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Estimating Greenhouse Gas Emissions from Soil Following Liquid Manure Applications
Using a Unit Response Curve Method
Gangsheng Wang, Shulin Chen*, and Craig Frear
Department of Biological Systems Engineering, Washington State University, Pullman, WA
99164-6120 USA
*Corresponding Author: Shulin Chen, PhD, PE, Professor, [email protected]
Bioprocessing and Bioproduct Engineering Laboratory
Department of Biological Systems Engineering
Washington State University
Pullman, WA 99164
509-335-3743 (phone)
509-335-2722 (fax)
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ABSTRACT
Quantitative information is critical in policy making related to the roles of agriculture in
greenhouse gas (GHG) emissions. A Unit Response (UR) curve methodology was presented in
this study for modeling GHG emission processes from soil after liquid manure applications. The
emission sources (soils and liquid manures) are conceptualized as a set of linear cascaded
chambers with equal storage-release coefficients, or two sets of cascaded chambers in parallel,
each set having equal storage-release coefficients. The model is based on two-parameter gamma
distribution. Three parameters in this model denote the number of cascaded chambers, the
storage-release coefficient, and the multiplier added to the gamma distribution function. These
parameters can be expressed as functions of the background fluxes. The model can also be used
to estimate global warming potential (GWP) with manure applications at an annual scale in
addition to predicting GHG emissions. The method was validated with actual data from five
fields in three dairy farms of Washington State. The results suggested that the contribution of
CH4 to total GWP was nearly negligible. The total annual GWP significantly increased by an
average of 117% at the sites with applications of undigested manure, while the increment was
only 15% for the sites with applications of digested manure. The UR methodology fills the gaps
between field measurements, simple emission factor (EF) method, and complex process-oriented
models. This method has potential to be used for estimating additional GHG emissions due to
manure/fertilizer applications based on short-term field measurements.
Key words: anaerobic digestion; gamma distribution; global warming potential; greenhouse gas;
manure; unit response.
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Abbreviations: DM, digested manure; GHG, greenhouse gas; GWP, global warming potential;
IUH, instantaneous unit hydrograph; UDM, undigested manure; UH, unit hydrograph; UR, unit
response; WFPS, water-filled pore space.
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1. INTRODUCTION
In order to estimate greenhouse gas (GHG) emissions from soil after manure or fertilizer
applications, field measurements of GHG fluxes are usually required . Long-term field
experiments are able to provide ample data for this purpose . However, in situ data collection is
not only time-consuming but also limited by the financial resources. Therefore, process-based
mathematical models have been developed to validate and extend the results based on field
observations, such as CENTURY/DAYCENT , DNDC , NLEAP , DAISY , ECOSSE , ECOSYS
, and many other models . The advantages of process-based models can provide more detailed
temporal and spatial outputs as well as predictions and scenario analysis. However, these
modeling approaches are hampered by difficulties with data availability and model verifications.
Therefore, simple emission factor (EF) method is used to estimate the total annual emissions in
cases of data scarcity . However, the EF method only yields an estimation of the total emission
and is unable to provide information such as the temporal variation of fluxes and the peak flux.
For these reasons, new methodologies are needed to fill the gaps between field
measurements, simple EF method, and complex process-oriented modeling. Such methodologies
should have the capacity of (i) fully utilizing short-term field experimental data; (ii) simulating
GHG fluxes over time; (iii) estimating annual emissions by up-scaling the results from short-
term (e.g., several days) observations; and (iv) accommodating explanatory parameters related to
site-specific properties.
The methodology of the unit hydrograph (UH) in hydrology can be enlightenment for
describing the emission processes of GHGs. UH is a direct runoff hydrograph produced by one
unit of excess precipitation over a specified duration. UH has been successfully used to convert
excess rainfall to streamflow process in a watershed for even-based rainfall-runoff modeling .
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The unit excess rainfall is assumed to occur for an effective duration uniformly over the
watershed. The UH is expressed by an instantaneous UH (IUH) if this effective duration is
infinitely close to zero . Typically, Nash IUH is represented by a two-parameter gamma
distribution . The two parameters denote the number of linear reservoirs and the storage
coefficient of reservoirs. The rationale of UH is validated not only by its applicability , but also
by its connection with the geomorphological characteristics as well as flow velocities, which is
well known as geomorphological IUH (GIUH) . The gamma distribution was determined to be
the most suitable in a comparative study by Rai et al. . Even better, Cudennec et al. provided
theoretical explanations for some assumptions of UH and GIUH, especially the gamma law and
the exponential distribution of residence time.
The purpose of this paper is to report a new methodology—a unit response (UR) curve
approach to estimate the temporal emission processes of three major GHGs (CO 2, N2O, and
CH4). UH is used to describe the response of runoff to precipitation. Similar to UH, UR can be
used to quantify the additional GHG emission process produced by one unit of carbon/nitrogen
input in manure or fertilizer over a specified duration. The assumptions of UR include: (i) the
UR curve reflects the ensemble of characteristics of the soil; (ii) the shape characteristics of UR
are time invariant; (iii) the emission sources (soils and liquid manures) are conceptualized as a
set of linear cascaded chambers with equal storage-release coefficients, or two sets of cascaded
chambers in parallel, each set having equal storage-release coefficients. This paper is organized
as follows: The materials and methods section describes experimental data analysis, the UR
methodology and its derivation from field data, and the concept of global warming potential. The
subsequent three sections present the results, discussion, and conclusions, respectively.
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2. MATERIALS AND METHODS
2.1. Study Sites and Data Analysis
Baseline monitoring of GHG emissions before and after field applications of dairy waste was
conducted on three dairy farms in Washington State in 2005 and 2006 (Table 1 and Fig. 1). Two
dairy farms, labeled Lynden 1 and Lynden 2, both of which utilized anaerobic digestion (AD)
technology and therefore applied digested manure (DM), are located in Lynden, Washington
(48º 54´ N, 122º 30´ W), and are characterized by medial-skeletal and medial soils formed in
volcanic ash and loess over glacial outwash terraces . The surface layer and subsoil are sandy
loam, and the substratum is sand . Based on the long-term daily baseline climate data (period:
1915–2008; data source: http://www.ncdc.noaa.gov/oa/ncdc.html at Bellingham, Washington
(48º 47´ N, 122º 29´ W), 21 km south of Lynden), the mean annual precipitation is about 902
mm and the average air temperature is about 10.1ºC. Both dairies applied their DM in Spring of
2006 via injection on farm lands prepared for production and harvest of hay.
The other dairy, with three fields of manure application, WSU Dairy Field 8, WSU Dairy
Field 22, and WSU Dairy North Pasture (hereinafter referred to as WSU 8, WSU 22, and WSU
North), is located in Pullman, Washington (46º 45´ N, 117º 11´ W) and are dominated by loam
soils. According to the historical climate data (1941–2008) for Pullman, the annual precipitation
ranges from 308 to 758 mm, with average annual precipitation of about 535 mm. The mean
annual air temperature is about 8.4ºC. Rotational grazing of perennial grasses and periodic
undigested manure (UDM) application were conducted at all three Pullman sites. The field
experiments were carried out during August of 2006 on WSU 8 and WSU 22, and during August
of 2005 on WSU North.
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Manure gauges were deployed before manures were applied. The gauges were placed on
level ground among sampling chambers to represent the amount of manure applied to the
chambers. After application and after the first hour, samples were collected and the depth of
manure in each gauge was measured with a ruler. After measurement, manure in the gauges was
completely stirred to suspend all the solids, and 1-L sample was collected from the gauge into a
labeled sample bottle. The manure samples were then frozen to be shipped to the lab for analysis.
Total Kjeldahl Nitrogen (TKN) with units of mg L−1 was analyzed using a Tecator 2300 Kjeltec
Analyzer (Eden Prairie, MN, USA; SM 4500-Norg B procedure). The total nitrogen per unit area
(kg N ha−1) applied can be calculated via TKN and liquid manure depth (see Table 1).
The static closed-chamber method was used to measure GHG fluxes. Twelve chambers
(cylinders) were randomly placed in the undisturbed soils where manure was applied. Before
manure spraying, background trace gas samples were collected to be compared with the gas
emission rates after manure applications. In general, except for one set of background samples,
12 or 13 sets of samples after manure application were collected during a 10 day period with
each set including 12 replicates.
Cumulative concentrations in ppm(v) or volumetric parts per million of N2O, CO2, and CH4
were determined using a Varian CP-3800 Gas Chromatograph (Varian, Palo Alto, CA). The
GHG gas flux was calculated using the rate of change of the concentration (i.e., the slope of the
cumulative gas concentration over time) .
In order to intuitively understand the gas flux, it is necessary to covert gas flux values from a
volumetric basis (ppm min−1) to a mass basis (kg ha−1 h−1 or kg ha−1 d−1) . Generally, mass fluxes
have units of kg CO2-C ha−1 d−1, kg CH4-C ha−1 d−1, and kg N2O-N ha−1 d−1. The ideal gas law is
used to calculate the number of moles of gas per unit volume:
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where denotes the number of moles per unit volume (mol m−3); V is the volume of the
vessel (m3); n is the number of moles of gas (mol); R is the universal gas constant (8.314 J mol-1
K-1); T is the absolute temperature (K); and P is the atmospheric pressure (Pa).
If H (m) is the height of the chamber, the GHG mass flux rate may be expressed as:
where fm denotes mass flux of gas (kg C ha−1 d−1 or kg N ha−1 d−1); C is the gas emission rate
(ppm min−1) calculated by linear regression of accumulated gas concentration against time; H is
the height of chamber (m); M is mole mass of carbon in CO2 and CH4 (12×10−3 kg C mol−1), or
nitrogen in N2O (28×10−3 kg N mol−1).
2.2. Unit Response with a Single Set of Cascaded Chambers
Similar to the concept of the Nash IUH model , the emission sources can be represented by n
linear cascaded chambers of equal storage-release coefficient k (in units of time). The
Instantaneous Unit Response (IUR) function may be expressed in the form of a two-parameter
gamma function:
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where t is time (e.g., h, hour); u(t) is IUR ordinates (h−1); n denotes the number of linear
chambers and can be any real number greater than 1; is the gamma function; and k is the
gas storage-release coefficient (h).
The time to peak can be derived by differentiating the natural logarithm of u(t):
where tp is the time to peak (h), which may be estimated from the observed gas emission data.
If tp and n are given, the storage-release coefficient k can be calculated by:
2.3. Unit Response with Two Sets of Cascaded Chambers in Parallel
However, the response of GHG emission is a little different from the hydrograph. The right
tail of a direct runoff hydrograph usually approaches to zero much faster than that of gas
emission. Based on the field data of this study (described later), the right tail of the excess gas
(CO2 and N2O) emission process remains positive for a long time (the excess gas emission rate is
the background emission rate subtracted from the gas emission rate). This non-zero tail is
difficult to express by Eq. (i.e., a single set of n-linear chambers with the same storage-release
coefficient). Therefore, a double-set chamber system is proposed in this paper: the first set
consists of n chambers with storage-release coefficient k, and the second set includes n´
chambers with storage-release coefficient k´, and the two sets of cascaded chambers are
connected in parallel. Thus, the IUR is expressed by:
where w is a weighting coefficient between 0 and 1, and
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where 0 < kc ≤ 1 so that , and Eq. reduces to Eq. when kc = 1.
It can be verified that
Since greater n results in higher peak and shorter right tail, the set contributes more to
the peak part of the curve, while the set helps to extend the tail part. An example that
explains the advantage of Eq. over Eq. is shown in Fig. 2. In the case where kc = 1 (Eq. is
used), the peak value is much greater. When kc = 0.1, (Eq. is used), the right tail remains non-
zero for longer time (solid line).
The UR of desired duration (∆t) can be derived by:
where UR(∆t,t) denotes ordinates of UR at time t of ∆t duration (h−1); ∆t is the duration of UR
(h); and I(n, t/k) is the lower incomplete gamma function of order n at (t/k) expressed by:
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2.4. Derivation of Unit Response Using Field Greenhouse Gas Emission Data
Two approaches are generally followed for deriving a UR described in the previous section.
The first is to fit the functional curves with the parameters by means of optimization of an
objective function . The second is to derive the parameters from site-specific properties (e.g., soil
and climate). Take the UH method in hydrology as an example, IUH has been developed in
terms of geomorphological parameters . However, the GHG emission process is less likely to be
controlled by geomorphy, but more related to the environmental physical/chemical/biological
conditions. Additionally, the relationships between the UR parameters and environmental factors
are unknown. It is the complex processes in terms of physical/chemical/biological conditions and
data scarcity that make the second approach difficult to implement.
In this section, the first approach is developed to derive UR. Based on the parameter values
derived from this approach, the relationships between UR parameters and site-specific properties
will be established using the statistical regression method, which will be presented in the Results
section.
The steps involved in derivation of a UR of a specific duration using the field GHG emission
data are as follows:
(1) Draw the graph of mass flux rate (fm) against time in hours. Since fm is calculated based
on a duration of 1-h observations, the duration of UR (∆t) is set as 1 h. The parameter
range for n is set to:
(2) Assuming the abscissas (sampling time) are , where (q + 1) is the number
of observations (each observation refers to a fm from the 1-h duration), and the observed
peak value corresponds to ti (i > 0), the range for tp should be:
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(3) Compute the excess mass flux rate (fme) by subtracting the background flux rate from
each fm. Compute the total excess mass flux (Fme) over the whole sampling time from
the graph of fme vs. time.
(4) Compute the observed UR, by:
where B is the normalized carbon or nitrogen amount:
(i) N2O: , where TKN is the total nitrogen in the manure (kg N ha−1), and
the denominator, 100 (kg N ha−1), is the unit mass of applied nitrogen for calculating
observed UR. The normalization is to avoid the appearance of at a very
small order of magnitude.
(ii) CO2 and CH4: , where CN is the C:N ratio of the manure, and
the denominator, 1000 (kg C ha−1), is the unit mass of applied carbon for calculating
observed UR. Typical C:N values based on the research of Harrison were adopted in
this study (i.e., C:N = 19 and 13 for UDM and DM, respectively).
(5) Determine the range of the multiplier for the simulated UR, . In Step 4, 100 kg N
ha−1 and 1000 kg C ha−1 are defined as the basic unit mass of applied nitrogen and carbon,
respectively. However, the integration Eq. over (0, ∞) is 1 (see Eq. [8]). Thus, a
multiplier is required to scale the UR in Eq. :
where is calculated by Eq. , and β > 0 is a multiplier.
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(6) Fit the observed UR using Eq. . The changing variables include: . The simplified
heteroscedastic maximum likelihood error (HMLE) is used as the objective function, and
the objective is to minimize HMLE within the constraints of Eqs. and :
where λ is a transformation parameter, λ >1 means higher values are more important
during curve fitting, and λ < 1 implies that lower values are emphasized.
(7) Estimate the maximum excess mass flux induced by manure application:
where is the maximum excess mass flux (kg N2O-N ha−1, kg CO2-C ha−1, or kg
CH4-C ha−1).
2.5. Application of UR Method to Estimation of Global Warming Potential
Global warming potential (GWP) was proposed by the IPCC to evaluate the total cumulative
global warming effects of different GHGs. GWP is calculated in units of CO2 equivalents (kg
CO2-eq ha−1) using molecular stoichiometry. N2O and CH4 are assumed to have 296 and 23 times,
respectively, the radiative forcing of CO2 on a per-molecule basis .
The estimation of GWP usually covers a long-term period (a seasonal or annual scale) rather
than a short term such as several days. UR is a useful tool to predict the total GHG emissions
with manure application based on short-term observations. In this paper, GWP is calculated at an
annual scale. The background flux (kg ha−1 d−1) is assumed to be invariant during the whole year,
thus the annual background emissions are the product of the background flux and the number of
days (365 for common years and 366 for leap years). The annual emissions with manure
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applications are the sum of annual background emissions and total excess emissions due to
manure applications calculated by Eq. . However, the background CO2 flux is part of the short
term carbon cycle (soil-atmosphere-soil) and should not be regarded as contribution to GWP.
Therefore, the contribution of background CO2 to GWP is assumed to zero, while the excess CO2
emission accounts for the GWP with manure application.
3. RESULTS
3.1. Gas Fluxes
Since the rate of change of GHG concentration was nearly constant in most of the cases,
linear regression was used to calculate gas flux in this study. The results from different sites
indicate that most of the R2 (coefficient of determination) values were greater than 0.80, which
can guarantee the reliability of flux calculations using linear regressions. Comparisons of GHG
fluxes after manure (UDM or DM) application with the background (NM) value at each site are
shown in Table 2. In the following results and discussion, when the five fields are mentioned
they are presented in the order of WSU 8, WSU 22, WSU North, Lynden 1, and Lynden 2.
The background fluxes of CH4 were below zero at all sites except WSU 22 (see Table 2). The
background CH4 flux from WSU 22 was just slightly above zero (0.001 kg CH4-C ha−1 d−1). The
mean background CH4 flux was −0.0007 kg CH4-C ha−1 d−1 at Pullman, and −0.004 kg CH4-C
ha−1 d−1 at Lynden. With manure application, the CH4 fluxes quickly switched from negative to
positive values. However, after about 1 day, CH4 fluxes dropped to negative values again.
During the sampling period, average CH4 fluxes from the five sites ranged from 0.040 to 0.196
kg CH4-C ha−1 d−1.
CO2 flux patterns at the five sites showed that CO2 fluxes after manure applications were
generally greater than the background fluxes. The background fluxes at the five sites were 2.381,
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4.526, 2.950, 6.584, and 16.050 kg CO2-C ha−1 d−1, respectively. The mean background CO2
fluxes were 3.286 and 11.317 kg CO2-C ha−1 d−1 at Pullman and Lynden, respectively. The
average fluxes during the sampling period after manure applications were 20.7, 8.6, 7.4, 2.6, and
1.2 times greater than the background emissions at the five sites, respectively. The peak value of
CO2 fluxes usually occurred within the first 2 days after manure applications. At the end of the
sampling period, the CO2 fluxes went down to lower values but could still be higher than the
background values. For example, field measurements at WSU 8 indicated that CO2 flux was
13.515 kg CO2-C ha−1 d−1 after 4 days, which was 5.7 times greater than the background value.
The background emission rates of N2O were very low (0.002–0.013 kg N2O-N ha−1 d−1; see
Table 2). The mean background N2O fluxes were 0.005 and 0.008 kg N2O-N ha−1 d−1 at Pullman
and Lynden, respectively. Similar to CO2, the two sites at Lynden with lower temperature and
greater water-filed pore space (WFPS) during the sampling period had higher background N2O
fluxes. The average fluxes during the sampling period after manure applications were 0.085,
0.106, 0.026, 0.016, and 0.015 kg N2O-N ha−1 d−1, which were 17.0, 15.1, 13.0, 4.0, and 1.2 times
greater than the backgrounds at the five sites, respectively. The N2O emissions during the
sampling period were 0.35, 0.45, 0.24, 0.031, and 0.021 kg N2O-N ha−1, which accounted for
only 0.12%, 0.19%, 0.08%, 0.01%, and 0.01%, respectively, of the total applied nitrogen. The
measurements at WSU 8 indicated that after 4 days, N2O flux reduced to 0.028 kg N2O-N ha−1
d−1, which was still 5.9 times higher than the background value.
3.2. Unit Response for Greenhouse Gas Emissions
Because CH4 flux was usually close to zero at the end of the measurement periods, the UR
with a single set of cascaded chambers (kc = 1, see Eq. ) was used in this study. As for CO2 and
N2O, kc was set to 0.1. The parameters ( ) in Eqs. and were estimated using the procedure
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developed above. The values of parameters for three GHGs at the three dairy farms are shown in
Table 3. The comparisons between simulated and observed UR curves and cumulative excess
fluxes for three GHGs at the five sites are shown in Fig. 3 through Fig. 7. The results for UR
derivation are summarized as follows:
(1) Generally, the simulated UR at a 1-h time step (“UR_simulated_1h”) agrees very well
with the observed UR (“UR_observed”), as do the cumulative excess fluxes calculated by
the trapezoidal integral method. Some significant disagreements occur if the observed UR
is multimodal, for example, CO2 and N2O at WSU 22, and N2O at WSU North and
Lynden 2, but the overall goodness-of-fit is satisfactory.
(2) The UR_simulated_1h provides more details than the observations. UR_simulated-1h
may reproduce the “real” peak value, which was not observed during sampling period.
The “real” time to peak (tp) can be shorter or longer than the observed time to peak.
Moreover, tp values were different between GHGs even at the same site.
(3) Usually, tp for N2O (occurring from 0.82 h at WSU North to 11.43 h at WSU 8) was
longer than tp for CO2 (occurring from 0.24 h at WSU North to 10.93 h at WSU 8). n and
k had the same tendencies as tp for N2O against CO2.
(4) β (~41 kg CO2-C ha−1) for CO2 was consistent at the three Pullman sites, but was much
smaller at the Lynden 1 and Lynden 2 sites (14.2 and 3.1 kg CO2-C ha−1, respectively).
Although β for N2O varied from 0.084 to 0.191 kg N2O-N ha−1 at the three Pullman
dairies, they were greater than those at the Lynden 1 and Lynden 2 sites (0.024 and 0.002
kg N2O-N ha−1, respectively) by an order of magnitude.
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3.3. Total Excess Fluxes
The total excess fluxes can be estimated by Eq. after UR is derived (see Table 3). The
emission ratio (ER) is the total excess flux (kg N2O-N ha−1, kg CO2-C ha−1, or kg CH4-C ha−1)
divided by the amount of carbon/nitrogen in manures. ER for N2O was 0.14%, 0.19%, and 0.08%
at WSU 8, WSU 22 and WSU North, respectively; but it was insignificant at the Lynden 1 and
Lynden 2 sites with DM applications. ER for CO2 ranged from 3.90% to 4.28% at the three
Pullman sites, while it was 1.42% and 0.31% at the Lynden 1 and Lynden 2 sites, respectively.
ER for CH4 is about 0.01%, which may be neglected.
3.4. Relationships between Unit Response Parameters and Site Specific Properties
The UR parameters (k, n, β) in Eqs. and are derived by curve fittings based on the observed
UR. They should have certain relationships to site-specific properties. Specifically, the
background GHG flux is a comprehensive indicator reflecting the soil properties, soil organic
matters, microbial activities and other related factors (e.g., soil moisture and temperature).
The models describing such relationships are established using the PROC REG component of
SAS. The significances of the models are tested at the same time. A model is significant if the
probability (Pr in SAS output) is less than the significance level α = 0.05. The coefficient of
determination (R2 in SAS output) is used to show the goodness-of-fit. In short, a model is “good”
if Pr < α and R2 approaches 1.0.
The parameters of the UR for CO2 can be expressed as:
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where are storage-release coefficient (h), number of cascaded chambers, and
multiplier, respectively, for calculating the UR of CO2 (see Eqs. and ); denotes the
background CO2 flux (i.e., before manure application) in units of kg CO2-C ha−1 d−1. The
regression analyses of Eqs. , , and are shown in Fig. 8a-8c.
The parameters of the UR for N2O can be related to the corresponding parameters for CO2:
Since Pr is slightly higher than 0.05 in Eq. , Eq. can be used to replace Eq. because can
be calculated from and (see Eq. ). The regression analyses of Eqs. , and are shown in
Fig. 8d–8f.
3.5. Annual Global Warming Potential
The contributions of the three GHGs from the five fields to GWP at an annual scale are
shown in Table 4. Regarding background emissions, GWPs due to CH4 were negative (−44.77 to
−11.99 kg CO2-eq ha−1) at all the study sites except WSU22 (11.19 kg CO2-eq ha−1). At the
Pullman sites with UDM applications, GWP due to CH4 increased by 12.02 kg CO2-eq ha−1 on
average, while the average incremental GWP was 5.13 kg CO2-eq ha−1 for the Lynden sites with
DM applications. Especially, GWP due to CH4 switched to positive at WSU 8, whereas GWPs
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due to CH4 at WSU North, Lynden 1 and Lynden 2 remained negative. In a word, the
contribution of CH4 to total GWP after manure applications was insignificant compared with
CO2 and N2O in this study.
Although N2O flux was very low relative to CO2, its contribution to GWP is considerable
because its radiative forcing is 296 times higher than that of CO2. The proportions of N2O
contributing to total GWP after manure applications were 55%, 68%, 48%, 87%, and 99% at the
five sites, respectively. The average contributions of N2O account for 59% and 93% of the total
annual GWP at Pullman and Lynden, respectively.
From the perspective of total GWP at each site (see Fig. 9), after the applications of UDM at
the Pullman sites, the total annual GWP gained 125%, 73%, and 154% at WSU 8, WSU 22, and
WSU North, respectively. However, the increases of total annual GWP at Lynden 1 and Lynden
2 were relatively small (only 28% and 2%, respectively).
4. DISCUSSIONS
4.1. Gas Emissions
The short duration flux increases in CH4 imply that the released CH4 was from the manure
itself and not a result of biological action within the soil. The reason was that the DMs were
stored in lagoon for long period of time and therefore any super-saturation of methane resulting
from AD was removed or diminished. If AD effluent was taken directly (not lagoon stored AD
effluent), a much larger spike in the first day would emerge as compared to UDM. The presence
of dissolved CH4 within the manure has notable implications on dairy manure management and
development of carbon credit protocols for dairies, as this additional release should be
incorporated into any baseline calculations.
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Higher temperature and greater WFPS corresponds to higher background CO2 fluxes. This is
in accord with the review work by Wu and McGechan who conclude that the decomposition rate
increases with increasing temperature and SWC (of course, the decomposition rate may decrease
with increasing SWC at very high value). The temperatures of the two sites at Lynden were
much lower than those of the other three sites at Pullman (8 vs. 20ºC), and Lynden had higher
background CO2 fluxes than Pullman (11.317 vs. 3.286 kg CO2-C ha−1 d−1), which implied that
low temperature was not a limiting factor for GHG emissions from the farms at Lynden. The
higher background CO2 fluxes at these two sites might be caused by the higher decomposable
soil organic matter contents enhanced by relatively high SWCs. In addition, it is worth noting
that the average daily CO2 fluxes at Lynden were calculated from a period of ~2 days, which was
much less than the 4 to 9 days of observations at Pullman. Even so, the two Lynden sites
produced lower average CO2 fluxes. The proposed mechanism behind this response is that liquid
manure applications do increase decomposable carbon and CO2 fluxes.
Similar to CO2, the two sites at Lynden with lower temperature and greater WFPS during the
sampling period had higher background N2O fluxes. Although the results for N2O varied from
those for CO2, they conveyed the same important information about the difference between the
two areas. Under conditions of indistinct background emissions, average daily N2O fluxes
following manure applications were much lower at Lynden than at Pullman.
Other researchers have verified that increases of N2O fluxes occurred in the first few days
after manure applications which were dominated by denitrification conditions . According to
Stevens and Laughlin and van der Meer , basic denitrifying conditions include: (i) readily
decomposable carbon in manures; (ii) NO3− in the soils; and (iii) O2 deficiency. The second
condition (NO3−) was also satisfied at Lynden with DM, since the background N2O emissions
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were higher than those from Pullman (0.008 vs. 0.005 kg N2O-N ha−2 d−1). The third condition
(O2) should be more favorable at Lynden because of their high WFPS before manure
applications. Therefore, the first condition actually created by the applied manures could be the
controlling factor. Compared with the Pullman sites, the narrow C:N ratio resulting in less
decomposable carbon in the Lynden sites might inhibit the denitrification process to produce
N2O .
4.2. Necessity, and Pros and Cons of the Unit Response Curve Method
UR can be calculated based on the field measurements of GHG fluxes (this UR is called
“observed UR” in this paper). However, the observed UR is inadequate for practical applications.
First, the observed UR is derived by discontinuous sampling data due to experimental
limitations. This means the intervals between any two points of the observed UR are usually
unequal. The unequal time intervals signify information loss (for example, the real peak values).
In order to use the UR, an equal-interval UR may be generated by interpolation using the
observed UR. This kind of interpolation is only to enable use of the prior information, and cannot
generate new information. Second, the observed UR (unequal-interval or equal-interval) is
denoted by a series of numbers. The internal relationships between these numbers are ambiguous
and cannot be explained simply and explicitly. Third, observation errors are introduced into the
observed UR, which may make the UR look strange and irregular. Also, some outliers may be
present in the observed UR. Finally, it is hard to directly relate the observed UR to site-specific
properties, which makes it difficult to use, especially, for transplantation to a data-deficient
region.
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In view of these facts, it is necessary to develop an explanatory model to fit the observed UR.
The gamma distribution-based UR (simulated UR) curve method can serve this purpose and is
also has some advantages over the other approaches, such as the simple EF method and complex
process-oriented modeling. First, the UR curve method is feasible and applicable, and the
simulated UR agrees well with the field measurement data. Second, the simulated UR is derived
from short-term observations but it shows more information than the EF method, viz, the
temporal flux variation, the “real” peak value, the time to peak, and the total (potential)
emissions in the long run. Third, there are only three parameters in it to determine the shape and
quantities of UR, which makes it much easier to use and has less uncertainty than the process-
based models with numerous parameters . Finally, the three parameters can be expressed as
functions of site-specific factors such as the background flux. Although the case studies in this
paper only considered manure as surface input, the UR method may also be employed to analyze
the impact of fertilizer applications on GHG emissions.
There are also some limitations in UR compared with the process-based models. First, UR is
a systematic and synthetic approach. Although its parameters are related to site-specific
properties, it does not focus on the detailed transformation processes and their specific
physical/chemical/biological mechanisms. Second, the outputs of UR only concern the amount
and temporal variations of major GHG fluxes after manure applications. It is not like process-
based models which provide plenty of information about the input, output, transformation, and
storage of all forms of carbon and nitrogen in each process. Therefore, the UR method could be
useful for a restricted objective of quantifying GHG emissions after manure applications.
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4.3. Parameter Sensitivity
The factor perturbation (FP) method was used for sensitivity analysis of two parameters (n
and k) for the simulation of CO2 emissions at WSU 8 . The FP method was conducted by
changing one factor regarding to its optimum while keeping the other one unchanged. The
sensitivity analysis result is shown in Fig. 10. The changing magnitude ranged from −50% to
+50% with an interval of 10%. The absolute value of the ratio of Δy (change in objective
function value, i.e., HMLE in Eq. ) to Δx (change in parameter) is a measure of the parameter
sensitivity. As shown in Fig. 10, for the equal variation percentage of n and k, higher relative
sensitivity (|Δy / Δx|) is noted when n is varied as compared to that when k is varied.
4.4. Implications of Unit Response and Its Parameters
The gamma distribution is the common basis for UH and UR. A single gamma distribution is
capable of characterize the hydrograph. However, a combination of two gamma distributions is
more suitable than a single gamma function to quantify the GHG emission processes because the
right tail of the excess gas emission process remains positive for a long time. Some differences
between UH and UR and their derivations are summarized as follows: (i) UH in hydrology, used
in the runoff-routing process, transforms the areal excess rainfall to a direct runoff (the
difference between total runoff and baseflow) process at a specific cross section, viz, the outlet
of a watershed; however, for GHGs, it is expected to estimate the average areal excess GHG
emission process from excess manure application. (ii) The excess rainfall can be estimated by
certain runoff-generation mechanisms before UH is used for flow routing, but it is not easy to
determine the excess (effective) nitrogen/carbon for N2O, CO2, and CH4 emissions. (iii) Long-
term continuous runoff data are available for many watersheds, but GHG flux data are available
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only if a specific experiment is implemented. (iv) The hydrograph of direct runoff usually has a
zero right end, but the time-series curve of excess GHG flux (background flux subtracted from
GHG flux after manure application) usually has a non-zero right tail during a short-term
experiment, which is difficult to describe by a simple gamma distribution. (v) UH is closely
related to the geomorphy of a watershed, viz, UH is characterized by a two or three-dimensional
domain but GHG flux is usually estimated at a point scale (may be up-scaled to a large domain,
such as a farm, a watershed, or a region), it is controlled by the local soil, water, nutrient input,
and carbon–nitrogen dynamics.
The GHG emission rate is influenced by the net gas production (the difference between
production and consumption) process, and is also affected by the parameters governing mass
transfer (mainly referring to gas diffusion) . The parameter β in UR denotes the total amount of
net production of gas in terms of the unit mass of applied nitrogen or carbon (i.e., 100 kg N ha−1
or 1000 kg C ha−1) in manures, and the other two parameters (n and k) correspond to the mass
transfer process of gas. Therefore, the net production and transfer processes are reflected in the
UR method: β determines the total net production, while n and k control the temporal distribution
of the gas emission process.
The physical meaning of the storage-release coefficient (k) demonstrates how long it will
take for the storage to be totally released. A higher soil temperature or bulk density usually
results in a smaller k value. Lower porosity due to higher bulk density, and higher temperature
could shorten the storage period by accelerating the gas release. The parameters for N2O are
highly correlated with the parameters for CO2. Such a consistency between emissions of N2O and
CO2 after manure applications was reported by Ball et al. . This is in accordance with the fact
that the dynamics of carbon and nitrogen are interdependent .
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Obviously, the unimodal UR has provided satisfactory results in this investigation. However,
the response of CO2 and N2O fluxes to manure applications might not always be unimodal. For
example, a strong increase in N2O flux was observed after one week, but only a slight increase
occurred within one week . The field data in this study also indicate that the response curves
were not exactly unimodal, possibly due to experimental errors. Actually, multimodal responses
can also be simulated by the gamma distribution-based UR. For example, a bimodal response can
be easily set up by removing the constraints in Eq., viz, two sets of n and k giving different tp.
5. CONCLUSIONS
A two-parameter gamma distribution-based UR curve methodology is developed in this
paper. It can be used to characterize the GHG emission processes after liquid manure
applications. The estimation of GWP at an annual scale becomes more reliable based on the
developed UR method, which is capable of calculating the total excess GHG fluxes due to
manure applications. In the case studies at the three dairy farms in Washington State, the
background CH4 emissions from the soil in terms of GWP were negligible compared with CO2
and N2O. The results from these studies suggest that the soils in these dairy farms act as a
terrestrial sink for CH4 without manure applications due to the microbial oxidation of CH4
exceeding the CH4 production. However, the manure application can, to a certain degree, change
these fields from a sink to a source within one day, which implies that the CH4 may be released
directly from the liquid manures. After manure applications, the contributions of N2O to the total
GWP accounted for 59% and 93% at Pullman and Lynden, respectively. The total annual GWP
significantly increased by an average of 117% after the applications of UDM at the Pullman
sites, while the increment was only 15% with regard to DM applications at the Lynden sites.
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It is worth noting that this study has attempted to find relationships between the model
parameters and the background GHG fluxes. More data and further studies are needed to
investigate the correlations between the parameters and other site-specific properties.
Acknowledgement: The authors thank the Paul Allen Family Foundation and Climate Friendly
Farming project for providing funding for this research. The authors also thank the unselfish
helps in field data collection and sample analysis from Marc St. Pierre, William Bill, Dr.
Bingcheng Zhao, Jonathan Lomber, Kathleen Dorgan, and Colin Dole.
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Tables
Table 1. Experimental sites for greenhouse gases sampling
Site Geographical location(Latitude, Longitude, Elevation) Sampling period Treatment†
Nitrogen in manure
application (kg N ha−1)
WSU 8 46°41′9″N, 117°14′40″ W, 792 m 8/28/2006–9/1/2006 NM, UDM 282.5
WSU 22 46°41′14″ N, 117°14′33″ W, 796 m 8/7/2006–8/11/2006 NM, UDM 241.1
WSU North 46°41′38″ N, 117°14′12″ W, 750 m 8/11/2005–8/20/2005 NM, UDM 309.2
Lynden 1 48°59′58″ N, 122°28′57″ W, 30 m 3/28/2006–3/30/2006 NM, DM 222.0
Lynden 2 48°57′39″ N, 122°29′26″ W, 30 m 2/28/2006–3/1/2006 NM, DM 235.0†NM, UDM, and DM denote no manure application, undigested manure application, and digested manure application, respectively.
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672
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Table 2. Comparison of greenhouse gas fluxes during sampling period after manure applications with background values
Site
CH4 Mass flux (kg CH4-C ha−1 d−1) CO2 mass flux (kg CO2-C ha−1 d−1) N2O mass flux (kg N2O-N ha−1 d−1)
BackgroundManure application
BackgroundManure application
BackgroundManure application
Average Min Max‡ Average Min Max Average Min Max
WSU 8 -0.001
(0.001) †
0.196
(0.071)
-0.008 1.661 2.381
(0.935)
49.401
(14.844)
13.515 154.570 0.005
(0.014)
0.085
(0.030)
-0.018 0.385
WSU 22 0.001
(0.002)
0.053
(0.048)
-0.002 0.668 4.526
(1.085)
38.818
(10.581)
15.815 149.378 0.007
(0.014)
0.106
(0.042)
0.040 0.238
WSU North -0.002
(0.002)
0.056
(0.013)
-0.003 0.802 2.950
(2.612)
21.867
(5.282)
10.599 117.303 0.002
(0.015)
0.026
(0.007)
0.014 0.085
Lynden 1 -0.004
(0.002)
0.040
(0.020)
0.000 0.192 6.584
(4.036)
17.295
(3.749)
8.696 34.998 0.004
(0.010)
0.016
(0.013)
0.010 0.024
Lynden 2 -0.003
(0.003)
0.192
(0.182)
-0.003 1.171 16.050
(7.713)
18.791
(7.330)
8.342 53.545 0.013
(0.025)
0.015
(0.008)
0.009 0.034
†Numbers in parentheses are standard deviation calculated from 12 replicates (chambers).
‡Min and Max are respectively minimum and maximum (peak) flux calculated by the 1-h measurement during the sampling period.
31
673
674
675
676
3334
35
Table 3. Derivation of parameters for Unit Response (UR) curve
Dairy Farm GHG β† tp (h)‡ n‡ k (h) ‡ NormalizedManure Application¶
Total Excess Flux# (kg ha−1)
Emission Ratio††
WSU 8
CH4 0.111 7.14 5.60 1.55 5.37 0.60 0.01%
CO2 42.838 10.93 2.92 5.69 5.37 229.93 4.28%
N2O 0.139 11.43 10.00 1.27 2.83 0.39 0.14%
WSU 22
CH4 0.060 6.08 5.23 1.44 4.58 0.27 0.01%
CO2 39.011 6.00 1.96 6.22 4.58 178.71 3.90%
N2O 0.191 15.03 2.96 7.66 2.41 0.46 0.19%
WSU North
CH4 0.052 1.83 2.58 1.16 5.87 0.31 0.01%
CO2 41.000 0.24 1.01 23.60 5.87 240.87 4.10%
N2O 0.084 0.82 1.02 43.00 3.09 0.26 0.08%
Lynden 1
CH4 0.045 4.44 2.15 3.85 2.89 0.13 0.00%
CO2 14.161 2.00 1.25 7.97 2.89 40.87 1.42%
N2O 0.024 6.69 1.30 22.30 2.22 0.05 0.02%
Lynden 2
CH4 0.067 2.65 4.67 0.72 3.06 0.20 0.01%
CO2 3.119 2.89 7.67 0.43 3.06 9.53 0.31%
N2O 0.002 2.00 2.79 1.12 2.35 0.005 0.002%†Multiplier for UR in Eq. (14), in units of kg N ha−1 for N2O, kg C ha−1 for CO2 and CH4.‡ tp is the time to peak; n is the number of cascaded chambers; k is the storage-release coefficient. §kg N ha−1 for N2O and kg C ha−1 for CO2 and CH4.¶Normalized by 100 kg N ha−1 for N2O and 1000 kg C ha−1 for CO2 and CH4.
#Total excess flux (kg N ha−1 for N2O, and kg C ha−1 for CO2 and CH4) due to manure application.
††Total excess flux divided by manure application.
32
677
678
679680681682
683
684
3637
38
Table 4. Estimated annual GHG emissions and global warming potential (GWP)
Dairy Farm GHG
Background emissions Emissions after manure applications
Flux† GWP‡ Flux GWP
(kg ha−1) (kg CO2-eq ha−1) (kg ha−1) (kg CO2-eq ha−1)
WSU 8CH4 -0.49 -11.19 0.31 7.08CO2 3186.57 0.00 4029.66 843.09N2O 2.87 848.89 3.48 1031.54
WSU 22 CH4 0.49 11.19 0.85 19.62CO2 6057.30 6057.30 6712.55 655.25N2O 4.02 1188.44 4.74 1402.64
WSU NORTH
CH4 -0.97 -22.39 -0.57 -13.02CO2 3948.08 0.00 4831.26 883.18N2O 2.29 679.11 2.70 799.92
Lynden 1
CH4 -1.95 -44.77 -1.77 -40.79CO2 8811.59 0.00 8961.44 149.85N2O 2.29 679.11 2.38 703.89
Lynden 2
CH4 -1.46 -33.58 -1.19 -27.30CO2 21480.25 0.00 21515.19 34.94N2O 7.456 2207.10 7.464 2209.29
†kg CH4 ha−1, kg CO2 ha−1 and kg N2O ha−1for CH4, CO2 and N2O, respectively. The background CO2 has no contribution to GWP.‡CO2-eq = CO2-equivalents based on the GWP of greenhouse gases relative to CO2; CO2-equivalents of N2O and CH4 are 296 and 23 times that of CO2, respectively.
33
685
686687688689690
3940
41
Figures
Figure captions
Figure 1. Experimental sites in Whitman and Whatcom Counties, Washington for Greenhouse Gases sampling.
Figure 2. Instantaneous Unit Response (IUR) curve, n = 2.5, k = 7.6, w = 0.5, kc = 0.1 for two sets of cascaded chambers in parallel expressed by Eq. (6), kc = 1 corresponds to a single set of chambers expressed by Eq. (3).
Figure 3(a–c). Unit Response (UR) curve and Cumulative excess flux at the WSU 8 site during the sampling period. (a) CH4; (b) CO2; (c) N2O. UR for N2O is based on 100 kg N ha−1, and UR for CH4 and CO2 is based on 1000 kg C ha−1 in the manure; UR_observed is the observed UR; UR_simulated_1h means the UR simulated with a 1-hour time step.
Figure 4(a–c). The same as in Figure 3 but for the WSU 22 site.
Figure 5(a–c). The same as in Figure 3 but for the WSU North site.
Figure 6(a–c). The same as in Figure 3 but for the Lynden 1 site.
Figure 7(a–c). The same as in Figure 3 but for the Lynden 2 site.
Figure 8(a–f). Relationships between UR parameters and the background CO2 flux rate. (a), (b), and (c) correspond to natural logarithm of the storage-release coefficient ( ),
number of cascaded chambers in UR ( ), and natural logarithm of the multiplier (
) depending on the background CO2 flux rate, respectively; (d), (e), and (f) show the storage-release coefficient (k), inverse of time to peak (tp), and inverse of multiplier (β) of N2O vs. CO2, respectively.
Figure 9. Comparison of annual global warming potentials (GWPs) between background emissions and emissions due to manure applications (WSU sites with undigested manure, and Lynden sites with digested manure)
Figure 10. Parameter sensitivity for CO2 emissions at WSU 8. n and k refer to the number of chambers and the storage-release coefficient, respectively; x* denotes the optimal parameter value (n or k); Δx denotes the change in parameter value (n or k) pertaining to x*; Δy means the change in the objective function value (HMLE); and |Δy / Δx| is the absolute value of the ratio of Δy to Δx.
34
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699700701702
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710711712
713714715
716717718719720
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Figure. 1
Figure 2
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4546
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(a) CH4
36
726
727728
729
730
4849
50
(b) CO2
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731
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733
5152
53
(c) N2O
Figure 3(a–c)
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5455
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(a) CH4
39
738739
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741
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59
(b) CO2
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743
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745
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(c) N2O
Figure 4(a–c)
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65
(a) CH4
42
750751
752
753
6667
68
(b) CO2
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6970
71
(c) N2O
Figure 5(a–c)
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7273
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(a) CH4
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763764
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(b) CO2
46
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769
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(c) N2O
Figure 6(a–c)
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(a) CH4
48
776777
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779
8485
86
(b) CO2
49
780
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782
8788
89
(c) N2O
Figure 7(a–c)
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787
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92
(a)
(b)
51
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(c)
(d)
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(e)
(f)
Figure 8(a–f)
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101
0
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1000
1500
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WSU 8 WSU 22 WSU North Lynden 1 Lynden 2
Annu
al G
loba
l War
min
g Po
tent
ial
(kg
CO
2-E h
a−1)
Dairy Farm
Background
Manure Application
Figure 9
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808
102103
104
0.0
0.5
1.0
1.5
2.0
-50 -40 -30 -20 -10 0 10 20 30 40 50
|Δy
/ Δx|
Δx / x*(%)
kn
Figure 10
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