remote sensing
Article
Geostatistical Analysis of CH4 Columns over
Monsoon Asia Using Five Years of
GOSAT Observations
Min Liu 1,2 , Liping Lei 1 , Da Liu 1,2 and Zhao-Cheng Zeng 1,3, *
1
2
3
*
Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth,
Chinese Academy of Sciences, Beijing 100094, China; [email protected] (M.L.);
[email protected] (L.L.); [email protected] (D.L.)
University of Chinese Academy of Sciences, Beijing 100049, China
Institute of Space and Earth Information Science, The Chinese University of Hong Kong, Shatin 999077,
Hong Kong, China
Correspondence: [email protected]; Tel.: +852-5571-6425
Academic Editors: Xiaofeng Li and Prasad S. Thenkabail
Received: 24 January 2016; Accepted: 20 April 2016; Published: 26 April 2016
Abstract: The aim of this study is to evaluate the Greenhouse gases Observation SATellite (GOSAT)
column-averaged CH4 dry air mole fraction (XCH4 ) data by using geostatistical analysis and
conducting comparisons with model simulations and surface emissions. Firstly, we propose the use
of a data-driven mapping approach based on spatio-temporal geostatistics to generate a regular and
gridded mapping dataset of XCH4 over Monsoon Asia using five years of XCH4 retrievals by GOSAT
from June 2009 to May 2014. The prediction accuracy of the mapping approach is assessed by using
cross-validation, which results in a significantly high correlation of 0.91 and a small mean absolute
prediction error of 8.77 ppb between the observed dataset and the prediction dataset. Secondly, with
the mapping data, we investigate the spatial and temporal variations of XCH4 over Monsoon Asia
and compare the results with previous studies on ground and other satellite observations. Thirdly,
we compare the mapping XCH4 with model simulations from CarbonTracker-CH4 and find their
spatial patterns very consistent, but GOSAT observations are more able to capture the local variability
of XCH4 . Finally, by correlating the mapping data with surface emission inventory, we find the
geographical distribution of high CH4 values correspond well with strong emissions as indicated in
the inventory map. Over the five-year period, the two datasets show a significant high correlation
coefficient (0.80), indicating the dominant role of surface emissions in determining the distribution of
XCH4 concentration in this region and suggesting a promising statistical way of constraining surface
CH4 sources and sinks, which is simple and easy to implement using satellite observations over
a long term period.
Keywords: GOSAT; XCH4 ; spatio-temporal geostatistics; Monsoon Asia
1. Introduction
Atmospheric methane (CH4 ) is the second most important anthropogenic greenhouse gas after
carbon dioxide (CO2 ). Under the driving influence of human activities, such as fossil fuel combustion,
global averaged CH4 concentration has increased from pre-industrial levels of 722 ppb to 1833 ppb in
2014 [1] and has kept an average growth rate of about 6 ppb per year since 2007 [2]. CH4 has a stronger
global warming potential than carbon dioxide; therefore, monitoring CH4 might be a more effective
way to mitigate the short-term greenhouse effects [3].
Current ground-based observation station networks have provided long-term greenhouse gas
observations with high precision; however, the stations are still sparse and inhomogeneous [4]. Satellite
Remote Sens. 2016, 8, 361; doi:10.3390/rs8050361
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observations of CH4 columns, because of their global coverage and high measurement density, can
complement the surface network and be used to improve our understanding of carbon cycle and its
changes. Current satellite instruments for measuring the atmospheric CH4 total column include the
SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) onboard
the European Space Agency’s Environmental Satellite (ENVISAT) [5] and the Thermal And Near
infrared Sensor for carbon Observation Fourier Transform Spectrometer (TANSO-FTS) operated on
the Greenhouse gases Observation SATelite (GOSAT) [6]. CH4 retrievals from SCIAMACHY, which
began operation in 2003, showed the promising role of satellite observations in understanding the
global CH4 distribution and variation [7], but communication with ENVISAT was unfortunately lost
in 2012. The Japanese GOSAT, which was successfully launched in 2009, is the world’s first spacecraft
dedicated to quantifying the atmospheric CO2 and CH4 concentrations [6]. The column-averaged
dry-air mole fractions of atmospheric CH4 (XCH4 ) are retrieved from Short-Wavelength InfraRed
(SWIR) solar spectra observed by TANSO-FTS [8]. The GOSAT aims at providing XCH4 measurements
with accuracy of 2% at a spatial scale of 1000 km square and in three-month averages [9]. The major
sources of CH4 retrieval errors are aerosols and clouds, especially in high altitude, because of their
strongly modification of the equivalent optical path length [8].
However, due to the TANSO-FTS footprint observation mode, sky conditions and retrieval
constraints, valid XCH4 retrievals from GOSAT are greatly reduced and irregularly distributed in
space and time, and have a lot of gaps between them. These limitations make it difficult to directly
infer the spatio-temporal variations of XCH4 and meet the requirements of practical application and
further scientific research using the data. Therefore, it is essential to develop a gap-filling method
for generating regular XCH4 mapping products from the satellite patchy observations. A series
of studies have been carried out in mapping GOSAT retrievals based on the effective geostatistics
framework [10,11], due to its great advantages in utilizing correlation structure within the greenhouse
gas observations and its best linear unbiased prediction capability. The ordinary kriging (OK) approach
was first applied by Tomosada et al. [12] to predict global XCO2 concentration, by considering the
spatial variability of GOSAT Level 2 XCO2 data in different land types and directions. The method was
further adopted by National Institute for Environmental Studies (NIES) GOSAT to generate the GOSAT
Level 3 data products of global monthly mean XCO2 and XCH4 [13]. Hammerling et al. [14] improved
the OK method by applying a moving window technique to generate global XCO2 distribution
map and found that the prediction precisions are the best for temporal resolution in two to four
days. Tadić et al. [15,16] further explored the combination of the moving window block kriging
technique and ensemble neural networks. To optimize calculation of large satellite datasets, fixed
rank kriging (FRK) approach was introduced by Katzfuss et al. [17] to interpolate simulated Orbiting
Carbon Observatory (OCO) XCO2 data, combined with expectation maximization (EM) algorithm,
which resulted in a more rapid and accurate prediction. Furthermore, to improve the spatial-only
geostatistics in mapping by previous studies, Zeng et al. [18–20] proposed the use of the spatio-temporal
geostatistical prediction by incorporating the inherent temporal correlation structure between XCO2
observations. The spatio-temporal geostatistical method was carried out to fill the gaps in GOSAT
XCO2 data and demonstrated a better predicted precision compared with spatial-only method. More
descriptions about spatio-temporal geostatistics and analysis on the mapping data can be found in
Guo et al. [21] and Liu et al. [22]. However, these studies mostly focused on XCO2 data, while the
effectiveness of these mapping methods on XCH4 data, especially the spatio-temporal geostatistical
approach, has not been comprehensively studied yet. Given the important role of atmospheric CH4
dataset in understanding global carbon cycle, our study is dedicated to developing a mapping method
for satellite-observed XCH4 data based on spatio-temporal geostatistics and applying the method
to five years of GOSAT XCH4 data over most of Monsoon Asia, which covers all or part of east and
central Asia, southeast Asia and the Indian sub-continent. As shown in Figure 1a, the study region
extends from 18˝ N to 57˝ N in latitude and from 70˝ E to 138˝ E in longitude.
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250
Count
200
150
100
50
0
2010/01
2011/01
2012/01 2013/01
2014/01
Time
(a)
(b)
Figure
(a)spatial
spatialdistribution
distributionof
ofavailable
available GOSAT
GOSAT XCH
XCH44 data
Figure
1.1.(a)
data number
number in
in each
each1°
1˝by
by1°1˝grid
gridand
and(b)
temporal
variation
of
available
GOSAT
XCH
4
data
number
every
three
days.
(b) temporal variation of available GOSAT XCH4 data number every three days.
Previous studies based on satellite and ground-based observations [7,23–25] have showed that
Previous studies based on satellite and ground-based observations [7,23–25] have showed that
Monsoon Asia is one of the highest CH4 emission regions in the world, due to its strong
Monsoon Asia is one of the highest CH4 emission regions in the world, due to its strong anthropogenic
anthropogenic emissions, such as those from rice paddies, and natural emissions, such as those from
emissions, such as those from rice paddies, and natural emissions, such as those from natural wetlands.
natural wetlands. The spatial and temporal variations of CH4 over this region have been investigated
The spatial and temporal variations of CH4 over this region have been investigated in several previous
in several previous studies. Xiong et al. [26] investigated the CH4 enhancement in the middle to upper
studies. Xiong et al. [26] investigated the CH4 enhancement in the middle to upper troposphere in
troposphere in South Asia from July to September by comparing satellite CH4 retrievals from the
South Asia from July to September by comparing satellite CH4 retrievals from the Atmospheric Infrared
Atmospheric Infrared Sounder (AIRS) on the Earth Observing System (EOS)/Aqua platform with the
Sounder (AIRS) on the Earth Observing System (EOS)/Aqua platform with the model simulations from
model simulations from global tracer transport model version 3 (TM3), and concluded that the
global tracer transport model version 3 (TM3), and concluded that the enhancement is contributed by
enhancement is contributed by both local surface emissions and convective transport processes. This
both local surface emissions and convective transport processes. This study is complemented with the
study is complemented with the work by Qin et al. [27], which analyzed the spatio-temporal
work by Qin et al. [27], which analyzed the spatio-temporal variations of XCH4 over the Sichuan Basin
variations of XCH4 over the Sichuan Basin using GOSAT data, and attributed the consistent high
using GOSAT data, and attributed the consistent high XCH4 values in the basin to the strong regional
XCH4 values in the basin to the strong regional paddy field emissions and typical closed topography
paddy field emissions and typical closed topography of the basin. Moreover, Ishizawa et al. [28]
of the basin. Moreover, Ishizawa et al. [28] analyzed the large XCH4 anomaly in summer 2013 over
analyzed the large XCH4 anomaly in summer 2013 over Northeast Asia, as observed by GOSAT and
Northeast Asia, as observed by GOSAT and ground-based instruments, and attributed the anomaly
ground-based instruments, and attributed the anomaly to the transport of CH4 -rich air to Japan from
to the transport of CH4-rich air to Japan from strong CH4 source areas in East China. A more
strong CH4 source areas in East China. A more comprehensive study by Hayashida et al. [25] conducted
comprehensive study by Hayashida et al. [25] conducted detailed analysis on the characteristics of
detailed analysis on the characteristics of XCH4 data in Monsoon Asia using SCIAMACHY retrievals,
XCH4 data in Monsoon Asia using SCIAMACHY retrievals, and concluded that the distribution of
and concluded that the distribution of high XCH4 values agreed well with regional emissions over
high XCH4 values agreed well with regional emissions over this region. Though insights on CH4
this region. Though insights on CH4 distribution and variation were gained from these studies, they
distribution and variation were gained from these studies, they were only focusing on some specific
were only focusing on some specific regions and using simple data binning and averaging methods
regions and using simple data binning and averaging methods to generate monthly or seasonal data
to generate monthly or seasonal data for their analysis. The binning and averaging method ignores
for their analysis. The binning and averaging method ignores the XCH4 variation within the binning
the XCH4 variation within the binning blocks and lacks quantitative uncertainty assessment [15].
blocks and lacks quantitative uncertainty assessment [15]. In addition, the GOSAT XCH4 data, which
In addition, the GOSAT XCH4 data, which have higher precision than SCIAMACHY data, over the
have higher precision than SCIAMACHY data, over the whole Monsoon Asia region, has not been
whole Monsoon Asia region, has not been studied and assessed, mainly due to the limitation of the data
studied and assessed, mainly due to the limitation of the data coverage. In this study, we aim to
coverage. In this study, we aim to evaluate five years of GOSAT XCH4 retrievals over Monsoon Asia by
evaluate five years of GOSAT XCH4 retrievals over Monsoon Asia by first proposing the use of spatiofirst proposing the use of spatio-temporal geostatistics for mapping the XCH4 data over the Monsoon
temporal geostatistics for mapping the XCH4 data over the Monsoon Asia region using five years of
Asia region using five years of GOSAT data. This spatio-temporal geostatistical approach has the
GOSAT data. This spatio-temporal geostatistical approach has the advantage of utilizing the joint
advantage of utilizing the joint spatial and temporal dependences between observations and including
spatial and temporal dependences between observations and including a larger dataset both in space
a larger dataset both in space and time to support stable parameter estimation and prediction [11,29].
and time to support stable parameter estimation and prediction [11,29]. With the mapping XCH4 data,
With the mapping XCH4 data, we further analyze the spatio-temporal variations of XCH4 , and compare
we further analyze the spatio-temporal variations of XCH4, and compare the results with model
the results with model simulations and surface CH4 emissions from bottom-up estimation.
simulations and surface CH4 emissions from bottom-up estimation.
In Section 2, we describe all the used data, and in Section 3, we introduce the spatio-temporal
In Section 2, we describe all the used data, and in Section 3, we introduce the spatio-temporal
geostatistics and evaluation method of mapping precision. Sections 4 and 5 demonstrate results and
geostatistics and evaluation method of mapping precision. Sections 4 and 5 demonstrate results and
discussions from analysis of the spatio-temporal XCH4 variations, comparison with model simulations
discussions from analysis of the spatio-temporal XCH4 variations, comparison with model
and correlation with surface emissions. The summary is presented in Section 6.
simulations and correlation with surface emissions. The summary is presented in Section 6.
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2. Data
2.1. GOSAT XCH4 Retrievals
We collected five years of GOSAT Level 2 XCH4 data products (version 02.xx) for General Users [8],
ranging from June 2009 to May 2014 over the land area of the Monsoon Asia region, as shown in
Figure 1a. Validated by the Total Carbon Column Observing Network (TCCON), the GOSAT XCH4
data show a mean global bias of ´5.9 ppb and standard deviation of 12.6 ppb [30]. GOSAT has
a recurrent cycle of three days, and, therefore, in this study we set the basic time unit of the mapping
data to be three days. The instantaneous field of view of TANSO-FTS is 15.8 mrad, corresponding
to a nadir footprint diameter of 10.5 km approximately. Figure 1 shows the spatial distribution and
temporal variation of the available data number from satellite observations. The total number of
retrievals is irregularly distributed both in space and time. From Figure 1a, it can be seen that the
number of retrievals is larger over northern China and India than the western China and high latitude
areas, mainly due to the limitations of clear sky conditions or large solar zenith angle. From Figure 1b,
we can see the number of retrievals is larger in winter than in summer when Monsoon brings much
more cloudiness in this region.
2.2. CH4 Simulations from CarbonTracker
CarbonTracker-CH4 is an assimilating system for atmospheric CH4 developed by the National
Oceanic and Atmospheric Administration (NOAA). Coupled with the atmospheric tracer transport
model version 5 (TM5), CarbonTracker-CH4 assimilates global atmosphere CH4 observations from
surface air samples and tall towers to track global CH4 sources and sinks [31,32]. The current release
of CarbonTracker-CH4 , CT2010, produces estimates of global atmospheric CH4 mole fractions and
surface-atmosphere fluxes from January 2000 to December 2010. The model produces regularly
gridded CH4 at a spatial resolution of 4˝ in latitude by 6˝ in longitude with 34 vertical levels, and with
a temporal resolution of one day. In comparison with surface observations, the model outputs show
a mean bias of ´10.4 ppb [32]. The CH4 mole fractions profile data from the model are transformed to
XCH4 by using the pressure-averaged method described by Connor et al. [33]. When comparing XCH4
data from GOSAT and CT2010, the difference due to averaging kernel effect [34] is not considered here,
since the difference between applying and not applying the averaging kernel smoothing on model
simulations is very small, which is less than 0.1% in XCO2 as shown in Cogan et al. [35].
2.3. Emission Inventory from EDGAR
CH4 Emission inventory data are derived by bottom-up estimates using CH4 emissions statistics
from human activities and natural processes, which corresponds to anthropogenic sources and
natural sources, respectively. In this study, we collected annual CH4 emissions data in 2010 from
Emission Database for Global Atmospheric Research (EDGAR) in version 4.2 FT2010, released by
the European Commission’s Joint Research Centre and Netherlands Environmental Assessment
Agency [36]. The inventory data have a spatial resolution of 0.1˝ . The EDGAR CH4 emission data
have been used as a fundamental reference for many surface emission related studies [37].
3. Mapping Based on Spatio-Temporal Geostatistics
3.1. Methodology
We applied the spatio-temporal geostatistics to the five years of GOSAT XCH4 retrievals to produce
the XCH4 mapping data product in spatial resolution of 1˝ by 1˝ and temporal resolution of three days.
A theoretical framework of the spatio-temporal geostatistical mapping approach for XCO2 can be
found in Zeng et al. [19]. Here, we introduce the essential procedures of implementing spatio-temporal
geostatistics and describe some adjustments necessary for XCH4 . Spatio-temporal geostatistical
methods are concerned with analyzing the spatial-temporal correlation structure of regional variables
Remote Sens. 2016, 8, 361
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using
the variogram, and optimal prediction (kriging) of the variable at an unsampled location and
Remote Sens. 2016, 82016, 8, 361
time [11]. The implementation of spatio-temporal geostatistics in this study can be divided into the
following
threelocation
main steps,
XCH
and
time, modelinggeostatistics
of correlationinstructure,
4 trend in space of
unsampled
and analysis
time [11].ofThe
implementation
spatio-temporal
this study
and
space-time
kriging
prediction.
can be divided into the following three main steps, analysis of XCH4 trend in space and time,
modeling of correlation structure, and space-time kriging prediction.
3.1.1. Analysis of XCH4 Trend in Space and Time
3.1.1.
of XCH4 Trend
in Space
Time
TheAnalysis
spatio-temporal
variations
ofand
XCH
4 data can be represented by a variable Z “
tZ ps, tq|s
P
S,
t
P
Tu
that
varies
within
a
spatial
domain
S and
time interval
T. We decompose
The spatio-temporal variations of XCH4 data
can be
represented
by a variable
= { ( , the
)| ∈
spatio-temporal
variations
into
an
inherent
and
deterministic
trend
component
m
ps,
tq
and
a
stochastic
, ∈ } that varies within a spatial domain
and time interval . We decompose the spatioresidual
component
R ps,
tq, an
as shown
in and
Equation
(1),
temporal
variations
into
inherent
deterministic
trend component ( , ) and a stochastic
( , ), as shown in Equation (1),
Z ps, tq “ m ps, tq ` R ps, tq .
(1)
( , ) = ( , ) + ( , ).
(1)
The deterministic spatial trend is determined by the spatial distribution of CH4 sources and
The deterministic spatial trend is determined by the spatial distribution of CH4 sources and
sinks, while the deterministic temporal trend, which consists of the inherent seasonal CH4 cycle and
sinks, while the deterministic temporal trend, which consists of the inherent seasonal CH4 cycle and
an annual CH4 increase, is determined by temporal variation of CH4 sources and sinks [2]. As in
an annual CH4 increase, is determined by temporal variation of CH4 sources and sinks [2]. As in Zeng
Zeng et al. [19], we used a linear surface function for modeling the spatial trend, and a set of annual
et al. [19], we used a linear surface function for modeling the spatial trend, and a set of annual
harmonic functions with a simple linear function for the temporal trend, as shown in Equation (2),
harmonic functions with a simple linear function for the temporal trend, as shown in Equation (2),
ÿ
m ps, tq (“ ,ra)0=
` [a
a1 ˚+s ap1q∗` (1)
a2 ˚+s p2q
ra3 +
˚ t[a` ∗ 4i“
piωtqqs,
(2)(2)
i cos
(β piωtq
a ∗s `(2)]
+1∑pβi sin
sin( ω`)γ+
γ cos(
ω ))],
residual component
∗π
2 ˚π
since the period is 12 months, (1) and (2) are latitude and longitude of the spatial
where
ω=
where
ω“
12 since the period is 12 months, s p1q and s p2q are latitude and longitude of the spatial
location,
and aa0´3,,ββ1´4and
andγγ1´4are
areparameters
parameters
estimated
using
the
toto
bebe
estimated
using
the leastlocation,t is
t istime
timein
in months, and
least-squares
technique.
The
modeled
trend
components
in
space
and
time
are
shown
in
Figure
squares technique. The modeled trend components in space and time are shown in Figure 2. 2.
An
Anincreasing
increasingspatial
spatialtrend
trendfrom
from north
north to
to south
south can
can be
be clearly
clearly seen,
seen,which
whichisisdetermined
determinedbybythethe
distribution
ofof
surface
emissions
[25].
On
the
other
hand,
the
temporal
trend
shows
a clear
annual
distribution
surface
emissions
[25].
On
the
other
hand,
the
temporal
trend
shows
a clear
annual
increase
and
a
seasonal
cycle.
The
trend
component
is
then
subtracted
from
the
full
dataset
to
produce
increase and a seasonal cycle. The trend component is then subtracted from the full dataset to produce
thethe
residual
component
forfor
thethe
following
analysis.
residual
component
following
analysis.
CH4 residual (ppb)
50
25
0
-25
-50
2010/01
2011/01
2012/01
2013/01
2014/01
Time
(a)
(b)
Figure
2. (a)
spatial
trend
surface
XCH
4 in the study area derived from five years of GOSAT data
Figure
2. (a)
spatial
trend
surface
of of
XCH
4 in the study area derived from five years of GOSAT data
from
June
2009
to
May
2014,
and
(b)
the
temporal
trend
(red
line)
obtained
fitting
annual
from June 2009 to May 2014; and (b) the temporal
trend
(red
line)
obtained
byby
fitting
thethe
annual
harmonic
function
and
a
linear
function
to
the
time
series
of
XCH
4
residuals
(black
dots),
which
harmonic function and a linear function to the time series of XCH4 residuals (black dots), which is is
4 data in the whole study area.
calculated
from
averaging
spatially
detrended
XCH
calculated
from
averaging
thethe
spatially
detrended
XCH
4 data in the whole study area.
3.1.2.
Modeling
Correlation
Structure
XCH4
3.1.2.
Modeling
Correlation
Structure
of of
XCH
4
Thespatio-temporal
spatio-temporalcorrelation
correlationstructure
structureof
of the
the XCH
between
any
The
XCH44 data
datadescribes
describesthe
thecorrelation
correlation
between
two
points
separated
in
space
and
time.
The
correlation
structure
can
be
characterized
by
the
spatioany two points separated in space and time. The correlation structure can be characterized by the
temporal variogram
model
[11].[11].
The The
experimental
variogram
at spatial
laglag
ℎ hand
temporal lag ℎ ,
spatio-temporal
variogram
model
experimental
variogram
at spatial
s and temporal lag
h ,22γ̂(ℎph, ℎ, h),q,isiscomputed
computedby
byEquation
Equation(3),
(3),
t
s
t
2 (ℎ , ℎ ) =
(
,
)
∑
(
,
)[
( , ) − ( + ℎ , +ℎ )] ,
(3)
where (ℎ , ℎ ) is the number of pairs in the space and time lags. Following Zeng et al. [19], we set
the intervals for spatial lag and temporal lag to be 100 km and 3-day, respectively. That is, the
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Remote Sens. 2016, 8, 361
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2γ̂ phs , ht q “
ÿ
1
2
N phs ,ht q rR ps, tq ´ R ps ` hs , t ` ht qs ,
N phs , ht q
(3)
where N phs , ht q is the number of pairs in the space and time lags. Following Zeng et al. [19], we
set the intervals for spatial lag and temporal lag to be 100 km and 3-day, respectively. That is, the
tolerances for spatial and temporal lags, as defined in De Iaco et al. [29], in calculating the variogram,
are set to be 50 km and 1.5 days, respectively. In this study, the distance between observations is
defined by the great-circle distance based on the latitude and longitude of the observations. Half of
Remote Sens. 2016, 82016, 8, 361
a variogram
quantity, γ̂ phs , ht q, has been called a semi-variance. A spatio-temporal variogram model,
γ phs , ht q,
is
then
fitted
to experimental
variogram.
The
spatio-temporal
variogram
model adopted
tolerances for
spatial
and temporal lags,
as defined in
De Iaco
et al. [29], in calculating
the variogram,
here is aare
combination
of
the
product-sum
model
[29,38]
and
an
extra
global
nugget
N
the
set to be 50 km and 1.5 days, respectively. In this study, the distance between observations
is
ST to capture
defined[10],
by the
great-circle
based on
nugget effect
and
is givendistance
by Equation
(4),the latitude and longitude of the observations. Half of a
variogram quantity, (ℎ , ℎ ), has been called a semi-variance. A spatio-temporal variogram model,
(ℎ , ℎ ), is then fitted
to experimental
variogram.
variogram model adopted
γ ph,
uq “ γS phq `
γT puq ´The
κ ¨ γspatio-temporal
(4)
S phq γT puq ` NST ,
here is a combination of the product-sum model [29,38] and an extra global nugget
to capture
nugget
given by Equation
(4), variograms in space and time, and κ is a constant
where γthephq
and γeffect
puq[10],
areand
theisexponential
marginal
T
S
⋅ (ℎ) ( ) +
= (ℎ) + ( ) − κvariogram
, study, all parameters
(4)
to be estimated. For modeling (ℎ,
the )spatio-temporal
in this
are
estimated
simultaneously
in the
Zeng
et al. [19]
instead
of sequentially
as in
Deand
Iaco
(ℎ) and
( as
) are
exponential
marginal
variograms
in space and
time,
κ isetaal. [29].
where
As shown
in Zeng
al. [19],For
this
simultaneous
estimation
method
is more
for GOSAT
constant
to be et
estimated.
modeling
the spatio-temporal
variogram
in this
study, precise
all parameters
are
estimated
simultaneously
as
in
Zeng
et
al.
[19]
instead
of
sequentially
as
in
De
Iaco
et
al.
[29].
As least
data than the conventional sequential estimation method. The iterative nonlinear weighted
shown
in
Zeng
et
al.
[19],
this
simultaneous
estimation
method
is
more
precise
for
GOSAT
data
than
squared technique [10] has been used to estimate the model parameters. The calculated experimental
the conventional sequential estimation method. The iterative nonlinear weighted least squared
spatio-temporal variogram and the corresponding modeled spatio-temporal variogram are shown
technique [10] has been used to estimate the model parameters. The calculated experimental spatioin Figure
3. In the
variogram,
semi-variance
values
when spatial
and temporal
lag
are closest
temporal
variogram
and thethe
corresponding
modeled
spatio-temporal
variogram
are shown in
Figure
to 0 and3. infinity
are
called
nugget
and
sill,
respectively.
The
ratio
of
nugget
to
sill,
expressed
as
In the variogram, the semi-variance values when spatial and temporal lag are closest to 0 and
infinity
are
called
nugget
and
sill,
respectively.
The
ratio
of
nugget
to
sill,
expressed
as
a
percentage,
a percentage, can be used as an indicator to classify data dependence [39]. In general, a ratio less than
can be used
as an indicator
data dependence,
dependence [39].between
In general,
a ratio
less
thana0.25
indicates spatial
0.25 indicates
a strong
spatial to
orclassify
temporal
0.25
and
0.75,
moderate
a strong spatial or temporal dependence, between 0.25 and 0.75, a moderate spatial or temporal
or temporal dependence, and larger than 0.75 a weak spatial or temporal dependence. In this study,
dependence, and larger than 0.75 a weak spatial or temporal dependence. In this study, the ratio of
the rationugget
of nugget
to spatial sill, temporal sill and global sill are 0.20, 0.48 and 0.16, respectively,
to spatial sill, temporal sill and global sill are 0.20, 0.48 and 0.16, respectively, indicating a
indicating
a
strong
dependence
XCH4 retrievals
space, a dependence
moderate dependence
strong dependence betweenbetween
XCH4 retrievals
in space, ainmoderate
between XCHbetween
4
XCH4 retrievals
in
time,
and
a
strong
overall
spatio-temporal
dependence.
retrievals in time, and a strong overall spatio-temporal dependence.
2
Semivariance (ppb )
350
2
Semivariance (ppb )
350
300
250
200
150
45
Te m 30
por
al
(da
y) 0
200
0
Spati
200
150
Te m 30
por
al
400
g
al L a
250
45
600
Lag15
300
(km)
(a)
600
Lag15
(da
y) 0
200
0
Spati
400
g
al L a
(km)
(b)
Figure 3. The experimental spatial-temporal variogram surface of the XCH4 residuals in (a) and its
Figure 3. The experimental spatial-temporal variogram surface of the XCH4 residuals in (a) and its
fitted variogram model in (b).
fitted variogram model in (b).
3.1.3. Space-Time Kriging Prediction of XCH4
3.1.3. Space-Time
Kriging Prediction of XCH4 variogram, space-time kriging can be implemented to
Based on the modeled spatio-temporal
predict
4 value at unobserved locations using surrounding observations and produce the
Based
on the
theXCH
modeled
spatio-temporal variogram, space-time kriging can be implemented to
mapping XCH4 over Monsoon Asia. The kriging makes an optimal prediction ( , ) as the linear
predict the XCH4 value at unobserved locations using surrounding observations and produce the
weighted sum of the surrounding GOSAT XCH4 observations that minimizes the mean squared
mapping
XCH4 over
Asia.
The(5),
kriging makes an optimal prediction R ps0 , t0 q as the linear
prediction
error,Monsoon
as shown in
Equation
weighted sum of the surrounding GOSAT XCH4 observations that minimizes the mean squared
( , ) = ∑ [λ ( , )],
(5)
prediction error, as shown in Equation (5),
where λ is the weight assigned to a known sample ( , ). The weights for the observations are
determined by the geometry of the observations and the modeled spatio-temporal variogram. The
kriging prediction variance, a measurement of prediction uncertainty, is given by Equation (6),
6
Remote Sens. 2016, 8, 361
7 of 15
R̂ ps0 , t0 q “
ÿ
n
i“1 rλi R psi , ti qs ,
(5)
where λi is the weight assigned to a known sample R psi , ti q. The weights for the observations are
determined by the geometry of the observations and the modeled spatio-temporal variogram. The
kriging prediction variance, a measurement of prediction uncertainty, is given by Equation (6),
˘2
1T Γ´1 γ0 ´ 1
γ0 ´
,
1T Γ´1 1
`
2
T ´1
σ “ γ0 Γ
(6)
ˇ˘
`ˇ
where Γ pi, jq “ γ ˇsi ´ s j |, | ti ´ t j ˇ , γ0 pi, 1q “ γ p|si ´ s0 | , |ti ´ t0 |q, and 1 is n ˆ 1 unit vector.
In each kriging prediction, theoretically, the optimal prediction is achieved when using all available
observations. However, the total number of N = 51742 in this study makes it not practically feasible
for the kriging calculation because, to solve the inversion of such N by N matrix for each prediction,
is almost computationally impossible. Following Zeng et al. [19], we used the kriging neighborhood,
which is a cylinder in space and time, to define the surrounding data. The radii of the neighborhood
vary from 200 to 300 km in space and 15 to 45 days in time to make sure the number of observations
in the cylinder neighborhood is no less than 20. In order to verify the validity of the used kriging
neighborhood in representing local data variability, two key parameters [40], weight of the mean
(WM) and slope of the regression (SR) are used in this study. WM indicates the dependency of kriging
prediction on the data in the neighborhood, while SR shows whether the neighborhood size is suitable
for a valid kriging. The more WM is closer to zero, and the more SR is closer to one will indicate a better
kriging neighborhood. Our kriging prediction results in an averaged WM = 0.040 and SR = 0.964 for
the used cylinder neighborhood. The results show a low WM closer to zero and high SR closer to one,
which indicate that the chosen kriging neighborhood is suitable in representing local variability, and
the prediction would not be much improved by searching further. The mapping XCH4 are described
in detail in Section 4, and a discussion on prediction uncertainties of the mapping XCH4 is in Section 5.
3.2. Precision Evaluation Using Cross-Validation
Cross-validation is a widely used method for assessing prediction accuracy of statistical
models [40]. In this study, we used the leave-one-out cross-validation to assess the prediction accuracy
of the spatio-temporal geostatistical approach for mapping the GOSAT XCH4 observations. A detailed
description of the method can be referred to in Cressie [10]. The cross-validation is carried out by
`
˘
`
˘
first removing one observation datum Z s j , t j and then making its prediction Ẑ s j , t j using the
remaining dataset. This process is repeated for each observation in Z ps, tq. As a result, two datasets,
`
˘
`
˘
the predicted dataset {Ẑ s j , t j j = 1 . . . N} and the corresponding original dataset {Z s j , t j j = 1 . . . N}
can be obtained. The following three summary statistics from the two datasets were derived to
assess prediction precision. The correlation coefficient (R) between Z ps, tq and Ẑ ps, tq is 0.91, the
˘
`
˘ˇ
ř ˇˇ `
ˇ
mean absolute prediction error (MAE; N
j“1 Z s j , t j ´ Ẑ s j , t j {N) is 8.77 ppb, and the percentage
of prediction error less than 15 ppb is 82%. These cross-validation results show a significant high
correlation coefficient and small prediction errors between the original XCH4 data and the predicted
XCH4 data. The histogram of the prediction errors are shown in Figure 4. It indicates that the
spatio-temporal geostatistical prediction method developed for GOSAT XCH4 data is effective, and we
can therefore generate precise maps of XCH4 over Monsoon Asia using the method from the five years
of GOSAT XCH4 observations.
Moreover, we compare the prediction accuracy between spatio-temporal and spatial-only method
based on the cross-validation statistics. The spatial-only method implemented here is similar to that for
generating monthly GOSAT Level 3 data [13]. The whole XCH4 dataset is firstly grouped into monthly
datasets (five years = 60 months), and then the variogram for each month is calculated and modeled
by the exponential variogram model. Finally, based on the monthly modeled variograms, spatial-only
kriging is applied for predictions of XCH4 in each month. As a result, R and MAE for the spatial-only
Remote Sens. 2016, 8, 361
8 of 15
method are 0.90 and 8.97 ppb, respectively. Compared with this spatial-only method, we can see that
the spatio-temporal
method
Remote Sens. 2016, 82016,
8, 361 shows a slightly higher correlation coefficient and lower prediction error.
2500
2000
Frequency
Frequency
Remote Sens. 2016, 82016, 8, 361
MAE= 8.77 ppb
ST D =11.80 ppb
1500
2500
1000
2000
MAE= 8.77 ppb
ST D =11.80 ppb
1500
500
1000
0
-50 -40 -30 -20 -10
500
0
10
20
30
40
50
Prediction error (ppb)
Figure
4. Histogram
of the
predictionerrors
errorsbetween
between the
values
toward
the the
corresponding
Figure
4. Histogram
of the
prediction
thepredicted
predicted
values
toward
corresponding
0
observed values in cross-validation.
The
mean
absolute
prediction
error
(MAE) and the standard
-50
-40
-30
-20
-10
0
10
20
30
40
50
observed values in cross-validation. The mean absolute prediction error (MAE) and the standard
deviation (STD) of the errors are also given. Prediction error (ppb)
deviation (STD) of the errors are also given.
Figure 4. Histogram of the prediction errors between the predicted values toward the corresponding
4. Assessment
of Five Years of the XCH4 Mapping Dataset
observed
values
in cross-validation.
mean absolute prediction
4. Assessment
of Five
Years
of the XCHThe
4 Mapping Dataset
error (MAE) and the standard
deviation (STD) of the errors are also given.
4.1. Spatio-Temporal Variations of XCH4
4.1. Spatio-Temporal Variations of XCH4
4. Figure
Assessment
of Five
ofvariations
the XCH4 Mapping
Dataset
5 shows
the Years
overall
of mapping
XCH4 in space and time. Spatial variation of
XCH4 from
south the
to north
andvariations
strong seasonal
variationXCH
can be
observed
fromtime.
FigureSpatial
5a,b. Spatially,
Figure
5 shows
overall
of mapping
space and
variation of
4 in
4.1.
Spatio-Temporal
Variations
of XCH4
XCH
4 shows
obvious
latitude,
as shown
5a, infrom
whichFigure
higher5a,b.
averaged
XCH4the
from
south
to an
north
and change
strong with
seasonal
variation
caninbeFigure
observed
Spatially,
values
can
be
seen
in
area
between
18°N
to
32°N.
This
latitude
contrast
shows
stronger
emissions
of
Figure
5
shows
the
overall
variations
of
mapping
XCH
4
in
space
and
time.
Spatial
variation
of
the XCH4 shows an obvious change with latitude, as shown in Figure 5a, in which higher averaged
XCH
from south
to north
and
strong
seasonal
variation
can be observed
from
Figure
5a,b. Spatially,the
CH
4 in 4southern
Asia
than
northern
Asia,
which
is
further
shown
in
Figure
6.
Temporally,
˝
˝
values can be seen in area between 18 N to 32 N. This latitude contrast shows stronger emissions of
the XCH
4 shows
an obvious from
change
with
as the
shown
in Figure
in which
averaged
averaged
XCH
4 is increasing
year
tolatitude,
year, and
annual
mean5a,
increase
is higher
5.97 ppb
over the
CH4 in southern
Asia than
northern Asia,
which is further
shown in Figure
6.stronger
Temporally,
the averaged
values period.
can be seen
area between
18°N to 32°N.
This latitude
shows
emissions
five-year
Thisinannual
mean increase
is consistent
with contrast
the annual
mean
increase
of 5.60of
ppb
XCH4 isCH
increasing
from
year
to year, and
thewhich
annual
mean shown
increase
is 5.976.ppb
over thethe
five-year
4 in southern
Asia
than
is further
in Figure
Temporally,
from surface
observations
fromnorthern
2007 to Asia,
2013 [41].
Seasonally,
the averaged
seasonal
cycle amplitude
period.
This annual
mean
increase
isAugust
consistent
with
increase
5.60
ppb
from
averaged
4 is increasing
from
year to
year,
andthe
theannual
annual mean
mean
increase
5.97
ppb
the surface
is 22.47
ppb,XCH
with
maximum
in
and
minimum
around
February
andisof
March,
asover
shown
in
five-year
period.
This
annual
mean
increase
is
consistent
with
the
annual
mean
increase
of
5.60
ppb
observations
2007 the
to 2013
[41].cycle
Seasonally,
the averaged
seasonal
amplitude
is 22.47
Figure 5b.from
However,
seasonal
peak generally
varies with
latitude,cycle
as shown
in Figure
5a. In ppb,
from surface
observations
from 2007 toaround
2013 [41].
Seasonally,
the
averaged
seasonalincycle
amplitude
with maximum
and
minimum
February
and
March,
as shown
Figure
However,
areas
southin
ofAugust
25°N,
the
peak
appears around
September,
while
in areas
north of 30°N,
it5b.
appears
is 22.47 ppb, with maximum in August and minimum around February and March, as shown in
around July
August.
The varies
patternwith
of seasonal
peak isinconsistent
the result
the seasonal
cycleand
peak
generally
latitude,cycle
as shown
Figure 5a.with
In areas
southfrom
of 25˝ N,
Figure 5b. However, the seasonal cycle peak generally varies with
latitude,
as
shown
in
Figure
5a.
In
SCIAMACHY
as described in Figure
6a ofinHayashida
et al.
[25].
They
found that
the Monsoon
the peak
appears
while
areas
north
ofwhile
30˝ N,
appears
andAsia
August.
areas
southaround
of 25°N,September,
the peak appears
around
September,
in it
areas
north around
of 30°N, July
it appears
region
includes
different
phases
of
seasonal
variation
of
XCH
4, which also corresponds to a wide
The pattern
of
seasonal
cycle
peak
is
consistent
with
the
result
from
SCIAMACHY
as
described
in
around July and August. The pattern of seasonal cycle peak is consistent with the result from
range of climate zones in this region.
Figure
6a
of Hayashida
et al. [25].
that the Monsoon
Asiafound
region
includes
different
SCIAMACHY
as described
in They
Figurefound
6a of Hayashida
et al. [25]. They
that
the Monsoon
Asia phases
region
includesof
different
seasonal
variation to
of 1860
4, which
corresponds
to ainwide
of seasonal
variation
XCH4 ,phases
whichofalso
corresponds
aXCH
wide
rangealso
of climate
zones
this region.
CH4 (ppb)
CH4 (ppb)
range of climate zones in this region.
1860
1820
1820
1780
1780
1740
1740
(a)
2010/01 2011/01 2012/01 2013/01 2014/01
Time
2010/01 2011/01(b)
2012/01 2013/01 2014/01
Time
Figure 5. (a) overview of(a)
the regional spatio-temporal distribution of XCH4 over
(b) Monsoon Asia as a
function of latitude and time from five years of mapping XCH4 dataset with a grid resolution of 1° in
Figure 5. (a) overview of the regional spatio-temporal distribution of XCH4 over Monsoon Asia as a
Figure
5.
(a) and
overview
of the regional
spatio-temporal
distribution
of XCHof
Monsoon
Asia as
latitude
one time-unit
(three days)
in time, and (b)
temporal variation
monthly
averaged
4 over
function of latitude and time from five years of mapping XCH4 dataset with a grid resolution of 1° in
mapping
XCH4 (red
dots)
over
Monsoon
Asia and
the corresponding
standard
deviation
lines). of 1˝
a function
of latitude
and
time
from
five years
of mapping
XCH4 dataset
with
a grid (grey
resolution
latitude and one time-unit (three days) in time, and (b) temporal variation of monthly averaged
in latitude
and one
(three days) in time, and (b) temporal variation of monthly averaged
mapping
XCHtime-unit
4 (red dots) over Monsoon Asia and the corresponding standard deviation (grey lines).
mapping XCH4 (red dots) over Monsoon Asia and the corresponding standard deviation (grey lines).
8
8
Remote Sens. 2016, 8, 361
9 of 15
Remote
2016, the
82016,seasonal
8, 361
Figure
6 Sens.
shows
means of XCH4 over the five-year period. The spatial patterns
of XCH4 distribution in the four seasons are similar. Wetlands and rice paddy fields are among
Figure 6 shows the seasonal means of XCH4 over the five-year period. The spatial patterns of
the primary
sources of atmospheric CH4 , which
are responsible for the higher XCH arewhich
can be
XCH4 distribution in the four seasons
are similar. Wetlands and rice paddy fields 4,
among the
observedprimary
in all seasons
in
southern
Asia
and
south-eastern
China.
This
spatial
pattern
is
also
sources of atmospheric CH4, which are responsible for the higher XCH4, which can well
be
consistent
with
that
from
a six-year
average
(2003
2008)China.
of SCIAMACHY
XCH4 is
retrievals
observed in all
seasons
in southern
Asia
and through
south-eastern
This spatial pattern
also wellas
shown inconsistent
Figure 14
of that
Frankenberg
et al.average
[7]. Moreover,
obvious
seasonal
variationXCH
can4 retrievals
be observed.
with
from a six-year
(2003 through
2008)
of SCIAMACHY
as
shown insummer
Figure 14and
of Frankenberg
al. [7].
obvious seasonal
variation
can and
be observed.
XCH4 between
autumn is et
close,
asMoreover,
well as between
winter and
spring,
XCH4 of
betweenare
summer
and autumn
close,
as well
as latter
between
winter
and spring,
XCH4 of
the first XCH
two 4seasons
generally
higher isthan
that
of the
two
seasons.
This isand
because,
inthe
this
first
two
seasons
are
generally
higher
than
that
of
the
latter
two
seasons.
This
is
because,
in
this
region,
region, summer and autumn are warmer and wetter seasons, as well as the growing seasons of rice,
summer and autumn are warmer and wetter seasons, as well as the growing seasons of rice, which
which result
in stronger emissions from rice paddies and wetlands compared to the dry season in
result in stronger emissions from rice paddies and wetlands compared to the dry season in winter
winter and spring [25,42]. Several high value areas stand out, including the Pearl River Delta region in
and spring [25,42]. Several high value areas stand out, including the Pearl River Delta region in south
south China
probably due to strong human activity related emissions, the Ganges Delta in south Asia
China probably due to strong human activity related emissions, the Ganges Delta in south Asia
probablyprobably
due to strong
wetland
emissions,
and and
the Sichuan
Basin
inin
west
Basinshows
shows
due to strong
wetland
emissions,
the Sichuan
Basin
westChina.
China. Sichuan
Sichuan Basin
a consistent
high anomalous
valuevalue
in allinseasons,
which
is related
totoitsitsstrong
sourceas
aswell
wellasas
a consistent
high anomalous
all seasons,
which
is related
stronglocal
local source
the stagnant
effect due
to due
its special
basinbasin
terrain
topography
[27].
the stagnant
effect
to its special
terrain
topography
[27].
(a) Spring
(b) Summer
(c) Autumn
(d) Winter
Figure 6. Seasonally averaged XCH4 calculated from five years of spatio-temporal mapping XCH4,
Figure 6. Seasonally averaged XCH4 calculated from five years of spatio-temporal mapping XCH4 ,
including (a) Spring (March to May); (b) Summer (June to August), (c) Autumn (September to
including (a) Spring (March to May); (b) Summer (June to August); (c) Autumn (September to
November), and (d) Winter (December and January and February the next year).
November); and (d) Winter (December and January and February the next year).
4.2. Comparison with Model Simulations of XCH4
4.2. Comparison with Model Simulations of XCH4
Atmospheric modeling of greenhouse gases, such as CarbonTracker, can reproduce large scale
features of the
atmospheric
CH4 distribution
well.
Figure
7 shows the annual
of mapping
XCH
4
Atmospheric
modeling
of greenhouse
gases,
such
as CarbonTracker,
canmean
reproduce
large
scale
4 in 2010 from CarbonTracker-CH4. We can
data
in
2010
and
the
corresponding
model
output
of
XCH
features of the atmospheric CH4 distribution well. Figure 7 shows the annual mean of mapping
see that the spatial patterns of mapping data and the modeling well agree with each other, with high
XCH4 data
in 2010 and the corresponding model output of XCH4 in 2010 from CarbonTracker-CH4 .
XCH4 in southern and south-eastern Asia and low values in northern and north-western Asia,
We can see that the spatial patterns of mapping data and the modeling well agree with each other,
especially the high altitude Tibet area. However, the model data shows a lower XCH4 in the low
with high
XCH4area
in southern
and south-eastern
Asia
values in
northern
north-western
latitude
than the mapping
data, especially
inand
two low
key regions,
including
theand
Sichuan
Basin and
Asia, especially
the
high
altitude
Tibet
area.
However,
the
model
data
shows
a
lower
XCHIn4 in
the
the Ganges Basin, where CH4 emissions from rice paddy fields and wetlands dominate.
high
low latitude
areaareas,
thanthe
themodel
mapping
data, especially
twomapping
key regions,
including
the Sichuan
Basin
latitude
simulations
are higherin
than
satellite
observations,
especially
in
and the Ganges
Basin, where
CH4 emissions
rice
paddy
fields
andThe
wetlands
high
Tibet, Mongolia
and north-eastern
China,from
where
XCH
4 values
are low.
satellitedominate.
data, on theIn
other
latitude areas, the model simulations are higher than mapping satellite observations, especially in
Tibet, Mongolia and north-eastern China, where XCH94 values are low. The satellite data, on the other
Remote Sens. 2016, 8, 361
10 of 15
Remote Sens. 2016, 82016, 8, 361
hand, show
of XCH
can therefore capture the local variability and present
4 and
hand,direct
show observations
direct observations
of XCH
4 and can therefore capture the local variability and present a
Sens. 2016, 82016, 8, 361
a moreRemote
detailed
characteristic
of
XCH
variation
compared
totomodel
Morediscussions
discussionsareare
4
more detailed characteristic of XCH
4 variation
compared
modelsimulations.
simulations. More
presented
in Section
5.
presented
in Section
5.
hand, show direct observations of XCH4 and can therefore capture the local variability and present a
more detailed characteristic of XCH4 variation compared to model simulations. More discussions are
presented in Section 5.
(a) Mapping XCH4
(b) CarbonTracker XCH4
(a) Mapping XCH4
(b) CarbonTracker XCH4
Figure 7. (a) the annual averaged XCH4 for the year 2010 from mapping dataset, and (b) the
Figure 7.corresponding
(a) the annual
for the year 2010
from mapping dataset; and (b) the
XCH4averaged
simulationsXCH
from4 CarbonTracker-CH
4 in 2010.
corresponding XCH4 simulations from CarbonTracker-CH4 in 2010.
Figure 7. (a) the annual averaged XCH4 for the year 2010 from mapping dataset, and (b) the
corresponding XCH4 simulations from CarbonTracker-CH4 in 2010.
4.3. Correlation with Surface Emission Inventory
4.3. Correlation
with Surface
Surface
emissionEmission
of CH4 isInventory
the main driver of the atmospheric XCH4 distributions. Figure 8a
4.3.
Correlation
with surface
Emission
Inventory
shows
the annual
CH
4 emission
in 2010of
derived
from EDGARXCH
emission
inventory. The spatial
Surface
emission
ofSurface
CH4 is
the
main
driver
the atmospheric
4 distributions. Figure 8a
distribution
pattern
of
high
CH
4 emissions is determined by both anthropogenic emissions (such as
Surface surface
emissionCH
of 4CH
4 is the main
driver
of the
atmospheric
4 distributions.
8a
shows the annual
emission
in 2010
derived
from
EDGAR XCH
emission
inventory.Figure
The spatial
fossilthe
fuel
combustion,
biomass
burning
andderived
rice paddies)
and natural
emissions
(such
asspatial
natural
shows
annual
surface
CH
4
emission
in
2010
from
EDGAR
emission
inventory.
The
distribution pattern of high CH4 emissions is determined by both anthropogenic emissions (such as
wetlands). pattern
By comparing
8a and Figure 7a, we can see their spatial patterns agree with each
distribution
of high Figure
CH
4 emissions is determined by both anthropogenic emissions (such as
fossil fuel
combustion,
biomass
burning
and rice paddies)
and
natural
emissions (such as natural
other
well.
It
indicates
the
variation
of multi-year
averagedand
XCH
4 can well represent the variation of
fossil fuel combustion, biomass burning
and rice paddies)
natural
emissions (such as natural
wetlands).
By comparing
Figures
8a and 7a, we can see their spatial patterns agree with each other
annual
averaged
CH
4 surface emissions. Figure 8b shows the relationship between CH4 surface
wetlands).
By comparing
Figure 8a and Figure 7a, we can see their spatial patterns agree with each
well. It indicates
the
variation
of
multi-year
averaged
wellannual
represent
the variation
of annual
4 can
emissions,
hasthe
been
rearranged
into
1° byaveraged
1°XCH
grids,
and
averaged
XCH4 value
from
other
well. Itwhich
indicates
variation
of multi-year
XCHthe
4 can well represent the variation of
averaged
CH
surface
emissions.
Figure
8b
shows
the
relationship
between
CH
surface
emissions,
the
mapping
dataset
as
shown
in
Figure
7a.
A
significant
linear
relationship
can
be
observed,
with
4
4
annual averaged CH4 surface emissions. Figure 8b shows the relationship between CH4 surface
˝ by
˝ grids,ofand
2) of 0.64 and psignificantly
high
correlation
coefficient
0.80
and
the
coefficient
of
determination
(R
which has
been
rearranged
into
1
1
the
annual
averaged
XCH
value
from
the
mapping
4
emissions, which has been rearranged into 1° by 1° grids, and the annual averaged XCH4 value from
value
lessinthan
0.01.
This
significant
linear
relationship
indicates
the dominant
role of surface
datasetthe
as
shown
Figure
7a.shown
A significant
can
be observed,
with
significantly
mapping
dataset
as
in Figurelinear
7a. A relationship
significant
linear
relationship
can
be observed,
withhigh
emissions
in
determining
the
distribution
of
XCH
4 concentration2over such regions.2
correlation
coefficient
0.80 and the
coefficient
of and
determination
(R of) of
0.64 and p-value
less and
thanp-0.01.
significantly
highofcorrelation
coefficient
of 0.80
the coefficient
determination
(R ) of 0.64
value lesslinear
than relationship
0.01. This significant
relationship
theemissions
dominantinrole
of surface the
This significant
indicateslinear
the dominant
roleindicates
of surface
determining
emissions
in determining
the distribution of XCH4 concentration over such regions.
distribution
of XCH
4 concentration over such regions.
(a)
(b)
Figure 8. (a) annual CH4 emission in 2010 derived from EDGAR emission inventory in a spatial
(b)emissions and the averaged
resolution of 0.1° (a)
by 0.1°, and (b) The relationship between CH4 surface
XCH4 value in 1° by 1° grids drived from the five years of mapping XCH4 data. The color grids
(a) annual
4 emission in 2010 derived from EDGAR emission inventory in a spatial
FigureFigure
8.represent
(a) 8.
annual
CH4CH
emission
in 2010 derived
emission
inaveraged
a spatial
the density
of data distribution.
The blackfrom
line isEDGAR
derived from
linear inventory
regression of
resolution ˝of 0.1° by
0.1°,
and (b) The relationship between CH4 surface emissions and the averaged
˝
resolution
of 0.1
by(Y)
0.1and
; and
(b) The
relationship
between
emissions
and the
averaged
4 surface(X),
4 data
the base
10 logarithm
of surface
CHCH
4 emissions
which shows
a significant
XCH
XCH4 value˝ in 1° ˝by 1° grids drived from the five years of mapping XCH4 data. The color grids
2 equals from
XCH4 value
1 by 1 grids
the five
years of mapping XCH4 data. The color grids
linearinrelationship
with Rdrived
0.64 (p-value
< 0.01).
represent the density of data distribution. The black line is derived from linear regression of averaged
represent the density of data distribution. The black line is derived from linear regression of averaged
XCH4 data (Y) and the base 10 logarithm of surface CH4 emissions (X), which shows a significant
10 emissions (X), which shows a significant linear
XCH4 data
and the base
surface< CH
4
linear(Y)
relationship
with10
R2logarithm
equals 0.64of(p-value
0.01).
relationship with R2 equals 0.64 (p-value < 0.01).
10
Remote Sens. 2016, 82016, 8, 361
Remote Sens. 2016, 8, 361
11 of 15
5. Discussion
5. Discussion
5.1.
Prediction Uncertainty of Mapping XCH4 Data
5.1. Prediction
Uncertainty
of Mapping
XCHwe
In geostatistics,
for each
prediction,
can get a corresponding kriging variance at the same
4 Data
time, as shown in Equation (6). The variance is determined by both the density of GOSAT XCH4
In geostatistics, for each prediction, we can get a corresponding kriging variance at the same time,
observations and the data homogeneity in the neighborhood of the prediction position. Theoretically,
as shown in Equation (6). The variance is determined by both the density of GOSAT XCH4 observations
in conditions of denser observations and more homogeneous XCH4 variation surrounding the
and the data homogeneity in the neighborhood of the prediction position. Theoretically, in conditions
prediction location there will be lower prediction uncertainty [14]. Therefore, the kriging variance
of denser observations and more homogeneous XCH4 variation surrounding the prediction location
indicates how uncertain each XCH4 prediction is given the available satellite observations. Figure 9
there will be lower prediction uncertainty [14]. Therefore, the kriging variance indicates how uncertain
shows the spatial variation of the kriging standard deviation (root of kriging variance) from the
each XCH4 prediction is given the available satellite observations. Figure 9 shows the spatial variation
mapping XCH4 data in Monsoon Asia averaged over a five-year period. The values change from
of the kriging standard deviation (root of kriging variance) from the mapping XCH4 data in Monsoon
about 11 ppb to 16 ppb with mean of 13.70 ppb. As expected, in areas with denser observations as
Asia averaged over a five-year period. The values change from about 11 ppb to 16 ppb with mean of
shown in Figure 1a, including northern China and India, the prediction uncertainty is lower. In some
13.70 ppb. As expected, in areas with denser observations as shown in Figure 1a, including northern
parts of south China and west China, the uncertainty is relatively high due to the relatively sparseness
China and India, the prediction uncertainty is lower. In some parts of south China and west China,
of the satellite observations, and, therefore, more verifications are required for the mapping dataset
the uncertainty is relatively high due to the relatively sparseness of the satellite observations, and,
in these areas. The spatio-temporal geostatistical approach developed in this study has the advantage
therefore, more verifications are required for the mapping dataset in these areas. The spatio-temporal
of utilizing a larger dataset both in space and time to support stable parameter estimation and
geostatistical approach developed in this study has the advantage of utilizing a larger dataset both in
prediction. Therefore, as more observation data will become available in the coming future, we can
space and time to support stable parameter estimation and prediction. Therefore, as more observation
anticipate that a more robust mapping dataset with lower uncertainty using spatio-temporal
data will become available in the coming future, we can anticipate that a more robust mapping dataset
geostatistics can be produced.
with lower uncertainty using spatio-temporal geostatistics can be produced.
Figure 9.9.Spatial
distribution
of kriging
standard
deviations,
a measurement
of prediction
Figure
Spatial
distribution
of kriging
standard
deviations,
a measurement
of uncertainty,
prediction
is
obtained
by
averaging
the
kriging
standard
deviations
over
five
years
of
mapping
XCH
in
4
uncertainty, is obtained by averaging the kriging standard deviations over five years of dataset
mapping
Monsoon
Asia.
Blank
pixels
are
grids
where
less
than
three
of
the
five
annual
means
are
available,
in
XCH4 dataset in Monsoon Asia. Blank pixels are grids where less than three of the five annual means
which
the annual
meanthe
is obtained
by averaging
at least
11 monthly
mean11data.
are available,
in which
annual mean
is obtained
by averaging
at least
monthly mean data.
5.2. Discrepancies
Discrepancies in
in Sichuan
Sichuan Basin
Basin between
5.2.
between Observation
Observation and
and Modeling
Modeling
As suggested
by Hammerling
et al.
data with
As
suggested by
Hammerling et
al. [43],
[43], mapping
mapping greenhouse
greenhouse gas
gas concentration
concentration data
with
uncertainty
estimation
can
be
used
for
comparison
with
simulation
data
from
the
atmospheric
transport
uncertainty estimation can be used for comparison with simulation data from the atmospheric
model coupled
with
carbonwith
flux estimates.
Asestimates.
shown in Figure
7, theinlargest
difference
between
satellite
transport
model
coupled
carbon flux
As shown
Figure
7, the largest
difference
observations
andobservations
model simulations
of XCH
in the
of west China,
4 is located
between
satellite
and model
simulations
of XCH
4 isSichuan
located Basin
in the Sichuan
Basin ofwhere
west
a
large
anomaly
is
shown
in
GOSAT
data
while
not
in
model
data.
As
suggested
by
Qin
et
al.
China, where a large anomaly is shown in GOSAT data while not in model data. As suggested[27],
by
CH4etemission
from
rice paddy
fields
wetlands
andwetlands
the stagnant
of the basin
have
Qin
al. [27], CH
4 emission
from
rice and
paddy
fields and
and effect
the stagnant
effectterrain
of the basin
the biggest
to this anomaly.
This
same feature
can also
be seen
satellite
observations
terrain
havecontribution
the biggest contribution
to this
anomaly.
This same
feature
canin
also
be seen
in satellite
of
CO
columns
and
NO
columns
[44].
However,
the
model
simulations
with
ground
observations
2
observations of CO columns
and NO2 columns [44]. However, the model simulations with ground
assimilated fail
to reproduce
local variability
overvariability
this basin.over
Thisthis
maybasin.
be due
to the
observations
assimilated
failthis
to reproduce
this local
This
mayineffectiveness
be due to the
of
CarbonTracker
[23],
which
assimilates
only
the
sparse
ground
based
observations
in
representing
the
ineffectiveness of CarbonTracker [23], which assimilates only the sparse ground based observations
local
features
of
XCH
in
this
area,
where,
unfortunately,
ground-based
observations
are
not
available
in representing the 4local features of XCH4 in this area, where, unfortunately, ground-based
to constrain the
fluxes. to constrain the CH4 fluxes.
observations
areCH
not4 available
11
Remote Sens. 2016, 8, 361
12 of 15
5.3. Long Term XCH4 Observations in Constraining Surface Emissions
The distribution and variation of column-averaged greenhouse gas can be attributed to spatial
distribution of surface emissions, sinks of the gas, and large-scale eddy-driven transport [45]. For XCH4
over the Monsoon region, emissions from human-related activities including paddy fields, and natural
wetlands are the dominant emissions, while the reaction of CH4 with hydroxyl radicals (OH), which
removes almost 90% of CH4 [46], is the main sink of atmospheric CH4 . For a specific CH4 column, the
number of CH4 molecules going out (loss) and coming in (gain) the column due to transport varies
from time to time. However, on a yearly basis, the averaged transport component of CH4 leads to net
gain or loss and can be approximately quantified as an invariable constant. For the CH4 sinks due
to chemical reaction over multi-year periods, the amount of sinks is determined by the total amount
and can therefore be quantified as an averaged ratio to the total amount of CH4 molecules in the
atmosphere. Therefore, the multi-year averaged XCH4 data observed by GOSAT is approximately
a remaining ratio of CH4 emissions from surface after excluding the averaged transport component and
chemical sink component. As a result, the distribution of observed XCH4 averaged over a long term
period will be indicating the surface sources of CH4 , as we see in Figure 8b. This significant correlation
between XCH4 observations and surface emissions provides a promising statistical way, which is
simple and easy to implement, of constraining surface CH4 sources using satellite observations over
a long term period.
6. Conclusions
In this study, we propose the use of a data-driven mapping approach based on spatio-temporal
geostatistics to generate a mapping dataset of XCH4 and evaluate the five years of GOSAT XCH4
retrievals over Monsoon Asia from June 2009 to May 2014. The prediction precision using
cross-validation results in a significantly high correlation of 0.91 and a small mean absolute prediction
error of 8.77 ppb between the original dataset and prediction dataset. Spatio-temporal distribution and
variation of XCH4 mapping data agree with results from SCIAMACHY and ground-based observations
well. This XCH4 mapping data also provide a new way to assess the model simulations of CH4
coupled with atmospheric transport model. Comparison between XCH4 and model simulations
from CarbonTracker-CH4 shows consistent spatial patterns, but the satellite observations are more
able to resolve the local variability of XCH4 , such as the constant anomaly shown in the Sichuan
Basin. Finally, by comparing the mapping data with surface emission inventory, we found that the
geographical distribution of high CH4 values well corresponds to strong emissions as indicated in
the inventory map. Over the five-year period, the two datasets show a significantly high correlation
coefficient (0.80), indicating the dominant role of surface emissions in determining the distribution
of averaged XCH4 concentrations over such regions and a promising statistical way of constraining
surface CH4 sources using satellite observations over a long term period. In conclusion, this study
provides new mapping datasets of XCH4 over Monsoon Asia derived from satellite observations,
and suggests a simple statistical way to constrain the surface CH4 emissions using long term satellite
XCH4 retrievals. Moreover, this study provides a complementary work to previous studies using
SCIAMACHY, and AIRS over this Monsoon Asia region.
However, some assumptions in this study need further verifications. Firstly, spatio-temporal
correlation structure is assumed to be similar over the entire Monsoon Asia area, but this is not always
true since the spatio-temporal variations in difference locations are different. However, the irregular
distribution of the data do not enable us to resolve this problem in this study. Secondly, in geostatistical
mapping, we adopted the kriging neighborhood to reduce computational complexity and preserve
local variability. Theoretically, the minimum mean square error in kriging is achieved by using a global
neighborhood which includes all points. However, a global neighborhood is not practically feasible for
kriging calculations because it may lead to a kriging matrix that is too large to be numerically inverted.
As a result, the use of a kriging neighborhood might introduce some errors to our results.
Remote Sens. 2016, 8, 361
13 of 15
Gaps in observations are common in XCH4 retrievals from greenhouse gas observation satellites,
such as GOSAT and SCIAMACHY. Therefore, application of the mapping method to SCIAMACHY
and comparison between the two data sources will provide us a new way to investigate their
differences in this developed geostatistical way. In comparison of prediction accuracy between
spatio-temporal and spatial-only approaches using cross-validation, leaving out larger areas of data
would conceivably better highlight the advantage of a spatio-temporal approach because the temporal
correlation considered in spatio-temporal approach can provide large benefits given the lack of nearby
data. This will be our future work. In addition, although cross-validation gives us a comprehensive
statistical assessment of prediction accuracy, it is essential to carry out comparison with independent
observations. As some TCCON stations are being set up over this Monsoon Asia region, a comparison
with TCCON will also be our work in the coming future.
Acknowledgments: This work was supported by the Strategic Priority Research Program–Climate
Change (XDA05040401) and the National High Technology Research and Development Program of China
(2012AA12A301). We acknowledge the GOSAT retrieved XCH4 data products provided by JAXA/NIES/MOE
(https://data.gosat.nies.go.jp/) and EDGAR data (http://edgar.jrc.ec.europa.eu/). The current development
of EDGAR is a joint project of the European Commission Joint Research Centre (JRC) and the Netherlands
Environmental Assessment Agency (PBL). CarbonTracker-CH4 results are provided by NOAA ESRL, Boulder,
Colorado, USA from the website at http://www.esrl.noaa.gov/gmd/ccgg/carbontracker-CH4/.
Author Contributions: L.L. and Z.Z. conceived and designed the experiments; M.L. performed the experiments;
All authors analyzed the data; D.L. and Z.Z. contributed analysis tools; M.L. and Z.Z. wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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