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Atmospheric Inversion of the Global Surface Carbon Flux with Consideration of the Spatial Distributions of US Crop
Production and Consumption
by
Jonathan Winston Fung
A thesis submitted in conformity with the requirements for the degree of Masters of Science
Department of Geography & Planning University of Toronto
© Copyright by Jonathan Winston Fung, 2012
ii
Atmospheric Inversion of the Global Surface Carbon Flux with Consideration of the Spatial Distributions of US Crop Production
and Consumption
Jonathan Winston Fung
Masters of Science
Department of Geography and Planning
University of Toronto
2012
Abstract
Carbon dioxide is taken up by crops during production and released back to the atmosphere at
different geographical locations through respiration of consumed crop commodities. In this
study, spatially distributed county-level US cropland net primary productivity, harvested
biomass, changes in soil carbon, and human and livestock consumption data were integrated
into the prior terrestrial biosphere flux generated by the Boreal Ecosystem Productivity
Simulator (BEPS). A global time-dependent Bayesian synthesis inversion with a nested focus
on North America was carried out based on CO2 observations at 210 stations. Overall, the
inverted annual North American CO2 sink weakened by 6.5% over the period from 2002 to 2007
compared to simulations disregarding US crop statistical data. The US Midwest is found to be
the major sink of 0.36±0.13 PgC yr-1
whereas the large sink in the US Southeast forests
weakened to 0.16±0.12 PgC yr-1
partly due to local CO2 sources from crop consumption.
iii
Acknowledgement
I would like to express my deep appreciation to Professor Jing Chen for giving me this
opportunity to pursue this master’s degree and presenting me with a research topic that is both
interesting and relevant. He has been very supportive and encouraging throughout these two
years of my program and provided clear guidance and directions in solving problems
encountered.
I am also grateful for all the guidance Feng Deng has provided me in helping me
understand the topic of atmospheric inversion. He has also provided numerous codes, datasets
and technical support that has been crucial to this research.
Special thanks to Dr. Tristram West for providing the cropland carbon datasets as well as
clear guidance and explanation on the composition and usage of the datasets.
The Chen lab has been an integral part of my life as a master’s student. Special thanks
to Gang Mo for all the technical support he has provided which really moved this research
forward. I would also like to specially mention Rong, Ting, Min, Alemu and all the others in
the lab for all their support, help and fun they have given me in these past two years.
I would also like to acknowledge Dylan Jones for the encouragements he has given me
to deepen my understanding of data assimilation and atmospheric inversion techniques as well
as Danny Harvey for the course he taught called “perspectives on global warming” which
presents the bigger picture on the importance of this research.
Finally, I would like to thank my family as well as my friends from church and
fellowship for their continual support and prayer throughout this master’s program.
iv
Table of Contents
Acknowledgement ........................................................................................................................ iii
List of Tables ................................................................................................................................ vi
List of Figures .............................................................................................................................. vii
List of Acronyms .......................................................................................................................... ix
1 Introduction............................................................................................................................ 1
1.1 Current estimate of the global and North American carbon budget ................................. 2
1.2 Main approaches to quantifying terrestrial carbon fluxes ............................................... 6
1.3 Research objectives and structure of thesis ..................................................................... 9
2 Atmospheric CO2 Inversion Methodology .......................................................................... 10
2.1 Forward modeling .......................................................................................................... 11
2.1.1 Prior fluxes and their uncertainties ........................................................................ 11
2.1.2 Atmospheric transport ........................................................................................... 14
2.1.3 CO2 observations ................................................................................................... 15
2.2 Inverse modeling ........................................................................................................... 16
2.2.1 Inversion regions and concentration locations ...................................................... 16
2.2.2 Time-dependent Bayesian synthesis approach ...................................................... 18
2.2.3 Transport (observation) operator, model-data mismatch and prior uncertainties.. 19
3 US Cropland Carbon Integration Methodology .................................................................. 22
3.1 US cropland carbon budget based on inventory data .................................................... 22
v
3.1.1 Crop NPP, harvest, biomass decomposition and changes in soil carbon pool ...... 23
3.1.2 Human and Livestock consumption ...................................................................... 24
3.2 Prior flux adjustments for US croplands ....................................................................... 25
3.2.1 Production adjustment ........................................................................................... 27
3.2.2 Consumption adjustment ....................................................................................... 28
3.3 Schemes of experiments ................................................................................................ 29
4 Results and discussion ......................................................................................................... 31
4.1 Multi-year regional carbon budget ................................................................................ 31
4.1.1 Average annual flux ............................................................................................... 31
4.2 Multi-year global carbon budget ................................................................................... 41
4.2.1 Seasonal variation .................................................................................................. 45
4.3 Discussion ...................................................................................................................... 51
5 Summary .............................................................................................................................. 55
References.................................................................................................................................... 58
vi
List of Tables
Table 2-1 – Summary of background prior fluxes and their uncertainties .................................. 13
Table 2-2 – Grouping of inversion regions to the US census regions ......................................... 16
Table 3-1 Two sets of experiments using seven inversion schemes designed to evaluate the
impact of crop production and consumption adjustment in the prior flux towards the inverted
results ........................................................................................................................................... 30
Table 4-1 shows 2002 to 2007 mean inverted CO2 flux (, the error (ε) in Tg C yr-1
and the
percentage change1 (Δ% ) for US regions. .................................................................................. 40
Table 4-2 shows 2002 to 2007 mean inverted CO2 flux (, the error (ε) in Pg C yr-1
and the
percentage change1 (Δ%) for global regions. .............................................................................. 44
vii
List of Figures
Figure 2-1 – Defining the 30 regions for North America and 20 regions for the rest of the globe.
The 210 measurement locations are also indicated. This figure is taken from Deng & Chen
(2011). .......................................................................................................................................... 17
Figure 3-1 – Maps showing spatial distributions of annual crop production (top); crop
consumption (middle); and crop NEP (bottom) for 2003. Data taken from (CDIAC) website:
http://cdiac.ornl.gov. .................................................................................................................... 26
Figure 4-1 – Mean annual inverted CO2 flux (-ve represents uptake) for Experiments 1 –
annually balanced terrestrial prior fluxes with (a) no adjustments; (b) production adjustments;
(c) crop production adjustments and consumption as additional source; and (d) crop production
and consumption adjustment during 2002 to 2007 for US regions (top), US census regions
(middle) and North American regions (bottom). ......................................................................... 35
Figure 4-2 – Mean annual inverted CO2 flux (-ve represents uptake) for Experiments 2 –
annually varying terrestrial prior fluxes with (a) no adjustments; (b) production adjustments; (c)
crop production and consumption adjustments during 2002 to 2007 for US regions (top), US
census regions (middle) and North American regions (bottom). ................................................ 37
Figure 4-3 – Map of mean annual inverted CO2 flux (-ve represents uptake) for Experiment 1
during 2002 to 2007 over contiguous US regions. ...................................................................... 38
Figure 4-4 – Map of mean annual inverted (left) and prior (right) CO2 flux (-ve represents
uptake) for Experiment 2 during 2002 to 2007 over contiguous US. .......................................... 39
Figure 4-5 – Mean annual inverted CO2 flux (-ve represents uptake) for Experiments 1 –
annually balanced terrestrial prior fluxes with (a) no adjustments; (b) production adjustments;
(c) crop production adjustments and consumption as additional source; and (d) crop production
and consumption adjustment during 2002 to 2007 for global regions (top) and global carbon
budget (bottom). .......................................................................................................................... 42
Figure 4-6 – Mean annual inverted CO2 flux (-ve represents uptake) for Experiments 2 –
annually varying terrestrial prior fluxes with (a) no adjustments; (b) production adjustments; (c)
viii
crop production and consumption adjustments during 2002 to 2007 for global regions (top) and
global carbon budget (bottom). ................................................................................................... 43
Figure 4-7 – Monthly inverted (solid lines) and prior (dashed lines) CO2 flux (-ve represents
uptake) averaged over 2002 to 2007 for Experiments 1 – annually balanced terrestrial prior
fluxes with (a) no adjustments – blue; (b) production adjustments – red; (c) crop production
adjustments and consumption as additional source – green; and (d) crop production and
consumption adjustment – purple. ............................................................................................... 46
Figure 4-8 – Monthly inverted (solid lines) and prior (dashed lines) CO2 flux (-ve represents
uptake) averaged over 2002 to 2007 for Experiments 2 – annually varying terrestrial prior fluxes
with (a) no adjustments – blue; (b) production adjustments – red; (c) crop production and
consumption adjustments – green. .............................................................................................. 48
Figure 4-9 – Graph showing the correlation between the US Midwest (region 20) flux during
July and the fluxes in other regions during other months of the year. ......................................... 50
ix
List of Acronyms
GPP Gross Primary Productivity – The amount of carbon fixed from the
atmosphere through photosynthesis.
Ra Autotrophic Respiration – Respiration by photosynthetic organisms
(plants).
Rh Heterotrophic respiration – The conversion of organic matter to CO2 by
organisms other than plants
NPP
Net Primary Productivity – The increase in plant biomass or carbon of a
unit of a landscape. NPP is equal to the Gross Primary Production minus
carbon lost through autotrophic respiration.
NEP
Net Ecosystem Productivity – Net gain or loss of carbon from an
ecosystem. NEP is equal to the Net Primary Productivity minus the carbon
lost through heterotrophic respiration.
NEE Net Ecosystem Exchange – The reverse of Net Ecosystem productivity.
Sink Absorption of carbon from the atmosphere by an ecosystem.
Source Emission of carbon from an ecosystem to the atmosphere.
TBM Terrestrial Biosphere Model
BEPS Boreal Ecosystem Productivity Simulator
Mg Megagrams (106 grams)
Tg Teragrams (1012
grams)
Pg Petagrams (1015
grams)
1
Chapter 1 Introduction
1 Introduction
The climate system has warmed by a total amount of 0.74ºC (0.56ºC to 0.92ºC) from
1906 to 2005 with a linear trend of 0.13ºC increase per decade over the last 50 years as reported
in the IPCC fourth assessment report. The projected warming for the next two decade is 0.2ºC
per decade under a range of different scenarios. The report describes this warming of climate as
“unequivocal” as evident from observations of increases in global average air and sea
temperatures, widespread melting of snow and ice, and rising of sea levels.
The modern changes in global surface temperature based on more than a century of
instrumental data are firmly believed to be a response to the atmospheric CO2 buildup since the
industrial revolution (Harvey, 2010). The global atmospheric concentration of CO2 has
increased by 35% from a pre-industrial value of about 280 ppm to 379 ppm in 2005 with 50 ppm
of the increase in the recent 30 years and 1.9 ppm yr-1
increase in the last decade from 1995 to
2005. While some may argue that the increase in CO2 concentration is due to natural variations
in the earth’s system, the gas composition of air bubbles trapped in the Antarctic ice cores show
that atmospheric CO2 concentration over the past 650,000 years only fluctuated between the
extremes of 190 ppm to 300 ppm. These geological records and numerous other lines of
evidence show without doubt that the CO2 increase observed since the pre-industrial amounts
(which drastically exceeded both the natural range and the rate of increase during ice age cycles)
is due to anthropogenic emissions (Solomon, 2007). While CO2 is not the only greenhouse gas
with drastically increased concentration since pre-industrial time, it is the most important
anthropogenic greenhouse gas contributing to climate warming in the 21st century, responsible
for 60% of the additional radiative forcing from all long-lived greenhouse gases. In 2005,
anthropogenic CO2 contributed an average radiative forcing amount of 1.66 (1.49 to 1.83) W/m2
compared to 0.98 W/m2 from all the other long-lived greenhouse gases (CH4, N2O and
halocarbons) combined (Solomon, 2007). In the last half-century, on average only ~43% of the
anthropogenic CO2 emissions remained in the atmosphere (Le Quéré et al., 2009) while the
remainder was taken up by the terrestrial biosphere and the oceans. A method of mitigating the
2
rapid atmospheric CO2 increase is to potentially manage the carbon cycle by means of carbon
sequestration on regional scales. Monitoring of the current surface CO2 fluxes and
understanding the underlying processes responsible for these fluxes are crucial for the scientific
community as well as policy makers.
The North American terrestrial biosphere is an important component of the global
carbon budget, as it is a large CO2 sink (Peters et al., 2007). However, the spatial distribution of
carbon within the North American carbon budget is still very uncertain due to the heterogeneity
of vegetation across the contiguous North American terrestrial biosphere (Huntzinger et al.,
2012). Therefore, the overall goal of this research is to investigate the role that US croplands
play in the North America and global carbon budget. The objectives of this chapter are i) to
give a brief overview of the current estimate of the global and North American carbon budget,
ii) to describe the main approaches in quantifying global and regional terrestrial carbon fluxes,
and iv) to outline the research objectives and the structure of this thesis.
1.1 Current estimate of the global and North American carbon budget
The natural carbon cycle globally consists of four main components, known as carbon
pools, which differ in their magnitude: the atmosphere; land (soil and plants); oceans (surface
ocean and deep ocean); and the geological reserves (recoverable fossil fuel). The approximate
sizes in Pg are 780; 2300 (1500-2000 and ~550); 38000 (700-1000 and ~37000) and 5000-
10000, respectively (Houghton, 2007). While the geological reservoirs and the deep ocean are
the largest carbon pool, the dominant processes that transfer carbon from these pools into the
atmosphere (such as weathering, volcanism and sea floor spreading for geological reservoirs and
upwelling for deep oceans) happen on long time scales of millennia. For this reason, the surface
carbon fluxes relating to atmosphere-ocean (upper oceans) and atmosphere-terrestrial biosphere
interactions (which occur on scales of hours to centuries) are the main focus in carbon cycle
studies. The main processes responsible for CO2 uptake in the oceans are 1) the partial pressure
difference of CO2 concentration in seawater and in the overlying air (Takahashi et al., 2009) and
2) growth of phytoplankton in the ocean (Aumont, 2003; Buitenhuis et al., 2006). For terrestrial
3
CO2 uptake, it is driven by higher annual photosynthesis (mainly during growing seasons) than
the respiration.
Since the industrial revolution in the 1750s to 1850s, there have been large human
perturbations towards the natural carbon cycle such as changes in agricultural practices,
manufacturing, mining and transportation. The main sources of anthropogenic CO2 are fossil
fuel consumption and cement production, currently emitting 7.6 Pg C yr-1
into the atmosphere,
and land use change contributing an additional 1.5 Pg C yr-1
(Canadell et al., 2007).
Consumption of fossil fuels such as coal, oil and natural gas effectively burn the fossil fuel and
transfer carbon from the geological reserves into the atmosphere. As anthropogenic emissions
increased over the past century, the uptake from the natural carbon cycle was also observed to
increase due to CO2 fertilization. However, the fraction of human emissions remaining in the
atmosphere (known as the airborne fraction, AF) to also been observed to increased. Over the
past 50 years the AF has increased from 40% to 45% (Le Quéré et al., 2009). A further increase
in AF is projected in the future partly due to the future changing climate decreasing the
efficiency of the earth system (ocean and terrestrial biosphere) to absorb anthropogenic carbon
perturbations (Friedlingstein et al., 2006). The weakening of ocean sink efficiency in recent
decades was observed from reconstruction of anthropogenic carbon over the oceans (Khatiwala
et al., 2009) which attributes the weakening to the Southern Ocean CO2 sink which decreased by
~0.1 Pg C yr-1
decade-1
from 1980 to 2004 (Le Quéré et al., 2007; Lovenduski & Gruber, 2008).
Furthermore, terrestrial carbon uptake is also expected to weaken from impacts of climate
change but the rate and mechanisms are uncertain.
Sabine et al. (2004) estimated that the total oceanic uptake from 1800 to 1994 is 118±19
Pg C accounting for ~48% of the total fossil-fuel and cement-manufacturing emissions. By
balancing the carbon cycle, the inferred net terrestrial balance over the same period is 39±28 Pg
C net source. While taking into account emissions from land use change (100 to 180 Pg C), the
terrestrial biosphere sink is calculated to be 61 to 141. The same method was applied to the
period of 1980 to 1999 showing the terrestrial biosphere and oceanic sink to be 39±18 and 37±8
Pg C averaging ~1.95 and ~1.85 Pg C year-1
net uptake, respectively. Using sea-air pCO2
difference and air-sea gas transfer rate, Takahashi et al. (2009) found the net ocean flux in 2000
to be a sink of 1.6±0.9 Pg C yr-1
and 2.0±1.0 Pg C yr-1
when taking into account the pre-
4
industrial steady-state ocean source. More recently, from 2000 to 2006, the mean CO2 flux for
the oceans globally (not including fossil fuels) has been a sink of ~2.2±0.4 Pg C yr-1
with the
interannual range varying from sinks of 1.7 to 2.9 Pg C yr-1
(Canadell et al., 2007; Khatiwala et
al., 2009; Le Quéré et al., 2009). The mean CO2 flux for the terrestrial biosphere globally over
the same period has been a sink of ~2.5 Pg C yr-1
(without taking into account land use changes)
and the interannual variation ranging from 1.2 to 4.25 Pg C yr-1
sinks and the uncertainties being
±2.3 Pg C yr-1
(Le Quéré et al., 2009; Peters et al., 2007). Although there seems to be general
consensus on the size of global carbon pools, continental scale spatial distributions of the fluxes
are still largely uncertain.
Fan (1998) estimated North America to be a large terrestrial sink of 1.7 Pg C yr-1
during
the period of 1988 to 1992 playing an important role in the global carbon cycle. More recent
studies using the atmospheric inversion approach performed over different time periods during
1992 to 2007 have shown the sink size to be ranging from 0.54 to 1.06 Pg C yr-1
(Baker et al.,
2006; Deng et al., 2007; Deng & Chen, 2011; Gurney et al., 2002, 2003; Gurney, 2004; Peters et
al., 2007; Rödenbeck et al., 2003). In most studies of the North American carbon budget, the
continent is separated into the northern boreal regions (Canada) and southern temperate regions
(contiguous US).
The estimated flux of North America boreal forests from Fan (1998) was a sink of -
0.2±0.4 Pg C yr-1
during 1988 to 1992 while a TransCom 3 experiment (Gurney et al. 2003)
showed the same region in 1992 to 1996 to be a source of 0.26±0.39 Pg C yr-1
. When the
TranCom 3 experiment was repeated with updated data from 1992 to 1996, it showed a sink of -
0.003±0.28 Pg C yr-1
(Yuen et al., 2005). In using an ecosystem modeling study, the Canadian
forests was found to be a weak sink of -0.05 Pg C yr-1
during 1980s to 1990s (Chen et al. 2003).
Studies generally have shown the boreal forests to be a weak sink or a source. The differences
in the studies may be due to the accounting of land use change and the data selection (Yuen,
2005). Since North America is generally found to be a significant carbon sink, the majority of
the sink is believed to be in the conterminous US.
The contiguous US consists of approximately 32% of the total area of North America.
Most studies have attributed the large carbon sink to the temperate forests as forests have
5
significantly larger carbon stock density relative to other vegetation land cover types. However,
the carbon stock density for temperate forests is only 60% that of tropical and boreal forests
(Pan et al., 2011). Despite lower carbon stock density than other forest types, the carbon sink in
US temperate forests has increased by 33% from the 1990s to 2000s due to increased forest
area, forest regrowth after land use changes and environmental factors such as CO2 fertilization
and N deposition (Pan et al., 2011). However, given that the mechanisms responsible for carbon
uptake from other ecosystems in the contiguous US is not well understood, the magnitude and
spatial distribution of the sink across the North American are still uncertain.
Through land- and atmospheric-based methods, Pacala et al. (2001) estimates the
contiguous US sink to be between 0.3 to 0.58 Pg C yr-1
for 1980 to 1989 while the TransCom 3
experiments for temperate US show mean annual sinks of 0.82±0.4, 0.89±0.22 and 1.26 Pg C yr-
1 for the annual mean inversion, seasonal inversion and the long term mean of the interannual
variation inversion over 1992 to 1996 (Baker et al., 2006; Gurney et al., 2003; Gurney, 2004).
In a more recent study, Crevoisier et al. (2010) used a simple budgeting approach to estimate
land-atmosphere fluxes across North America based on balancing the inflow and outflow of
CO2 concentration in the troposphere. The study found a moderate sink of 0.5 ± 0.4 Pg C yr-1
for the period of 2004 to 2006 in the contiguous US. By comparing biosphere terrestrial
models, Huntzinger et al. (2012) shows that the average North American carbon flux taken
across all the models to be a CO2 sink of 0.65 Pg C yr-1
. Peters et al. (2007) using an
atmospheric inversion data assimilation system, CarbonTracker, showed similar values,
calculating the mean annual net ecosystem exchange (NEE) over North America and temperate
North America from 2000 to 2005 to be -0.65±0.75 and -0.50±0.60 Pg C yr-1
(sinks),
respectively. While the results from the study gave a mean annual NEE value over the US to be
in approximate agreement with the results from other studies, the main contribution towards the
CO2 sink was spatially distributed over the US Midwest croplands (0.11 Pg C yr-1
) instead of the
temperate forest which is mainly found in the US Southeast. Other inversion studies with high
spatial resolution over North America (Deng et al., 2007; Deng & Chen, 2011) have shown the
CO2 sink in the US to be in temperate forests, while croplands are either a weak sink or are
carbon neutral annually. In order to reconcile this difference, accurate accounting methods for
US cropland carbon are crucial to further understanding of the North American carbon budget.
6
The following section will outline the main approaches used in quantifying global and regional
carbon fluxes.
1.2 Main approaches to quantifying terrestrial carbon fluxes
There are currently three main approaches to estimating terrestrial carbon fluxes: 1)
direct measurements (Barford et al., 2001; Friend et al., 2007; Pan et al., 2011; West et al.,
2010; Xiao et al., 2008), 2) bottom-up ecosystem modeling (Chen et al. 2003, Liu et al. 1999,
Schaefer et al. 2008) and 3) top-down atmospheric inversion (Baker et al., 2006; Deng & Chen,
2011; Gurney et al., 2002, 2003; Gurney, 2004; Law et al., 2003; Peters et al., 2007; Stephens et
al., 2007). While many results using the same type of approaches show general consistency in
the carbon flux estimates, there are still significant variations among results from the different
approaches. These discrepancies are a result of the limitations of each respective approach.
Direct measurement include: 1) census/inventory data, which are generally available for
forests and croplands on annual or multi-year timescales; and 2) tower measurements from eddy
covariance flux stations. Census/inventory data are commonly collected for forest and crop
products for the purpose of management and accounting. Using the eddy covariance technique,
the net CO2 flux between terrestrial ecosystems and the atmosphere can be measured giving
information that can potentially improve our interpretation of regional CO2 source-sink patterns,
CO2 flux responses to forcings, and predictions of the future terrestrial carbon balance (Friend et
al., 2007). These direct measurements, such as the FLUXNET network (Friend et al., 2007),
have capabilities of model validation, calibration and other applications. However, the carbon
fluxes at the spatial scale of about 1km based on flux tower measurements, will have to be
extrapolated from over a large area in order to upscale it to quantify regional terrestrial CO2
fluxes (Xiao et al., 2008). Given the large heterogeneity of vegetation covers over land, a very
dense network of flux tower measurements, which is currently not available in most regions,
will be needed for precise quantification of terrestrial carbon fluxes.
Terrestrial biosphere models (TBMs) are important tools for quantifying terrestrial CO2
fluxes, as they extrapolate local observations and understandings to large terrestrial regions.
7
There are classes of TBMs which differ in methodological approaches (Huntzinger et al., 2012):
diagnostic (Chen et al., 2003; Ju et al., 2006) and prognostic (Bondeau et al., 2007; Randerson et
al., 2009). The diagnostic models use direct and indirect satellite data or externally forced data
to specify the internal state of the system. The prognostic models calculate the internal state of
the system as part of the system equations based on empirical methods and statistics. In
comparing different TBMs, Huntzinger et al. (2012) show that in boreal regions of North
America, there appears to be consistency in the carbon flux calculation while other regions such
as the US Midwest show a carbon source according to some models. While some of the
mechanisms responsible for the sinks are understood (e.g forest regrowth), the current and
future role of other mechanisms controlling the North American carbon cycle, such as extreme
weather events, changes in land-use, CO2 and nitrogen fertilization, and other carbon-climate
feedbacks, are still highly uncertain (Huntzinger et al., 2012). As well, only one of the TBMs
takes into account the amount of carbon harvested from the croplands in its NEE calculation.
Although the primary production between models seems to show consistency, there is large
variability in the NEE (-2.2 to 0.7 Pg C yr-1
) which may be due to uncertainty in the estimations
of soil carbon pools (Wang et al., 2011).
The basic idea of atmospheric inversion consist of finding a set of statistically optimized
fluxes satisfying the measurements and the prior fluxes within their respective uncertainties
(Ciais et al., 2010; I. Enting & Trudinger, 1995). Atmospheric inversion techniques used in
quantifying CO2 fluxes hence require 1) spatially and temporally distributed initial prior CO2
surface fluxes, 2) an atmospheric transport model and 3) a set of measured atmospheric CO2
concentrations. In principle, atmospheric inversion models capture the atmospheric signal. In
using the prior knowledge of known contributions from fossil fuel and land use change
emissions as well as atmosphere-ocean and atmosphere terrestrial interactions, the inverted
fluxes effectively distribute the “residual flux” spatially and temporally based on prior
information (Rödenbeck et al., 2003). However, due to lack of data availability and poorly
constrained initial fluxes from bottom-up approaches, this method only remains complementary
to methods based on surface flux models or local observations (Ciais et al., 2010). On the other
hand, at well constrained regions such as North America and Europe, atmospheric inversion
methods may be useful in inferring the spatial distribution of carbon sources and sinks given
reliable prior information.
8
From the atmospheric perspective using inversion and data assimilation techniques,
Peters et al. (2007) found the US sink to be mainly distributed over the Midwest cropland. He
explains that this large uptake observed over the croplands may be due to the system’s
“atmospheric view” not designed to capture lateral transport of carbon from regions of
production to regions of consumption (Ciais et al., 2007). Therefore, the results show strong
CO2 uptake during the growing season but a much smaller return flux from respiration during
the non-growing season. Pacala et al. (2001) suggests that the terrestrial carbon sink in the US
has significant contributions from ecosystems other than forests, in which croplands are
believed to be a significant contributor (Ciais et al., 2007). While the methods of inventory
data, terrestrial biosphere modeling and atmospheric inversion approaches differ in the carbon
sink/source sizes and distributions (Hayes et al., 2012), there is value in attempting to reconcile
the carbon budget over contiguous US by including cropland inventory data in the prior flux for
inverting CO2 fluxes. Cropland inventory data based on statistical census provide accurate
information for accounting the US cropland carbon budget, as they take into account human
processes such as crop harvest and consumption which are not easily modeled in TBMs (West et
al., 2011).
9
1.3 Research objectives and structure of thesis
The main objectives of this thesis are:
1. To integrate US production and consumption inventory data into constraining
prior flux estimates of surface CO2 fluxes used in atmospheric inversion. Chapter 2
outlines the models, methods and datasets used for the atmospheric inversion approach.
Chapter 3 describes how the cropland carbon is being integrated into the prior fluxes.
2. To reconcile the discrepancy in the large sink found in the US Midwest from the
“atmospheric view” with US cropland statistics. Chapter 4 shows the results and
discussion of the inverted fluxes after integrating US agricultural census data.
3. To provide a robust view of the lateral movement of US cropland carbon and its
impacts on regional and global carbon budgets. Chapter 5 summarizes the main
findings of this research and future work.
10
Chapter 2 Atmospheric CO2 Inversion Methodology
2 Atmospheric CO2 Inversion Methodology
This chapter describes the model, method and datasets used in atmospheric inversion.
The atmospheric inversion technique used for quantifying CO2 fluxes requires 1) a set of initial
surface fluxes, 2) an atmospheric transport model, and 3) a set of atmospheric observations.
Forward modeling projects the set of initial background fluxes through the atmospheric
transport model to simulate the contributions of these fluxes to the atmospheric concentrations.
Inversion modeling then takes the difference between the simulated atmospheric concentrations
and the actual set of atmospheric CO2 measurements, known as the estimated contribution from
the “residual” fluxes, and simulates a set of optimized inverted fluxes taking into account the
uncertainties in the initial model fluxes, the atmospheric transport model and the atmospheric
measurements. This chapter is divided into two main sections: 1) forward modeling and 2)
inverse modeling.
11
2.1 Forward modeling
2.1.1 Prior fluxes and their uncertainties
In atmospheric inversion the initial fluxes are known as the a priori fluxes. These are
the background fluxes from CO2 sources and sinks that are known to be contributing to the
carbon cycle. These include sources from fossil fuel and fire emissions, net carbon exchange
from atmosphere-biosphere and ocean-atmosphere interactions. The initial fluxes used in this
thesis are based on the initial fluxes used in the global atmospheric inversion study by Deng &
Chen (2011) and are summarized in Table 2-1. The prior fluxes are prepared for the time period
from 2000 to 2007.
Emissions from fossil fuel consumption and cement production are large sources of CO2
in the atmosphere. The fossil fuel emission field used in this study is constructed based on the
fossil fuel CO2 emission inventory from 1871 to 2006 from the CDIAC (Marland et al., 2009)
and the EDGAR 4 databases on a 1º × 1º grid (Olivier & Aardenne, 2005).
Vegetation fire emissions are a large part of land use changes emissions contributing up
to 2 Pg C yr-1
. The grid point fire emission field used in this research is from the Global
Emissions Fire Database version 2 (GFEDv2) (Randerson et al., 2007; van der Werf et al.,
2006).
Carbon fluxes at the land surface are driven by the interactions between the terrestrial
biosphere and the atmosphere. During the growing season, vegetation takes in CO2 from the
atmosphere through the process of photosynthesis. The rate of photosynthesis is often measured
by the gross primary productivity (GPP). Conversely, in non-growing seasons, CO2 is released
back into the atmosphere through the process of respiration. Autotrophic respiration (Ra) refers
to the process of CO2 release back into the atmosphere from plants whereas heterotrophic
respiration (Rh) refers to the process of CO2 release from the soil, roots and litter, usually
involving decomposition of these materials. Net primary productivity (NPP) is given by the
difference between the GPP and Ra; and net ecosystem productivity (NEP) is given by the
difference between NPP and Rh, as shown in eq. (1) and (2):
aR GPPNPP (1)
12
)(GPPNPPNEP hah RRR (2)
Given that changes in soil carbon pools are not often well modeled by terrestrial
biosphere models, biosphere models may not be able to accurately capture the actual values for
surface carbon fluxes but they are capable in modeling seasonal and diurnal patterns in response
to changes in environmental conditions. Therefore, in most atmospheric inversion studies the
prior annual mean NEE from land surfaces at each grid is set to zero (Gurney, 2004; Rödenbeck
et al., 2003). The use of seasonally and diurnally varying initial fluxes allows for the annual
mean inversion to include contributions to annual mean concentrations due to covariance of
atmospheric transport and seasonal/diurnal fluxes (Deng & Chen, 2011; Denning et al., 1995;
Gurney, 2004; Randerson et al., 1997).
The process-based terrestrial biosphere model, Boreal Ecosystem Productivity Simulator
(BEPS), is chosen to produce seasonally varying net ecosystem exchange (NEE = –NEP) fluxes
due to its capabilities in generating the aforementioned canopy processes at an hourly time-step
globally (Chen et al., 1999; Ju et al., 2006). While the principles in BEPS are based on
FOREST Biogeochemical Cycles (FOREST-BGC) (Running & Coughlan, 1988) and is
originally intended to model Canadian forests (Chen et al., 2007; Ju et al., 2006; Liu et al., 1999,
2002), validation studies for other ecosystems in other countries have also yielded desirable
results (Higuchi et al., 2005; Matsushita & Tamura, 2002; Sun et al., 2004). The basic
framework of BEPS involves using remotely-sensed leaf area index (LAI) (Deng et al., 2006),
land cover type from Global Land Cover (GLC2000), boundary layer meteorology within the
boundary layer from NCEP-reanalysis (Kalnay et al., 1996), and other land cover specific
biophysical parameters to calculate soil-water balance, stomatal conductance, and
photosynthesis/respiration rates. A unique feature for BEPS is the separation of sunlit and
shaded components in the canopy when calculating photosynthesis (Liu, 2003; Liu et al., 2002).
In this study, two sets of control terrestrial biosphere fluxes from BEPS are prepared: 1)
annually, seasonally and diurnally varying NEE fluxes and 2) annually balanced but seasonally
and diurnally varying NEE fluxes. The annually balanced NEE fluxes are prepared by using a
special treatment to set the annual mean NEE to be zero, resulting in no interannual variability,
while the seasonal variability is retained. In fulfilling the objectives of this research, cropland
13
carbon adjustments are made to the prior control NEE fluxes. These adjustments are described
in detail in Chapter 3.
The main processes responsible for ocean CO2 uptake from the atmosphere is the partial
pressure difference between the sea surface and the overlying air which in part depends on the
seasonal growth of phytoplankton in the oceans. The daily air-sea CO2 fluxes across the sea
surface in this research are simulated by OPA-PISCES-T model. The OPA-PISCES-T is a
coupled global circulation model (OPA) (Madec, Delecluse, Imbard, & Levy, 1998) with an
ocean biochemistry model (PISCES-T) (Aumont, 2003; Buitenhuis et al., 2006). This coupled
model is forced by daily wind stress, heat and water fluxes from NCEP reanalysis (Kalnay et al.,
1996).
The four background surface CO2 fluxes from 2000 to 2007 are fitted to an hourly 1º ×
1º spatial scale as inputs for the forward modeling.
Table 2-1 – Summary of background prior fluxes and their uncertainties
Background
flux Data source
Temporal
variability Uncertainty
Fossil Fuel
CDIAC (Marland et al., 2009) +
EDGAR 4 database (Olivier &
Aardenne, 2005)
Interannual n/a
Fire GFEDv2(Randerson et al., 2007) Interannual n/a
Biosphere BEPS model (Chen et al., 2003;
Ju et al., 2006)
Interannual,
seasonal,
diurnal
2.0 Pg C yr-1
(Gurney et al., 2003)
distributed globally over land
surfaces regions based on spatial
pattern of the GPP
Ocean OPA-PISCES-T model
(Buitenhuis et al., 2006) Seasonal
0.67 Pg C yr-1
distributed over
ocean regions (Deng & Chen,
2011)
14
2.1.2 Atmospheric transport
An atmospheric transport model is used to generate simulations of the contributions from
the surface CO2 fluxes to the concentration in the atmosphere. Strong seasonal and diurnal
variations in the terrestrial biotic CO2 fluxes are generally observed. The temporal covariance
between surface fluxes and vertical atmospheric transport produces a “rectifier effect” (Denning
et al., 1995; Randerson et al., 1997) which results in large seasonal and diurnal variations in CO2
concentration over land surfaces. Variations in the planetary boundary layer (PBL) height are
driven by vertical mixing within the PBL. The processes responsible for vertical mixing include
frictional drag from winds, cumulus convection from solar heating and turbulences related to
evapotranspiration rates. In the growing seasons during the summer when there is strong
photosynthesis, vigorous mixing and a relatively deep PBL lead to the atmospheric CO2
concentration to be diluted in addition to high uptake from the atmosphere to the surface. In the
winter, the CO2 flux is from surface to the atmosphere and the shallow PBL leads to high
surface CO2 concentrations. Gurney (2004) shows, through an intercomparison for atmospheric
inversion studies, that the background seasonality is important when calculating the strength of
carbon sinks and sources. Similarly, this PBL variations on the diurnal scale is also important in
atmospheric inversion studies as shown in Deng & Chen (2011).
The atmospheric transport model chosen for this research is transport-only version of the
global chemistry Transport Model, version 5 (TM5) which is able to reproduce the PBL
variations mentioned. TM5 is an offline model driven by meteorological data from the
European Centre for Medium Range Weather Forecast (ECMWF) model with two-way
zooming capabilities. In this study, we define a global grid of 6º×4º with nested grids focusing
on North America at 3º×2º based on Peters et al. (2005). The model consists of 25 vertical
layers: five layers in the boundary layer, ten in the free troposphere and ten in the stratosphere.
In this project, the background hourly fluxes are input into TM5 to generate forward
simulations of hourly concentrations at 311 locations in the atmosphere based on the four
separate contributions from fossil fuel emissions (ffc ), fire emissions ( firec ), terrestrial
biosphere ( bioc ) and oceans ( ocec ).
15
2.1.3 CO2 observations
The atmospheric CO2 concentrations used in this study are the monthly CO2 observation
data compiled from 2000 to 2007 from the GLOBALVIEW-CO2 2008 database. The
atmospheric measurements from GLOBALVIEW-CO2 are not actual data but baseline
conditions which are derived using data extension and data integration techniques described by
Masarie & Tans (1995). GLOBALVIEW-CO2 data are compiled with CO2 measurements from
many collaborations and different data measurement types such as surface flask measurements,
tower measurements, aircraft measurements and ship measurements. While the
GLOBALVIEW-CO2 network has more than 300 measurement locations, not all of the
locations have long term historically reliable CO2 measurements, given that some stations may
have only been set up in recent years while other stations stopped the measurements. For long
term data continuity, these gaps in the GLOBALVIEW-CO2 data at each station are filled by
marine boundary layer (MBL) reference data. In this research, selected months that used
measurement-based data from 210 measurement stations were taken to compile the CO2
concentration matrix. The locations of these stations are shown in Figure 2-1. This totals to
12181 station measurements during the 8 year time period from 2000 to 2007.
In order to find the concentration corresponding to the residual flux, the simulated
background concentrations from the initially modeled fluxes need to be subtracted from the CO2
measurements. However, the diurnal variations in the surface fluxes and PBL dynamics need to
be taken into account for atmospheric CO2 concentrations. GLOBALVIEW-CO2 already takes
these processes into account in its sampling method. For tower sites, the data have been
averaged weekly by using values from only afternoon hours. During the afternoon, the height of
the PBL is the highest hence the tower measurements would be able to capture the well-mixed
CO2 concentration within the boundary layer. In morning and nighttime, the PBL is lower than
the tower location which means the measurements would not be able to measure the well mixed
CO2 concentration within PBL. For non-tower sites, GLOBALVIEW-CO2 provides a summary
of the sample collection times for discrete observations. The reason for this sampling is similar
to that of the tower sites. These sampling methods were applied to the simulated background
concentrations such that it is consistent with the sampling from GLOBALVIEW-CO2, which
takes into account diurnal variations in surface fluxes and PBL dynamics. For the simulated
16
background fluxes corresponding to the locations at GLOBALVIEW-CO2 tower sites, only the
afternoon hours were used when taking the monthly average concentration. For the non-tower
sites, the hourly sampling distribution was multiplied by the concentration of the corresponding
hourly simulated background concentration, and then averaged monthly. Finally, the monthly
averaged simulated background concentrations are subtracted from the corresponding 12181
monthly CO2 measurements from GLOBALVIEW-CO2.
ocebiofireffobs cccccc (3)
2.2 Inverse modeling
2.2.1 Inversion regions and concentration locations
The atmospheric CO2 concentrations are used for inversion for 50 regions globally
including and 30 small regions in North America following the nested inversions by Deng et al.
(2007) and Deng & Chen (2011). The 30 small regions in North America are delineated based
on a 1 km resolution land cover map from AVHRR data (DeFries & Townshend, 1994) and
political boundaries. This delineation method allows for a reduction in errors due to spatial
aggregation and the heterogeneity of vegetation cover within a specific region.
Table 2-2 – Grouping of inversion regions to the US census regions
US census region Inversion region number
West 18, 19, 23, 24, 25
Midwest 20, 21
Northeast 22
South (Southeast) 26, 27, 28
17
Figure 2-1 – Defining the 30 regions for North America and 20 regions for the rest of the globe. The
210 measurement locations are also indicated. This figure is taken from Deng & Chen (2011).
18
2.2.2 Time-dependent Bayesian synthesis approach
The atmospheric inversion technique most commonly used in carbon flux estimates is
the Bayesian Synthesis method (Enting & Trudinger, 1995). In our atmospheric CO2 inversion,
we use the time-dependent Bayesian synthesis approach. The basic method involves seeking a
linear combination of source/sink processes such that the corresponding linear combination of
their calculated responses matches the observational data as shown by the equation below:
εAGfc 0c , (4)
where 1mc is a vector of m atmospheric CO2 observations at given space and times; 1mε is a
random error vector with a zero mean and a covariance matrix cov( ) m mε R ; ( 1)m n G is a
given matrix representing a transport (observation) operator, where n-1 is the number of fluxes
to be determined; 1mA is a unity vector (filled with 1s) that relates to the assumed initially
well-mixed atmospheric CO2 concentrations ( 0c ); and ( 1) 1n f is an unknown vector of carbon
fluxes of all studied regions. In this research, m = 12181 (the number of measurements as
mentioned in Section 2.1.3) and (n-1) = 4800 (50 regions × 8 years × 12 months).
In combining matrix G and A into ( , )m nM = G A and vector f and 0c as
1n 0c
T Ts = (f , ) , eq. (4) is rewritten as:
εMsc . (5)
While eq. (5) can be solved by conventional least-squared techniques by minimizing the
cost function, the problem is poorly constrained. The Bayes approach (Tarantola, 2005) is
generally used for ill-constrained problems in which a priori information is represented as
Gaussian probability distribution functions (PDFs) and combined with the likelihood functions
of the concentrations to yield a set of a posterior (or best guess) fluxes. The following
optimized fluxes can be found by minimizing the cost function:
)s(sQ)s(sc)(MsRc)(Ms p
1T
p
1T
2
1
2
1J , (6)
19
where 1nps is the a priori estimate of s (set to zero after subtracting the contributions to
atmospheric CO2 concentrations); the covariance matrix n nQ represents the uncertainty in the a
priori estimate; and m mR is the model-data mismatch error covariance. By minimizing this cost
function in eq. (6), the posterior best estimate of s (Enting, 2002) is given by:
)sQcR(M)QMR(Ms p
11T111T ˆ , (7)
with the posterior uncertainty given by:
11T1
M)RM(QQ ˆ . (8)
2.2.3 Transport (observation) operator, model-data mismatch and prior uncertainties
The matrices for transport (observation) operator, M , the model-data mismatch, R , and
the prior uncertainties, Q , are taken from Deng & Chen (2011).
The transport (observation) operator, M , is formed from 4800 forward simulations
(eight years and 50 regions). An initial flux of 1 Pg C for each month and region was prescribed
through the TM5 transport model to find the contribution of each region to each CO2
concentration at each observation location. The diurnal variation is handled appropriately in
taking into account tower sites and continental sites in order to invert monthly CO2 fluxes.
The model-data mismatch, R , reflects the difference between the modeled and the
observed CO2 concentrations which include both the systematic errors from transport modeling
and the measurement errors (such as instrument errors). The observation sites were divided into
5 categories, each with its own constant portion ( const ) and variable portion (GVsd) that is
computed monthly from the standard deviation data given in GLOBALVIEW-CO2 2008
variation (var) files. The constant portion is defined under the following categories: Antarctic
sites (0.15), oceanic sites (0.30), land and tower sites (1.25), mountain sites (0.90), and aircraft
samples (0.75). The variable portion is the statistical summary of average atmospheric
20
variability for each measurement record. Therefore, the covariance matrix R, is given as a
diagonal matrix that contains the error for each month, i:
22 GVsdR constii . (9)
Furthermore, a weighting factor, W, is inserted to the cost function in eq. (6) to account for the
vertical correlation errors existing at different levels of tower sites and aircraft sampling (Deng
& Chen, 2011).
)s(sQ)s(sc)W)((MsRc)W)((Ms p
1T
p
1T
2
1
2
1J (10)
This weighting, W , is a diagonal matrix with the diagonal terms given by:
))1(6.01(1 nwii , (11)
where n is the number of observations at different levels at the same geographic location. The
total information will be more at locations with more observation levels than that of fewer
observation levels. Therefore the amount of information from one level decreases as there are
more levels.
While the a priori fluxes are set to zero after subtracting their contribution toward the
CO2 concentrations, the a priori uncertainties, Q , are important in forcing the spatial
distribution of the inverted fluxes. These uncertainties are already summarized in Table 2-1.
The uncertainties for fossil fuel of ±6% (Marland et al., 2009) and the fire fluxes of ±20% (van
der Werf et al., 2010) were not taken into account in the prior uncertainties; hence, it is
important to take note that the inverted fluxes will be subjected to these uncertainties.
The 2 test (Gurney et al., 2003) is employed to test the consistency of the fit to data
and prior flux estimates simultaneously:
obs
1 12
2
2
2
obs
min2
()(
N
Q
)ss
R
cMs
N
J
p
m
m
n
n , (12)
21
where obsN is the number of degrees of freedom (number of observations) and minJ is the cost
function from eq. (6). The consistency of the fit is highest when the value of 2 is set to unity.
22
Chapter 3 US Cropland Carbon Integration Methodology
3 US Cropland Carbon Integration Methodology
During the growing season, cropland in the US Midwest represents a CO2 sink.
However, a large portion of the crops are taken away from the location of production during
harvest and transported to other regions for storage and consumption. When the crop products
are consumed by human and livestock, CO2 is released back into the atmosphere at geographic
locations that may differ from the area of crop production. It is important to take into account
these patterns, known as the lateral transport of cropland carbon, in the prior fluxes used in
atmospheric CO2 inversion studies. This chapter is divided into three main sections. The first
section briefly summarizes the US cropland carbon budget and the statistical data used in
calculating each component contributing to cropland carbon sources or sinks. The second
section describes the methods used to integrate the data from the US cropland carbon into the
terrestrial prior fluxes. The final section outlines the experiments designed in this research to
test for the impact of the adjusted fluxes on inverted terrestrial CO2 fluxes.
3.1 US cropland carbon budget based on inventory data
This research uses the regional patterns of CO2 uptake and release in US croplands
calculated by West et al. (2011) which is based on agricultural statistics. The datasets of the
carbon source and sink contributions can be downloaded from the Carbon Dioxide Information
Analysis Center (CDIAC) website: http://cdiac.ornl.gov. The data include county-level NPP,
harvest, and changes in soil carbon from 1990 to 2008, as well as human and livestock crop
consumption from 2000 to 2008. The national crop carbon budget for the US from 2000 to
2008 is balanced within 0.3 to 6.1% yr-1
based on the study from West et al. (2011). Although
many other important components are included in the overall US cropland carbon budget, such
as exports and crop carbon used for fuel, the vertical net carbon exchange (NCE) into the
atmosphere is given by the sum of net carbon uptake from NPP, net change in soil carbon and
23
the release of carbon from biomass decomposition, human consumption and livestock
consumption.
3.1.1 Crop NPP, harvest, biomass decomposition and changes in soil carbon pool
The cropland NPP used in West et al. (2011) is calculated based on annual statistics of
crop production (P) in units of tons of bushels and harvested crop area (HA) reported in the US
Department of Agriculture (USDA), National Agricultural Statistics Service. These statistics
are converted into county level NPP in units of carbon using the eq. (13), which is documented
in earlier studies (Hicke, 2004; Hicke & Lobell, 2004; Prince, Haskett, Steininger, Strand, &
Wright, 2001; West et al., 2010):
i iii
iicrops
f
CP
HAHI
)MC1(NPP
AG,
, (13)
where P is the reported crop production; MC is the harvest moisture content; C is the conversion
factor from biomass to carbon (0.45 g of C per g of dry mass); HI is the harvest index (related
directly to root:shoot ratio) given by the ratio of yield mass to above ground biomass; AGf is the
fraction of production allocated aboveground; and the subscript i indicates different crop types.
The harvested amount is calculated based on the crop yields. The carbon released from
biomass decomposition is calculated from the NPP by subtracting the amount that is harvested.
The remainder of the crops, i.e the amount not harvested, is left as residue and either sequesters
into the soil or decomposes within the same year. The estimated NPP and harvest amount used
in this research accounts for 17 crops (corn, soybean, oats, barley, wheat, sunflower, hay,
sorghum, cotton, rice, peanuts, potatoes, sugarbeets, sugarcane, tobacco, rye and beans)
representing the majority of the crops grown in the contiguous US (West et al., 2010, 2011).
Changes in soil carbon are calculated based on empirical relationships between land
management practices and soil carbon change (West et al., 2008). In order to capture the long
24
term impacts on soil carbon pools from a 20-year history of changes in crop rotation and tillage
intensity, estimates of soil carbon change were calculated from 1980 to 2008.
3.1.2 Human and Livestock consumption
Human crop carbon consumption data provided by West et al. (2011) are calculated
based on the per capita food consumption (taken from the food commodity intake inventory)
and the human population (taken from a population census). The livestock consumption data
are calculated using a similar method as human consumption but also take into account different
animals and their feed consumption amounts. The consumed amount is assumed to be released
back into the atmosphere within the same year as CO2 through respiration, excretion and flatus
(West et al., 2009). Excretion typically enters the waste treatment facilities within the county
and the emissions are taken into account in the consumption term above.
25
3.2 Prior flux adjustments for US croplands
In integrating the carbon exchange due to crop processes, the NEP in eq. (2) needs to be
adjusted. For crop processes, the harvested amount is taken away from the field and respired
back into the atmosphere when consumed by human, umptionhuman_consR and livestock,
nconsumptiolivestock_R . Therefore, crop NEP is given by:
soilnconsumptiolivestock_umptionhuman_consh,residuecropcrop cRRR NPPNEP (14)
Since the residue amount is the difference between the total crop biomass and the amount
harvested, eq. (14) can be rewritten as:
nconsumptioproduction
RRc nconsumptiolivestock_umptionhuman_conssoilharvestedcrop
NPPNEP , (15)
where,
soilharvested cproduction NPP (16)
nconsumptiolivestocknconsumptiohuman RRnconsumptio __ (17)
The spatial pattern of the crop production, consumption and NEP are shown in Figure 3-1.
26
Figure 3-1 – Maps showing spatial distributions of annual crop production (top); crop consumption
(middle); and crop NEP (bottom) for 2003. Data taken from (CDIAC) website: http://cdiac.ornl.gov.
27
The crop carbon related to production and consumption is taken into account to adjust for the
NEP of the terrestrial biosphere:
adjustedhadjustedadjusted R ,NPPNEP (18)
The production and the consumption in this research are adjusted to the terrestrial biosphere
fluxes separately due to the differences in temporal CO2 uptake and release patterns.
3.2.1 Production adjustment
The simulated terrestrial NPP can be adjusted to integrate cropland production over the
contiguous US using the equation below:
soilhbiosphereareacrop
biosphereareacrop
biosphereareacropbiosphereadjusted
cr
productionr
productionr
arvested_
_
_
NPPNPP1
NPP1
)NPP(NPPNPP
, (19)
where, biosphereNPP is the 1º x 1º NPP output from the BEPS model and crop_arear is the ratio of
harvested crop area within the 1º x 1º grid over the total area of the grid. The county level
cropland production is first extrapolated into a mean value for each 1º x 1º grid, then adjusted
using the equation above. The ratio crop_arear is calculated based on the harvested area data
provided by West (personal communications). The crop area ratio is used to subtract the
cropland NEP assumption from the original simulated NEP, as shown in eq. (19). The
originally simulated NEP uses GLC2000 as the land cover classifications, which does not
include a distinct cropland pixel assigned; hence, this crop area ratio method was used. Chan &
Lin (2011) cautions researchers against the direct comparison of carbon accounting based on
agricultural census data and TBM simulated fluxes due to the large differences of different land
cover type classifications used. For this reason, this research chooses to use the crop area ratio
method for the production adjustment.
Since the prior surface CO2 fluxes into the atmospheric transport model are on an hourly
time step, the annual crop carbon production data are interpolated into the seasonal and diurnal
28
patterns simulated in the BEPS model. Firstly, the annual biosphereNPP is converted to annual
adjustedNPP , then the ratio between the two is taken and multiplied by the biosphereNPP fluxes on
the hourly timescale, resulting in hourly adjusted fluxes from 2000 to 2008 for each 1º x 1º grid.
3.2.2 Consumption adjustment
The consumption terms are integrated into the simulated hR over the contiguous US using
the equation below:
nconsumptiolivestocknconsumptiohumanbiospherehareacrop
biospherehareacrop
biospherehareacropbiospherehadjustedh
RRRr
nconsumptioRr
nconsumptioRrRR
__,_
,_
,_,,
1
1
)(
(20)
where, biospherehR , is the 1º x 1º hR output from the BEPS model and crop_arear is the ratio of
harvested crop area within the 1º x 1º grid over the total area of the grid. The county level
cropland consumption is first extrapolated into a mean value for each 1º x 1º grid, then adjusted
using the equation above.
However, unlike the production adjustment, the temporal patterns of CO2 release from
human and livestock consumptions do not follow the seasonal and diurnal patterns observed in
the biosphere. In this research, we assume constant release of CO2 from crop consumption at
every hour. Therefore, the annual consumption amount is divided equally into the hourly values
and added to the hourly simulated biospherehR , from BEPS for the time period from 2000 to 2008 at
each 1º x 1º grid.
29
3.3 Schemes of experiments
A series of experiments outlined in Table 3-1 below was designed to test for the impact
of integrating the cropland carbon data into the prior terrestrial fluxes. Two sets of experiments
are used. The first set of experiments assumes there to be a balanced terrestrial biosphere,
meaning that the annual mean terrestrial flux is 0 for each grid cell. The prior terrestrial surface
fluxes in most atmospheric inversion studies only show the seasonal trend instead of the
interannual pattern (Gurney, 2004; Rödenbeck et al., 2003). This is done to allow the inverted
fluxes from the “atmospheric view” to determine the optimized annual terrestrial surface carbon
sink sizes. Experiment 1 uses the BEPS hourly NEP that is processed to result in an annually
balanced flux at each grid. However, it is important to account for the magnitude of the initial
annual carbon sink when adjusting for the cropland carbon. Experiment 2 uses the initial BEPS
output that includes a soil carbon pool of 3.2 Pg C in 2000. While the soil carbon pool from
terrestrial biosphere models are still largely uncertain (Wang et al., 2011), this experiment is
designed to assess the changes in US carbon budget from the impacts of US crop carbon instead
of the absolute magnitude of each sink.
In each set of experiments, there is a control run (Experiment 1a, 2a); the changes in the
inverted fluxes are tested for production adjustment only (Experiment 1b, 2b) and both
production and consumption adjustments (Experiment 1c, 1d, 2c). While both Experiment 1c
and 1d take into account production and consumption, Experiment 1c treats the consumption as
an additional source of CO2 on top of fluxes used in Experiment 1 b; whereas Experiment 1d
assumes the net carbon exchange in the crop production terms and the crop consumption are
more or less in balance (West et al., 2011); hence, a special treatment is taken to set the annual
NEE to be 0 after both the crop production and consumption adjustments.
The a priori uncertainty matrix Q described in Section 2.2.3 is adjusted to take into
account the uncertainties from the cropland production and consumption data. Uncertainties in
the agricultural production data are subjected to the large uncertainties found in the parameters
used such as the harvest index (HI) and reported crop production (P) (Chan & Lin, 2011).
Bolinder et al., (2007) and Prince et al. (2001) show the deviation of HI, the dominant source of
uncertainty towards NPP, to be 10%. Therefore, experiments that adjust for the production
30
only are prescribed 10% of the annual NPP found in the agricultural statistics data distributed
over the production regions and weighted with the original matrix Q. Experiments that adjust
for both the production and the consumption use the above method to include the production
uncertainty as well as an additional 1% of annual total human consumption (West et al., 2009)
and 20% of the annual total livestock consumption distributed over consumption areas (Ciais et
al., 2007). Furthermore, the 2 test from eq. (12) is employed to show the consistency of the
fit to data and prior flux estimates simultaneously. The 2 values are also shown in Table 3-1.
Table 3-1 Schemes of experiments designed to test for the impact of integrating information from crop
production and consumption data into the a priori fluxes
Experiment 1. Annually balanced terrestrial biosphere χ2
(a) Terrestrial prior fluxes from BEPS model (annual mean = 0) 1.09
(b) Terrestrial prior fluxes adjusted for crop production (annual mean = 0) 1.12
(c) Terrestrial prior fluxes adjusted for crop production (annual mean = 0) + crop consumption
added to the prior fluxes as a source
0.97
(d) Terrestrial prior fluxes adjusted for crop production and added crop consumption (annual
mean = 0)
0.94
Experiment 2. Interannual variability in terrestrial biosphere χ2
(a) Terrestrial prior fluxes from BEPS model (annual mean ≠ 0) 1.11
(b) Terrestrial prior fluxes adjusted for crop production (annual mean ≠ 0) 1.16
(c) Terrestrial prior fluxes adjusted for crop production and added crop consumption (annual
mean ≠ 0)
0.97
31
Chapter 4 Results and discussion
4 Results and discussion
The schemes of experiments described in Section 3.3 were used to test for the impact of
inventory cropland carbon data on the inverted CO2 fluxes. This chapter evaluates the regional
and global impacts found for each experiment. The impacts are evaluated based on the multi-
year mean annual values and seasonal variations.
4.1 Multi-year regional carbon budget
4.1.1 Average annual flux
The average annual inverted CO2 fluxes over the contiguous US are shown for
Experiment 1 and Experiment 2 in Figure 4-1 and Figure 4-2, respectively. Maps of the spatial
patterns of these inverted CO2 fluxes over the US for Experiment 1 and Experiment 2 are shown
in Figure 4-3 and Figure 4-4, respectively. Furthermore, Table 4-1 summarizes the mean
inverted CO2 fluxes ( and errors (ε), as well as percentage changes (Δ%) from the control
calculated by:
control
control
μ
μμ%
, (21)
where controlμ is the annual mean inverted flux for the control experiment.
To evaluate the impact of integrating crop production and consumption data into the
prior fluxes, comparisons of the inverted fluxes can be made between the experiments with crop
adjustments and those without. However, in order for these comparisons to be meaningful, the
differences in the inverted fluxes resulting from crop adjustments need to be larger than the
errors in the inverted fluxes. Therefore, a signal-to-noise ratio (SNR) is calculated for each
region, using the equation shown below:
32
ε
μμSNR
control . (22)
Note that in this case, the “signal” is defined as the mean differences in the inverted fluxes
between the control and crop adjusted experiment instead the value of the actual inverted fluxes.
If the SNR is less than unity, the observed changes due to the agricultural adjustments are less
than the errors hence the signal is within the noise level of the results. This means that the
observed changes may simply be a result of random errors. If the SNR is larger than unity, the
changes in the results are larger than the random errors hence these changes cannot be only
explained by random errors. Therefore the changes observed will be in part due to the
additional constraint in the prior fluxes given by the information from US cropland data. The
SNR for each region is shown in Table 4-1, where “*” denotes the SNR to be greater than unity.
In Figure 4-1, we can compare the impact of adjusting only crop production on the
overall inverted US carbon budget. The production adjustment shows that the carbon sink is
redistributed from the forested regions in the US Southeast (region 26 to 28) to the cropland area
in the US Midwest (regions 20 and 21). This is most clearly represented in the US maps shown
in Figure 4-3. The redistribution shows a strengthening of the CO2 sink in the US Midwest and
a weakening of the sink in the US Southeast forested region. The increase in the sink size in the
US Midwest can be attributed to the large CO2 uptake during the growing season, yet the carbon
is released in other geographic locations. The seasonal results are further discussed in the later
sections.
By looking at the results from Experiment 1c, the impact of the crop consumption
adjustment as an additional source can be evaluated. The results show that the US Midwest sink
to be 0.36 ± 0.13 Pg C yr-1
, which is ~23% of the 1.6 Pg C yr-1
annual US fossil fuel emissions
(Canadell et al., 2007). This sink is even larger than the sink of 0.34 ± 0.11 Pg C yr-1
observed
from Experiment 1b which only adjusts the prior terrestrial for the US crop production. The
large sink in the inverted results may be due to the “atmospheric view” allocating the
compensation for the additional crop consumption source into the sink at the crop production
regions in balancing the regional carbon budget. In the large crop consumption regions 28, the
contribution from the consumption is shown locally as a weakened sink. At other regions of
33
large crop consumption with low vegetation growth (regions 23 and 24) CO2 sources are also
shown locally. In comparing Experiment 1c with Experiment 1b, the influence of crop
consumption patterns can be isolated and a weakening of the CO2 sinks at regions of high
consumption is clearly noticeable. Furthermore, with the addition of the CO2 source from crop
consumption, the overall US and North American sinks are observed to be smaller by 0.026 and
0.06 Pg C yr-1
, respectively, representing ~4% and ~6.5% decreases from the control case,
respectively, as shown in Table 4-1.
Experiment 1d reflects the impact of an annually balanced terrestrial prior flux in which
the biosphere is in annual balance after the inclusion of consumption. While this experiment run
assumes that the crop consumption patterns are already taken into account in the seasonal
variations of the terrestrial biosphere, the reliability of this assumption is questionable as
suggested from the results. The results show less weakening of the sink in the forested regions
26 to 28 than results shown for Experiments 1b and 1c. The crop consumption patterns are not
reflected in the inverted results and the US Midwest and US Southeast are both found to be
large carbon sinks, resulting in an overall increase in sink of US and North America compared
to the control case, as shown in Table 4-1. Although these results are not a reliable source of
information towards the regional carbon budget, they reveal the inverted fluxes to be relatively
sensitive towards changes in the prior fluxes.
Table 4-1 summarizes the mean inverted CO2 fluxes ( and errors (ε), as well as
percentage changes (Δ%) from the control for US regions. While most of the changes in the
inverted CO2 fluxes caused by adjustments using the cropland carbon data seem to be smaller
than the errors in the results, a production region (20) and a consumption region (24) have SNR
values greater than 1. These changes also affect the larger the US census regions of US West
and the US Midwest, respectively, showing SNR values to be larger than 1. In the experiment
where only crop production is adjusted for, production region (20) is found to be the only region
with the SNR greater than 1. However, the US census regions in Experiment 1b that showed
SNR > 1 are not only the US Midwest but also the US Southeast.
Furthermore, the North America total and Canada (which was not adjusted for in the
prior fluxes) show large changes in sink sizes for experiments with agricultural adjustments.
34
This suggests that in atmospheric inversion, the changes resulting from different a priori fluxes
are not only observed locally (Gurney, 2004). This will be further discussed later.
35
Figure 4-1 – Mean annual inverted CO2 flux (-ve represents uptake) for Experiments 1 – annually
balanced terrestrial prior fluxes with (a) no adjustments; (b) production adjustments; (c) crop production
adjustments and consumption as additional source; and (d) crop production and consumption adjustment
during 2002 to 2007 for US regions (top), US census regions (middle) and North American regions
(bottom).
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
18 19 20 21 22 23 24 25 26 27 28
CO
2 f
lux
in P
g C
yr-1
Region
(a) (b) (c) (d)
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
US West US Midwest US Northeast US Southeast
CO
2 fl
ux
in P
g C
yr-1
(a) (b) (c) (d)
-1.5
-1
-0.5
0
Canada US North America Total
CO
2 fl
ux
in P
g C
yr-1
(a) (b) (c) (d)
36
Experiment 2 shows an a priori adjustment scheme that includes the interannual
variation of the biosphere since the crop production and consumption adjustments not only
affect the seasonal magnitude of the fluxes but also the overall annual total surface flux.
Although the magnitude of these inverted fluxes are highly sensitive to the uncertainty from the
soil carbon pool estimate in the a priori terrestrial fluxes, the general patterns of change can be
observed in the inverted CO2 fluxes, as shown in Figure 4-2. The production adjustments
(Experiment 2b) lead to an increase in the CO2 sink in both the US Midwest (region 20) and also
the US Southeast forested regions (regions 26 to 28). The consumption adjustments
(Experiment 2c) are shown to strengthen the sink in the US Midwest and weaken the sink in the
Southeast forested regions of high crop consumption. This result is consistent with the findings
from Experiment 1.
Figure 4-4 compares the a priori surface terrestrial fluxes with the inverted CO2 fluxes.
While the inverted CO2 flux shows a large sink in the US Midwest (region 20), the largest CO2
sink is observed in region 27, which is the forested region in Southeast US. This differs from
the findings from Experiment 1, which only takes into account the seasonal variations but not
the interannual variations. This difference stems from more fundamental differences between
bottom-up and top-down approaches, which will be discussed in Section 4.3. In comparing the
prior fluxes with the inverted fluxes for Experiment 2c, it can be seen that the atmospheric view
corrects the US Midwest region from a region of small CO2 source to a large CO2 sink. Without
the cropland carbon adjustments (Experiment 2a), the US Midwest sink in region 20 is only 0.11
± 0.05 Pg C yr-1
compared to a sink of 0.14 ± 0.09 Pg C yr-1
and 0.16 ± 0.1 Pg C yr-1
with
production adjustments only (Experiment 2b) and both production and consumption adjustments
(Experiment 2c), respectively. These values are comparable to the -0.11 Pg C yr-1
cropland
NEE value from 2001 to 2005 in Peters et al. (2007), in which the crop consumption is not taken
into account.
The overall US and North American CO2 sinks are both shown to have increased when
adjusted for production only, whereas the sink sizes are similar to the control experiment when
crop consumption patterns are also adjusted for. The percentages changes are only ~0.85% and
~1.85% respectively. This result reinforces our original assumption that the long term cropland
carbon budget can be balanced by the crop production and crop consumption (West et al., 2011).
37
Figure 4-2 – Mean annual inverted CO2 flux (-ve represents uptake) for Experiments 2 – annually
varying terrestrial prior fluxes with (a) no adjustments; (b) production adjustments; (c) crop production
and consumption adjustments during 2002 to 2007 for US regions (top), US census regions (middle) and
North American regions (bottom).
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
18 19 20 21 22 23 24 25 26 27 28
CO
2 in
Pg
C y
r-1
Region
(a) (b) (c)
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
US West US Midwest US Northeast US Southeast
CO
2 fl
ux
in P
g C
yr-1
(a) (b) (c)
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
Canada US North America Total
CO
2 fl
ux
in P
g C
yr-1
(a) (b) (c)
38
Figure 4-3 – Map of mean annual inverted CO2 flux (-ve represents uptake) for Experiment 1 during 2002 to 2007 over contiguous US
regions.
39
Figure 4-4 – Map of mean annual inverted (left) and prior (right) CO2 flux (-ve represents
uptake) for Experiment 2 during 2002 to 2007 over contiguous US.
40
Table 4-1 shows 2002 to 2007 mean inverted CO2 flux (, the error (ε) in Tg C yr-1
and the percentage change1 (Δ% ) for US regions.
Region
Experiment 1 Experiment 2
(a) (b) (c) (d) (a) (b) (c)
± ε ± ε Δ% ± ε Δ% ± ε Δ% ± ε ± ε Δ% ± ε Δ%
18 -43.23 ± 33.1 -25.28 ± 25.7 -41.53% -23.83 ± 28.4 -44.88% -28.19 ± 28.4 -34.78% -25.3 ± 33.1 -3.18 ± 25.7 -87.44% -2.1 ± 28.4 -91.68%
19 -10.79 ± 20.3 -6.32 ± 15.8 -41.44% -3.05 ± 17.7 -71.78% -6.84 ± 17.7 -36.62% -15.77 ± 20.3 -5.99 ± 15.8 -61.98% -2.7 ± 17.7 -82.9%
20 -71.58 ± 56.9 -189.02 ± 91.4 164.06%* -211.24 ± 102.4 195.1%* -207.71 ± 102.4 190.16%* -107.11 ± 56.9 -146.86 ± 91.4 37.11% -161.09 ± 102.4 50.41%
21 -117.08 ± 59.8 -151.65 ± 72.7 29.53% -147.24 ± 78.3 25.77% -152.59 ± 78.3 30.34% -132.69 ± 59.8 -158.04 ± 72.7 19.11% -153.62 ± 78.3 15.78%
22 -104.93 ± 57.7 -74.14 ± 46.1 -29.35% -70.1 ± 51.9 -33.19% -83.51 ± 51.9 -20.41% -146.53 ± 57.7 -132.4 ± 46.1 -9.64% -126.48 ± 51.9 -13.68%
23 -0.78 ± 8.9 -0.63 ± 7 -19.31% 7.26 ± 10.2 -1025.14% -0.37 ± 10.2 -52.92% 5.58 ± 8.9 3.72 ± 7 -33.36% 11.16 ± 10.2 99.85%
24 -0.05 ± 0 -0.12 ± 0 137.49% 3.97 ± 3.5 -7820.51%* -0.98 ± 3.5 1795.97% -6.77 ± 0 -1.58 ± 0 -76.71%* 2.49 ± 3.5 -136.87%*
25 -7.95 ± 14.2 -4.62 ± 10.9 -41.93% -0.93 ± 14.2 -88.31% -7.29 ± 14.2 -8.39% -20.83 ± 14.2 -17.11 ± 10.9 -17.87% -13.3 ± 14.2 -36.14%
26 -92.86 ± 59.8 -52.01 ± 47.5 -43.99% -49.77 ± 63.8 -46.41% -77.2 ± 63.8 -16.86% -141.55 ± 59.8 -149.58 ± 47.5 5.67% -128.79 ± 63.8 -9.02%
27 -111.1 ± 78.7 -79.15 ± 64.6 -28.76% -77.75 ± 82.9 -30.02% -106.62 ± 82.9 -4.03% -188.97 ± 78.7 -211.1 ± 64.6 11.71% -200.07 ± 82.9 5.87%
28 -69.23 ± 67.5 -44.76 ± 51 -35.35% -31.07 ± 64.5 -55.11% -59.13 ± 64.5 -14.58% -82.2 ± 67.5 -98.26 ± 51 19.54% -80.26 ± 64.5 -2.36%
West -62.81 ± 39.1 -36.97 ± 30.4 -41.14% -16.57 ± 32.7 -73.62%* -43.67 ± 34.5 -30.48% -63.08 ± 40.2 -24.13 ± 20.6 -61.74%* -4.45 ± 23.4 -92.94%*
Midwest -188.66 ± 80.7 -340.68 ± 116.8 80.58%* -358.48 ± 128.8 90.02%* -360.3 ± 128.9 90.98%* -239.79 ± 82.3 -304.9 ± 115.5 27.15% -314.72 ± 128.2 31.25%
Northeast -104.93 ± 57.7 -74.14 ± 46.1 -29.35% -70.1 ± 51.9 -33.19% -83.51 ± 51.9 -20.41% -146.53 ± 57.7 -132.4 ± 46.1 -9.64% -126.48 ± 51.9 -13.68%
Southeast -273.18 ± 118.2 -175.91 ± 94.2 -35.61%* -158.58 ± 119.3 -41.95% -242.96 ± 121.8 -11.06% -412.72 ± 115.5 -458.93 ± 93.1 11.2% -409.12 ± 119.4 -0.87%
US -629.6 ± 157.7 -627.7 ± 153.9 -0.3% -603.7 ± 172.7 -4.11% -730.4 ± 182.1 16.02% -862.1 ± 156.3 -920.4 ± 152.2 6.76% -854.8 ± 182.4 -0.85%
Canada -279.8 ± 142.8 -271.5 ± 139.5 -2.99% -256 ± 139.7 -8.53% -240.8 ± 139.3 -13.93% -215.1 ± 137.2 -214.7 ± 136.7 -0.16% -202.3 ± 136.3 -5.95%
NA -932.6 ± 205.9 -913.1 ± 195.9 -2.09% -872 ± 211.4 -6.49% -981.1 ± 208.6 5.21% -1127 ± 189.9 -1185 ± 181.8 5.15% -1106.1 ± 200.3 -1.85%
*represents regions with SNR > 1 1+ve percentage change, Δ%, represents increase in uptake/release
41
4.2 Multi-year global carbon budget
Although the cropland carbon adjustments were only made for the US regions, the
optimized CO2 fluxes are inverted globally. Figure 4-5 and Figure 4-6 show the average annual
inverted CO2 fluxes globally from 2002 to 2007 for Experiment 1 and Experiment 2,
respectively. Table 4-2 summarizes the mean inverted CO2 fluxes ( and errors (ε), as well as
percentage changes (Δ%) from the control case for the global regions.
In both global results for Experiment 1 and Experiment 2, changes are observed in many
regions outside of the US, as shown in Figure 4-5 and Figure 4-6. In regions outside the US, no
adjustments were made in the a priori fluxes nor in the a priori uncertainties yet noticeable
changes were still observed in their inverted fluxes. These results suggest that local changes in
the a prior CO2 fluxes affect the carbon budget on larger spatial scales. A plausible explanation
for these results is the global regions balancing the changes in carbon source and sink sizes
observed in North America, since the global carbon budget remains relatively constant, as
shown in Table 4-2. In an atmospheric inversion study, Gurney (2004) found contributions
from land fluxes to be observed in the adjacent ocean regions, and described this phenomenon
as “leakage”. In this research, a similar phenomenon is also observed, as local contributions
seem to be observed on larger regional and global scales. Therefore, our results seem to suggest
a large amount of leakage from the US terrestrial biosphere into other global regions when crop
adjustments are made. This puts into question the reliability of the atmospheric CO2
measurements in capturing atmospheric responses from local variations in terrestrial surface
fluxes, given that North America is one of the continents with strong data constrains.
Furthermore, the global land, global ocean and the global carbon budget for Experiment
1 do not seem to show large changes with the crop production or crop consumption adjustments
as shown in Figure 4-5. The inverted CO2 results show a larger global terrestrial sink and a
smaller ocean sink for Experiment 2, as shown in Figure 4-6. This may be due to the a priori
adjustments allocating North America as a larger sink while most regions outside of North
America adjust accordingly to balance the global carbon budget due to weak data constraints.
42
Figure 4-5 – Mean annual inverted CO2 flux (-ve represents uptake) for Experiments 1 – annually
balanced terrestrial prior fluxes with (a) no adjustments; (b) production adjustments; (c) crop production
adjustments and consumption as additional source; and (d) crop production and consumption adjustment
during 2002 to 2007 for global regions (top) and global carbon budget (bottom).
-1.50
-1.00
-0.50
0.00
0.50
1.00
CO
2 fl
ux
in P
g C
yr-1
Region
(a) (b) (c) (d)
-7
-6
-5
-4
-3
-2
-1
0
Global Land Global Ocean Global Total
CO
2 f
lux
in G
t C
yr-1
(a) (b) (c) (d)
43
Figure 4-6 – Mean annual inverted CO2 flux (-ve represents uptake) for Experiments 2 – annually
varying terrestrial prior fluxes with (a) no adjustments; (b) production adjustments; (c) crop production
and consumption adjustments during 2002 to 2007 for global regions (top) and global carbon budget
(bottom).
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
CO
2 f
lux
in G
t C
yr-1
Regions
(a) (b) (c)
-7
-6
-5
-4
-3
-2
-1
0
Global Land Global Ocean Global Total
CO
2 fl
ux
in P
g C
yr-1
(a) (b) (c)
44
Table 4-2 shows 2002 to 2007 mean inverted CO2 flux (, the error (ε) in Pg C yr-1
and the percentage change1 (Δ%) for global regions.
Region
Experiment 1 Experiment 2
(a) (b) (c) (d) (a) (b) (c)
% % % % %
NA-N -0.28 ± 0.14 -0.27 ± 0.14 -2.99% -0.26 ± 0.14 -8.53% -0.24 ± 0.14 -13.93% -0.22 ± 0.14 -0.21 ± 0.14 -0.16% -0.2 ± 0.14 -5.95%
NA-S -0.65 ± 0.16 -0.64 ± 0.16 -1.7% -0.62 ± 0.17 -5.62% -0.74 ± 0.18 13.41% -0.91 ± 0.16 -0.97 ± 0.16 6.4% -0.9 ± 0.19 -0.89%
31 0.36 ± 0.41 0.35 ± 0.41 -2.57% 0.34 ± 0.41 -5.25% 0.36 ± 0.41 -0.34% 0.36 ± 0.41 0.35 ± 0.41 -2.94% 0.32 ± 0.41 -10.16%
32 -0.07 ± 0.27 -0.06 ± 0.27 -3.09% -0.06 ± 0.27 -5.22% -0.07 ± 0.27 1.3% -0.1 ± 0.27 -0.1 ± 0.27 3.9% -0.1 ± 0.27 6.28%
33 -0.2 ± 0.28 -0.2 ± 0.28 -0.66% -0.22 ± 0.28 7.94% -0.19 ± 0.28 -5.88% -0.28 ± 0.28 -0.26 ± 0.28 -10.22% -0.29 ± 0.28 1.72%
34 -0.86 ± 0.27 -0.86 ± 0.27 -0.27% -0.86 ± 0.27 -0.41% -0.86 ± 0.27 0.07% -0.91 ± 0.27 -0.94 ± 0.27 2.6% -0.93 ± 0.27 1.77%
35 -0.89 ± 0.26 -0.87 ± 0.26 -3.22% -0.89 ± 0.26 -0.97% -0.86 ± 0.26 -3.59% -1 ± 0.26 -0.98 ± 0.26 -1.89% -1 ± 0.26 0.53%
36 -0.63 ± 0.24 -0.65 ± 0.24 2.44% -0.64 ± 0.24 1.66% -0.62 ± 0.24 -2.24% -0.52 ± 0.24 -0.53 ± 0.24 2.67% -0.52 ± 0.24 1.45%
37 -0.54 ± 0.24 -0.54 ± 0.24 0.28% -0.54 ± 0.24 0.43% -0.54 ± 0.24 0.24% -0.56 ± 0.24 -0.63 ± 0.24 14.22% -0.63 ± 0.24 13.91%
38 0.06 ± 0.08 0.05 ± 0.08 -4.82% 0.06 ± 0.08 1.17% 0.06 ± 0.08 0.32% 0.06 ± 0.08 0.04 ± 0.08 -37.43% 0.04 ± 0.08 -27.01%
39 -0.21 ± 0.21 -0.21 ± 0.21 1.39% -0.21 ± 0.21 3.46% -0.2 ± 0.21 -3.6% -0.05 ± 0.21 -0.05 ± 0.21 -11.63% -0.07 ± 0.21 19.75%
40 -0.58 ± 0.15 -0.59 ± 0.15 1.91% -0.59 ± 0.15 2.27% -0.58 ± 0.15 0.5% -0.64 ± 0.15 -0.63 ± 0.15 -0.77% -0.63 ± 0.15 -0.58%
41 -0.06 ± 0.12 -0.06 ± 0.12 -4.82% -0.06 ± 0.12 -5.79% -0.07 ± 0.12 3.08% -0.06 ± 0.12 0 ± 0.12 -94.88% 0 ± 0.12 -101.8%
42 0.74 ± 0.14 0.74 ± 0.14 -0.31% 0.74 ± 0.14 0.21% 0.74 ± 0.14 -0.38% 0.79 ± 0.14 0.79 ± 0.14 -0.69% 0.8 ± 0.14 0.44%
43 -0.58 ± 0.18 -0.58 ± 0.18 -0.51% -0.58 ± 0.18 -0.61% -0.58 ± 0.18 -0.03% -0.52 ± 0.18 -0.51 ± 0.18 -2.71% -0.51 ± 0.18 -3.36%
44 -0.27 ± 0.07 -0.28 ± 0.07 1.42% -0.27 ± 0.07 0.62% -0.28 ± 0.07 2.42% -0.28 ± 0.07 -0.28 ± 0.07 0.89% -0.27 ± 0.07 -0.92%
45 -0.34 ± 0.12 -0.36 ± 0.12 4.05% -0.36 ± 0.12 4.44% -0.34 ± 0.12 -0.65% -0.33 ± 0.12 -0.31 ± 0.12 -5.25% -0.32 ± 0.12 -3.23%
46 0.1 ± 0.12 0.1 ± 0.12 0.14% 0.1 ± 0.12 -0.42% 0.1 ± 0.12 -0.61% 0.14 ± 0.12 0.15 ± 0.12 7.55% 0.15 ± 0.12 7.26%
47 -0.32 ± 0.14 -0.32 ± 0.14 -0.11% -0.32 ± 0.14 -0.28% -0.32 ± 0.14 -0.04% -0.34 ± 0.14 -0.33 ± 0.14 -2.76% -0.33 ± 0.14 -2.74%
48 0.15 ± 0.06 0.15 ± 0.06 -0.16% 0.15 ± 0.06 0.3% 0.15 ± 0.06 0.04% 0.14 ± 0.06 0.14 ± 0.06 1.07% 0.14 ± 0.06 0.47%
49 0.06 ± 0.16 0.06 ± 0.16 6.29% 0.06 ± 0.16 3.15% 0.06 ± 0.16 -1.29% 0.12 ± 0.16 0.14 ± 0.16 20.34% 0.14 ± 0.16 19.94%
50 -0.56 ± 0.13 -0.56 ± 0.13 0.15% -0.56 ± 0.13 -0.23% -0.56 ± 0.13 0% -0.54 ± 0.13 -0.54 ± 0.13 -0.75% -0.53 ± 0.13 -1.58%
Land -3.93 ± 0.67 -3.9 ± 0.67 -0.57% -3.9 ± 0.67 -0.56% -3.91 ± 0.68 -0.34% -4.13 ± 0.66 -4.29 ± 0.65 3.77% -4.29 ± 0.66 3.84%
Oceans -1.67 ± 0.37 -1.69 ± 0.37 1.32% -1.68 ± 0.37 1.03% -1.68 ± 0.37 0.78% -1.52 ± 0.38 -1.39 ± 0.37 -8.56% -1.37 ± 0.37 -9.61%
Total -5.59 ± 0.75 -5.59 ± 0.75 -0.01% -5.59 ± 0.75 -0.09% -5.59 ± 0.76 -0.01% -5.65 ± 0.75 -5.67 ± 0.74 0.45% -5.66 ± 0.75 0.22%
*represents regions with SNR > 1 1+ve percentage change, Δ%, represents increase in uptake/release
45
4.2.1 Seasonal variation
The timings of the CO2 uptake and release from croplands are very important, as
different crops differ in their growth patterns. Furthermore, annual inverted fluxes are largely
affected by the seasonal fluxes due to the rectifier effect (Denning et al., 1995; Gurney, 2004).
The growth patterns of crops have large impacts on the atmospheric CO2 concentration (Corbin
et al., 2010). In this research, the a priori seasonal variations for croplands are based on the
BEPS which calculates seasonal fluxes based on remotely sensed LAI. Figure 4-7 and Figure
4-8 show the monthly a priori and inverted CO2 fluxes from 2002 to 2007 for regions of high
crop production and high crop consumption in the US.
In regions of high crop production (regions 20 and 21) the inverted monthly fluxes with
agricultural adjustments show higher uptake during the peak growing season of June, July and
August and a stronger release of during the non-growing season in October and November. The
months of March and April show a net uptake in the CO2 inverted fluxes of agriculturally
adjusted experiments in the US Midwest (region 20) instead of a CO2 release shown in the
control experiments or the a priori. In regions of high crop consumption with low vegetation
(regions 23 and 24), the impacts of crop consumption are most visibly seen in the inverted
fluxes, showing a consistent source of CO2 throughout the months. In the forests in the US
Southeast with high crop consumption (region 28), crop production experiments (Experiment
1b, 2b) and crop consumption experiments (Experiment 1c, 1d, 2c) all have an impact on the
size of the CO2 uptake during the growing season and during non-growing seasons.
Although changes in the monthly inverted fluxes are observed when adjusting for crop
production and crop consumption, the changes are mainly observed as changes in the magnitude
instead of the timing of the growing seasons. This shows the seasonal pattern of the inverted
CO2 fluxes to generally follow the seasonal trends of the a priori fluxes. In our method of US
cropland carbon adjustment, annual cropland census data are being used instead of actual
cropland seasonal variations. Therefore, these results are subject to certain uncertainties due to
the extrapolation of annual cropland CO2 fluxes into hourly inputs used in the atmospheric
inversion methodology. Furthermore, the spatial and temporal correlations between US regions
may also affect the observed changes in the seasonal fluxes.
46
Figure 4-7 – Monthly inverted (solid lines) and prior (dashed lines) CO2 flux (-ve represents uptake) averaged over 2002 to 2007 for Experiments
1 – annually balanced terrestrial prior fluxes with (a) no adjustments – blue; (b) production adjustments – red; (c) crop production adjustments and
consumption as additional source – green; and (d) crop production and consumption adjustment – purple.
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 20 – US Midwest source
sink -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 21 – US Midwest source
sink
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 22 – US Northeast source
sink -0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 23 – US West source
sink
47
Figure 4-7 (cont.) – Monthly inverted (solid lines) and prior (dashed lines) CO2 flux (-ve represents uptake) averaged over 2002 to 2007 for
Experiments 1 – annually balanced terrestrial prior fluxes with (a) no adjustments – blue; (b) production adjustments – red; (c) crop production
adjustments and consumption as additional source – green; and (d) crop production and consumption adjustment – purple.
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 24 – US West source
sink -0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 26 – US South source
sink
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
J F M A M J J A S O N D
CO
2 f
lux
in P
g C
yr-1
Month
Region 27 – US South source
sink -0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
J F M A M J J A S O N D
CO
2 f
lux
in P
g C
yr-1
Month
Region 28 – US South source
sink
48
Figure 4-8 – Monthly inverted (solid lines) and prior (dashed lines) CO2 flux (-ve represents uptake) averaged over 2002 to 2007 for Experiments
2 – annually varying terrestrial prior fluxes with (a) no adjustments – blue; (b) production adjustments – red; (c) crop production and consumption
adjustments – green.
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 20 – US Midwest source
sink -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 21 – US Midwest source
sink
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
J F M A M J J A S O N D
CO
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ux
in P
g C
yr-1
Month
Region 22 – US Northeast source
sink -0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 23 – US West source
sink
49
Figure 4-8 (cont.) – Monthly inverted (solid lines) and prior (dashed lines) CO2 flux (-ve represents uptake) averaged over 2002 to 2007 for
Experiments 2 – annually varying terrestrial prior fluxes with (a) no adjustments – blue; (b) production adjustments – red; (c) crop production and
consumption adjustments – green.
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 24 – US West source
sink -0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
J F M A M J J A S O N D
CO
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ux
in P
g C
yr-1
Month
Region 26 – US South source
sink
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 27 – US South source
sink -0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
J F M A M J J A S O N D
CO
2 fl
ux
in P
g C
yr-1
Month
Region 28 – US South source
sink
50
It is important to take into account the spatial and temporal correlations between the US
regions to determine its impacts on the observed changes in seasonal CO2 fluxes. If the CO2
fluxes between two regions are spatially and temporally correlated, this means that changes in
the flux in one region during a certain month may be responsible for changes in another region
during another month. In the seasonal inverted flux results, the peak growing season (July) in
region 20 shows the largest difference between the crop adjusted experiments and the control
experiment. Figure 4-9 shows the correlations between the flux in a production region (20)
during July with the fluxes from other US regions and months. The correlations values are
taken from the off-diagonal terms in the posterior uncertainty matrix, Q̂ . The results show that
region 20 during July is strongly correlated to some of the other US regions during other months
such as the November flux in region 26, the February flux in region 25 and the July flux of
region 21. Although there are strong correlations between these regions and the production
region (20), the other above mentioned regions do not show significant differences between the
cropland adjusted inverted fluxes and the control inverted fluxes in those months.
Figure 4-9 – Graph showing the correlation between the US Midwest (region 20) flux during July and
the fluxes in other regions during other months of the year.
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Flu
x co
rre
lati
on
Month
Correlations between US Midwest (region 20) July flux and other regions
18 19 20 21 22 23 24 25 26 27 28 Region:
51
4.3 Discussion
In this research, the US cropland carbon including the crop production and consumption
are taken into account when performing atmospheric inversion. Although the cropland carbon
data are calculated based on censuses which are on the annual timescale, the information is
fitted into hourly trends and incorporated in the prior fluxes used for atmospheric inversion.
Errors may be introduced when using this technique as the seasonal trend for croplands is only
given by the simulated pattern from BEPS instead of information from the cropland inventory
data. Therefore, the seasonal trends of the cropland may be incorrectly represented in the prior
fluxes. There is a tradeoff between the uncertain rectifier effect in the northern regions and the
poor tropical data constraint inducing compensating fluxes (Gurney et al., 2003). The results
show that by integrating cropland carbon data into the prior fluxes, changes are found in the
local CO2 source and sink sizes, and the spatial patterns of the US carbon budget, as well as in
the regional and global CO2 flux distributions. While Gurney et al. (2003) suggested that in
regions of strong data constraint such as North America, inverted fluxes are insensitive to prior
fluxes, significant changes were observed in the inverted fluxes when cropland adjustments
were made in the prior fluxes.
The impacts of integrating US crop production data shows the US Midwest to be a large
annual CO2 sink from 2002 to 2007. This is mainly due to the large uptake of CO2 during the
crop growing season (Peters et al., 2007). In showing the release of the CO2 from the harvested
crops in regions of high crop consumption by human and livestock, a weakening of the US
Southeast forest sink is observed; hence, the US Midwest is perceived by the “atmospheric
view” as the dominant sink in North America. While the croplands in the US Midwest take up
large amounts of carbon during the growing season, a large portion of it is also released during
the same year when the crops are harvested hence it is difficult to consider it a consistent CO2
“sink” as compared to US forests. In the West Coast near California, where there is high human
and livestock consumption, an overall CO2 source is obtained from the inversion. With the
incorporation of US cropland carbon data, the main US sink is redistributed from the US
Southeast forested region into the US Midwest cropland. The redistribution is shown in the
results for two sets of experiments. Experiment 1, which gives larger weights to the influence of
atmospheric CO2 observation than to the prior terrestrial flux, show the sink in the US Midwest
52
to be larger than the sink in the US Southeast, whereas Experiment 2, which gives larger
weights to the prior terrestrial flux, show the US Southeast forested region to be as dominant a
sink as the US Midwest. While the differences in these experiments show that there are still
discrepancies between the top-down atmospheric and the bottom-up surface approach,
agricultural inventory data are found to be a useful tool in reconciling some of the differences.
The overall size of the US and North American sink are also observed to have weakened
by ~4% and ~6.5% when the cropland carbon adjustments are made. Furthermore, regions
outside of the US are shown to be also affected by these changes. The Canadian carbon sinks
show noticeable weakening. The sources and sinks of other regions outside of North America,
which are not as well constrained, also show noticeable changes when crop consumption is
adjusted for in the prior fluxes. While this may be because of the additional error estimates used
in the uncertainty matrix of the prior fluxes, another explanation is the leakage of CO2 flux
information into regions outside of the adjusted region due to the poor constraints on the larger
regions (Gurney, 2004). While not conclusive, this phenomenon of leakage should urge further
investigation into the ability of atmospheric CO2 measurements to accurately capture the local
changes in CO2 uptake and release without proper a priori flux constraint.
During the period from 2002 to 2007, the annual mean crop production and crop
consumption over the contiguous US based on West et al. (2011) was ~0.27 Pg C yr-1
and ~0.24
Pg C yr-1
, respectively, resulting in the net uptake of US croplands to be approximately 0.03 Pg
C yr-1
. In the US Midwest, the inverted results with agricultural adjustments show a large sink
of 0.36 ± 0.13 Pg C yr-1
. Assuming the cropland carbon data to be relatively accurate, 0.27 Pg C
yr-1
of the sink is should be contributed by cropland meaning that the remaining small CO2 sink
of ~0.09 Pg C yr-1
is contributed by other vegetation types in the US Midwest.
The US Midwest sink is 0.17 Pg C yr-1
smaller if cropland adjustments are not taken into
account. This underestimation is relatively large as it is approximately 63% of the total annual
crop production in the US (West et al., 2011). This suggests that the NEP simulations from the
Boreal Ecosystem Productivity Simulator (BEPS) underestimate the processes that relate to
cropland CO2 uptake.
53
US West and the US southeast, being regions of strong crop consumption, show a
combined 0.16 Pg C yr-1
weakening of the sink. However, in comparing this to the source
estimated from the total annual crop consumption averaged over 2002 to 2007 (~0.24 Pg C yr-1
based on West et al. (2011)), approximately 33% of the emissions from crop consumption are
not captured in the inverted fluxes of the high consumption regions.
Using atmospheric inversion techniques over North America, Peters et al. (2007) show
the US Midwest to be the major sink in the US and the US Southeast forested region to be either
carbon neutral or a source from 2002 to 2007. In this research where the a priori fluxes take
into account crop production and consumption, the US Midwest is also shown to be a large CO2
sink. However, the US Southeast forested region in is found to be a carbon sink of 0.16 ± 0.12
Pg C yr-1
in the same period. Possible explanations for this difference may be understood by
carefully investigating the US cropland carbon budget presented by West et al. (2011). The
main components of the US cropland carbon budget presented by West et al. (2011) are the crop
production and consumption. However, there is also a significant portion of the crop products
being exported outside of the US. While this research only adjusts for domestic crop production
and consumption in the a priori, the inverted CO2 fluxes show changes globally. The changes
globally may be attributed to the export of crop products being observed in the atmospheric
measurements. Ciais et al. (2007) shows the importance of this lateral transport of carbon
internationally. In the study by Peters et al. (2007), the atmospheric inversion is performed
regionally over North America. If carbon is transported out of the region of interest (North
America) by means of US crop exports, then the loss of carbon is compensated within the region
of interest. Given that the US Midwest is observed as the main carbon sink over North America
in Peters et al. (2007), the compensating regions for the exported fluxes will be found in other
regions such as the US Southeast forested area, resulting in an overall multi-year balanced
regional carbon budget. In this research, however, global atmospheric inversion is performed,
meaning the effect of exports is being observed over regions outside of North America which
are poorly constrained by atmospheric CO2 data. Firstly, the US Midwest sink as found in this
research is greater than the crop production amount based on accurate inventory data. Secondly,
the weakening of the sinks in the US West and Southeast amounts to less CO2 release than the
inventory crop consumption amount. These two findings suggest that the atmospheric view in
this research is capturing signals from components of the US cropland carbon cycle other than
54
crop production and consumption. The US cropland exports seem to be observed by the
atmospheric view, as suggested by the leakage of information, and the impacts of other
noticeable components in the US cropland carbon budget may also be captured by the
atmospheric view.
While the use of census-based cropland carbon data is cautioned due to their potentially
large uncertainties (Chan & Lin, 2011), the research shows that agricultural statistical data give
valuable information on the spatial patterns and the size of the surface CO2 flux. Cropland
carbon data from agricultural census and atmospheric CO2 concentrations, when used in
combination, are shown to be able to constrain the simulated prior terrestrial CO2 flux and can
suggest areas of improvement in the TBMs. This research shows that for managed land cover
types such as croplands, where the carbon uptake and release are not simply determined by
biospheric processes, TBMs should not be the only tool used for generating prior terrestrial
surface CO2 fluxes (Ciais et al., 2007). Inventory data, such as agricultural statistics, are shown
in this research to have great potential in giving robust estimates of the regional carbon budget
over the US and North America. However, to more effectively constrain surface carbon fluxes,
a method will need to be developed to simulate seasonal and diurnal variations of crop growth
and the specific timing of crop harvest.
55
Chapter 5 Summary
5 Summary
Using atmospheric inversion techniques, Peters et al. (2007) showed the US Midwest
cropland to be the main carbon sink in the US. They explained that this is due to the system’s
“atmospheric view” that does not capture the lateral transport of cropland carbon. Ciais et al.
(2007) show globally the importance of incorporating the lateral transport of crop products in
global carbon accounting using the atmospheric inversion techniques. This thesis investigates
the impacts of lateral transport of crop products in the US towards the regional carbon budget in
the US and North American as well as the global carbon budget. The US cropland carbon
budget, in which the major components are crop production and crop consumption, was taken
from West et al. (2011) and integrated into the prior flux used in a time-dependent Bayesian
inversion of atmospheric CO2. The specific objectives of this thesis were: 1) integrate US
production and consumption inventory data into constraining prior flux used in atmospheric
inversion; 2) reconcile the discrepancy in the large sink found in the US Midwest from the
“atmospheric view” and; 3) provide a robust view of the lateral movement of US cropland
carbon and its impacts on regional and global carbon budgets. The main findings of this
research and future work are summarized below:
1. Inventory cropland carbon data are helpful in reconciling the spatial differences
between the top-down and the bottom-up modeling results. Peters et al. (2007)
found the US Midwest to be a large CO2 sink while the forested area in the US southeast
to be a weak sink or small source. In taking into account for crop production and
consumption patterns, the US Midwest is observed to be a large CO2 sink from our
“atmospheric view”, i.e. through atmospheric inversion. The large sink is observed
because there is large CO2 uptake during the crop growing season. The US Southeast
forested regions which are believed to be large CO2 sinks are also regions with CO2
sources due to a large amount of crop consumption by livestock. Therefore, the net CO2
flux observed by the atmosphere will show a weaker sink in the US Southeast forested
regions. Given the spatial discrepancies of CO2 fluxes between the top-down and
bottom-up approaches, we are still unable to confidently identify whether the major sink
56
contribution towards the annual mean CO2 flux is in the forests or in the croplands.
However, the usage of inventory data as suggested also by Hayes et al. (2012) shows
potential in reconciling top-down and bottom-up approaches. Furthermore, Ciais et al.,
(2007) suggest that simply forcing the prior fluxes in inversions to follow spatial patterns
of NPP is not compatible with regional patterns of CO2 source and sinks from crop
product displacement. Our results agree with this suggestion.
2. Cropland harvest, lateral transfer and consumption are important processes to
include when simulating continental scale terrestrial CO2 fluxes in the bottom-up
approach. The CO2 sinks found in US cropland areas are shown to be underestimated
in terrestrial biosphere models as suggested by comparing the prior fluxes with the
posterior fluxes. As various terrestrial biosphere models are being further developed to
include the influence of disturbance, the cropland harvest dynamics and the spatial
pattern of crop consumption would be important processes to consider.
3. The current agricultural statistics data are limited by the temporal resolution,
which can potentially lead to large errors. Seasonal and diurnal variations have large
impacts on the inverted CO2 fluxes (Deng & Chen, 2011; Gurney, 2004) due to the
rectifier effect (Denning et al., 1995). Without taking into account the accurate growing
season of crops, the inversion results may be subject to large errors. In using cropland
carbon data for reconciling regional carbon budgets, accurately simulated or observed
seasonal and diurnal patterns for CO2 uptake and release for crops will further help
improve the use of census crop production data as an additional constraint to the
atmospheric inversion.
4. A denser global network of CO2 measurement stations is needed to more accurately
constrain the North American carbon budget. Although, not conclusive, there seems
to be leakages of the CO2 flux from the US into other regions around the globe as
suggested also by other studies (Gurney, 2004). The reliability of the measurement
stations in capturing local changes in the CO2 flux needs to be investigated. Moreover, a
denser network of measurement stations or usage of satellite data in poorly constrained
areas such as the tropics can further help constrain the inverted CO2 fluxes over North
57
America. In comparing this research with the results from Peters et al. (2007), we have
shown that the global carbon budget can potentially have large impacts on regional
carbon budgets. Therefore, a dense global network of accurate atmospheric CO2
measurements contributes greatly to our understanding of important processes that relate
regional carbon budgets with global carbon budgets such as the lateral transport of
carbon through crop exports.
5. Inverted fluxes are sensitive to changes in the cropland carbon adjustments in a
priori fluxes. While Gurney et al. (2003) suggests that inverted fluxes are insensitive to
small changes in the a priori fluxes, this research shows that cropland carbon
adjustments made in the a priori show changes in the inverted fluxes that are larger than
the system errors. This shows that inverted CO2 fluxes are sensitive to changes
introduced by integrating the cropland carbon budget. Although West et al. (2011) show
the annual regional cropland carbon budget to be balanced, the spatial patterns of the
individual components of crop production and crop consumption show significant uptake
and release. In correcting the a priori fluxes, the posterior fluxes show high sensitivity
towards the crop production and consumption patterns.
Although this research did not fully reconcile the differences between the top-down and bottom-
up approach, it improved our understanding of the US carbon budget and the relative impacts of
different cropland processes. This thesis presents a method in which inventory cropland data
can be used as a tool to constrain regional carbon flux inversion. It also showed the sensitivity
of atmospheric inversion towards cropland carbon data. Advancements were made in
reconciling the large US cropland sink observed in the “atmospheric view” presented by (Peters
et al., 2007) and these findings would be of interest to the broader scientific community such as
the North American Carbon Program (NACP).
58
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