strongly suggests that spatial differences and temporal changes in even the structurally simplest arctic tundra canopies should be accounted for to reduce uncertainty in predictions of how tundra vegetation contributes to the biome's overall cycling and storage of carbon.Importantly, although Arctic tundra has been a carbon sink for tens of thousands of years (Miller et al 1983, McKane et al 1997)

Figure 1 .
Figure 1.Logic flow for analyzing Net Ecosystem Exchange (NEE, mmol CO2 m −2 ground s −1 ) in dry heath tundra community.The standard approach used byMin et al (2021)  combines carbon flux measurements (Fc ; mmol CO2 m −2 ground s −1 ) made byMin et al (2021), with environmental data (PPFD, photosynthetic proton flux density; mmol photons m −2 ground s −1 ) and T, air temperature; • C) and the Leaf Area Index (LAI, m 2 leaf m −2 ground) estimated from measurements of spectral reflectance (i.e.NDVI) to fit the PLIRTLE model of Shaver et al(2007)  and partition the observed NEE to the component fluxes of photosynthesis and respiration (GPP and RE, both in mmol CO2 m −2 ground s −1 ).The current approach incorporates canopy structure (using Structure From Motion (SFM)), and solar ray tracing to determine the fully illuminated and green (i.e.photosynthetically effective) leaf area index (LAIeff), thus accounting for shade within the canopy.LAIeff is substituted for LAI when fitting the GPP portion of PLIRTLE.Finally, carbon flux partitioning between GPP and RE from these two modeling approaches can be compared to the measured fluxes (seeMin et al 2021)  to assess strength of the model fits.
, green, and blue are derived from raw image data from the GoPro cameras and 255 is the maximum signal for each of these three bands.A suite of six CVIs that have previously been demonstrated to emphasize the green component of images (the defining trait of green vegetation) were calculated using the r, g, and b values.The CVIs that were calculated were: excess of blue(Mao et al 2003), excess of green(Woebbecke et al 1995), excess of red (Meyer et al 1999), excess of green minus excess red(Neto 2004), color index of vegetation extraction(Kataoka et al 2003)  and the normal greenred difference index(Woebbecke et al 1993, Mesas- Carrascosa et al 2020).To determine which of the six CVIs provides the best discrimination between green and non-green vegetation cells, an M-statistic (M) was calculated according to equation (3):

Figure 2 .
Figure 2. Photograph of camera and rig set up.The pin flags and clamp outside the base were used to indicate north.Five GoPro cameras were attached along the inner edge of the vertical arc.Photograph shows a control plot.

Figure 3 .
Figure 3. Average terrain ruggedness index (TRI) per treatment.The center black line within each box represents the median TRI value per subplot.Boxes are bound at the 25th and 75th percentiles and whiskers extend to 1.5 * the interquartile range beyond the boxes.Red points indicate outliers that were removed before statistical analyses.Letters indicate significant differences between treatments.

Figure 4 .
Figure 4. Average hourly PAR received by voxels identified as green vegetation per treatment (PARGveg).Boxplots are defined as in figure 3. Significant differences between treatments are indicated by colored asterisks according to the legend.

Figure 5 .
Figure 5. Average daily GPPLAI and GPPLAI eff (a) and NEELAI and NEELAI eff (b) per treatment.Boxplots are defined as in figure 3. Letters indicate significant differences between LAI-and LAI eff -based carbon flux estimates.Colored +s indicate significant differences between treatments for GPPLAI eff and NEELAI eff .Colored asterisks indicate significant differences between treatments for GPPLAI and NEELAI.The red asterisk (a) is to indicate that treatment has a statistically significant effect for GPPLAI but no pairwise comparisons were significant.

Figure 6 .
Figure 6.Average hourly GPPLAI, GPPLAI eff , NEELAI and NEELAI eff per treatment.CT averages are shown in (a) and (b).ExL treatment averages are shown in (c) and (d).ExLS treatment averages are shown in (e) and (f).Boxplots are defined as in figure 3. Shaded regions indicate hours where the difference between LAI-and LAI eff -based carbon flux estimates are significantly different.
, its present and future carbon balance remains in question with many studies reporting conflicting findings (Jones et al 1998, McGuire et al 2012, Fisher et al 2014, Euskirchen et al 2016, Commane et al 2017).Further, the work presented herein adds to a small body of tundra-specific studies that have also demonstrated the effective use of SFM based approaches to better understand the response of arctic tundra's ecological form and function to climate change (e.g.Cunliffe et al 2016, Fraser et al 2016, Korne et al 2020).