PRODUCTION AND MOVEMENT OF N2O IN THE FULL SOIL PROFILE
By
Iurii Shcherbak

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Crop and Soil Sciences - Doctor of Philosophy
2013

ABSTRACT
PRODUCTION AND MOVEMENT OF N2O IN THE FULL SOIL PROFILE
By
Iurii Shcherbak
Nitrous oxide (N2O) is a major greenhouse gas and cultivated soils are the dominant
anthropogenic source. In this dissertation, I examine some aspects of N2O where knowledge is
lacking: diffusion of N2O through the soil profile; production of N2O in soils below the A or Ap
horizon in relation to irrigation, tillage, and fertilization; and patterns of N2O response to
nitrogen (N) fertilizer rate.
In Chapter 2, I measure diffusion by comparing single and inter-port diffusivity
determinations using sparse sampling after sulfur hexafluoride (SF6) and N2O tracer injections at
Kellogg Biological Station in SW Michigan. In general, the sparse method provided accurate
measurements of soil diffusivity. Injection port diffusivities of SF6 and N2O had poorer
agreement in the summer (r2=0.49) than in the fall (r2=0.96), likely due to less uniform soil
moisture in summer. The low N2O to SF6 diffusivity ratio (0.67 compared to 1.82 in free air)
suggests that water solubility of N2O plays a significant role in retarding its movement in the
soil. Movement of SF6 is not obscured by dissolution in water, making SF6 a superior tracer
compared to N2O. Results show it is possible to estimate N2O diffusivity with sparse
measurements; accuracy can be improved with knowledge of soil moisture and texture in the
immediate vicinity of the ports.
In Chapter 3, I estimate the influence of crop and management practices on subsoil N2O
production in intensively managed cropping systems in a series of experiments also at KBS. N2O
concentrations showed a saturating increase with depth except immediately after fertilization and

in the winter when concentrations were highest in the surface horizon. Variability of N2O
concentrations declined with depth, in agreement with more constant soil conditions. Total N2O
fluxes from direct measurements and estimates by the concentration gradient method showed
good agreement, with correlations ranging from 0.55-0.73. N2O production in subsoil horizons
as estimated from concentration gradients is significant, with over 50% of total N2O produced in
moderately fertilized rainfed treatments. In highly fertilized sites where added N exceeded plant
N requirements only a small fraction of total N2O was produced in lower horizons. Dry
conditions deepened the maximum N2O production depth. Results show that the fraction of total
N2O produced in subsoil is controlled by the N and moisture status of the soil profile.
Knowledge of a more precise fertilizer N2O emission response could improve global and
regional N2O assessments and help to design more efficient mitigation strategies. Evidence now
suggests that the emission response is not linear, as assumed by IPCC methodologies, but rather
exponentially increases with fertilization. In Chapter 4, I performed a meta-analysis to test the
generalizability of these findings. I selected published studies with at least three N fertilizer rates
otherwise identical. From 78 available studies (231 site-years), I calculated the change in N2O
emission factors (ΔEFs) as the change in the percentage of applied N converted to N2O
emissions. I found that ΔEF grew with N additions for synthetic fertilizers, for a majority of the
crop types examined, and for soils with high organic carbon content, low mean annual
temperatures, or low pH. Nitrogen-fixing crops had a significantly higher ΔEF than non-fixing
crops. My results suggest a general trend of exponentially increasing N2O emissions as N
fertilizer rates increase to exceed crop N needs. Use of this knowledge in global and regional
greenhouse gas inventories could provide a more accurate assessment of fertilizer-derived N2O
emissions and help further close the global N2O cycle.

ACKNOWLEDGMENTS

I thank my adviser Dr. G. Philip Robertson for guidance through this dissertation work.
His patience and constructive criticism helped me withstand the pressures of graduate work and
see this project to completion. I am also grateful to my committee members, Bruno Basso,
Stephen K. Hamilton, Alexandra N. Kravchenko, for many helpful discussions of experimental
design and other suggestions on early drafts. I thank faculty colleagues and fellow graduate
students for invaluable discussions and feedback during the development of the experiments and
analysis. I am grateful to Kevin Kahmark, Stacey VanderWulp, Cathy McMinn, Leilei Ruan, and
Sven Bohm for suggestions on analytical techniques, help with building equipment, sampling,
and laboratory analyses. I thank Joe Simmons for agronomic management advice and guidance. I
thank Jane Schuette and Volodymyr Shcherbak for help with figure preparation. I thank Melissa
Yost for help in acquiring and Leilei Ruan for help with Chinese translations of primary papers
for Chapter 4. Funding was provided by the US National Science Foundation Doctoral
Dissertation Improvement Grant (DEB 1110683), Long-term Ecological Research (DEB
1027253), and Graduate STEM Fellows in K-12 Education (DGE 0538509) programs, the US
DOE Office of Science (DE-FCO2-07ER64494) and Office of Energy Efficiency and Renewable
Energy (DE-ACO5-76RL01830), and MSU AgBioResearch.

iv

TABLE OF CONTENTS

LIST OF TABLES

vii

LIST OF FIGURES

viii

CHAPTER 1
Thesis Introduction
SUBSOIL DENITRIFICATION
NONLINEARITY OF N2O EMISSIONS WITH N INPUT
REFERENCES
CHAPTER 2
Determining the Diffusivity of Nitrous Oxide in Soil Using In Situ Tracers
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
Site description
Soil Profile Gas Sampling
Nitrous oxide consumption in the soil
Tracer injection and data collection
Diffusivity calculations
RESULTS
N2O Consumption Experiment
Field experiments
DISCUSSION
N2O consumption
Diffusivity of a relatively soluble gas
Diffusivities measured by SF6 and N2O tracers
Diffusivities of rainfed and irrigated treatments
Single-port vs. inter-port diffusivities and comparison with
models
CONCLUSION
REFERENCES
CHAPTER 3
The Importance of Subsoil N2O Production in Response to Tillage, Fertilizer
and Irrigation Effects at a Site in Michigan USA
ABSTRACT
INTRODUCTION
METHODS
Site description
v

1
2
4
8

11
11
12
15
15
16
17
18
20
23
23
24
25
25
26
27
28
29
30
42

47
47
47
52
52

Experimental Approach
Monolith Lysimeters Experiment
Soil profile gas probes
N2O surface flux and N2O production by depth
RESULTS
Monolith Lysimeters Experiment
LTER Resource Gradient Experiment
LTER Main Cropping System Experiment
DISCUSSION
Patterns of N2O concentrations with soil depth
Predicting soil N2O fluxes to the atmosphere from profile N2O
concentrations and diffusivity
The contribution of different soil depths to seasonal N2O fluxes
CONCLUSION
REFERENCES

52
53
55
57
58
59
59
60
61
61
62
63
65
76

CHAPTER 4
A Meta-analysis of the Nonlinearity of Direct Annual N2O Emissions in
Response to Nitrogen Fertilization
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
Study Selection and Data Extraction
Emission Factor Change Rates (∆EFs)
Analysis
Comparison with previous studies
RESULTS
DISCUSSION
REFERENCES

81
81
82
85
85
86
86
88
88
91
105

APPENDICES
APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D

110
111
118
127
131

vi

LIST OF TABLES

Table 1.1. Summary of annual denitrification rates in agricultural soils (from Barton et al.
1999).

6

Table 2.1. Relative soil gas diffusivity (Dp/Do) models following the Buckingham–Currie
power-law function. Model references are as compiled in Jassal et al. (2005),
Resurreccion et al. (2010), and Blagodatsky and Smith (2012).

32

Table 2.2. Kellogg Biological Station Long-Term Ecological Research Site soil textures
(Kalamazoo and Ostemo Series). Texture is based on % of fraction less than 2 mm
(from Crum and Collins 1995). pH values assume no liming is performed at the
site.

33

Table 3.1. Horizon depths in the Monolith Lysimeters of Kalamazoo loam soil at KBS
(From Aiken 1992). Monolith Lysimeter labels refer to Figure 3.1.

66

Table B.1. Mean and median ΔEF values for different site-year groups by various
experimental and sampling factors with the respective standard errors.

118

Table B.2 a. T-test results for paired differences between mean ΔEF groups by crop.

120

Table B.2 b. T-test results for paired differences between mean ΔEF groups by N fertilizer
type.

120

Table B.2 c. T-test results for paired differences between mean ΔEF groups by
experimental factors.

121

Table B.2 d. T-test results for paired differences between mean ΔEF groups by sampling
factors.

121

Table B.3 a. Experimental factor associations in contingency tables.

122

Table B.3 b. Sampling factor associations in contingency tables.

122

Table B.4. Locations for the studies included in the analysis.

123

Table B.5. Variables collected in Dataset S2.

126

vii

LIST OF FIGURES

Figure 1.1. Major controls on denitrification from cellular (right) to landscape scales.
(From Robertson, 2000).

7

Figure 2.1. Soil profile gas probe with ports at 12, 24, 36, 60, and 90 cm depths. Diameter
of the probe is 6.4 mm and not shown to scale. For interpretation of the references
to color in this and all other figures, the reader is referred to the electronic version
of this dissertation.

34

Figure 2.2. Replicate (top view) consists of 7 soil profile gas probes arranged in 2
equilateral triangles with 90 cm sides and an additional injection sampler. Values
above probes indicate port used for gas injection (in addition to sampling).
Unmarked probes were used for sampling only.

35

Figure 2.3. Mean N2O to SF6 ratio over time in summer and fall microcosm experiments.
Only microcosms retaining more than 60% of original SF6 have been retained.
Error bars are lower and upper boundaries of the 95% confidence interval for the
median.

36

Figure 2.4. Comparison of SF6 and N2O diffusivities. Each replicate observation is a
separate point. Straight line is the regression line with best slope through the
origin.

37

Figure 2.5. SF6 and N2O diffusivities modeled for ports used for injections. SF6 is in the
left column and N2O is in the right column. Treatments are Rainfed and Irrigated.
Within each treatment there are values for 5 experimental dates arranged
chronologically: June 20, June 27, July 03, October 29, and November 1. Only
diffusivities with r2 above 0.85 for SF6 and 0.6 for N2O are included.

38

Figure 2.6. Comparison of SF6 diffusivities obtained from simulations involving only
ports used for tracer injections with a) corresponding diffusivities for the ports
used to inject tracers when diffusivities at other ports are taken into account
(r2=0.99) and b) median diffusivities for ports at the same depth that were not used
to inject tracers (r2=0.45).

39

Figure 2.7. Poor fit of common diffusivity models with measured SF6 diffusivity in this
study. Lines are models that best fit: Penman 1940 (Pn), Millington 1959 (Ml), and
Millington-Quirk 1961 (MQ).

41

Figure 3.1. Diagram of field plots established at the Kellogg Biological Station in 1986 to
investigate N supply and tillage effects on soil-plant interactions. Intact-profile

67

viii

monolith lysimeters are located in plots 2, 6, 9, and 13 (From Aiken 1992).
Figure 3.2. Schematic diagram of monolith lysimeter with instrumentation ports for
nondestructive sampling of soil atmosphere, soil solution, soil moisture, and soil
temperature. All units are in cm.

68

Figure 3.3. Schematic representation (top view) of nondestructive probes in a soil profile
layer in a monolith lysimeter.

69

Figure 3.4. Soil profile gas probe installed at 60° angle with sampling depths at 10, 20,
30, 50, and 75 cm (from Shcherbak and Robertson, in press).

70

Figure 3.5. Mean seasonal N2O concentration profiles observed in the experiments.
Atmospheric concentration is 0.38 ppmv. a) Tilled and no-till Monolith Lysimeters
treatments. b) Rainfed and irrigated Resource Gradient Experiment treatments. c)
Poplar, Alfalfa, Early-successional community, and Mown grassland (never tilled)
systems of the LTER Main Cropping System Experiment (MCSE).

71

Figure 3.6. Average temporal autocorrelations of concentrations at different depths and
temporal autocorrelation of surface fluxes of N2O. Autocorrelations close to one
indicate N2O concentrations (or fluxes) with low temporal variability, whereas
autocorrelations close to or below zero indicate highly variable and unstable
values. a) Tilled and no-till Monolith Lysimeter treatments. b) Rainfed and
irrigated and Resource Gradient Experiment treatments.

72

Figure 3.7. Change in correlation between N2O surface fluxes and soil N2O
concentrations with distance between measurement depths for rainfed and
irrigated Resource Gradient Experiment treatments. Each point represents a
correlation of N2O concentrations at two different depths in 2011 vs. absolute
differences between the depths.

73

Figure 3.8. Comparison of total seasonal N2O emissions measured by static or automatic
chamber method and modeled from N2O concentration and diffusivity at 10 cm
depth. a) Tilled and no-till Monolith Lysimeter treatments. b) Rainfed and irrigated
Resource Gradient Experiment treatments. c) Poplar, Alfalfa, Early-successional
community, and Mown grassland (never tilled) systems of the LTER MCSE.

74

Figure 3.9. Annual relative N2O production by depth as calculated from concentrations
and modeled diffusivity. a) Tilled and no-till Monolith Lysimeter treatments. b)
Rainfed and irrigated Resource Gradient Experiment treatments with rate of N
input (0-246 kg N ha-1) indicated next to the treatment. c) Poplar, Alfalfa, Earlysuccessional community, and Mown grassland (never tilled) systems of the LTER
MCSE.

75

Figure 4.1. Locations for the studies included in the analysis.

97

ix

Figure 4.2. Histogram of emission factor change rates (∆EFs) that indicate percentage of
EF change per 1 additional kg N ha-1 of fertilizer input. Zero, positive, and
negative ∆EFs indicate, respectively, a linear, faster-than-linear, and slower-thanlinear rate of N2O emissions increase with N input. ∆EFs < -0.02 are not shown
for clarity.

98

Figure 4.3. Mean ∆EF with standard errors by type of a) crop, b) fertilizer type, and c)
other experimental factors. *, **, and *** indicate difference from 0 at p=0.05,
0.01, and 0.001, respectively. Different letters indicate significant differences
between mean ∆EFs for groups of site-years by particular factor.

99

Figure 4.4. a) Comparison of IPCC 1% linear emission model, the Hoben et al. (2011)
model, and a model of average upland grain crop emissions from the current metaanalysis; and b) Relative N2O emission reductions for the three models when N
application rates are reduced by 50 kg ha-1 from three baseline N fertilization
scenarios: 200, 150, and 50 kg N ha-1.

102

Figure 4.5. Comparison of uncertainties between IPCC Tier 1 (1%), and range of six
models from Philbert et al. (2012) and mean quadratic model for all site years
without N-fixing crops and the bare soil site. Each of the three models is presented
with 95% CI range across 0-300 kg N ha-1 fertilizer input. IPCC Tier 1 95% CI is
0.3-3%. Philbert et al. (2012) 95% CI for model uncertainty is included with and
without parameter uncertainty.

104

Figure A.1. Daily precipitation measured at Kellogg Biological Station Long-Term
Ecological Research Site for 2011.

111

Figure A.2. Average daily soil moisture content for 0-25 cm depth in rainfed (Rain) and
irrigated (Irr) treatments of the N fertilizer gradient site in 2011.

112

Figure A.3. Mean daily soil temperature at 10 cm depth (Soil) and air temperature (Air)
and N fertilizer gradient site in 2011. Differences between rainfed and irrigated
treatments are less than 1 °C.

113

Figure A.4. N2O concentration profile in Resource Gradient Experiment Irrigated
treatment with 101 kg N ha-1 input rate on DOY 172 in 2011.

114

Figure A.5. N2O concentration profile in Monolith Lysimeter Conventional Tillage
treatment with in plot CT6 on DOY 66 in 2011.

115

Figure A.6. Temporal autocorrelation with depth of modelled water content for days of
N2O concentration measurements in Monolith Lysimeter No Till treatment in plot
CT6 in 2011.

116

Figure A.7. Temporal autocorrelation with depth of modelled soil temperature for days of

117

x

N2O concentration measurements in Monolith Lysimeter No Till treatment in plot
CT6 in 2011.
Figure C.1. Effect of nitrogen (N) input rate on total N2O emissions and emission factors
(EFs) for a) linear, b) slower-than-linear, and c) faster-than-linear response type.

127

Figure C.2. ∆EF plotted against mean EF for each site-year in meta-analysis. Best linear
regression line is plotted ∆𝐸𝐹 = −0.00045 + 0.0024𝐸𝐹. Standard error of the
linear parameter is 0.0003.

128

Figure C.3. Graph of mean ∆EF by type of sampling factor.

129

Figure C.4. Relationship between ∆EF and adjusted r2 of the quadratic function fit is
absent.

130

xi

CHAPTER 1
Thesis Introduction
Nitrogen has the most complex biogeochemical cycle of all the elements essential for life.
Since the last century, natural rates of active nitrogen fixation have been severely distorted by
human activity. In particular, industrial fixation via the Haber-Bosch process and the cultivation
of leguminous crops have added to the biosphere 150 Tg yr-1 in additional inputs of reactive
nitrogen (Robertson and Vitousek 2009). Almost all pathways within the nitrogen cycle have
been drastically changed through additions of biologically active nitrogen (e.g. nitrate,
ammonia), which makes it even more difficult to quantify the fate of nitrogen inputs. Vitousek et
al. (2009) note that one of the major constraints to reducing this uncertainty is the scarcity of
farm-scale nitrogen budgets. Galloway (2004) points out that the relative importance of storage
versus the production of N2 via denitrification is arguably the largest uncertainty that exists for
nitrogen budgets at almost any scale.
Denitrification represents one of the major pathways that active nitrogen leaves the site of
application, along with leaching, volatilization, and runoff, and is the major process in soils
capable of returning nitrogen to its inert form of dinitrogen (N2) gas (Robertson and Groffman
2014).
Denitrification flux rates are extremely variable due to their dependency at many levels
on temporally and spatially variable factors (Table 1.1). Microsite, field, and regional factors are
usually considered (Robertson 2000 and Figure 1.1). Microsite level factors include soil
temperature, redox status (soil moisture or oxygen concentration are usually used as proxies for
this factor), nitrate, and soluble organic carbon concentrations. Field scale factors are agricultural
practices and soil type. Regional factors are represented by temperature and moisture regimes.
Denitrification releases two long-lived components to the atmosphere: N2 and nitrous
1

oxide (N2O). N2 is an inert gas comprising approximately 78% of the modern atmosphere, which
makes direct measurements of its fluxes from soil very difficult. Nevertheless, accurate
assessment of N2 fluxes from agricultural soils could help our understanding of the global
nitrogen cycle by providing correct values for fluxes among soils, atmosphere, and the ocean.
Nitrous oxide is a potent greenhouse gas (GHG) with a 100-year global warming
potential of 298 (IPCC 2007). Agriculture is the single most important source of N2O,
accounting for about two thirds of global anthropogenic emissions (Robertson 2004). On a
micro-scale, N2O is produced from nitrate and transformed to N2 during denitrification by
separate enzymatic reactions, with the potential for some N2O to escape to the atmosphere
(Robertson and Groffman 2014).

SUBSOIL DENITRIFICATION
Denitrification processes in soil have been studied for more than a century, with most
attention being devoted to topsoil denitrification, i.e. top 10-20 cm of soil. More than 12,000
articles mention surface soil denitrification in Web of Science database. About thirty articles are
available on subsoil denitrification and only a few are from agricultural sites. As noted later,
subsoil denitrification could sometimes be a significant or even a major source of N2O and N2 in
the soil profile.
Chapters 2 and 3 of this dissertation are directed at answering the question “How large is
denitrification at depth in soil and how does this vary with land-use, and more specifically, with
agricultural practices?” Answering this question will help to reduce significant uncertainties
about the rates of N2/N2O emissions (Galloway et al. 2004). It will also help modern modeling
approaches more accurately represent temporal and spatial distributions of denitrification fluxes;
modeling today succeeds only in simulating averages across seasonal time scales. Knowing that
2

subsoil denitrification is significant changes flux estimations: the whole profile needs to be
considered instead of only of the surface horizon (with arbitrary thickness of 10, 5, or even 2
cm). Considering denitrification of the entire profile could lead to less variable N2/N2O
emissions estimates, which will not only decrease uncertainties in global nitrogen budgets, but
also give more precise estimates of global warming impact of particular agricultural practices
and agriculture overall.
Experiments in the second chapter measure the speed of N2O movement in the soil
profile, which forms the basis for the transformation of N2O concentrations in the profile into
fluxes to the atmosphere from the soil surface. In the third chapter I answer the general question
“How large is denitrification at depth in the soil profile and how does subsoil denitrification vary
with land-use, and more specifically, with agricultural practices?” I address this question in a
corn / soybean / wheat rotation at the KBS LTER site in southern Michigan.
My main objective is to test the global hypothesis that nitrous oxide production at depth
is significant and patterns change significantly along the soil profile and with land use because of
predictable underlying changes in primary controls: nitrate and dissolved organic carbon (SOC)
availability, soil temperature, and soil redox potential.
I subdivide this global hypothesis into three specific hypotheses tested with experiments
described in chapters:
H1

Significant denitrification occurs at depth in arable soils because subsoil layers
have significant levels of nitrate and higher average moisture content compared to
surface soils, with DOC a limiting factor for the reaction.

H2

Tillage, irrigation, and N fertilizer application rate have significant impact on N2O
concentrations in the soil and, in turn, on subsoil N2O fluxes due to agricultural
disturbances like plowing and compaction of the overlying surface soils, as well as
3

additions of N and carbon.
H3

Different cropping systems will have different patterns of subsoil N2O
concentrations and fluxes for the same reason as in H2 – differences in soil
disturbances.
Experimental results from my site represent only specific groups of soil and climate

conditions. With proper calibration, modeling allows extrapolating results to a much wider group
of soils and climates, thus providing a way to apply results in many practical situations. Such
extrapolation of the specific outcome is possible because many parts of integrated plant-soilatmosphere models have already been tested for a variety of environmental conditions, which
means that only the gas flux prediction module still requires validation.

NONLINEARITY OF N2O EMISSIONS WITH N INPUT
Total added N fertilizer from all sources is the most important single predictor of N2O
emissions from cultivated land (Millar et al. 2010). There are different models that describe N
fertilizer effect on N2O emissions. Better knowledge of N2O emission response to N fertilizer is
essential for improving global emission budgets of N2O, and understanding efficient mitigation
strategies for emission reduction is an important task.
The N2O emission factor (EF) is the percentage of applied N converted to N2O emissions
additional to emissions from the non-fertilized field. Global EFs for fertilizer-induced direct N2O
emissions have been determined by Bouwman (1990), Eichner (1990), Bouwman (1996), Mosier
et al. (1998), Bouwman et al. (2002a, b), and Stehfest and Bouwman (2006). The current global
mean value, derived from over 1000 field emissions measurements of N2O, is ~0.9% or 0.009
(Bouwman et al. 2002b, Stehfest and Bouwman 2006). This value is an approximate average of
synthetic fertilizer (1.0%) and animal manure (0.8%) induced emissions, and was rounded by the
4

IPCC to 1% or 0.01 due to uncertainties and the inclusion of other N inputs e.g., crop residues
(Novoa and Tejeda 2006) and SOM mineralization (IPCC 2007). In short, for every 100 kg of N
input, 1.0 kg of N in the form of N2O–N is assumed to be emitted directly. Constant EF assumes
a linear relationship between N fertilizer rate and N2O emissions that is indifferent to biological
thresholds, which might occur, for example, when the availability of inorganic N exceeds the
requirements of competing biota such as plants and soil heterotrophs (Erickson et al. 2001).
However, a growing number of studies (e.g., Hoben et al. 2011, McSwiney and Robertson
2005), including the meta-analyses and associated models that informed the IPCC default EF
(Tier 1) of 1% (Bouwman et al. 2002a, b, Stehfest and Bouwman 2006), indicate that emissions
of N2O respond non-linearly to increasing N fertilization rate across a range of fertilizer, climate,
and soil type, and that therefore EFs vary with respect to N addition. In chapter 4 of this
dissertation I investigated the rate of N2O EF change with N application increase to test the
IPCC (2007) assumption of constant EF.
This research will lead to a better understanding of the nitrogen cycle and provide the
potential for developing recommendations directed at mitigation of N2O’s impact on climate
change as well as other problems associated with reactive N in the environment (Robertson and
Vitousek 2009).

5

Table 1.1. Summary of annual denitrification rates in agricultural soils (from Barton et al. 1999)
System

Observations

Unfertilized, not irrigated
N-fertilized, not irrigated
N-fertilized, irrigated
Total

14
49
7
70

6

Range
(kg N ha-1 year -1)
0-17.4
0.5-110
49-239
0-239

Figure 1.1. Major controls on denitrification from cellular (right) to landscape scales. (From Robertson 2000)

7

REFERENCES

8

REFERENCES

Barton L, McLay CDA, Schipper LA, and Smith CT (1999) Annual denitrification rates in
agricultural and forest soils: a review. Australian Journal of Soil Research 37:1073-1093.
Bouwman AF (1990) in Soils and the greenhouse effect, ed Bouwman AF (John Wiley and Sons,
Chichester, UK), pp 61-127.
Bouwman AF (1996) Direct emission of nitrous oxide from agricultural soils. Nutr. Cycl.
Agroecosyst. 46(1):53-70.
Bouwman AF, Boumans LJM, Batjes NH (2002a) Emissions of N2O and NO from fertilized
fields: Summary of available measurement data. Glob. Biogeochem. Cycle 16(4):6.16.13.
Bouwman AF, Boumans LJM, Batjes NH (2002b) Modeling global annual N2O and NO
emissions from fertilized fields. Glob. Biogeochem. Cycle 16(4):28.1-28.8.
Eichner MJ (1990) Nitrous-oxide emissions from fertilized soils - summary of available data. J.
Environ. Qual. 19(2):272-280.
Hoben JP, Gehl RJ, Millar N, Grace PR, Robertson GP (2011) Nonlinear nitrous oxide (N2O)
response to nitrogen fertilizer in on-farm corn crops of the US Midwest. Global Change
Biology 17(2):1140-1152.
Galloway JN, et al. (2004) Nitrogen cycles: past, present, and future. Biogeochemistry
70(2):153-226.
IPCC (2007) Climate Change 2007: The Physical Science Basis. Contribution of Working Group
I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. ed
Solomon S, D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L.
Miller (eds.) (Intergovernmental Panel on Climate Change, Cambridge University Press,
Cambridge, United Kingdom and New York, NY).
McSwiney CP, Robertson GP (2005) Nonlinear response of N2O flux to incremental fertilizer
addition in a continuous maize (Zea mays L.) cropping system. Global Change Biology
11(10):1712-1719.
Millar N, Robertson G, Grace P, Gehl R, Hoben J (2010) Nitrogen fertilizer management for
nitrous oxide (N2O) mitigation in intensive corn (Maize) production: an emissions
reduction protocol for US Midwest agriculture. Mitig. Adapt. Strateg. Glob. Chang.
15(2):185-204.
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Mosier A, et al. (1998) Closing the global N2O budget: nitrous oxide emissions through the
agricultural nitrogen cycle - OECD/IPCC/IEA phase II development of IPCC guidelines
for national greenhouse gas inventory methodology. Nutr. Cycl. Agroecosyst. 52:225-248.
Novoa RSA, Tejeda HR (2006) Evaluation of the N2O emissions from N in plant residues as
affected by environmental and management factors. Nutr. Cycl. Agroecosyst. 75:29-46.
Robertson GP (2000) Denitrification In Handbook of Soil Science ed. Sumner ME (CRC Press,
Boca Raton, Florida, USA) pp C181-190
Robertson GP (2004) Abatement of nitrous oxide, methane, and the other non-CO2 greenhouse
gases: the need for a systems approach In The global carbon cycle: integrating humans,
climate and the natural world eds. Field CB, Raupach MR (Island Press, Washington,) pp
493-506.
Robertson GP, Groffman PM (2014) Nitrogen transformations. In Soil Microbiology, Ecology
and Biochemistry ed. Paul EA (4th Ed. Academic Press, Burlington, MA). In press.
Robertson GP, Vitousek PM (2009) Nitrogen in Agriculture: Balancing the Cost of an Essential
Resource. Annual Review of Environment and Resources, (Annual Reviews, Palo Alto),
34:97-125.
Stehfest E, Bouwman L (2006) N2O and NO emission from agricultural fields and soils under
natural vegetation: summarizing available measurement data and modeling of global
annual emissions. Nutr. Cycl. Agroecosyst. 74(3):207-228.
Vitousek, et al. (2009) Nutrient imbalances in agricultural development. Science 324:1519-1520.

10

CHAPTER 2
Determining the Diffusivity of Nitrous Oxide in Soil Using In Situ Tracers.
ABSTRACT
Diffusion is a key process for understanding the movement of nitrous oxide (N2O),
carbon dioxide (CO2), methane (CH4), oxygen (O2), and other biogeochemically important
gases in soil. Soil gas diffusivity is highly variable, which makes the application of generic
predictive models based on soil macrofeatures uncertain. In situ methods provide greater
certainty but intensive sampling usually makes such determinations expensive. I compared single
and inter-port diffusivity determinations using a sparse sampling alternative. I used 28 in situ
profile probes with ports at 5 depths for pulsed sulfur hexafluoride (SF6) and N2O tracer
injections at single ports followed by 2-3 measurements in 5 adjacent ports at an agricultural site
in SW Michigan, USA. I repeated this procedure for 3 dates in the summer and 2 in the fall. In
general, the sparse method provided accurate measurements of soil diffusivity. Estimated
diffusivities of SF6 and N2O had poorer agreement in the summer (r2=0.49) than in the fall
(r2=0.96), likely due to less uniform soil moisture in summer. The low N2O to SF6 diffusivity
ratio (0.67 compared to 1.82 in free air) suggests that water solubility of N2O plays a significant
role in retarding its movement in the soil. Movement of the relatively insoluble SF6 is not
obscured by dissolution in water making SF6 a superior tracer compared to N2O. Median
diffusivities in ports where the gas was injected were only moderately correlated (r2=0.45) with
diffusivities at the same depth measured by the inter-port method, likely due to an increase in the
variability of diffusivity with distance from the injection port. Results show it is possible to
estimate N2O diffusivity with sparse measurements; accuracy can likely be further improved
with knowledge of soil moisture and texture in the immediate vicinity of the injection and
sampling ports, as uncertainty in water modeling is reduced.
11

INTRODUCTION
Knowledge of soil gas dynamics is important for understanding soil aeration and the
movement of greenhouse and other important gases in soil, and as well for parameterizing
biogeochemical models used for predicting global change impacts (Li 1992a, 1992b, del Grosso
et al. 2006) and contaminant flows (Moldrup et al. 2000, Resurreccion et al. 2010). Diffusion is
the dominant process controlling soil gas movement (Jin and Jury 1996, Werner et al. 2004). It is
the result of the random movement of gas molecules and tends to equilibrate gas concentrations
without requiring mass flow. Diffusivity of gases in soils is variable because of the complex
structure of the pore network and changing soil moisture content.
Diffusion is usually characterized with a diffusivity or diffusion coefficient, which is a
proportionality constant that connects the gas concentration gradient with diffusive flux (Lide
2010). The diffusivity coefficient is central to gas dynamics models, and in recent decades much
effort has been devoted to developing practical and theoretical methods for measuring and
estimating diffusivity under various conditions in undisturbed and repacked soils in the
laboratory and in the field.
Most laboratory methods to measure the diffusivity coefficient employ a repacked or
intact soil column that has injection and sampling ports along the column sampled 10-15 times
over an injection period (Allaire et al. 2008). Diffusivity is then calculated either as the rate of
gas disappearance from the injection chamber or as the rate of gas accumulation at the opposite
end. While relatively straightforward, for repacked soil columns this method does not account for
in situ diffusion through macropores that are destroyed on repacking and that can otherwise have
a big influence on total diffusivity (Lange et al. 2009). Even intact soil columns are usually not
large enough to include all macro features (Allaire and van Bochove 2007). This problem can be
partly alleviated by instead measuring diffusion in intact soil monoliths in the lab (>0.5 m on a
12

side, Allaire et al. 2008). Monoliths are more difficult to keep at constant moisture, however,
and are very labor and cost intensive, especially for heterogeneous sites. Large monoliths also
cannot be readily replicated.
In situ field methods provide an attractive alternative that do not suffer from distorted
macropore or other soil structure issues associated with laboratory determinations. Field
measurements of gas diffusivity reviewed by Werner et al. (2004) include flux chamber,
atmospheric tracer, instantaneous point-source single-port, instantaneous point source inter-port,
and continuous point source inter-port methods.
The flux chamber method consists of a chamber that is placed with edges a few
centimeters into the soil and that is then injected with a tracer gas. The tracer diffuses into the
soil at a rate estimated by its disappearance from the chamber. This method works well for short
measurement intervals and provides diffusivity measurements in soil surface layers.
The atmospheric tracer method (Weeks et al. 1982) relies on gas concentrations measured
at several depths in the soil profile and historical gas concentrations in the atmosphere to
estimate diffusivity. A one-dimensional diffusion equation uses atmospheric gas concentration at
the surface and no flux at the water table as boundary conditions. The method is simple to
implement as only two measurements at each depth are required, but is limited to environments
where gases move very slowly, are not biologically active, and do not express large temporal or
spatial variations.
The instantaneous point-source single-port method (Lai et al. 1976) uses the same port to
introduce a tracer and remove samples. Diffusivity is calculated by analytical or numerical
methods. The method is relatively simple to implement and analyze and requires low numbers of
samples, but the measurement volume is poorly defined and some probe designs can disturb the
soil during installation. These limitations make the method useful for fast determinations of
13

diffusivity, but many sampling ports are required because of sampling volume uncertainty.
The instantaneous point-source inter-port method (Nicot and Bennett 1998, Werner 2002)
uses two or more ports. One is used for injection and others are sampled to determine the time to
maximum concentration at different distances from the injection port. A better defined sampling
volume allows fewer probes to estimate diffusion, but the method requires frequent sampling due
to high sensitivity of diffusivity estimates to the time it takes gases to reach maximum
concentration at some distance from the injection point.
The continuous point-source inter-port method (Kremer et al. 1988) also uses several
ports, but the tracer is released from the injection port at a constant rate. This method allows for
much simpler steady-state solutions to obtain the diffusivity constant and is presently the most
reliable field-based method. However it requires that significant amounts of tracer be injected at
a constant rate for long periods (up to several days depending on the inter-port distances), and
that soil conditions do not significantly change before steady-state is achieved for the soil
volume of interest.
Attempts have also been made to predict gas diffusivity from static soil characteristics
that are more readily available or estimable. Most models of soil diffusivity use total soil
porosity (Φ), the volume of air (ε), and pore geometry (tortuosity and connectivity) and have the
general form

𝑎ε 𝑏 Φ−𝑐 , where a, b, and c are numerical constants that account for pore

geometry and are used to bring the model into agreement with the data (Table 1). Other models
distinguish between inter- and intra-aggregate porosity and use more complicated relationships
of diffusivity to soil characteristics, often additionally requiring knowledge of soil air volume at
one or more matric potentials (e.g. ε100 – air volume at -100 cm H2O pressure head, Moldrup et
al. 2005) and representing diffusivity with a piecewise function where pieces relate to intervals
of the water-filled porosity (Resurreccion et al. 2010).
14

Despite much effort, a universal predictor of diffusivity for many soil types and
conditions has not been found (Jin and Jury 1996). Bruckler et al. (1989) concluded that such a
predictor cannot exist because it would necessarily be dependent on complex pore geometry,
which might not be possible to represent with soil parameters that are easily measured. For any
given site large differences in diffusivities are obtained by different models and it is difficult to
select the best one for the site on purely theoretical grounds. Many diffusivity models are also
very sensitive to air filled volume and total porosity since they are raised to high powers in many
popular models (Werner et al. 2004). Thus model selection for any given site is probably best
informed by in situ measurements at the site of application using equipment that is easy to install
and operate.
Here I describe an inexpensive soil atmosphere probe that can be used for in situ profile
measurements of gas concentrations to yield diffusivity as a numeric solution of the diffusion
equation. My specific objectives are 1) to test the applicability of in situ tracer measurement to
determine diffusivity with inverse methods, 2) to test if measurements made with SF6 are more
appropriate than direct measurements with N2O, and 3) to evaluate the effectiveness of single
port vs. inter-port methods. To address the second objective I also measured N2O consumption at
depth. I then compare measured diffusivities against values provided by models from the
literature.

MATERIALS AND METHODS
Site description
I measured diffusivities at the Resource Gradient Experiment at the W.K. Kellogg
Biological Station Long-Term Ecological Research Site (KBS LTER, kbs.msu.edu/lter), located
in southwest Michigan in the northeast portion of the U.S. Corn Belt (42° 24’ N, 85° 24’ W, with
15

average elevation 288 m). Mean annual temperature is 10 °C and annual rainfall averages 1027
mm/y with about half of the precipitation received as snow. Detailed weather and soil data for
the 2011 growing season are in Figure A.1-A.3. Soils are a mixture of Kalamazoo (fine-loamy,
mixed, semi-active, mesic Typic Hapludalfs) and Oshtemo (coarse-loamy, mixed, active, mesic
Typic Hapludalfs) loams (Mokma and Doolittle 1993, Crum and Collins 1999) (Table 2).
The KBS LTER Resource Gradient Experiment provides a range of nitrogen fertilization
levels under both rainfed and irrigated conditions in a corn–soybean–wheat rotation.
Experiments were performed in summer and fall 2012 with the field planted to soybean. Planting
occurred on May 22 at 45 seeds m-2 in 38 cm rows to a depth of 4 cm. Plots are 4.6 by 27.4 m
arranged in 4 replicate blocks. In this study I used plots with 56 and 74 kg N/ha in rainfed plots
and 37 and 93 kg N/ha in irrigated plots in one block.

Soil Profile Gas Sampling
I used 5-port soil profile gas probes to make tracer injections at different soil profile
depths and to collect gas samples, which I then used to determine diffusivities. I compared
diffusivities across treatments, injection depths, and seasons. I also compared measured
diffusivities with the diffusivities from published models.
My 5-port soil profile gas probe (Figure 2.1) consists of a master tube made of stainless
steel (90 cm long, ~6.4 mm o.d., ~4.8 mm i.d.) that contains 5 stainless steel sampling tubes
(~1.6 mm o.d., 0.5 mm i.d.) that protrude 3 cm from the outer walls of the master tube at 12, 24,
36, 60, and 90 cm depths. Openings around the protrusions are sealed with air-tight silicon-based
sealant to prevent gas diffusion into and out of the master tube. The upper ends of the sampling
tubes each fitted with a brass reducer (Swagelok, Solon, Ohio, USA) and rubber septum for
sampling access. The largest dead space for the port at 90 cm depth is about 1 ml.
16

To minimize the impact on future tracer concentrations, the protocol minimized the
volume of gas taken. To draw a sample, I pierced a septum with a needle attached to a syringe
and pumped the air inside the tube 3 times by drawing 10 mL of air and immediately injecting it
back into the port. Then I injected 5 mL of soil gas sample and 5 mL of atmospheric air to 5.9
mL non-evacuated Exetainer vials originally containing air at atmospheric pressure to create
overpressure. Samples were analyzed for N2O and SF6 as described above.

Nitrous oxide consumption in the soil
I performed microcosm experiments to determine the suitability of using N2O directly as
a non-consumable tracer for soil diffusivity determinations. If N2O is consumed then it cannot be
used to measure diffusivity reliably.
On 25 May 2012 I took 1 sample of 0-10 cm soil from the first four replicates of
soybeans in the Conventional, No-till, Reduced input, Biologically based , Alfalfa, Poplar, Early
Successional, and Mown Grassland (Never tilled) systems of the Main Cropping System
Experiment at the Kellogg Biological Station (KBS) Long-Term Ecological Research Site
(Robertson and Hamilton 2014), <500 m from the soil gas probe installations on the same soil
type. Soil samples were put through a 4 mm sieve. Moisture contents of the soil were estimated
by drying subsamples in an oven at 105°C. The next day two 200 g fresh weight subsamples
were placed in a 1 L mason jar (Jarden, Rye, NY, USA). I added 75 mL of deionized water to to
completely saturate the soil, with one subsample receiving nitrate at 150 mg N kg-1 soil. Jars
were then sealed with lids with septa to allow for gas sampling and to each jar was added 1 mL
of 45 nmole L-1 SF6 (1 ppmv) and 1 mL of 2.23 μmole L-1 N2O (5% by volume). An additional
60 mL of laboratory air were added to each jar to create an initial overpressure. Headspace
samples were taken 12, 24, 48, 72, 96, and 120 hours after the jars were sealed. At each
17

sampling I removed 5 ml of microcosm atmosphere to a 5.9 ml non-evacuated Exetainer vial
(Labco Ltd., High Wycombe, UK) to which I then added 5 mL of air to over-pressurize during
storage. Samples were analyzed within 10 days of collection.
Again, on 10 Oct., 2012, I took duplicate 6-cm diameter 1 m-deep soil cores from 2
rainfed and 2 irrigated locations on the Resource Gradient site with a hydraulic sampler
(Geoprobe, Salina, KS). The locations of these samples were less than 2 m from corresponding
soil gas probe installations as explained below. The next day three 300 g field moist samples
from each core at depths 5-25, 35-50, and 75-90 cm were sieved and placed in duplicate jars that
were then supplemented with 75 ml of deionized water and injected with SF6 and N2O as
described above. I took a total of 9 headspace samples per jar 0, 4, 8, 13, 19, 27, 37, 50, and 74
hours after the jars were closed.
Samples were analyzed for SF6 and N2O using a gas chromatograph (Aglilent 7890A)
equipped with an auto-sampler (Gerstel MPS 2 XL). SF6 and N2O were separated with one of
two Restek PP-Q 80/100 packed columns (length 3 m, ID 2 mm, OD 3.175 mm) and detected
using a 63Ni electron capture detector at 350°C. Carrier gas was 90% Ar and 10% CH4 (Ultra
High Purity Grade 5.0 with a Restek 21997 moisture trap and Restek 20601 oxygen scrubber) at
a 10±0.5 mL/min flow rate. Oven temperature was 78°C during the first 5.5 min of the run, and
then the column was back flushed and baked for 0.5 min (terminal temperature 105°C, increase
rate 55°C/min). The analytical coefficient of variation was below 2% for SF6 and N2O.

Tracer injection and data collection
I installed 28 soil profile gas probes in Block 1 of the Resource Gradient Experiment.
Seven probes were installed in each of 2 replicate rainfed and 2 replicate irrigated plots. Every
probe was installed into a predrilled vertical well made with a 6.35 mm × 0.9-m length drill-bit
18

(Model A36.250; Associated Industrial Distributors, Crystal Lake, IL). Sampling depths were 12,
24, 36, 60, and 90 cm (Figure 2.1). The 7 probes per plot were installed in a configuration
designed to check diffusivity not only in the vertical but also in the horizontal direction (Figure
2.2). I used two of the probes for gas injection at 90 cm depth, two for gas injection at 60 cm
depth, one probe for gas injection at 36 cm depth, and two control probes were not used for gas
injection. Probes were located at least 3 m from a plot edge. Each pair of probes used for
injection at 60 and 90 cm was grouped with a control probe to form an equilateral triangle with
0.9 m side (Figure 2.2) so that the concentrations at the horizontal distance from the injection
port could be measured. Installations were performed separately for summer and fall in the same
plots with probes installed into a well of the same diameter at least 10 days before first sampling
to allow soil to equilibrate post-installation and provide a good seal between sampling ports.
Experiments were performed over 5 dates in 2012: three in the summer (June 20, June 27,
and July 03) starting 29 days after planting, and two in the fall (Oct. 29 and Nov. 1) shortly after
harvest. Summer sampling occurred after three weeks without rain, whereas fall experiments
followed about 14 cm of rain during October, which completely recharged the profile as it holds
12 cm of water m-1. On each sampling date I sampled ports used for gas injection to determine
background concentrations of N2O and SF6. Direct measurement of baseline tracer
concentrations eliminated the need to measure concentration of the precursors: nitrate and
soluble organic carbon. I injected 2 mL of 45 nmole L-1 SF6 (1 ppmv) and later 2 mL of 44.6
μmole L-1 N2O (100% by volume) into the injection port with each gas followed by 8 mL of
atmospheric air to flush the dead volume of the injection ports. Injections of each gas into 20
injection ports took about 10 minutes to complete. Following the injections, I took three sets of
samples: 1) from 20 injection ports (taking 15 minutes), 2) from all 140 ports (taking 60
minutes), 3) from all 140 ports (taking 60 minutes). I allowed 15 minutes between the sampling
19

sets. I obtained 4 independent diffusivity estimates for the 36 cm injection depth, and 8 estimates
for the 60 and 90 cm injection depths. A total of 20, 40, and 40 diffusivity values for injection
depths at 36, 60, and 90 cm have been obtained, respectively.

Diffusivity calculations
I estimated only layered soil water content and temperature for 2012 with the System
Approach to Land Use Sustainability (SALUS, Basso et al. 2006) model, parameterized and
tested for the site earlier (Syswerda et al. 2012). I validated modeled averages for 0-25 cm soil
depth with measured data for the same depth. I did not measure particle density and assumed it is
2.65 g/cm3. To calculate porosity I assumed bulk density below 69 cm stayed the same at 1.8
g/cm3. Using total porosity and modeled water content I estimated air-filled porosity (ε) to be
used in diffusivity calculations.
I obtained diffusivity by numerical procedure performing an interval search for the
diffusivity value, minimizing the sum of squared differences of measured tracer concentrations
and tracer concentrations from the diffusion equation for the same position in space and time.
The general form of a nonhomogeneous 3-dimensional diffusion equation in cylindrical
coordinates is

𝜕(𝜀𝐶) 1 𝜕
𝜕𝐶
1 𝜕
𝜕𝐶
𝜕
𝜕𝐶
=
(𝐷𝑟 ) + 2
(𝐷 ) + (𝐷 ) + 𝑔 [1]
𝜕𝑡
𝑟 𝜕𝑟
𝜕𝑟
𝑟 𝜕𝜑
𝜕𝜑
𝜕𝑧
𝜕𝑧
where 𝑟 − radius,
𝜑 − angular coordinate,
𝑧 − vertical coordinate,
𝜀 − fraction of air-filled porosity,
20

𝐷 = 𝐷(𝑟, 𝜑, 𝑧) − diffusivity of gas,
𝑔 = 𝑔(𝑡, 𝑟, 𝜑, 𝑧) − production function,
𝐶 = 𝐶(𝑡, 𝑟, 𝜑, 𝑧) − concentration of gas.
Because there was no production or consumption of SF6 or N2O (see Results) I assumed
angular symmetry of concentrations. I assumed diffusion was constant at the same depth. I
assumed porosity to stay constant for each depth for the duration of the experiment. Therefore,
the equation simplifies to the 2-dimensional homogeneous form

𝜀

𝜕𝐶
𝐷 𝜕
𝜕𝐶
𝜕
𝜕𝐶
=
(𝑟 ) + (𝐷 ) [2]
𝜕𝑡
𝑟 𝜕𝑟
𝜕𝑟
𝜕𝑧
𝜕𝑧

Initial concentrations were assumed to follow the 2 dimensional error function

𝐶0,𝑟,𝑧
where 𝐶0,𝑟,𝑧

𝑣𝐶 𝑖𝑛𝑗 − 1 2 (𝑟 2 +(𝑧−𝑧0 )2 )
=
𝑒 2𝜎
[3]
2𝜋𝜎 2

− initial concentration at point (𝑟,

𝑧),

𝐶 𝑖𝑛𝑗 and 𝑉𝑖𝑛𝑗 − concentration and volume of the gas injected,
𝜎 − a parameter equal to 4 cm,

(0, 𝑧0 ) − point of injection,
𝑣 − parameter, adjusted so that ∬

𝑟𝐶0,𝑟,𝑧 𝑑𝑟𝑑𝑧 = 𝑉𝑖𝑛𝑗 𝐶 𝑖𝑛𝑗 .

Concentrations at the border were assumed to be 0 at all times. The exact initial distribution is
inconsequential, since the first sampling occurs at least 15 minutes after the injection and there
were no abrupt changes in concentrations. In a general case this equation with initial and
boundary conditions does not have an analytical solution, so I employed the alternating direction
implicit method (Peaceman and Rachford, 1955). Equations that describe the process are
1
𝑛+2
𝑛
1
1
𝐶 𝑖,𝑗 − 𝐶 𝑖,𝑗
𝐷𝑗
𝑛+2
𝑛+2
𝑛
𝑛
𝜀𝑗
=
𝛿 𝑟 𝐶 𝑖,𝑗 + 𝐷𝑗 𝛿 𝑟𝑟 𝐶 𝑖,𝑗 + 𝛿 𝑧 𝐷 𝑗 𝛿 𝑧 𝐶 𝑖,𝑗 + 𝐷𝑗 𝛿 𝑧𝑧 𝐶 𝑖,𝑗
∆𝑡⁄
𝑟𝑖

2

21

[4]

𝜀𝑗

𝑛+1
𝐶 𝑖,𝑗

1
𝑛+2

− 𝐶 𝑖,𝑗

∆𝑡⁄
2

1
1
𝐷𝑗
𝑛+2
𝑛+2
𝑛+1
𝑛+1
=
𝛿 𝑟 𝐶 𝑖,𝑗 + 𝐷𝑗 𝛿 𝑟𝑟 𝐶 𝑖,𝑗 + 𝛿 𝑧 𝐷 𝑗 𝛿 𝑧 𝐶 𝑖,𝑗 + 𝐷𝑗 𝛿 𝑧𝑧 𝐶 𝑖,𝑗 [5]
𝑟𝑖

where

𝑛
𝐶 𝑖,𝑗 − concentration at time

𝑛∆𝑡, at radius 𝑖∆𝑟, and depth 𝑗∆𝑧,

∆𝑟 − step in radial direction,
∆𝑧 − step in vertical direction,
∆𝑡 − time step,
𝐷 𝑗+1 −𝐷 𝑗−1
𝛿 𝑧 𝐷𝑗 =
,
2∆𝑧
𝐶 𝑖+1,𝑗 −𝐶 𝑖−1,𝑗
𝛿 𝑟 𝐶 𝑖,𝑗 =
,
2∆𝑟
𝐶 𝑖+1,𝑗 −2𝐶 𝑖,𝑗 +𝐶 𝑖−1,𝑗
𝛿 𝑟𝑟 𝐶 𝑖,𝑗 =
,
(∆𝑟)2
𝐶 𝑖,𝑗+1 −𝐶 𝑖,𝑗+1
𝛿 𝑧 𝐶 𝑖,𝑗 =
,
2∆𝑧
𝐶 𝑖,𝑗+1 −2𝐶 𝑖,𝑗 +𝐶 𝑖,𝑗−1
𝛿 𝑧𝑧 𝐶 𝑖,𝑗 =
.
(∆𝑧)2
The equations were run in a cycle from time 0 to T with a step ∆𝑡, where during each iteration
diffusion is assumed to occur in a horizontal direction for the first equation and in a vertical
direction for the second. During time step 𝑛 + 1, terms from previous time steps 𝑛 + 1/2 and 𝑛
are considered known. Assembling unknown terms on the right-hand side yields a set of
tridiagonal matrices that are solved (Thomas 1949) to find concentrations in the next time step.
I fit diffusivity parameters to the data using a program written in C# and run on the .NET
4.5 framework (Microsoft 2012, see supplemental materials for source code). The program
executed a search in diffusivity parameter space with an objective function to minimize the sum
of squared deviations between measured and simulated gas concentrations. Diffusivities ranged
from 10-9 to 1.38 10-5 m2/s, with limits of diffusivity being diffusivity in water and in air,

22

respectively. I ran the diffusivity adjustment model involving only the region with the injection
port for both N2O and SF6 and compared them.
I performed parametric (two-sided t-test) comparisons of diffusivities obtained for
injection ports by depth, presence of irrigation and time of year (summer or fall). For 60 and 90
cm depths I compared SF6 diffusivities for ports used for injections with median values of
diffusivities for ports at the same depth that were only used for sampling. Statistical analyses
were carried out in Wolfram Mathematica 9.0 (Wolfram Research 2012).
I performed full 5-port probe diffusivity adjustment for N2O and SF6. The parameter
space in each case consisted of independent diffusivities for consecutive layers with borders at 0,
18, 30, 41, 69, 120 cm. A 4 cm border region between every two layers has diffusivity as a linear
mixture of the layers. I compared diffusivities for injection ports in this procedure (full
diffusivity) with corresponding injection port diffusivities in simplified procedure (one-port
diffusivity). I then used resampling to compare median diffusivity of ports not used for gas
injection (sampling port diffusivity) with median diffusivity of ports used for injection at the
same depth (injection port diffusivity).
Using moisture content, temperature, and texture as inputs I obtained diffusivities using
existing soil diffusivity models (Table 2.1) and compared those to diffusivities I obtained by my
method.
RESULTS
N2O Consumption Experiment
Headspace concentrations of N2O relative to the inert tracer SF6 did not significantly
decline for the duration of the experiment, 77 h, in experiments with soil samples taken either in
summer or fall (Figure 2.3): measured N2O consumption was nil. I had to remove approximately
half of the microcosm replicates where more than 40% of original SF6 content was lost from a
23

jar due to a defective seal; the remaining dataset had significantly reduced variance.

Field experiments
Figure 2.4 compares soil gas diffusivity estimates for decreasing concentrations of
injected N2O to those for SF6 for summer and fall samplings. SF6 diffusivities have much better
agreement with the concentration measurements (only 5% of runs have r2 < 0.85) than N2O
diffusivities (60% of runs did not achieve r2 < 0.85). I have removed 6 SF6 diffusivity results
with r2 < 0.85 and 17 N2O diffusivity results with r2 < 0.6. However, SF6 and N2O diffusivities
agreed reasonably well (Figure 2.4 a, r2 = 0.64) when calculated only on remaining experiments.
By season, SF6 diffusivities were only weakly correlated with N2O diffusivities in the summer
experiments (Figure 2.4 b, r2 = 0.53), while SF6 and N2O diffusivities had very high agreement
in the fall experiments (Figure 2.4 c, r2 = 0.95). The N2O to SF6 diffusivity ratio for the fall
experiments was 1.24.
Diffusivities of SF6 in the rainfed treatments were significantly (p<0.02) higher than
respective values for irrigated treatments for all depths in summer tests (Figure 2.5) while
differences for diffusivities at 90 cm injection depth were also significant for the fall samples.
N2O diffusivities had similar differences between respective rainfed and irrigated treatments, but
larger variability and exclusion of some diffusivity values led to weaker results (p=0.10 - 0.15).
The soil layers show a declining difference between rainfed and irrigated treatment diffusivities
with depth. Diffusivities of SF6 in the rainfed treatment significantly declined with depth
(p<0.03) in the summer, with the first sampling date having a lower significance at p=0.1 a
minimum power of pairwise comparisons between diffusivities at 36, 60, and 90 cm depths.
SF6 diffusivities involving only the injection port almost perfectly coincided with
diffusivities for the injection port obtained from full scale simulations (Figure 2.6 a, r2 = 0.99).
24

Single-port vs. inter-port SF6 diffusivity comparisons yielded a weak correlation (Figure 2.6 b, r2
= 0.4). N2O diffusivities followed the same trends, but are much more variable and do not show
significant differences.
In my experiments models of diffusivity based on soil moisture content do not have
strong predictive ability for diffusivities since they all use soil moisture as a main predictor,
which is only weakly correlated with my diffusivity measurements (Figure 2.7).

DISCUSSION
Overall results suggest that the point source single port method is adequate for diffusivity
measurements and that the point source inter-port method does not improve results (as noted in
Figure 2.6 b) despite a better defined sampling volume. I also found that diffusivity is not easily
measured directly with N2O, probably due to its greater solubility in water. SF6 with its lower
solubility is a superior tracer because its movement is not obscured by absorption and release by
soil water. SF6 diffusivity can be converted to N2O diffusivity based on their mass differences.

N2O consumption
N2O dynamics in soil depend on its diffusion between the layers, as well as production
and consumption of the gas. To use N2O directly as a diffusivity tracer requires that N2O
dynamics be determined only by diffusion and not be lost or gained in the layers via biological
activity. N2O production in soil can be significant, but is not an obstacle for short term
experiments because background concentrations usually change slowly and can be measured at
the beginning of the experiment. Nevertheless, it is necessary to show that N2O consumption in a
given soil is insignificant in situ; otherwise measurements of diffusion could be an artifact of
substantial N2O consumption.
25

The ability of soils to consume N2O has only been tested for a limited range of soil types
and no comprehensive survey exists (Clough et al. 2005). While many researchers have found
evidence for N2O consumption in laboratory experiments (Clough et al. 1999), others have not
(van Bochove et al. 1998). Some field experiments have a significant number of small negative
fluxes that might indicate the possibility of consumption, but other explanations have been
proposed as well. Interactions of N2O with water complicate the in situ determinations of N2O
consumption at depth (Heincke and Kaupenjohann 1999).
Concentrations of N2O relative to SF6 did not decline in my laboratory incubations with
soil samples taken in summer or fall (Figure 2.3) regardless of profile depth and even under
optimal consumption conditions of a mixed slurry. This indicates that N2O was not consumed to
a measurable degree. This result allows us to consider using N2O as an inert tracer for my shortterm (<5 hours) and possibly longer in situ diffusivity experiments for these soils.

Diffusivity of a relatively soluble gas
Water content is a major determinant of gas diffusivity in soil by occupying pore space.
Its influence becomes even more complex when the gas of interest is relatively soluble (e.g.
N2O) or reacts with water to form other compounds (e.g. CO2). Below I derive a theoretical ratio
of apparent diffusivities of two gases with different masses and solubility under equal
concentration gradients and soil conditions. For equal gradients of concentrations in air or soil (if
solubility and reactions with water can be ignored) two gases have the ratio of diffusivities
approximately inversely proportional to the square root of their molar mass ratio

(𝐷2 ⁄ 𝐷1 ~√𝑀1 ⁄ 𝑀2 ). For example, for N2O to SF6 this ratio is 1.82 (SF6 and N2O masses are
146 g mol-1 and 44 g mol-1, respectively). Differences in the solubility of gases modify this
relationship. To derive an adjustment factor for the diffusivities of the two gases with solubility
26

𝑓1 and 𝑓2 (expressed as Bunsen absorption coefficients or ratios of equilibrated gas
concentrations in water to concentration in the headspace) I assume that both gases achieve
instantaneous equilibrium between air (a) and water (w) fractions of total porosity. The flux of
the gas through the air-filled phase depends only on the concentration gradient and not the
solubility. Since soluble gas has (𝑎 + 𝑓𝑖 𝑤) of combined gas in water and air phases, the change
in concentration will be slower by a factor 𝑎⁄(𝑎 + 𝑓𝑖 𝑤) compared with an insoluble gas ( 𝑓𝑖 =

0) of the same molar mass. Since apparent diffusion is proportional to observed change in
concentrations, the ratio of diffusivities ( 𝐷 𝑖 ) of the two gases is

𝐷2
𝑀1 𝑎 + 𝑓1 𝑤
=√
[6].
𝐷1
𝑀2 𝑎 + 𝑓2 𝑤
Heincke and Kaupenjohann (1999) have reviewed in detail other factors that influence N2O
solubility, including temperature, salt concentration and type, pH of the solvent, and possibly
dissolved organic matter. Clay content can also influence apparent solubility through adsorption
effects.

Diffusivities measured by SF6 and N2O tracers
For SF6 only 5% of the measured diffusivities had an r2<0.85, whereas for N2O over
60% of diffusivities lacked this fit. This difference is likely due to heterogeneous distribution of
soil water that influences the diffusion of N2O because of the relatively high N2O solubility of
1.47 g L-1 (Gevantman 2010) as compared to SF6’s solubility of 0.036 g L-1 (Friedman 1954).
Diffusivities of SF6 and N2O are highly correlated for the fall measurements but only
weakly correlated for the summer. This is likely due to differences in soil moisture.
Heterogeneity of the water content is caused by variation of soil physical properties (texture,

27

aggregation, porosity), precipitation, and temperature (Allaire at al. 2008). During the growing
season variation in water content is increased due to the heterogeneous distribution of roots; this
variation is present in both rainfed and irrigated treatments, despite the higher overall water
content in the irrigated treatment.
The slope of the best fit line for the ratio of N2O and SF6 diffusivities combines the
effects of mass and solubility differences and possible other differences in their interaction with
the medium. The lower slope of only 0.67 for fall (Figure 2.4) compared to the ratio of
diffusivities in free air indicates that the high solubility of N2O has a major influence on its
apparent diffusivity. Fall diffusivity ratios of N2O and SF6 are consistent because water content
was more uniform after the soil profile had been recharged and no plant uptake influenced the
distribution of water, as shown by modeling with SALUS. Substituting measured diffusivity
ratio, molar mass ratio, and air filled porosity (1–10% modeled in SALUS) into Eq. [6] I obtain
the ratio of water to air N2O concentrations of 0.1-0.6 (at 32-40% porosity based on a bulk
density of 1.6-1.8), a value that is lower than equilibrium partitioning (0.6-0.8 at temperatures of
13-23°C). This suggests that N2O is a poor choice of tracer gas, since it behaves differently from
N2O produced in soil that is in equilibrium with soil water. This might not be true for air-filled
porosity values above 10%, where N2O will be more in equilibrium with water, behaving
similarly to N2O produced in the soil. Therefore, using SF6 as a tracer gas and then applying
modifications to adjust diffusivity for mass and solubility differences between SF6 and N2O (or
another soluble gas of interest) is a more appropriate strategy for soils with low air-filled
porosity.

Diffusivities of rainfed and irrigated treatments
Comparing SF6 and N2O diffusivities from rainfed and irrigated treatments (Figure 2.5)
28

agrees with the general prediction that diffusivity will grow with air-filled porosity since the
diffusivity of gases in air is usually several orders of magnitude greater than their diffusivity in
water. So, a larger diffusivity in rainfed compared to irrigated treatments in the summer is likely
due to the greater percentage of soil pores occupied by air in the rainfed treatment. The irrigated
treatment did not receive any additional water after the summer, so its water content was mostly
equilibrated and diffusivity differences between the two treatments that were present in the
summer disappeared in the fall, except for the deepest layer, which was not completely saturated
by November in the rainfed treatment. Smaller differences between SF6 and N2O diffusivities of
rainfed and irrigated treatments in deeper layers are likely also caused by a similarity in water
content even in the summer due to the relative scarcity of roots at 90 cm depth. The decrease in
SF6 diffusivities of rainfed treatment in the summer are also caused by the modeled decrease in
air-filled porosity with depth.

Single-port vs. inter-port diffusivities and comparison with models
Diffusivities for ports not used for injection have much higher variability than
diffusivities for ports used for gas injection. The main reason for this is that spatial variability
compounds with more layers between injection and measurements (Figure 2.6 b).
It is usually more practical to use diffusivity models instead of in situ measurements,
especially in projects that do not allow the use of convenient tracers. Modeling informed by in
situ data is an optimal approach in this case. I calculated diffusivities using modeled soil air and
moisture content to compare with results from existing diffusivity models. Existing models
yielded poor fits (Figure 2.7) and this failure is attributable to 1) the fact that moisture was not
measured in the immediate vicinity of the ports, 2) the natural variability of diffusivity due to
soil macro features, and 3) the poor ability of generic soil diffusivity models to predict diffusivity
29

on a particular site without prior calibration.
Overall my results show that the single-port pulse injection method with SF6 as an inert
tracer provides a viable approach for obtaining quick estimates of gas diffusivity for a particular
site. Adjusting predictive diffusivity models with measurements for use at a specific site is
simple and does not require a significant expenditure of resources. Using SF6 as a tracer avoids
complications related to the high solubility of N2O and its production and perhaps consumption
in a given soil.
My method could be improved and better applied in other soils with more precise
estimates of moisture and temperature, making them more informative to generic soil diffusivity
models on the site of interest. With additional resources, the continuous-injection method is
likely to provide more precise estimates of N2O diffusivity for any given soil by achieving a
stationary SF6 concentration profile and simplifying analytical procedures. For general use,
however, my method provides estimates that should be sufficient and an improvement over static
models for parameterizing most quantitative biogeochemical models.

CONCLUSIONS
1. I found no evidence of N2O consumption in my site either in summer or fall.
2. The point source single-port method with sparse measurements yielded reliable
estimates of diffusivity; the inter-port method did not improve precision.
3. Diffusivity estimates were higher in rainfed than irrigated treatments during the
summer measurements, likely due to lower soil moisture under rainfed conditions. Likewise, in
the fall when there were no modeled soil moisture differences between treatments at 36 and 60
cm, diffusivities were similar.
4. Measurements performed with SF6 to estimate N2O diffusivity were more appropriate
30

than direct measurements with N2O, which may be subject to the incomplete equilibration of
N2O with soil water.
5. My diffusivity estimates with modeled water content did not have strong agreement
with published diffusivity models that are very sensitive to proper determination of the water
content, which I could not directly measure at the injection points.

31

Table 2.1. Relative soil gas diffusivity (Dp/Do) models following the Buckingham–Currie powerlaw function. Model references are as compiled in Jassal et al. (2005), Resurreccion et al.
(2010), and Blagodatsky and Smith (2012).
Formula†

Model
Buckingham (1904)

ε2

Penman (1940)

0.66ε

Millington (1959)

ε4/3

Marshall (1959)

ε1.5

Millington and Quirk (1960)

ε4/3/ Φ2

Millington and Quirk (1961)

ε2/ Φ2/3

Moldrup et al. (2000)

ε2.5/ Φ

Jassal (2005)

1.18ε2.27

Moldrup et al. (2005)

Φ2 (ε/ Φ)X100

𝑋100 = 2 +
Cannavo (2006)

ln(𝜀100 )
4ln(𝜀100 /Φ)

1.12ε2.13

† ε is the soil air content, ε100 is soil air content at -100 cm of matric potential, Φ is the total
porosity

32

Table 2.2. Kellogg Biological Station Long-Term Ecological Research Site soil textures
(Kalamazoo and Ostemo Series). Texture is based on % of fraction less than 2 mm (from
Crum and Collins 1995). pH values assume no liming is performed at the site.
Horizon Depth
cm
Ap
E
Bt1
2Bt2
2E/Bt
Ap
E
Bt1
2Bt2
2E/Bt

Texture
Sand Silt Clay

Texture

CEC Total C Total N pH Bulk Density
cmol+kg-1 g kg-1 g kg-1
Mg m-3

Kalamazoo series: Fine-loamy, mixed mesic Typic Hapludalfs
0-30
43 38 19 Loam
8.4
12.85 1.31 5.5
30-41
39 41 20 Loam
11.5
3.25
0.53 5.7
Sandy clay
41-69
48 23 29
15.3
2.25
0.42 5.3
loam
69-88
79 4 17 Sandy loam
4.1
0.67
0.42 5.2
88-152 93 0 7 Sand
2.3
0.2
0.18 5.6
Oshtemo series: Coarse-loamy, mixed, mesic Typic Hapludalfs
0-25
59 27 14 Sandy loam
7.1
9.67
1.04 5.7
25-41
64 22 14 Sandy loam
6.8
2.52
0.43 5.7
Sandy clay
41-57
67 13 20
8.1
1.99
0.4 5.8
loam
57-97
83 4 13 Sandy loam
6.4
1.28
0.53 5.8
97-152 92 0 8 Sand
2.4
0.25
0.18 6

33

1.6
1.7
1.8
nd
nd
1.6
1.7
1.8
nd
nd

Figure 2.1. Soil profile gas probe with ports at 12, 24, 36, 60, and 90 cm depths. Diameter of the
probe is 6.4 mm and is not shown to scale. For interpretation of the references to color in
this and all other figures, the reader is referred to the electronic version of this
dissertation.

34

Figure 2.2. Replicate (top view) consists of seven soil profile gas probes arranged in two
equilateral triangles with 90 cm sides and an additional injection sampler. Values above
probes indicate port used for gas injection (in addition to sampling). Unmarked probes
were used for sampling only.

35

Figure 2.3. Mean N2O to SF6 ratio over time in summer and fall microcosm experiments. Only
microcosms retaining more than 60% of original SF6 have been retained. Error bars are
lower and upper boundaries of the 95% confidence interval for the median.

36

a) All (r2=0.63)

b) Summer (r2=0.49)

c) Fall (r2=0.95)

Figure 2.4. Comparison of SF6 and N2O diffusivities. Each replicate observation is a separate
point. Straight line is the regression line with best slope through the origin.

37

Diffusivity (10-7 m2/s)

5
3

Rainfed

Irrigated

Diffusivity (10-7 m2/s)

1
0
7
5
3
1
0

Rainfed

Irrigated

Diffusivity (10-7 m2/s)

Diffusivity (10-7 m2/s)
Diffusivity (10-7 m2/s)

Diffusivity (10-7 m2/s)

7

7
5
3
1
0

Rainfed

Irrigated

7
5
3
1
0

Rainfed

Irrigated

Rainfed

Irrigated

Rainfed

Irrigated

7
5
3
1
0
7
5
3
1
0

Figure 2.5. SF6 and N2O diffusivities modeled for ports used for injections. SF6 is in the left
column and N2O is in the right column. Treatments are Rainfed and Irrigated. Within
each treatment there are values for 5 experimental dates arranged chronologically: June
20, June 27, July 03, October 29, and November 1. Only diffusivities with r2 above 0.85
for SF6 and 0.6 for N2O are included.

38

Figure 2.6. Comparison of SF6 diffusivities obtained from simulations involving only ports used
for tracer injections with a) corresponding diffusivities for the ports used to inject tracers
when diffusivities at other ports are taken into account (r2=0.99) and b) median
diffusivities for ports at the same depth that were not used to inject tracers (r2=0.45).

39

Figure 2.6. (Cont’d)

40

Fig 2.7. Poor fit of common diffusivity models with measured SF6 diffusivity in this study. Lines
are models that best fit: Penman 1940 (Pn), Millington 1959 (Ml), and Millington-Quirk
1961 (MQ).

41

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42

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46

CHAPTER 3
The Importance of Subsoil N2O Production in Response to Tillage, Fertilizer and Irrigation
at a Site in Michigan USA
ABSTRACT
Nitrous oxide (N2O) is a major greenhouse gas and cultivated soils are the dominant
anthropogenic source. Potential N2O production and consumption at depths deeper than the A or
Ap horizon have been largely neglected in agricultural soils. I performed a series of experiments
at a site in SW Michigan USA to estimate the influence of crop and management practices on
subsoil N2O production in intensively managed cropping systems. N2O concentrations at depth
were enriched up to 900 times atmospheric concentrations in the presence of irrigation and
nitrogen (N) fertilization. N2O concentrations showed a saturating increase with depth except
immediately after fertilization and in the winter when concentrations were highest in the surface
horizon. Variability of N2O concentrations declined with depth in agreement with more constant
soil moisture and temperature. Comparisons of total N2O emissions from direct chamber flux
measurements with estimates made by the concentration gradient method showed good
agreement, with correlations ranging from 0.4-0.7. N2O production in subsoil horizons is
significant, contributing over 50% of total N2O production in subsoils of moderately fertilized
rainfed treatments. Subsoils of highly fertilized sites that exceed plant N requirements produced
25-35% of total N2O emission. Dry conditions deepened the maximum N2O production depth.
Results show that the fraction of total N2O produced in subsoil can be substantial and appears to
be controlled by the N and moisture status of the soil profile and is unaffected by tillage.

INTRODUCTION
Nitrous oxide (N2O) is a major greenhouse gas and cultivated soils produce ~84% of all
47

anthropogenic emissions (Robertson 2013). Emissions of N2O from cultivated soils have been
studied extensively for many years, with most attention directed towards emissions produced in
the top few centimeters of surface soil. However, N2O can also be produced and consumed at
depths deeper than the A or Ap horizon.
Subsoil N2O production has been studied in a variety of environments and depth ranges,
but little in agricultural soils (Clough et al. 2006). Measurements of subsoil N2O production are
limited to a small number of experimental methods. Methods usually include either
denitrification enzyme activity (DEA) assays (e.g., Castle et al. 1998, Kamewada 2007) to
estimate total nitrogen gas production (N2O + N2), or measurements of N2O emissions
combined with soil profile isotopic concentrations of N2O to estimate N2O production (e.g.,
Clough et al. 1999, Van Groenigen et al. 2005b).
Sharp increases in N2O concentrations with depth have been found in a number of sites.
Van Groenigen et al. (2005a), Goldberg et al. (2009) and Wang et al. (2013) observed N2O
concentrations 20-30 times free-atmosphere concentrations at their deepest subsoil sampling
points, suggesting an N2O production rate in subsoil sufficient to maintain a very steep N2O
concentration gradient through the soil profile.
N2O is produced by denitrification and nitrification in soil (Robertson and Groffman
2014). Denitrification potentials assayed by DEA usually decline substantially with soil depth.
For example, Kamewada (2007) observed an abrupt drop in DEA in samples from an Andisol
soil at depths between 0.5 and 1m, below which DEA was constant to 5 m. He concluded that
subsoil denitrification was negligible. Other authors have also observed a substantial decrease in
volumetric (per m3) or gravimetric (per kg) denitrification rates with depth in different
environments (Hashimoto and Niimi 2001, Murray et al. 2004, Goldberg et al. 2008). However,
even a 20-fold decrease could be significant – and even exceed surface soil rates – when
48

expressed on an areal (per m2) basis for the entire depth of the subsoil, which could be meters
deep.
N2O can also be produced by nitrification. Especially in forest surface soils nitrification
can be a significant source of N2O, and by extension subsoil N2O might also be produced from
nitrification. However, in most soils, including agricultural, only trace amounts of ammonium
leach from surface horizons because of cation exchange processes that slow the movement of
NH4+ to deeper horizons and rapid uptake of ammonium in surface horizons by nitrifiers and
plants. Nitrification is thus unlikely to be a significant source of subsoil N2O (e.g., Page et al.
2002, Khalili and Nourbakhsh 2012).
Subsoil N2O production could be especially important during dry periods, because
surface horizons are too dry to produce N2O (Goldberg and Gebauer 2009). And van Groenigen
et al. (2005a) attributed high wintertime N2O fluxes to subsoil denitrification when surface soils
were frozen to a depth of several centimeters. The importance of subsoil N2O production has
been noted other studies in a variety of systems (Kammann et al. 2001, Addy et al. 2002, Well
and Myrold 2002, Clough et al. 2006).
There are two fates for N2O produced at depth: it can be consumed in place or it can
diffuse to other locations in the profile, where it can also be consumed before diffusing
elsewhere. Eventually N2O not consumed will be lost to groundwater or emitted to the
atmosphere. N2O emitted at deeper depths has a higher chance of being consumed and
transformed to N2 due to a longer residence time in soil arising from a longer diffusion path
(Castle et al. 1998). In any given soil layer diffusion is controlled by the N2O gradient, soil
porosity, water filled pore space (WFPS), and temperature (Shcherbak and Robertson 2014).
Goldberg (2008) concluded that N2O was likely consumed during upward diffusion
based on increasing δ 15N values and decreasing N2O concentrations, although precise estimates
49

of consumption were obscured by high diffusion rates. Clough et al. (1999) and Van Groenigen
et al. (2005b) also combined in situ measurements of N2O emissions to the atmosphere and soil
profile concentrations with isotopic signatures of N2O and found consumption during upward
N2O movement. WFPS rather than N or temperature primarily controlled N2O production. In a
repacked soil column, Clough et al. (2006) used 15N-N2O to show that consumption could
deplete 1/3 of the N2O produced, although estimates of N2O production and consumption in
sieved subsoil columns may not reliably approximate subsoil processes in the field because
sieving changes the structure of the soil and allows oxygen to diffuse to denitrification microsites
faster, which can significantly impede its ability to denitrify (Robertson 2000) or change the
molar ratio of N2:N2O produced by denitrification (Cavigelli and Robertson 2001).
The factors that control denitrification in subsoils are the same as those in surface soils.
Robertson and Groffman (2014) identify three proximal factors that control denitrification at the
cellular level: carbon (C), oxygen, and nitrate (NO3-) concentrations (Chapter 1, Figure 3.1). A
number of more distal factors, such as WFPS, vegetation, grazing, N fertilization, irrigation,
other management operations, climate and soil type, influence oxygen, C, and NO3- to produce a
very diverse range of denitrification rates in arable soils, from 0 to 250 kg N ha-1 year-1 (Barton
et al. 1999, Robertson and Groffman 2014).
Subsoil denitrification in cropped soils is likely colimited by NO3-, C, and WFPS (the
latter determines O2 availability). Soil nitrate concentrations in unfertilized systems in the range
1-10 mg NO3-N kg dry soil-1 have been reported to limit denitrification rate (Barton et al. 1999).
Nitrate leached from surface soils (e.g. Syswerda et al. 2012) can raise subsoil NO3concentrations to above 50 mg NO3-N kg dry soil-1 as evidenced by studies of groundwater next
to heavily fertilized sites (Thorburn et al. 2003, Nisi et al. 2013).
Soil C most commonly limits denitrification in N-fertilized surface soils (Myrold and
50

Tiedje 1985, Myrold 1988, Weier et al. 1993) where nitrate availability is high. In subsoils C can
also limit denitrification as shown by dissolved organic carbon (DOC) addition experiments
(Weier at al. 1993, McCarty and Bremner 1992, Murray et al. 2004). Although low soil C and
NO3- concentrations deeper in the soil may restrict denitrification, significant values occure at
depths greater than 1m in forest soils with no amendments (Barkle et al. 2007, Funk et al. 1996).
Castle et al. (1998) observed denitrification rates as high as 0.1-0.7 mg N2O-N kg dry soil -1 h-1
in intact subsoil cores with no C or N additions. Manure application to topsoil can lessen the C
limitation for subsoil denitrification, as shown by Bhogal and Shepherd (1997). Subsoil slurries
(from long-term arable treatments in Iowa and SE England) amended with C or both C and N
increased denitrification to 1-5.1 mg N2O-N kg dry soil -1 h-1 at depth up to 2 m (Yeomans et al.
1992, Jarvis and Hatch 1994) on par with C and N amended surface soil denitrification rates
(Hoffman et al. 2000, Bradley et al. 2011).
Oxygen depletion in soil is strongly controlled by WFPS, which controls soil aeration
status by restricting oxygen movement in the soil. The WFPS threshold for denitrification
depends on soil texture and is lower for finer textured soils. Barton et al. (1999) reported this
threshold to be 74% to 83% in sandy and sandy loam soils, from 62% to 83% in loam soils, and
from 50% to 74% WFPS in clay loam soils. Loam soils consequently tend to have higher annual
rates of denitrification (as high as 110 kg N ha-1 year-1) than either sandy or clayey soils (<10 kg
ha-1 year-1).
In this study I examine subsoil N2O production in intensively managed cropping systems
at a site in the US Midwest on the same soil series 1) to identify patterns of N2O concentrations
with soil depth; 2) to test the ability to use profile N2O concentrations and diffusivity
measurements to predict soil N2O fluxes to the atmosphere; and 3) to measure N2O production
and movement in the soil profile in order to estimate the relative contribution of different soil
51

depths to seasonal N2O fluxes to the atmosphere as affected by tillage, irrigation, and N fertilizer
input.

METHODS
Site description
I performed experiments at the Kellogg Biological Station (KBS) Long-Term Ecological
Research (LTER) site, located in southwest Michigan in the northeast portion of the U.S. Corn
Belt (42° 24' N, 85° 24' W, average elevation 288 m). Annual rainfall at KBS averages 1,027 mm
y-1 with an average snowfall of ~1.4 m. Mean annual temperature is 9.9 °C ranging from a
monthly mean of -4.2 °C in January to 22.8 °C in July (Robertson and Hamilton 2014). Soils are
co-mingled Kalamazoo (fine-loamy, mixed, semi-active, mesic Typic Hapludalfs) and Oshtemo
(coarse-loamy, mixed, active, mesic Typic Hapludalfs) loams (Mokma and Doolittle 1993).

Experimental Approach
I used two experimental systems to address my objectives: in situ monolith lysimeters to
test the effect of tillage on subsoil N2O production and soil profile gas probes to test the effects
of irrigation, N fertilizer input, and vegetation. Monolith lysimeters provided better resolution
and more measured variables than soil profile gas probes. Probes, on the other hand, are easily
installed in different locations without disturbing normal field operations and thus can be
deployed extensively. I sampled monolith lysimeters from May 2010 to November 2011. I
sampled soil profile gas probes in different treatments of the LTER Resource Gradient
Experiment and the LTER Main Cropping System Experiment (MCSE) from May to November
2011.

52

Monolith Lysimeters Experiment
Field plots for monolith lysimeters were established in 1986 to study tillage and N supply
effects on plant-soil interactions. Sixteen 27 × 40 m plots were randomly assigned within blocks
to N fertilized vs. non-fertilized and till vs. no-till treatments in a randomized complete block
design with 4 replicate blocks per treatment (Figure 3.1). I used four of these plots, in which
monolith lysimeters were installed in 1990. A lysimeter was installed in each of two unfertilized
no-till plots (NT6 and NT9 in Figure 3.1) and two unfertilized tilled plots (CT2 and CT13). The
lysimeters (Figure 3.2) were installed in spring 1986 by excavating around 8 m3 (2.29 × 1.22 ×
2.03 m) pedons located at least 5 m from the edges of the respective plots. A stainless steel
chamber was simultaneously lowered over the undisturbed portion of the pedon following the
procedure of Brown et al. (1974). The intact pedon was temporarily capped, removed by crane as
an assemblage, and inverted in order to weld onto the bottom of the pedon a 0.43 m extension
that was then filled with C-horizon sand followed by a layer of pea gravel separated from the
sand by a Teflon screen. The base of the extension was sloped to the center drain. The lysimeter
assembly was then returned to its original upright position and surrounding soil was replaced by
profile layer. Soil profile mappings of the excavation provide a detailed description of soil
horizon depths (Table 3.1).
From 1985-2002 all plots were in a corn-soybean rotation and from 2004-2009 in a
wheat-corn-soybean rotation. For this study in 2010 and 2011 all plots including over the
lysimeters were planted to corn and N fertilizer was applied at the recommended rate of 145 kg
N ha-1 (Warncke et al. 2004). Corn was planted in 3 rows across the top of each lysimeter at a
standard row spacing of 70 cm with 15 cm between plants in the same row. Tillage within the
two lysimeters assigned to till treatments was performed by hand-spading to mimic chisel
plowing used elsewhere in the plots.
53

For each lysimeter, an outlet at depth provided drainage, and an access tunnel provided
underground access to one side. Instruments to measure solute, gas, moisture, and temperature
(Figure 3.3) within the entire volume of soil were installed 2 cm above and below the borders of
major horizons directly below the center row of corn (Figure 3.2). I also measured N2O flux
from the surface of the soil profile.
Soil temperature in the profile was measured with type T (copper-nickel alloy junction)
thermocouples (Scervini 2009) every 15 minutes at six soil depths (7, 20, 50, 75, 100, and 125
cm) with a 1°C limit of error. Soil moisture was measured with Time Domain Reflectometry
(TDR, Cerny 2009) every 15 minutes at 5 depths (20, 25, 50, 55, and 75 cm) with paired 0.5 ×
30 cm stainless steel rods as TDR wave guides. Each of the lysimeters was connected to a
multiplexer that connected 5 pairs of rods. Two TDR units (Campbell Scientific TDR100)
received measurements from four monolith lysimeters, with the closest lysimeters paired (CT2
paired with NT6, and NT9 with CT13, Figure 3.1) to keep distances within the 70 m limit of the
instrument and avoid signal degradation. Data for temperature and moisture were stored in a
Campbell Scientific datalogger CR10X.
Soil atmosphere was sampled using a system of stainless steel tubing. Tubes were
installed at 10 different depths in the profile: 3, 7, 15, 20, 25, 50, 55, 75, 80, and 180 cm. All
tubes were ~1.6 mm o.d., 0.5 mm i.d. Tubes for sampling at 3, 7, and 15 cm depths were
installed vertically from the top of the profile. The rest of the tubes were installed horizontally
with ends 30 cm from the lysimeter wall to avoid edge effects. Tubes were capped with septa
inside the access tunnel, creating a system with a dead volume of ≤ 2 mL.
Nitrous oxide fluxes were measured at the top of the profile using the static chamber
method. A closed-cover flux chamber was placed on the soil surface to trap soil gases emitted to
the atmosphere. Chambers stayed open except for the period of measurement (~2 hours). During
54

this period samples from chamber headspace were taken every 30 min by inserting a syringe into
the rubber septa and drawing 10 mL, which was placed in a 3.9 mL glass vial (Exetainer
LABCO); overpressure avoided contamination during transport and storage (Kahmark and Millar
2008).
Gas measurements of soil atmosphere concentrations and surface fluxes were taken at the
same locations twice per week with some additional measurements after major rain events and
management operations. In both cases, a 10 mL syringe and non-coring needle were used for
sampling. For each sample, an initial 10 mL volume was taken to flush the system’s dead space
and a second 10 mL volume was used to flush the 3.9 mL vial. A third 10 mL volume was added
to the vial to create an overpressure to guard against leakage.
Gas samples were analyzed for N2O, CO2, and CH4 using a gas chromatograph (Aglilent
7890A) equipped with an auto-sampler (Gerstel MPS 2 XL). N2O was separated with one of two
Restek PP-Q 80/100 packed columns (length 3 m, ID 2 mm, OD 3.175 mm) and detected using a
63

Ni electron capture detector at 350°C. Carrier gas was 90% Ar and 10% CH4 (Ultra High

Purity Grade 5.0 with a Restek 21997 moisture trap and Restek 20601 oxygen scrubber) at a
10±0.5 mL/min flow rate. Oven temperature was 78°C during the first 5.5 min of the run, and
then the column was back flushed and baked for 0.5 min (terminal temperature 105°C, increase
rate 55°C/min) prior to the next sample.

Soil profile gas probes
I used soil profile gas probes that are fully described in Shcherbak and Robertson (2014).
Each probe consisted of a 90 cm long 0.64 cm o.d. master tube that contained five stainless steel
sampling tubes that protruded at different points along the master tube 3 cm from its outer wall. I
installed the probes at a 60° angle to minimize the potential for vertical pores serving as channels
55

for preferential airflow. The sampling depths were 10, 20, 30, 50, and 75 cm (Figure 3.4). Gas
sampling using soil profile gas probes was performed according to the same protocol as for gas
probes in the monolith lysimeters.
The soil profile gas probes were placed in the LTER Resource Gradient Experiment and
the LTER MCSE (Robertson and Hamilton 2014). The Resource Gradient Experiment is a
randomized complete block design experiment with irrigation × fertilizer treatments in 4
replicates. Rainfed and irrigated portions in each replicate include 9 fertilizer input levels planted
to corn in 2011. Irrigation was sufficient to meet crop needs. For this study I selected a subset of
plots with 6 fertilizer input levels (0, 67, 101, 134, 168, and 202 kg N ha-1) in unreplicated
rainfed and irrigated blocks equipped with automatic chambers that monitor gas fluxes from the
soil surface. The 12 soil profile gas probes were each sampled 36 times during the season, with
more intensive sampling after fertilization and with sampling frequency decreasing as the season
progressed. Automatic chambers measured soil surface N2O, CO2, and CH4 fluxes every 6 hours
via a gas chromatograph installed in the field (Millar et al. 2013). Both rainfed and irrigated plots
had replicated continuous measurements of surface temperature and moisture.
In the MCSE soil profile gas probes were installed in four replicates each of two
perennial cropping systems and in two reference communities. The two perennial cropping
systems were Alfalfa (Medicago sativa L., herbaceous) and hybrid Poplar (Populus sp., woody).
The two reference communities were a minimally managed Early Successional community and a
Mown Grassland (never tilled) community. Robertson and Hamilton (2014) provide more
cropping system details. Each of the replicates had a soil profile gas probe installed as described
above and sampled weekly at mid-growing season and then bi-weekly later in the season. I
measured N2O surface fluxes bi-weekly by the static chamber method together with surface
horizon temperature and moisture.
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N2O surface flux and N2O production by depth
I calculated average temporal autocorrelations and their standard errors for surface N2O
fluxes and N2O concentrations at all depths to estimate temporal continuity. Autocorrelation
close to one indicates high temporal continuity such that most measurements are very similar to
the preceding measurement and the following measurement. Autocorrelation close to or below 0
indicates no continuity between measurements over time. I obtained average correlations and
standard errors among N2O fluxes and N2O concentrations. Different levels of N input in the
Resource Gradient Experiment were used as replicates for the calculations. I searched for an
extinction parameter 𝑡 minimizing sum of squared residuals for the 𝑒 −𝑡𝑑 correlation model,
where 𝑑 is the distance between the depths of measurements.
Daily N2O flux in a given soil layer was calculated as N2O diffusivity in that layer
multiplied by the N2O concentration gradient (Fick’s First law), i.e. concentration increase per
cm of increasing depth. I assumed for this calculation that daily concentration profiles are static.
Total N2O production (or consumption, if negative) plus a concentration change for a given layer
is equal to N2O flux into the layer less N2O flux out of the layer. Previous laboratory
experiments on soils from the MCSE and Resource Gradient Experiment sites show that
consumption of N2O during its diffusion towards the soil surface is likely nil (Figure 3 in
Shcherbak and Robertson 2014). Diffusivity of N2O was calculated based on modeled soil water
content and the best fit diffusivity model (Millington 1959) most appropriate for the
experimental site (Chapter 2, Shcherbak and Robertson 2014). Water content in each stratum
estimated using the System Approach to Land Use Sustainability (SALUS) model (Basso et al.
2006) and calibrated with water content measured at 0-25 cm. SALUS model required soil
conditions (soil texture, bulk density, carbon and nitrogen content, initial moisture), daily
weather (rain, temperature, solar radiation), and agronomic management data in order to simulate
57

daily water balance. To bring the concentration profiles to a monotonic or unimodal shape where
required I used a smoothing function of depth

N2 O(d) = N2 O 𝑎𝑡𝑚 + 𝐶1 𝑑 + 𝐶2 (1 − 𝑒 −𝐶3 𝑑 ).
When concentration profiles were already uni-modal, I used linear interpolations of measured
N2O concentrations to create a concentration profile (N2O concentration at 0 cm depth was
assumed equal to the atmospheric N2O concentration of 0.325 ppmv). Seasonal N2O production
for each layer and N2O surface flux was calculated by linear interpolation of respective daily
values across the season.

RESULTS
I observed steep and consistent increases in N2O concentrations with depth for 80-90%
of the sampling period on all three sites (Figure 3.5): the Monolith Lysimeters Experiment, the
Resource Gradient Experiment, and the MCSE. Mean seasonal N2O concentrations increased
with depth for every treatment in the three experiments.
Temporal autocorrelation of N2O concentrations also increased with depth for all
experimental treatments, starting as low as 0.1-0.2 for the top depth measured and reaching
values as high as 0.8 for N2O concentrations at the deepest horizons measured (Figure 3.6).
Paired correlations among N2O surface fluxes and N2O concentrations are positive and
significant. The correlations are highest for values measured at similar depths and significantly
decline for values further apart (Figure 3.7).
Total annual N2O emissions interpolated from chamber measurements and calculated
from soil N2O concentration profiles had high positive correlations for the three experiments
(Figure 3.8). N2O production declined with depth in all treatments (Figure 3.9). Surface soil
layers (0-20 cm) produced >50% of total annual N2O emissions for most treatments with some
58

exceptions in the Resource Gradient Experiment treatments. The exceptions were rainfed
treatments with 0-135 kg N ha-1 input and the irrigated treatment with 135 kg N ha-1 input,
where surface soil layer produced 25-40% of the annual N2O emissions.

Monolith Lysimeters Experiment
N2O concentrations in the monolith lysimeters usually increased with depth, but in the
winter and early spring N2O concentrations were highest in surface layers and decreased with
depth (data not shown here; in Dataset S1). Mean annual N2O concentrations were significantly
higher in the No-till treatment than in the tilled treatment at every depth, reaching values of 7 and
3 ppmv, respectively at 140 cm sampling depth (Figure 3.5 a).
Total N2O emissions calculated from N2O concentration gradients correlated well (r2 =
0.73) with emissions directly measured by static chambers (Figure 3.8 a). Total N2O emissions
for tilled treatment were not statistically different from these for no-tillage when either measured
directly (p=0.16) or calculated from concentrations and diffusivity estimates (p=0.08). The
proportion of total N2O emission produced in surface horizons was 40-60% across 2010-2011
and does not differ by tillage (p=0.7, Figure 3.9 a).

LTER Resource Gradient Experiment
Highest seasonal concentrations at each depth in fertilized treatments of the Resource
Gradient Experiment occurred within 30-days following N fertilization. N2O concentrations
usually increased with depth, with the exception of the 246 kg N ha-1 rainfed treatment on day
173 and 101 kg N ha-1 irrigated treatment on days 173-186, where N2O concentrations declined
with depth. Rainfed treatments had higher mean seasonal N2O concentrations than irrigated
treatments for the entire profile and for all N input levels except for the 101 kg N ha-1 treatment,
59

where N2O concentrations reached 300 ppmv on one day, and for one week N2O concentrations
were above 40 ppm.
Mean temporal autocorrelation for N2O concentrations in the irrigated treatment is
significantly above the mean for the rainfed treatment (p=0.002, Figure 3.7). Results show a
significantly sharper decline for rainfed treatment correlations than for irrigated (p<0.01).
Measured total annual N2O emissions increased with N fertilizer input for both rainfed
and irrigated treatments (Figure 3.8 b) as did total annual N2O emissions modeled from
concentration gradient and diffusivity estimates. Correlations between measured and modeled
emissions averaged 0.41; they were higher for rainfed (0.65) than for irrigated treatments (0.34).
The fraction of total N2O produced lower in the profile for rainfed treatments was large and
declined with N fertilizer input. Modeled N2O production indicated that irrigated treatments
produced 80-95% of total modeled emissions in the top 20 cm of soil, with the exception of the
135 kg N ha-1 fertilizer input level, where N2O emissions from surface horizons were ~40% of
total modeled emissions.

LTER Main Cropping System Experiment
The Alfalfa system had much higher mean annual N2O concentrations than the Poplar,
Early-successional, and Mown grassland systems, which all had very low mean seasonal N2O
concentrations of below 0.7 ppmv. Correlations between N2O concentrations at two different
depths declined with increased distance between the two depths. This decline in correlation with
depth was significantly (p < 0.01) sharper for Poplar and Alfalfa systems than for the
Successional systems.
Modeled total N2O emissions were higher in Alfalfa than in the Poplar and Successional
systems (Figure 3.8 c). Measured total N2O emissions for Alfalfa and Poplar systems were
60

higher than successional communities. The correlations between measured and modeled annual
N2O emissions in the Alfalfa, Poplar and Successional systems is r2 = 0.55. In the Alfalfa and
Successional systems almost 90% of the total N2O emission was produced in the top 20 cm
horizon. In the Poplar system only 80% was produced in the surface horizon.

DISCUSSION
Patterns of N2O concentrations with soil depth
I observed two distinct types of N2O concentration profiles created by the relative rates
of N2O production and diffusion processes. The most common profile shape is a concentration
increasing with depth showing saturation in deeper horizons. This pattern has also been observed
by others (e.g. Clough et al. 2006, Goldberg et al. 2009) and occurs when diffusion is fast
enough to carry produced N2O to the atmosphere.
The other N2O profile shape has the highest concentration near the surface and decreases
or stays nearly constant with depth due to relatively slow diffusion. This happens in soils under
two contrasting sets of conditions: in late spring or summer after N fertilization followed by
sufficient rain (Figure A4), and in winter with surface emissions entrapped by water or ice
(Figure A5). Conditions in the former case lead to intensive N2O production concentrated at the
top of the profile, with the possibility of N2O concentration increase up to 100-1000 times the
atmospheric concentration. Such N2O concentration responses to N fertilization have been
reported by Wang et al. (2013), who found maximum concentrations at shallowest sampling
point (30 cm). N2O production in winter is severely restricted in the surface horizon if it is
saturated or blocked by ice. Highest N2O production at the top of unfrozen part of the soil with
extremely limited diffusion to the surface leads to highest concentration.
Daily and annual N2O concentration profiles that increase with depth and show saturation
61

in deeper horizons have been reported before (Wang et al. 2013). Observed differences in mean
annual N2O concentrations between treatments are driven by daily N2O concentration
differences in the period of most intensive N2O production after fertilizer input; at other times
concentrations are relatively low and uniform. This shows the important role of management on
belowground N2O dynamics that lead to changes in N2O fluxes to the atmosphere. The amount
of mineral N in the profile influences the average annual N2O concentrations in the profile:
Alfalfa with intermediate N2O concentrations likely has intermediate levels of mineral N in the
profile, between those of the N-poor successional communities and those of N-fertilized corn.
Variability in N2O concentrations reflects the spatial and temporal variability of soil
conditions (temperature, moisture, and NO3- and soluble organic C concentrations) that declined
with depth in SALUS model simulations (Figure A.6 and A.7). Autocorrelation results show that
N2O concentration variability declines with depth (Figure 3.6). Relative constancy of conditions
below 70 cm explains autocorrelations close to one. Lower temporal and spatial variability in
irrigated compared to rainfed treatments in the Resource Gradient Experiment follows from a
more constant modeled moisture content under irrigation, as confirmed by temporal
autocorrelation of N2O concentrations and the correlation between N2O fluxes and
concentrations (Figure 3.6 a and 3.7, respectively).

Predicting soil N2O fluxes to the atmosphere from profile N2O concentrations and
diffusivity
Total annual N2O emissions measured directly and calculated from the N2O
concentration gradients and diffusion rates agree well for most treatments examined. Previous
studies comparing direct N2O emission measurements with calculations by the gas gradient
method have had mixed success at best (Rolston et al. 1976, Yoh et al. 1997, and Maljanen et al.
62

2003). Jury et al. (1982) showed that surface N2O flux measurements may not be quantitatively
related to the rate of N2O production in the profile due to the time lag caused by slow diffusivity
and potential for N2O consumption in some soils.
Total calculated N2O emissions were higher than measured emissions in the Monolith
Lysimeter treatments (Figure 3.8 a) probably due to overestimation of diffusivity of N2O in the
surface horizon of the profile. Both methods showed similar total N2O emissions in tilled and
no-till treatments possibly due to balancing somewhat wetter surface soil horizon under no-till by
dryer subsoil horizons (Robertson et al. 2014), leading to greater N2O production. Measured
total annual N2O emissions agreed with calculations by concentration gradient method, and
increased with N inputs in the Resource Gradient Experiment in both rainfed and irrigated
treatments. The MCSE alfalfa treatment has larger measured annual N2O emissions than
successional communities (p=0.001), but modeled N2O fluxes did not show significant
differences among the treatments (Figure 3.8 c).

The contribution of different soil depths to seasonal N2O fluxes
My results show that subsoil N2O production is important in a variety of management
systems across the KBS landscape. Two major profile factors most influence total N2O
production and fractions of N2O produced by depth: NO3- concentration and moisture content.
Tillage does not appear to have an influence on the fraction of subsoil N2O produced (Figure
3.9).
Soil profile NO3- concentration is one of the major drivers of total N2O production and
fractions produced in each soil horizon. High N inputs (168-246 kg N ha-1) exceeding plant N
requirements produce high N2O fluxes from surface horizons in Resource Gradient Experiment
due to very high inorganic N content during wet periods even if they are relatively short. In low
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to moderate N fertilizer input (0-135 kg N ha-1) rainfed treatments in the Resource Gradient and
Monolith Lysimeter Experiments (Figure 3.9 a and 3.9 b) the fraction of total N2O produced in
the subsoil is as high as 40-60%. In contrast with the low fertilization treatments of Resource
Gradient Experiment, less intensive and minimal management systems at MCSE have only 1020% of total annual N2O production attributed to soil below the plow layer (Figure 3.9 c).
Water status of the soil profile and especially the surface horizon is another crucial factor
in determining total N2O production in the profile and the fractions produced in each horizon. In
the irrigated treatments in the Resource Gradient Experiment (Figure 3.9 b) ~75% of N2O
production was concentrated in the surface horizon (except for the 135 kg N ha-1 treatment),
which is a much larger fraction than in rainfed treatments with low to moderate N input. Dry
surface horizons in rainfed treatments shifts N2O production lower into horizons that are
relatively wet. Clough et al. (2006) observed a similar N2O production shift in unfertilized forest
during summer drought. Tillage in the Monolith Lysimeter Experiments did not change the
fraction of N2O produced in subsoil (Figure 3.9 a).
My results show correspondence between total annual N2O fluxes measured directly and
modeled from concentration profiles, but there is room for improvement. Much of the difference
between the two ways to estimate total N2O flux may be sampling artefact. For example, one
source of error is the difference in sampling time between measured and modeled fluxes that in
my study was up to 3 hours during some sampling events. Another source of error in the large
spatial variability of N2O emissions; that emissions measured just a couple of meters away may
differ considerably. In my study, the samples taken by the two methods were at a distance of up
to 5 m. Finally, error may also result from errors in estimating moisture content and subsequent
choice of gas diffusivity model. There are possible improvements to all those areas of potential
error. An automatic system for sampling N2O concentrations positioned close to and
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synchronized with system for measurement of surface fluxes will reduce temporal and spatial
discrepancy between the measurements. The automatic sampling system needs to have dead
space and sampling volumes comparable with the manual system to minimize potential effects
on gas in the soil (e.g. displacing it with atmospheric air). Additionally, direct measurements of
moisture will bring improvements by eliminating error in modeling moisture.
My research suggests that we must consider not only surface but also subsoil conditions
when trying to minimize greenhouse gas emissions from agricultural soil management. Models
need to consider subsoil layers below the plow layer to improve simulation of daily and seasonal
N2O production, storage, movement, and emission to the atmosphere.

CONCLUSIONS
1. N2O concentrations increased with depth in my agricultural soils except after fertilization
when surface soil N2O production was intense and in the winter when the profile was
saturated or blocked by ice and snow.
2. Total annual N2O fluxes measured directly and calculated by the concentration gradient
method are in moderate agreement.
3. N2O production in subsoil horizons is significant, with over 50% of total N2O produced in
subsoils of moderately fertilized rainfed treatments.
4. The fraction of total N2O produced in subsoil at my site was controlled by the NO3availability and moisture status of the soil profile, and was not affected by tillage.
5. Subsoils of sites fertilized at levels that well exceed plant N requirements produce a small
fraction of total N2O emission compared to the surface horizon.
6. Dry surface soil horizons in rainfed treatments shifted relative N2O production into lower
horizons where moisture was available.
65

Table 3.1. Horizon depths in the Monolith Lysimeters of Kalamazoo loam soil at KBS (From
Aiken 1992). Monolith Lysimeter labels refer to Figure 3.1.
Monolith Lysimeter
Soil layer CT2 CT13 NT6
NT9
cm
Ap
0-25 0-23
0-21
0-21
E
24-30 21-30 21-30
Bt
25-53 30-64 30-56 30-48
2Bt2B
53-73 64-84 56-66 48-55
2Bt2C
66-83
2Bt3
83-107 55-78
3E\Bt
738410778-

66

Figure 3.1. Diagram of field plots established at the Kellogg Biological Station in 1986 to
investigate N supply and tillage effects on soil-plant interactions. Intact-profile monolith
lysimeters are located in plots 2, 6, 9, and 13 (From Aiken 1992).

67

Figure 3.2. Schematic diagram of monolith lysimeter with instrumentation ports for
nondestructive sampling of soil atmosphere, soil solution, soil moisture, and soil
temperature. All units are in cm.

68

Figure 3.3. Schematic representation (top view) of nondestructive probes in a soil profile layer in
a monolith lysimeter.

69

OD 1.6 mm
ID 0.5 mm

6 mm

Figure 3.4. Soil profile gas probe installed at 60° angle with sampling depths at 10, 20, 30, 50,
and 75 cm (from Shcherbak and Robertson, in press).

70

Figure 3.5. Mean seasonal N2O concentration profiles observed in the experiments. Atmospheric
concentration is 0.38 ppmv. a) Tilled and no-till Monolith Lysimeters treatments. b)
Rainfed and irrigated Resource Gradient Experiment treatments. c) Poplar, Alfalfa, Earlysuccessional community, and Mown grassland (never tilled) systems of the LTER Main
Cropping System Experiment (MCSE).
71

Figure 3.6. Average temporal autocorrelations of concentrations at different depths and temporal
autocorrelation of surface fluxes of N2O. Autocorrelations close to one indicate N2O
concentrations (or fluxes) with low temporal variability, whereas autocorrelations close to
or below zero indicate highly variable and unstable values. a) Tilled and no-till Monolith
Lysimeter treatments. b) Rainfed and irrigated and Resource Gradient Experiment
treatments.

72

Figure 3.7. Change in correlation between N2O surface fluxes and soil N2O concentrations with
distance between measurement depths for rainfed and irrigated Resource Gradient
Experiment treatments. Each point represents a correlation of N2O concentrations at two
different depths in 2011 vs. absolute differences between the depths.

73

Figure 3.8. Comparison of total seasonal N2O emissions measured by static or automatic
chamber method and modeled from N2O concentration and diffusivity at 10 cm depth. a)
Tilled and no-till Monolith Lysimeter treatments. b) Rainfed and irrigated Resource
Gradient Experiment treatments. c) Poplar, Alfalfa, Early-successional community, and
Mown grassland (never tilled) systems of the LTER MCSE.

74

Fig 3.9. Annual relative N2O production by depth as calculated from concentrations and modeled diffusivity. a) Tilled and no-till
Monolith Lysimeter treatments. b) Rainfed and irrigated Resource Gradient Experiment treatments with rate of N input (0-246
kg N ha-1) indicated next to the treatment. c) Poplar, Alfalfa, Early-successional community, and Mown grassland (never tilled)
systems of the LTER MCSE.

75

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76

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80

CHAPTER 4
A Meta-analysis of the Nonlinearity of Direct Annual N2O Emissions in Response to
Nitrogen Fertilization
ABSTRACT
Nitrogen (N) fertilizer rate is the best single predictor of N2O emissions from agricultural
soils, which are responsible for ~50% of the total global anthropogenic N2O flux, but is a
relatively imprecise estimator. More precise knowledge of the fertilizer N2O emission response
could improve global and regional N2O assessments and help to design more efficient mitigation
strategies. Evidence now suggests that the emission response is not linear, as assumed by IPCC
methodologies, but rather exponentially increases with fertilization. I performed a meta-analysis
to test the generalizability of these findings. I selected published studies with at least three N
fertilizer rates and identical soil management. From 78 available studies (231 site-years) I
calculated N2O emission factors (EFs) as a percentage of applied N converted to N2O emissions.
I found that the rate of change in N2O EF (ΔEF) grew significantly faster than linear for
synthetic fertilizers, for a majority of the crop types examined, and for soils with high organic
carbon content, low mean annual temperatures, or low pH. Nitrogen-fixing crops had a
significantly higher ΔEF than non-fixing crops. A higher ΔEF is also evident in soils with organic
carbon content > 1.5%, in acidic soils, and in experiments with a single fertilizer application. My
results suggest a general trend of exponentially increasing N2O emissions as N fertilizer rates
increase to exceed crop N needs. Use of this knowledge in global and regional greenhouse gas
inventories should provide a more accurate assessment of fertilizer-derived N2O emissions and
help further close the global N2O cycle.

81

INTRODUCTION
Nitrous oxide is a major greenhouse gas (GHG) with a global warming potential ~300
times that of CO2 over a 100 year time period (IPCC 2007). Additionally, N2O is the largest of
all the ozone depleting substances and is projected to remain so for the remainder of this century
(Ravishankara et al. 2009). Nitrous oxide emissions from agricultural soils, produced
predominantly by the microbial processes of nitrification (oxidation of ammonium to nitrate) and
denitrification (reduction of nitrate, via N2O, to N2) (Robertson and Groffman, 2014), constitute
~50% of global anthropogenic N2O emissions (IPCC 2007), primarily as a result of the addition
of synthetic nitrogen (N) fertilizers and animal manure to soil (Bouwman et al. 2002a). The total
input of N to soil and its subsequent availability is a robust predictor of N2O fluxes from most
soils and has been used to construct most national GHG inventories using an emission factor
(EF) approach (de Klein et al. 2006).
The N2O EF is a percentage of the fertilizer N applied that is transformed into fertilizerinduced emissions, which for IPCC GHG inventories is calculated as the difference in emission
between a fertilized and unfertilized soil under otherwise identical conditions. Global EFs for
fertilizer-induced direct N2O emissions have been determined by Eichner (1990), Bouwman
(1990, 1996), Mosier et al. (1998), Bouwman et al. (2002a, b), and Stehfest and Bouwman
(2006). The current global mean value, derived from over 1000 field measurements of N2O
emissions, is ~0.9% (Bouwman et al. 2002b, Stehfest and Bouwman 2006). This value is an
approximate average of synthetic fertilizer (1.0%) and animal manure (0.8%) induced emissions,
and was rounded by the IPCC (de Klein et al. 2006) to 1% due to uncertainties and the inclusion
of other N inputs such as crop residues (Novoa and Tejeda 2006) and soil organic matter
mineralization (IPCC 2007). In short, for every 100 kg of N input, 1.0 kg of N in the form of
N2O is estimated to be emitted directly from soil.
82

A 1% constant EF assumes a linear relationship between N fertilizer rate and N2O
emissions that is indifferent to biological thresholds that might occur, e.g., when the availability
of soil inorganic N exceeds crop N demands. Because the vast majority of studies on N2O
emissions from crops have examined a single fertilizer rate (many without a zero fertilizer rate
comparison), there is no power in these studies for detecting such thresholds. Yet results from a
growing number of field experiments with multiple N fertilizer rates indicate that emissions of
N2O respond non-linearly to increasing N rates across a range of fertilizer formulations,
climates, and soil types (e.g. McSwiney and Robertson 2005, Ma et al. 2010, Hoben et al. 2011,
Signor et al. 2013), and that EFs in fact change monotonically with respect to N addition.
Incorporating this knowledge into large-scale N2O models could help to close the gap between
bottom-up and top-down estimates of fertilizer N2O contributions to regional and global fluxes
(Crutzen et al. 2008, Smith et al. 2012).
Grace et al. (2011), for example, used a nonlinear N2O emission function to model total
direct emissions of N2O from the U.S. North Central Region between 1964 and 2005. Their
estimate was equivalent to an EF of 1.75% of applied N over this period, substantially higher
than the global default IPCC value of 1%. More recently, Griffis et al. (2013) estimated for
contemporary fluxes an overall North Central Region EF of 1.8% using a large tower eddy
covariance approach.
Global, top down estimates of N2O from anthropogenic sources of reactive N, including
animal manure (Davidson 2009), yield an overall EF of 4 ± 1% (Crutzen et al. 2008, Smith et al.
2012). Bottom-up models are in broad agreement (del Grosso et al. 2008), but there are large
uncertainties and the agreement breaks down at regional and sub-regional scales (Reay et al.
2012). The use of EFs that vary with N input (IPCC Tier 2) may help to reconcile this difference
and augment the local to regional insights urgently needed to stem the projected 20% increase in
83

agricultural N2O emissions expected by 2030 (Reay et al. 2012).
Response curves for N2O flux as a function of N rate have recently become more
common. McSwiney and Robertson (2005), for example, reported an exponentially increasing
N2O response to fertilizer N along a nine-point fertilizer N gradient for non-irrigated corn in
Michigan. In their study N2O fluxes more than doubled (20 vs. >50g N2O–N ha-1 day-1) at N
rates greater than 100 kg N ha-1, the level at which yield was maximized. Hoben et al. (2011)
documented a similar response for five on-farm sites in Michigan under corn–soybean rotation
with six fertilizer N rates (0–225 kg N ha-1 yr-1). Others (Ma et al. 2010, Signor et al. 2013) but
not all (Halvorson et al. 2008) have since found similar patterns for multi-point N fertilizer
gradients. Kim et al. (2013) documented 18 published instances with non-linear responses to four
or more N-input levels.
Here I test the generality of these findings globally. While there are very few N2O
response studies with a sufficient number of N-input levels to characterize an exact non-linear
response with confidence, I located over 200 studies with more than two levels in addition to a
zero-N control. And while it is not possible to define a response curve without additional levels, I
compare EFs for nonzero levels to determine the presence of a change, its direction, and an
aggregate ∆EF (change in EF with N input). Here I report the results of a meta-analysis on this
global dataset, and also investigate the potential interaction of ∆EF with other factors such as
crop type, fertilizer source, and soil texture. I also test for possible biases caused by reported
differences in measurement characteristics: the duration, number, and frequency of
measurements, flux chamber area, number of samples per flux measurement, and numbers of
replicates. I then compare results to prior EF determinations, including those used as a basis for
current IPCC Tier 1 methodologies (Bouwman et al. 2002a, b) and carbon credit markets (Millar
et al. 2010, 2012).
84

MATERIALS AND METHODS
Study Selection and Data Extraction
I selected field studies from the literature where in-situ measurements of at least three
different levels of N fertilizer input including a zero N rate (control) were applied under
otherwise identical conditions including site, growing season, crop, fertilizer type, measurement
length, frequency, and method. I included in my search all published datasets from the Web of
Science (selected from 1330 papers found using keywords “nitrous oxide fertilizer rate” in June
2013), studies identified in reviews by Bouwman (1996), Jungkunst et al. (2006), Kim et al.
(2012), and several forthcoming papers. Laboratory and greenhouse studies were excluded from
my analysis as were studies where different N fertilizer rates were confounded by differences in
management practices.
I used all site-years present in original studies averaged by replicates (if reported). I did
not average measurements for a particular site if years, crops, fertilizers, or other significant
factors were different. I converted units of fertilizer input, mean N2O emission, and standard
error to kg N ha-1 for the study period.
Papers with data presented only as graphs of total or daily emissions were digitized using
Get Data Graph Digitizer (2013). Digitization errors were less than 1% in newer papers to ~3-5%
for old graphs with poor image quality or where daily emission values were used.
I include key characteristics for each study in the dataset (Dataset S2): literature
reference, location name and coordinates of experiment; mean annual precipitation and
temperature; soil texture, organic carbon, organic nitrogen, pH, and bulk density; some crop and
management details; year, duration, total number of measurements, and number of replicates;
chamber area and number of measurements per sample; and fertilizer type, mode of application,
and number of applications per measurement period. Where necessary I contacted corresponding
85

authors to make this table as complete as possible.

Emission Factor Change Rates (∆EFs)
I calculated emission factors for every nonzero N application rate as a difference between
N2O emissions (ERN) at the application rate (N) and control (ER0) divided by the (N).

𝐸𝐹 𝑁 =

𝐸𝑅 𝑁 − 𝐸𝑅0
𝑁

The least squares linear relation between the emission factor and N application rate was found
for each site-year:

𝐸𝐹 𝑁 = 𝐸𝐹0 + ∆𝐸𝐹 𝑁
EF change rate (∆𝐸𝐹; Figure C.1) of this relationship is degree of nonlinearity of emission
increase with N input: zero ∆𝐸𝐹 indicates that N2O emissions grow linearly with N input
(constant EF), a positive ∆𝐸𝐹 indicates a faster than linear emission increase (increasing EF),
and a negative ∆𝐸𝐹 means that emissions grow at a rate slower than linear (decreasing EF). The
model of linear change in EF assumes quadratic growth in emissions with N rate 𝐸𝑅 𝑁 =

𝐸𝑅0 + (𝐸𝐹0 + ∆𝐸𝐹𝑁)𝑁, but my goal was to analyze the nonlinear component (∆𝐸𝐹,
Dataset S2) and not to determine the specific shape of the response.

Analysis
Data analysis was performed using Mathematica (2013). I performed a KolmogorovSmirnov test and determined that distribution of ∆𝐸𝐹 is not normal (p < 0.0001). I used
nonparametric (resampling) and parametric procedures for further analysis. Resampling
procedures (bootstrap, i.e. sampling with replacement of the size equal to initial size of subset
repeated N=100,000 times) were used for analysis of means, medians, and confidence intervals
86

(CIs) for all ∆𝐸𝐹𝑠 in the study as well as subsets of ∆𝐸𝐹𝑠 and parametric statistics used to
compare results.
I removed four outlier ∆𝐸𝐹s with largest absolute values (-0.065, -0.05, 0.077, and 0.108)
from further analysis because of their undue influence on subgroup means. The remaining 227
∆𝐸𝐹s were divided into categories based on type of crop (corn, rice, small grains, vegetables, Nfixing, forage, and woody), fertilizer type (ammonium nitrate – AN, calcium ammonium nitrate –
CAN, urea – U, manure – M, and mixed fertilizer), SOC content, soil pH (nonalkaline and
alkaline), mean annual amount of rainfall, mean annual temperature, and first nonzero N input
rate (0-100 and above 100 kg N ha-1). Mean ∆𝐸𝐹s for subgroups were compared using a
bootstrap test for differences (N=100,000 between means obtained by sampling with replacement
equal to initial size of the subset) across categories for the same factor. I used Benjamini and
Hochberg adjustment to control the false discovery rate (Benjamini and Hochberg 1995). I
performed a linear regression analysis of ∆𝐸𝐹 relative to mean EF.
I analyzed mean ∆𝐸𝐹s for potential biases due to measurement techniques. I selected the
value of a parameter that split the dataset into two categories of similar size. I repeated the above
procedure for each of the following factors: number of replicates, study duration, total number of
samples, sampling frequency, chamber area, number of samples per flux measurement, number
of fertilizer applications, and number of input levels. I performed bootstrap tests for differences
as above, but without adjustment for the total number of comparisons. I further selected only
site-years with at least four N input levels and that fit a quadratic function. I then divided the
dataset into two categories of similar size by quality of the fit (r2 < 0.93 and r2 ≥ 0.93) and tested
the differences in ∆𝐸𝐹s.
I tested relatedness of pairs of different tested factors to each other to avoid relating the
same influence to two different factors. For each pair of experimental and sampling factors I
87

calculated the phi-coefficient (φ), which is a measure of association of the two variables forming
a two-by-two contingency table. Phi-coefficient is

φ=√

𝛸2
𝑛

,

where X2 is derived from Pearson's chi-squared test and n is total number of observations
(Everitt, 1992).

Comparison with previous studies
I obtained the average quadratic model and its 95% CI for all the site-years in my dataset
excluding sites with N-fixing crops and the single site with bare soil. I compared this CI with
95% CIs for IPCC Tier 1 methodology and for the range of six models in Philbert et al. (2012)
including and not including parameter uncertainty.
Selecting only studies with 4 or more N input rates in my dataset, I performed a
procedure described in Kim et al. (2013) to classify all site-years into categories of linear, fasterthan-linear (exponential), and slower-than-linear (hyperbolic) N2O emission increase with N
input.
I obtained an average quadratic model for all the site-years and a subset of fields planted
to corn. I compared this estimate to the Hoben et al. (2011) model and the IPCC 1% EF model. I
estimated the differences in emissions reductions predicted by each model under reduction in N
fertilizer input from 200 to 150 kg N ha-1, from 150 to 100 kg N ha-1, and from 50 to 0 kg N ha1

.

RESULTS
I identified (Dataset S2) 78 papers, covering 84 locations (Figure 4.1) and 231 site-years
88

that satisfied my selection criteria of in situ flux measurements from sites fertilized at three or
more N rates with a zero N control. A Kolmogorov-Smirnov test confirmed that ∆EFs are not
normally distributed (p < 0.0001, Figure 4.2). In 155 cases (64%) ∆EFs are positive; in the
remainder rates are zero or negative. A resampling procedure on all ∆EFs showed that mean
(0.0027) and median (0.0005) ∆EFs (% increase per kg added N) are significantly larger than 0,
with 95% confidence intervals (CI) of 0.0011–0.0044 and 0.0003–0.0009, respectively.
Removing four outlier site-years from the dataset slightly decreased the average ∆EF (to 0.0024),
decreased the standard error substantially (from 8.5 x 10-4 to 5.4 x 10-4), and did not affect the
median ∆EF or its standard error (Figure 4.3 and Table B.1).
Nitrogen-fixing crops, upland grain crops, rice, and forage all had positive ∆EFs
significantly different from 0 (p<0.01, Figure 4.3 a and Table B.1). N-fixing crops (including
those present in rotation with other crops) had the highest mean ∆EF (0.018), followed by forage
(0.0033), upland grain crops (0.0017), and rice (0.001). The ∆EF for bare soil was 0.03 based on
a single study (site-year). The only significant difference among land uses was N-fixing crops vs.
all others (p=0.001), vs. upland grain crops (p=0.001), vs. rice (p=0.0006), and vs. perennial
grasses (p=0.004) (Table B2a). All of these tests remain significant after Benjamini and
Hochberg adjustment for the total number of tests.
Synthetic fertilizers (n=187, including organic formulations) dominate other available
fertilizer types (manure, n=16; mixture of synthetic and manure, n=10) so their mean ∆EF
(0.0027, Figure 4.3 b and Table B.1) is similar to that of all treatments. Among synthetic
fertilizers, ammonium nitrate (AN) and urea had significant (p < 0.002) positive mean ∆EFs,
while calcium-ammonium nitrate (CAN), controlled-release urea (CRU), urea ammonium nitrate
(UAN), manure, and mixed fertilizer (Mix) had ∆EFs not different from 0. A difference (t-test)
among synthetic fertilizers (Table B.2 b) showed that mean ∆EFs for AN are significantly (p <
89

0.01) different than those of CAN, UAN, and CRU; the ∆EF for urea is significantly different
(p=0.0034) from that of CRU. Benjamini and Hochberg adjustment leaves all differences
significant.
Among the other experimental factors I tested (Figure 4.3 c and Table B.1: soil carbon,
precipitation, temperature, pH, and number of fertilizer applications), ∆EFs were all different
from 0, except for sites with soil organic carbon (SOC) contents below 1.5%, mean annual
temperature above 10 °C, or alkaline soils (pH above 7), which have mean ∆EFs significantly
lower than sites with SOC above 1.5%, mean temperature below 10 °C, or nonalkaline soils (pH
below 7) (p<0.03, Table B.2 c). Benjamini and Hochberg adjustment removes the first two
differences, while mean ∆EFs for alkaline and nonalkaline sites remains significant (p=0.01).
Sites with pH < 7 have a variance in ∆EF that is approximately 4 times larger than that for sites
with pH > 7.
The average EF for site-year was positively correlated with ∆EF (Adjusted r2 = 0.22,
Figure C.2), with a slope of 0.0024 (±0.0003 SE). Site-years with smallest N input rate after
control below 100 kg N ha-1 had mean ∆EF (0.0034) significantly larger (p=0.007, Figure 4.3 c)
than mean ∆EF for the site-years with smallest N input rate after control above 100 kg N ha-1
(0.0009). Both groups have mean ∆EFs larger than 0 (p=5 x 10-5 and 0.01, respectively).
Among sampling-related factors, the annual number of measurements, duration of the
experiment, number of replicates, and number of samples per flux measurement did not
significantly affect the mean ∆EF at the 95% confidence level (Figure C.3 and Table B.2 d).
Chamber area was the exception with large chambers (>0.2 m2 , equivalent to 4545 cm square)
corresponding to a small but significantly lower mean ∆EF (p < 0.0003) as compared to small
chambers (<0.2 m2). Sites with three or more nonzero N input rates showed no significant
relationship between ∆EF and adjusted r2 of the quadratic function fit (Figure C.4).
90

The largest experimental factor associations in contingency tables (Table B.3 a) were
between mean annual temperature and SOC (φ = -0.59), SOC and soil pH (φ = 0.44), and
between soil pH and mean annual temperature (φ = -0.36). The sampling factor associations
(Table B.3 b) were weaker yet, with strongest associations between chamber area and number of
replicates (φ = -0.56) and between number of measurements and duration of the experiment (φ=
0.45).

DISCUSSION
My results show that N2O emissions tend to grow in response to N fertilizer additions at a
rate significantly greater than linear, i.e. there is a positive mean ∆EF for all site-years as well as
for the majority of groupings by crop, type of N fertilizer applied, and other study and sampling
characteristics. This main result is in agreement with results from most sites with five or more Ninput levels (McSwiney et al. 2005, Hoben et al. 2011, Kim et al. 2013) and suggests that the
current global EF of 1% (de Klein et al. 2006) is too conservative for high N input rates.
That the majority of N2O ∆EFs are positive (Figure 4.2) means that N2O emissions grow
with N input at a rate that is significantly faster than linear. The significantly larger ∆EF for Nfixing crops compared to upland grain crops, rice, and perennial grasses (Figure 4.3 a) is likely
due to crop N saturation without any additional N input. Likewise the ∆EF value for the single
bare soil site, lacking all plant uptake, was higher yet (0.03, Table B.1). In contrast, controlledrelease urea delivers N at a slower rate than urea, ammonium nitrate, and other synthetic
fertilizers and has a lower ∆EF than other fertilizers, which also supports the hypothesis that
plant-heterotroph competition exerts control on the N2O emission rate. Likewise, split fertilizer
applications also had a lower ∆EF than single applications. All the outcomes above are consistent
with the N surplus approach of van Groenigen et al. (2010). Site-years with pH below 7 or SOC
91

above 1.5% had both higher mean EF and mean ∆EF, which is consistent with acidic soils and
carbon-rich soils having higher average N2O emissions (Figure 4.3 c) and consistent with a
positive correlation between mean EF and mean ∆EF.
There were no significant differences in ∆EF based on sampling factors except for
chamber size. Chambers larger than 0.2 m2 (~4545 cm on a side if square) had somewhat lower
∆EFs than smaller chambers. Contingency tables of experimental and sampling factors did not
reveal strong associations among factors (Table B.3 a, B.3 b), which means that tests for different
experimental or sampling factors do not rely on the same set of site-years. However, one source
of potential bias is that site-years with an initial nonzero N input rate below 100 kg N ha-1 are
associated with higher ∆EFs compared to site-years with larger initial nonzero N input rates
(Figure 4.3 c). This is likely because for a larger portion of these experiments, the crop N
saturation point is surpassed with the initial nonzero N application rate. Another potential source
of bias is the small number of studies with multiple N rates (Table B.1), which probably explains
my inability to detect the difference in ∆EFs with increasing number of N levels (Figure C.3).
Quality of data did not decline with increasing ∆EF (Figure C.4).
The significant presence of negative ∆EFs (i.e. a slower than linear emission growth rate
with N input, Figure 4.2) does not have a satisfactory theoretical explanation. Such a response
might imply higher plant nitrogen use efficiency at higher N rates, which has never been
observed, or a higher N2:N2O mole ratio at higher N application rates, which conflicts with our
understanding of the microbiological basis for N2O production (Senbayram et al. 2012). The
remaining explanation is measurement errors arising from large variability in N2O emissions
both spatially and temporally. Were I to remove studies with negative ∆EFs the emission
response to N rate would become even more nonlinear.
My findings agree in general with most prior work. Bouwman et al. (2002b) assumed an
92

exponential relationship between N2O emissions and N input rates in their model, but the
majority of their site-years had a single N application rate, and only a few had a zero-N control.
My work explicitly tests the changes in EF for each experiment with multiple N inputs, arriving
at the same general conclusion of a faster than linear N2O emission increase but with
quantitative and higher confidence outcome.
The model with all site-years but excluding N-fixers and the site with bare soil has a
much narrower confidence interval compared to IPCC Tier 1 methodology (Figure 4.5). Philbert
et al. (2012) show an improved CI for the range of nonlinear and linear models. When not
accounting for parameter uncertainty, the lower boundary in Philbert et al. (2012) coincides with
mine, while the upper boundary is more conservative than mine for N input levels > 150 kg N
ha-1. Parameter uncertainty widens the CI in Philbert et al. (2012) and brings my estimate
entirely within for N input values up to 250 kg N ha-1.
Kim et al. (2013) did not estimate the degree of EF nonlinearity in their dataset but
provided a robust qualitative assessment of EF behavior that showed 6 linear, 18 exponential,
and 2 hyperbolic responses out of 26 total studies. Using the same technique on the subset of my
site-years with more than three nonzero N input rates yields 30 linear EF responses, 54
exponential, and 11 hyperbolic – in good agreement.
Hoben et al. (2011) provide a strong case for a faster than linear N2O emission increase
for U.S. Midwest maize crops with a model based on log-transformed values to make emissions
more conservative. The model forms the basis for approved methodologies at American Carbon
Registry (Millar et al. 2012) and Verified Carbon Standard (Millar et al. 2013):

𝐸𝑚𝑖𝑠 = 6.7(𝑒 0.0067 𝑁 − 1)/𝑁,
with best quadratic approximation of 𝐸𝑚𝑖𝑠 = (4.00  + 0.026 𝑁)𝑁. The quadratic model
I constructed based on Hoben et al. (2011) untransformed emissions has the form 𝐸𝑚𝑖𝑠 =
93

(4.36 + 0.025𝑁)𝑁, where 𝑁 is N input rate in kg N ha-1, and 𝐸𝑚𝑖𝑠 is g N2O-N ha-1. A model
based directly on Hoben et al. (2011) measurements is somewhat more nonlinear than a model
for upland grain crops derived in this study: 𝐸𝑚𝑖𝑠 = (6.93 + 0.017𝑁)𝑁. Models from Hoben et
al. (2011) predict lower emissions than the model derived for the average of upland grain crop
experiments in this paper for N input rates below 325 kg N ha-1.
Regional budgets might be significantly altered by replacement of the constant IPCC 1%
EF with N rate-dependent EF. In particular, this change would likely lower estimated emissions
from regions predominantly fertilized at a low N rate, while increasing emissions from highly
fertilized areas. This would be consistent with observations that global but not regional bottomup estimates are consistent with top down estimates of N2O emissions (del Grosso et al. 2008,
Smith et al. 2012, Reay et al. 2012).
The nonlinearity of N2O EFs means that the IPCC constant global 1% EF is inadequate
to capture emission reductions due to lowered N fertilizer input in cases of high baseline N
fertilization rates. In Figure 4.4 a I compare modeled estimates derived from measurements in
Hoben et al. (2011), from the IPCC 1% EF, and from my ∆EF for upland grain crops for a 50 kg
ha-1 reduction in N input at 3 baseline application rates: 200, 150, and 50 kg N ha-1 (Figure 4.4
b). When reducing from 200 to 150 kg N ha-1 the IPCC emission reduction estimate is 0.5 kg
N2O-N ha-1, 30% below the 0.65 kg N2O-N ha-1 estimate for the other two models. For a
reduction from 150 to 100 kg N ha-1, all 3 models had about the same emission reduction
estimate (0.5-0.56 kg N2O-N ha-1). For a reduction from 50 kg N ha-1 to no fertilizer
application, the IPCC model estimated an emission reduction of 0.5 kg N2O-N ha-1, whereas the
Hoben et al. (2011) and upland grain crop models estimate reductions of 0.28 and 0.39 kg N2ON ha-1, respectively.
When models are to be used to estimate the impact of N fertilizer reductions on N2O
94

emissions (e.g. Millar et al. 2010), it will thus be especially important to avoid overestimating
the impact of reductions where N is applied at rates close to crop N needs and, conversely,
underestimating the impact of reductions where N is over-applied. This means that the largest
mitigation gains are to be made where fertilizer N is applied in excess, such as many areas of
China, and little mitigation will be gained where fertilizer N is in greatest need, such as many
areas of Africa (Vitousek et al. 2009). Regional and global estimates of emissions are thus likely
underestimating emission reductions due to lowered N application rates (see example above).
This underestimation will not be balanced by overestimating reductions elsewhere, since
economical N application reductions (with respect to yield) can only be made in fields where N
is currently being applied in excess, so at higher N rates. ∆EF model predicts higher N2O
emission reductions than IPCC Tier 1 model for N applications above 90 kg N ha-1, covering
mast land in need of N input reduction.
I believe my global default variable EF (EF0 + ∆EF N, Tier 1, Figure 4.3 a) can be used
as a more biologically appropriate value for estimating direct N2O emissions from agricultural
cropland than the current IPCC 1% default. ∆EFs for particular crops and soil types where the
dataset is sufficiently abundant can separately function as Tier 2 ∆EFs for these particular
conditions (Figure 4.3). The use of one or more of these ∆EFs should improve the accuracy of
national and regional inventories for direct N2O emissions from fertilized agricultural land.
A significant shortcoming of this analysis is the few number of site-years with four or
more nonzero N-input levels. With a sufficient number of fully-resolved N2O response curves, I
would be able to generalize the shape of the ∆EF function with higher confidence. More studies
with five or more input levels are needed, especially for heavily fertilized crops such as maize
and vegetables. Needed especially are additional studies in climate zones other than north
temperate, in rice and upland grain crops, and with different fertilizer formulations and
95

application timings. Further knowledge of the factors and practices that affect N2O emissions
from agricultural soils are crucial for mitigating emissions of this important greenhouse gas
(Venterea et al. 2012, Reay et al. 2012, Smith et al. 2012).

96

Figure 4.1. Locations for the studies included in the analysis.

97

Figure 4.2. Histogram of emission factor change rates (∆EFs) that indicate percentage of EF
change per 1 additional kg N ha-1 of fertilizer input. Zero, positive, and negative ∆EFs
indicate, respectively, a linear, faster-than-linear, and slower-than-linear rate of N2O
emissions increase with N input. ∆EFs < 0.02 are not shown for clarity.

98

Figure 4.3. Mean ∆EF with standard errors by type of a) crop, b) fertilizer type, and c) other
experimental factors. *, **, and *** indicate difference from 0 at p=0.05, 0.01, and 0.001,
respectively. Different letters indicate significant differences between mean ∆EFs for
groups of site-years by particular factor.

99

Figure 4.3. (Cont’d)

100

Figure 4.3. (Cont’d)

101

Figure 4.4. a) Comparison of IPCC 1% linear emission model, the Hoben et al. (2011) model,
and a model of average upland grain crop emissions from the current meta-analysis; and
b) Relative N2O emission reductions for the three models when N application rates are
reduced by 50 kg ha-1 from three baseline N fertilization scenarios: 200, 150, and 50 kg N
ha-1.

102

Figure 4.4. (Cont’d)

103

Figure 4.5. Comparison of uncertainties between IPCC Tier 1 (1%), and range of six models
from Philbert et al. (2012) and mean quadratic model for all site years without N-fixing
crops and the bare soil site. Each of the three models is presented with 95% CI range
across 0-300 kg N ha-1 fertilizer input. IPCC Tier 1 95% CI is 0.3-3%. Philbert et al.
(2012) 95% CI for model uncertainty is included with and without parameter uncertainty.

104

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105

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109

APPENDICES

110

APPENDIX A

Figure A.1. Daily precipitation measured at Kellogg Biological Station Long-Term Ecological
Research Site for 2011.

111

Figure A.2. Average daily soil moisture content for 0-25 depth in rainfed (Rain) and irrigated
(Irr) treatments of N fertilizer gradient site for 2011.

112

Figure A.3. Mean daily soil temperature at 10 cm depth (Soil) and air temperature (Air) and N
fertilizer gradient site in 2011. Differences between rainfed and irrigated treatments are
less than 1 °C.

113

Figure A.4. N2O concentration profile in Resource Gradient Experiment Irrigated treatment with
101 kg N ha-1 input rate on DOY 172 in 2011.

114

Figure A.5. N2O concentration profile in Monolith Lysimeter Conventional Tillage treatment
with in plot CT6 on DOY 66 in 2011.

115

Figure A.6. Temporal autocorrelation with depth of modelled water content for days of N2O
concentration measurements in Monolith Lysimeter No Till treatment in plot CT6 in
2011.

116

Figure A.7. Temporal autocorrelation with depth of modelled soil temperature for days of N2O
concentration measurements in Monolith Lysimeter No Till treatment in plot CT6 in
2011.

117

APPENDIX B
Table B.1. Mean and median ΔEF values for different site-year groups by various experimental
and sampling factors with the respective standard errors.
Group

n

With outliers
All
No N fixers
N-fixers
Bare Soil
Upland Grain Crops
Rice
Perennial Grasses

231
227
219
7
1
118
15
41

Synthetic
Ammonium Nitrate (AN)
Calcium Ammonium Nitrate
(CAN)
Controlled-Release Urea (CRU)
Urea
Urea Ammonium Nitrate
(UAN)
Manure

187
27

Mixed Fertilizer
≤ 1.5
> 1.5
≤ 700
> 700
≤ 10
> 10
Acidic
Basic

Mean
STE
Median
STE
Land Use
0.0027 0.00085 0.0005 0.00017
0.0024 0.00054 0.0005 0.00017
0.0018 0.00048 0.0005 0.00016
0.0181 0.00498 0.0201 0.00964
0.0311
0.0017 0.00056 0.0007 0.00027
0.0009 0.00028 0.0007 0.00028
0.0033 0.00126 0.0003 0.00056
Fertilizer Type
0.0027 0.00060 0.0006 0.00019
0.0075 0.00217 0.0020 0.00339

p-value

Dif.

0.0015
0.0000
0.0002
0.0003 a
0.0019 b
0.0012 b
0.0079 b
0.0000
0.0005 a

36
6
58

0.0011 0.00084
0.0001 0.00045
0.0030 0.00097

0.0010 0.00049
0.0002 0.00058
0.0005 0.00022

0.2052 bc
0.8512 c
0.0017 ab

34
16

0.0005 0.00165
0.0022 0.00213

0.0003 0.00054
0.0000 0.00104
0.0004 0.00083

0.7817 bc
0.2932

10

0.0001 0.00174
Soil Carbon (%)
64 0.0006 0.00087 0.0003
100 0.0033 0.00088 0.0006
Precipitation (mm)
58 0.0029 0.00096 0.0009
63 0.0030 0.00102 0.0003
Mean Annual Temperature (°C)
54 0.0027 0.00102 0.0011
51 0.0008 0.00060 0.0001
pH
91 0.0039 0.00110 0.0005
51 0.0005 0.00027 0.0004

118

0.9361

0.00022
0.00042

0.4730
0.0001

0.00042
0.00021

0.0024
0.0030

0.00044
0.00019

0.0093
0.1881

0.00032
0.00030

0.0004 a
0.0521 b

Table B.1. (cont’d)
Group
One-Time
Split
≤30
>30
≤0.2
>0.2
≤3
>3
≤200
>200
≤3
>3
≤100
>100

n
Mean
STE Median
Fertilizer Application
55 0.0052 0.00136 0.0009
90 0.0019 0.00066 0.0004
Total Number of Measurements
92 0.0034 0.00098 0.0009
104 0.0018 0.00075 0.0004
Chamber area (m2)
115 0.0042 0.00079 0.0011
95 0.0008 0.00075 0.0003
Number of Measurements per Sample
110 0.0030 0.00084 0.0007
98 0.0022 0.00073 0.0005
Duration of the Experiment (days)
110 0.0023 0.00071 0.0007
104 0.0029 0.00087 0.0005
Number of Replicates
110 0.0018 0.00084 0.0004
107 0.0034 0.00069 0.0009
Lowest N input level above control (kg ha-1)
139 0.0034 0.00084
88 0.0009 0.00036

119

STE

p-value Dif.

0.00037
0.00014

0.0001
0.0036

0.00034
0.00019

0.0004
0.0136

0.00037
0.00020

0.0000 a
0.2834 b

0.00029
0.00019

0.0003
0.0027

0.00025
0.00027

0.0012
0.0009

0.00019
0.00028

0.0300
0.0001
0.0001 a
0.0102 b

Table B.2 a. T-test results for paired differences between mean ΔEF groups by crop

N-fixers
Upland Grain Crops
Rice
Perennial Grasses

N-fixers
1

Upland Grain Crops
0.001
1

Rice
0.000
0.193
1

Perennial Grasses
0.004
0.231
0.057
1

Table B.2 b. T-test results for paired differences between mean ΔEF groups by N fertilizer type
Syn
Syn
AN
CAN
CRF
Urea
UAN

0.038
0.095
0.000
0.833
0.182

AN
0.038
0.006
0.001
0.062
0.010

CAN
0.095
0.006
0.228
0.124
0.740

120

CRF
0.000
0.001
0.228
0.003
0.752

Urea
0.833
0.062
0.124
0.003
0.176

UAN
0.182
0.010
0.740
0.752
0.176

Table B.2 c. T-test results for paired differences between mean ΔEF groups by experimental
factors
Groups of Experiments Tested
Soil Carbon (≤ 1.5% vs. > 1.5%)
Annual Precipitation (≤700 mm vs. > 700 mm)
Mean Annual Temperature (≤10 °C vs. > 10 °C)
pH (Acidic vs. Basic)
N Applications (One-Time vs. Split)
Lowest N input level above control (≤ 100 kg ha-1 vs. > 100 kg
ha-1)

p-value
0.029
0.931
0.115
0.003
0.027
0.007

Table B.2 d. T-test results for paired differences between mean ΔEF groups by sampling factors
Groups of Experiments Tested
Number of Measurements (≤ 30 vs. >30)
Chamber Area (≤ 0.2 m2 vs. > 0.2 m2)
Number of Measurements per Sample (≤ 3 vs. >3)
Total Duration of Experiment (≤ 200 days vs. > 200 days)
Number of Replicates (≤ 3 vs. > 3)

121

p-value
0.196
0.008
0.451
0.594
0.149

Table B.3 a. Experimental factor associations in contingency tables
Experimental Factors
Annual Precipitation (P)
Mean Annual Temperature (T)
Soil Carbon (C)
pH
Number of Fertilizer Applications (N
App)

P

T
0.027

C
0.329
-0.585

pH
-0.308
0.437
-0.362

105
81
73

73
66

140

77

62

120

109

MpS
-0.188
0.151

D
0.439
0.110
-0.269

N App
-0.063
0.184
-0.021
0.078

Table B.3 b. Sampling factor associations in contingency tables
Sampling Factors
Measurements (Meas)
Chamber Area (Area)
Measurements per Sample (MpS)
Duration (D)
Number of Replicates (Rep)

Mea
184
180
189
188

122

Area
0.294
198
198
204

196
205

205

Rep
-0.194
-0.554
0.013
0.005

Table B.4. Locations for the studies included in the analysis.
Reference
Abdalla et al. 2010
Allen et al. 2010
Anger et al. 2003
Augustin et al. 1999
Balezentiene and Kusta 2012
Breitenbeck and Bremner 1986
Brummer et al. 2008
Cai et al. 1997
Cardenas et al. 2010

Country
Ireland
Australia
Germany
Germany
Lithuania
USA
Burkina Faso
China
UK

Chang et al. 1998
Cheng et al. 2002
Chiaradia et al. 2009
Ciampitti et al. 2005
Ding et al. 2007
Dong et al. 2005
Dusenbury et al. 2008
Fernandez-Luqueno et al. 2009

Canada
Japan
Brazil
Brazil
China
China
USA
Mexico

Gagnon et al. 2011
Gao et al. 2013
Halvorson et al. 2008
Hansen et al. 1993
Harrison et al. 1995
Henault et al. 1998

Canada
Canada
USA
Norway
UK
France

Hoben et al. 2011

USA

Hoffman et al. 2001

Germany

123

Location
Carlow
Jacobs Well, Brisbane
Daun
Paulinenaue
Kaunas
Ames, Iowa
Dano, Ioba
Nanjing, Jiangsu
Aberystwyth, Wales
Devon
North Yorkshire
Lethbridge
Tsukuba
Capivari, San Paolo
Buenos Aires
Henan
Dianzi, Yucheng
Bozeman, Montana
Otumba, State of
Mexico
Quebec City, Quebec
Carberry, Manitoba
Fort Collins, Colorado
Surnadal
Harpenden
Chalons, Champagne
Messigny, Champagne
Longchamp,
Champagne
Fairgrove, Michigan
Hickory Corners,
Michigan
Reese, Michigan
Mason, Michigan
Stockbridge, Michigan
Rengen, Eifel
Kleve, Niederrhein
Heubach, Munsterland

Coordinates
52.85°N
6.91°W
27.72°S 153.27°E
50.19°N
6.82°E
52.77°N
12.77°E
54.87°N
23.83°E
41.95°N 93.71°W
11.16°N
3.08°W
32.04°N 118.87°E
52.43°N
4.02°W
50.77°N
3.90°W
54.11°N
0.67°W
49.70°N 112.75°E
36.02°N 140.12°E
22.93°S 47.57°W
34.60°S 58.48°W
35.00°N 114.40°E
36.95°N 116.63°E
45.67°N 111.15°W
19.70°N 98.81°W
46.78°N 71.13°W
49.90°N 99.35°W
40.73°N 104.98°W
63.00°N
8.88°E
51.81°N
0.36°W
48.95°N
2.42°E
47.46°N
4.95°E
47.27°N
5.30°E
43.52°N
42.41°N

83.64°W
85.37°W

43.45°N
42.47°N
42.48°N

83.65°W
84.27°W
84.27°W

Table B.4. (cont’d)
Reference
Hoogendoorn et al. 2008

Country
New Zealand

Huang et al. 2005
Hyde et al. 2006

China
Ireland

Iqbal 2009
Izaurralde et al. 2004

China
Canada

Ji et al. 2012
Kaiser et al. 1998
Kammann et al. 1998
Kavdir et al. 2008
Kern et al. 2008
Khan et al. 2010

China
Germany
Germany
Germany
Germany
New Zealand

Lampe et al. 2004
Lessard et al. 1996
Letica et al. 2010

Germany
Canada
New Zealand

Li et al. 2002
Lin et al. 2011

Japan
China

Liu et al. 2004
Liu et al. 2005
Liu et al. 2012
Lou et al. 2012
Ma et al. 2007
Ma et al. 2010

China
USA
China
China
China
Canada

MacKenzie et al. 1997

Canada

MacKenzie et al. 1998
McKenney et al. 1980
McSwiney and Robertson 2005

Canada
USA

124

Location
Ballantrae, North
Island
Invermay, South
Island
Jian Xing, Zhejiang
Johnstown Castle,
Co.Wexford
Zhejiang
Swift Current,
Saskatchewan
Jurong, Jiangsu
Brunswick
Giessen
Potsdam
Potsdam
Lincoln, Canterbury,
South Island
Kiel
Ottawa, Ontario
Invermay, Otago,
South Island
Matsudo
Heshengqiao,
Xianning, Hubei
Beijing
Fort Collins, Colorado
Yongji, Shanxi
Shenyang
Dapu, Yixing, Jiangsu
Guelph, Ontario
Ottawa, Ontario
Saint-Valentin,
Quebec
Ormstown, Quebec
Sainte-Rosalie,
Quebec
Ormstown, Quebec
Harrow
Hickory Corners,
Michigan

Coordinates
40.00°S 176.70°E
46.00°S

170.40°E

52.00°N

6.00°W

30.50°N 120.40°E
50.00°N 107.00°W
31.97°N
52.27°N
50.53°N
52.44°N
52.44°N
43.64°S

119.30°E
10.53°E
8.72°E
13.00°E
13.00°E
172.50°E

54.32°N
45.36°N
45.86°S

10.12°E
75.72°W
170.40°E

35.78°N
29.63°N

139.90°E
114.60°E

39.95°N 116.30°E
40.65°N 104.98°W
34.93°N 110.72°E
41.52°N 123.40°E
31.28°N 119.90°E
43.57°N 80.42°W
45.30°N 75.72°W
45.10°N 73.35°W
45.13°N
45.64°N

74.00°W
72.90°W

45.13°N

74.00°W

42.40°N

85.40°W

Table B.4. (cont’d)
Reference
Mori and Hojito 2011
Mosier et al. 2006
Pelster et al. 2011
Pennock and Corre 2001

Country
Japan
USA
Canada
Canada

Pfab et al. 2011

Germany

Qin et al. 2012
Ruser et al. 2001
Ryden 1983
Schils et al. 2008
Signor et al. 2013

China
Germany
UK
Netherlands
Brazil

Situala et al. 1995
Song and Zhang 2009
Thornton and Valente 1996
van Groenigen et al. 2004

China
USA
Netherlands

Velthof et al. 1996

Netherlands

Velthof et al. 1997
Velthof and Mosquera 2011

Netherlands
Netherlands

Venterea et al. 2003
Wang et al. 2011
Xiang et al. 2007
Yao et al. 2012

USA
China
China
China

Zebarth et al. 2008
Zhang et al. 2007

Canada
China

Zhang and Han 2008

China

Zhao et al. 2009
Zhou et al. 2013
Zou et al. 2005

China
China
China

125

Location
Nasu
Fort Collins, Colorado
L'Acadie, Quebec
southern
Saskatchewan
Stuttgart
Luancheng, North
China Plain
Munich
Bracknell, Berkshire
Wageningen
Piracicaba, San Paulo
Goianesia, Goias

Coordinates
36.90°N 139.90°E
40.65°N 104.98°W
45.30°N 73.35°W

Sanjiang Plain
Jackson, Tennessee
Wageningen
Leeuwarden
Heino
Lelystad
Zegveld
Bennekom
Wageningen
Harvard Forest,
Massachusetts
Nanjing, Jiangsu
Yanting, Sichuan
Yangtze River Delta
Fredericton, New
Brunswick
Sanjiang Plain
Duolun County, Inner
Mongolia
Taihu Lake, Yangtze
River Delta
Sichuan Basin
Nanjing, Jiangsu

48.75°N

9.18°E

37.90°N
48.50°N
51.42°N
51.95°N
22.73°S
15.33°S

114.67°E
11.35°E
0.75°W
5.66°E
47.65°W
49.12°W

47.60°N
35.62°N
51.95°N
53.20°N
52.43°N
52.52°N
52.12°N
52.00°N
51.95°N

133.50°E
88.80°W
5.66°E
5.80°E
6.23°E
5.47°E
4.83°E
5.67°E
5.66°E

42.50°N
31.90°N
31.27°N
32.60°N

72.67°W
118.80°E
105.45°E
119.70°E

45.90°N
47.35°N

66.50°W
133.31°E

42.00°N

116.20°E

31.32°N
31.16°N
32.00°N

120.42°E
105.28°E
118.80°E

Table B.5. Variables collected in Dataset S2
Name of Variable
Reference
Location
Coordinates (latitude and Longitude)
Precipitation
Mean Annual Temperature
Texture Class
Soil Classification
Texture (Sand, Silt, and Clay content)
Soil Organic Carbon (SOC)
Soil Organic Nitrogen (SON)
Bulk Density (BD)
pH
Crop
Management
Total Number of Measurements
Method (Static, Automatic)
Chamber Area
Number of Measurements per Sample
Year
Duration
Number of Replicates
Fertilizer Type
Mode of Fertilizer Application
Number of Fertilizer Applications
Min nonzero nitrogen (N) rate
Max N rate
N rate
Total N2O Emission
Standard Error of N2O Emission
Emission Factor (EF)
Emission Factor Change Rate (∆EF)
Remarks

126

Unit
°
mm y-1
°C
%
%
%
g cm-3
m2
d
kg N ha-1
kg N ha-1
kg N ha-1
kg N2O-N ha-1
kg N2O-N ha-1
%
% kg N-1 ha
-

APPENDIX C

Figure C.1. Effect of nitrogen (N) input rate on the total N2O emissions and emission factors
(EFs) for a) linear, b) slower-than-linear, and c) faster-than-linear response type.
127

Figure C.2. ∆EF plotted against mean EF for each site-year in meta-analysis. Best linear
regression line is plotted ∆𝐸𝐹 = −0.00045 + 0.0024𝐸𝐹. Standard error of the linear
parameter is 0.0003.

128

Figure C.3. Graph of mean ∆EF by type of sampling factor.

129

Figure C.4. Relationship between ∆EF and adjusted r2 of the quadratic function fit is absent.

130

APPENDIX D

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