# Drivers of shortwave radiation fluxes in Arctic tundra across scales

Inge Juszak, Maitane Iturrate-Garcia, Jean-Philippe Gastellu-Etchegorry,

Michael Schaepman, Trofim Maximov, Gabriela Schaepman-Strub

► To cite this version:

Inge Juszak, Maitane Iturrate-Garcia, Jean-Philippe Gastellu-Etchegorry, Michael Schaepman, Trofim Maximov, et al. Drivers of shortwave radiation fluxes in Arctic tundra across scales. Remote Sensing of Environment, 2017, 193 (6), pp.86-102. 10.1016/j.rse.2017.02.017. hal-04651539

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# Drivers of shortwave radiation fluxes in Arctic tundra
across scales

Inge Juszak<sup>a</sup>, Maitane Iturrate-Garcia<sup>a</sup>, Jean-Philippe Gastellu-Etchegorry<sup>b</sup>,
Michael E. Schaepman<sup>c</sup>, Trofim C. Maximov<sup>d</sup>, Gabriela Schaepman-Strub<sup>a</sup>

## Abstract

Vegetation composition and water surface area are changing in many tundra regions due to climate warming, which is twice as strong in the Arctic as compared to the global mean. Such land cover changes feed back to climate and permafrost thaw through altering the surface energy budget. We quantified the influence of vegetation type, canopy characteristics, and patchiness on the tundra shortwave radiation components. We used in situ measurements and vegetation mapping to parametrise a 3D radiative transfer model (DART) for summer conditions at the Kytalyk test site in northeast Siberia. We analysed model results assessing the most important drivers of canopy albedo, transmittance, and absorptance of photosynthetically active radiation (PAR). Tundra albedo was strongly influenced by the fractional cover of water surfaces. Albedo decreased with increasing shrub cover. However, plant area index effects on albedo were not statistically significant. Canopy transmittance and PAR absorptance (f<sub>APAR</sub>) were almost entirely controlled by plant area index at the landscape scale. Only about one half of the total plant area index consisted of green leaves, while wood and standing dead leaves contributed equally to the

<footnote><sup>a</sup>Department of Evolutionary Biology and Environmental Studies, University of Zurich,
Winterthurerstrasse 190, 8057 Zurich, Switzerland</footnote>

<footnote><sup>b</sup>Centre d'Etudes Spatiales de la BIOsphère (CESBIO) - CNES, CNRS, IRD, Université de
Toulouse, 31401 Toulouse cedex 9, France</footnote>

<footnote><sup>c</sup>Remote Sensing Laboratories, University of Zurich, Winterthurerstrasse 190, 8057 Zurich,
Switzerland</footnote>

<footnote><sup>d</sup>Institute for Biological Problems of Cryolithozone, Siberian Branch of Russian Academy of
Sciences, 41 Lenin Avenue, Yakutsk, Yakutia 677980, Russian Federation</footnote>

<footnote>*Corresponding author</footnote>

<footnote>Email address: inge.juszak@gmx.de (Inge Juszak)</footnote>
other half. While spatial patterns and patch sizes of vegetation types and open water did not significantly influence the radiation budget at the landscape scale, it contributed to the large variability at the local scale. Such local variability of shortwave radiation may impact evapotranspiration and primary productivity at a range of scales. Therefore, the variation of radiation fluxes within single vegetation types potentially affects larger scale energy, water, and carbon fluxes.

*Keywords:* 3D radiative transfer modelling; DART; In situ data; Vegetation type; Canopy properties; Albedo; Transmittance; Soil shading; fAPAR; Shrub; Sedge; Wood area index; Leaf angle distribution; Spatial heterogeneity

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**1. Introduction**

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Vegetation is an important part of the climate system as it reacts to climate drivers and influences climate through changing Earth's surface properties. Arc-tic greening, in particular the expansion of shrubs in tundra areas, is associated with recent climate warming (Sturm et al., 2001; Myers-Smith et al., 2011; Fraser et al., 2014). This greening directly affects the surface albedo, which feeds back to climate through large scale warming (Chapin et al., 2005; Loranty et al., 2011). Vegetation effects on permafrost thaw are more complex since increased vegetation density not only leads to atmospheric warming but also partly decouple permafrost from the atmosphere through insulation and soil shading (Eugster et al., 2000; Walker et al., 2003; Cannone & Guglielmin, 2009; Briggs et al., 2014).

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Encroachment of dense shrub canopies in previously graminoid or lichen dominated tundra reduces the average surface albedo and thus amplifies warming (Thompson et al., 2004; Beringer et al., 2005; Blok et al., 2011b). Furthermore, vegetation alters surface roughness and transpiration, which leads to changes in sensible and latent heat fluxes (Boudreau & Rouse, 1995). Within the canopy, transpiration strongly depends on the light regime, in particular on the small scale heterogeneity (Song et al., 2009; He et al., 2014). Thus, resolving the shortwave energy budget helps understanding and modelling multiple land
21 surface - climate feedback processes.

22 Permafrost is affected by vegetation cover in multiple ways. On one hand, 23 vegetation shades the ground and thus reduces the amount of shortwave radia- 24 tion that is absorbed by the soil (Benninghoff, 1952; Briggs et al., 2014). On the 25 other hand, increasing vascular plant biomass reduces moss abundance through 26 shading and litter production (van Wijk et al., 2003). Decreased moss abun- 27 dance affects the soil heat flux as mosses can strongly insulate the soil from air 28 temperature (Beringer et al., 2001; Blok et al., 2011a). Additional processes, 29 such as trapping of snow by vegetation (Pomeroy et al., 2006), further influence 30 the interaction between vegetation and permafrost thaw.

31 Tundra landscapes typically show small scale patterns, such as hummocks 32 and polygons, which are associated with small water bodies and distinct vegeta- 33 tion types (Walker et al., 2008). Landscape variation and associated differences 34 in soil moisture, nutrients, and pH can lead to different vegetation composition 35 within meters (Walker et al., 2011; Muster et al., 2012). These patterns can 36 either remain stable over decades (Gamon et al., 2012) or change rapidly for 37 example due to permafrost degradation (Schuur et al., 2007). Large scale vege- 38 tation dynamics are also affected by wetland area and the water budget. While 39 an increase in lake and wetland area has been observed in the Siberian tundra 40 (Smith et al., 2005; Lin et al., 2012), the American Arctic shows a drying trend 41 (Oechel et al., 2000; Carroll et al., 2011; Jones et al., 2011; Lin et al., 2012). 42 Shrubs such as dwarf birch (*Betula nana*) profit from warming and fertilisation 43 and become increasingly dominant (Bret-Harte et al., 2001).

44 The radiation budget of patterned tundra landscapes is expected to vary 45 among and within vegetation types at fine scale (few centimetres) due to vari- 46 ations in canopy properties and edge effects. Currently, little is known about 47 the radiation budget of such patterned landscapes, as satellite observations are 48 too coarse to resolve the fine scale differences (Muster et al., 2012). The aim of 49 this study is to analyse the shortwave radiation budget of heterogeneous tundra 50 at the Kytalyk research site in northeast Siberia by using 3D radiative transfer 51 modelling to resolve such fine scales. The focus is on increasing the understand-
ing of drivers of albedo, transmittance, and absorbed radiation of the canopy
from patch to landscape scale in summer. Using a 3D radiative transfer model,
we provide insights into typical length scales of horizontal interaction between
vegetation types and the influence of local land cover variability on the radia-
tion budget at different scales. This is the first time that such a complex 3D
radiation model has been parametrised with such high detailed structural and
compositional measurements for the tundra.

## 2. Methods

### 2.1. Field site

Our field site is the Kytalyk nature reserve located in the Indigirka lowlands,
northeast Siberia (70.8°N, 147.5°E, Figure 1a). According to the circumpolar
Arctic vegetation map, vegetation is classified as tussock sedge, dwarf shrub,
moss tundra (Walker et al., 2005). Low shrub tundra (mainly *Salix pulchra*)
occurs along rivers and at lake shores. The area is dominated by continuous
permafrost of several hundred meters depth (Romanovskii et al., 2004) with an
active layer thickness of 12 to 50 cm (Mi et al., 2014). The Kytalyk field site is
described in more detail in van der Molen et al. (2007); Nauta et al. (2015) and
Juszak et al. (2016). The size of our study area is 1.4 km × 2 km (Figure 1b).

### 2.2. Remote sensing data and products

We used a ground referenced orthomosaic from a UAV (unmanned aerial
vehicle, eBee, senseFly), acquired with digital cameras in four spectral bands
(red, green, blue, and near infra-red (NIR)) to generate a NDVI (Normalized
Difference Vegetation Index) map, a DSM (digital surface model), and a land
cover map of dominant vegetation types. The map products have a spatial
resolution of 5 cm and an extent of 1.4 km × 2 km.

#### 2.2.1. Orthomosaic, NDVI, and DSM

The orthomosaic, which we obtained from the drone flights between 10 July
and 10 August 2014, revealed some artefacts due to inhomogeneous illumination
<figure><img src="image_2.png" /><figcaption>Figure 1: (a) Location of the study site in northeast Siberia (extent of Arctic tundra from Walker et al., 2005) and (b) orthomosaic of the study site including measurement locations of vegetation properties (red) and reference points for vegetation mapping (yellow, point size indicates represented area).</figcaption></figure>

during and between flights (Figure 2a). As these artefacts propagated to the NDVI map, spatial input variables, and the vegetation map (Figure 2b), we chose the sub-sets for modelling in the least affected area (Section 2.4.3). We estimated the NDVI from the red ($\rho_{red}$) and NIR reflectance ($\rho_{NIR}$):

$$ \text{NDVI} = \frac{\rho_{\text{NIR}} - \rho_{\text{red}}}{\rho_{\text{NIR}} + \rho_{\text{red}}} \quad (1) $$

The DSM was generated from the point cloud which was created during the image matching. Interpolation was performed using inverse distance weighting, minimizing artefacts (Chaplot et al. (2006); Postflight Terra 3D, Version 4.0.83). The DSM represented a level between the top of canopy and the soil surface. The uncertainty is due to variability in canopy height and not related to topography. Since the vegetation was low (< 0.8 m) and mostly sparse (average LAI of all vascular vegetation types < 1.5), some of the reference points for the DSM may have been mapped at the soil surface. Thus we considered the DSM an appropriate approximation of the ground elevation and used it as topographic
<figure><img src="image_3.png" /><figcaption>Figure 2: (a) Orthomosaic of the study area (1.4 km × 2 km) including the locations of 21 strip transects and (b) vegetation map.</figcaption></figure>
input for modelling. The elevation difference between the river and the highest area of the ridge was about 23 m. Fine scale drainage patterns could be detected in the DSM, for example in the area of the drained thaw lake bed. The DSM showed small scale height differences between the elevated shrub patches and wet sedge depressions.

## 2.2.2. Vegetation map

The reference points for training and validation of the vegetation map were acquired in the field 04 – 08 July 2015 (Figure 1b). We defined eight vegetation types based on the class definition in the circumpolar Arctic vegetation map (Walker et al., 2005) which we split into sub-classes depending on species composition and canopy properties (Table 1). We performed supervised classification (ENVI, Version 5.2) as described in more detail in the appendix (Section A.1). To assess the classification accuracy, we took a random subset of the validation points with an equal amount of pixels per vegetation type (732 pixels). We computed the confusion matrix, user’s accuracy, producer’s accuracy, and the Kappa coefficient (Congalton, 1991).

## 2.3. Vegetation characteristics used as model input variables and parameters

The above vegetation classes were modelled in the 3D radiative transfer model DART based on vegetation type specific input variables and parameters. We use the term ‘variable’ for spatially varying model input data and the term ‘parameter’ for spatially invariant model input within a given vegetation type. The variables are green and standing dead leaf, and wood area index as well as canopy and standing dead leaf height.

For each vegetation type, we either measured the variables in the field during the peak growing season or compiled values from literature (see Section A.2 for details). We computed spatially varying green leaf area index (LAI) from NDVI following Street et al. (2007); Campioli et al. (2009):

$$LAI = a \cdot \exp(b \cdot \text{NDVI}). \qquad (2)$$
<table><caption>Table 1: Vegetation classes from the circumpolar Arctic vegetation map (Walker et al., 2005) and sub-classes as defined for this study; the background colours indicate the colour used for this vegetation type in maps and graphs.</caption><thead><tr><th>Class</th><th>Sub-class</th><th>Description</th></tr></thead><tbody><tr><td>G4</td><td></td><td>Tussock sedge (<i>Eriophorum vaginatum</i>), dwarf shrub, moss tundra</td></tr><tr><td rowspan="3">S1</td><td></td><td>Erect dwarf shrub tundra (&lt; 40 cm)</td></tr><tr><td>S1-1</td><td>Dwarf birch (<i>Betula nana</i>) dominated</td></tr><tr><td>S1-2</td><td>Lichen-rich shrub, <i>Vaccinium</i> spp. dominated</td></tr><tr><td>S2</td><td></td><td>Low shrub tundra (&gt; 40 cm, <i>Salix pulchra</i>)</td></tr><tr><td rowspan="5">W2</td><td></td><td>Sedge, moss, dwarf shrub (&lt; 40 cm) wetland</td></tr><tr><td>W2-1</td><td>Wet sedge, <i>Eriophorum angustifolium</i> dominated, dense, green</td></tr><tr><td>W2-2</td><td>Dry sedge, <i>Eriophorum angustifolium</i> and <i>Sphagnum</i> spp. dominated</td></tr><tr><td>W2-3</td><td>Peat moss (<i>Sphagnum</i> spp.) dominated</td></tr><tr><td>W2-4</td><td>Waterlogged sedge, <i>Carex</i> spp. dominated, few standing dead leaves</td></tr><tr><td>Water</td><td></td><td>Open water</td></tr></tbody></table>

We obtained *a* and *b* by fitting the exponential relationship on five quantiles (0.05, 0.25, 0.50, 0.75, and 0.95) of the in situ LAI measurements and UAV-derived NDVI of all pixels within the vegetation type in question (see Appendix, Table A1).

We used linear regressions with observed LAI to spatially extrapolate wood and standing dead leaf area index as well as canopy and standing dead leaf height:

$$x = p \cdot \text{LAI} + q \quad (3)$$

where *x* is the extrapolated variable and *p* and *q* represent vegetation type specific parameters (see Appendix, Table A1). The average and standard deviation of all variables for each vegetation type were computed for the entire strip
130 transects (Table 2).

<table><caption>Table 2: Summary of canopy properties used as model input; for plant area index and canopy height mean ± standard deviation of all cells are provided; the species column indicates which species was used for measuring the input parameters inclination angle and optical properties.</caption><thead><tr><th rowspan="2">Class</th><th rowspan="2">Description</th><th colspan="5">Input variables</th><th colspan="2">Input parameters</th></tr><tr><th colspan="3">Area index</th><th colspan="2">Height (cm)</th><th rowspan="2">Species</th><th rowspan="2">Background</th></tr><tr><th></th><th></th><th>Green leaf</th><th>Wood</th><th>Standing dead leaf</th><th>Canopy</th><th>Standing dead leaf</th><th></th><th></th></tr></thead><tbody><tr><td>G4</td><td>Tussock sedge</td><td>0.24±0.10</td><td>-</td><td>-</td><td>12.2±0.0</td><td>-</td><td>E. vagina- tum</td><td>S1-2</td></tr><tr><td>S1-1</td><td>Dwarf birch</td><td>1.08±0.16</td><td>1.02±0.09</td><td>-</td><td>26.6±1.2</td><td>-</td><td>B. nana</td><td>S1-1, removal</td></tr><tr><td>S1-2</td><td>Lichen-rich shrub</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>S1-2</td></tr><tr><td>W2-1</td><td>Wet sedge</td><td>1.32±0.33</td><td>-</td><td>1.53±0.38</td><td>47.6±5.4</td><td>22.1±2.6</td><td>E. angusti- folium</td><td>Water</td></tr><tr><td>W2-2</td><td>Dry sedge</td><td>0.55±0.23</td><td>-</td><td>0.64±0.26</td><td>24.4±1.9</td><td>15.8±1.8</td><td>E. angusti- folium</td><td>W2-3</td></tr><tr><td>W2-3</td><td>Peat moss</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>W2-3</td></tr><tr><td>W2-4</td><td>Waterlogged sedge</td><td>0.46±0.12</td><td>-</td><td>-</td><td>33.2±2.0</td><td>-</td><td>E. angusti- folium</td><td>Water</td></tr><tr><td>Water</td><td>Shallow water</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>Water</td></tr></tbody></table>

An example of all input variables for one strip transect is shown in Figure 3.

The LAI included *Betula* and *Salix* shrubs as well as *Eriophorum* and *Carex* sedges but neither dwarf shrubs < 5 cm such as *Vaccinium* spp. and *Ledum palustre*, nor grasses nor forbs. The LAI only made up for about half of the total plant area index (PAI) with about one fourth being wood and one fourth standing dead leaves. The average canopy height was 25.3 cm in the study area.
<figure><img src="image_4.png" /><figcaption>Figure 3: Input variables for one strip transect (10 m × 25 m) as an example; (a) RGB image, (b) near infra-red image, (c) vegetation map, (d) digital surface model, (e) canopy height, (f) standing dead leaf height, (g) green leaf area index, (h) standing dead leaf area index, and (i) wood area index.</figcaption></figure>
Input parameters were the angular distribution and the optical properties of green leaves, standing dead leaves, and wood and the background reflectance. We measured the input parameters during the peak growing season. We estimated the leaf angle distribution with the method by Pisek et al. (2011) and applied a correction for green and standing dead sedge leaves and wood (Appendix, Figure A2). The correction was necessary because it was not possible to identify wood or sedge leaves that were perpendicular to the image plane (see Section A.3 for details).

Optical properties of green and standing dead leaves and wood were measured in the field with a dual integrating sphere design for reflected and transmitted light in the spectral range from 400-950 nm (Jaz & SpectroClip, Ocean Optics). From 950-2500 nm, we used dwarf birch (*Betula nana*) optical properties measured at the same field site for leaves, standing dead leaves, and wood of all species (Fieldspec4, ASD Inc., Juszak et al., 2014, Appendix, Figure A3a).

We measured spectral background reflectance on canopies lower than 5 cm and on shallow water 13 - 23 July 2008 (Fieldspec4, ASD Inc.). Reflectance measurements of *Vaccinium* dominated lichen-rich shrub communities (S1-2) were selected as background for tussock sedge tundra as the species composition was similar. Peat moss (W2-3) dominated below dry sedge vegetation and was thus used as background for modelling. For wet and waterlogged sedges we used measurements of shallow water as background (Table 2). Additionally, we used the background reflectance below dwarf birch (S1-1) after removing the shrubs (see Juszak et al., 2014). At least four measurements were averaged per background type (Appendix, Figure A3b).

## 2.4. Radiation budget simulations with DART

We simulated the radiation budget using the DART 3D radiative transfer model (Gastellu-Etchegorry et al., 1996; Grau & Gastellu-Etchegorry, 2013; Gastellu-Etchegorry et al., 2015, Version 5.6.1). The DART model tracks radiation fluxes within the 3D canopy including multiple reflections and mutual shading (Schneider et al., 2014). This model has been applied and validated
extensively, for example for forest canopies (Malenovský et al., 2008; Schneider 167 et al., 2014), crops (Duthoit et al., 2008), and tundra dwarf shrubs (Juszak 168 et al., 2014). The DART model formed part of the radiation transfer model 169 intercomparison (RAMI) (Pinty et al., 2001; Widlowski et al., 2015). 170

### 2.4.1. *Model configuration*

We parametrised the DART radiative transfer model for 21 strip transects 172 and 9 homogeneous cover types for one point in time in the peak growing sea- 173 son. Vegetation was parametrised in a voxel grid filled with turbid media scat- 174 terers (Schneider et al., 2014). Three types of turbid media were simultane- 175 ously considered: green leaves, dead leaves, and wood. Each turbid medium 176 was simulated as a vertically homogeneous column within its respective height. 177 However, standing dead leaves of wet and dry sedges were implemented with 178 a lower height than green leaves (Table 2). Thus, voxels at low height were 179 dominated by standing dead leaves and higher voxels by green leaves in these 180 two vegetation classes. For the strip transects, we used the DSM as topography 181 while we simulated the homogeneous cover types without topography (Table 3). 182

We simulated shortwave radiation fluxes for MODIS bands 1 to 7 (Table 3) 183 and derived broadband shortwave quantities (full shortwave albedo and full 184 shortwave transmittance) from a linear combination of bands with coefficients 185 by Liang et al. (1999). Additionally, we simulated broadband photosynthetically 186 active radiation (PAR) to assess the fraction of PAR which is absorbed by the 187 canopy ($f_{APAR}$) and to compare the results with the PAR conversion from three 188 MODIS bands by Liang et al. (1999). In the simulations, the illumination 189 was defined by the total irradiance and the fraction of diffuse light for each 190 spectral band (Table 3). The spectral irradiance was defined as the reflectance 191 of a Spectralon panel measured around solar noon on 11/07/2012 under clear 192 sky conditions using a spectrometer (Fieldspec4, ASD Inc.). All spectrometer 193 measurements within a MODIS full width at half maximum band width or the 194 PAR range were averaged to obtain the irradiance within the band in question. 195 The diffuse fraction in the PAR range was obtained from field measurements 196
under clear sky conditions (Delta-T Devices, BF3). In other wavebands, diffuse fractions were obtained with DART simulations of atmosphere radiative transfer for conditions at noon mid of July with a subarctic summer atmosphere. We adjusted the aerosol optical depth factor so that the simulated diffuse fraction in the PAR range matched the observations.

<table><caption>Table 3: General model configuration and spectral bands with respective irradiance and diffuse fraction (SKYL); the spectral bands represent the full width at half maximum (FWHM) of the MODIS instrument.</caption><thead><tr><th>Characteristic</th><th>Value</th></tr></thead><tbody><tr><td>Mode</td><td>Flux-tracking</td></tr><tr><td>x, y, z resolution<br>(voxel grid)</td><td>5.0 cm</td></tr><tr><td>Scene size</td><td></td></tr><tr><td>- homogeneous cover type</td><td>1 m × 1 m</td></tr><tr><td>- strip transects</td><td>10 m × 25 m</td></tr><tr><td>Scene type</td><td>Repetitive</td></tr><tr><td>Topography</td><td></td></tr><tr><td>- homogeneous cover type</td><td>no</td></tr><tr><td>- strip transects</td><td>yes</td></tr><tr><td>Vegetation representation</td><td>Turbid media</td></tr><tr><td>Sun position</td><td>15/07/2015, 1 hour before solar noon</td></tr><tr><td>Atmosphere</td><td>Spectral SKYL (from DART)</td></tr><tr><td>No. of directions</td><td>193</td></tr><tr><td>Wavelengths (nm)</td><td>400–700 459–479 545–565 620–670 841–876 1230–1250 1628–1652 2105–2155</td></tr><tr><td>MODIS bands</td><td>- 3 4 1 2 5 6 7</td></tr><tr><td>Irradiance (W m<sup>-2</sup> µm<sup>-1</sup>)</td><td>968 1079 1044 930 636 310 154 58</td></tr><tr><td>Diffuse fraction (%)</td><td>19.0 25.4 13.5 13.2 7.5 3.6 2.0 1.3</td></tr></tbody></table>
### 2.4.2. Model outputs

We analysed three major model outputs. The first output was the short-wave albedo one metre above the soil surface, which we converted from spectral to shortwave albedo (Liang et al., 1999). The second output was shortwave irradiance at the soil surface divided by above canopy shortwave irradiance. We call this variable ‘transmittance’, which equals to ‘1 - soil shading’ (Bninghoff, 1952). Canopy transmittance influences soil heat flux and permafrost thaw (Briggs et al., 2014). We considered the fraction of photosynthetically active radiation absorbed by the canopy ($f_{APAR}$) as the third output. We defined the canopy as vascular vegetation parametrised in the radiative transfer model. Therefore, mosses, lichen and vascular plants lower than 5 cm, which we treated as background, did not contribute to $f_{APAR}$ and soil shading. Although $f_{APAR}$ is closely linked to canopy transmittance, it provides additional information as it is associated with photosynthesis and thus the carbon cycle (Ruimy et al., 1994; Huemmrich et al., 2010). Before analysing the model output, we removed 2 m borders on all sides of the strip transects to eliminate edge effects. Thus the remaining strip transect size was 6 m × 21 m (120 × 420 pixels).

### 2.4.3. Selection of subsets for modelling

Model simulations were done with two different land cover complexities. First, we simulated homogeneous land cover types without topography and second, we simulated the radiation budget of 21 strip transects including heterogeneous tundra vegetation. We refer to this complex 3D simulation at the landscape scale as direct 3D simulations. For both complexities, we used the same average canopy variables and parameters (Table 2).

To quantify the shortwave radiation budget of heterogeneous tundra, we selected subsets of the study area on the vegetation map (Figure 2b). We chose strip transects within a single flight area (flown twice, 23 and 31 July 2014) because of artefacts due to inhomogeneous illumination (Figure 2a). Due to the low vegetation height of the tundra in our study area (Table 2) and the small scale spatial variability of vegetation type, we selected 21 strip transects
of 10 m × 25 m representative of the landscape scale. Each strip transect repre-
sented a transition between dwarf birch dominated vegetation (S1-1) and other
vegetation types or water (Figure 4). As low shrub tundra (S2) was restricted to
lake and river banks, we did not choose strip transects in this vegetation type.
The remaining six vegetation types and water were each dominating three strip
transects. Additionally, all vegetation types were represented in smaller frac-
tions also in the other strip transects. The patch size distribution differed among
the strip transects.

We computed explanatory variables at two different levels, for the whole
strip transects and for each vegetation patch. For the strip transects, we used
the explanatory variables (I) average PAI including green leaves, standing dead
leaves, and wood, (II) fractional cover of each vegetation type, and (III) mean
characteristic length, which we defined as mean ratio of patch area to patch
perimeter. We used the characteristic length as proxy for edge effects, which
are more important for strip transects with a small mean characteristic length.
The radiation budget of a single patch is influenced by its vegetation type, PAI,
canopy height, neighbouring vegetation, and topography. Topography influences
the radiation budget more at the patch scale than at the transect scale, because
the strip transects are mostly flat on average while mounds and tussocks influ-
ence local slope and exposition. We assessed the influence of local variability
and edge effects using the characteristic length of the single vegetation patches
in relation with their radiation budget.
<figure><img src="image_5.png" /><figcaption>Figure 4: Vegetation maps of 21 strip transects (10 m × 25 m); the rows represent different major vegetation types sorted by the mean characteristic length of the major type with simple polygons on the left and more complex polygons on the right.</figcaption></figure>
## 2.5. Weighted averages

In addition to the direct 3D radiative transfer simulations, we estimated the radiation budget of each strip transect using weighted averages. The weighted averages were calculated using the radiation budget for each land-cover type, weighted by the fraction of the cover types within each strip transect. The weighted averages were computed in two steps. In a first step, we computed the 3D radiation budget of homogeneous vegetation types with DART using the same mean vegetation type specific variables as for the strip transect simulations in a small and repetitive scene (Table 2). DART was configured in the same way as for the strip transects, but the scene was smaller and did not include topography (Table 3). In a second step, we computed the average albedo, transmittance, and $f_{APAR}$ weighted by land cover type fraction for each strip transect. Thus the weighted averages are an easy and fast method to estimate radiation quantities, which does not take into account the spatial distribution of the land cover types or any other interactions between them.

## 2.6. Statistical analysis

We estimated the importance of different strip transect characteristics on the mean radiation budget using an analysis of variance (ANOVA, f-test) (R Core Team, 2015, Version 3.2.3). The response variables were strip transect albedo, transmittance, and $f_{APAR}$. The explanatory variables of each strip transect were the fraction of shrub cover (S1-1), the combined fraction of water and waterlogged sedges (W2-4), mean PAI, and mean patch characteristic length. We did a 4-way ANOVA per response variable without taking into account interactions between explanatory variables. Our model first accounted for the explanatory variable with the highest correlation coefficient with the response. We changed the order of the other three response variables in the model to assess the robustness of the model results and possible relationships among the explanatory variables. The radiation budget simulated directly with the 3D radiative transfer model was compared with the weighted averages using a paired t-test (R Core Team, 2015, Version 3.2.3).
## 3. Results

### 3.1. Vegetation map

Betula dwarf shrubs (S1-1) and Salix low shrubs (S2) covered about 20% of the landscape, another 39% was covered by densely vegetated wetlands (W2-1, W2-2, W2-3) and 8% by water bodies and waterlogged sedges (W2-4). The remaining area was classified as either tussock sedge (G4) or lichen-rich dwarf shrub tundra (S1-2). The Kappa coefficient of the vegetation classification was 0.44, the overall accuracy was 50%. The confusion matrix (Table 4) indicates that tussock tundra (G4) was similar to lichen-rich shrub tundra (S1-2). Therefore, large parts of the tussock tundra in the area of the ridge were misclassified as S1-2 (Figure 2b). Furthermore, dry sedges (W2-2) and peat moss tundra (W2-3) resembled each other in appearance and (shallow) water was often classified as waterlogged sedges (W2-4).

<table><caption>Table 4: Confusion matrix of the vegetation map calculated from a random subset of the validation data with an equal number of validation pixels per class.</caption><thead><tr><th rowspan="2"></th><th colspan="9">Map</th><th>Producer's</th></tr><tr><th>G4</th><th>S1-1</th><th>S1-2</th><th>S2</th><th>W2-1</th><th>W2-2</th><th>W2-3</th><th>W2-4</th><th>Water</th><th>accuracy (%)</th></tr></thead><tbody><tr><td>G4</td><td><strong>160</strong></td><td>41</td><td>468</td><td>0</td><td>47</td><td>6</td><td>10</td><td>0</td><td>0</td><td>22</td></tr><tr><td>S1-1</td><td>133</td><td><strong>297</strong></td><td>240</td><td>0</td><td>43</td><td>15</td><td>0</td><td>4</td><td>0</td><td>41</td></tr><tr><td>S1-2</td><td>54</td><td>43</td><td><strong>483</strong></td><td>0</td><td>99</td><td>37</td><td>16</td><td>0</td><td>0</td><td>66</td></tr><tr><td>S2</td><td>1</td><td>27</td><td>2</td><td><strong>652</strong></td><td>19</td><td>2</td><td>0</td><td>28</td><td>1</td><td>89</td></tr><tr><td>W2-1</td><td>18</td><td>104</td><td>14</td><td>0</td><td><strong>338</strong></td><td>188</td><td>49</td><td>21</td><td>0</td><td>46</td></tr><tr><td>W2-2</td><td>18</td><td>0</td><td>162</td><td>0</td><td>17</td><td><strong>407</strong></td><td>128</td><td>0</td><td>0</td><td>56</td></tr><tr><td>W2-3</td><td>0</td><td>0</td><td>78</td><td>0</td><td>0</td><td>424</td><td><strong>230</strong></td><td>0</td><td>0</td><td>31</td></tr><tr><td>W2-4</td><td>19</td><td>27</td><td>0</td><td>0</td><td>10</td><td>3</td><td>0</td><td><strong>654</strong></td><td>19</td><td>89</td></tr><tr><td>Water</td><td>0</td><td>0</td><td>4</td><td>0</td><td>15</td><td>1</td><td>0</td><td>629</td><td><strong>83</strong></td><td>11</td></tr><tr><td>User's accuracy (%)</td><td>40</td><td>55</td><td>33</td><td>100</td><td>57</td><td>38</td><td>53</td><td>49</td><td>81</td><td>Overall <strong>50%</strong></td></tr></tbody></table>
## 3.2. Small scale spatial variation in albedo, transmittance, and f<sub>APAR</sub>

At the patch scale, variations in PAI, canopy height, topography, and neighbouring vegetation type led to considerable variation in albedo, transmittance, and f<sub>APAR</sub> among cells of the same type (Figure 5). Albedo was on average lower in the direct 3D simulation as compared to the simulation of single vegetation types (Figure 5a). However, this was not the case for the vegetation types with relatively low albedo (dwarf birch (S1-1), waterlogged sedges (W2-4)) and water. While the transmittance of highly transmitting vegetation types was reduced due to edge effects, it was increased in denser vegetation (Figure 5b). Edge effects strongly increased f<sub>APAR</sub>, especially for vegetation types with dense canopies that absorb much radiation anyway (Figure 5c).

<figure><img src="image_6.png" /><figcaption>Figure 5: Modelled radiation budget components for all cells of all strip transects, (a) albedo, (b) transmittance, and (c) fraction of PAR absorbed by the canopy (f<sub>APAR</sub>); the boxes indicate the 0.25, 0.5, and 0.75 quantiles, the whiskers are the 0.02 and 0.98 quantiles; red dots indicate the modelling results using homogeneous cover types.</figcaption></figure>

At the patch scale, albedo was not related to transmittance (R = 0.00) or f<sub>APAR</sub> (R = -0.05, results not shown). While transmittance and f<sub>APAR</sub> were highly negatively correlated at the landscape scale, the negative correlation between them was reduced to R = -0.43 at the patch scale. Patch f<sub>APAR</sub> was highly positively correlated with PAI (R = 0.96). However, the correlation
between patch transmittance and PAI was less strongly negative ($R = -0.57$) than at the landscape scale.

The larger the patch area was in relation to its perimeter, the smaller was the influence of bordering vegetation, LAI variation, and topography on the patch average albedo, transmittance, and $f_{APAR}$ (Figure 6). The characteristic length at which a radiation budget component is independent of edge effects can be estimated from the convergence of an upper and a lower hull curve. Depending on the vegetation type, variation in patch albedo and $f_{APAR}$ was small for patches with characteristic lengths above 0.5 m on average, while patch transmittance was variable until 0.7 m. However, the variability among vegetation types was large (Figure 6). Thus, the characteristic length scale depended on the radiation quantity in question and on vegetation type. In terms of patch area, converging hull functions indicated small edge effects for patches of 7 m² or more for albedo and $f_{APAR}$ and 10 m² area for transmittance, respectively. Although only 2% of the patches were larger than 7 m², such large patches represented 65% of the total area in the modelled strip transects.
<figure><img src="image_7.png" /><figcaption>Figure 6: Mean patch (a,b) albedo, (c,d) transmittance, and (e) fraction of PAR absorbed by the canopy ($f_{APAR}$) as a function of characteristic length (patch area to perimeter ratio) for wet sedges (W2-1) and lichen-rich shrubs (S1-2); one point per patch; the green lines represent exponential curves fitted to the outer points as hull curves and converging at the indicated point (threshold = 0.001).</figcaption></figure>
### 3.3. Drivers of the radiation budget at the landscape scale

We compared modelled radiation budgets of different strip transects to estimate the importance of different landscape elements. Strip transect albedo was strongly negatively related with water fractional cover (including waterlogged sedges (W2-4), Pearson correlation $R = -0.91$, Figure 7b). Shrub cover significantly affected the albedo when the statistical model accounted for the water effect first (Table 5). Higher shrub cover was associated with lower albedo values. If all data were taken into account, the relationship between shrub cover and albedo was concealed by the strong influence of water cover ($R = 0.19$, Figure 7a). However, excluding the strip transects with more than 20% water cover (coloured red in Figure 7a), the relationship was more clear ($R = -0.91$). After accounting for water cover, neither PAI nor the average patch characteristic length were significantly related to strip transect albedo, even if the model did not account for shrub cover first. The correlation between each pair of explanatory variables was less than $|R| = 0.55$. Landscape albedo was only weakly related with transmittance ($R = -0.40$) and $f_{APAR}$ ($R = 0.38$).

<table><caption>Table 5: The effect of strip transect characteristics on simulated albedo and transmittance expressed as ANOVA results; water cover includes waterlogged sedges (W2-4). Each characteristic takes one of 20 degrees of freedom (df); please note the different variable order; *** $P \le 0.001$; ** $P \le 0.01$; ns: not significant.</caption><thead><tr><th></th><th>df</th><th>F</th><th>P</th></tr></thead><tbody><tr><td><strong>Albedo</strong></td><td></td><td></td><td></td></tr><tr><td>Water cover</td><td>1</td><td>277.90</td><td>***</td></tr><tr><td>Shrub cover</td><td>1</td><td>38.15</td><td>***</td></tr><tr><td>Plant area index</td><td>1</td><td>0.01</td><td>ns</td></tr><tr><td>Characteristic length</td><td>1</td><td>0.89</td><td>ns</td></tr><tr><td><strong>Transmittance</strong></td><td></td><td></td><td></td></tr><tr><td>Plant area index</td><td>1</td><td>617.38</td><td>***</td></tr><tr><td>Shrub cover</td><td>1</td><td>9.71</td><td>**</td></tr><tr><td>Water cover</td><td>1</td><td>2.13</td><td>ns</td></tr><tr><td>Characteristic length</td><td>1</td><td>0.91</td><td>ns</td></tr></tbody></table>
Modelled strip transect f<sub>APAR</sub> and shortwave transmittance were strongly negatively correlated (*R* = -0.99). PAI strongly reduced canopy transmittance (*R* = -0.98, Figure 7g) and increased f<sub>APAR</sub> (*R* = 0.98, Figure 7k). The second most important driver of both variables was shrub cover (*R* = -0.34 and *R* = 0.28 for transmittance and f<sub>APAR</sub>, respectively, Figure 7e, i), which significantly influenced transmittance but not f<sub>APAR</sub> when PAI was accounted for (Table 5). Water cover and average patch characteristic length did not significantly affect transmittance and f<sub>APAR</sub>.
<figure><img src="image_8.png" /><figcaption>Figure 7: Modelled DART strip transect (a–d) albedo, (e–h) transmittance, and (i–l) fraction of PAR absorbed by the canopy (f<sub>APAR</sub>) as a function of (a, e, i) shrub fractional cover (S1-1), (b, f, j) combined fractional cover of water and waterlogged sedges (W2-4), (c, g, k) plant area index, and (d, h, l) average characteristic length; regression lines are included for data with |R| > 0.5; in (a) and (b) strip transects with water cover above 20% are highlighted in red.</figcaption></figure>
353 3.4. Influence of spatial distribution and interaction of land cover types

354 We analysed results of direct 3D radiative transfer simulations as compared
to a weighted average of the radiation budget with given fractional cover per
355 vegetation type and average type properties. While the direct 3D simulations
356 included the spatial distribution and interactions between land cover types, such
357 effects were not accounted for in the weighted average approach. Using the 3D
358 model, strip transect albedo values were significantly lower than the weighted
359 average (p < 0.001, Figure 8a). On average, the albedo reduction when using
360 the direct 3D approach was 0.004, corresponding to 3% of the average albedo,
361 and the maximum absolute difference was 0.01.
362

362

<figure><img src="image_9.png" /><figcaption>Figure 8: (a) Albedo, (b) transmittance, and (c) fraction of PAR absorbed by the canopy ($f_{APAR}$) modelled for each strip transect with DART and computed with weighted averages of the radiation quantities of land cover types occurring in the strip transect; each point represents one strip transect, the mean of all strip transects is the red square, the line represents a 1:1 relationship.</figcaption></figure>

363 Canopy transmittance was on average 3% higher in the direct 3D model
364 results as compared to the weighted average (Figure 8b). However, this was
365 not the case for all strip transects. For single strip transects, the absolute
366 transmittance difference was between -0.06 and 0.09. The 3D model results were
367 significantly different from the weighted averages (p < 0.05). Transmittance
368 modelled with the 3D approach was generally higher than with the weighted
average for strip transects with low PAI and low shrub cover (results not shown).

As described above, f<sub>APAR</sub> was strongly negatively related with transmit-
tance. Consequently, f<sub>APAR</sub> was slightly reduced when using the direct 3D
radiative transfer model as compared to the weighted average (Figure 8c). The
absolute difference varied between -0.10 and 0.06, on average 3% of the total
f<sub>APAR</sub>. However, the difference between f<sub>APAR</sub> modelled with DART and f<sub>APAR</sub>
calculated from weighted averages was not significant (*p* > 0.1).

376 4. Discussion

377 4.1. *Vegetation map and canopy characteristics*

378 Our vegetation map had a Kappa coefficient of 0.44 with the original nine
379 land cover classes. The achieved accuracy was lower than in other studies clas-
380 sifying tundra vegetation using orthomosaics (Lantz et al., 2010; Muster et al.,
381 2012) or high resolution satellite imagery (Atkinson & Treitz, 2012; Virtanen &
382 Ek, 2014; Siewert et al., 2015). The lower accuracies of our classification were
383 mostly due to similar reflectance properties of several classes in the four spectral
384 bands which were available.

The vegetation classification accuracy and the 3D modelling (Figure 5a) indicate that several of the pre-defined vegetation classes have similar reflectance properties. This functional similarity is in contrast to the differences among vegetation types in terms of species composition and canopy properties such as height or PAI. As these canopy properties translate into specific radiation transmittance and absorptance characteristics, they play an important part in the radiation budget at the landscape scale and are thus included in the 3D radiative transfer modelling. Given that several structurally different classes had similar reflectance properties, more information is needed to reliably estimate tundra vegetation distribution and structural complexity. One approach is to use more spectral bands for vegetation mapping. Several studies show that hyperspectral data enable estimates of canopy composition (Antonarakis et al., 2014; Bratsch et al., 2016) and structure (Asner, 1998). At the local scale,
the use of LiDAR to estimate canopy structural properties could be considered (Antonarakis et al., 2014; Schneider et al., 2014).

Model input variables and parameters were subject to uncertainties based on the field measurements and the spatial extrapolation. Despite our correction, the Ocean Optics leaf optical properties measurements were affected by the small size of the two integrating spheres (Section A.3). Furthermore, we used optical properties of a single species for all species in the three near-infrared wavebands (Figure A3). However, pre-experimental tests with the DART model showed that leaf optical properties were generally less important than other factors, in particular the leaf angle distribution, PAI, and leaf to wood ratio. Thus, we expect that other differences between the vegetation types, such as the LAI, are more important controls of the (broadband) radiation budget.

We used field observations of spatial LAI variability within vegetation classes and an NDVI map to extrapolate LAI over the whole study region. Several studies have shown strong relationships between NDVI and LAI in Arctic tundra (Shippert et al., 1995; Riedel et al., 2005; Campioli et al., 2009), especially if each vegetation type was treated separately (Street et al., 2007). Williams et al. (2001) estimated a mean error of prediction of around 16% when extrapolating tundra LAI based on NDVI. However, we were not able to validate the spatial LAI distribution due to a lack of observations in the same time period as the orthophotos. All other input variables, namely wood area index, standing dead leaf area index, canopy height, and standing dead leaf height, were extrapolated based on linear relationships with LAI. We are not aware of any other study which spatially extrapolated these canopy characteristics in a tundra ecosystem. Given the uncertainties in the field measurements, the NDVI, and the vegetation map, the spatial distribution of LAI and the other canopy variables is uncertain. However, we ensured that the range, mean values, and variability were well-represented in the modelling. While the uncertainty of input variables limits our ability to predict the radiation budget at specific locations, it still allows us to investigate the importance of different drivers for the radiation budget at local and landscape scale as well as the role of the spatial vegetation distribution.
We found that green leaves only contributed about one half to the total PAI. The importance of wood for Arctic shrub canopies has been highlighted by Thompson et al. (2004) who measured larger wood area indices than leaf area indices in tundra shrubs. Juszak et al. (2014) emphasised the role of wood for the radiation absorption of tundra dwarf shrubs. The large area of standing dead sedge leaves found at our study site is relevant for the radiation budget, as dead leaves can contribute significantly to canopy reflectance (Chapin et al., 2000) and shading (Caldwell et al., 1974). We included all vegetation above 5 cm height (cell size) as turbid media in the radiative transfer model, while lower vegetation and mosses were included as background and thus did not contribute to f<sub>APAR</sub> and soil shading. Therefore, we likely underestimate f<sub>APAR</sub> at most vegetation types as moss and lichen cover is very common. However, understory light extinction is not commonly included in the f<sub>APAR</sub> definition (Huemmrich et al., 2010). As mosses may account for a significant part of tundra absorbed radiation and gross ecosystem production (Huemmrich et al., 2010), further research is required on how to accurately represent mosses in radiation transfer and land surface models.

## 4.2. *Small scale spatial variation in albedo, transmittance, and f<sub>APAR</sub>*

In agreement with Oliphant et al. (2006), we found that at the 5 cm pixel and the patch scale albedo, transmittance, and f<sub>APAR</sub> can be substantially different from mean values of the respective vegetation types (Figure 5). We found that the scale of the variability in radiation budget components is much smaller than what we can observe from satellites, posing challenges for driving models from conventional remote sensing. The suitability of satellite observations for shortwave radiation budget studies is also limited by the low correlation between albedo and transmittance or f<sub>APAR</sub>, in particular at the local scale. This weak relationship between the more easily observable albedo and transmittance is relevant for permafrost research. Shading (i.e. inverse of transmittance) by shrubs has been found to influence permafrost thaw locally (Briggs et al., 2014) through the amount of solar energy at the soil surfaces. Canopy transmittance
also affects soil surface temperature (Smith, 1975) and thus longwave radiation and sensible heat fluxes (Ni-Meister & Gao, 2011). Our results concerning transmittance indicate, that the shortwave radiation budget at the soil surface is highly variable, strongly related to plant area, and only weakly related with canopy reflectance.

Several studies have shown that the heterogeneity of the light regime within the canopy affects ecosystem processes. In particular, f<sub>APAR</sub> and its variability affect the canopy energy, water, and carbon budget of tundra ecosystems (Caldwell et al., 1974; Huemmrich et al., 2010; Tagesson et al., 2012; Huemmrich et al., 2013). For example, evapotranspiration is sensitive to spatial heterogeneity of radiation within the canopy (Song et al., 2009; He et al., 2014). He et al. (2014) simulated lower water stress in a forest with a model that included 3D radiative fluxes and canopy structure as compared to a homogeneous case due to the light limited vegetation in shaded areas. Furthermore, the carbon budget is influenced by spatial heterogeneity of radiation. Light Use Efficiency not only depends strongly on vegetation type and related hydrological conditions (Huemmrich et al., 2013), but also on light heterogeneity caused by self-shading (Huemmrich et al., 2010; Williams et al., 2014). Consequently, Sprintsin et al. (2012) showed strong effects of the radiation scheme on modelled gross primary production. Thus, the high local variability of the shortwave radiation budget is relevant for a number of land-climate feedbacks.

Edge effects extended to larger patches for canopy transmittance as compared to albedo and f<sub>APAR</sub>. This may be a consequence of the different heights being relevant for each radiation process. While albedo and f<sub>APAR</sub> are determined by the mean scattering centre of the canopy, transmittance is defined below canopy. Thus lateral shading may affect the radiation at soil level further away from the tall elements. The characteristic length scale differed between vegetation types, which indicates complex interaction between the spatial vegetation distribution and the radiation budget.

The edge effects and length scales found in this study likely depend on the irradiance conditions. Our work was conducted for a unique illumination con-
figuration. While we simulated clear-sky conditions, a higher fraction of diffuse light generally lowers the albedo (Eugster et al., 2000), an effect observed more strongly in wet sedge tundra as compared to dwarf shrub tundra (Juszak et al., 2016). Cloud cover also increases wet sedge transmittance more strongly than dwarf shrub transmittance (Juszak et al., 2016). Therefore changes in irradiance conditions will likely have different effects on the spatial variability of the radiation budget, depending on vegetation type. Furthermore, the time within the growing season influences sun angles and canopy and background properties and thus the radiation budget. Field measurements generally show an increase in tundra (and shrub specifically) albedo in the course of the summer (Lafleur et al., 1997; Lloyd et al., 2001). This seasonal albedo variation is influenced by vegetation development, structure, and background properties, and therefore depends on vegetation type (Juszak et al., 2016). As our study focusses on a single time-point, this temporal evolution is not included. Further research and temporally-resolved input and validation data are needed to quantify the seasonal cycle of all radiation budget components for each vegetation type.

## 4.3. Drivers of the radiation budget at the landscape scale

We found that the fraction of standing water was by far the most important driver of landscape albedo (Table 5). Thus, currently observed changes in water cover (Smith et al., 2005; Carroll et al., 2011; Lin et al., 2012) will likely affect the tundra energy budget strongly. The importance of standing water for spatial and temporal tundra albedo variations has been highlighted in several studies (Lafleur et al., 1997; Gamon et al., 2012) and has been acknowledged by defining lake area as essential climate variable (Bojinski et al., 2014). However, we consider water bodies of very small spatial extent, typically covering only a few square metres. Arctic tundra often comprises such small scale water bodies that cannot be detected based on medium resolution satellite imagery such as Landsat-7 (Muster et al., 2012; Virtanen & Ek, 2014). In polygonal tundra, this can lead to a 35% lower estimate of water surface area and translate into high uncertainties in energy fluxes, especially evapotranspiration (Muster et al.,
2012). While small water bodies are included in the satellite albedo estimates, they are neglected in medium and large scale land cover maps (such as Gould et al., 2003; Walker et al., 2005). As our modelling results highlighted that the fraction of standing water was strongly influencing tundra albedo, simplified land cover maps and underestimation of the water surface area can affect large scale modelling results, especially in wetlands. Our results showed that wetlands with high cover of peat mosses or dry sedges had the highest albedo within the tundra landscape at our site, while water bodies and waterlogged sedges had the lowest albedo (Figure 5). Land cover and vegetation type in these lowlands are highly dependent on the hydrological conditions. Even under predicted permafrost thaw, the hydrological implications are highly uncertain (Walvoord & Kurylyk, 2016).

The second significant driver of landscape albedo was shrub cover, which was more important than PAI. The importance of shrub cover is well known, as shrub expansion is associated with a positive feedback to global warming (Chapin et al., 2005; Blok et al., 2011b; Lawrence & Swenson, 2011). However, at the larger scales shrub cover and PAI are linked (Thompson et al., 2004; Beringer et al., 2005) and their relative importance for growing season albedo cannot easily be disentangled in modelling studies that increase both values simultaneously (such as in Lawrence & Swenson, 2011; Bonfils et al., 2012).

PAI explained almost all variability in transmittance and f<sub>APAR</sub> among the strip transects. The importance of PAI for f<sub>APAR</sub> (Myneni et al., 1997; Asner et al., 1998; Shabanov et al., 2000) and transmittance has been highlighted in other studies (Flerchinger et al., 2009; Juszak et al., 2014). At the landscape scale, edge effects did not significantly influence the radiative budget (Table 5).

Albedo was only weakly related to transmittance and f<sub>APAR</sub> at the landscape scale and even less at the local scale. An accurate estimate of PAI is important for transmittance estimates and thus for assessing the energy budget at the soil surface.
4.4. Influence of spatial distribution and interaction of land cover types

At the landscape scale, our direct 3D model results were very similar to the results of the weighted averages and the difference of 3% is likely within the model uncertainty (Figure 8). However, the higher albedo estimate using simple weighted averages in a complex landscape is consistent with studies of the forest and the global radiation budget (Rowe, 1993; Yuan et al., 2014). The small effect may be due to low canopy height in our simulations (Dickinson et al., 2008). The bias in albedo resulting from the direct 3D versus weighted average modelling approaches needs further investigation, such as a comparison to field measurements with fully characterized uncertainties. This detailed validation will help to identify the appropriate model complexity and grain size depending on the scale of interest.

Simulations with the direct 3D approach on average increased canopy transmittance by only 3% as compared to the simple approach. The lower transmittance estimate by simple models is consistent with Knyazikhin et al. (1997), who found that 1D simulations overestimate the decline of solar radiation in a canopy with depth.

In line with albedo and transmittance, the f<sub>APAR</sub> results revealed little differences between the direct 3D model and a weighted average, while other studies report significant underestimation of f<sub>APAR</sub> using 1D models (Kobayashi et al., 2014; Loew et al., 2014; Yuan et al., 2014). Kobayashi et al. (2014) show that 1D simulations in boreal forests underestimate the fraction of light absorbed by the canopy (f<sub>APAR</sub>) by about 50%. As for albedo and transmittance, the small differences between the direct 3D model and weighted averages that we found is most likely due to the short-statured vegetation at our study site. The tundra canopy in our model is less than 80 cm tall. Additionally, we explicitly include canopy gaps as independent vegetation types in both simulations, direct 3D and weighted averages.

Overall, we find that tundra albedo, transmittance, and f<sub>APAR</sub> are less sensitive to the spatial distribution and interaction of land cover types (as indicated by different model complexities) than to land cover type and canopy charac-
teristics at the landscape scale. As the effect of different model complexities is much smaller than the variability among the strip transects, we suggest that more effort should be made to estimate water cover, shrub cover, and PAI than toward more physically based modelling at the landscape scale. However, the 3D model results depend on the model parametrisation and may differ more strongly from weighted averages when plants are simulated as objects instead of turbid media, or when the turbid media include vertical gradients. Furthermore, the influence of model complexity on the results strongly depends on the scale of interest. While direct 3D radiative transfer modelling may not be needed for radiative fluxes at the landscape scale, we find that at the small scale the heterogeneity of the radiation budget can be substantial. Thus, 3D modelling may be required in case of non-linear feedbacks.

## 5. Conclusions

Our modelling results show that the surface area of water bodies and water-logged sedges is the most important driver of tundra albedo in summer, even at small scales where current Earth observation satellites will not be able to assess the process of dynamic changes in water body size due to their spatial resolution. Shrub cover is the second most important control and explains more of the spatial albedo variations than PAI. Canopy transmittance and absorbed PAR are almost entirely controlled by PAI at the landscape scale. At the landscape scale, the effect of model complexities with and without spatial heterogeneity is much smaller than the variability depending on the cover type and canopy plant area. Therefore, accurate validation data would be needed to determine the most suitable model complexity. However, using the direct 3D radiative transfer model we found considerable variability of albedo, transmittance, and canopy absorbed PAR at the scale of a few centimetres, which cannot be easily observed from satellite. As local radiation variability influences photosynthesis and evapotranspiration, it should be considered in modelling studies of the tundra energy or water budget. If coarse satellite data are the major model input,
the local radiation variability and associated feedbacks should be parametrised using sub-grid scale models. We recommend assessing this local scale radiation variability at large scales as well, to determine if water cover and PAI influence albedo in a similar fashion. Building on our results on the shortwave radiation budget, an analysis of non-linear feedback mechanisms between radiation, evaporation, and photosynthesis is needed to draw conclusions on changes of the Arctic energy budget. Our results highlight the importance of small water bodies, shrub cover, and the PAI, which does not only include green leaves but also standing dead leaves and wood. As very little data on standing dead leaves and wood are currently available, we propose more field measurements of these components to allow for more detailed parametrisations in land surface models. Furthermore, we propose to extend the analysis from spatial to spatio-temporal radiation variability. In this way, vegetation, irradiance, and snow dynamics could be included.

## Acknowledgements

We thank Tim Grünberg, Institute of Fluid Dynamics, ETH Zurich, for helping with the projection of leaf angles, raster calculations, and computational resources. This work is supported by the Swiss National Science Foundation through project grant 140631 and by the University of Zurich research priority program on Global Change and Biodiversity (URPP GCB).

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## 1013 Appendix. Detailed description of the methods

### 1014 A.1. *Vegetation map*

1015 *Vegetation reference points.* To train and validate the vegetation map, we visually selected 187 points in the study area which were clearly within one vegetation type and estimated the radius for which each point was representative (point size in Figure 1b). As we were using a hand-held GPS with ±3 m
accuracy, we needed to validate the point locations in comparison with the orthomosaic. We removed points that lay outside the vegetation type in question (22 points) and shifted points which lay on the border of a vegetation patch (32 points). For 40 points, we reduced the size of the estimated radius because they intersected with other vegetation types on the orthomosaic. Half of the points were used for training of the vegetation classifier, the other half for validating the final map. We chose additional water training points based on the orthomosaic as they were difficult to access in the field.

**Classification.** We classified the vegetation based on the four image bands (RGB and NIR) as well as hue and saturation, which we calculated from the RGB image. We additionally used the entropy of the hue image as seventh input channel. For more robust mapping results, we reduced the image resolution to 15 cm. The supervised classification was done with a maximum likelihood classifier (ENVI, Version 5.2). Based on field observations, we restricted low shrubs (S2) to areas close to rivers and floodplains in a post-processing step. In order to reduce the number of patches smaller than 4 pixels, we sequentially assigned those pixels to classes with a similar likelihood if that increased the patch size.

**Classification accuracy.** For comparison with other tundra maps, we aggregated the nine original classes to four classes as defined by the circumpolar Arctic vegetation map (Walker et al., 2005). These are tussock-sedge, dwarf shrub, moss tundra (G4), erect dwarf shrub tundra (S1-1, S1-2), low shrub tundra (S2), and sedge, moss, dwarf shrub wetland (W2-1, W2-2, W2-3, W2-4, and shallow water). For these four classes we obtained an overall accuracy of 65% and a Kappa coefficient of 0.53 using an equal amount of validation pixels per class. The best accuracy was achieved by including the lichen-rich shrub tundra (S1-2) in the tussock tundra class (G4). The map with four classes aggregated in this way had an overall accuracy of 74% and a Kappa coefficient of 0.65.

The classification accuracy was lower than in other studies due to three main reasons. First, we were not able to collect water reference points in deep
ponds or the river. We added additional points representing deep water to the training data based on visual inspection of the orthomosaic. Thus, the classifier was trained on points which included deep water bodies in the water class. Shallow water was mostly classified as waterlogged sedges (W2-4). As we did not add additional points to the validation data, the classification accuracy of water was only computed for shallow ponds which we were able to access in the field. Given the typically low vegetation density of waterlogged sedges and the strong background effects in both, waterlogged sedges and shallow water, this classification imprecision is not problematic and mainly due to suboptimal field sampling of reference points.

Second, the sub-classes dry sedges (W2-2) and peat moss (W2-3) were often misclassified because they appeared very similar on the orthomosaic. While peat moss occurred in both classes, the classes could be distinguished in the field based on the cover of sedges. However, dry sedges have a high cover of light-coloured standing dead leaves, which have a similar reflectance as peat moss areas, at least in the four spectral bands covered by the orthomosaic. The albedo of W2-2 and W2-3 was almost identical (Figure 5). These two sub-classes were mainly distinguished for modelling canopy transmittance and absorptance and should be merged in a vegetation map.

Third and most importantly, erect dwarf shrub tundra (S1-1 and S1-2) can-
not be clearly distinguished from tussock sedge tundra (G4) by the classifier.
This difficulty has been pointed out by Siewert et al. (2015) in a classification
of a GeoEye-1 satellite image of the same field site. Several other studies do
not distinguish, or do not have, tussock tundra (Lantz et al., 2010; Atkinson &
Treitz, 2012; Muster et al., 2012; Virtanen & Ek, 2014). The similarity between
lichen-rich shrubs and tussock tundra is a consequence of the similarity of the
two classes in terms of species composition. The major difference is the pres-
ence of *Eriophorum vaginatum*, a tussock forming sedge. However, this sedge
has a low leaf area and canopy height at the site (Table 2) and thus does not
dominate the surface reflectance. As we modelled very similar albedo values for
S1-2 and G4, landscape scale albedo is insensitive to misclassification between
these classes.

The classification accuracy could potentially be improved by including the
NDVI. However, we used the NDVI to spatially extrapolate model input vari-
ables and thus avoided circular reasoning by not including NDVI in the vegeta-
tion classification. A second potential classification input is microtopography.
However, we used topography as input for the radiative transfer model and
thus wanted to keep the vegetation classification independent of the topogra-
phy. Spectrally similar vegetation classes could also have been avoided using an
unsupervised classification approach (Atkinson & Treitz, 2012). However, un-
supervised classification of tundra areas does not necessarily yield homogeneous
vegetation classes (Schneider et al., 2009). Furthermore, we collected input data
for the radiative transfer model for specific vegetation classes in the field and
thus were restricted to those for the modelling.

### A.2. *Input variables for radiative transfer modelling*

**Plant area index.** We used different methods to measure green leaf area index (LAI) for shrubs and graminoids in the field in the peak growing seasons 2013 and 2014. *Betula nana* (S1-1) projected LAI and wood area index were measured non-destructively using 1 m × 1 m point quadrat grids where we vertically lowered a needle at 81 points and recorded all contacts with leaves or wood (Juszak et al., 2016). We collected in total 25 measurements distributed over 10 plots within two growing seasons. We computed LAI by dividing projected LAI by the average point quadrat efficiency. The point quadrat efficiency was estimated in two destructive harvests to be 0.78 for *B. nana* leaves and 0.76 for *B. nana* wood. In case of LAI, this estimate contains the total one-sided LAI, while the wood area index is a projection of the cylindrical elements, approximately the product of branch diameter and length.

For estimating *Eriophorum angustifolium* (W2-1 and W2-2) LAI, we used an
allometric approach, which involved counting leaves and destructively measuring
single leaf areas (Juszak et al., 2016). For sub-class W2-1, we measured canopy
height and counted all tillers and the number of green leaves per tiller on 16
squares of 100 cm² on 1 m². We collected in total 30 measurements distributed over 11 plots within two growing seasons. For sub-class W2-2, we measured canopy height, counted tillers and leaves on four plots of 50 cm × 50 cm. We combined the information of both *E. angustifolium* sub-classes with destructively measured leaf sizes. We measured the total standing dead leaf area of *E. angustifolium* on three destructive plots of wet sedge tundra (W2-1) by weighing all standing dead leaves and scanning a subset.

*Eriophorum vaginatum* (G4) LAI was estimated on seven plots of 50 cm × 50 cm. We counted the number of leaves per plot and multiplied it by the average area of single leaves that was obtained from scanning.

We extrapolated the LAI spatially using the NDVI and an exponential function (Equation 2). To avoid unrealistically large LAI values, we reduced all LAI which were more than 1.5 times higher than the maximum observation to the maximum observed LAI. The parameters *a* and *b* are shown in Table A1 and the statistics of the modelled LAI per vegetation type in the strip transects in Table 2. We used literature values of LAI for low shrub tundra (S2) and waterlogged sedge tundra (W2-4). For low shrub tundra we took the minimum (LAI=0.77) and maximum (LAI=1.95) values from Imnavait creek water tracks, Alaska by Williams et al. (2006) and fitted them to the 0.05 and 0.95 quantiles of the NDVI data. The literature LAI values were consistent with other sources (Beringer et al., 2005). For *Carex* spp. dominated waterlogged sedge tundra we used LAI=0.4 (*Carex* spp. dominated wetland near Toolik, Alaska, Shaver & Chapin (1991); McFadden et al. (2003)) as median and took the maximum value of LAI=0.65 (wet sedges without shrubs, S3, Imnavait creek, Alaska, Williams et al. (2006)) to fit to the 0.95 quantile.

We used linear regressions with observed LAI to spatially extrapolate the other input variables (Equation 3, Table A1). Due to the lack of observations for low shrub tundra wood area index, we used the same parameters that we obtained from the fit of dwarf birch leaf and wood area index (Table A1). We estimated standing dead leaf area and green leaf area index destructively at three plots of wet sedges (*E. angustifolium*, W2-1). Due to the limited number
<table><caption>Table A1: Parameters *a* and *b* for computing LAI from NDVI with an exponential equation (Equation 2) and parameters *p* and *q* for computing other variables from LAI with a linear equation (Equation 3) for each vegetation type; canopy and standing dead leaf height in mm.</caption><thead><tr><th>Variable \ Type</th><th></th><th>G4</th><th>S1-1</th><th>S2</th><th>W2-1</th><th>W2-2</th><th>W2-4</th></tr></thead><tbody><tr><td rowspan="2">LAI</td><td><i>a</i></td><td>0.00002976</td><td>0.02618681</td><td>0.05929370</td><td>0.01425009</td><td>0.00202313</td><td>0.01523543</td></tr><tr><td><i>b</i></td><td>12.6308</td><td>4.8927</td><td>4.4051</td><td>6.1931</td><td>8.8501</td><td>4.7804</td></tr><tr><td rowspan="2">Wood area index</td><td><i>p</i></td><td>0</td><td>0.536</td><td>0.536</td><td>0</td><td>0</td><td>0</td></tr><tr><td><i>q</i></td><td>0</td><td>0.439</td><td>0.439</td><td>0</td><td>0</td><td>0</td></tr><tr><td rowspan="2">Standing dead leaf area index</td><td><i>p</i></td><td>0</td><td>0</td><td>0</td><td>1.16</td><td>1.16</td><td>0</td></tr><tr><td><i>q</i></td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td rowspan="2">Canopy height</td><td><i>p</i></td><td>0</td><td>7.21</td><td>80</td><td>16.7</td><td>8.51</td><td>16.7</td></tr><tr><td><i>q</i></td><td>12.2</td><td>18.8</td><td>40</td><td>25.5</td><td>19.7</td><td>25.5</td></tr><tr><td rowspan="2">Standing dead leaf height</td><td><i>p</i></td><td>0</td><td>0</td><td>0</td><td>8.13</td><td>8.13</td><td>0</td></tr><tr><td><i>q</i></td><td>0</td><td>0</td><td>0</td><td>11.3</td><td>11.3</td><td>0</td></tr></tbody></table>

of observations, we forced the regression through zero assuming that standing dead leaves are always associated with plants which also have green leaves. We used the same parameters also for dry sedges (*E. angustifolium*, W2-2).

**Canopy and standing dead leaf height.** We used two different approaches to measure canopy height in the growing seasons 2013 and 2014. For dwarf birch (*B. nana*, S1-1) and wet sedges (*E. angustifolium*, W2-1) we measured canopy height at 25 points of a 1 m × 1 m point quadrat grid at the same time and plots as our LAI estimate (Juszak et al., 2016). At the *E. angustifolium* plots, we also measured standing dead leaf height above the water or wet litter surface at the same points as canopy height. On the other hand, we measured canopy height of single individuals on six tussock sedge plots (*E. vaginatum*, G4) and five dry sedge plots (*E. angustifolium*, W2-2).

We extrapolated canopy height spatially for each type using a linear regression between canopy height and LAI measured at the same plots at the same time (Equation 3). For tussock tundra, the linear fit showed a negative relationship between LAI and canopy height for the six observations. Instead of a negative slope, we used a constant canopy height independent of the leaf area.
For low shrub tundra we adjusted the parameters *p* and *q* in a way that the final canopy height varied between 1 and 2 m (Table 2), a range that we observed in the field. We used the parameters of *E. angustifolium* dominated wet sedge tundra (W2-1) also for *Carex* ssp. dominated waterlogged sedge tundra (W2-4, Table A1). We only observed a layer of standing dead leaves below *E. angustifolium*, in the vegetation types W2-1 and W2-2. Standing dead leaf height was related to LAI using the same parameters for both types although our field measurements covered only type W2-1.

### A.3. Input parameters for radiative transfer modelling

**Leaf and wood angle distribution.** We measured the leaf angle distribution in three different ways depending on species and organ. For *B. nana* leaves, we used the method by Pisek et al. (2011). This method employs carefully levelled photography of the vegetation taken from all cardinal directions. In each image, we identified leaves which were perpendicular to the image plane. We marked these leaves in the image and calculated the leaf inclination angle (Leaf normal - nadir, Figure A1a). In total, we measured 1294 *B. nana* leaves. We fitted a beta function to the data to reduce the scatter (Figure A2a). Beta functions are commonly used for leaf inclination angle distributions (e.g. Goel & Strebel, 1984; Strebel et al., 1985; Wang et al., 2007).

We had to modify the method by Pisek et al. (2011) for *B. nana* wood and *E. angustifolium* green and standing dead leaves as it was not possible to identify cylindrical or triangular objects perpendicular to the image plane. In this case, we marked all segments of green leaves, standing dead leaves, and wood that were visible on the images, even the segments pointing towards or away from the camera, in total more than 8000 per organ (Figure A1b). For leaves that were inclined towards or away from the camera, this raw data overestimated the leaf inclination angle. We corrected for this effect in three steps. First, we weighted the histograms of measured inclination angles by the length of each identified segment. We did that for each azimuth view direction separately and then took the mean of all probability distributions as we did not identify an
<figure><img src="image_10.png" /><figcaption>Figure A1: Sample pictures used for measuring leaf angle distribution of (a) *B. nana* and (b) *E. angustifolium*; red numbers indicate the leaf inclination angle of a leaf or leaf segment.</figcaption></figure>

equal amount of segments in each view direction. Second, we converted the observed, projected leaf inclination angle distribution to the real inclination angle distribution assuming a random distribution of leaf azimuth angles. This step involved binning the leaf inclination angles and computing weights for each bin which describe, how much of which original leaf angle has contributed to this bin given random azimuth angles. The real leaf angle distribution was computed by solving a linear system of equations with the projected leaf angle distribution and the weights of all bins. Third, we corrected for the fact that leaves appeared shorter on the images if they were not perpendicular to the image plane. Finally, we fitted a beta function to the data (Figure A2b–d) in the same way as for *B. nana* leaves.

For *E. vaginatum* and *Salix pulchra*, we manually measured the leaf inclination angles of 21 and 39 leaves, respectively. As the number of measured leaves was small, we did not fit a beta function to the data but selected the best fitting standard leaf angle distributions, ‘erectophil’ for *E. vaginatum* and ‘uniform’ for *S. pulchra* (Figure A2e, f) (de Wit, 1965).

**Leaf and wood optical properties.** We measured optical properties of plant organs in the field using an Ocean Optics SpectroClip probe in the peak grow-
<figure><img src="image_11.png" /><figcaption>Figure A2: Probability density (bin width: 1 rad = 57.3°) of measured green leaf, standing dead leaf, and wood inclination angle distributions and fitted functions of (a) *Betula nana* leaves, (b) *B. nana* wood, (c) *Eriophorum angustifolium* green leaves, (d) *E. angustifolium* standing dead leaves, (e) *Eriophorum vaginatum* leaves, and (f) *Salix pulchra* leaves.</figcaption></figure>
ing seasons 2013 and 2014 (Figure A3). The probe features two integrating spheres of about 3.5 cm diameter, one for the reflectance and the second for the transmittance of the sample. The sample is fitted between the two spheres with a measurement area of 5 mm diameter. In addition to our measurements of samples, we regularly took reference measurements with a 99% and a 50% reflectance standard and without sample. The integrating spheres were too small in comparison to the sample size to provide data without correction for multiple interactions between light and sample (Jacquez & Kuppenheim, 1955). Thus we did a first-order correction of the raw reflectance and transmittance measurements. We estimated the fraction of light that interacted twice with the sample before being recorded using a comparison between the readings of the 99% standard and the 50% standard. Although we could only calibrate this fraction for non-transmitting samples, we used the same value also for the correction of the transmittance signal. The correction of the samples transmittance involved assuming equal reflectance and transmittance of both leaf sides. We tested the correction for leaves which we measured with the standard procedure, including transmittance, and on a black background.

E. vaginatum leaves were too thin to be measured with the SpectroClip probe in the standard procedure. Therefore, we fixed multiple leaves next to each other on a sample holder. As all leaves together covered the measurement area, we could use the reflectance measurement without further correction. However, for the transmittance measurement, we had to adjust for the reduced transmittance due to the holder. We estimated the E. vaginatum leaf transmittance (T) from the corrected transmittance measurement (T<sub>measured</sub>) and the transmittance of the empty holder (T<sub>empty holder</sub>):

$$T = \frac{T_{\text{measured}}}{T_{\text{empty holder}}^2} \qquad (A1)$$
<figure><img src="image_12.png" /></figure>

Figure A3: (a) Upper face reflectance (bottom half) and transmittance (top half) of the major species (bottom face reflectance not shown for clarity) and (b) background reflectance; the grey lines indicate the MODIS bands 1–7 used for modelling.