Introduction
Rice cultivation is a major source of anthropogenic methane and a prime
target of greenhouse gas mitigation efforts (Tian et al., 2016; Smith et al.,
2008). Globally, the methane emission from rice cultivation was about
18.3 Tg CH4 yr-1 under intermittent irrigation and
38.8 Tg CH4 yr-1 under continuous flooding in the 2000s (Zhang
et al., 2016). Methane fluxes in rice paddies varied extensively with
environmental and agronomic factors. Certain factors, such as rice biomass
(Bachelet and Neue, 1993), organic matter input (Kern et al., 1995), water
management (Khosa et al., 2011; Mishra et al., 1997), paddy soil properties
(Yao et al., 1999; Gaunt et al., 1997), climate (Sass et al., 1991), and rice
varieties (Su et al., 2015; Ding et al., 1999), have been recognized as
having significant impacts on methane emissions. Other factors, such as
atmospheric CO2 and ozone contents (Dijkstra et al., 2012; Bhatia et
al., 2011; Inubushi et al., 2011), N fertilizer application (Banger et al.,
2012; Xie et al., 2010a), and active soil organic C (Zhan et al., 2011), and
even the field management of rotation crops
(Weller et al., 2016), are also receiving increasing attention. Because so
many factors affect the production, oxidation, and emission of methane from
rice cultivation, the observed methane fluxes varied extensively both
spatially and temporally.
Numerous methods have been applied for estimating national and global
inventories of rice paddy methane emissions, including metanalysis of
direct measurements, process models, and empirically based statistical models.
However, the range of national and/or global source estimates remains large (Cao et
al., 1996; Sass et al., 1999; Chen et al., 2013). The major factors that are
known to regulate rice paddy methane emissions include agricultural
management practices (Khosa et al., 2011; Sanchis et al., 2012; Sass et al.,
1992; Bodelier and Laanbroek, 2006) and environmental conditions, such as
climate and soil properties (Conrad et al., 2007; Inubushi et al., 2011; Sass
et al., 1991). Currently, techniques for calculating methane emissions differ
substantially and usually consist of scenario simulations (Ito and
Inatomi, 2012; Van Bodegom et al., 2002a, b; Verburg et al., 2006), without
integrated consideration of methodological fallacy and data insufficiency.
By extrapolating field measurements obtained from experiments, methane
emissions from the 30 million ha of land under rice cultivation in China were
estimated to range from 21.6 to 30 Tg CH4 yr-1 (Matthews et al.,
1991; Taylor et al., 1991), much larger than the result of a recent study
(Zhang et al., 2016). The extrapolation of methane emission rates from site
measurements to larger regions is unlikely to yield reliable results because
of the tremendous spatial heterogeneity in
environmental conditions and agronomic activities (Ogle et al., 2010). Other
studies have described the relationships between methane emissions and rice
NPP (net primary productivity) (Bachelet and Neue, 1993) and organic matter
inputs
(Bachelet et al., 1995). Ambient temperature and the use of nitrogen (N)
fertilizer have also been identified as determinants of methane emissions
(Kern et al., 1995; Bachelet et al., 1995). Until the significant reduction
in methane emissions caused by mid-season drainage was confirmed (Sass and
Fisher, 1997; Yagi et al., 1997; Li et al., 2002; Yan et al., 2005), all
previous regional and national estimates (obtained using extrapolation or
regression equations) were derived from continuously flooded rice fields.
More factors, such as the (Watanabe et al., 1995;
Butterbach-Bahl et al., 1997; Ding et al., 1999; Inubushi et al., 2011) soil
properties (Sass et al., 1994; Yao et al., 1999), atmospheric CO2
(Dijkstra et al., 2012; Xie et al., 2010b), and ozone (Bhatia et al., 2011)
concentrations involved in rice cultivation, have also been incorporated into models designed to estimate
methane emissions from rice paddies. Complex interactions among these factors
have spurred model development (Cao et al., 1995; Li, 2000; Matthews et al.,
2001; Huang et al., 1998, 2004; Van Bodegom et al., 2001). To delineate
variations in methane emissions and to reduce uncertainties, the impacts of
these factors on the production, oxidation, and emission of methane were
mathematically incorporated into the models. Models with more factors
are able to reduce uncertainties in estimating methane emissions,
but the estimates generated by these models still differ significantly across
multiple spatial and temporal scales (Butenhoff et al., 2009; Ren et al.,
2011; Chen et al., 2013).
Reduction of the uncertainty in estimated methane emissions requires the
development of an effective and reliable model that incorporates various
paddy environments and agronomic activities. However, our understanding of
the complex biogeochemical processes that occur in paddy soils is poor. When
estimating methane emissions from rice agriculture, only factors that are
thought to be key determinants of methane emissions have been incorporated
into the models. Excluding other factors introduces errors into the model
output (Eqs. S6 and S7 in the Supplement). Improving our knowledge of methane
processes in the future will increase the number of factors that are
integrated into models and potentially delineate details related to
spatiotemporal variations.
Uncertainties in regional estimates of methane emissions from rice paddies
stem not only from fallacy in the applied models but also from errors and
inadequate data, which we discussed in a previous study (Zhang et al., 2014;
Sect. S4 in the Supplement). A model with more factors generally performs
better than a model with fewer factors but requires a larger amount of data
to facilitate model application. A model with good performance (less fallacy)
can still result in large uncertainties when the available input data (e.g.,
soil properties, rice irrigation, types and amount of organic matter) are
insufficient (Zhang et al., 2014; Ito et al., 2012).
Methods and their input scenarios.
Methods
Input scenario
Reference
R1: CCH4=0.3×Cinput
R1–S0: case-specific C input, adjusted with the water regimea.
Neue et al. (1990)
R2: CH4=-0.006×Cinput
R2–S0: case-specific C and N input.
Kern et al. (1997)
+0.078×Ninput
R2–S1: case-specific C input, averaged N input in all cases.
+0.885×RC/N+21.15
M: CH4MOD model
M–S0: case-specific inputs of all model variables: e.g., organic matter amendments, soil properties, and water regimesb.
Huang et al. (1998, 2004);Xie et al. (2010a)
M–S1: case-specific inputs of soil properties and water regimes; other model variables use averaged values for all 495 cases.
M–S2: case-specific inputs of organic matter amendments; all other model variables use averaged values for all 495 cases; the water regime was assumed to be multi-drainage irrigation.
M–S3: no case-specific inputs used for soil properties or organic matter amendments; the water regime was assumed to be multi-drainage irrigation.
a Regression equation R1 was developed according to
measurements conducted in continuously flooded fields, and the calculated
flux was therefore adjusted by a scaling factor of 1.00, 0.65, or 0.56 for
continuous flooding, single drainage, or multi-drainage irrigation,
respectively (IPCC, 2006). b The water regimes in the CH4MOD model
(Huang et al., 2004) are more specifically defined and differ from those of
the IPCC (2006).
In the present study, we analyzed the uncertainties in experimental
measurements of methane fluxes in different rice paddies. We also evaluated
the performance of different methods involving a diversity of input
variables and the influence of data availability on the performance of these
methods. Finally, the uncertainty in the national emissions inventory as a
consequence of variable model performance and according to the quality and
availability of input data was discussed.
Materials and methods
Field measurements of methane emissions from rice paddies in
China
The observational data used in this study (Table 1) consisted of field
methane fluxes measured at 33 sites (Fig. 1). We obtained these measurements
from the published literature concerning all crop rotations with rice
cultivation in China (double rice, winter wheat, and rice rotation; single
rice crop cultivation; and so forth) (Wei, 2012). A total of 495 measurements
were taken at the 33 sites, after excluding those that had been used for the model
calibration (Neue et al., 1990; Kern et al., 1997; Huang et al., 2004). The
amount of organic matter added to the rice paddies ranged from 0 to
15.3 t C ha-1 and included animal manure, green manure, crop straw,
biogas residuals, and their various components. The applied water regimes
consisted of continuous flooding, single mid-season drainage, and
multi-drainage irrigations.
Locations of the experimental sites (red stars). The background map
represents the spatial distribution of rice paddies in China. The size of the
red stars is proportional to the number of measured methane fluxes at the
site. The polygons show zones of different crop rotation systems involving
rice: I – double rice rotation, II – mixed zone of rice and rice rotation
and rice and upland crop rotation, III & IV – rice and upland crop
rotation or rice and fallow rotation, V & VI – rice and fallow rotation,
and VII – no rice.
Flowchart for estimating regional and national methane emissions and the
uncertainties associated with field measurements and modeling.
Model performance was assessed by comparing the model estimates with the
measurements. To drive the models, data pertaining to rice yields, soil
properties, and crop phenologies were collected from the relevant literature
(Sect. S2 in the Supplement).
Performance of the methods used to estimate methane emissions
The uncertainties produced by the models derive from model fallacy (Kennedy
and O'Hagan, 2001; Sect. S3 in the Supplement) as well as from the quality
and availability of data (Fig. 2). Model performance was assessed by
comparing model outputs with the direct measurements (left part in Fig. 2).
Errors in the input data of the model can be propagated in the obtained
estimates (right side of Fig. 2, Sect. S4 in the Supplement).
Many techniques are available for calculating estimates of rice paddy methane
emissions, such as extrapolation of measured emission rates (Khalil et al.,
1991, 1993), statistical regression equations (Bachelet et al., 1995; Kern et
al., 1995, 1997), and the application of models of varying complexity (Cao et
al., 1995; Matthews et al., 2001; Van Bodegom et al., 2001; Huang et al.,
1998; Li, 2000). Here we chose two regression models (Neue et al., 1990; Kern
et al., 1997) and CH4MOD (Huang et al., 2004) because they differed
explicitly in levels of structural complexity. We compared the performance of
these methods under different levels of data availability (Table 1) using
experimental field measurements as a point of reference (Fig. 1). In Table 1,
R1 represents a simple regression equation in which the carbon (C) input is
the sole predictor (Neue et al., 1990). Regression equation R2 is slightly
more complicated in that it uses organic C and fertilizer N application as
inputs (Kern et al., 1997). We assumed two data availability scenarios for
R2. In R2–S0, both the C and N inputs are available; in R2–S1, only the C
input is available (Table 1).
The third approach consists of a semiempirical model, CH4MOD. This model was
developed to simulate methane emissions from rice paddies under diverse
environmental conditions and various agricultural practices (Huang et al.,
1998, 2004). The input variables of the model include the climate, soil
conditions, water management type, organic matter application, and crop
rotations. The model consists of two modules: the derivation of methanogenic
substrates from added organic matter and rice root exudates and the
production and emission of methane. Rice biomass is a key variable used to
calculate the root exudates and the fraction of the methane emitted by rice
plants and bubbles. The daily changes in the soil redox potential (Eh) were
calculated according to various water manipulations conducted in the rice
paddies (Xie et al., 2010b). The influences of other environmental factors,
such as soil temperature and texture, on the decomposition of organic matter
and the production of methane were expressed as specific coefficient
functions (Huang et al., 1998). The input variables of the CH4MOD model
(Sect. S2 in the Supplement) include the daily air temperature, soil sand
percentage (SAND), organic matter amendment (OM), rice grain yield (GY),
water management pattern (Wptn), and rice cultivar index (VI).
Four model input scenarios (Table 1) were scheduled to evaluate the
performance of CH4MOD under different levels of data availability. In M–S0,
all of the model variables were assigned specific values. In M–S1, the
application of organic matter was assigned the average value for all
experiments, thus assuming a situation where no detailed information on
organic matter application was available. In M–S2, detailed information on
the water regime and soil properties was assumed to be unavailable. In M–S3,
detailed information on all three major factors (organic matter application,
soil properties, and water regime) was assumed to be unavailable.
The estimation residuals (Δy, Eq. 1), relative bias (rb,
Eq. 2), and coefficient of variations (rv, Eq. 3) were thus
evaluated as follows:
Δyk=y^k-yk,i=1,2,…,nrb=E(Δy)E(y)×100%rv=E((Δy)2)-(E(Δy))2E(y)×100%,
where y represents the measured methane fluxes, y^ is the estimate
of y, and n is the total number of measurements. E(⋅) indicates the
statistical mean. The mean of the squared errors (MSE) of the estimation is
calculated as follows:
MSE=E((Δy)2)=(E((Δy)2)-(E(Δy))2)+(E(Δy))2=(F×rv)2+(F×rb)2,
where F=E(y) represents the mean of the measured methane fluxes
(yk).
Uncertainties in estimating rice paddy methane emissions on
national scales: data error and availability
In addition to model fallacy, the difficulties in estimating national rice
paddy methane emissions also stem from errors in, and limited availability
of, input data. To measure the uncertainties in model outputs due to
insufficient data quality and availability, we applied Monte Carlo
simulations (Penman, 2000) to the CH4MOD model. Statistical characteristics
were derived from the available datasets to develop probability distribution
functions (PDFs) for each model input variable (Tables S1 and S2 of Sect. S2
in the Supplement). We performed Monte Carlo simulations by randomly drawing
values of the model input variables from their PDFs and then running the
model. This process was iterated 1000 times and at the last step the mean and
95 % CI (confidence interval) of the calculated methane fluxes were
derived from the iterations.
The factors involved in the uncertainty analysis included organic matter
application, soil properties, and water regimes; these variables (OM, SAND,
and Wptn) were parameterized as input variables in the CH4MOD model
(Huang et al., 2006; Zhang et al., 2011). The other two model input variables
were the rice grain yield and daily ambient air temperature. These two
variables were not used in the uncertainty analysis because sufficient
relevant data were available, which were characterized by less errors compared
with the other variables (Zhang et al., 2014).
The SAND data were obtained from a 10 km × 10 km grid dataset
interpolated from soil survey data (Oberthür et al., 1999; Shi et al.,
2004; Liu et al., 2006). It is possible that approximately half (Van Bodegom
et al., 2002b) of the immense spatial variation in soil properties can be
lost after spatial interpolation (Goovaerts, 2001); as a result, the missing
spatial variation was attributed to the PDF of the gridded SAND data
(Sect. S2 in the Supplement).
The organic matter inputs in the rice fields consisted of various types of
farm manure (green manure and animal feces), crop straw, and dead roots and
stubble leftover from previous harvests. Root and straw biomass were
calculated using the root / shoot ratio and harvest indices (Huang et al.,
2007; Gao et al., 2002; Xie et al., 2010c). Stubble was assumed to represent
1/10 of the straw biomass (Huang et al., 2004). The proportions of
incorporated straw and applied farm manure were derived from data obtained
from two large-scale investigations, the First National Census of Pollution
Sources conducted by China's Ministry of Environmental Protection (CFPC,
2011) and a census conducted by the Institute of Atmospheric Physics, Chinese
Academy of Sciences. The proportion of straw and the amount of manure
incorporated into the crop fields were summarized by province. Table S1 shows
the statistical parameters of the PDF of organic matter incorporation in each
province.
The irrigation in rice cultivation were grouped into five general irrigation
patterns: (1) flooding-drainage-flooding-intermittent irrigation,
(2) flooding-drainage-intermittent irrigation, (3) flooding-intermittent
irrigation, (4) continuous flooding, and (5) continuously intermittent
irrigation (Gao and Li, 1992; Huang et al., 2004). Data pertaining to
Wptn were only very rarely available on a regional scale. The
limited information provided in a few studies (Mao, 1981; Liang, 1983; Xiong
et al., 1992; Cai et al., 2003; Ma et al., 2005; MWRUC, 1996) could only
yield rough estimates related to irrigation in regions of major rice
cultivation. The PDFs of field irrigation were defined by the occurrence
percentage of each irrigation pattern (Table S2 in the Supplement).
The data pertaining to the rice grain yield and harvesting area as of 2005
were obtained from China's Statistical Yearbook (EBCAY, 2006) and the
nation's agricultural database maintained by the Chinese Academy of
Agricultural Sciences, respectively. The spatial distributions of all rice
paddies in 2005 and the rice paddy area within each 1 km × 1 km
grid were obtained from the Data Center for Resources and Environmental
Sciences of the Chinese Academy of Sciences (RESDC, CAS). Daily mean air
temperature data from 678 meteorological stations throughout China for 2005
were acquired from the National Meteorological Information Center (NMIC) of
the China Meteorological Administration (CMA) (http://data.cma.cn/).
The temperatures were then spatially interpolated into
10 km × 10 km grids for each day according to the method described
by Thornton et al. (1997). Details on the datasets used in this study can be
found in Sect. S2.
To preserve details related to spatial variations, all data input into the
model were converted into 10 km × 10 km grids. The applied
rasterization techniques and details of how the model was run on raster
datasets were provided in previously published papers (Huang et al., 2006).
Statistical representations of the measured methane fluxes.
(a) Statistical parameters and (b) histogram of the
measurements. The solid circles represent the sample mean, and the vertical
bars are the 95 % confidence intervals of the samples, from the 2.5 %
percentile to the 97.5 % percentile. The dashed line indicates the
arithmetic average of all measured fluxes (mc). The solid line is
the area-weighted mean of the methane fluxes (mw), in reference to
the areal proportion of each water regime in the national total rice
harvesting area: 10 % continuous flooding (Flooded), 20 % single
drainage (Single-D), and 70 % multi-drainage (Multi-D) (Xiong et al.,
1992; MWRUC, 1996; Li, 2001; Zou et al., 2009).
Combining uncertainty and spatial aggregation
In each 10 km × 10 km grid, the uncertainties in our estimates
originated from both the model fallacy (Eq. 4) and error in the input data.
Equation (5) was used to merge the two uncertainty sources where MSE was
again split into two parts as showed in Eq. (4):
σT,i2=σb,i2+σv,i2+σd,i2=(Fi×rb)2+(Fi×rv)2+σd,i2,
where σT,i represents the uncertainty of the methane flux in grid
i, and Fi and σd,i represent the mean and standard
deviation of the Monte Carlo simulation results in grid i, respectively.
rb and rv represent the same entities as in Eqs. (2) and
(3).
σd,i2 signifies the uncertainty caused by the error and
availability of data, (Fi×rb)2 represents the modeling
bias, and (Fi×rv)2 represents the rest parts of the
model fallacy apart from (Fi×rb)2. To produce the
uncertainty of the national inventory, the three components ((Fi×rb)2, (Fi×rv)2, and
σd,i2 in Eq. 5) of the estimation uncertainties in all
grids were separately aggregated (Eqs. S15, S16, S17, and S18 in Sect. S4 of
the Supplement) and summed as follows:
σT2=σb2+σv2+σd2.
Results
Methane emissions and the uncertainties derived from field
measurements
Among the 495 methane flux measurements (the accumulative methane emission
from transplanting to harvesting), 184 (37 % of all cases) came from
paddies that were continuously flooded during the entire rice growing period,
50 (10 % of all cases) came from paddies with single mid-season drainage,
and 261 (53 % of all cases) came from paddies under multi-drainage. The
average methane fluxes associated with the three water regimes were
531.6 ± 512.6, 251.6 ± 231.1, and
224.1 ± 207.5 kg CH4 ha-1 (Fig. 3a). The
overall arithmetic average of the 495 measurements (represented hereafter by
mc) was 341.2 ± 383.2 kg CH4 ha-1. However, the
simple arithmetic average might be a biased representation of the “true”
mean methane flux of rice paddies in China since far less than 37 % of the
rice paddies in China are continuously flooded. In the literature, 10, 20, and
70 % of the rice area was reported to be under continuous flooding,
single drainage, and multi-drainage water regimes, respectively (Xiong et al.,
1992; MWRUC, 1996), and the harvested-area-weighted mean (Sect. S1 in the
Supplement) of the measured fluxes (represented hereafter by mw)
was 260.4 ± 281.6 kg CH4 ha-1 (Fig. 3a).
P-P plots of the cumulative probability of the measured methane
fluxes vs. the gamma distribution. (a) Single-drainage irrigation
cases, (b) multi-drainage irrigation cases, (c) continuous
flooding irrigation cases, and (d) all cases after being area
weighted (Sect. S1). n, avg., and SD represent the sample size, statistical
mean, and standard deviation of the sample methane fluxes, respectively.
α and β represent the shape and scale parameters of the gamma
distribution, which were calculated with the statistical mean and variance of
the measured methane fluxes; β=(SD)2/(avg.) and
α=(avg.)/β. The diagonal line is the 1 : 1 straight
line for a perfect gamma distribution match.
The 95 % CIs of the methane flux measurements were
61.1–2145.9, 9.6–809.9, and 14.0–797.7 kg CH4 ha-1,
respectively, for the three water regimes (continuous flooding, single
drainage, and multi-drainage in Fig. 3a). The 95 % CI of all combined
area-weighted measurements (Sect. S1 in the Supplement) was
13.7–1115.4 kg CH4 ha-1. The measurements were not normally or
symmetrically distributed (Fig. 3b). The P-P plots (Fig. 4) showed that the
parameterized gamma distributions matched the sample distributions. The
95 % CIs calculated with the parameterized gamma functions were
16.8–1900.8, 10.4–863.4, and 8.9–774.2 kg CH4 ha-1,
respectively, for the three water regimes (continuous flooding, single
drainage, and multi-drainage); these values overlapped the CIs
derived directly from the measurements by 88.2, 99.9, and 97.0 %,
respectively.
The national methane emissions from rice agriculture calculated by
multiplying the rice harvesting area (yearbook data in 2005) by the
area-weighted mean flux (260.4 ± 281.6 kg CH4 ha-1) was
7.51 Tg CH4 (Fig. 3a). When the measurements are statistically
independent, the standard error (SE) of the summation is n-1 (n is the
sample size of the measurements) times smaller than the standard deviation
(±281.6 kg CH4 ha-1), which consists of the representative
and measurement errors of the measured fluxes (Van Bodegom et al., 2002a;
Verburg et al., 2006). Assuming that the measurements were statistically
independent, the 95 % CI of the national inventory was
7.20–8.58 Tg CH4 (Eq. S3 in the Supplement). However, the
independency assumption is questionable because of the spatial correlations
between the spatially correlated background environmental conditions and
agricultural activities (Legendre, 1993; Dormann et al., 2007). The
equivalent sample size used to calculate SE may be smaller than 495, and the
95 % CI of the national inventory is therefore larger than that with the
independency assumption.
Model performance under different situations of data
availability
The averaged bias of the estimate obtained with R1 was
212.0 kg CH4 ha-1 (Table 2) or 62.1 % of the measured mean
(mc=341.2 kg CH4 ha-1). The average bias of R2, in
contrast, was -1.3 kg CH4 ha-1. R1 was more likely to
overestimate the amount of methane emitted than R2 (Table 2), especially when
more organic matter was incorporated (Fig. 5a). For example, in one case the
modeled CH4 flux was more than 6000 kg CH4 ha-1, whereas
the measured flux was less than 3000 kg CH4 ha-1 (Fig. 5a). The
estimates obtained using R2 did not show significant variations and appeared
to decline when the measured methane fluxes increased (Fig. 5b). The CH4MOD
model also produced a small averaged bias, representing 7.1 % of the
measured mean. The MSE was 253.0, 407.8, and 596.0 kg CH4 ha-1
for the M–S0, R2–S0, and R1–S0 scenarios, respectively (Table 2), which
demonstrates that model performance improves when more factors are
incorporated into the model.
Methane fluxes in the experiments plotted against the respective
simulation results through different methods. (a) R1–S0,
(b) R2–S0, and (c) M–S0, which are described in Table 1.
Histograms and their fitting gamma probability lines for the
calculated methane fluxes (via CH4MOD) of the 10 km × 10 km rice
paddy grids in China. (a) Single rice rotations, including
rice-fallow rotations, and rotations of rice with upland crops;
(b) early and (c) late rice in double rice rotations. The
vertical bars are the histograms of the calculated Fj (Eq. 5), and the
solid line is the theoretic gamma PDF line, the parameters for which were
derived from the statistics for Fj via momentum methods.
Performance of the methods under different scenarios of data
availability.
Method
Bias of the
SD of the estimation
Root of
estimation (rb)
residues (rv)
MSE (RMSE)
R1–S0
212.0 (62.1 %)*
577.1 (163.3 %)
596.0 (174.7 %)
R2–S0
-1.3 (-0.4 %)
407.8 (119.5 %)
407.8 (119.5 %)
R2–S1
-4.9 (-1.4 %)
415.7 (121.8 %)
415.7 (121.9 %)
M–S0
-24.2 (-7.1 %)
251.8 (73.8 %)
253.0 (74.1 %)
M–S1
-30.8 (-9.0 %)
343.9 (100.8 %)
345.2 (101.2 %)
M–S2
-120.7 (-35.4 %)
341.3 (100.0 %)
362.9 (106.1 %)
M–S3
-109.8 (-32.2 %)
401.8 (117.8 %)
416.6 (122.1 %)
* Percentages in parentheses indicate
the magnitude of the error relative to the overall average methane flux
(341.2 kg CH4 ha-1) for all cases.
Although the CH4MOD model produced better simulation results than the simple
regression equations, its performance fundamentally depends on data
availability. When no case-specific data were available (as in scenario
M–S3), rb was -32.2 % and MSE was 122.1 % of the mean
flux; the results obtained under this scenario were even worse than the
results obtained under the R2–S0 scenario (Table 2). For the M–S1 scenario,
where the data pertaining to the soil properties and water regime were
case-specific, the magnitude of rb decreased to 9.0 % of the
mean flux, and the MSE decreased to 101.2 % of the mean flux. The M–S0
scenario produced much better results than the other scenarios since more data
were available for the key model input variables (Table 2). Even no
case-specific input data used in M–S3 had smaller rb,
rv,
and MSE than R1–S0. In Table 2, larger rv of R1–S0 than M–S3
might come from the too simple explanation of the influence from organic
matter inputs on methane emission that added extra error to the estimation.
Inventory of rice paddy methane emissions and the uncertainties
with different approaches
Because of the spatial heterogeneity in the climate and soil properties, organic
matter incorporation, and field irrigation in rice cultivation, the methane
fluxes simulated by CH4MOD varied spatially between 17.2 and
708.3 kg CH4 ha-1 from grid to grid (Fig. 6). The national means
for the simulated methane fluxes were 217.9, 204.6, and
255.8 kg CH4 ha-1 for single, early, and late rice cultivation,
respectively. The within-grid estimation error (σT,i, calculated
with Eq. 5) represented 81.2–95.5 % of the mean fluxes Fi in the
grids. In the present study, model fallacy, represented by
Ub,i+Uv,i, contributed 79.5–88.9 % to the
uncertainty σT,i2, with σd,i2 accounting
for the remaining 11.1–20.5 %. This implies that a model with better
performance is needed to reduce the uncertainty of σT,i in each
grid.
As shown in Fig. 7, the highest levels of emitted methane occurred in
southern China, with the northeast also representing a major source of
methane, despite this region being climatically cool. The total amount of
methane emitted, as calculated by the M–S0 approach, was 6.43
(3.79–9.77) Tg CH4 yr-1 (Table 3), which is close to the
7.51 Tg CH4 yr-1 derived from the experimental field
measurements.
Methane emissions inventory and the uncertainties caused by model
imperfection and errors in model input data.
Scenario
CH4 emission (Tg)
σb+v*
σd
σd/σb+v
σT (Tg)
95 % CI (Tg)
R1–S0
13.59
9.89
1.11
0.11
9.99
1.45–38.98
R2–S0
10.37
2.74
0.14
0.05
2.74
5.71–16.39
R2–S1
10.24
2.91
0.07
0.02
2.91
5.83–17.16
M–S0
6.43
1.15
1.00
0.87
1.53
3.79–9.77
M–S1
7.94
1.89
0.97
0.51
2.13
4.33–12.62
M–S2
7.40
3.16
0.56
0.18
3.12
2.56–14.75
M–S3
9.23
3.79
0.00
0.00
3.79
3.37–18.01
* Root of Ub+Uv, uncertainty owing to
model fallacy in the national inventory.
In Table 3, the estimated national CH4 emissions ranged from 6.43
(3.79–9.77) to 13.59 (1.45–38.98) Tg CH4 yr-1 for the M–S0
scenario and R1–S0 scenario, respectively. The 95 % CIs of the national
estimation differed more among the approaches than those among the
data availability scenarios of each approach. With M–S0, the fallacy of
CH4MOD contributed 56.6 % of the total uncertainty, with the remaining
43.4 % being attributed to errors and the scarcity of the spatial
datasets of the model inputs (Table 4). As an indicator of the trade-off
between the complexity of the approach and data availability, the
σd/σb+v ratio in Table 3 was 0.87 for
M–S0, closer to 1 than those for the other approaches and scenarios, which
also yielded the narrowest 95 % CI in Table 3.
Spatial distributions of rice paddy methane emissions
(× 106 g CH4 per 10 km × 10 km grid).
Discussion
Contributions of different error sources to the uncertainties in
the inventory
In the experimental field measurements (Fig. 1), the variations in rice paddy
methane fluxes ranged from 3.2 to 2451.7 kg CH4 ha-1, averaging
341.2 ± 383.2 kg CH4 ha-1. The average simulated methane
fluxes in the 10 km × 10 km grids varied from 17.2 to
708.3 kg CH4 ha-1 (Fig. 6). The extremely high methane fluxes
obtained from experimental measurements were not reproduced by the model
estimations. This was partly due to the discrepancy in the spatial
representativeness of the methane fluxes in field observations and model
estimations (Verburg et al., 2006). The experimental measurements represented
methane fluxes from an area of less than 1 ha, while the modeled
fluxes were the averages from 10 km × 10 km grids. This mismatch in
spatial representativeness might also be due to errors in the model input
data as well as to the impacts of other unknown factors (Singh and Dubey,
2012; Bhatia et al., 2011; Zheng et al., 2010; Gauci et al., 2008). Methane
emissions could be estimated using a limited number of factors and simplified
equations to express the complex relationships between methane emissions and
influential factors, but such simplification resulted in poor performance of
the methods (Table 2). In Eq. (5),
σd,i is the uncertainty due to errors in the input
data. With an increasing number of explanatory factors, rb and
rv might decrease (which means better performance of the method),
but σd,i might increase because of the cumulative errors
resulting from the increasing number of factors incorporated in the models.
To reduce uncertainties in the estimates and improve the performance of the
model, the input data need to be available and of good quality.
Components of the uncertainty in the national inventory.
Rice
Due to model
Due to data quality
Total
performance
and availability,
Ub
Uv
Ud
UT
σT
Early rice
0.01
0.06 (0.00–0.81)*
0.08
0.15
0.39
Late rice
0.01
0.10 (0.00–1.28)
0.05
0.16
0.40
Single rice
0.07
0.25 (0.00–5.15)
0.24
0.56
0.75
All rice
0.21
1.12 (0.00–22.56)
1.00
2.35
1.53
* Numbers in parentheses represent the range of Uv
depending on the spatial correlation of the model simulation residuals.
Long-distance correlation results in a large aggregated Uv, whereas
short-distance correlation results in a small aggregated Uv.
The aggregated uncertainty of the national inventory depended not only on the
magnitude of σv,i and σd,i in each grid
(i) but also on the spatial correlation between these variables (Eq. S6 in
the Supplement). The spatial correlation of σd,i depends on
the availability of input data for the model and on spatial aggregation
(Table S3 in the Supplement). However, the spatial correlation of
σv,i could not be assessed analytically because it was
a result of model fallacy and errors in measurements. In the case of a strong
correlation of σv,i values, the aggregated
σv2 will account for a large proportion of
σT2 (right side in Fig. 8). However, if the
spatial correlation is confined to a short distance, such as less than four
grids (Dormann et al., 2007; Dray et al., 2006), the contribution of
σv2 to σT2 will be negligible (left side in
Fig. 8). At the midpoint of DC (Eq. S6, 30 grids, equal to
300 km), as shown in Fig. 8, the model uncertainty (σr2+σv2) accounted for 56.6 % of the uncertainty in
σT2 (Table 4).
Composition of the aggregated uncertainty of the national inventory
along with the spatial autocorrelation of the variances of the model residues
in grids. Distance criteria (Dc) are used to define the step
functions of spatial autocorrelation: if two grids diverge by a distance
beyond Dc, the autocorrelation is 0; otherwise, it is 1. The step
function is a simplified version and represents the upper limit of the true
spatial autocorrelation. With the step function, a larger Dc
indicates stronger autocorrelation.
Consistency of errors between model validation and model
upscaling
Upscaling a site-scale model (e.g., CH4MOD in this study) to a national
scale poses enormous challenges when data are scarce. Enhancing the spatial
abundance of the input data minimizes the propagation of data error into the
aggregated uncertainties. Many environmental and agricultural factors impact
methane emissions from rice paddies. In the CH4MOD model, the key factors
were parameterized as model inputs (Huang et al., 2004). However, when
assessing the uncertainty of a model, the explanatory variables are
arbitrarily included (Verburg et al., 2006). Li et al. (2004) found that soil
properties were the “most sensitive factor” and therefore used this
parameter in the uncertainty analysis. The inclusion of as many of the highly
sensitive key factors as possible in the uncertainty analysis should generate
more accurate and reliable results (right part in Fig. 2).
Experimental field studies have shown that the rice variety has substantial
impacts on methane emissions (Aulakh et al., 2008; Inubushi et al., 2011; Jia
et al., 2002). A study of field observations (Su et al., 2015) showed that
transfer of the barley gene SUSIBA2 to rice favors the allocation of
photosynthates to the aboveground biomass over allocation to the roots.
Moreover, less biomass allocation to root exudates results in reduced
methane emissions. The impact that the rice variety has on methane emissions
was parameterized as the variety index (VI) in CH4MOD. According to Huang et
al. (1998), VI ranges from 0.5 to 1.5 and averages 1.0 for most rice
varieties. To validate the CH4MOD model (left portion of Fig. 2) using the
495 methane emission measurements included in the present study, VI was
assigned a default value of 1.0 regardless of the rice variety because until
now no dedicated attempts were made to quantify the VI of different
rice varieties. Therefore, the rb and rv values presented
in Table 2 incorporate the uncertainty in model performance that can be
attributed to different rice varieties (Mf(x) in Eq. S6 of the
Supplement). To maintain consistency, VI was assigned the same default value
(1.0) when the model was scaled-up to the national scale (right side of
Fig. 2), and no PDF was built for the uncertainty calculation conducted with
the Monte Carlo simulation. If a PDF had been incorporated into the
uncertainty calculation when the model was scaled-up, the overall
uncertainties (Table 4) would have been overestimated. However, if different
VI values were assigned to rice varieties during model validation, the error
caused by the inaccuracy of VI would also need to be considered during the
scaling-up of the model to prevent underestimation of the overall
uncertainty.