# Structural complexity biases vegetation greenness measures

Yelu Zeng, Dalei Hao, Taejin Park, Peng Zhu, Alfredo Huete, Ranga Myneni, Yuri Knyazikhin, Jianbo Qi, Ramakrishna Nemani, Fa Li, et al.

► To cite this version:

Yelu Zeng, Dalei Hao, Taejin Park, Peng Zhu, Alfredo Huete, et al. Structural complexity biases vegetation greenness measures. Nature Ecology & Evolution, 2023, 7 (11), pp.1790-1798. 10.1038/s41559-023-02187-6. hal-04928975

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Structural complexity biases global vegetation greenness measures

Yelu Zeng<sup>a,b,*,+</sup>, Dalei Hao<sup>c,*,+</sup>, Taejin Park<sup>d,e,+</sup>, Peng Zhu<sup>f</sup>, Alfredo Huete<sup>g</sup>, Ranga Myneni<sup>h</sup>, Yuri Knyazikhin<sup>h</sup>, Jianbo Qi<sup>i</sup>, Ramakrishna R. Nemani<sup>d,e</sup>, Fa Li<sup>b</sup>, Jianxi Huang<sup>a</sup>, Yongyuan Gao<sup>a</sup>, Baoguo Li<sup>a</sup>, Fujiang Ji<sup>b</sup>, Philipp Köhler<sup>j</sup>, Christian Frankenberg<sup>k</sup>, Joseph A. Berry<sup>l</sup>, Min Chen<sup>b,*</sup>

Abstract

Vegetation 'greenness' characterized by spectral vegetation indices (VIs) is an integrative measure of vegetation leaf abundance, biochemical properties, and pigment composition. Despite greater leaf area in forests, satellite observations of some major VIs are higher over crops (e.g., the Corn Belt in the United States) than over the forests (e.g., the Amazon rainforest) during the peak growing season of crops. This contradicting pattern can lead to critical misinterpretations in global vegetation studies, and thus understanding its underlying drivers and impacts is essential. Our analysis of multi-sensor satellite observations and radiative transfer model simulations reveals that macroscale shadows cast by complex structures of forests lead to lower greenness measures compared to structurally simple and homogeneous crops. The observed differential response of VIs is inevitable because most Earth Observing satellites do not view the earth in the solar direction and thus view shadows due to the sun-sensor geometry. This shadowing effect is evident not only for the reflectance-based optical remote sensing observations, but also for the emerging solar-induced chlorophyll fluorescence. Our findings have important implications for interpreting VIs in global vegetation changes. For instance, the land conversion process over the Amazon from forests to crops shows significant increases in VIs despite a decrease in leaf area due to the diminishing shadow impact resulting from the sudden replacement of forest shadows by sunlit crops. Our findings highlight the importance of taking the shadow impacts into account for correctly interpreting remotely sensed VIs in global spatial and temporal vegetation changes.

<footnote><sup>a</sup> College of Land Science and Technology, China Agricultural University, Beijing, China</footnote>

<footnote><sup>b</sup> Department of Forest and Wildlife Ecology, University of Wisconsin-Madison, Madison, WI, USA</footnote>

<footnote><sup>c</sup> Atmospheric Sciences and Global Change Division, Pacific Northwest National Laboratory, Richland, WA, USA</footnote>

<footnote><sup>d</sup> NASA Ames Research Center, Moffett Field, CA, USA</footnote>

<footnote><sup>e</sup> Bay Area Environmental Research Institute, Moffett Field, CA, USA</footnote>

<footnote><sup>f</sup> Laboratoire des Sciences du Climat et de l'Environnement CEA-UVSQ-CNRS, Gif sur Yvette, France</footnote>

<footnote><sup>g</sup> Faculty of Science, University of Technology Sydney, Sydney, NSW, Australia</footnote>

<footnote><sup>h</sup> Department of Earth and Environment, Boston University, Boston, MA, USA</footnote>

<footnote><sup>i</sup> Centre d'Etudes Spatiales de la Biosphere, Toulouse, France</footnote>

<footnote><sup>j</sup> EUMETSAT, Darmstadt, Germany</footnote>

<footnote><sup>k</sup> Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA</footnote>

<footnote><sup>l</sup> Department of Global Ecology, Carnegie Institution for Science, Stanford, CA, USA</footnote>
**P1:** Terrestrial vegetation plays important roles in carbon, water, and energy exchanges between the land and the atmosphere. Changes in global vegetation structure and function have been observed as changes in so-called vegetation greenness, an integrative measure of leaf chlorophyll content, leaf area, species composition, canopy cover, and structure. Spectral vegetation indices (VIs) and green Leaf Area Index (LAI) from Earth-observing satellites are commonly used as proxies of vegetation phenology and provide quantitative, timely, and accurate information on the vegetation growing status ¹⁻⁶. These VIs are typically calculated as the ratio of surface reflectance at specific wavelengths due to the contrasting spectral signatures of vegetative and non-vegetative (e.g., background substrate and atmosphere) features, at these wavelengths. A greenness index typically contrasts a primary absorption band against a non-absorbing one. In this case the best green-vegetation absorption band is in the 'red' wavelengths (600-750 nm), and the best reflection band is in the near-infrared (NIR) wavelengths (750-1, 100 nm), rather than the 'green' wavelengths (440-600 nm). The red vs. NIR contrast on vegetation is stronger than the red vs. green contrast and thus is more widely used, although NIR is beyond the visible colour 'green'. Example VIs include the widely used ratio-based normalized difference vegetation index (NDVI), the enhanced vegetation index (EVI) and Near-Infrared Reflectance of Vegetation (NIRv) which includes the ratio plus a dependence on the absolute value of NIR reflectance ¹,⁷,⁸. Their simplicity has enabled various Earth science applications since the 1970s such as monitoring crop growth status ⁹,¹⁰, detecting vegetation phenophase ⁷,¹¹⁻¹³, and assessing climate change impacts on terrestrial ecosystems ²,⁴,¹⁴,¹⁵.

**P2:** Remotely sensed LAI is usually retrieved from a full radiative transfer model explicitly accounting for the vegetation structural characteristics of diverse biome types, and thus is theoretically not influenced by the sun-sensor geometry or shadows ⁵,¹¹,¹⁶. VI-informed greenness is not explicit about the underlying physical mechanisms and can result in important ambiguities, thus misinterpretation. For example, VIs from satellites are typically sensitive to the variation of seasonal sun-sensor geometry, which thus have been suggested to be normalized to a nadir view direction and a constant solar zenith angle or at local solar noon¹⁷,¹⁸. This angular normalization is critical because geometry-induced seasonal VI changes can be misinterpreted as ecological signals leading to controversial debates, e.g., seasonality in the Amazon rainforest¹¹,¹⁸,¹⁹. In addition, sensors on board satellites only sample a small and variable fraction of the total canopy reflected photons in a certain view direction, and therefore there remains a large gap between the satellite-observed signal and the total signal reflected by the canopy. Recent advances in radiative transfer theory bridge such a gap by introducing a new physical parameter, namely, the photon escape probability (*fesc*)³,²⁰. The concept of *fesc* was initially introduced to measure the photon escape probability of solar-induced chlorophyll fluorescence (SIF)²⁰, and subsequent research³ has demonstrated that *fesc* can also be used for characterizing the ratio of canopy reflected photons (i.e., top-of-canopy reflectance) in the visible-near infrared region and thus the derived VIs such as NIRv.
**P3:** *fesc* is defined as the ratio of photons escaping from the canopy that are observed by the sensor to the canopy intercepted and then reflected or emitted photons, and is mostly dependent on the canopy structure and sun-sensor geometry. *fesc* can be regarded as a physical structural property of vegetation that is directly measurable, and thus may be used as a key metric to diagnose and explain biases between the satellite-received and the canopy intercepted and then reflected or emitted light. *fesc* in the NIR band can be approximated by the ratio of NIRv to the Fraction of Photosynthetically Active Radiation (FPAR)²⁰, and is approaching to the NIR reflectance or albedo for dense canopies, which means shaded canopy leads to smaller reflectance or albedo and *fesc*. *fesc* may help answer questions regarding our longstanding view of the global distribution and trends of vegetation greenness, as the typical VIs do not fully take into account the structural complexities of vegetation canopies²¹ in their derivations. Different degrees of structural complexity of biomes will lead to varying levels of *fesc* and result in incomparable spectral greenness measures, i.e., the fraction of sensor measured signal to total signal interacting with the canopy differs ³,²⁰,²². Thus, VIs would be particularly challenged by patterns over the biomes where canopy structural complexity significantly differs, e.g., forests vs. croplands. Meanwhile, green LAI, as a measure of abundance of green leaves, is also widely used to represent vegetation greenness ⁴,¹⁶. In contrast to VIs, LAI-based vegetation greenness analyses account for shadows and theoretically do not suffer the impacts of the complex vegetation canopy structure ²³. Given the theoretical foundation for *fesc*, we hypothesize that higher structural complexity in forest ecosystems associated with smaller *fesc* complicates spectral greenness and biases global vegetation greenness relative to the satellite LAI products as the reference, and therefore may result in inconsistent findings of the variations of vegetation greenness. We combine three independent investigations to test our hypothesis (see Methods).

## Contrasting patterns in spectral greenness over Corn Belt and Amazon rainforest

**P4:** First we examine the spatial patterns of satellite derived global VIs (NDVI, EVI and NIRv) and LAI together with *fesc* in the NIR band. At global scale, we find that all VIs derived from Moderate Resolution Imaging Spectroradiometer (MODIS), except NDVI, exhibit similar spatial patterns during the peak growing season of crops in Northern Hemisphere summer. Specifically, these VIs show greater values over cropland-dominated regions compared to densely forested regions covering most tropical rainforests, although they have higher LAIs (Supplementary Fig. 1). This contrasting pattern is most obvious in the Amazon rainforest region and United States (US) Corn Belt during the Northern Hemisphere summer. We focus on these two dense biomes as representatives for the structurally complex forest and uniform cropland, respectively. Over the US Corn Belt, we observe higher EVI (0.61±0.06) and NIRv (0.33±0.04) with the mean value (± standard deviation) compared to those over the Amazon (EVI = 0.55±0.04, NIRv = 0.27±0.02), while the rainforest has higher LAI (5.7±0.6) than the Corn Belt (2.6±0.3) (Fig. 1). As hypothesized, this contrasting pattern in VIs and
LAI is strongly associated with *fesc* in the NIR band, i.e., high LAI with low *fesc* (0.31±0.03) in Amazon leads to low VIs, whereas low LAI with high *fesc* (0.45±0.04) in the Corn Belt produces high EVI or NIRv. The responsive degree of VIs (EVI and NIRv) to LAI theoretically can be an empirical indicator of *fesc*²⁰. For instance, the slope of LAI-EVI over the Corn Belt was at least twice as high as the slope over the Amazon rainforest (Supplementary Fig. 3), implying a lower (or higher) *fesc* in the Amazon (or Corn Belt). This suggests the spatial or temporal analysis of VI-based greenness across biomes could be biased, because the same VI can correspond to dramatically different amounts of leaves (i.e., LAI). To avoid the possible anomaly of VIs and LAI caused by climate extremes in certain years, the yearly data in August during 2001-2019 were evaluated (Supplementary Fig. 5) as a comparison to the long-term average data in Fig. 1. A few more global VI and LAI products, including the MOD13 NDVI/EVI, GEOV LAI and GLASS LAI were used for the analysis (see Methods and Supplementary Fig. 6) as a comparison to the MCD43 NDVI/EVI and MODIS LAI in Fig. 1, and the MCD43-based Difference Vegetation Index (DVI), the two-band version of the Enhanced Vegetation Index (EVI2) and the newly proposed kNDVI²⁴ in Supplementary Fig. 2. The Green-Red Vegetation Index (GRVI)²⁵ was used as a proxy of canopy pigment pools to evaluate the contrast under the control of similar pigments (Supplementary Fig. 7). A forest region in North America near the Corn Belt with the same season and similar latitude and solar-viewing geometry was included for the analysis (Supplementary Figs. 8-10). The observation-based findings are consistent across different LAI data from different algorithms and satellite data (Supplementary Fig. 6), years (Supplementary Fig. 5), regions (Supplementary Fig. 8), and VIs (Supplementary Fig. 2).

**Structural complexity biases spectral vegetation greenness**

**P5:** We then use multi-angular satellite observations to examine the role of vegetation structure and associated shadow impacts on the identified discrepancy of VIs over the Amazon forests and Corn Belt. Two important indicators are used, i.e., angular variation of VIs and hotspot direction VIs. The angular variation of VIs can be a proxy of canopy structural complexity because more complex canopy casts more shadows leading to a larger angular variation. The hotspot direction VIs offers valuable insights into surface vegetation by minimizing shadows in view and maximizing *fesc*, regardless vegetation types. Note that the hotspot direction is an observing condition when the solar and sensor directions coincide (i.e., phase angle $γ = 0°$). Two multi-angle imaging satellites are used: Polarization and Directionality of the Earth's Reflectances (POLDER) and Multi-angle Imaging Spectro Radiometer (MISR) ²⁶,²⁷. Both multi-angular observations from POLDER and MISR capture general hotspot angular signatures of VIs revealing larger angular variations over the Amazon rainforest compared to the Corn Belt in EVI and NIRv. For EVI, the coefficient of variation (CV=σ/μ) of POLDER (MISR) across the entire angular range was 0.20 (0.16) over the Amazon rainforest, while these are only 0.09 (0.06) over the Corn Belt. Similarly, the CV of NIRv from POLDER
(MISR) was 0.27 (0.22) over the Amazon rainforest, while was only 0.12 (0.07) over the Corn Belt. At the condition of angular normalization we used for MODIS ( =28.8°±2.1° for Corn Belt, 19.4°±6.0° for Amazon rainforest), we detect similar VI patterns observed from the MODIS, i.e., higher EVI and NIRv over the Corn Belt compared to the Amazon rainforest. However, this pattern over the two biomes is reversed when the sensors see vegetation canopy at hotspot direction ( =0°). As the sensor direction deviates from the solar direction (i.e., the phase angle increases), there are different change rates for the two biomes: the Amazon rainforest EVI and NIRv on POLDER (MISR) decrease as large as 7.8% (7.3%) and 9.5% (9.3%) every 10° increase of phase angle, while the Corn Belt EVI and NIRv on POLDER (MISR) only decrease 3.7% (3.4%) and 3.8% (3.7%), respectively. This suggests VI-based greenness (away from hotspot direction) could be impacted differently by the structure complexities while the impact may be removed if the VIs are angularly normalized to the hotspot direction. Unlike EVI and NIRv, we observe that the NDVI in the hotspot direction is lower than those in other directions while there is no obvious NDVI change along the range of phase angles, which is possibly due to the saturation of NDVI over dense canopies²⁸ and that *fesc* partially cancels out from the numerator and denominator of the ratio-based VIs, while *fesc* does not cancel for NIRv with the additional NIR scalar. We also find no significant angular variations in POLDER and MISR NDVIs for both biomes, with changes no more than 2.0% observed for every 10° increase of phase angle (Kolmogorov-Smirnov test: *p*<0.05). This suggests the issue of shadow-induced bias affects many commonly used VIs, except for some purely ratio-based indices like NDVI.

**P6:** Finally, we use a state-of-the-art 3D photon ray-tracing model (LargE-Scale remote sensing simulation, LESS) ²⁹ to explicitly quantify the roles of visible sunlit or shaded leaf fraction in view together with *fesc*. The vegetation structure parameters and leaf/soil spectrum of the two regions are prepared from the field data, airborne Light Detection and Ranging (LiDAR) measurements, and literature review (Supplementary Table 1 and Supplementary Fig. 11) ¹²,³⁰. The angular signatures of VIs over the biomes from the LESS simulation capture vegetation-photon interactions at various sun-sensor geometry and structural complexity of vegetation canopy (Fig. 2a,b). Our analysis points out that the visible sunlit leaf fraction in view and *fesc* for the two biomes decrease but their change rates are greater in the Amazon forest (10.5% and 7.7% every 10° phase angle) compared to the US Corn belt (6.6% and 5.1% every 10°), similar to how EVI and NIRv behave. Similarly, the visible shaded leaf fraction in view for the two biomes increases but their change rates are also greater in the Amazon forest (8.4% per 10°) compared to the Corn belt (4.7% per 10°). These simulated angular variations conform the patterns observed in two multi-angle imaging satellites (Fig. 2a,b). To mediate impacts of soil-leaf optic characteristics in the two biomes, we repeated the simulation of the corn field by adopting the soil-leaf spectrum of the Amazon rainforest. The simulation of the corn field with the soil-leaf spectrum from the Amazon forest reveals minimal changes. Additional sensitivity
experiments show that *fesc* in view was primarily driven by the shadowing impacts from canopy structure and sun-sensor geometry instead of the leaf and soil optical properties (Fig. 2c). For most satellites, when the phase angle is larger than 15° or at nadir view such as Landsat, the visible sunlit leaf fraction in view and *fesc* for Corn Belt can be always larger than the Amazon rainforest (Fig. 2c).

**P7:** We further conduct both the remote sensing observations (Supplementary Fig. 10) and 3D model simulation-based sensitivity analyses (Supplementary Fig. 12) for a more systematic and unbiased comparison. First, we control the chlorophyll content (Cab), soil background and LAI parameters (see Supplementary Table 2) in LESS simulations to evaluate the shadow effect under a possible range of canopy structural and leaf-soil optical properties (Supplementary Fig. 12). The EVI and NIRv under the control of similar LAI (2.5 or 5) are smaller over forest than crops, especially when the LAI is relatively large at 5. Second, as the chlorophyll content could potentially impact the VIs in the remote sensing data-based analysis, we further test GRVI as a proxy of canopy pigment pools to examine the impacts of the pigments. We add the comparisons under the control of similar GRVI (such as 0.1~0.15, 0.15~0.20, 0.20~0.25) (Supplementary Fig. 7). The results suggest that the MODIS EVI, NIRv and *fesc* under the control of similar GRVI are smaller over the Amazon rainforest than over the Corn Belt, while the MODIS LAI shows the opposite pattern. Lastly, considering the forest in Amazon has much larger LAI values than the crops in the Corn Belt, we have compared in the Corn Belt and a nearby forest region in North America. These two regions have more similar LAI and share the same season, similar latitudes, and solar-viewing geometry (Supplementary Figs. 8-10). Supplementary Fig. 10 suggests the MODIS EVI under the control of similar LAI (2.0~2.5, 2.5~3.0, 3.0~3.5) and GRVI (0.1~0.15, 0.15~0.20, 0.20~0.25) are smaller over the nearby forest region in North America than over the Corn Belt. After we compare the VIs under the control of similar LAI and canopy pigment content, the results in the comparison of VIs between forest and cropland draw a solid conclusion that the observed VIs are strongly affected by the shadow effect.

**P8:** The impact of macroscale shadows due to forest canopy structure (Fig. 3) has been ignored in conventional VI-based greenness studies 4,18. In this study, we find even if the satellite observations are normalized to nadir viewing geometry and at local solar noon following the common recommendation¹⁸, there still can be varying proportions of macroscale shadows in view for forest and crops with different complexity of vegetation structures. These shadows play a first-order role in further complicating the remote sensing signals. The observed shadow impact also applies to remotely sensed SIF because SIF and optical photons at the same wavelengths undergo similar radiative transfer processes and share a common *fesc* ²⁰,³¹. Our supplemental analysis of SIF and PAR-normalized SIF show a consistent global pattern with those of EVI and NIRv, displaying a higher SIF
over the Corn Belt compared to the Amazon rainforest, but this pattern is opposite to that of LAI
(Supplementary Fig. 2).

Significant spectral greenness bias in land cover transition

**P9:** We have shown that shadows driven by complex vegetation structures and observing geometry conditions can bias the vegetation greenness derived from satellite spectral VIs, especially over the Amazon rainforest. The consequences of these findings extend far beyond the technical interpretation of satellite data. First, the stronger negative greenness bias observed by satellite VIs for forest than crops can lead to unexpected biases in quantifying and interpreting ecological processes, especially regarding their spatial patterns. More importantly satellite VIs may become more difficult to interpret when the abrupt land conversion from forest to crops occurs, e.g. deforestation and crop expansion <sup>10,32</sup>. Our analysis of MODIS EVI and LAI over Amazon forests experiencing a recent land conversion from forest to crops reveals divergent trends in EVI and LAI at site- (see the eight randomly selected sites in Fig. 4a, Supplementary Fig. 13) and regional-scale (EVI = 1.69% per year, LAI = -0.24% per year) (Fig. 4b) with the relative variation (divided by multi-year mean).

Implications for ecological studies

**P10:** The shadows driven by complex vegetation structure can decrease the surface reflectance and albedo (Fig. 3), which can reconcile the seemingly contradictory conclusions about the change of land surface albedo due to earth greening across biomes. Surface albedo has been considered to decrease over greener crops and grassland without strong shadowing effects <sup>33,34</sup>, while an unexpected increase of albedo are reported in greener forests because of the decreasing dark shadows and increasing bright sunlit canopy coverage <sup>33,35,36</sup>. For short and sparse canopies, the canopy coverage and the leaf-soil spectrum contrast are the main impact factors of the greening-albedo changes, while for tall and dense canopies with less soil background impacts, the shadows driven by complex structure is another important factor that determines the greening-albedo trends. The impact of shadows may become another layer of uncertainty to several downstream applications including canopy nitrogen estimations (Fig. 4 in <sup>37</sup>) urging to consider biome-specific calibrations for accounting varying canopy structures.

**P11:** In addition, VIs are widely used as a proxy for FPAR which is a critical component of remote sensing-based models of terrestrial carbon (e.g., gross primary productivity) <sup>38-40</sup> and water (e.g., evapotranspiration) <sup>41-43</sup> cycles. As shown in our study, EVI and NIRv are 11.5% and 21.8% higher in terms of the mean value in the Corn Belt than in the Amazon rainforest, while FPAR is 14.5% lower (Fig. 1 and Supplementary Fig. 2). Therefore, it is unlikely that there exists a universal VI-FPAR relationship across different biomes (Supplementary Fig. 3), which brings additional challenge in
parameterizing global remote sensing-based carbon and water models. Although NDVI is less impacted by the shadow than many other VIs such as DVI and NIRv, the slope of the NDVI-FPAR relationship still varies due to different soil background and the saturation of NDVI over dense canopies. To minimize the shadowing effect, it is more ideal to use the surface reflectance at the hotspot direction which is often not directly measured by most satellite missions but possible to infer from kernel-driven bi-directional reflectance models.

## Conclusions and perspective

**P12:** Because nearly all the satellite sensors do not view the earth in the hotspot directions and thus macroscale shadows in view are inevitable, the direct use of EVI or NIRv to indicate vegetation greenness can be biased, especially for structurally complex forests. This leads to spatial biases of global vegetation greenness from crops to forest with different complexities of vegetation structure. Considering that cropland expansion is being driven by increasing food production demand, omitting the complexity of vegetation structure might result in greater uncertainty in assessing vegetation changes and growth trends, hindering the accurate quantification of regional and global carbon budgets. Our results highlight such biases and limitations of the widely used VI-based remote sensing greenness over past decades. However, it is important to clarify that shadows are a real component of vegetation canopies and the shaded cohort usually contributes a large portion of the whole vegetation canopy carbon, water and energy budget ⁴⁴. Therefore, satellite products do not necessarily need to be corrected for shadows in many applications; but in order to minimize the ambiguities in global vegetation greenness with spatio-temporal biome changes, it is beneficial to correct satellite-observed VIs to the hotspot directions ⁴⁵.

## Materials and Methods

### Datasets and processing

#### MODIS surface reflectance, VIs and LAI products

We used the daily MODIS MCD43A4 V6.1 Nadir Bidirectional Reflectance Distribution Function (BRDF)-Adjusted Reflectance (NBAR) ¹⁷, the 8-day MOD15A2H V6.1 Combined Leaf Area Index (LAI) and Fraction of Photosynthetically Active Radiation (FPAR)⁴⁶, the 16-day MOD13A2 V6.1 EVI/NDVI products, and the yearly MCD12Q1 V6.1 Land Cover Type datasets⁴⁷. All MODIS datasets from 2001-2019 with 500 m spatial resolution were obtained from the Google Earth Engine (GEE) platform⁴⁸. We only used snow-free MODIS NBAR and other data with good Quality Assurance (QA)/ Quality Control (QC) flags. The GEOV LAI product was acquired at https://land.copernicus.eu/global/products/lai, and the GLASS LAI product was acquired at
http://www.glass.umd.edu/LAI/MODIS/0.1D/. We used the International Geosphere-Biosphere Programme (IGBP) classification layer in the MCD12Q1 data to calculate the proportions of each land cover type within a given pixel. The data were aggregated to monthly temporally and 0.1° spatially. For our analysis, we excluded all pixels in which non-vegetation types (such as snow/ice, water, barren land, and urban areas) comprised more than 50% of the total area. Additionally, we analyzed only homogeneous pixels composed of more than 80% forest or crop within vegetated areas.

## TROPOMI SIF and EPIC PAR

We used the TROPOMI far-red daily SIF dataset with a spatial resolution of 7 km × 3.5 km at nadir ⁴⁹ from ftp://fluo.gps.caltech.edu/data/tropomi, and DSCOVR/EPIC-derived daily PAR data with 0.1° × 0.1° spatial resolution ⁵⁰,⁵¹. The SIF normalized by PAR was calculated and compared with VIs. We used the time period of 2018.03-2019.02 to be consistent with the TROPOMI SIF dataset, which started in March, 2018.

## POLDER and MISR multi-angular surface reflectance

This study utilized multi-angular observations of surface reflectance from POLDER and MISR during the summer season over the Corn Belt and Amazon rainforest. The POLDER observations were obtained between July and August 2008, with a spatial resolution of approximately 6.2 km ²⁶. The MISR observations were collected during July and August 2017, with a spatial resolution of 1.1 km and a temporal resolution of 9 days ¹¹,⁵².

## Earth Observing-1 Hyperion based canopy spectrum

Two Earth Observing-1 Hyperion images acquired over the Amazon rainforest and Corn Belt in summer were used in this study. The Hyperion image over the Corn Belt was acquired on Day of Year (DOY) 210 in 2014, while the Hyperion image over the Amazon rainforest was acquired on DOY 221 in 2002. The Hyperion images were atmospherically corrected with the available visibility data to convert radiance to surface reflectance ⁵³. The spectrum <500 nm over the Corn Belt was extrapolated due to the imperfect atmospheric correction of the Hyperion data at shorter wavelength.

## LiDAR dataset and 3D ray-tracing model simulations

The point cloud data was collected during LiDAR surveys over a forest research site (E 54.99°, S 3.37°) at the Amazon rainforest in Brazil in 2018 ³⁰. The LiDAR data was collected to characterize the canopy profile and leaf area density, which were used to drive the 3D ray-tracing model simulations. In this study, the LiDAR data of a 100 m × 100 m area was extracted and simulated, and this dataset was available through the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC) at https://daac.ornl.gov/cgi-bin/dsviewer.pl?ds_id=1644. The 3D radiative transfer simulation framework, LESS (large-scale remote sensing data and image simulation framework over heterogeneous 3D scenes), was used in this study to incorporate the soil-leaf-canopy structure and
optical properties ²⁹. Typical parameters of the row-planted corn field were used in the comparative
LESS-based simulations ⁹. The 3D LESS model can simulate the multi-angular surface reflectance
and visible sunlit/shaded leaf fraction in view. The corresponding multi-angular VIs and photon
escape probability (*fesc*) were calculated based on the surface reflectance and FPAR. To avoid the
potential impact of soi-leaf optics and isolate the impact of canopy structure and sun-sensor geometry,
we added a comparative simulation of the corn field with the soil-leaf spectrum replaced by the
spectrum of the Amazon rainforest.

**Methods**

First, we examine spatial patterns of spectral VIs (EVI, NDVI and NIRv) and leaf area index (LAI) from MODIS. LAI, defined as one half of the total leaf surface area per unit ground area, is also related to vegetation greenness and, more importantly, can serve as the reference to different VI-based greenness due to its clear physical interpretation. Second, we use multi-angular satellite VI observations at different sun-sensor geometry with different macroscale shadows in view. Third, for mechanistic understanding, we use a 3D photon ray-tracing model to evaluate the impact of macroscale shadows in view with vegetation structures reconstructed by airborne LiDAR data to more directly quantify what is observed by the sensor that leads to the biases.

We mainly focus on the US Corn Belt and Amazon rainforest, since they are representative
landscapes with relatively homogeneous (Corn Belt) and complex (Amazon rainforest) canopy
structures, and are crucially important regions for global agricultural production, the terrestrial carbon
cycle and biodiversity conservation. To ensure a fair comparison between forest pixels in Amazon and
cropland pixels in the US Corn Belt, we analyzed only homogeneous pixels composed of more than
80% forest or crop. Our analyses excluded non-forest regions, such as savanna in the eastern part of
the Amazon and grassland in the southern part of the Amazon, as identified by the MCD12 land cover
product (see Fig. 1). We also have conducted the comparison between the crop in the Corn Belt and a
nearby forest region in North America with the same season and similar latitude and solar-viewing
geometry (Supplementary Figs. 8-10).

To make the comparison more reliable and systematic, we have conducted both remote sensing
observation and 3D model simulation-based sensitivity analyses. In the simulation-based analysis, we
control the chlorophyll content (Cab), soil background and LAI parameters in Supplementary Table 2,
and the corresponding results at different levels of LAI are shown in Supplementary Fig. 12. In the
remote sensing data-based analysis, we further test GRVI as a proxy of canopy pigment pools and
conduct the comparisons under the control of similar LAI (2.0~2.5, 2.5~3.0, 3.0~3.5) and GRVI
(0.1~0.15, 0.15~0.20, 0.20~0.25) as shown in Supplementary Fig. 10.

To shed light on how vegetation structure biases the interpretation of temporal vegetation greenness
changes, we further evaluated the temporal changes of MODIS EVI and LAI at Amazonian regions
where rapid land cover transition occurs from rainforest to crops during 2001-2019, as identified by
the MCD12 land cover product.

## Acknowledgements

Support for this research was provided by the University of Wisconsin-Madison, Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation. M.C. also acknowledges support by a McIntire-Stennis grant (1027576) from the National Institute of Food and Agriculture (NIFA), United States Department of Agriculture (USDA). D.H. acknowledges support by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Earth System Model Development program area, as part of the Climate Process Team projects. T.P. acknowledges support by NASA's Earth Science Division. The authors thank G. Badgley for fruitful discussions on SIF.

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<figure><img src="image_2.png" /><figcaption>**Fig. 1** Comparisons of VIs, LAI and *fesc* between the US. Midwest Corn Belt (upper panels, 43°N/94°W, 824,871 km²) and Amazon rainforest (lower panels, 5°S/62°W, 7,755,160 km²) during 2001-2019. The corresponding violin plots display the quartile and mean of the target variables. The MODIS EVI, NIRv and *fesc* were lower over the Amazon rainforest compared to the Corn Belt, due to the stronger shadows in view. In contrast, the MODIS LAI was higher in the Amazon rainforest than in the Corn Belt.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Fig. 2** For POLDER (July-August, 2008), MISR (July-August, 2017) and 3D ray-tracing model simulated multi-angular observations in summer, the EVI, NIRv, *fesc* and visible sunlit/shaded leaf fraction of the Corn Belt and Amazon rainforest are similar at the hotspot (Phase Angle=0 when the solar and sensor directions coincide), while the EVI, NIRv, *fesc* and visible sunlit leaf fraction of Corn</figcaption></figure>
Belt is always much higher than the Amazon rainforest at the off-hotspot directions (Phase Angle>>0, e.g., at nadir view but the solar zenith angle is 45° for the standard MAIAC surface reflectance product). The Phase Angle is the angle between the solar and sensor directions. The “Spectrum Replaced” represents the simulation of the corn field while the soil-leaf spectrum was replaced by the spectrum of the Amazon rainforest. The minimal changes after replacing the soil-leaf spectrum suggest the *fesc* was primarily driven by the canopy structure and sun-sensor geometry instead of the leaf optics.

<figure><img src="image_4.png" /></figure>

**Fig. 3** An example of the canopy spectrum in summer over the Amazon rainforest and Corn Belt acquired by Earth Observing-1 Hyperion sensor (left). More proportion of shadows in the field-of-view per unit area are observed over the Amazon rainforest than over the Corn Belt by the PhenoCam images (right). The sample spectrum over the Corn Belt was acquired on Day of Year (DOY) 210 in 2014, while the spectrum over the Amazon rainforest was acquired on DOY 221 in 2002. The Hyperion images were atmospherically corrected with the available visibility data to convert radiance to surface reflectance ⁴⁵.
<figure><img src="image_5.png" /><figcaption>**Fig. 4** (a) The opposite trend of the MODIS annual maximum LAI (insignificant or significant decrease) and EVI (significant increase; *p*<0.05) time-series during 2001-2019 at eight deforestation locations (Supplementary Fig. 13) with the land cover change from forest to crops within 2005-2015 over Amazon rainforest. (b) The opposite trend of the annual maximum MODIS LAI (insignificant decrease; *p*>0.05) and EVI (significant increase; *p*<0.05) time-series for all the deforestation pixels from forest to crops (within 2005-2015) over the whole Amazon rainforest. Note crops can have higher EVI than forest at the same LAI due to less impact of shadows. The LAI or EVI data were normalized by (LAI or EVI-mean)/mean. The trendlines were fitted by the Ordinary Least Squares regression (OLS).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Supplementary Fig. 1** The contrasting patterns between the Corn Belt (upper circle) and Amazon rainforest (lower circle) in August during 2001-2019 at global maps. The same as in Fig. 1, the MODIS EVI, NIRv and *fesc* were smaller over the Amazon rainforest than over the Corn Belt, while the MODIS LAI shows the opposite pattern. This effect is also found in the cropland in Northeast Asia, the rainforest in Southeast Asia, and the eastern forest region in North America near the Corn Belt with the same season and similar latitude.</figcaption></figure>

a

<figure><img src="image_7.png" /></figure>

b

<figure><img src="image_8.png" /><figcaption>**Supplementary Fig. 2** Comparison of VIs, FPAR and SIF between the Corn Belt (upper panels) and Amazon rainforest (lower panels) in August during 2001-2019.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Supplementary Fig. 3** The relationship between LAI or FPAR with EVI, NIRv, SIF/PAR and NDVI over the Corn Belt (in red) and Amazon rainforest (in blue) in August during 2001-2019. The linear slopes over the Corn Belt were at least twice as high as those over the Amazon rainforest. In each panel, the degree of point transparency represents the point density.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Supplementary Fig. 4** The correlation coefficient among LAI, FPAR, SIF and VIs over the Corn Belt (upper region) and Amazon rainforest (lower region) in August during 2001-2019. The relationship among VIs and SIF were much higher than they were compared to FPAR and LAI, especially over the Corn Belt.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Supplementary Fig. 5** Comparisons of VIs, LAI and *fesc* between the Corn Belt and Amazon rainforest in August of each year during 2001-2019.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Supplementary Fig. 6** The comparison of the Corn Belt (upper panels) and Amazon rainforest (lower panels) in August during the period of 2001-2019. Additional global VI and LAI products, including MOD13 NDVI/EVI, GEOV LAI and GLASS LAI, were used for the analysis in addition to the</figcaption></figure>
MCD43 NDVI/EVI and MODIS LAI shown in Fig. 1. Similar to Fig. 1, the EVI values are lower
over the Amazon rainforest compared to the Corn Belt, while the LAI shows the opposite pattern,
with larger values observed in the Amazon rainforest.

<figure><img src="image_13.png" /></figure>

**Supplementary Fig. 7** Comparison of VIs, LAI and *fesc* between the Corn Belt and Amazon rainforest in August during 2001-2019 at different levels of GRVI, which was used as a proxy of canopy pigment pools.

<figure><img src="image_14.png" /></figure>

**Supplementary Fig. 8** Comparisons of VIs, LAI and *fesc* between the US Corn Belt (upper panels) and a nearby forest region in the Northeastern North America (NA) in August during 2001-2019. The corresponding violin plots display the quartile and mean of the target variables, and as well as their distributions. The MODIS EVI, NIRv and *fesc* were lower over the forest region compared to the
Corn Belt, due to the stronger shadows in view. In contrast, the MODIS LAI was higher in the forest region than in the Corn Belt.

<figure><img src="image_15.png" /></figure>

**Supplementary Fig. 9** Comparison of VIs, LAI and *fesc* between the Corn Belt and a nearby forest region in North America (Supplementary Fig. 8a) in August during 2001-2019 at different levels of GRVI, which was used as a proxy of canopy pigment pools.

<figure><img src="image_16.png" /></figure>

**Supplementary Fig. 10** Comparison of EVI between the Corn Belt and a nearby forest region in North America (Supplementary Fig. 8a) in August during 2001-2019 at different levels of GRVI and LAI.
<figure><img src="image_17.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>c</figcaption></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

**Supplementary Fig. 11** The canopy structure reconstructed by the 3D ray-tracing model over the Amazon rainforest (a, 100 m × 100 m) and the corn field (b, 50 m × 50 m). The Amazon rainforest structure was extracted by the LiDAR data acquired over a site located at (E 54.99, S 3.37) in 2018²². Detailed input soil-leaf-canopy parameters were as in Supplementary Table 1. Multi-angular EVI, NIRv and NDVI simulations by the 3D ray-tracing model over the Corn Belt and Amazon rainforest (c) had close values at the hotspot direction (Phase Angle=0 when the solar and sensor directions coincide), while EVI and NIRv were always much higher over the Corn Belt than the Amazon rainforest at the off-hotspot directions (Phase Angle>0, e.g., at nadir view but the solar zenith angle is 45° for the standard MAIAC surface reflectance product). The Phase Angle in (c) is the angle between the solar and sensor directions. The “Spectrum Replaced” represents the simulation of the corn field while the soil-leaf spectrum was replaced by the spectrum of the Amazon rainforest (c).
<figure><img src="image_25.png" /><figcaption>**Supplementary Fig. 12** Sensitivity analysis by the LESS 3D ray-tracing model simulations of forest and crops with varied parameters in Supplementary Table 2, especially under the control of the same LAI. The same as the contrast in **Supplementary Fig. 10**, the EVI and NIRv under the control of similar LAI (2.5 or 5) were smaller over forest than crops, especially when the LAI was relatively large at 5.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Supplementary Fig. 13** The eight deforestation locations in **Fig. 4a** with the land cover change from forest to crops within 2005-2015 over Amazon rainforest.</figcaption></figure>
<table><caption>**Supplementary Table 1** Input soil-leaf-canopy parameters in the 3D ray-tracing model simulation over the Amazon rainforest and the corn field.</caption><tr><td rowspan="7">Amazon rainforest</td><td>Scene size</td><td>100 m × 100 m</td></tr><tr><td>LAI</td><td>5.12</td></tr><tr><td>Data source</td><td>From Lidar data (Dos-Santos et al., 2019, pp. 2008–2018)</td></tr><tr><td>Spectrum bands</td><td>469 nm, 645 nm, 858 nm</td></tr><tr><td>Leaf reflectance/transmittance</td><td>0.0189/0.0096, 0.0474/0.059, 0.443/0.44 (Wu et al., 2018)</td></tr><tr><td>Ground reflectance</td><td>0.04, 0.0748, 0.289 (Wu et al., 2018)</td></tr><tr><td>Scene size</td><td>50 m × 50 m</td></tr><tr><td rowspan="7">Corn field</td><td>LAI</td><td>4.0</td></tr><tr><td>Line spacing</td><td>0.76 m</td></tr><tr><td>Row spacing</td><td>0.17m</td></tr><tr><td>Spectrum bands</td><td>469 nm, 645 nm, 858 nm</td></tr><tr><td>Leaf reflectance/transmittance</td><td>0.0409/0.0016, 0.0406/0.0157, 0.4418/0.4738 (From PROSPECT-D, with Cab=54.33 µg·cm<sup>-2</sup>)</td></tr><tr><td>Ground reflectance</td><td>0.0293, 0.1053, 0.2033 (brown loam soil)</td></tr></table>

<table><caption>**Supplementary Table 2** Specifications of the soil-leaf-canopy parameters in the 3D ray-tracing model simulations for forest and crops in the sensitivity analysis.</caption><thead><tr><th></th><th>Parameters</th><th>Range</th></tr></thead><tbody><tr><td rowspan="7"></td><td>Spectrum bands</td><td>469 nm, 645 nm, 858 nm</td></tr><tr><td rowspan="3">Soil spectrum</td><td>Soil1: 0.1781, 0.4597, 0.5294</td></tr><tr><td>Soil2: 0.1507, 0.2733, 0.3258</td></tr><tr><td>Soil3: 0.1411, 0.2950, 0.3591</td></tr><tr><td>Cab/ µg·cm<sup>-2</sup></td><td>30; 60; 90</td></tr><tr><td>Solar zenith angle</td><td>45</td></tr><tr><td>View zenith angle</td><td>0°~75°, every 2°</td></tr><tr><td>Relative azimuth angle</td><td>0°; 180°</td></tr><tr><td rowspan="2">Forest</td><td>Scene size</td><td>100 m × 100 m</td></tr><tr><td>LAI</td><td>2.5; 5.0; 7.0</td></tr><tr><td rowspan="2">Crops</td><td>Scene size</td><td>50 m × 50 m</td></tr><tr><td>LAI</td><td>2.5; 5.0</td></tr></tbody></table>