Downscaling the Maximum Carboxylation Rate ( 𝑎 Derived

Downscaling the Maximum Carboxylation Rate (𝑉𝑐𝑚𝑎𝑥) Derived from Satellite Sun-induced Chlorophyll

Fluorescence Data Using High-resolution Remote Sensing Products

by

Jiye Leng

A thesis submitted in conformity with the requirements for the degree of Master of Science

Department of Geography and Planning University of Toronto

© Copyright by Jiye Leng, 2020

ii

Downscaling the Maximum Carboxylation Rate (𝑉𝑐𝑚𝑎𝑥) Derived

from Satellite Sun-induced Chlorophyll Fluorescence Data Using

High-resolution Remote Sensing Products

Jiye Leng

Master of Science

Department of Geography & Planning

University of Toronto

2020

Abstract

The maximum carboxylation rate (𝑉𝑐𝑚𝑎𝑥) influences the magnitude of gross primary productivity

(GPP). Currently, reliable global 𝑉𝑐𝑚𝑎𝑥 products derived from satellite sun-induced chlorophyll

fluorescence (SIF) data are at coarse resolutions, which cannot meet the demand of global

ecological research. In this thesis, the 𝑉𝑐𝑚𝑎𝑥25 (𝑉𝑐𝑚𝑎𝑥 normalized to 25°C) dataset derived from

satellite SIF at a coarse resolution (0.1°, ~11 km) is downscaled to a higher resolution (1 km)

through a downscaling scheme using photochemical reflectance index (PRI) and spatial scaling

algorithms based on leaf chlorophyll content (LCC) and normalized difference vegetation index

(NDVI). The Boreal Ecosystem Productivity Simulator (BEPS) is used to evaluate the downscaled

𝑉𝑐𝑚𝑎𝑥25 using tower flux data. The results show that the LCC-downscaled 𝑉𝑐𝑚𝑎𝑥

25 data appreciatively

improve GPP simulations at the tower sites, indicating LCC as a feasible way for downscaling the

𝑉𝑐𝑚𝑎𝑥25 dataset. GPP estimations at the 0.1° resolution decrease by 2-7% after 𝑉𝑐𝑚𝑎𝑥

25 downscaling.

iii

Acknowledgments

I was fortunate to be admitted into University of Toronto. Life was unusual during this year with

the unprecedented pandemic, and I’m writing to express appreciation to the people around me

throughout my master's study.

I would like to first thank my supervisor, Prof. Jing Chen, for offering me the opportunity to pursue

an M.Sc. degree and a Ph.D. degree at this university. He has always been supportive, willing to

help, and enlighten me when I encountered obstacles in my research. He is a role model for me as

a scientist and a bright lighthouse who leads me to step into the research career and encourages

me to fulfill my dream.

I also would like to thank my course instructor and TA instructor, Prof. Jane Liu, for guiding me

into the new scientific field. The three individual classes built me with a foundation of the

knowledge for exploring this new field and fostered my ability of logical and critical thinking.

I want to thank all the group members for their advice, help, and care during this year. Special

thanks to Yihong Liu, Dr. Rong Wang, Xinyao Xie, and Cheryl Rogers for their valuable

contributions to this thesis. Yihong has given me enormous help as a friend and as a senior. He

shared his datasets and gave useful suggestions when I was struggling with the research. Rong is

so supportive that she always responded to my questions with a smile as well as shared her own

experience of studying in U of T, even when she returned to China. Xinyao taught me code writing,

illuminated me with her unique learning experience, and exchanged her perspectives with me.

Cheryl helped me improve my academic writing and discussed the research with me. Besides,

thanks also go to Dr. Weiliang Fan, Dr. Zhaoying Zhang, etc. for the happy time we had during

my life in Toronto.

Finally, I want to express my sincere gratitude to my parents for their support of my dream of

studying abroad all the time. They are always open-minded and giving me the freedom to take my

own road. A particular ‘Thank you’ also goes to my dear girlfriend, Jing Zhang, for the company

and help during this difficult and emotionally challenging year.

iv

Table of Contents

Acknowledgments.......................................................................................................................... iii

Table of Contents ........................................................................................................................... iv

List of Tables ................................................................................................................................ vii

List of Figures .............................................................................................................................. viii

Glossary of Acronyms and Abbreviations ..................................................................................... xi

Chapter 1 ..........................................................................................................................................1

Introduction .................................................................................................................................1

1.1 Introduction of 𝑉𝑐𝑚𝑎𝑥 and methods of estimating 𝑉𝑐𝑚𝑎𝑥 ................................................2

1.1.1 Definition of 𝑉𝑐𝑚𝑎𝑥 ................................................................................................2

1.1.2 𝑉𝑐𝑚𝑎𝑥25 estimation from field measurements and flux measurements ................2

1.1.3 𝑉𝑐𝑚𝑎𝑥25 estimation from remote sensing .............................................................3

1.1.3.1 Direct correlations between 𝑉𝑐𝑚𝑎𝑥25 and VIs ........................................3

1.1.3.2 Indirect estimation of 𝑉𝑐𝑚𝑎𝑥25 from other parameters ...........................4

1.2 Introduction of spatial scaling, upscaling, and downscaling in remote sensing ..................5

1.2.1 Introduction of intra-pixel spatial heterogeneity......................................................5

1.2.2 Introduction to spatial scaling ..................................................................................5

1.2.3 Introduction to upscaling and downscaling .............................................................6

1.3 Significance of downscaling 𝑉𝑐𝑚𝑎𝑥25 ..............................................................................8

1.3.1 Introduction of the eddy covariance and flux tower measurements ........................8

1.3.2 Building a bridge linking 𝑉𝑐𝑚𝑎𝑥25 from coarse to high resolutions .....................9

1.4 Objectives and main structure of this research ..................................................................10

1.4.1 Research objectives ................................................................................................10

1.4.2 Structure of this research .......................................................................................11

1.5 References ..........................................................................................................................13

Chapter 2 ........................................................................................................................................19

v

Trial of photochemical reflectance index (PRI) on downscaling 𝑉𝑐𝑚𝑎𝑥25 ...........................19

2.1 Introduction ........................................................................................................................19

2.2 Data and methods ...............................................................................................................21

2.2.1 Data ........................................................................................................................21

2.2.2 Estimating GPP based on PRI................................................................................22

2.2.2.1 Trial of establishing generic correlations between PRI and LUE ...........22

2.2.2.2 Trial of establishing correlations between PRI and LUE at flux sites.....23

2.2.3 Retrieving 𝑉𝑐𝑚𝑎𝑥25 based on GPP estimated from PRI .....................................24

2.2.3.1 Model description ....................................................................................24

2.2.3.2 Lookup-table establishment and 𝑉𝑐𝑚𝑎𝑥25 searching ............................25

2.3 Discussion ..........................................................................................................................26

2.3.1 Results and problems found in the progress ..........................................................26

2.3.1.1 Trial of establishing generic PRI-LUE correlations for each PFT ..........26

2.3.1.2 Trial of establishing PRI-LUE correlations at each site ..........................30

2.3.2 Further work for solving the issues ........................................................................33

2.4 References ..........................................................................................................................34

Chapter 3 ........................................................................................................................................37

Leaf chlorophyll content (LCC) as a feasible way for downscaling 𝑉𝑐𝑚𝑎𝑥25 .......................37

3.1 Introduction ........................................................................................................................37

3.2 Data and methods ...............................................................................................................39

3.2.1 Data ........................................................................................................................39

3.2.2 Algorithms for downscaling 𝑉𝑐𝑚𝑎𝑥25 .................................................................41

3.2.3 Evaluation and Statistical Analysis ........................................................................42

3.3 Results and discussion .......................................................................................................43

3.3.1 The intra-pixel heterogeneity of the TROPOMI 𝑉𝑐𝑚𝑎𝑥25 product .....................43

3.3.2 The 𝑉𝑐𝑚𝑎𝑥25 seasonal variation ..........................................................................47

vi

3.3.3 Evaluation of downscaled 𝑉𝑐𝑚𝑎𝑥25 at sites.........................................................49

3.3.3.1 The comparison of GPP simulation results .............................................49

3.3.3.2 The seasonal variation of GPP simulation results ...................................51

3.3.3.3 Statistical analysis of GPP simulation results .........................................54

3.3.3.4 GPP responses to 𝑉𝑐𝑚𝑎𝑥25 before and after downscaling ....................56

3.3.4 Applying the downscaling method to regional and global scales ..........................58

3.4 Conclusion .........................................................................................................................63

3.5 References ..........................................................................................................................65

Chapter 4 ........................................................................................................................................69

Summary ...................................................................................................................................69

4.1 Main conclusions ...............................................................................................................69

4.2 Limitation of current work and plan for further work .......................................................71

4.3 References ..........................................................................................................................73

vii

List of Tables

Table 2-1 Basic information of datasets for establishing the lookup table. ................................. 22

Table 2-2 The abbreviations and full forms of the nine PFTs. ..................................................... 23

Table 2-3 Squared Pearson correlation coefficient between PRI and LUE using MODIS bands

10, 12, and 13 at 190 sites for nine plant functional types............................................................ 29

Table 2-4 Squared Pearson correlation coefficient between sPRI and LUE using MODIS band

10, 12, and 13 at five sites............................................................................................................. 30

Table 3-1 Site specifications for five flux sites ............................................................................ 39

Table 3-2 Statistical evaluation results of the downscaled 𝑉𝑐𝑚𝑎𝑥25 based on GPP simulated

with 𝑉𝑐𝑚𝑎𝑥25 before and after downscaling against GPP derived from tower flux measurements

....................................................................................................................................................... 55

Table 3-3 The summary of GPP responses to 𝑉𝑐𝑚𝑎𝑥25 before and after downscaling .............. 56

viii

List of Figures

Figure 1-1 Variations of LAI retrieval biases of coarse resolution pixels with different water area

fraction using an NDVI-based non-linear LAI retrieval algorithm, expressed as the relative

difference in LAI. Source: Chen (1999). ........................................................................................ 6

Figure 1-2 Basic operations involving upscaling and downscaling in remote sensing. Source:

Bierkens et al. (2000). ..................................................................................................................... 7

Figure 1-3 Variation of global annual GPP with 𝑉𝑐𝑚𝑎𝑥25 in the sensitivity analysis of the High-

Dimensional Model Representation (HDMR). Source: Ziehn and Tomlin (2017). ....................... 9

Figure 1-4 The theoretical framework and flowchart of downscaling 𝑉𝑐𝑚𝑎𝑥25 and evaluation.11

Figure 2-1 The xanthophyll cycle involving the de-epoxidation and epoxidation of xanthophyll

pigments. Source: Demmig-Adams (1990). ................................................................................. 19

Figure 2-2 PRI-LUE correlations for each PFT, using band 10 as the reference band. Unit of

LUE: gC/MJ. The blue lines are regression lines of the scatter points in each subplot................ 27





Figure 2-5 sPRI-LUE correlations at each site using bands 10, 12, and 13. Unit of LUE: gC/MJ.

The blue lines are regression lines of the scatter points in each subplot. ..................................... 32

Figure 3-1 Typical leaf reflectance spectra, from 400nm to 2500nm. Source: Croft and Chen

(2018). ........................................................................................................................................... 38

Figure 3-2 The correlation between MTCI and measured leaf chlorophyll content. Source: Croft

et al. (2014). .................................................................................................................................. 40

Figure 3-3 Intra-pixel heterogeneous 𝑉𝑐𝑚𝑎𝑥25 distribution within the TROPOMI pixel of each

site on the closest cloud-free day to the day of year 190. The 𝑉𝑐𝑚𝑎𝑥25 values at 1 km×1 km are

ix

downscaled through LCC. The red point represents the relative location of the site (1 km×1 km)

in the TROPOMI pixel (0.1°×0.1°). ............................................................................................. 45

Figure 3-4 Intra-pixel heterogeneous 𝑉𝑐𝑚𝑎𝑥25 distribution within the TROPOMI pixel of each

site on the closest cloud-free day to the day of year 190. The 𝑉𝑐𝑚𝑎𝑥25 values at 1 km×1 km are

downscaled through NDVI. The red point represents the relative location of the site (1 km×1

km) in the TROPOMI pixel (0.1°×0.1°). ..................................................................................... 46

Figure 3-5 𝑉𝑐𝑚𝑎𝑥25 seasonal variation of each site from the day of year 100 to 300................ 48

Figure 3-6 GPP scatter plot of each site from the day of year 100 to 300. The Y-axis represents

GPP estimates and the X-axis represents flux measured GPP. ..................................................... 51

Figure 3-7 GPP scatter plot of all sites from the day of year 100 to 300...................................... 51

Figure 3-8 GPP seasonal variation of each site from the day of year 100 to 300. The daily EC

GPP data were merged from half-hourly EC measurements. The daily modeled GPP data were

merged from hourly BEPS GPP simulation results. ..................................................................... 52

Figure 3-9 Temporal patterns of the bias of GPP estimated with TROPOMI and downscaled

𝑉𝑐𝑚𝑎𝑥25 ...................................................................................................................................... 53

Figure 3-10 GPP responses to 𝑉𝑐𝑚𝑎𝑥25 in the BEPS model. The Y-axis represents the GPP

estimates. Other inputs are kept consistent, using data on the day of year 124 at US-WCr site.

The X-axis represents 𝑉𝑐𝑚𝑎𝑥25 values changing from 0 to 80 µmol/m2/s. The blue curve shows

the GPP responses to change of 𝑉𝑐𝑚𝑎𝑥25. The black line is the straightened version of the curve

between mean 𝑉𝑐𝑚𝑎𝑥25 – SD and 𝑉𝑐𝑚𝑎𝑥25 + SD. The blue point represents lumped GPP,

simulated using 𝑉𝑐𝑚𝑎𝑥25 at the 0.1˚ resolution. The red point represents distributed, the mean

of GPP simulated based on the LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 within the 0.1˚ pixel. .................... 57

Figure 3-11 Spatial distribution of standard deviation of downscaled 𝑉𝑐𝑚𝑎𝑥25 values in

TROPOMI 𝑉𝑐𝑚𝑎𝑥25 pixels on the day of year 200. ................................................................... 58

Figure 3-12 Comparison of global 𝑉𝑐𝑚𝑎𝑥25 maps on the day of year 200. a) The 0.1°×0.1°

TROPOMI 𝑉𝑐𝑚𝑎𝑥25 map; b) The downscaled 1 km×1 km 𝑉𝑐𝑚𝑎𝑥25 map. ........................... 59

x

Figure 3-13 Comparison of 𝑉𝑐𝑚𝑎𝑥25 maps of North America on the day of year 150. a) The

0.1°×0.1° TROPOMI 𝑉𝑐𝑚𝑎𝑥25 map; b) The downscaled 1 km×1 km 𝑉𝑐𝑚𝑎𝑥25 map; c) and d)

Partially enlarged details of the red labeled region in a) and b); e) and f) Partially enlarged details

of the red labeled region in c) and d). ........................................................................................... 60









xi

Glossary of Acronyms and Abbreviations

APAR Absorbed Photosynthetically Active Radiation

BEPS Boreal Ecosystem Productivity Simulator

CI Clumping Index

EC Eddy Covariance

FPAR Fraction of Photosynthetically Active Radiation Absorbed by Vegetation

GEE Google Earth Engine

GPP Gross Primary Productivity

IOA Index Of Agreement

LAI Leaf Area Index

LCC Leaf Chlorophyll Content

LUE Light Use Efficiency

MAE Mean Absolute Error

MERIS MEdium Resolution Imaging Spectrometer

MODIS MODerate-resolution Imaging Spectroradiometer

MTCI MERIS Terrestrial Chlorophyll Index

NDVI Normalized Difference Vegetation Index

PAR Photosynthetically Active Radiation

PFT Plant Functional Type

PRI Photochemical Reflectance Index

R2 Squared Pearson correlation coefficient

RMSE Root Mean Square Error

SIF Sun-Induced chlorophyll Fluorescence

TROPOMI TROPOspheric Monitoring Instrument

𝑉𝑐𝑚𝑎𝑥 The maximum carboxylation rate

𝑉𝑐𝑚𝑎𝑥25 𝑉𝑐𝑚𝑎𝑥 normalized to 25°C

VI Vegetation Index

1

Chapter 1

Introduction

The carbon cycle is an essential part of the earth system dynamics. To understand the carbon cycle,

various models have been developed to simulate carbon cycle processes (IPCC, 2013). Terrestrial

ecosystems play an essential role in the climate system through carbon cycling among vegetation,

soil, and atmosphere (Cao and Woodward, 1998). Process-based models are important for

understanding the terrestrial carbon cycle. In the widely-adopted Farquhar’s scheme (Farquhar et

al., 1980), the maximum carboxylation velocity (𝑉𝑐𝑚𝑎𝑥) is a crucial parameter in modeling gross

primary productivity (GPP). The magnitude of 𝑉𝑐𝑚𝑎𝑥 exerts an impact on the magnitude of GPP,

and the uncertainty in 𝑉𝑐𝑚𝑎𝑥 will propagate through the model and be even magnified by the model

(Bonan et al., 2011, Chen et al., 2011), inducing errors in the final simulation results. Therefore,

reliable 𝑉𝑐𝑚𝑎𝑥 datasets are prerequisite for accurate GPP modeling.

Remote sensing offers continuous observations of the globe, providing frequent and extensive

coverage of terrestrial ecosystems. Reflectance measurements taken by satellite sensors have been

successfully used for estimating 𝑉𝑐𝑚𝑎𝑥, through vegetation indices (VIs), leaf chlorophyll content,

sun-induced chlorophyll fluorescence, etc. (Croft et al., 2017; He et al., 2019; Jin et al., 2012; Zhou

et al., 2014). Those measurements are at moderate spatial resolutions ranging from several hundred

meters (MERIS/ENVISAT, MODIS/TERRA) to several kilometers (TROPOMI/Sentinel-5P). At

such moderate resolutions, the field of view of the measurements would be heterogeneous due to

the nature of the land (Garrigues et al., 2006b). Radiometric sensors integrate the surface

reflectance over each pixel, so the intra-pixel heterogeneous information is lost during

measurement. The intra-pixel spatial heterogeneity causes biases in retrieved parameters if the

retrieval algorithm is nonlinear (Chen, 1999; Hu and Islam, 1997; Raffy, 1994; Tian et al., 2002).

Therefore, the intra-pixel spatial heterogeneity has been a subject of intensive studies for the

purpose to accurately retrieve land surface parameters (Chasmer et al., 2009; Duveiller and

Cescatti, 2016; Hong et al., 2011; Kim and Barros, 2002; Piles et al., 2011).

In this thesis, three factors were selected to investigate the intra-pixel spatial heterogeneity of

𝑉𝑐𝑚𝑎𝑥 and to examine if they can provide information for downscaling the 𝑉𝑐𝑚𝑎𝑥 dataset derived

2

from sun-induced chlorophyll fluorescence. The factors are photochemical reflectance index

(PRI), leaf chlorophyll content (LCC), and normalized difference vegetation index (NDVI).

This chapter introduces the background and main structure of this study. It serves three purposes:

1) to review various methods of estimating 𝑉𝑐𝑚𝑎𝑥 ; 2) to review concepts of spatial scaling,

upscaling, and downscaling using remote sensing images; 3) to introduce the eddy covariance

techniques and state the significance of downscaling 𝑉𝑐𝑚𝑎𝑥 ; and 4) to outline the research

objectives and main structure of this thesis.

1.1 Introduction of 𝑉𝑐𝑚𝑎𝑥 and methods of estimating 𝑉𝑐𝑚𝑎𝑥

1.1.1 Definition of 𝑉𝑐𝑚𝑎𝑥

Terrestrial ecosystems “breathe” in carbon dioxide through the photosynthetic process and

“release” carbon dioxide into the atmosphere by autotrophic respiration and heterotrophic

respiration (Schimel, 1995). The feedbacks from the terrestrial carbon cycle can dramatically exert

effects on the biosphere-atmosphere carbon fluxes and the future climate change (Schimel et al.,

2015). Photosynthesis is the key driver of the terrestrial carbon cycle (Cadule et al., 2010; Canadell

et al., 2007), and it is an essential part of carbon cycle models (Bonan et al., 2011; Sitch et al.,

2003). Within the photosynthetic process, carboxylation fixes carbon dioxide in the air into

carbohydrates by adding carbon dioxide to ribulose 1,5 bisphosphate. In the Farquhar–von

Caemmerer–Berry model (Farquhar et al., 1980), 𝑉𝑐𝑚𝑎𝑥 (the maximum carboxylation rate) is a

fundamental parameter in simulating the photosynthetic activity of vegetation, which determines

the maximum photosynthetic capacity of leaves, and directly influences the amount of gross

primary productivity (GPP) in terrestrial ecosystems (Cramer and Field, 1999; Running et al.,

2004). In most process-based models, the 𝑉𝑐𝑚𝑎𝑥 normalized to 25 °C (𝑉𝑐𝑚𝑎𝑥25 ) is used. There are

several methods to estimate 𝑉𝑐𝑚𝑎𝑥25 , including the field measurements, the flux measurements, and

the remote sensing.

1.1.2 𝑉𝑐𝑚𝑎𝑥25 estimation from field measurements and flux measurements

𝑉𝑐𝑚𝑎𝑥25 can be estimated based on field measurements. As a key parameter of understanding the

capacity of a leaf for CO2 assimilation, 𝑉𝑐𝑚𝑎𝑥25 can be retrieved through gas-exchange process

analysis (Harley and Baldocchi, 1995; Wullschleger, 1993). 𝑉𝑐𝑚𝑎𝑥25 is obtained from the A/Ci

curves by measuring the photosynthesis rates under different carbon dioxide levels, where A

3

represents the leaf photosynthesis rate and Ci stands for the intercellular carbon dioxide

concentration of the leaf. 𝑉𝑐𝑚𝑎𝑥25 values of different species and different plant functional types

(PFTs) have been measured from field experiments in many studies (Kosugi and Matsuo, 2006;

Kosugi et al., 2003). Bahar et al. (2017) compared 𝑉𝑐𝑚𝑎𝑥25 values of 210 species at 18 field sites in

tropical moist forests. These field measurements provide substantial 𝑉𝑐𝑚𝑎𝑥25 data for global carbon

cycle simulation. However, the field gas exchange experiments cannot provide 𝑉𝑐𝑚𝑎𝑥25 values for

large geographical areas, for it is time and labor-consuming for data collections.

To address the limitations of gas exchange experiments, many studies utilized flux measurements

using the eddy covariance technique to improve the efficiency and accuracy of 𝑉𝑐𝑚𝑎𝑥25 estimation

(Wolf et al., 2006). Eddy covariance is a micro-meteorological method which can directly observe

the energy and gas exchange between ecosystems and the atmosphere (Liang et al., 2012a). The

eddy covariance technique can directly, accurately, and continuously measure the carbon exchange

and evapotranspiration of an ecosystem (Baldocchi, 2008). Many studies estimated 𝑉𝑐𝑚𝑎𝑥25 based

on eddy covariance flux measurements. Wang et al. (2007) applied data assimilation techniques to

invert models to derive 𝑉𝑐𝑚𝑎𝑥25 values from flux measurements. The 𝑉𝑐𝑚𝑎𝑥

25 values estimated from

eddy covariance flux data agree well with the 𝑉𝑐𝑚𝑎𝑥25 retrieved from field measurements, indicating

the usefulness of flux data for 𝑉𝑐𝑚𝑎𝑥25 estimates (Zheng et al., 2017).

1.1.3 𝑉𝑐𝑚𝑎𝑥25 estimation from remote sensing

Remote sensing provides spatially continuous observation of the Earth's surface, covering

extensive spatial and temporal land surface processes at the global scale. Based on the reflectance

spectra of ground objects, data from satellite sensors offer information on biophysical and

physiological characteristics of terrestrial ecosystems. However, remotely measured reflectance

cannot estimate 𝑉𝑐𝑚𝑎𝑥25 , because the variations of 𝑉𝑐𝑚𝑎𝑥

25 cannot lead to directly detectable spectral

signals in the reflectance received by the sensors. To solve this issue, many efforts have been made

to retrieve 𝑉𝑐𝑚𝑎𝑥25 indirectly from remotely sensed data.

1.1.3.1 Direct correlations between 𝑉𝑐𝑚𝑎𝑥25 and VIs

Vegetation indices (VIs) are compositions of reflectances in several spectral bands of remotely

sensed data to assess a particular property of vegetation. VIs designed for assessing vegetation

physiological status are often composed of spectral bands that are sensitive to the physiological

4

change of vegetation, often together with bands as references to exclude the influence of the plant

structure and the background. Various VIs have been designed to trace structural, biophysical and

physiological traits of vegetation from remote sensing data, and have been successfully used to

estimate structural parameters, including leaf area index (Chen and Cihlar, 1996; Zheng and

Moskal, 2009) and clumping index (Chen et al., 2005; He et al., 2012) and physiological

parameters, including leaf chlorophyll content (Croft et al., 2014). Wang et al. (2008) found the

correlation between 𝑉𝑐𝑚𝑎𝑥25 and the broadband simple ratio for beech stands in the cold-temperate

zone of Japan and concluded different VI-𝑉𝑐𝑚𝑎𝑥25 correlations at different elevations. Zhou et al.

(2014) observed close VI-𝑉𝑐𝑚𝑎𝑥25 relationships in deciduous and mixed forests. Jin et al. (2012)

investigated the correlation between NDVI and 𝑉𝑐𝑚𝑎𝑥25 and found tight exponential relationships,

showing the feasibility of NDVI to derive the interannual trajectory of photosynthetic capacity.

However, the interseasonal and interannual variations of VI- 𝑉𝑐𝑚𝑎𝑥25 relationships restrict the

reliability of the retrieval of 𝑉𝑐𝑚𝑎𝑥25 through VIs (Croft et al., 2020).

1.1.3.2 Indirect estimation of 𝑉𝑐𝑚𝑎𝑥25 from other parameters

Sun-induced chlorophyll fluorescence (SIF) has been widely used to study and track vegetation

traits (Guan et al., 2016; Guanter et al., 2014; He et al., 2017; Joiner et al., 2013; Köhler et al.,

2018; Sun et al., 2017). Zhang et al. (2014) generated unique relationships between SIF and 𝑉𝑐𝑚𝑎𝑥25 ,

and obtained 𝑉𝑐𝑚𝑎𝑥25 values using remotely sensed SIF through model inversion. He et al. (2019)

retrieved a 𝑉𝑐𝑚𝑎𝑥25 dataset from a data assimilation system based on the significant correlation

between SIF and GPP, showing the feasibility of using satellite SIF data to retrieve the information

on leaf photosynthetic capacity. Liu (2019) adopted the main framework of He et al. (2019) and

used the SIF data from the newly launched sensor, TROPOMI onboard Sentinel-5P, to produce a

𝑉𝑐𝑚𝑎𝑥25 map. Besides, leaf chlorophyll content (LCC), which is an essential parameter responsible

for the light harvest as part of photosynthetic processes, can be retrieved from remote sensing data

(Croft et al., 2020; Croft et al., 2014; Croft et al., 2015). Croft et al. (2017) found a significant

relationship between LCC and 𝑉𝑐𝑚𝑎𝑥25 , and assessed the feasibility of LCC retrieved from satellite

data to estimate 𝑉𝑐𝑚𝑎𝑥25 . Other studies also show strong correlations between LCC and 𝑉𝑐𝑚𝑎𝑥

25

(Homolová et al., 2013; Houborg et al., 2013), suggesting the potential for retrieving 𝑉𝑐𝑚𝑎𝑥25 over

large areas based on LCC. 𝑉𝑐𝑚𝑎𝑥25 can also be quantified considering leaf nitrogen content and

nitrogen use efficiency (Kattge et al., 2009).

5

1.2 Introduction of spatial scaling, upscaling, and downscaling in remote sensing

1.2.1 Introduction of intra-pixel spatial heterogeneity

Remote sensing techniques provide observations covering large spatial extents at high temporal

frequencies. However, those observations are often at moderate or coarse spatial resolutions from

several hundred meters to several tens of kilometers, which may contain very heterogeneous land

surfaces in the footprint of the sensors (Garrigues et al., 2006b). The landscape features within a

moderate-resolution pixel, such as agricultural fields and vegetation patches, are relatively small

in comparison with the pixel dimension. Many such features are included within one pixel, and

this within-pixel heterogeneous information is lost in moderate resolution images. Therefore, it is

of great importance to explore how the intra-pixel spatial heterogeneity of remote sensing data

affects the retrieval of land surface parameters and the simulation results of satellite-data driven

models.

1.2.2 Introduction to spatial scaling

The spatial heterogeneity includes two components, the spatial variability and the spatial structures

(Garrigues et al., 2006b). To understand the subpixel information, intra-pixel heterogeneity and

their effects, spatial scaling has been widely adopted to link information across scales. Spatial

scaling refers to using the information at one scale to derive information at another scale (Jarvis,

1995). If the algorithms used for retrieving land surface parameters are non-linear, the intra-pixel

heterogeneity induces biases in the retrieved parameters over pixels at coarse resolutions because

the reflectance acquired at the coarse resolutions is an averaging process that masks subpixel

variations (Chen, 1999).

Several studies have been carried out to investigate the effect of spatial scaling and to correct the

biases of retrieved parameters at coarse resolutions. Garrigues et al. (2006a) founded that if the

pixel is heterogeneous and the transfer function from remote sensing data to LAI is not linear,

biases would exist in the computation of LAI, and then they proposed a model to estimate and

correct the errors in LAI estimates. Similar results in Chen (1999) showed that negative biases of

LAI estimates occurred in heterogeneous pixels. Chen et al. (2013) studied the effect of vegetation

heterogeneity and surface topography on net primary productivity (NPP) estimates at a coarse

resolution (1 km) using an eco-hydrological model applied to a fine resolution (30 m). Biases were

6

introduced when averaging subpixel inputs for NPP estimation and a scaling algorithm was

developed to correct the biases in NPP retrieval at coarse resolutions. El Maayar and Chen (2006)

proposed a method to use subpixel information to correct the evapotranspiration at a coarse

resolution, considering the spatial heterogeneity of vegetation, topography, and soil texture.

Chasmer et al. (2009) assessed the influence of spatial heterogeneity on GPP estimation using

airborne light detection and ranging (Lidar), scaling from 1 m to 1000 m, and pointed out Lidar as

an appropriate method for scaling between tower flux GPP and satellite-based GPP products.

Therefore, it is essential to investigate the spatial scaling effect for accurate land surface

parameters derived from remote sensing data.

Figure 1-1 Variations of LAI retrieval biases of coarse resolution pixels with different water

area fraction using an NDVI-based non-linear LAI retrieval algorithm, expressed as the

relative difference in LAI. Source: Chen (1999).

1.2.3 Introduction to upscaling and downscaling

Differing from spatial scaling studies, which focus on the biases of retrieved surface parameters

from non-linear algorithms in heterogeneous pixels, upscaling and downscaling are aggregation

and disaggregation of the original dataset, combined with other data for better retrieval of land

surface parameters. Upscaling is defined as a decrease in spatial resolution or extrapolation from

point to grid (Bierkens et al., 2000). In situ measurements can be upscaled with remote sensing

data and models to regional scales. Ueyama et al. (2013) upscaled CO2 fluxes from 21 towers to

7

estimate the Alaskan CO2 budget by combining remote sensing data based on a support vector

regression model and the predicted upscaled regional fluxes were found to be consistent with GPP

and respiration field observations. Kang et al. (2015) developed a regression Kriging model to

upscale soil moisture measurements with MODIS products and the upscaling model showed high

prediction accuracy. Fu et al. (2014) combined tower flux measurements with satellite data based

on an upscaling model framework to estimate net ecosystem exchange (NEE) at high spatial-

temporal resolutions. The modeled results showed consistency with observed data and they found

that higher spatial resolution remote sensing products with tower flux measurements resulted in

better upscaled results. Thus, the upscaling method can integrate in situ measurements with

satellite data for precise regional environmental monitoring.

Figure 1-2 Basic operations involving upscaling and downscaling in remote sensing. Source:

Bierkens et al. (2000).

On the contrary, downscaling is defined as an increase in spatial resolution and also referred to as

the disaggregation of the original dataset into finer spatial units (Bierkens et al., 2000). Data at

coarse resolutions provide useful information and the downscaled results at high resolutions are

obtained through various methods based on the coarse-resolution data. The downscaling process

requires useful and available information at that resolution and the downscaled results restore the

spatial variation at a finer scale (Price et al., 2000).

Downscaling methods have been extensively used in remote sensing to infer information at a fine

resolution from data at a coarse resolution. Hong et al. (2011) downscaled an evapotranspiration

map at 250 m resolution derived from MODIS data using Landsat imagery at 30 m resolution. The

8

spatial distribution patterns of the disaggregated evapotranspiration maps were investigated from

the downscaled imagery. Duveiller and Cescatti (2016) performed a spatial downscaling of SIF,

which led to an improved temporal correlation between SIF and GPP. Their results supported that

the downscaled SIF could be used as new datasets for estimating GPP using satellite data. Kim

and Barros (2002) proposed a downscaling model to investigate the heterogeneous subpixel

information of remotely sensed soil moisture data. Their model adopted a modified fractal

interpolation method, which generated unique fractal surfaces to study the heterogeneity.

Therefore, downscaling can explore subpixel information and bring datasets from coarse to high

spatial resolutions.

1.3 Significance of downscaling 𝑉𝑐𝑚𝑎𝑥25

1.3.1 Introduction of the eddy covariance and flux tower measurements

Eddy covariance, a micro-meteorological method, is prevailing in observing the exchanges of gas,

energy, and momentum between ecosystems and the atmosphere (Liang et al., 2012a, b). The eddy

covariance method can directly, precisely, and continuously measure the carbon, water, and heat

fluxes at various time scales ranging from hour, day, month to year. The spatial scales of

observations at each tower site extend through the flux footprint around the tower, ranging from

100 m to 1000 m (Göckede et al., 2004). The eddy covariance technique has been proved to be the

most efficient way to measure the interactions between terrestrial ecosystems and the atmosphere

at the ecosystem scale (Baldocchi, 2008; Friend et al., 2007).

Photosynthesis happens during the day, absorbing solar energy and transforming it into vegetation

productivity, and stops at night. The observed flux at night represents the respiration activities of

the terrestrial ecosystem, including the plant autotrophic respiration and the heterotrophic soil

respiration. Without the influence of soil water, the respiration of terrestrial ecosystems (𝐸𝑅) can

be calculated as below (Liang et al., 2012a):

𝐸𝑅 = 𝐸𝑅0 × 𝑄10

𝑇 − 𝑇0𝑇0 (1-1)

where 𝐸𝑅0 is the respiration rate at the base temperature 𝑇0 . 𝑇 is the temperature at the

measurement time and 𝑄10 is the temperature-sensitivity factor of ecosystem respiration, which is

defined as the increase of the ecosystem respiration rate with the increase in temperature every 10

9

°C. Therefore, when photosynthesis, plant autotrophic, and heterotrophic soil respiration co-occur

during the day, the observed flux represents the net ecosystem productivity (NEP) and GPP can

be obtained as:

𝐺𝑃𝑃 = 𝑁𝐸𝑃 + 𝐸𝑅𝑑𝑎𝑦 (1-2)

where 𝐸𝑅𝑑𝑎𝑦 represents the ecosystem respiration during the day, and it is positive for losing

carbon from the ecosystem. NEP is positive for carbon uptake by the ecosystem. In this way, GPP

at each tower site can be accurately and continuously measured.

1.3.2 Building a bridge linking 𝑉𝑐𝑚𝑎𝑥25 from coarse to high resolutions

As one of the key parameters in terrestrial biosphere process-based models, 𝑉𝑐𝑚𝑎𝑥25 accounts for the

photosynthetic capacity of plants. However, little attention has been drawn to the intra-pixel spatial

heterogeneity of 𝑉𝑐𝑚𝑎𝑥25 . Since GPP is sensitive to the variation of 𝑉𝑐𝑚𝑎𝑥

25 (Ziehn and Tomlin, 2017),

biases in 𝑉𝑐𝑚𝑎𝑥25 would induce errors in GPP estimates, as shown in Figure 1-3. Currently, the

spatial resolution of 𝑉𝑐𝑚𝑎𝑥25 datasets derived from remote sensing data ranges from several to

several tens of kilometers while tower flux footprints are only about one kilometer. Therefore,

there is an apparent mismatch between the spatial resolutions of tower flux footprints and available

𝑉𝑐𝑚𝑎𝑥25 datasets derived from satellite data. This mismatch will induce biases in GPP estimates using

flux tower measurements as model inputs if the intra-pixel 𝑉𝑐𝑚𝑎𝑥25 values are not homogeneous.

Thus, the intra-pixel spatial distribution of 𝑉𝑐𝑚𝑎𝑥25 datasets needs to be explored.

Figure 1-3 Variation of global annual GPP with 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 in the sensitivity analysis of the High-

Dimensional Model Representation (HDMR). Source: Ziehn and Tomlin (2017).

10

In order to better understand the intra-pixel heterogeneous information of 𝑉𝑐𝑚𝑎𝑥25 datasets, it is

necessary to downscale 𝑉𝑐𝑚𝑎𝑥25 with the useful and available information at a finer resolution. This

will also enhance the accuracy of GPP estimates at a finer resolution within the pixel such as tower

flux sites and support investigation into the intra-pixel spatial distribution of 𝑉𝑐𝑚𝑎𝑥25 . Hence, the

downscaling process builds a bridge linking the 𝑉𝑐𝑚𝑎𝑥25 datasets from coarse to high spatial

resolutions and resolves the mismatch between the 𝑉𝑐𝑚𝑎𝑥25 datasets and tower flux footprints.

1.4 Objectives and main structure of this research

1.4.1 Research objectives

This research is designed to quantitively analyze the heterogeneity and the spatial distribution of

𝑉𝑐𝑚𝑎𝑥25 within the pixels of the 𝑉𝑐𝑚𝑎𝑥

25 dataset produced by Liu (2019) and downscale the 𝑉𝑐𝑚𝑎𝑥25

dataset to 1 km, same as the footprint of tower sites. This dataset was produced by firstly,

estimating GPP from angularly normalized TROPOMI SIF data, and then retrieval 𝑉𝑐𝑚𝑎𝑥25 at the

0.1°×0.1° resolution from an Ensemble Kalman filter (EnKF) data assimilation system (He et al.,

2019). Photochemical reflectance index (PRI), normalized difference vegetation index (NDVI),

and leaf chlorophyll content (LCC) are selected to investigate whether they can provide useful

information at a high spatial resolution for downscaling 𝑉𝑐𝑚𝑎𝑥25 . A spatial scaling algorithm is also

developed for the downscaling purpose.

The theoretical framework of this study is presented in the flowchart below.

This thesis research encompasses the following four objectives:

1. To quantify the heterogeneity within the pixels of the 𝑉𝑐𝑚𝑎𝑥25 product derived from satellite sun-

induced chlorophyll fluorescence;

2. To explore a feasible and effective way to downscale 𝑉𝑐𝑚𝑎𝑥25 using high-resolution remote

sensing images;

3. To demonstrate the improvement of GPP simulation at tower flux sites using the downscaled

𝑉𝑐𝑚𝑎𝑥25 .

11

4. To produce the first global 1 km 𝑉𝑐𝑚𝑎𝑥25 map with the downscaling method satisfactorily

evaluated with the flux-derived GPP.

Figure 1-4 The theoretical framework and flowchart of downscaling 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 and evaluation.

1.4.2 Structure of this research

The thesis is organized following the research objectives mentioned in Chapter 1.4.1.

In Chapter 2, PRI is selected for downscaling 𝑉𝑐𝑚𝑎𝑥25 derived from satellite sun-induced chlorophyll

fluorescence from Liu (2019) at 0.1-degree resolution (approximately 11 km) to 1 km resolution.

Generic correlations of PRI-LUE for each plant functional type and unique correlations of PRI-

LUE of five sites are established based on historical data from FLUXNET and AMERIFLUX,

respectively. GPP estimates at the downscaled resolution are then derived following the

established PRI-LUE correlations. A lookup table approach for searching 𝑉𝑐𝑚𝑎𝑥25 values is

established based on BEPS simulations that determine the relationship between 𝑉𝑐𝑚𝑎𝑥25 and GPP

12

under given meteorological conditions. The downscaling results are found to be unsatisfactory and

are analyzed, leading to the development of alternatives shown in Chapter 3.

In Chapter 3, LCC and NDVI are selected for downscaling the 𝑉𝑐𝑚𝑎𝑥25 dataset mentioned above. A

scaling algorithm for obtaining downscaled 𝑉𝑐𝑚𝑎𝑥25 at 1 km resolution is developed and a scaling

ratio is designed. To evaluate the results, the original 𝑉𝑐𝑚𝑎𝑥25 and the downscaled 𝑉𝑐𝑚𝑎𝑥

25 are used as

inputs to the BEPS model to simulate GPP. The downscaled 𝑉𝑐𝑚𝑎𝑥25 is evaluated over five different

sites from AMERIFLUX with available GPP measurements in 2018, by comparing GPP from EC

towers with GPP values simulated from the original 𝑉𝑐𝑚𝑎𝑥25 and the downscaled 𝑉𝑐𝑚𝑎𝑥

25 . After a

downscaling method is satisfactorily evaluated with the flux-derived GPP at the tower sites, a

𝑉𝑐𝑚𝑎𝑥25 map at 1 km resolution for North America is produced as an example.

In Chapter 4, the main conclusions of this thesis are summarized. The limitations are discussed

and a plan for future work is proposed.

13

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Chapter 2

Trial of photochemical reflectance index (PRI)

on downscaling 𝑉𝑐𝑚𝑎𝑥25

2.1 Introduction

When plants receive excessive photosynthetic active radiation, the xanthophyll pigments in leaves

dissipate the excessive energy and prevent plants from photodamage. This energy dissipation is

achieved through the interconversion of three xanthophyll pigments in the xanthophyll cycling.

When plants receive excess energy, the light-harvesting xanthophyll, violaxanthin is de-

epoxidized to the energy quenching xanthophyll, zeaxanthin via antheraxanthin, and this process

is reversed under light-limiting conditions (Demmig-Adams, 1990; Demmig-Adams and Adams,

1996). Therefore, the xanthophyll cycle is associated with the efficiency of light harvesting, thus

the photosynthetic efficiency.

Under excessive light conditions, the content of zeaxanthin increases in the xanthophyll cycle and

a decrement in the leaf reflectance at around 531nm (𝑅531) has been observed (Gamon et al., 1990).

Then, Gamon et al. (1992) proposed a narrow band index, the physiological reflectance index

(PRI), using the signal at 𝑅531 and a reference band (𝑅𝑟𝑒𝑓) to minimize the effects of other factors

on the xanthophyll signal. The original formula was presented by:

𝑃𝑅𝐼 = 𝑅𝑟𝑒𝑓 − 𝑅531

𝑅𝑟𝑒𝑓 + 𝑅531 (2-1)

Figure 2-1 The xanthophyll cycle involving the de-epoxidation and epoxidation of

xanthophyll pigments. Source: Demmig-Adams (1990).

20

Gamon et al. (1992) used 𝑅550 as the reference band and observed its capacity to track diurnal

photosynthetic efficiency. The relationship between PRI and LUE was also tested under nitrogen

stressed and water stress situations in sunflower canopies. PeÑUelas et al. (1995) used 𝑅570 as the

reference band and renamed the index as photochemical reflectance index (PRI), which was

calculated as:

𝑃𝑅𝐼 = 𝑅531 − 𝑅570

𝑅531 + 𝑅570

(2-2)

The rearranged PRI was found to yield a positive correlation with LUE and this formula became

the PRI definition.

Many studies have been done to use remotely sensed PRI to capture LUE changes across different

species, at sites, and over regional areas. Rahman et al. (2004) first used PRI derived from band

11 (bandwidth 526-536nm) and band 12 (546-556nm) of the Moderate Resolution Imaging

Spectroradiometer (MODIS) onboard the Terra and Aqua platforms to track the seasonal variation

of LUE. The correlation between PRI and LUE was used to improve the LUE model (Monteith,

1972) for better net primary productivity simulation. Drolet et al. (2005) tested MODIS bands 1

(620-670nm), 4 (545-565nm), 12, and 13 (662-672nm) as potential reference bands for PRI and

selected band 13 to correlate the scaled PRI with LUE over a boreal trembling aspen site. Drolet

et al. (2008) later tested the relationship between MODIS-derived PRI and LUE over eight boreal

eddy covariance (EC) towers and found a strong PRI-LUE correlation when all sites points were

combined. Goerner et al. (2009) used MODIS-derived PRI to track LUE under seasonal drought

conditions in a Mediterranean forest. The relationship between MODIS PRI and LUE has been

studied and tested in many studies in various ecosystems (Garbulsky et al., 2008; Guarini et al.,

2014; Middleton et al., 2016; Moreno et al., 2012), showing the capacity of MODIS PRI to track

LUE changes.

Therefore, PRI can provide useful physiological information of plants at a higher spatial resolution.

In this chapter, the PRI data obtained from MODIS are used to downscale the 𝑉𝑐𝑚𝑎𝑥25 dataset. In

Section 2.3, the data preprocessing process and the designed methodology are introduced. The

BEPS model used for establishing the lookup table is also introduced. In Section 2.4, the results

are presented. The problems found in the process are discussed, and further works for solving those

issues are proposed.

21

2.2 Data and methods

2.2.1 Data

A total number of 190 sites from FLUXNET (https://fluxnet.fluxdata.org) were selected to

establish generic correlations between PRI and LUE for nine plant functional types (The basic

information of the sites can be found at https://fluxnet.fluxdata.org/sites/site-list-and-

pages/?view=table). Five sites from AMERIFLUX (https://ameriflux.lbl.gov/) were selected to

establish unique correlations between PRI and LUE at each site, including US-Bi2 (Sanchez et al.,

2017-), US-Los (Sulman et al., 2009), US-Rpf (Ueyama et al., 2019), US-Tw4 (Sanchez et al.,

2013-), and US-WCr (Cook et al., 2004). For PFT-level correlations between PRI and LUE, all

historical data from FLUXNET (2001-2015) were used. For site-level correlations between PRI

and LUE, data of five sites in 2017 were used. The established correlations were used for the GPP

estimation of 2018. The meteorological data as inputs for GPP simulation were obtained from the

flux measurements, including shortwave radiation, air temperature, vapor pressure deficit,

precipitation, and wind speed.

Google earth engine (GEE) as a cloud-based platform for planetary-scale geospatial analysis

provides an efficient cloud-computing tool for remote sensing studies (Gorelick et al., 2017).

Surface reflectance data were collected from the MODIS Terra surface spectral reflectance data

product (MODOCGA) at a resolution of 1 km from GEE. LAI and FPAR data were collected from

MODIS LAI/FPAR 4-Day 500 m product (MCD15A3H) from GEE. And the LAI/FPAR data

were smoothed and resampled to a daily 1 km product. Clumping index (CI) data used for

calculating the gap fraction of a canopy were derived from the MODIS BRDF product (He et al.,

2016). Global 𝑉𝑐𝑚𝑎𝑥25 data were derived from TROPOMI SIF datasets at a resolution of 0.1 degrees

(Liu, 2019).

For establishing the lookup table to search the 𝑉𝑐𝑚𝑎𝑥25 values with GPP derived from PRI, the input

data of the BEPS model corresponds to the data used by Liu (2019), as shown in Table 2-1. The

data were all spatially interpolated to a 0.1° × 0.1° grid.

22

Table 2-1 Basic information of datasets for establishing the lookup table.

Input data Data source Original Spatial

Resolution References

Surface wind speed

Air temperature

Shortwave radiation

Surface precipitation

Atmosphere pressure

MERRA-2 0.625° × 0.5°

LAI MODIS & AVHRR 8 km × 8 km Liu et al. (2012)

CI MODIS 36 km × 36 km He et al. (2016)

PFT MODIS 1 km × 1 km Friedl et al. (2002)

2.2.2 Estimating GPP based on PRI

The LUE model was adopted to link PRI and GPP. The LUE model was initially established from

the linear relationship between the amount of PAR absorbed by plants, and their GPP (Monteith,

1972; Monteith et al., 1977), where the APAR can be further estimated by introducing a factor

referring to as the fraction of incident PAR absorbed by plants (FPAR).

𝐺𝑃𝑃 = 𝐿𝑈𝐸 ∗ 𝐴𝑃𝐴𝑅 (2-3)

The LUE values of each day with available data can be obtained by:

𝐿𝑈𝐸 = 𝐺𝑃𝑃

𝑃𝐴𝑅 ∗ 𝐹𝑃𝐴𝑅(2-4)

2.2.2.1 Trial of establishing generic correlations between PRI and LUE

To estimate the global GPP distributions of 2018 at 1 km resolution, reliable PRI-LUE correlations

should be initially established. In this part, the generic correlations were firstly established based

on all historical flux measurements from FLUXNET. Band 11 (centered at 531nm) was selected

as the signal band of PRI. Band 10 (centered at 488nm), band 12 (centered at 551nm), and band

13 (centered at 667nm) were selected as the reference band of PRI, respectively. PRI was

calculated as:

23

𝑃𝑅𝐼 = 𝐵11 − 𝐵𝑟𝑒𝑓

𝐵11 + 𝐵𝑟𝑒𝑓

(2-5)

From the first day with available data to the ending day of each site, PRIs using those three bands

were derived on cloud-free days on the pixels of each site. Then noise filters were applied to

exclude noises and errors.

Considering different physiological characteristics among different plant species, nine PFTs were

selected. The abbreviations and full forms of the nine PFTs are listed in Table 2-2 below.

Table 2-2 The abbreviations and full forms of the nine PFTs.

Abbreviation Full form

DBF Deciduous Broadleaf Forest

EBF Evergreen Broadleaf Forest

DNF Deciduous Needleleaf Forest

ENF Evergreen Needleleaf Forest

MF Mixed Forest

GRA Grassland

CRO Cropland

SH Shrubs

WET Wetlands

The GPP and PAR data derived from half-hourly flux measurements during all daytime were

averaged to daily GPP and PAR, to obtain daily LUE data. All available PRIs of each PFT were

aggregated to perform regression analysis against the corresponding LUE. The PRI reference band

with the best correlations was finally selected to derive the generic correlations for each PFT,

which would be further used to estimate the GPP of 2018 at a 1 km resolution.

2.2.2.2 Trial of establishing correlations between PRI and LUE at flux sites

In this part, unique PRI-LUE correlations at each site were established based on flux

measurements, the MODIS reflectance product, and the MODIS LAI/FPAR product (mentioned

in Chapter 2.3.1) of 2017. Band 10 (centered at 488nm), band 12 (centered at 551nm), and band

13 (centered at 667nm) were selected as the reference band of PRI, respectively. The LUE data

were calculated from the GPP and PAR data derived from half-hourly flux measurements from 10

24

am to 12 pm at local time, which approximately corresponds to the crossing time of MODIS Terra

(Drolet et al., 2008). In order to obtain only positive values, PRIs using those four bands were

scaled using the mathematical transformation (Rahman et al., 2004):

𝑠𝑃𝑅𝐼 = 𝑃𝑅𝐼 + 1

2(2-6)

The scaled PRI (sPRI) derived on cloud-free days on the pixels of each site and noise filters were

applied to exclude noises and errors of sPRI. The sPRI reference band with the best correlations

was finally selected to derive the unique correlation between sPRI and LUE for that site. Then

following the established correlations of each site, the GPP estimates were retrieved.

2.2.3 Retrieving 𝑉𝑐𝑚𝑎𝑥25 based on GPP estimated from PRI

2.2.3.1 Model description

In this study, the Boreal Ecosystem Productivity Simulator (BEPS) was adopted to link 𝑉𝑐𝑚𝑎𝑥25 with

the GPP estimated from PRI. The BEPS model is a diagnostic enzyme kinetic model, which has

been frequently used for regional and global carbon cycle simulation (Chen et al., 2019; Gonsamo

et al., 2013; Wang et al., 2004). BEPS was first developed for the Boreal Ecosystem-Atmosphere

Study, coupling water and carbon cycles at regional scales (Liu et al., 1999, 2002; Liu et al., 1997).

BEPS adopts a two-leaf theory, separating sunlit and shaded leaves during the modeling process

(Chen et al., 1999). The total photosynthesis (Ac) at the canopy level is modeled by combining the

photosynthetic rates of sunlit and shaded leaves (𝐴𝑠𝑢𝑛 and 𝐴𝑠ℎ𝑎𝑑𝑒). GPP at the canopy level is

modeled by multiplying the corresponding LAI to the photosynthetic rates of sunlit and shaded

leaf groups:

𝐺𝑃𝑃 = 𝐴𝑠𝑢𝑛𝐿𝐴𝐼𝑠𝑢𝑛 + 𝐴𝑠ℎ𝑎𝑑𝑒𝐿𝐴𝐼𝑠ℎ𝑎𝑑𝑒 (2-7)

In this study, the MODIS LAI represents the total LAI of the canopy, where 𝐿𝐴𝐼𝑠𝑢𝑛 and 𝐿𝐴𝐼𝑠ℎ𝑎𝑑𝑒

stand for LAI of sunlit and shaded leaves. When separating 𝐿𝐴𝐼𝑠𝑢𝑛 and 𝐿𝐴𝐼𝑠ℎ𝑎𝑑𝑒, the clumping

index (Ω) is adopted to consider the non-random distribution patterns of the leaves inside the

canopy (Chen, 1996). The clumping index characterizes the extent of clumping of the foliage,

where the Ω equals to 1 in canopies with randomly distributed foliage. The more clumping of the

leaves, the smaller the Ω is. Then 𝐿𝐴𝐼𝑠𝑢𝑛 and 𝐿𝐴𝐼𝑠ℎ𝑎𝑑𝑒 are calculated as:

25

𝐿𝐴𝐼𝑠𝑢𝑛 = 2𝑐𝑜𝑠𝜃 (1 − 𝑒−0.5Ω𝐿𝐴𝐼

𝑐𝑜𝑠𝜃 ) (2-8)

𝐿𝐴𝐼𝑠ℎ𝑎𝑑𝑒 = 𝐿𝐴𝐼 − 𝐿𝐴𝐼𝑠𝑢𝑛 (2-9)

BEPS follows Farquhar’s principle (Farquhar et al., 1980) to calculate the photosynthetic rate of a

leaf as the minimum value between 𝑊𝑗 (radiation-limited gross photosynthesis rate) and 𝑊𝑐

(Rubisco-limited gross photosynthetic rate), where:

𝑊𝑗 = 𝐽𝐶𝑖 − Γ

4.5𝐶𝑖 + 10.5Γ(2-10)

𝑊𝑐 = 𝑉𝑚

𝐶𝑖 − Γ

𝐶𝑖 + 𝐾(2-11)

𝐴𝑐 = min{𝑊𝑗 , 𝑊𝑐} − 𝑅𝑑 (2-12)

𝐽, 𝑉𝑚, 𝐶𝑖 , Γ, 𝐾, and 𝑅𝑑 represent the radiation-dependent electron transport rate, the maximum

carboxylation rate, intercellular carbon dioxide concentration, temperature-dependent carbon

dioxide compensation point without dark respiration, the temperature-dependent function of

enzyme kinetics, and daytime leaf dark respiration, respectively. Following this method, with

given 𝑉𝑐𝑚𝑎𝑥25 values, LAI and clumping data, meteorological data, and other inputs, BEPS can

simulate hourly GPP of that day. Likewise, when given a GPP value, together with other

environmental conditions, the 𝑉𝑐𝑚𝑎𝑥25 value can be estimated.

2.2.3.2 Lookup-table establishment and 𝑉𝑐𝑚𝑎𝑥25 searching

In order to invert an ecological model, for example, to assess the physiological conditions of plants

based on remote sensing or flux measurements, many methods have been employed, including

iterative optimization methods, neural networks, lookup-tables, etc. (Croft and Chen, 2018).

Among various methods, the lookup-table method provides a computationally efficient way to

model the physiological characteristics. In this study, the BEPS model was iteratively run using

the input data described in Chapter 2.3.1. The simulated GPP and meteorological data were

averaged to each day, and the daily GPP, daily meteorological conditions, PFT, LAI, and 𝑉𝑐𝑚𝑎𝑥25

formed the lookup-table. Then, the GPP estimated from PRI at 1 km resolution was used to search

26

the nearest 𝑉𝑐𝑚𝑎𝑥25 value from the lookup-table as the downscaled 𝑉𝑐𝑚𝑎𝑥

25 . The criteria here were: 1)

whether the scatters of PRI and LUE were clustered; 2) whether the Pearson coefficients of PRI

and LUE were good enough to achieve reliable GPP estimations. However, due to the

unsatisfactory accuracy of GPP estimates from PRI, this part of work was not completed.

2.3 Discussion

2.3.1 Results and problems found in the progress

2.3.1.1 Trial of establishing generic PRI-LUE correlations for each PFT

The generic PRI-LUE correlations were established using MODIS bands 10, 12, and 13 as the

reference band. The PRI data were derived using MODIS bands 10, 12, and 13 as the reference

band (𝑃𝑅𝐼𝐵10, 𝑃𝑅𝐼𝐵12, and 𝑃𝑅𝐼𝐵13), respectively.

As shown in Figure 2-2, the scatter points are dispersed, indicating weak correlations between

either 𝑃𝑅𝐼𝐵10, 𝑃𝑅𝐼𝐵12 or 𝑃𝑅𝐼𝐵13 and LUE. Similar results can also be observed in Figure 2-3, and

Figure 2-4. The R2 values are all low though most of the correlations are significant (p<0.001), as

shown in Table 2-3.

27


LUE: gC/MJ. The blue lines are regression lines of the scatter points in each subplot.

28



29



Table 2-3 Squared Pearson correlation coefficient between PRI and LUE using MODIS

bands 10, 12, and 13 at 190 sites for nine plant functional types.

Plant Functional Type 𝑃𝑅𝐼𝐵10 𝑃𝑅𝐼𝐵12 𝑃𝑅𝐼𝐵13

30

ENF 0.02* 0.02* 0.01*

EBF 0.15* 0.04* 0.00*

DNF 0.06* 0.02 0.01

DBF 0.00 0.00 0.11*

MF 0.00 0.01* 0.01*

SH 0.10* 0.06* 0.07*

GRA 0.08* 0.02* 0.05*

WET 0.02* 0.02* 0.01*

CRO 0.00* 0.00 0.14*

*p<0.001

2.3.1.2 Trial of establishing PRI-LUE correlations at each site

The PRI-LUE correlations at each site also used MODIS bands 10, 12, and 13 as the reference

band. As shown in Figure 2-5, the PRI data of five sites were derived using MODIS band 10, 12,

and 13 as the reference band (𝑃𝑅𝐼𝐵10, 𝑃𝑅𝐼𝐵12, and 𝑃𝑅𝐼𝐵13), respectively.

Table 2-4 Squared Pearson correlation coefficient between sPRI and LUE using MODIS

band 10, 12, and 13 at five sites.

Site Code 𝑠𝑃𝑅𝐼𝐵10 𝑠𝑃𝑅𝐼𝐵12 𝑠𝑃𝑅𝐼𝐵13

US-Bi2 0.29* 0.26* 0.49*

US-Los 0.00 0.02 0.25*

US-Rpf 0.10* 0.13* 0.04

US-Tw4 0.12* 0.01 0.37*

US-WCr 0.11* 0.09* 0.28*

*p<0.001

31

32

Figure 2-5 sPRI-LUE correlations at each site using bands 10, 12, and 13. Unit of LUE:

gC/MJ. The blue lines are regression lines of the scatter points in each subplot.

Most of the correlations between sPRI and LUE are weak, as shown in Figure 2-5 and Table 2-4.

Though 𝑠𝑃𝑅𝐼𝐵13 correlates well with LUE at some sites and the 𝑠𝑃𝑅𝐼𝐵13-LUE correlations are

significant, the scatter points are dispersed and the correlations can induce bias in creating the LUE

map and GPP estimation.

In establishing PRI-LUE correlations, several problems were found:

1) Though the correlations of MODIS PRI and LUE have been tested at several sites (Drolet et al.,

2008; Goerner et al., 2009), a generic relationship between the two parameters cannot be

established. In this chapter, generic relationships of PRI-LUE for each plant functional type were

proposed to be established. However, the regressions are weak and cannot support further GPP

estimation based on the LUE derived from MODIS PRI. The locations and climate conditions of

sites were not considered. In establishing unique PRI-LUE correlations at five sites, GPP

measurements from 10 am to 12 pm at the local time were merged to derive LUE at Terra passing

time but the results were unsatisfying.

2) There are many noisy data points in the MODIS reflectance product but the filtering conditions

failed to exclude the outliers. In establishing PRI-LUE correlations, many PRI outliers exist and

exert negative impacts on the correlations. The data points in the regression are scattered widely

and the regressions are weak. However, the p values indicate that the correlations between PRI

and LUE are statistically significant or informative, indicating a certain value of PRI.

3) LUE, defined as the ratio of gross primary productivity and absorbed photosynthetically active

ration, can be influenced by temperature, moisture, and phenology (Liang et al., 2012). In

establishing PRI-LUE correlations at five sites, the air temperature was considered as an additional

factor but its consideration does not lead to improved results. The weak correlations after

considering environmental factors originate from noisy data in the MODIS reflectance product.

33

2.3.2 Further work for solving the issues

1) In addition to plant functional types, the geographical locations and climate conditions will also

be considered in establishing generic PRI-LUE correlations. GPP at corresponding satellite

passing time will be merged for LUE calculation following the method by Drolet et al. (2008).

2) Some improvements will be made in preprocessing MODIS reflectance data. Instead of using

the MODIS reflectance product, MODIS at-sensor radiance data (MOD/MYD021) will be used.

Besides, the corresponding geolocation data (MOD/MYD03) and cloud mask data

(MOD/MYD35) will be used to generate geolocations and remove the contaminated data,

following the method by Zheng (2017) and Drolet et al. (2008).

3) Environmental factors including air temperature and soil moisture will be considered in

establishing PRI-LUE correlations, by adopting the factors as coefficients in the correlations.

Besides, NDVI will also be adopted to generate PRI*NDVI-LUE correlations following the

method by (Zheng and Chen, 2017).

Overall, some future works are proposed to enhance the correlations between PRI and LUE.

Reliable GPP data can only be estimated if the PRI-LUE correlations are significant and thus the

downscaled 𝑉𝑐𝑚𝑎𝑥25 dataset can be derived.

34

2.4 References

Camilo Rey Sanchez, Cove Sturtevant, Daphne Szutu, Dennis Baldocchi, Elke Eichelmann, Sara

Knox (2013-) AmeriFlux US-Tw4 Twitchell East End Wetland, Dataset.

https://doi.org/10.17190/AMF/1246151

Camilo Rey-Sanchez, Daphne Szutu, Dennis Baldocchi, Kyle Hemes (2017-) AmeriFlux US-Bi2

Bouldin Island corn, Dataset. https://doi.org/10.17190/AMF/1419513

Chen, J.M. (1996). Optically-based methods for measuring seasonal variation of leaf area index in

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37

Chapter 3

Leaf chlorophyll content (LCC) as a feasible way for

downscaling 𝑉𝑐𝑚𝑎𝑥25

3.1 Introduction

Leaf chlorophyll is essential to the cycles of carbon, water, and energy between the biosphere and

atmosphere, and to the functioning of terrestrial ecosystems (Croft et al., 2017; Croft et al., 2020).

As a crucial constituent involved in plant photosynthetic processes, chlorophyll is responsible for

harvesting photons and transporting electrons to facilitate the production of biochemical energy,

which supports the Calvin-Benson cycle (Alton, 2017; Porcar-Castell et al., 2014). Many studies

have been carried out to estimate LCC using remotely sensed data, through vegetation indices

(VIs) and biophysical modeling approaches. Leaf reflectance is controlled by the existence of

foliar constituents, including chlorophyll, carotenoids, nitrogen, and water (Ustin et al., 2004). The

spectral signals in the red-edge region (690-750 nm) are particularly sensitive to the changes in

chlorophyll content (Curran et al., 1990). Several narrowband VIs using reflectance bands in the

red-edge region have been tested to estimate chlorophyll content (Dash and Curran, 2004;

Haboudane et al., 2004; Wu et al., 2008). Besides, several studies coupled canopy models and leaf

models to retrieve chlorophyll content, and a two-step model inversion method has been

demonstrated to perform well. Zhang et al. (2008) combined the 4-Scale model (Chen and Leblanc,

1997) and the PROSPECT model (Jacquemoud and Baret, 1990) and retrieved chlorophyll content

at 20 m resolution using airborne hyperspectral data over a boreal landscape. Similar results were

also achieved by Croft et al. (2013) and Croft et al. (2015). As one of the key constituents

associated with plant photosynthetic activities, chlorophyll content can reflect vegetation growth

status and has been found to correlate well with plant photosynthetic capacity. Croft et al. (2017)

found that chlorophyll content strongly correlates with 𝑉𝑐𝑚𝑎𝑥25 for four tree species in a temperate

forest and a global chlorophyll distribution map was later derived by Croft et al. (2020). Luo et al.

(2019) showed that GPP estimation at 124 tower sites (555 site-years) distributed around the globe

is significantly improved with R2 increasing from 0.74 to 0.84 after considering the seasonal

variation of 𝑉𝑐𝑚𝑎𝑥25 at these sites using a global LCC map. Therefore, LCC can capture informative

vegetation traits, and the LCC at 1 km resolution can be a proxy for downscaling the 𝑉𝑐𝑚𝑎𝑥25 product

at about 11 km resolution.

38

Figure 3-1 Typical leaf reflectance spectra, from 400nm to 2500nm. Source: Croft and Chen

(2018).

Besides, VIs have been widely adopted to monitor vegetation greenness (Boegh et al., 2002;

Haboudane et al., 2004; Huete et al., 2002), to track light use efficiency (PeÑUelas et al., 1995),

to estimate canopy nitrogen (Serrano et al., 2002), and to retrieve canopy water content (Ceccato

et al., 2001; Jackson et al., 2004). As one of the widely used VIs, normalized difference vegetation

index (NDVI) was first used to monitor vegetation growth conditions in rangeland (Rouse et al.,

1973), calculated as:

𝑁𝐷𝑉𝐼 = 𝑅𝑛𝑖𝑟 − 𝑅𝑟𝑒𝑑

𝑅𝑛𝑖𝑟 + 𝑅𝑟𝑒𝑑

(3-1)

where 𝑅𝑟𝑒𝑑 and 𝑅𝑛𝑖𝑟 represent the spectral reflectance measurements obtained in the visible red

and near-infrared regions, respectively. NDVI has been tested to strongly correlate with green leaf

biomass, foliar nitrogen content, and maximum canopy CO2 uptake (Gamon et al., 1995). Jin et al.

(2012) correlated NDVI with 𝑉𝑐𝑚𝑎𝑥 and found an exponential relationship after combining all sites

and similar conclusions were reached by Zhou et al. (2014), showing the capacity of NDVI for

capturing plant growth and photosynthetic status.

39

Therefore, LCC and NDVI can provide useful information for vegetation traits at higher spatial

resolutions than the existing 𝑉𝑐𝑚𝑎𝑥25 product. In this chapter, LCC and NDVI data are used to

downscale the 𝑉𝑐𝑚𝑎𝑥25 product. In Section 3.3, the data preprocessing process and the spatial scaling

algorithm are introduced, using the information of LCC and NDVI, respectively. The validation

and statistical analysis methods are also introduced. In Section 3.4, the downscaled results are

presented and discussed. The conclusions are reached in Section 3.5.

3.2 Data and methods

3.2.1 Data

Five flux sites with available GPP and meteorological measurements of 2018 were selected in this

research, including US-Bi2 (Sanchez et al., 2017-), US-Los (Sulman et al., 2009), US-Rpf

(Ueyama et al., 2019), US-Tw4 (Sanchez et al., 2013-), and US-WCr (Cook et al., 2004). Data of

these five sites were collected from AMERIFLUX ((https://ameriflux.lbl.gov/). The biological and

geographical specifications of these sites are summarized in Table 3-1. The clumping indices were

derived from the product by He et al. (2016), and the LAI data of each site were derived from

GLOBMAP LAI product by Liu et al. (2012). The LAI data were resampled to a daily LAI dataset

with a 1 km×1 km resolution.

Table 3-1 Site specifications for five flux sites

Site Code Longitude Latitude Plant Functional Type Year Clumping Index Peak LAI

US-Bi2 -121.535° 38.109° CRO 2018 0.70 7.25

US-Los -89.979° 46.083° WET 2018 0.64 8.18

US-Rpf -147.429° 65.120° DBF 2018 0.66 3.92

US-Tw4 -121.641° 38.103° WET 2018 0.69 2.18

US-WCr -90.080° 45.806° DBF 2018 0.64 6.14

*CRO: croplands, WET: wetlands, DBF: deciduous broadleaf forest

40

Leaf chlorophyll content data were derived from the Medium Resolution Imaging Spectrometer

(MERIS) Terrestrial Chlorophyll Index (MTCI), according to a linear equation outlined in Croft

et al. (2014):

𝐿𝐶𝐶 =𝑀𝑇𝐶𝐼 + 0.16

0.04(3-2)

where the MTCI was originally calculated as (Dash and Curran, 2004):

𝑀𝑇𝐶𝐼 = 𝑅754 − 𝑅709

𝑅709 − 𝑅681

(3-3)

The MTCI has demonstrated that it could use red edge positions bands to estimate chlorophyll

content over a large spatial area (Dash and Curran, 2006). However, due to lack of data from

MERIS since 2012, in this study, the Sentinel-2 data were used as a substitution. The red edge

position bands of Sentinel-2 have been evaluated to provide estimates of biophysical variables in

Figure 3-2 The correlation between MTCI and measured leaf chlorophyll content. Source:

Croft et al. (2014).

vegetation (Clevers and Gitelson, 2013; Frampton et al., 2013). Hence, the modified MTCI

(𝑀𝑇𝐶𝐼𝑚) using reference bands of Sentinel-2 was calculated as (Frampton et al., 2013):

𝑀𝑇𝐶𝐼𝑚 = 𝐵6 − 𝐵5

𝐵5 − 𝐵4(3-4)

where B4, B5, and B6 center at 665 nm, 705 nm, and 740 nm, with a bandwidth of 30 nm, 15 nm,

and 15nm and a spatial resolution of 10 m, 20 m, and 20 m, respectively. All the images were

41

collected from the Sentinel-2 Multi-Spectral Instrument Level-1C dataset (COPERNICUS/S2) and

resampled to a 1 km×1 km resolution on Google Earth Engine. Only cloud-free images were

selected for further analysis.

NDVI data were collected from the Terra Vegetation Indices 16-Day Global 500 m dataset

(MOD13A1) and resampled to a 1 km×1 km resolution on Google Earth Engine. The SummaryQA

band was used to exclude outliers.

3.2.2 Algorithms for downscaling 𝑉𝑐𝑚𝑎𝑥25

The TROPOMI 𝑉𝑐𝑚𝑎𝑥25 dataset was firstly gap-filled by assigning the nearest available values to the

days with no data available. The TROPOMI 𝑉𝑐𝑚𝑎𝑥25 dataset was assumed to be numerically reliable

and the downscaling factors only provided spatial variation information for distributing the

TROPOMI 𝑉𝑐𝑚𝑎𝑥25 data within each 0.1°×0.1° pixel. The downscaled 𝑉𝑐𝑚𝑎𝑥

25 values were then

obtained by applying a spatial scaling ratio 𝑆𝑆𝑅 to TROPOMI Vcmax, as described in the

following equation:

𝑉𝑐𝑚𝑎𝑥−𝑘𝑚 = 𝑆𝑆𝑅 × 𝑉𝑐𝑚𝑎𝑥−𝑑𝑔 (3-5)

where 𝑉𝑐𝑚𝑎𝑥−𝑘𝑚, 𝑉𝑐𝑚𝑎𝑥−𝑑𝑔 represent the downscaled 𝑉𝑐𝑚𝑎𝑥25 with a 1 km×1 km resolution, and

TROPOMI 𝑉𝑐𝑚𝑎𝑥25 with a 0.1°×0.1° resolution, respectively.

The spatial scaling ratios of each pixel were derived as described in the following equations:

𝑆𝑆𝑅𝐿𝐶𝐶𝑖,𝑗=

𝐿𝐶𝐶𝑖,𝑗

𝐿𝐶𝐶̅̅ ̅̅ ̅(3-6)

𝑆𝑆𝑅𝑁𝐷𝑉𝐼𝑖,𝑗=

𝑁𝐷𝑉𝐼𝑖,𝑗

𝑁𝐷𝑉𝐼̅̅ ̅̅ ̅̅ ̅̅(3-7)

where 𝐿𝐶𝐶𝑖,𝑗 and 𝑁𝐷𝑉𝐼𝑖,𝑗 represent LCC and NDVI of that 1 km×1k m pixel; 𝐿𝐶𝐶̅̅ ̅̅ ̅ and 𝑁𝐷𝑉𝐼̅̅ ̅̅ ̅̅ ̅̅

represent the mean LCC and NDVI of that 0.1°×0.1° pixel, respectively. When calculating the

mean LCC and the mean NDVI, outliers were replaced with the nearest available data in the

0.1°×0.1° pixel. The mean values of all downscaled 𝑉𝑐𝑚𝑎𝑥25 values in 0.1°×0.1° pixels were kept

the same as the TROPOMI 𝑉𝑐𝑚𝑎𝑥25 data. The downscaled 𝑉𝑐𝑚𝑎𝑥

25 data for each site in this study using

42

two methods mentioned above were obtained, after gap-filling the days with missing data using

available 𝑉𝑐𝑚𝑎𝑥25 values of the nearest day.

3.2.3 Evaluation and Statistical Analysis

The Boreal Ecosystem Productivity Simulator (BEPS) was adopted in this study to evaluate the

downscaled 𝑉𝑐𝑚𝑎𝑥25 , and it is described in Chapter 2.3.3.1. The original 𝑉𝑐𝑚𝑎𝑥

25 data and downscaled

𝑉𝑐𝑚𝑎𝑥25 data from LCC and NDVI were input to BEPS for GPP simulation. To evaluate the

performance of downscaled 𝑉𝑐𝑚𝑎𝑥25 , simulated GPP based on original TROPOMI 𝑉𝑐𝑚𝑎𝑥

25 data,

NDVI-downscaled 𝑉𝑐𝑚𝑎𝑥25 data, and LCC-downscaled 𝑉𝑐𝑚𝑎𝑥

25 data were compared with eddy

covariance (EC) flux GPP measurements, where squared Pearson correlation coefficient (R2),

mean absolute error (MAE) and root mean square error (RMSE) were used. The performance of

downscaled 𝑉𝑐𝑚𝑎𝑥25 was also evaluated using the agreement index ( 𝐼𝑂𝐴 ), which was firstly

proposed by Willmott (1981, 1982) and has been widely adopted in model assessments (Gu et al.,

2002; Wang et al., 2001; Zhou et al., 2016). This index of agreement represents the ratio of the

mean square error and the potential error, taking both R2 and RMSE into consideration. The index

𝐼𝑂𝐴 is calculated as:

𝐼𝑂𝐴 = 1 −∑ (𝑃𝑘 − 𝑂𝑘)2𝑛

𝑘=1

∑ (|𝑃′𝑘| − |𝑂′

𝑘|)2𝑛𝑘=1

(3-8)

where 𝑃′𝑘 = 𝑃𝑘 − �̅� and 𝑂′𝑘 = 𝑂𝑘 − �̅� ; 𝑛 is the total number of measurements; 𝑃𝑘 and 𝑂𝑘

represent GPP simulated from BEPS and EC GPP measurements, respectively; �̅� is the mean

value of EC GPP. The value of 𝐼𝑂𝐴 ranges from 𝐼𝑂𝐴 = 0, for no agreement between 𝑃𝑘 and 𝑂𝑘,

to 𝐼𝑂𝐴 = 1, for perfect agreement between simulations and observations.

Based on the downscaling factor with higher GPP estimation accuracy, a global 1 km 𝑉𝑐𝑚𝑎𝑥25 map

was produced. To evaluate the spatial distribution and variation within the TROPOMI pixels, the

standard deviation (𝑆𝐷0.1𝐷) of each TROPOMI pixel was calculated and the standard deviations

of all global pixels (𝑆𝐷) were averaged, as described in the following equations:

𝑆𝐷0.1𝐷 = √∑(𝑉𝑐𝑚𝑎𝑥𝑖

25 − 𝑉𝑐𝑚𝑎𝑥25̅̅ ̅̅ ̅̅ ̅)

𝑛1𝑘𝑚

(3-9)

43

𝑆𝐷 = ∑𝑆𝐷0.1𝐷𝑖

𝑛0.1𝐷

(3-10)

where 𝑉𝑐𝑚𝑎𝑥𝑖25 , 𝑉𝑐𝑚𝑎𝑥

25̅̅ ̅̅ ̅̅ ̅, 𝑛1𝑘𝑚 , and 𝑛0.1𝐷 stand for the 1 km 𝑉𝑐𝑚𝑎𝑥25 values, the average of 1 km

𝑉𝑐𝑚𝑎𝑥25 values within the TROPOMI pixel, the total number of 1 km 𝑉𝑐𝑚𝑎𝑥

25 pixels within the

TROPOMI pixel, and the total number of global TROPOMI pixels, respectively.

3.3 Results and discussion

Due to the availability of the 𝑉𝑐𝑚𝑎𝑥25 dataset, the downscaled 𝑉𝑐𝑚𝑎𝑥

25 starts from March 7th, 2018

(the day of year 66) to October 31st, 2018 (the day of year 304). The following analysis and results

are all in the range of the day of year 100 to 300, from the beginning to the end of the growing

season.

3.3.1 The intra-pixel heterogeneity of the TROPOMI 𝑉𝑐𝑚𝑎𝑥25 product

As shown in Figure 3-3, significant intra-pixel heterogeneities exist in the 0.1°×0.1° 𝑉𝑐𝑚𝑎𝑥25 pixels

on the day of year 190, in the middle of the growing season. The red points in the figures are the

relative location of the sites in the TROPOMI pixel. The downscaled 𝑉𝑐𝑚𝑎𝑥25 values were retrieved

by applying the scaling ratio derived from LCC, 𝑆𝑆𝑅𝐿𝐶𝐶, of that day. The blue, green and yellow

pixels represent low, moderate and high 𝑉𝑐𝑚𝑎𝑥25 values of that downscaled pixel. The vertical and

horizontal axes indicate the relative location of each downscaled pixel in the TROPOMI pixel.

US-Bi2 is a crop site, with growing corn on an island in the Sacramento San Joaquin Delta. The

site has deep peat, thus providing ideal environments for farming and the 𝑉𝑐𝑚𝑎𝑥25 values are high in

that region. The site is located at the bottom of that TROPOMI pixel and there are some high

estimates of 𝑉𝑐𝑚𝑎𝑥25 in the middle right of that TROPOMI pixel. The main landcover in that

TROPOMI pixel is crop, but the growing status of various subpixels differs, leading to

heterogeneous downscaled 𝑉𝑐𝑚𝑎𝑥25 values. US-Los is a shrub wetland site with some coniferous and

grassy stands. It is located in the top left of that TROPOMI pixel and the landcover within that

TROPOMI pixel is intensively heterogeneous. Different types of plants have individual growing

patterns and physiological characteristics, which indicates that the variation of 𝑉𝑐𝑚𝑎𝑥25 differs

among plant functional types. The middle right downscaled pixels have lower 𝑉𝑐𝑚𝑎𝑥25 while the top

right downscaled pixels have higher values. US-Rpf is a deciduous broadleaf forest in Alaska. It

44

is located in the middle right of that TROPOMI pixel and there are lower downscaled 𝑉𝑐𝑚𝑎𝑥25

estimates in the left part of that TROPOMI pixel. US-Tw4 is a permanent wetland site with woody

vegetation. It is located at the bottom of that TROPOMI pixel and intensive variation of 𝑉𝑐𝑚𝑎𝑥25 can

be seen from the figure of US-Tw4. Lower values are situated in the left part and higher values

situate in the bottom right corner. US-WCr is a deciduous broadleaf forest site in Wisconsin,

mainly with sugar maple and basswood. It is located in the bottom-left part of that TROPOMI

pixel and lower downscaled 𝑉𝑐𝑚𝑎𝑥25 values cluster around the bottom right corner.

45

Figure 3-3 Intra-pixel heterogeneous 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 distribution within the TROPOMI pixel of each

site on the closest cloud-free day to the day of year 190. The 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 values at 1 km×1 km are

downscaled through LCC. The red point represents the relative location of the site (1 km×1

km) in the TROPOMI pixel (0.1°×0.1°).

46

Figure 3-4 Intra-pixel heterogeneous 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 distribution within the TROPOMI pixel of

each site on the closest cloud-free day to the day of year 190. The 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 values at 1 km×1

km are downscaled through NDVI. The red point represents the relative location of the site

(1 km×1 km) in the TROPOMI pixel (0.1°×0.1°).

47

3.3.2 The 𝑉𝑐𝑚𝑎𝑥25 seasonal variation

With the downscaled 𝑉𝑐𝑚𝑎𝑥25 using 𝑆𝑆𝑅𝐿𝐶𝐶 and 𝑆𝑆𝑅𝑁𝐷𝑉𝐼 , the temporal patterns of 𝑉𝑐𝑚𝑎𝑥

25 at each site

can be generalized. At some sites, the seasonal variation of downscaled 𝑉𝑐𝑚𝑎𝑥25 shows similar

patterns to the TROPOMI 𝑉𝑐𝑚𝑎𝑥25 product, while at other sites, the patterns differ a lot.

As shown in Figure 3-5, in US-Bi2 and US-WCr, the LCC-downscaled and NDVI-downscaled

𝑉𝑐𝑚𝑎𝑥25 curves intersect at two points with the TROPOMI 𝑉𝑐𝑚𝑎𝑥

25 curve. Interestingly, the

downscaled 𝑉𝑐𝑚𝑎𝑥25 values at sites are higher than the TROPOMI 𝑉𝑐𝑚𝑎𝑥

25 values in the interval

between the two intercepts, which is in the middle of the growing season. The LCC-downscaled

𝑉𝑐𝑚𝑎𝑥25 values at sites are higher than the NDVI-downscaled values at sites between the intercepts.

Beyond the two intercepts, i.e., before and after the growing season, the opposite situation occurs.

The downscaled 𝑉𝑐𝑚𝑎𝑥25 values are lower than the TROPOMI 𝑉𝑐𝑚𝑎𝑥

25 values. In US-Bi2, the peak

𝑉𝑐𝑚𝑎𝑥25 values are very high mainly because the soil fertility and the values are low before sowing

in spring and harvesting in autumn. In US-Los, the LCC downscaled 𝑉𝑐𝑚𝑎𝑥25 values are all lower

than the TROPOMI 𝑉𝑐𝑚𝑎𝑥25 values and the seasonal variation of the LCC-downscaled 𝑉𝑐𝑚𝑎𝑥

25 is

similar to that of the TROPOMI 𝑉𝑐𝑚𝑎𝑥25 , indicating the 𝑆𝑆𝑅𝐿𝐶𝐶 of this site undulates slightly near

1. The downscaled NDVI 𝑉𝑐𝑚𝑎𝑥25 curve is found to fluctuate moderately near the TROPOMI 𝑉𝑐𝑚𝑎𝑥

25

curve. In US-Rpf, over the period of the day of year 180 to 220, a slight decrease occurs to the

LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 values while the trends of the LCC-downscaled 𝑉𝑐𝑚𝑎𝑥

25 and the TROPOMI

𝑉𝑐𝑚𝑎𝑥25 become consistent afterwards. In US-Tw4, a steady upward trend is observed in all the

𝑉𝑐𝑚𝑎𝑥25 curves, in which the LCC-downscaled 𝑉𝑐𝑚𝑎𝑥

25 curve stays near the TROPOMI 𝑉𝑐𝑚𝑎𝑥25 curve

but the NDVI-downscaled 𝑉𝑐𝑚𝑎𝑥25 curve diverges drastically.

48

Figure 3-5 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 seasonal variation of each site from the day of year 100 to 300.

49

3.3.3 Evaluation of downscaled 𝑉𝑐𝑚𝑎𝑥25 at sites

Due to the lack of available 𝑉𝑐𝑚𝑎𝑥25 measurements for validation, the downscaled results were

evaluated indirectly through terrestrial biosphere models. The original and downscaled 𝑉𝑐𝑚𝑎𝑥25 data

were adopted as the input parameter into the BEPS model for GPP simulation.

3.3.3.1 The comparison of GPP simulation results

In Figure 3-6, the vertical and horizontal axes represent the GPP simulation and EC GPP

measurements. The blue, orange, and green points indicate the GPP simulation results with

TROPOMI 𝑉𝑐𝑚𝑎𝑥25 , LCC-downscaled 𝑉𝑐𝑚𝑎𝑥

25 , and NDVI-downscaled 𝑉𝑐𝑚𝑎𝑥25 , and the blue, orange,

and green lines indicate the linear regression of the scatter points, respectively. It can be observed

that at all sites, the regression lines of LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 scatter points are most aligned with

the 1:1 line and similar results are also exhibited after combining points from all 5 sites, as shown

in Figure 3-7. However, some of the regression lines of NDVI-downscaled 𝑉𝑐𝑚𝑎𝑥25 scatter points

are more aligned with the 1:1 line compared to the original TROPOMI 𝑉𝑐𝑚𝑎𝑥25 ones while some are

less aligned. This is because NDVI catches up to the greenness of plants but the physiological

connection between NDVI and photosynthetic capacity is weak.

50

51

Figure 3-6 GPP scatter plot of each site from the day of year 100 to 300. The Y-axis represents

GPP estimates and the X-axis represents flux measured GPP.

Figure 3-7 GPP scatter plot of all sites from the day of year 100 to 300.

3.3.3.2 The seasonal variation of GPP simulation results

In Figure 3-8, the vertical and horizontal axes represent the daily GPP simulation or GPP

measurements and day of year. The red, orange, blue, and green curves indicate the GPP seasonal

variation of EC measurements, simulation with TROPOMI 𝑉𝑐𝑚𝑎𝑥25 , simulation with LCC-

52

downscaled 𝑉𝑐𝑚𝑎𝑥25 , and simulation with NDVI-downscaled 𝑉𝑐𝑚𝑎𝑥

25 . Overall, the GPP simulation

results with LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 show most aligned patterns to the EC GPP measurements. In

Figure 3-8 GPP seasonal variation of each site from the day of year 100 to 300. The daily EC

GPP data were merged from half-hourly EC measurements. The daily modeled GPP data

were merged from hourly BEPS GPP simulation results.

53

Figure 3-9 Temporal patterns of the bias of GPP estimated with TROPOMI and downscaled

𝑽𝒄𝒎𝒂𝒙𝟐𝟓

US-Bi2, LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 data considerably improve the GPP simulation between the day

of year 150 to the day of year 250 and NDVI-downscaled 𝑉𝑐𝑚𝑎𝑥25 data also improve the result to

54

some extent. The underestimates of GPP simulation during the growing season originate from a

lack of consideration of fertilization and irrigation. In US-Los and US-Rpf, significant

overestimates of simulated GPP are observed before the day of year 150, though GPP simulation

results with LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 are closer to the EC measurements. There are overestimates

of GPP simulation in US-Tw4 and the estimates with LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 show a gradual

decline from the estimates with TROPOMI 𝑉𝑐𝑚𝑎𝑥25 . In US-WCr, GPP estimates with LCC-

downscaled 𝑉𝑐𝑚𝑎𝑥25 capture the fluctuation of daily variation best. As shown in Figure 3-9, the

temporal patterns of the bias of GPP estimation with TROPOMI and downscaled 𝑉𝑐𝑚𝑎𝑥25 are

presented. Due to the consistency of other parameters except 𝑉𝑐𝑚𝑎𝑥25 in BEPS modeling, the

temporal patterns of the bias are similar. However, the LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 reduces the bias of

GPP estimates at all sites.

3.3.3.3 Statistical analysis of GPP simulation results

In Table 3-2, the TROPOMI 𝑉𝑐𝑚𝑎𝑥25 data and the downscaled 𝑉𝑐𝑚𝑎𝑥

25 data are used as input of BEPS

to simulate GPP. The simulated GPP data are compared with EC GPP measurements. Squared

Pearson correlation coefficient (R2), mean absolute error (MAE), root mean square error (RMSE),

and the agreement index (𝐼𝑂𝐴) are calculated for statistical analysis. The results of each site and

combined-all-sites are presented at all sites the GPP simulation results with LCC-downscaled

𝑉𝑐𝑚𝑎𝑥25 are observed to achieve the least RMSE and MAE, and highest IOA. After combining points

from all sites, LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 data remarkably improve the simulation results from R2 =

0.80 to R2 = 0.85 and IOA = 0.93 to IOA = 0.95. The RMSE and MAE decrease from RMSE =

2.49 to RMSE = 2.15 gC/m2/d and MAE = 1.74 to MAE = 1.55 gC/m2/d. Although NDVI-

downscaled 𝑉𝑐𝑚𝑎𝑥25 data improve the IOA and RMSE slightly, the same R2 and worse MAE indicate

the limits of NDVI for downscaling. However, the overall improvement of GPP estimates with

LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 is not large because the improvements are small at four sites except US-

Bi2. Only US-Bi2 has obvious differences between the downscaled and TROPOMI 𝑉𝑐𝑚𝑎𝑥25 values

while the other four sites have the downscaled 𝑉𝑐𝑚𝑎𝑥25 values close to the TROPOMI 𝑉𝑐𝑚𝑎𝑥

25 values,

as shown in Figure 3-5. These small improvements could be mostly because the landscapes over

the available tower flux sites are relatively homogeneous so that the downscaled 𝑉𝑐𝑚𝑎𝑥25 values do

not differ greatly from original values before downscaling. Besides, LAI and CI can affect the

magnitude of simulated GPP (Chen et al., 2012; Liu et al., 2018). Errors in the input data such as

55

LAI and CI to BEPS used to evaluate 𝑉𝑐𝑚𝑎𝑥25 downscaling through simulated GPP would also have

considerable influence on the accuracy of simulated GPP and hence on the 𝑉𝑐𝑚𝑎𝑥25 evaluation.

Table 3-2 Statistical evaluation results of the downscaled 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 based on GPP simulated

with 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 before and after downscaling against GPP derived from tower flux

measurements

Site Code 𝑉𝑐𝑚𝑎𝑥25 Source R2 RMSE MAE IOA

US-Bi2

TROPOMI 0.91 3.69 2.37 0.92

LCC-Downscaled 0.92 2.95 1.94 0.95

NDVI-Downscaled 0.91 3.25 2.09 0.94

US-Los

TROPOMI 0.84 1.75 1.32 0.94

LCC-Downscaled 0.87 1.47 1.10 0.95


US-Rpf

TROPOMI 0.84 1.86 1.43 0.94

LCC-Downscaled 0.82 1.80 1.38 0.94


US-Tw4

TROPOMI 0.81 1.80 1.43 0.89

LCC-Downscaled 0.82 1.59 1.37 0.93


US-WCr

TROPOMI 0.79 2.75 2.15 0.92

LCC-Downscaled 0.81 2.53 1.96 0.94


All Sites

TROPOMI 0.80 2.49 1.74 0.93

LCC-Downscaled 0.85 2.15 1.55 0.95


*Unit of RMSE and MAE: gC/m2/d

56

3.3.3.4 GPP responses to 𝑉𝑐𝑚𝑎𝑥25 before and after downscaling

The percentage change of GPP estimates before and after downscaling is related to the standard

deviation of downscaled 𝑉𝑐𝑚𝑎𝑥25 in 0.1˚ pixels, LAI, and the landcover. GPP was estimated at each

1 km pixel using LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 and then averaged to 0.1˚ pixels, named as the distributed

GPP. GPP estimated using TROPOMI-𝑉𝑐𝑚𝑎𝑥25 data, i.e., one value for each 0.1˚ pixel, named as the

lumped GPP, was compared with the distributed GPP and thus the percentage change was

obtained. The standard deviation of LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 was calculated at each 0.1˚ pixel. At

all 0.1˚ pixels of sites, GPP estimations at 0.1˚ resolution decrease by 2-7% after 𝑉𝑐𝑚𝑎𝑥25

downscaling using the LCC method, as shown in Table 3-3.

Table 3-3 The summary of GPP responses to 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 before and after downscaling

Site Code 𝑉𝑐𝑚𝑎𝑥25 𝑆𝐷

𝑉𝑐𝑚𝑎𝑥25 𝑆𝐷

𝑉𝑐𝑚𝑎𝑥25̅̅ ̅̅ ̅̅ ̅̅

Percentage

Change Mean LAI

US-Bi2 37.39 0.32 -2.14 2.29

US-Los 6.54 0.21 -2.03 4.09

US-Rpf 10.76 0.30 -2.16 1.76

US-Tw4 76.29 0.65 -5.33 1.47

US-WCr 8.12 0.23 -7.21 3.00

*SD: Standard Deviation, Unit of 𝑉𝑐𝑚𝑎𝑥25 : µmol/m2/s

The distributed GPP estimates were lower than the lumped GPP at all sites because of the nonlinear

relationship between GPP and 𝑉𝑐𝑚𝑎𝑥25 . As shown in Figure 3-10, the blue curve represents GPP

responses to changes of 𝑉𝑐𝑚𝑎𝑥25 in the BEPS model. The black line is the straightened version of

the blue curve between 𝑉𝑐𝑚𝑎𝑥25 – SD and 𝑉𝑐𝑚𝑎𝑥

25 + SD. The black straight line provides quick

estimations of distributed GPP because the downscaled 𝑉𝑐𝑚𝑎𝑥25 is most located in that range. The

GPP estimates were retrieved using environmental data on the day of year 124 at US-WCr site

with 𝑉𝑐𝑚𝑎𝑥25 ranging from 0 to 80 µmol/m2/s. As 𝑉𝑐𝑚𝑎𝑥

25 gets higher, GPP estimates grow slower.

The downscaled 𝑉𝑐𝑚𝑎𝑥25 within the 0.1˚ pixel fluctuates in a certain range with a mean value equal

to the 𝑉𝑐𝑚𝑎𝑥25 value of the 0.1˚ pixel. However, the downscaled 𝑉𝑐𝑚𝑎𝑥

25 lower than the mean value

57

exerts a greater influence on the change of GPP than the downscaled 𝑉𝑐𝑚𝑎𝑥25 higher than the mean

value. The red point is the middle point of the black straight line, indicating the mean value of

distributed GPP. Therefore, a decrement of GPP estimates can be observed after downscaling and

thus the overestimation of lumped GPP can be corrected.

Figure 3-10 GPP responses to 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 in the BEPS model. The Y-axis represents the GPP

estimates. Other inputs are kept consistent, using data on the day of year 124 at US-WCr

site. The X-axis represents 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 values changing from 0 to 80 µmol/m2/s. The blue curve

shows the GPP responses to change of 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 . The black line is the straightened version of

the curve between mean 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 – SD and 𝑽𝒄𝒎𝒂𝒙

𝟐𝟓 + SD. The blue point represents lumped

GPP, simulated using 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 at the 0.1˚ resolution. The red point represents distributed, the

mean of GPP simulated based on the LCC-downscaled 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 within the 0.1˚ pixel.

58

3.3.4 Applying the downscaling method to regional and global scales

As discussed in Chapter 3.4.3, the LCC downscaled 𝑉𝑐𝑚𝑎𝑥25 achieves better performance in GPP

simulation, indicating LCC as a feasible way to downscale the 𝑉𝑐𝑚𝑎𝑥25 dataset. Therefore, the LCC-

downscaling method was further applied from site to regional and global scales. For the global

map, as shown in Figure 3-12, the distributions of 𝑉𝑐𝑚𝑎𝑥25 values in the original and the downscaled

𝑉𝑐𝑚𝑎𝑥25 map show similar patterns because the downscaling considers the spatial distribution of

LCC within each TROPOMI pixel while the average 𝑉𝑐𝑚𝑎𝑥25 for the pixel is unchanged. . However,

the global averaged intra-pixel standard deviation is 6.72 µmol/m2/s, showing the heterogeneity in

TROPOMI 𝑉𝑐𝑚𝑎𝑥25 pixels and the spatial variation of the downscaled 𝑉𝑐𝑚𝑎𝑥

25 map, as shown in

Figure 3-11. For the regional maps of North America, as shown in Figure 3-13, Figure 3-14, and

Figure 3-15, details can be observed in the enlarged portions of regional maps. For example, the

spatial distribution and variation of 𝑉𝑐𝑚𝑎𝑥25 can be clearly captured in the subfigure f) in each figure.

The seasonal variation patterns of 𝑉𝑐𝑚𝑎𝑥25 are also shown in the comparison of the three figures. The

downscaled 𝑉𝑐𝑚𝑎𝑥25 maps preserve the values of the coarse-resolution 𝑉𝑐𝑚𝑎𝑥

25 dataset and

simultaneously contain the within-pixel spatial information of LCC.

Figure 3-11 Spatial distribution of standard deviation of downscaled 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 values in

TROPOMI 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 pixels on the day of year 200.

59

Figure 3-12 Comparison of global 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 maps on the day of year 200. a) The 0.1°×0.1°

TROPOMI 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 map; b) The downscaled 1 km×1 km 𝑽𝒄𝒎𝒂𝒙

𝟐𝟓 map.

60

Figure 3-13 Comparison of 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 maps of North America on the day of year 150. a) The 0.1°×0.1° TROPOMI 𝑽𝒄𝒎𝒂𝒙

𝟐𝟓 map; b)

The downscaled 1 km×1 km 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 map; c) and d) Partially enlarged details of the red labeled region in a) and b); e) and f)

Partially enlarged details of the red labeled region in c) and d).

61


𝟐𝟓 map; b)



62


𝟐𝟓 map; b)



63

3.4 Conclusion

Due to the nature of the heterogeneous land surface, the intra-pixel heterogeneity and the scaling

effect have been widely discussed in previous studies (Chen, 1999; Chen et al., 2013; Garrigues et

al., 2006). However, the heterogeneity in 𝑉𝑐𝑚𝑎𝑥25 derived from remotely sensed data has not yet

been studied. In this chapter, the intra-pixel heterogeneities of a 𝑉𝑐𝑚𝑎𝑥25 dataset derived from sun-

induced chlorophyll fluorescence by (Liu, 2019) are quantitatively investigated. A spatial scaling

method to downscale the 𝑉𝑐𝑚𝑎𝑥25 dataset to a resolution appropriate for comparison with flux

measurements at eddy covariance towers was developed. The spatial scaling ratio (SSR) is

calculated as the proportion of the informative factor in the 1 km pixel and the averaged

informative factor in the TROPOMI pixel. Two separate downscaling factors, leaf chlorophyll

content (LCC) and normalized difference vegetation index (NDVI) were used to provide useful

information at a higher spatial resolution for downscaling. The seasonal variation patterns and

intra-pixel heterogeneities of 𝑉𝑐𝑚𝑎𝑥25 were presented and analyzed. The downscaled 𝑉𝑐𝑚𝑎𝑥

25 with the

two factors mentioned above were evaluated by adopting the downscaled 𝑉𝑐𝑚𝑎𝑥25 into BEPS for

GPP simulation and by validating the GPP simulation results with GPP derived from EC

measurements. The other parameters of BEPS except 𝑉𝑐𝑚𝑎𝑥25 were kept consistent for the evaluation

of downscaled 𝑉𝑐𝑚𝑎𝑥25 . The bias of GPP estimates, temporal patterns of GPP, and statistical analysis

of simulated GPP were presented. Based on the SSR with better GPP estimates, the first global 1

km 𝑉𝑐𝑚𝑎𝑥25 map was produced.

The main conclusions of this chapter are: 1) Intra-pixel heterogeneities of the 𝑉𝑐𝑚𝑎𝑥25 dataset

retrieved from the TROPOMI SIF data at 0.1-degree resolution were significant at selected 5

locations. The seasonal variation pattern of downscaled 𝑉𝑐𝑚𝑎𝑥25 differed considerably from those at

the original coarse resolution at some sites. When adopting the coarse 𝑉𝑐𝑚𝑎𝑥25 data into terrestrial

ecosystem models, the intra-pixel heterogeneity will induce bias in simulation results over tower

flux sites with footprints much smaller than the pixel size. 2) A spatial scaling algorithm was

developed and LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 achieve the best results in terms of matching simulated

GPP with tower-measured GPP. The downscaling processes were implemented at five sites with

available GPP measurements in 2018. The spatial scaling ratios derived from LCC and NDVI were

experimented and the LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 improved the GPP simulation most. LCC has been

tested as the proxy of the photosynthetic capacity (Croft et al., 2017). Thus LCC is more

64

physiologically related to plant photosynthetic process than NDVI, indicating that a factor with

tighter connections with plant photosynthetic capacity can better support 𝑉𝑐𝑚𝑎𝑥25 downscaling. On

the contrary, if the informative factor for downscaling is not physiologically connected with plant

photosynthesis, the downscaling will cause error propagation, leading to unreliable results. 3) The

first 1 km 𝑉𝑐𝑚𝑎𝑥25 map was produced following the LCC downscaling method. Within-pixel details

of 𝑉𝑐𝑚𝑎𝑥25 can be observed after the downscaling.

Overall, intra-pixel heterogeneities indeed exist within the 𝑉𝑐𝑚𝑎𝑥25 dataset derived from TROPOMI

SIF measurements. The spatial scaling algorithm is reliable and LCC can provide a feasible method

for downscaling 𝑉𝑐𝑚𝑎𝑥25 datasets and studying the intra-pixel spatial distribution pattern of the

𝑉𝑐𝑚𝑎𝑥25 dataset. Since LCC datasets are not widely available, NDVI can also be used for

downscaling 𝑉𝑐𝑚𝑎𝑥25 as the first-order approximation, but because NDVI is a surrogate of canopy

structure (e.g., LAI) and leaf greenness, it is not as ideal as LCC, which represents a leaf trait that

is closely linked to leaf photosynthetic capacity.

65

3.5 References

Alton, P.B. (2017). Retrieval of seasonal Rubisco-limited photosynthetic capacity at global

FLUXNET sites from hyperspectral satellite remote sensing: Impact on carbon modeling.

Agricultural and Forest Meteorology, 232, 74-88

Boegh, E., Soegaard, H., Broge, N., Hasager, C.B., Jensen, N.O., Schelde, K., & Thomsen, A.

(2002). Airborne multispectral data for quantifying leaf area index, nitrogen concentration,

and photosynthetic efficiency in agriculture. Remote Sensing of Environment, 81, 179-193

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Chapter 4

Summary

4.1 Main conclusions

1) Heterogeneities exist within the pixels of the 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 product derived from TROPOMI sun-

induced chlorophyll fluorescence measurements. A downscaling algorithm was designed for

downscaling the 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 dataset.

The intra-pixel heterogeneity of the 𝑉𝑐𝑚𝑎𝑥25 dataset was explored at five tower flux sites in the USA.

Obvious heterogeneity was observed within the TROPOMI pixels over these sites. A downscaling

algorithm was designed to downscale 𝑉𝑐𝑚𝑎𝑥25 by multiplying the TROPOMI 𝑉𝑐𝑚𝑎𝑥

25 with a spatial

scaling ratio (SSR) at a higher resolution. The SSR considered informative downscaling factors,

such as leaf chlorophyll content (LCC) and normalized difference vegetation index (NDVI) in this

study. The SSR of each pixel was calculated as the proportion of the downscaling factor at that 1

km pixel and the averaged downscaling factor at that TROPOMI pixel at 0.1° resolution.

2) Leaf chlorophyll content (LCC) can be a feasible method for downscaling the 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 data

from 0.1° × 0.1° to 1 km × 1 km. The LCC-downscaled 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 data achieve better GPP

simulation results.

The downscaled 𝑉𝑐𝑚𝑎𝑥25 data were evaluated by using the 𝑉𝑐𝑚𝑎𝑥

25 as inputs to the Boreal Ecosystem

Productivity Simulator (BEPS). The GPP simulation with LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25 data was

improved with better statistical metrics. As a proxy of plant photosynthetic capacity (Croft et al.,

2017), remotely sensed LCC can be informative at a higher spatial resolution for downscaling the

𝑉𝑐𝑚𝑎𝑥25 dataset. The improvement in GPP simulation after downscaling with LCC is not very large

because some of the tower flux sites selected in this study have downscaled 𝑉𝑐𝑚𝑎𝑥25 values close to

the values of the TROPOMI pixels.

3) Downscaling with a factor having tight physiological connections with 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 can achieve

satisfying results, such as chlorophyll content in this study. Otherwise, it will introduce other

factors, such as NDVI, which may cause error propagation.

70

Although some studies have indicated the correlations between NDVI and 𝑉𝑐𝑚𝑎𝑥25 (Jin et al., 2012;

Zhou et al., 2014), weak physiological connections exist between those two parameters. NDVI

captures the greenness of the vegetation canopy, which is not only influenced by leaf optical

properties by also canopy structure, while 𝑉𝑐𝑚𝑎𝑥25 indicates the maximum photosynthetic capacity

of leaves. The NDVI-based SSR improved the GPP estimates at some sites but worsened the

estimates at other sites, indicating interference of the variation in the canopy structure in the

downscaling process.

4) The first global 1 km 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 map was produced based on the LCC-downscaling method

satisfactorily tested at sites.

The global downscaled 1 km 𝑉𝑐𝑚𝑎𝑥25 map can capture details and intra-pixel spatial distribution of

𝑉𝑐𝑚𝑎𝑥25 . The downscaled map comprehensively considers the accurate numerical values of the

coarse-resolution 𝑉𝑐𝑚𝑎𝑥25 dataset derived from TROPOMI solar-induced chlorophyll fluorescence

data and the within-pixel spatial information of LCC derived from Sentinel-2 data. The

downscaling method eliminates the mismatch between satellite-based 𝑉𝑐𝑚𝑎𝑥25 datasets and the

footprint of tower fluxes and this new map will further enhance accurate global GPP estimates.

5) The correlations between PRI and LUE are not as pronounced as expected, though

statistically significant. The PRI-LUE correlations need to be further explored for the

purpose of downscaling 𝑽𝒄𝒎𝒂𝒙𝟐𝟓 .

The PRI-LUE correlations were experimented for each plant functional types using historical eddy

covariance measurements from 190 sites and for each of the five AmeriFlux sites available for

2018. The MODIS ocean band 11 (centered at 531nm) covers the signal band of PRI (Drolet et al.,

2005; Drolet et al., 2008; Middleton et al., 2016) and band 10 (centered at 488nm), band 12

(centered at 551nm), and band 13 (centered at 667nm) were tested as the reference band of PRI.

However, weak correlations were observed and the PRI-LUE points were widely dispersed from

their regression line. However, the PRI-LUE relationships are still statistically significant (p<0.05)

at most individual sites and for most plant functional types, suggesting that PRI contains

information for 𝑉𝑐𝑚𝑎𝑥25 that may be useful for its downscaling in some ways which need to be

further explored.

71

4.2 Limitation of current work and plan for further work

1) The design of the spatial scaling algorithm

In this study, a spatial scaling factor was adopted in the downscaling process, which was derived

as the proportion of the informative downscaling factor of the 1 km pixel and the averaged factor

of the TROPOMI pixel. However, the surface heterogeneity originates from two sources of

ecosystem heterogeneity, endogenous (biotic) and exogenous (abiotic) one (Chen et al., 2013).

Other factors, such as land cover, will be considered in further optimization of the spatial scaling

algorithm. Besides, temporal filtering will also be introduced to exclude outliers and generate the

seasonal variation of the downscaled 𝑉𝑐𝑚𝑎𝑥25 .

2) The evaluation of the downscaled 𝑽𝒄𝒎𝒂𝒙𝟐𝟓

The downscaled 𝑉𝑐𝑚𝑎𝑥25 data were evaluated indirectly by using the downscaled 𝑉𝑐𝑚𝑎𝑥

25 as the input

to the BEPS model for GPP simulation. The simulated GPP data were then compared with EC

GPP measurements for evaluation. Although in the GPP simulation all other parameters except

𝑉𝑐𝑚𝑎𝑥25 were consistent, the GPP simulation results were not only affected solely by 𝑉𝑐𝑚𝑎𝑥

25 , but also

soil moisture, leaf area index, etc. (Liu et al., 1999; Liu et al., 1997). The LCC-downscaled 𝑉𝑐𝑚𝑎𝑥25

improved the GPP simulation while some overestimations and underestimations were observed.

In further research, ground-based 𝑉𝑐𝑚𝑎𝑥25 data or 𝑉𝑐𝑚𝑎𝑥

25 products at higher resolutions when

available can be used to directly evaluate the accuracy of the downscaled 𝑉𝑐𝑚𝑎𝑥25 .

3) The establishment of PRI-LUE correlations

The correlations of PRI-LUE for nine plant function types and for five sites were weak and could

not generate reliable GPP estimates through the LUE model (Monteith, 1972). Due to the lack of

an ideal reference band of PRI among MODIS reflectance bands, some substituting bands were

used. Many other complicating factors affect the signal of PRI (Gitelson et al., 2017a) and were

not considered in this study. In order to use remotely sensed PRI, careful consideration of the

optional definitions such as LUE formulation is also needed (Gitelson et al., 2017b). As discussed

in Section 2.4.1 and Section 2.4.2, the PRI retrieval and PRI-LUE correlations need to be improved

in further work. Besides, the Fluorescence Explorer (FLEX) mission of the European Space

Agency will be launched in the near future and the fluorescence imaging spectrometer (FLORIS)

72

including a PRI band will be on board. The PRI band has a bandwidth of 500-600 nm and a spectral

resolution of 3 nm (Coppo et al., 2017), which will significantly enhance the quality of remotely

sensed PRI. With the FLEX PRI, better PRI-LUE correlations may be derived for various purposes

including 𝑉𝑐𝑚𝑎𝑥25 downscaling.

73

4.3 References



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efficiency using MODIS spectral indices. Remote Sensing of Environment, 112, 3064-3078

Gitelson, A.A., Gamon, J.A., & Solovchenko, A. (2017a). Multiple drivers of seasonal change in

PRI: Implications for photosynthesis 1. Leaf level. Remote Sensing of Environment, 191,

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PRI: Implications for photosynthesis 2. Stand level. Remote Sensing of Environment, 190,

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Liu, J., Chen, J.M., Cihlar, J., & Chen, W. (1999). Net primary productivity distribution in the

BOREAS region from a process model using satellite and surface data. Journal of

Geophysical Research: Atmospheres, 104, 27735-27754

Liu, J., Chen, J.M., Cihlar, J., & Park, W.M. (1997). A process-based boreal ecosystem productivity

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Middleton, E.M., Huemmrich, K.F., Landis, D.R., Black, T.A., Barr, A.G., & McCaughey, J.H.

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