#### 2.1. Study Area and Field Measurements

This study was carried out at the Viikki agricultural test field located in Helsinki (Finland) (60.224°N, 25.021°E). The size of the research area was approximately 4 km × 4 km. The annual average temperature in Helsinki is 6 °C; in July, the average temperature is 18 °C. Six crop species were included in this study growing on 162 plots: faba bean (

Vicia faba L. “Kontu”), narrow-leafed lupin (

Lupinus angustifolius L. “Haags Blaue”), turnip rape (

Brassica rapa L. ssp.

oleifera (DC.) Metzg. “Apollo”), wheat (

Triticum aestivum L. emend Thell. “Amaretto”), barley (

Hordeum vulgare L. “Streif”, “Chill” and “Fairytale”) and oat (

Avena sativa L. “Ivory” and “Mirella”). The largest plots were 600 m

^{2} (50 m × 12 m) and the smallest ones 20 m

^{2} (10 m × 2 m). The soil types in the area were fertile luvic stagnosol, haplic gleysol and sulfic cryaquept. The plots differed in seeding density (55–700 m

^{−2}) and fertilizer treatment (0–150 kg N m

^{−2}) leading to LAI range of 1.1–5.0 and a chlorophyll content range of 26–94 μg cm

^{−2} (see the Table 1 in the reference [

20]).

Canopy leaf-angle distribution was determined using the photographic approach [

17], validated and extended to field crops [

20] on 6 July 2012 in the same growth stage as during the spectroscopy measurement. Canopy photographs were taken using a Nikon D1X digital camera mounted on a tripod and leveled with bubble level outside of the plots approximately 1 m away from the edge of the field. The camera height was between 30 and 50 cm depending on crop height. Five to six photographs were taken for each species from one or several plots. Finally, the inclination angles of 75–100 leaves or leaf fragments oriented perpendicularly to the viewing direction were measured using ImageJ 1.47 software, which is an open source image processing program [

34], and used for the calculation of the leaf mean tilt angle (MTA). We assumed LAD to be species-specific, as it has been shown to vary more among species than within species [

8,

13,

35]. A more detailed description of the test site and the photographic method was given by Zou et al. [

20].

Airborne spectroscopy imagery covering the study area was acquired using an AISA Eagle II imaging spectrometer (Specim Ltd., Oulu, Finland) on 25 July 2011. The data were collected between 09:36 and 10:00 local time at approximately 600 m above ground. The flight direction was parallel with the sunrays. The solar zenith angle varied between 50.4° and 48.1° and the measurement zenith angle between 0 and 18.9° was determined by the swath width of the sensor and aircraft orientation changes. Reflected radiation was measured in 64 channels in the visible and NIR spectrum (400–1000 nm) with a spectral resolution of 9–10 nm and a spatial resolution of 0.4 m. The spectroscopic imagery was radiometrically calibrated using the CaliGeo 4.9.9 software package (Specim Ltd., Oulu, Finland) and georectifed using Parge (ReSe Applications Schläpfer, Wil, Switzerland). Finally, the radiometric data were converted to top-of-canopy hemispherical-directional reflectance factors using ATCOR-4 (ReSe Applications Schläpfer, Wil, Switzerland). The spectroscopic data were extracted from the imagery and averaged as average plot spectra.

A SunScan ceptometer (Delta-T Devices, Cambridge, UK) was used to measure LAI in the field. The data used in this study were collected within five days of the airborne campaign. The SunScan ceptometer bar was entered from the edge of the plot at approximately 45° to the row direction to minimize the row effects on LAI measurement as suggested in the instrument manual. LAI was calculated from the measured transmittance following the model implemented in the SunScan hardware. The possibility of light transmitted through the canopy at polar angle

$\theta $ can be modeled for a random spatial distribution element canopy using an exponential model:

where

$a$ is the leaf absorptivity for light set to 0.85 in this study (SunScan SSI user manual) and

$k\left(\theta ,\chi \right)$ is the canopy directional light extinction coefficient depending on LAD. The canopy transmittance model used by SunScan uses an ellipsoidal LAD model depending on the single parameter

$\chi $ to characterize LAD. Commonly,

$\chi $ is assumed to have equal unity corresponding to random distribution of leaf normals due to a lack of information on the actual LAD. In this study, we calculated

$\chi $ from the measured MTA using the following function derived from Equation (16) in [

36]:

For an ellipsoidal leaf angle distribution model,

$k\left(\theta ,\chi \right)$ can now be calculated as [

13]:

The calculations were performed as follows. First, we determined MTA from the measured leaf angles. Next, we calculated the species-specific ellipsoidal leaf angle distribution parameter

$\chi $ from Equation (2) and two extinction coefficient values from Equation (3):

$k\left({\theta}_{S},\chi \right)$ corresponding to the solar zenith angle

${\theta}_{S}$ at the time of the SunScan measurements, and

$k\left(0,\chi \right)$ for the nadir direction. To obtain the LAI, we solved Equation (1) for LAI and used the SunScan-measured

$P\left({\theta}_{S}\right)$ and

$k\left({\theta}_{S},\chi \right)$. Finally, the LAI for each plot was averaged from 4–5 sequential SunScan readings. We used the LAI value for each plot to calculate the fraction of the canopy cover as:

where the light transmission in the nadir direction,

$P\left(0\right)$, was calculated from Equation (2) with

$\theta =0$. Fcover can also be directly related to SunScan measurements. After making all the substitutions listed above, we can write an equation relating Fcover and SunScan-measured transmittance measurements:

A portable spectroradiometer (ASD Handheld, Boulder, CO, USA) with spectral range between 325 and 1075 nm and a spectral resolution of 3 nm was used to measure the bare soil reflectance in four sample plots in a harvested area on 7 October 2011. Bare soil reflected radiation was collected at a distance approximately 40 cm above the soil surface and a field of view of 25°. Soil reflectance was calculated as the ratio of soil-reflected radiance to that measured above a calibrated white Spectralon panel (Labsphere Inc., Sutton, NH, USA). Due to the different solar illumination conditions between soil spectral and airborne spectral measurements, the measured soil reflectance was corrected with a bidirectional reflectance distribution function (BRDF) model developed by Walthall et al. [

37] and modified by Nilson and Kuusk [

38]. The soil spectrum used for PROSAIL model simulation is presented in

Figure 1.

#### 2.3. PROSAIL Simulations

We studied the sensitivity of the VIs to canopy structure (MTA and LAI) using the PROSAIL canopy reflectance model. The model is a combination of the leaf optical reflectance model PROSPECT-5 [

39] and the canopy reflectance model SAILH [

40,

41]. The PROSPECT-5 model simulates leaf reflectance and transmittance from six input parameters: leaf chlorophyll a and b content (

${C}_{ab}$), leaf carotenoid content (

${C}_{Car}$), leaf dry matter content (

${C}_{m}$), leaf water content (

${C}_{w}$), leaf brown pigment content (

${C}_{bp}$), and the mesophyll structure parameter

$N$. The SAILH sub-model simulates canopy reflectance using LAI, MTA, hot spot size parameter, soil reflectance, solar zenith angle, sensor view angle, sensor azimuth angle and the fraction of incident diffuse sky radiation. The leaf inclination angle distribution is characterized from the leaf mean tilt angle to generate an ellipsoidal leaf angle distribution [

42].

First, to illustrate the effects of LAI and MTA on VIs, we varied the MTA between 15 and 75 degrees, set the LAI value to 1, 3 and 5, and set all other parameters to values characteristic of healthy green vegetation:

${C}_{ab}=40\mathsf{\mu}\mathrm{g}{\mathrm{cm}}^{-2}$,

${C}_{Car}=8\mathsf{\mu}\mathrm{g}{\mathrm{cm}}^{-2}$,

${C}_{w}=0.001-0.02\mathrm{cm}$. Other parameters were fixed to values taken from the literature:

${C}_{m}=0.005\mathrm{g}{\mathrm{cm}}^{-2}$ (the average value of the six species [

43,

44,

45,

46]),

$N=1.55$ (the average value of various crops [

27]),

${C}_{bp}=0$ (assuming the leaves were green during the measurements), and the hot spot parameter was set to 0.01 (this parameter has no practical influence on the results as the view direction was far from the hot spot because of low sun). The fraction of diffuse radiation was calculated using the 6S atmosphere radiative transfer model [

47] from actual observation geometry and nearby sun photometer measurements. The parameters describing the illumination and view geometry in the model were set to coincide with the airborne spectroscopy imagery acquisition: solar zenith angle 49.4°, sensor zenith angle 9°, and azimuth angle 90°.

Next, we generated 100,000 parameter combinations by uniformly sampling the variation ranges of

${C}_{ab}$,

${C}_{w}$, LAI and MTA within the measured (for field-measured parameters) or natural variation range (for parameters for which this information was available). According to measurements [

20],

${C}_{ab}$ varied between 25 and 100 μg cm

^{−2}, LAI between one and five, and MTA between 15 and 70 degrees (MTA = 15, 30, 40, 50, 60 and 70°).

${C}_{w}$ varied in a wide natural range of the parameter, between 0.001 and 0.020 cm;

${C}_{car}$ was linked to

${C}_{ab}$ as 1:5 based on the LOPEX93 dataset [

48].