Adjusting solar-induced fluorescence to nadir-viewing provides a better proxy for GPP

Dalei Hao, Yelu Zeng, Zhaoying Zhang, Yongguang Zhang, Han Qiu, Khelvi Biriukova, Marco Celesti, Micol Rossini, Peng Zhu, Ghassem R. Asrar, et al.

► To cite this version:

Dalei Hao, Yelu Zeng, Zhaoying Zhang, Yongguang Zhang, Han Qiu, et al. Adjusting solar-induced fluorescence to nadir-viewing provides a better proxy for GPP. ISPRS Journal of Photogrammetry and Remote Sensing, 2022, 186, pp.157-169. 10.1016/j.isprsjprs.2022.01.016. insu-03721931

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Distributed under a Creative Commons Attribution 4.0 International License
1 **Adjusting Solar-induced Fluorescence to Nadir-viewing Provides a Better Proxy for**

2 **GPP**

3 Dalei Hao¹, Yelu Zeng¹,⁷,*, Zhaoying Zhang², Yongguang Zhang²,³, Han Qiu¹,⁷, Khelvi

4 Biriukova⁴, Marco Celesti⁴, Micol Rossini⁴, Peng Zhu⁵, Ghassem R. Asrar⁶, and Min

5 Chen¹,⁷,⁸,*

6 ¹Joint Global Change Research Institute, Pacific Northwest National Laboratory, College Park,

7 MD, USA.

8 ²International Institute for Earth System Sciences, Nanjing University, Nanjing, China.

9 ³Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Key
10 Laboratory for Land Satellite Remote Sensing Applications of Ministry of Natural Resources,
11 School of Geography and Ocean Science, Nanjing University, Nanjing, Jiangsu, China.

12 ⁴Remote Sensing of Environmental Dynamics Laboratory, Department of Earth and
13 Environmental Sciences (DISAT), University of Milano-Bicocca, Piazza della Scienza 1,
14 Milano, Italy.

15 ⁵Laboratoire des Sciences du Climat et de l'Environnement, CEA-CNRS-UVSQ, UMR8212,
16 Gif-sur-Yvette, France.

17 ⁶Universities Space Research Association, Columbia, MD, USA.

18 ⁷Department of Forest and Wildlife Ecology, University of Wisconsin-Madison, Madison, WI,
19 USA

20 ⁸Nelson Institute Center for Climatic Research, University of Wisconsin-Madison, Madison, WI,
21 USA

22
23 Corresponding author: Min Chen (mchen392@wisc.edu); Yelu Zeng (zeng74@wisc.edu)

24

25

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31

32
33 **Abstract**

Solar-induced fluorescence (SIF) provides key information for inferring terrestrial gross primary productivity (GPP). However, there is little research on analyzing the performance of nadir-adjusted SIF ($SIF_{nadir}$) on GPP, compared to total SIF emitted by all leaves ($SIF_{total}$) for reducing the viewing angle effects and estimating GPP. Besides, there have been controversial opinions on whether $SIF_{total}$ is better correlated to GPP than raw SIF observations ($SIF_{obs}$). Here we systematically analyzed the relationship between raw/nadir/total SIF (i.e., $SIF_{obs}$, $SIF_{nadir}$ and $SIF_{total}$) and GPP and investigated the underlying mechanism, using multi-angular field measurements and eddy covariance data in wheat and corn crops at sub-daily scale. We further compared the performance of $SIF_{obs}$, $SIF_{nadir}$ and $SIF_{total}$ in estimating GPP using the TROPOspheric Monitoring Instrument (TROPOMI) SIF and concurrent AmeriFlux measurements at daily scale. The results indicate that diurnal $SIF_{nadir}$ has stronger correlations to GPP than $SIF_{obs}$ for field measurements, with the increase of mean coefficient of determination (R²) by 0.05~0.07 for far-red band and 0.11~0.20 for red band. $SIF_{nadir}$ shows comparable performance with $SIF_{total}$ for both far-red and red bands. Although the viewing angle effects dominate the difference in estimating GPP between $SIF_{nadir}$ and $SIF_{obs}$, the correlation between light use efficiency (LUE) and $f_{esc}$ further determines the different performance of $SIF_{nadir}$ and $SIF_{total}$ in estimating GPP. TROPOMI-based analysis further confirms that $SIF_{nadir}$ overall has higher correlations to AmeriFlux GPP than $SIF_{obs}$ for different plant functional types and shows similar performance with $SIF_{total}$. Compared to $SIF_{total}$, the estimation of $SIF_{nadir}$ independent of viewing angle effects does not require any canopy structure parameters, and thus offers promising potential for reliably estimating regional and global GPP.

56

57 **Keywords:** SIF, gross primary productivity, viewing-angle effects, nadir viewing, canopy structure effects, TROPOMI.

58
## 1 Introduction

The emerging spaceborne solar-induced fluorescence (SIF) measurements offer a novel opportunity for monitoring and interpreting large-scale ecosystem carbon cycle (Frankenberg et al., 2011; Joiner et al., 2011; Magney et al., 2020; Meroni et al., 2009; Mohammed et al., 2019; Ryu et al., 2019). Compared to traditional vegetation indices, SIF has more inherent linkages to vegetation photosynthetic activities (Gu et al., 2019; Magney et al., 2019). SIF has been increasingly used for tracking terrestrial gross primary productivity (GPP) (Sun et al., 2017), detecting plant stress (He et al., 2020b; Song et al., 2018), monitoring vegetation phenology (Wang et al., 2019; Zhang et al., 2020a), estimating crop yield (Guan et al., 2016; He et al., 2020a) and diagnosing ecosystem transpiration (Lu et al., 2018; Maes et al., 2020; Shan et al., 2019; Shan et al., 2021).

However, viewing-angle effects have considerable impact on the top-of-canopy SIF observations ($SIF_{obs}$) and their applications. Similar to surface reflectance, $SIF_{obs}$ is sensitive to viewing angles due to the canopy scattering and re-absorption processes (Van der Tol et al., 2019), which has been confirmed by field measurements (Biriukova et al., 2020; Liu et al., 2015; Pinto et al., 2017; Rogers et al., 2020; Zhang et al., 2020c), model simulations (Sakai et al., 2020; Zeng et al., 2020; Zhao et al., 2016) and remote sensing observations (Doughty et al., 2019; Guanter et al., 2012). The viewing-angle effects on SIF can distort the SIF-GPP relationship (Zhang et al., 2019a; Zhang et al., 2018b; Zhang et al., 2021). Considering that most existing and upcoming SIF observations from spaceborne instruments such as the Second Global Ozone Monitoring Experiment (GOME-2), Orbiting Carbon Observatory-2 (OCO-2) and TROPOspheric Monitoring Instrument (TROPOMI) have varying scanning angles, reducing the view-angle effects is urgently needed for SIF applications.
Compared to SIF<sub>obs</sub>, the total SIF emitted by all leaves (hereinafter referred to as total SIF, SIF<sub>total</sub>) is less affected by scattering and reabsorption processes, and thus has been considered to be better correlated to GPP (He et al., 2017; Lu et al., 2020; Zhang et al., 2019b; Zhang et al., 2020b; Zhang et al., 2020c). A few recent studies developed practical methods to estimate SIF<sub>total</sub> based on radiative transfer modeling (Liu et al., 2019; Yang and Van der Tol, 2018; Yang et al., 2020; Zeng et al., 2019). These methods typically require knowledge of canopy structure parameters such as leaf area index (LAI), clumping index (CI) and leaf angle distribution (LAD), but their estimations from remote sensing still have large uncertainties (Fang et al., 2019; Pisek et al., 2015; Zhang et al., 2020d) and hinder robust applications of SIF<sub>total</sub>.

Moreover, there have been controversial opinions on whether SIF<sub>total</sub> is better correlated to GPP than SIF<sub>obs</sub>. Zhang et al. (2019, 2020b) used the spaceborne TROPOMI and OCO-2 data and demonstrated that SIF<sub>total</sub> outperformed SIF<sub>obs</sub> because of the reduced impact of canopy structure effect. Lu et al. (2020) showed SIF<sub>total</sub> improved the estimate of diurnal GPP at Harvard Forest with complex canopy structure. Zhang et al. (2020c) showed that SIF<sub>total</sub> had less angular dependencies and stronger relationship with GPP in crops. In contrast, Dechant et al. (2020) showed SIF<sub>obs</sub> better served as a proxy for GPP in crops, benefited by the positive correlations of the ratio of SIF photons escaping from canopy with photosynthetic light use efficiency (LUE). It is worth noting that the viewing angle of SIF measurements was fixed at nadir or hemispheric in Dechant et al. (2020), whereas SIF observations were collected at varying viewing angles in Zhang et al. (2019, 2020b, 2020c), and with a fixed view zenith angle (VZA) of 30° in Lu et al. (2020). The datasets used in the existing studies were collected using different modes of fixed (nadir or off-nadir) or varying viewing angles, and thus the conclusions of these studies may not be directly comparable and scalable. The viewing-angle effects have
smaller impacts on analyzing the SIF-GPP relationship in Dechant et al. (2020) due to nadir or hemispherical viewing conditions, as compared with other studies (e.g., Zhang et al. (2019, 2020b, 2020c) and Lu et al. (2020)) with time varying viewing conditions, which may explain the contradictory conclusions from these studies.

Therefore, normalizing SIF<sub>obs</sub> to a standard viewing angle (i.e., nadir in this study) is proposed in this study to minimize the viewing-angle effects on SIF<sub>obs</sub>. This effort will facilitate a systematic analysis on the impacts of viewing angle on the SIF-GPP relationship and an evaluation of the capabilities of nadir-adjusted SIF (SIF<sub>nadir</sub>) and SIF<sub>total</sub> for approximating GPP, which can potentially resolve the aforementioned debate. To the best of our knowledge, no such analysis has been carried out before. Compared to off-nadir viewing angles, SIF<sub>nadir</sub> is less prone to be affected by hotspot effects caused by the variation of solar angles (Hao et al., 2021a). Liu et al. (2016) explored the potential of kernel-driven (KD) Bidirectional-Reflectance-Distribution-Function (BRDF) models in fitting multi-angular SIF measurements. Hao et al. (2021b) developed two practical methods to normalize SIF to nadir-viewing: one was based on multi-angular reflectance while the other leveraged a KD model (Hao et al., 2020b). Neither method requires input of canopy structural parameters, and their performance only depends on high-quality reflectance and SIF data.

Our study aims to comprehensively assess and understand the performance of SIF<sub>nadir</sub> and SIF<sub>total</sub> on approximating GPP estimations. We primarily focus on answering the following four questions : 1) how effective are different SIF normalization methods in reducing the viewing-angle effects? 2) how does SIF<sub>obs</sub> normalized to nadir viewing perform in estimating GPP, compared to the raw off-nadir SIF<sub>obs</sub>? 3) which is better for estimating photosynthesis,
127 SIF<sub>nadir</sub> or SIF<sub>total</sub>? and 4) what are the contributing factors leading to the differences between
128 the performance of SIF<sub>nadir</sub> and SIF<sub>total</sub>?

129

130 **2 Materials and methods**

131 **2.1 Multi-angular field SIF measurements at sub-daily scale**

132 First, two field datasets (wheat and corn crops) were used in our analysis, with the
133 characteristics presented in Table 1. Both wheat and corn canopies show the erectophile leaf
134 inclination distribution (empirically identified from the field). Specifically, a high-resolution
135 spectrometer QEPro (Ocean Optics, Dunedin, FL, USA) installed in a multi-angular
136 measurement system (Multi-Fluo) was used to collect multi-angular observations. It had a field-
137 of-view (FOV) of 25° and a spectral range of 650-800 nm, with a full width at half maximum of
138 0.3 nm. For each day, the Multi-Fluo system (Figure S1) collected 24 groups (with different
139 VZAs) of multi-angular data from 6:00 to 18:00 (UTC+8). The system acquired one group of
140 multi-angular observations with the same VZA every 30 min, which covered 25 different view
141 azimuth angles (VAA) changing from 60° to 300° at a 10° interval. During the measurements,
142 VZA was dynamically adjusted to track the solar zenith angle (SZA) and to capture the hotspot
143 effects, and it was fixed at 40° when SZA>40° to avoid the effects of large instantaneous FOVs.
144 An advanced spectral fitting method (Cogliati et al., 2015) was used to retrieve SIF for far-red
145 (760 nm) and red (687 nm) wavelengths. We used the averaged reflectance for 686-691 nm and
146 757-768 nm spectral bandwidths as Red and near-infrared (NIR) reflectance, respectively.
147 During the growing season, an eddy covariance flux system was installed to continuously
148 measure net ecosystem CO₂ exchange (NEE). Accompanying meteorological data composed of
shortwave radiation, air temperature, relative humidity and vapor pressure deficit were observed regularly. GPP was estimated at a half-hourly interval using a nighttime-based partitioning method (Reichstein et al., 2005) provided in the REddyProc tool (Wutzler et al., 2018). Effective LAI (equal to LAI·CI, denoted as eLAI) was measured with LAI-2200 plant canopy analyzer (LI-COR, Lincoln, NE, USA). The photosynthetically active radiation (PAR) and fraction of PAR absorbed by chlorophyll (FPAR) were measured via six LI-190SL quantum sensors (LI-COR Inc., Lincoln, NE, USA) installed both above and below the canopy, and LUE was calculated as GPP/(PAR·FPAR). We only used the data acquired under clear sky conditions when the clearness index (defined as the ratio of top-of-canopy to top-of-atmosphere solar radiation) was larger than 0.6 to avoid the interference of clouds. Finally, the field data obtained for five days were used in the analysis. Detailed descriptions of the field datasets and associated quality control can be found in Zhang et al. (2020c).

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163

<caption>**Table 1.** Characteristics of the field measurements for wheat and corn crops.</caption>

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<table><thead><tr><th>Variables</th><th></th><th>Wheat</th><th>Corn</th></tr></thead><tbody><tr><td>Location</td><td>Latitude (°N)</td><td>34.5199</td><td>34.5199</td></tr><tr><td></td><td>Longitude (°E)</td><td>115.5916</td><td>115.5916</td></tr><tr><td>Measured Time</td><td>Year</td><td>2018</td><td>2018</td></tr><tr><td></td><td>Day of Year (DOY)</td><td>124-133</td><td>235-239</td></tr><tr><td></td><td>Hour of day</td><td>6:00-18:00</td><td>6:00-18:00</td></tr><tr><td>Viewing angle</td><td>View Zenith Angle (VZA, °)</td><td>20-40</td><td>15-40</td></tr><tr><td></td><td>View Azimuth Angle (VAA, °)</td><td>60-300 at 10 intervals</td><td>60-300 at 10 intervals</td></tr><tr><td>Leaf parameter</td><td>Leaf chlorophyll content (Cab, µg cm<sup>-2</sup>)</td><td>66-71</td><td>51-54</td></tr><tr><td>Canopy structure</td><td>Effective leaf area index (eLAI, m<sup>2</sup> m<sup>-2</sup>)</td><td>5.2-5.8</td><td>2.8-2.9</td></tr><tr><td>Field Image</td><td>Leaf inclination angle distribution</td><td>Erectophile</td><td>Erectophile</td></tr></tbody></table>

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

165

166
167 **2.2 TROPOMI SIF and MODIS data**

168 We also used daily TROPOMI SIF data over 2018-2019 together with corresponding
169 MODIS products and flux tower GPP data from AmeriFlux sites (see Section 2.3) to evaluate our
170 analysis at the large spatial scale. TROPOMI onboard the Sentinel-5 Precursor provides near-
171 daily (around 13:30) SIF data with global coverage and a spatial resolution of 3.5-km × 7-km at
172 nadir (Köhler et al., 2018). Considering that retrieved red SIF from TROPOMI still has high
173 relative uncertainties (Köhler et al., 2020), we only used far-red (740 nm) SIF in this study. We
174 used both instantaneous and daily averaged SIF and calculated the daily averaged SIF using the
175 day-length correction factors (Zhang et al., 2018a). To reduce the cloud contamination and keep
176 the most possible valid SIF data, the SIF soundings with the cloud fraction greater than 0.5 were
177 excluded and the sensitivity of our results to this threshold was tested (see Section 3.3).
178 Considering the large uncertainty in a single TROPOMI measurement (Köhler et al., 2018), SIF
179 measurements centering within a 10-km radius of the flux towers were averaged to reduce the
180 SIF uncertainties (Frankenberg et al., 2014) and match the AmeriFlux GPP.

181 A set of 500-m MODIS data were collected at the selected AmeriFlux sites using the
182 Google Earth Engine (GEE) (Gorelick et al., 2017) to provide vegetation information.
183 Specifically, the IGBP layer in the yearly MCD12Q1-v6 land cover products (Friedl et al., 2002)
184 for 2018 was used to evaluate the homogeneity of AmeriFlux sites. The sites with larger than 50%
185 being covered by the dominant PFT within a 10-km radius of the tower were considered as
186 homogeneous. The 4-day MCD15A3H-v6 LAI/FPAR products (Myneni et al., 2002b) were
187 selected to provide LAI and FPAR. The 8-day CI data retrieved from MODIS were acquired from
188 Wei et al. (2019). Daily MCD43A1-v6 BRDF/Albedo Model Parameters products (Schaaf et al.,
189 2002) were used to estimate multi-angular reflectance. The MODIS pixels within a 1.5-km
190 radius of the flux towers were spatially-averaged and temporally-interpolated using a nearest neighbor methods to match with the AmeriFlux GPP.

192

193 **2.3 AmeriFlux GPP data**

194 Overall, 102 AmeriFlux sites which have coincident measurements with TROPOMI SIF during 2018-2019 were selected for our analysis (see Table S1 and Figure 1 for site information and spatial distribution, respectively). These sites cover eight International-Geosphere-Biosphere-Programme (IGBP) PFTs (Belward et al., 1999): Evergreen needleleaf forests (ENF), Deciduous broadleaf forests (DBF), Mixed forests (MF), Open shrublands (OSH), Woody savannas (WSA), Grasslands (GRA), Wetlands (WET), and Croplands (CRO). Half-hourly GPP data estimated from partitioning NEE measurements at these sites were aggregated to acquire the daily values. Both half-hourly and daily GPP data were used to match with the instantaneous and daily averaged TROPOMI SIF data, respectively. Only the GPP data during the growing seasons from April to October were used to avoid the impact of dormancy in winter.

204

205
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Spatial distribution of AmeriFlux sites used in our study. Black pentagram represents the site location. The background color represents the IGBP PFTs: 1: Evergreen needleleaf forests, ENF; 2: Evergreen broadleaf forests, EBF; 3: Deciduous needleleaf forests, DNF; 4: Deciduous broadleaf forests, DBF; 5: Mixed forests, MF; 6: Closed shrublands, CSH; 7: Open shrublands, OSH; 8: Wood savannas, WSA; 9: Savannas, SAV; 10: Grasslands, GRA; 11: Permanent wetlands, WET; 12: Croplands, CRO; 13: Urban and built-up lands, URB; 14: Cropland/natural vegetation mosaics: CVM; 15: Snow and ice, SNO; and 16: Barren, BSV.</figcaption></figure>

## 2.4 Decoupling viewing-angle and scattering/reabsorption effects on SIF

### 2.4.1 Overall framework

Due to the BRDF effect, $SIF_{obs}$ is impacted by both the solar and viewing angles. With a certain solar angle, $SIF_{obs}$ at a wavelength ($\lambda$) and a viewing angle ($\Omega$) can be conceptually modeled as (Lee et al., 2013; Sun et al., 2017):

$$SIF_{obs}(\Omega, \lambda) = PAR \cdot FPAR \cdot \Phi_{F}(\lambda) \cdot f_{esc}(\Omega, \lambda) \quad (1)$$

where $\Phi_F$ is the quantum yield of SIF, and $f_{esc}$ represents the fraction of SIF photons escaping from canopy. The product of first three terms represents $SIF_{total}$ within a canopy.

We can directly derive $SIF_{total}$ from $SIF_{obs}$ using Equation 1 as:
$$SIF_{total}(\lambda) = \frac{SIF_{obs}(\Omega, \lambda)}{f_{esc}(\Omega, \lambda)} \qquad (2)$$

Equation 2 suggests that the effects of viewing-angle and scattering/reabsorption can be simultaneously minimized. However, to evaluate their separate effects on $SIF_{obs}$, we need to decouple them into two independent terms. A practical solution for achieving this objective is to:
1) normalize $SIF_{obs}$ with varying viewing angles to a standard viewing geometry (e.g., nadir) and 2) estimate $SIF_{total}$ from $SIF_{nadir}$. In the first step, all SIF observations are corrected to an identical viewing angle and thus the viewing-angle effects are minimized/eliminated; and in the second step, the scattering/reabsorption effects can be further minimized by estimating $SIF_{total}$.

### 2.4.2 Calculating $f_{esc}$ for deriving total SIF

Equation 2 shows that the key to disentangling the effects of viewing-angle and scattering/reabsorption is to accurately calculate $f_{esc}$. Based on the spectral invariants theory, Yang et al. (2018b) derived a simple method to calculate far-red $f_{esc}$:

$$f_{esc}(\Omega, far\_red) = \frac{Ref(\Omega, far\_red)}{i_0 \cdot \omega(far\_red)} \qquad (3)$$

where Ref represents the NIR reflectance, $i_0$ is the canopy interceptance which represents the probability of a photon interacting with the vegetation canopy (Smolander and Stenberg, 2005), and $\omega$ is the leaf single scattering albedo (equal to the sum of leaf reflectance and transmittance). This method is only suitable for dense vegetation canopy (Yang et al., 2018b). Zhang et al. (2020c) used this equation to empirically estimate red $f_{esc}$. $i_0$ can be calculated using canopy structure parameters (Chen and Leblanc, 2001):

$$i_0 = 1 - \exp\left(-\frac{G(SZA) \cdot LAI \cdot CI}{\cos(SZA)}\right) \qquad (4)$$
where G(SZA) is the leaf projection function which quantifies the projection coefficient of unit foliage area on a plane perpendicular to the illumination direction. This method requires accurate canopy structure parameters (e.g., LAI, CI and LAD).

Meanwhile, Zeng et al. (2019) developed a practical method for estimating far-red $f_{esc}$ using the near-infrared reflectance of vegetation (NIRv) (Badgley et al., 2017) and FPAR:

$$f_{esc}(\Omega, far\_red) = \frac{NIRv(\Omega)}{FPAR \cdot \omega(far\_red)} \quad (5)$$

$$NIRv \approx NIR \cdot NDVI \quad (6)$$

where NIRv represents the fraction of reflected NIR light that originates from vegetation, and NDVI is the normalized difference vegetation index (Tucker, 1979). This method requires accurate estimation of NIRv and FPAR. Compared to Eq. 3, this method is suitable for both dense and sparse vegetation canopies (Zeng et al., 2019).

Similarly, Liu et al. (2020) developed a method for estimating red $f_{esc}$ using the red reflectance of vegetation (Redv) and FPAR:

$$f_{esc}(\Omega, red) = \frac{Redv(\Omega)}{FPAR \cdot \omega(red)} \quad (7)$$

$$Redv(\Omega) \approx Red \cdot NDVI^2 \quad (8)$$

where Redv represents the fraction of reflected red light that originates from vegetation. NDVI² is used to reduce the contribution of soil to red reflectance, which is only an approximation acquired based on the PROSAIL model (Liu et al., 2020). This method also requires an accurate estimation of Redv and FPAR.

Hereinafter, we named the methods expressed in Equations 3-4 and Equation 5-8 as i₀-based and FPAR-based methods, respectively. In this study, we also compared the difference between derived SIFₜotal using Ref (Equation 3) and NIRv (Equation 6) or Redv (Equation 8).
267

268 **2.4.3 Viewing-angle normalization methods**

Based on Equation 1, SIF$_{nadir}$ can be calculated by

$$
270 \qquad SIF_{nadir}(\lambda) = SIF_{obs}(\Omega, \lambda) \cdot \frac{f_{esc}(nadir,\lambda)}{f_{esc}(\Omega,\lambda)} \qquad (9)
$$

Combining Equations 5-8 and 9, we can normalize SIF$_{obs}$ to SIF$_{nadir}$ only with NIRv or Redv at both nadir and observed directions, which can be acquired from the KD model. This method is hereafter referred as the NIRv/Redv-based method. This method is applicable when multi-angular reflectance data are available, but its performance depends on the reduced sensitivity of NIRv and Redv to soil contribution (Hao et al., 2021b).

Hao et al. (2021b) suggested an alternative method that uses the KD model to fit PAR-normalized multi-angular SIF observations (hereinafter referred to as KD-based method):

$$
278 \qquad \frac{SIF_{obs}(\Omega, \lambda)}{PAR} = f_{iso}(\lambda) \cdot K_{iso}(\Omega) + f_{vol}(\lambda) \cdot K_{vol}(\Omega) + f_{geo}(\lambda) \cdot K_{geo}(\Omega) \qquad (10)
$$

where $f_{iso}$, $f_{vol}$ and $f_{geo}$ represent the fitting parameters, and $K_{iso}$, $K_{vol}$ and $K_{geo}$ represent the isotropic, volumetric-scattering and geometric-optical kernels. In this study, we used a constant value of 1, RossThick kernel and LiTransit kernel as $K_{iso}$, $K_{vol}$ and $K_{geo}$, respectively, to capture the BRDF shapes caused by volumetric-scattering and surface-scattering. The RossThick kernel was derived from a single scattering approximation of the radiative transfer theory for dense vegetation canopy (Roujean et al., 1992), and the LiTransit kernel was derived from the geometric-optical mutual shadowing BRDF model for sparse vegetation canopy (Li et al., 1999). RossThick kernel and LiTransit kernel can be used to characterize bowl-shaped and dome-shaped BRDF curves, respectively.
Considering relatively small variations of $\Phi_F$ within one day (Yang et al., 2018) or during the growing season (Wang et al., 2020) and relatively stable canopy structure in a short time period, we can use multiple SIF observations to fit the KD model in Equation 10 and then derive the ratio of $SIF_{nadir}$ to $SIF_{obs}$. This method is efficient only when multi-angular SIF and PAR data are available, and its performance also depends on employed KD models (Hao et al., 2021b).

## 2.5 Analysis and evaluation methods

Using the field dataset at sub-daily scale, we first fitted the KD models to all reflectance and SIF observations for each day; then used the fitted models to calculate nadir reflectance and SIF at each time of that day. Finally, $SIF_{nadir}$ and $SIF_{total}$ were estimated using the methods in Sections 2.4.2 and 2.4.3. We evaluated the performance of adjusted SIFs by four methods (two methods for estimating $SIF_{nadir}$ and two methods for estimating $SIF_{total}$) for estimating GPP. Note that for $i_0$-based and FPAR-based methods, $\omega$ were assumed as 0.9 and 0.1 for far-red and red bands, respectively (Liu et al., 2019), assuming that $\omega$ has little variation during the short measurement periods (Table 1). $i_0$ was estimated based on measured eLAI and a simplified approximation of G(SZA)=0.5 under the spherical distribution. For the FPAR-based method, we used the measured FPAR. We assume that the SIF variation is caused mainly by the variation of viewing angle in a short time window (i.e., 30 min) under no-stress conditions and thus the coefficient of variation (CV) was used to evaluate the performance of different methods for reducing the viewing-angle effects, calculated as the ratio of standard deviation to mean value:

$$CV = \frac{\text{std}(\{SIF_i\})}{\text{mean}(\{SIF_i\})} \qquad (11)$$

where $\{SIF_i\}$ represents the group of observed/nadir/total SIF. Specifically, we calculated the CVs for each group of SIF values with the same VZA but different VAAs, where the raw SIF
observed data were acquired at a short time window of about 30 min and thus the variation of the solar angle can be neglected. Smaller CVs indicate better performance for reducing the viewing-angle effects.

We used both linear and hyperbolic models (Damm et al., 2015) to approximate the empirical SIF-GPP relationship:

$$GPP = a1 \cdot SIF + b1 \quad (12)$$

$$GPP = \frac{a2 \cdot SIF}{SIF+b2} \quad (13)$$

where SIF represents observed/nadir/total SIF, and a1, a2, b1 and b2 are the fitting parameters. We used the coefficient of determination (R²) and root mean square errors (RMSE) to test the goodness of fit for linear models, and the RMSE for hyperbolic models. The relationship was considered statistically significant if the significance level (p-value) was smaller than 0.05.

We used the TROPOMI and AmeriFlux data (both instantaneous at the overpass time of TROPOMI and daily averaged values) over the 2018-2019 period to evaluate the SIF-GPP relationship at the large spatial scale. Table S2 provides an overview of the data source for canopy structure parameters and reflectance, used for different methods. With the KD-based method, TROPOMI SIF data in a 16-day window were used to fit the parameters in the KD model. With the i₀-based method, the far-red ω were assumed to be 0.9 (Asner, 1998; Gates et al., 1965; Liu et al., 2019) and relatively conservative both within and across species and is relatively invariant across time and space. LAD was assumed to be spherical, and then i₀ was estimated using MODIS LAI and CI data. With the FPAR-based method, ω was also assumed to be 0.9 and MODIS FPAR data was used. The magnitude of far-red ω only affected the magnitude of fₐ₉₅c and had minimal impacts on the results in our study due to its small variations with time.
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## 3 Results

336

### 3.1 Minimizing viewing-angle effects on SIF

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Both $SIF_{nadir}$ and $SIF_{total}$ reduce the angular heterogeneity of SIF observations in wheat and corn, compared to raw directional SIF observations (Figures 2 and 3). Overall, the KD model fits well with the reflectance and SIF for wheat and corn (Figure 2). Nadir SIF has smaller CVs than the raw directional SIF observations (Figure 3). For wheat, nadir SIF normalized by $NIRv/Redv$-based method has mean CVs of about 14.2% (far-red) and 29.8% (red), and the mean CVs of KD-based method are 17.7% (far-red) and 25.3% (red), while the raw multi-angular observations have mean CVs of 18.7% (far-red) and 44.6% (red). For corn, nadir SIF normalized by $NIRv/Redv$-based method has mean CVs of 14.0% (far-red) and 24.7% (red), and the mean CVs of KD-based method are 18.7% (far-red) and 22.8% (red), while observed SIF has CV values of 20.5% and 32.8%, respectively. In contrast, the two methods ($FPAR$-based and $i_0$-based) for calculating total SIF have similar mean CVs of 14.2% (far-red) and 29.9% (red) for wheat and 14.2% (far-red) and 24.6% (red) for corn, respectively. Overall, nadir SIF performs similarly as total SIF in reducing the viewing angle effects. Using TOC reflectance instead of $NIRv/Redv$ leads to similar results (Figure S2). Figure S2 shows that the relative SIF (calculated as the ratio of raw SIF to reflected radiance) also has good performance in reducing the view-angle effects, which is identical to the TROPOMI-based analysis reported by Magney et al. (2019). Figure 4 shows the time series of half-hourly observed, nadir and total SIFs, and the shaded areas of both nadir and total SIFs representing the standard deviations of SIFs are
generally narrower than raw observed SIF. This further demonstrates that both nadir and total SIFs reduce the viewing-angle effects, when compared to raw SIF observations.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Comparison between observed and fitted reflectance and SIF values with the kernel-driven model for red and far-red bands for (a) wheat and (b) corn. In each subplot, the degree of transparency for each point represents the data density from low (white) to high (black); the red line represents the linear regression line; and the R² and p-values of the linear fitting are also presented.</figcaption></figure>

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<figure><img src="image_6.png" /><figcaption>**Figure 3.** The coefficient of variation (CV) for observed/nadir/total SIFs for far-red and red bands for wheat (a-b) and corn (c-d). Here, CVs were calculated from each group of SIF values with the same VZA but different VAAs, where the raw observed data were acquired at a short time window of about 30 min. 'Raw-data', 'Nadir-NIRv/Redv', 'Nadir-KD', 'Total-FPAR' and 'Total-i₀' represent the raw observed SIF, nadir SIFs normalized by NIRv/Redv- and the KD-based methods, and total SIFs calculated by FPAR- or i₀-based methods, respectively. For each boxplot, white circles represent the mean values; the central lines represent the median values; boxes represent the interquartile ranges of the 25th (Q₂₅) and 75th (Q₇₅) percentiles; whiskers represent the values of Q₂₅-1.5*(Q₇₅-Q₂₅) and Q₇₅+1.5*(Q₇₅-Q₂₅); and grey points represent all CV values, whose degree of transparency represents the data density from low (white) to high (black).</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Time series of half-hourly raw observed, nadir and total SIFs (mW m⁻² nm⁻¹ (sr⁻¹)) from 6:00-17:30 (UTC+8) in 2018, for wheat and corn. The black lines and shaded areas represent the mean and standard deviations of SIF values, every 30 min.</figcaption></figure>
381 **3.2 SIF-GPP relationship based on multi-angular field measurements at sub-daily scale**

382 *SIF*<sub>nadir</sub> is better correlated to GPP than observed multi-angular *SIF*<sub>obs</sub> (Figure 5), due
383 to the reduced viewing-angle effects (Section 3.1). For the linear relationship, when the VAA is
384 fixed to be 240° and varying VZA (as a case), *SIF*<sub>obs</sub> has R<sup>2</sup> values of 0.68 (far-red) and 0.35 (red)
385 in wheat, and 0.59 (far-red) and 0.36 (red) in corn, respectively, while *SIF*<sub>nadir</sub> normalized by
386 the NIRv/Redv-based method has R<sup>2</sup> values of 0.78 (far-red) and 0.60 (red) in wheat and 0.68
387 (far-red) and 0.66 (red) in corn; and *SIF*<sub>nadir</sub> normalized by the KD-based method has R<sup>2</sup> values
388 of 0.77 (far-red) and 0.68 (red) in wheat and 0.74 (far-red) and 0.78 (red) in corn (see Figure 5).
389 For all cases of VAA in Figure 6, *SIF*<sub>obs</sub> has mean R<sup>2</sup> values of 0.66 (far-red) and 0.37 (red) in
390 wheat and 0.60 (far-red) and 0.53 (red) in corn; the NIRv/Redv-based method has mean R<sup>2</sup>
391 values of 0.73 (far-red) and 0.52 (red) in wheat and 0.64 (far-red) and 0.64 (red) in corn; and the
392 KD-based method has mean R<sup>2</sup> values of 0.70 (far-red) and 0.58 (red) in wheat and 0.65 (far-red)
393 and 0.63 (red) in corn. The improvements (i.e., the increases of R<sup>2</sup> value, ΔR<sup>2</sup>) of SIF<sub>nadir</sub>
394 estimated by the two viewing angle normalization methods can reach up to 0.27 (far-red) and
395 0.31 (red) in wheat, and 0.18 (far-red) and 0.28 (red) in corn (see Figure S3). Specifically, for
396 wheat, the ΔR<sup>2</sup> values for the KD-based method vary from -0.01 to 0.10 for far-red band with an
397 average value of 0.04, and from 0.02 to 0.49 with an average value of 0.20 for red band; and the
398 ΔR<sup>2</sup> values for corn vary from -0.09 to 0.35 for far-red band with an average value of 0.10 and
399 from -0.06 to 0.17 for red band with an average value of 0.05 (Figure S3). The hyperbolic model
400 generally has smaller RMSEs than linear model, especially for the red band in wheat, but
401 *SIF*<sub>nadir</sub> has smaller RMSEs than *SIF*<sub>obs</sub> for the two models (Figures 5 and S4-S5).

402 *SIF*<sub>nadir</sub> shows comparable performance for estimating GPP to *SIF*<sub>total</sub>. The FPAR-
403 based and *i*<sub>0</sub>-based methods of calculating *SIF*<sub>total</sub> achieve very similar results. Here we only
report the results of SIF<sub>total</sub> calculated based on FPAR. For the linear relationship, when VAA is 240°, SIF<sub>total</sub> has R<sup>2</sup> values of 0.76 (far-red) and 0.63 (red) in wheat, and 0.69 (far-red) and 0.66 (red) in corn, which are similar to SIF<sub>nadir</sub> results (Figure 5). For all cases of VAA shown in Figure 6, the mean R<sup>2</sup> values are 0.69 (far-red) and 0.59 (red) in wheat, and 0.64 (far-red) and 0.63 (red); and the ΔR<sup>2</sup> values for SIF<sub>total</sub> are similar to those for SIF<sub>nadir</sub> (Figure 3). For RMSE, SIF<sub>nadir</sub> and SIF<sub>total</sub> still hold the similar results for linear and hyperbolic models (see Figures 6 and S4-S5).
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Performance of observed/nadir/total SIFs for far-red and red bands in predicting GPP under the VAA of 240° but varying VZAs for wheat and corn. In each subplot, the red and blue lines represent the linear and hyperbolic fitting lines, respectively; and R² and RMSEs of linear fitting are marked by red colors, and RMSEs of hyperbolic fitting are marked by blue colors; p-values are not included because they are smaller than 0.05 in all cases.</figcaption></figure>
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<figure><img src="image_9.png" /><figcaption>**Figure 6.** The R² values for the linear relationships between observed/nadir/total SIFs for far-red and red bands and GPP under different VAAs for wheat (a-b) and corn (c-d). For each boxplot, white circles represent the mean values and grey points represent R² values.</figcaption></figure>

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425 **3.3** *f*<sub>esc</sub> explains the different performance of *SIF*<sub>total</sub> and *SIF*<sub>nadir</sub>

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As shown in Equation 2, the SIF photon escape ratio in the viewing angle, f<sub>esc</sub>, represents the
differences between SIF<sub>nadir</sub> and SIF<sub>total</sub>. Thus the relative performance of SIF<sub>nadir</sub> and SIF<sub>total</sub>
on approximating GPP depends on how well f<sub>esc</sub> is correlated with LUE. Figure 7 shows that
nadir f<sub>esc</sub> at the far-red wavelength has a strong positive correlation to LUE, which is consistent
with results reported by Dechant et al., (2020). This explains why SIF<sub>nadir</sub> is slightly better than
SIF<sub>total</sub> in Figures 5-6. However, the red f<sub>esc</sub> is weakly or even negatively correlated with LUE,
resulting that SIF<sub>nadir</sub> is slightly inferior compared to SIF<sub>total</sub> (Figures 5-6). It is worth noting
that Equations 7-8 are empirical approximations and large uncertainties remain in calculating red
f<sub>esc</sub> (Liu et al., 2020) due to the large differences between leaf reflectance and transmittance in
red band (Van der Tol et al., 2019; Yang et al., 2020).

<figure><img src="image_10.png" /></figure>

Figure 7. The relationships between LUE and nadir fesc at the far-red and red wavelengths for (a) wheat and (b) corn. Here, ‘fesc-FPAR’ and ‘fesc-i0’ represent the derived fesc values by FPAR- and i0-based methods. In each subplot, the degree of transparency of each point represents the data density from low (white) to high (black); the red line represents the linear regression line; and both R2 values and p-values of linear relationships are also presented.
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**3.4 Applications to daily TROPOMI data**

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Overall, the TROPOMI far-red SIFnadir has higher correlations to AmeriFlux GPP than SIFobs and shows similar performance with SIFtotal for different PFTs, except MF and OSH (Figure 8). Both SIFnadir and SIFtotal improved instantaneous SIF-GPP relationship at most of the study sites, and the improvement of R² and RMSE (i.e., ΔR² and ΔRMSE) can exceed 0.1 and 1 umol·m⁻²·s⁻¹ at several sites for ENF and CRO. Specifically, with the KD-based method, the ΔR² values of all ENF sites vary from -0.13 to 0.21 and its average value is 0.05; and the ΔR² values for CRO vary from -0.01 to 0.11 with an average value of 0.05. However, after correcting to SIFnadir and SIFtotal, the SIF-GPP relationship becomes weaker at a few sites. For example, for the KD-based method, the ΔR² values of all GRA sites vary from -0.18 to 0.10 and its average value is 0.02. With the daily values, the improvements in R² and RMSE can exceed 0.2 and 1 gC·m⁻²·day⁻¹ at several CRO sites. Specifically, with the KD-based method, the ΔR² values at ENF sites vary from -0.16 to 0.24 with an average value of 0.06; and the ΔR² values at CRO sites vary from -0.01 to 0.18 with an average value of 0.06; and at GRA sites they vary from -0.19 to 0.18 and with average value of 0.02. Different viewing angle normalization methods generally show similar performance, but NIRv/Redv-based method performs the best for MF; the KD-based method performs the best for ENF and CRO; and FPAR-based and i0-based methods has better performance for sparse vegetation canopies (i.e., OSH, WSA and GRA). Overall, the results from our analyses of using only homogeneous sites (Figure S6) are similar to those using all study sites (Figure 8). In addition, Figures 8 and S7-S8 show that using different cloud fractions thresholds (i.e., 0.2, 0.5 and 0.8) has minimal impact on the results.
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Changes in goodness of fit (ΔR² and ΔRMSE) for the linear fitting between TROPOMI far-red SIF and AmeriFlux GPP after normalizing observed SIFs to nadir or total SIFs for all sites with different PFTs. The units of ΔRMSE for instantaneous and daily scales are umol·m⁻²·s⁻¹ and gC·m⁻²·day⁻¹, respectively.</figcaption></figure>

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471 **4 Discussion**

472 *SIF*<sub>nadir</sub> shows better performance than raw multi-angular *SIF* observations and it has
473 comparable performance as *SIF*<sub>total</sub> in estimating *GPP* at both sub-daily and daily scales.
474 Compared to *SIF*<sub>obs</sub> with varying viewing angles, both *SIF*<sub>nadir</sub> and *SIF*<sub>total</sub> effectively reduce
475 the viewing-angle effects (Section 3.1). This explains why *SIF*<sub>total</sub> shows better correlations to
476 *GPP* as reported by Zhang et al. (2019, 2020b, 2020c). Furthermore, even if we adjusted the raw
477 observations to a fixed off-nadir viewing angle (e.g., VZA=40°) following Lu et al., 2020, both
478 *SIF*<sub>nadir</sub> and *SIF*<sub>total</sub> are still better correlated to *GPP* (Figure S9). This is likely because *SIF*<sub>obs</sub>
479 for an off-nadir angle can be subject to hotspot effects due to solar angle changes, while both
480 *SIF*<sub>nadir</sub> and *SIF*<sub>total</sub> are less affected by hotspot effects. However, *SIFs* for different viewing
481 angles can convey extra useful information about vegetation canopies. Off-nadir *SIF*
482 measurements may work better at the beginning of the growing season, during which off-nadir
483 sensors receive less soil background (Li et al., 2020). How to make full use of these
484 complementary multi-angular *SIF* data to improve the *GPP* estimations deserves further
485 investigations. It is worth noting that the KD-based method requires high-quality multi-angular
486 *SIF* data but not *f*<sub>esc</sub>, and shows better performance in red band than the *NIRv/Redv*-based
487 method (Figures 3 and 5). However, the performance of the KD model is sensitive to the errors
488 and uncertainties of the input *SIF* data (Figure 2), which likely account for its relatively worse
489 performance in far-red band for wheat (Figure 6), indicating the necessity of reducing the
490 uncertainties of *SIF* retrievals (Chang et al., 2020). The assumptions of constant vegetation
491 structure and *Φ*<sub>F</sub> stands in most cases with sufficient SIF measurements in a short time period,
492 but attentions should be called when the period is long enough or at particular vegetation
493 growing stages, e.g., the early growing season when the plants change rapidly. This method also
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depends on the choice of kernels in the KD model (Hao et al., 2021b), whose performance needs to be evaluated comprehensively before application.

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In concept, *SIF*<sub>total</sub> further reduces the scattering/reabsorption effects in addition to the viewing-angle effects, but the correlation between *LUE* and *f*<sub>esc</sub> is the key to determine the different performance of *SIF*<sub>nadir</sub> and *SIF*<sub>total</sub> in approximating GPP (Dechant et al., 2020; Figure 7). This finding explains the divergent conclusions and debates on the whether *SIF*<sub>total</sub> or *SIF*<sub>obs</sub> better approximates GPP in previous studies. However, estimating *SIF*<sub>total</sub> requires accurate information about canopy structure parameters, while normalizing *SIF*<sub>obs</sub> to nadir viewing can be achieved using only reflectance or *SIF* data. Recently, a series of global-scale *PAR*, *FPAR*, *LAI* and *CI* datasets have been produced (Hao et al., 2019; Hao et al., 2020a; He et al., 2012; Myneni et al., 2002a; Wei et al., 2019), while their uncertainties are widely recognized but usually not well quantified (Fang et al., 2019; Pisek et al., 2015; Zhang et al., 2020d). There is no global *LAD* dataset available yet and a simplified assumption of spherical distribution or prescribed biome-specific *LADs* can introduce additional uncertainties. Accounting for the spatio-temporal variations of ω especially for red band and the effects of diffuse skylight are necessary for estimating *SIF*<sub>total</sub> in global applications (Lu et al., 2020).

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The relative *SIF* (the ratio of *SIF* to reflected radiance) also has good performance in reducing the view-angle effects (Figure S2; Magney et al., 2019). However, because the relative *SIF* is calculated as the ratio of *SIF* to reflected radiance, it has a different unit from *SIF* and does not contain the *PAR* information. In fact, the relative *SIF* is proportional to *Φ*<sub>F</sub> (Zeng et al., 2019), which is promising for capturing the physiological response of vegetation to abiotic changes and stresses.
Although overall performance of different methods to angular-normalizing TROPOMI SIF data were similar (Figure 8), small differences can be found due to divergent assumptions of the model/method as well as the quality and accuracy of remote sensing data. Compared to the two methods for estimating SIF<sub>total</sub>, the two methods for estimating SIF<sub>nadir</sub> do not rely on any inputs of canopy structure parameters and thus they should be more robust across PFTs. The NIRv-based method was derived from Equations 5-6, and thus its performance relies on how well NIRv can approximate the true NIR reflectance of vegetation (Zeng et al., 2021). Zeng et al. (2021) developed a simple framework for estimating the true NIRv from hyperspectral data (NIRvH) with minimized soil contamination, which could be a promising approach for further improving the performance of this method for sparse vegetation canopies. In theory, the KD-based method is suitable for any PFT if the high-quality SIF data is available. However, this method shows poor performance over OSH, WSA and GRA (Figure 8), possibly due to the large relative errors of SIF retrievals for sparse vegetation canopies. For the methods of estimating SIF<sub>total</sub>, in principle, the FPAR-based method can be applied for both dense and sparse vegetation canopies, while the i<sub>0</sub>-based method is primarily suitable for dense canopies. For example, FPAR-based method performs the best over WSA for the instantaneous SIFs. The fact that these two methods show overall similar performance in our study is possibly due to the uncertainties of canopy structure parameters. Compared to the i<sub>0</sub>-based method, the FPAR-based method only requires the input of FPAR, which is easier to acquire but its accuracy require further improvement (Zhang et al., 2020d). Overall, the SIF data quality and canopy structure parameters play important roles and may limit their applications in the performance for different PFTs, although the field measurement-based analysis shows that these methods work well for nearly all cases for wheat and corn canopies in this study (Figures 6 and S3).
We also used both linear and hyperbolic models to test the SIF-GPP relationship with and without viewing angle normalizations. The hyperbolic model generally has higher R² values than the linear model (Figure 5), because LUE can be expressed more realistically as a hyperbolic function of absorbed PAR (Damm et al., 2015). This emphasizes the importance of underlying assumptions associated with the model used when evaluating the SIF-GPP relationship.

Our results highlight the necessity and feasibility of viewing angle normalization when estimating GPP using remotely sensed SIF. The two methods for estimating SIFnadir are applicable to TROPOMI data, and SIFnadir from TROPOMI shows a stronger relationship with AmeriFlux GPP for most PFTs as compared with SIFobs. These results are not sensitive to the cloud cover (Figures 7 and S6-S7), confirming the robustness of the methods. In addition, most of the existing remote sensing SIF data have a varying or off-nadir viewing angle. For example, GOME-2 has a VZA of up to 54°; both OCO-2 and OCO-3 (Taylor et al., 2020) have large viewing angles at glint and target modes; and the Geostationary Carbon Observatory (GeoCarb) (Moore III et al., 2018) will have large off-nadir viewing angles over the high-latitude regions. To better estimate GPP, the viewing-angle effects of SIF observations need to be minimized first. Normalizing SIF observations to nadir viewing provides a promising way which can avoid the effects of the uncertainties of vegetation canopy parameters. Although simply averaging SIF observations over space and time can reduce the viewing angle effects, our study shows the feasibility of viewing angle normalized nadir SIF with high spatio-temporal resolutions without a need for any space-time smoothing. However, the footprints of TROPOMI can be large if the SIF observations are from the edge of the swath, which may not be representative for the dominant PFT of an eddy covariance tower site. Our results confirm that, our methods can
generally work well for both heterogenerous and homogenous study sites (Figures 7 and S6).

The spatial mismatch issues between TROPOMI, MODIS, and AmeriFlux data, spatial heterogeneities and the representativeness of eddy-flux footprints for the tower sites (Chu et al., 2021), may explain the degraded performance of normalized SIF for some PFTs (Figure 8). This issue merits further investigations.

There are still a few limitations in our study. The field datasets we used only cover a short period of a few days of observations and for homogeneous canopies. Using field measurements for the entire growing season, or multiple seasons, over sparse canopies are needed to further evaluate robustness of our proposed methodology. The multi-angular measurements in the study were acquired by dynamically rotating the optical probe, which means the target footprint under different viewing angles was different. The measurements did not cover the full principal (PP) and cross-principal (CPP) planes and thus cannot capture completely the BRDF shapes in PP and CPP. The spectrometer used to obtain the field measurements had a large FOV of 25°, which may lead to uncertainties in the measured multi-angular data. Although TROPOMI data provide unprecedented temporal resolutions, satellite-based SIF retrievals are still noisy and have high relative uncertainties for red band (Köhler et al., 2020). Further improving the quality of satellite-based SIF retrievals are required for detailed quantitative analysis and applications. In addition, TROPOMI SIF data still have sparse spatial resolution, which are hopefully resolved by future missions, such as GeoCarb and the forthcoming Fluorescence Explorer (FLEX) mission of the European Space Agency (Kraft et al., 2017).

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584 **5 Conclusions**

Directional effects of SIF measurements greatly hinder the robust estimation of GPP. In this study, we used two practical methods to normalize SIF observations to nadir viewing, and used two simple methods to calculate the total SIF. We used the multi-angular field measurements for wheat and corn at sub-daily scale, TROPOMI SIF and AmeriFlux GPP data at daily scale to evaluate their relationships with GPP. Our results show that, overall, the four methods show good performance in reducing the viewing angle effects on SIF. Nadir SIF can better track GPP than raw multi-angular observations, due to the reduced viewing angle effects. Nadir SIF also shows comparable performance with total SIF, but estimating nadir SIF only requires reflectance or SIF observations, rather than detailed canopy structure parameters generally needed for estimated total SIF. The varying relationship of LUE and $f_{esc}$ can account for the relative performance of nadir and total SIFs on approximating GPP. Our results underline the significance, effectiveness and feasibility of using normalized nadir SIF to better estimate GPP, especially over large areas.

598

599 **Acknowledgments**

This research was supported a Laboratory Directed Research and Development project sponsored by the Pacific Northwest National Laboratory (PNNL) of the U.S. Department of Energy to Min Chen. PNNL is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830. Khelvi Biriukova, Marco Celesti, and Micol Rossini were supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 721995. Marco Celesti was supported by a Living
606 Planet Fellowship (ESA/Contract No. 4000125442/18/I-NS) of the European Space Agency.

607 Multi-angular field data is available through https://doi.org/10.6084/m9.fishshare.13011470.v2.

608 We thank Mirco Migliavacca for his contribution to the viewing angle-normalization methods.

609 We acknowledge the AmeriFlux community for sharing the flux data (available at
610 https://ameriflux.lbl.gov/). We also acknowledge Philipp Köhler and Christian Frankenberg for

611 providing useful suggestions and TROPOMI SIF data (available at
612 ftp://fluo.gps.caltech.edu/data/tropomi/). All MODIS data are available from GEE. Codes to

613 reproduce all results are available at https://github.com/daleihao/SIFNormalization.

614
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