Introduction
Quantitative knowledge of biogeochemical processes regulating global
carbon–climate feedbacks remains highly uncertain (Friedlingstein et al.,
2013). Quantifying the sensitivity of biogeochemistry to climate variables
directly from observations of atmospheric concentrations has long been a goal
of researchers (Bacastow et al., 1980; Vukicevic et al., 2001; Gurney et al.,
2008). Estimating the climate sensitivity of carbon fluxes is complicated by
both the spatial scale and structure of climate anomalies and the variations
of factors affecting ecosystem responses: soils, vegetation, land use and
natural disturbance (King et al., 2015). Current ground-based and even
space-based carbon cycle observing systems (OSs) produce flux estimates at
continental or even zonal resolution, limiting direct estimation of
relationships between climate forcing, ecosystem properties and carbon fluxes
(Huntzinger et al., 2012; Peylin et al., 2013). The uncertainty of carbon
fluxes at continental and finer scales is high, and different systems for
flux estimation often produce strikingly different spatial patterns (Schimel
et al., 2015a; Bloom et al., 2016). Because of the high uncertainty in the
spatial regionalization of fluxes, some of the most compelling studies of
carbon and climate have eliminated the spatial information and instead have
used correlative approaches to identify the regions likely to be responsible
for observed global concentration anomalies (Braswell et al., 1997; Cox et
al., 2013; Chen et al., 2015; Franklin et al., 2016).
The expansion of surface and aircraft observing networks has increased our
understanding of the carbon cycle and is essential for precise
quantification of trace-gas concentrations (Andrews et al., 2014; Sweeney et
al., 2015; Wilson et al., 2016). Surface networks are intrinsically limited
in their density, by cost, access to remote terrestrial and marine
environments, environmental conditions and other logistical constraints
(Schimel et al., 2015b). The first-generation trace-gas observing satellites
were designed to make global-scale measurements of concentrations with
unprecedented frequency and accuracy but were not designed to test specific
hypotheses about biogeochemical processes. The successes of GOSAT (Yokota et
al., 2009) and OCO-2 (Crisp et al., 2004) open the door to designing a next
generation of spaceborne greenhouse gas measurements to test specific
hypotheses about the terrestrial biosphere or the oceans. In this paper, we
report an observing system design exercise aimed at identifying the observing
system needed to increase understanding of a long-standing uncertainty in the
global carbon budget, specifically the role of tropical wetlands in the
global CH4 budget (Mitsch et al., 2010; Bloom et al., 2010; Melton et
al., 2013). While we focus this analysis on CH4, we note that the models
and methodology are equally applicable to other gases (such as CO2), as
well as
other regions or mechanisms.
Mean annual wetland and rice CH4 emissions (central
map), and associated longitudinal and latitudinal
uncertainty (grey bands), based on the WETCHIMP model inter-comparison
project (Melton et al., 2013). Inset: WETCHIMP model total Amazon basin
monthly CH4 emissions.
Wetland CH4 emissions
Biogenic methane (CH4) emission processes are one of the principal
components of global carbon–climate interactions; CH4 is a potent
greenhouse gas (Myhre et al., 2013) and wetlands account for roughly
20–40 % of the global CH4 source (Kirschke et al., 2013). The
processes controlling the magnitude and temporal evolution of CH4
outgassing from wetland environments remain largely unquantified on
continental scales. As a result, global-scale wetland CH4 emissions
(Melton et al., 2013) and their role in the interannual growth of
atmospheric CH4 remain highly uncertain.
Global wetland CH4 emissions largely depend on soil inundation,
temperature and substrate carbon availability. The major sources of wetland
CH4 emissions include boreal North America, boreal Eurasia, the
Indonesian archipelago, the Congo and Amazon River basins (Fig. 1, map), which
are all characterized by high soil carbon content (Hiederer and Köchy,
2011) and substantial seasonal or year-round inundation extent (Prigent et
al., 2012). By and large, Amazon wetland CH4 emissions dominate both the
magnitude and uncertainty of global wetland CH4 emissions (Melton et
al., 2013). Estimates of Amazon wetland CH4 emissions range between
20 and 60 Tg CH4 year-1 (Fung et al., 1991; Riley et al., 2011;
Bloom et al., 2012; Melack et al., 2004), roughly equivalent to 10–30 %
of the global wetland CH4 source. Major uncertainties are also
associated with the spatial and temporal variability of CH4 emissions
(Fig. 1). Uncertainties in tropical wetland CH4 emission estimates
largely stem from a lack of quantitative knowledge of process controls on
wetland CH4 emissions and a lack of data constraints on the drivers of
wetland emissions. In terms of processes, a range of factors including soil
pH, wetland vegetation cover, wetland depth, salinity and air–water gas
exchange dynamics, likely impose fundamental controls on the rate of wetland
CH4 emissions. On a continental scale, spatially explicit knowledge of
carbon cycling and inundation remain highly uncertain in the wet tropics,
primarily due to a sparse in situ measurement network, high cloud cover and
biomass density.
Top-down CH4 flux estimates
Top-down constraints on CH4 fluxes – from atmospheric CH4
observations – are key to retrieving quantitative information on
continental-scale CH4 biogeochemistry (Bousquet et al., 2011; Pison et
al., 2013; Basso et al., 2016; Wilson et al., 2016). Low-earth orbit (LEO)
satellite missions, including SCIAMACHY, IASI, TES and GOSAT, have surveyed
global CH4 concentrations for over a decade (Frankenberg et al., 2008;
Crevoisier et al., 2009; Butz et al., 2011; Worden et al., 2012). In
particular, column CH4 retrievals from SCIAMACHY have proven sensitive
to wetland and other CH4 emissions (Bloom et al., 2010; Bergamaschi et
al., 2013). However, cloud cover is a major inhibiting factor when measuring
atmospheric greenhouse gas concentrations within the proximity of tropical
wetland regions. In particular, densely vegetated seasonally inundated areas
of the Amazon and Congo River basins can experience more than 95 %
monthly mean cloud cover. With fewer cloud-free observations of lower
tropospheric CH4 concentrations, atmospheric inversion estimates of
wetland CH4 emissions remain exceedingly difficult, especially in the
absence of well-characterized prior information on the magnitude, location
and timing of emissions.
Atmospheric inverse estimates of CH4 emissions are expected to improve
with tropospheric CH4 measurements from the upcoming ESA TROPOMI mission
(Butz et al., 2012; Veefkind et al., 2012). Furthermore, geostationary
missions (such as GEOCAPE) will potentially provide the measurements needed
to substantially improve CH4 emission estimates (Wecht et al., 2014;
Bousserez et al., 2016). Ultimately, the precision and sampling configuration
of atmospheric CH4 observations both determine the OS
capability of retrieving surface CH4 fluxes. It is currently unclear
whether future CH4 measurements will be sufficient to resolve key
CH4 fluxes – such as the Amazon basin wetlands – at a process-relevant
resolution.
In this study we characterize the satellite observations required to quantify
the biogeochemical process controls on Amazon wetland CH4 emissions.
Specifically, we identify and characterize the Amazon CH4 emission
processes (Sect. 2.1), define the process-relevant CH4 flux resolution
and precision required to statistically distinguish between hypothesized
wetland CH4 emission scenarios
based on several hydrological and carbon datasets (Sect. 2.2), simulate
atmospheric measurements throughout the Amazon basin for a range of LEO and
geostationary orbit (GEO) satellite OSs, and derive the corresponding
CH4 flux uncertainty using an idealized atmospheric inversion
(Sect. 2.3). Based on our results, we establish the OS requirements and
discuss the potential of future OSs to resolve Amazon wetland CH4
emission processes (Sect. 3). We conclude our paper in Sect. 4.
Methods
We construct an Observing System Simulation Experiment (OSSE) dedicated to
characterizing the spaceborne OS needed to resolve the processes controlling
wetland CH4 fluxes from Amazon basin (Fig. 2). Our OSSE involves the
following three steps: we (1) characterize the variability of wetland CH4
process controls, (2) define CH4 flux resolution and precision
requirements and (3) derive the atmospheric CH4 concentration OS
requirements. We define the atmospheric CH4 OS requirement as the
ability to meet the CH4 flux resolution and precision requirements
during the cloudiest time of year. We focus our analysis on March 2007: all
temporally resolved carbon and hydrological observations chosen for this
study overlap in 2007, and March 2007 mean cloud cover (84 %) amounts to
the highest cloud cover across the whole Amazon River basin within the
January–April 2007 wet season (cloud-cover range = 76–84 %) and is
considerably higher than the June–September 2007 dry season cloud cover
(46–56 %).
Wetland CH4 emissions into the atmosphere are regulated by
wetland biogeochemical processes (left column). Continental-scale wetland
CH4 process controls can be retrieved by (i) resolving surface CH4
fluxes from retrieved satellite CH4 observations and (ii) resolving
process parameters from retrieved CH4 fluxes (middle column). The
optimal satellite CH4 observation requirements are a function of the
flux resolution and precision required to resolve wetland CH4 process
controls (right column): OSSE steps 1–3 are described in Sects. 2.1–2.3.
Wetland process controls
Wetland CH4 emissions are controlled by a range of biogeochemical
processes: inundation is likely to be a first-order control of wetland
emissions, as soil CH4 production largely occurs in oxygen-depleted
soils (Whalen, 2005). However, extensive studies of wetland CH4
emissions suggest that inundation is not the sole determinant of spatial and
temporal CH4 emission dynamics. CH4 can be transferred directly
into the atmosphere via macrophytes, thus circumventing the aerobic soil
layer (Whalen, 2005). Water-body depth (Mitsch et al., 2010), type
(Devol et al., 1990) and aquatic macrophyte density (Laanbroek,
2010) can affect the proportion of wetland CH4transferred to the
atmosphere.
Carbon (C) availability is also a determinant of wetland CH4 emissions.
Methanogen-available C turnover rates (Miyajima et al., 1997), composition
(Wania et al., 2010), temporal dynamics (Bloom et al., 2012) and C stocks
together drive spatial and temporal variability of carbon limitation on
CH4 production in wetlands. C cycle state variables, including the
spatial variability of total biomass (Saatchi et al., 2011; Baccini et al.,
2012) and soil carbon (Hiederer and Köchy, 2011), vary at < 1000 km
scales. Methanogen-available C sources – such as gross primary production
(GPP) and leaf litter – vary substantially at monthly timescales in the wet
tropics (Beer et al., 2010; Chave et al., 2010; Caldararu et al., 2012). In
the next section, we establish the CH4 flux resolution and precision
requirements based on the variability of potential tropical wetland CH4
emissions process controls (namely carbon uptake, live biomass and dead
organic matter stocks, inundation and precipitation).
Wetland CH4 flux requirements
Here we define a set of wetland CH4 flux precision and resolution
requirements suitable for the formulation and testing of wetland CH4
emissions process control hypotheses. Measurement and model-based analyses of
Amazon wetland CH4 emissions provide a range of contradictory estimates
on spatial patterns and seasonality (Devol et al., 1990; Riley et al., 2011;
Bloom et al., 2012; Melton et al., 2013; Basso et al., 2016) suggesting that
the basin-wide process controls on wetland CH4 emissions remain
virtually unknown. Here, our aim is to provide a first-order,
model-independent characterization of wetland CH4 flux resolution and
precision requirements based on the basin-wide variations in carbon and
hydrological processes. Our resolution requirement is based on the
correlation lengths of hypothesized wetland CH4 emission process
controls. At the required resolution, our precision requirement is that
wetland CH4 emissions scenarios – derived from a range of hypothesized
carbon and hydrological process controls – are (a) statistically
inter-distinguishable and (b) distinguishable from a spatiotemporally
uniform wetland CH4 flux (i.e., a null hypothesis).
Given our process-level understanding of wetland CH4 emissions, we
propose four carbon and three hydrological proxies as the dominant drivers of
wetland CH4 emission variability (C1–C4 and H1–H3 respectively). We
use carbon stocks and fluxes as proxies for variation in C availability for
wetland CH4 production. We characterize the spatial variability of
carbon uptake based on the Jung et al. (2009) eddy-covariance-based monthly
0.5∘ × 0.5∘ GPP product (C1) and monthly
0.5∘ × 0.5∘ solar-induced fluorescence retrieved
from the Global Ozone Monitoring Experiment measurements (Joiner et al.,
2013; C2). We use the Saatchi et al. (2011) biomass map (C3) and the
Harmonized World Soil Database soil carbon stocks (C4; Hiederer and
Köchy, 2011). We define the spatial variability of hydrological controls
over methane flux based on two inundation fraction datasets (Prigent et al.,
2012; Schroeder et al., 2015; H1 and H2) and the NASA Tropical Rainfall
Measuring Mission (TRMM; Huffman et al., 2007) precipitation retrievals (H3).
Spatial autocorrelation (Moran's I) for potential carbon controls
(left column) and hydrological controls (right column) on wetland CH4
emissions. The spatial variability of carbon controls are derived from
satellite observations (biomass in Saatchi et al., 2011; solar-induced
fluorescence in Joiner et al., 2013), the Harmonized World Soil Database
(soil carbon; Hiederer and Köchy, 2011) and FLUXNET-derived GPP (Jung et
al., 2009). The spatial variability estimates for hydrological controls are
based on satellite measurements of inundation (A: Prigent et al., 2012;
B: Schroeder et al., 2015) and precipitation (the NASA Tropical Rainfall
Measuring Mission). Significant Moran's I values (where the Moran's I
p value < 0.05) are highlighted as circles. We set a ∼ 333 km
spatial resolution requirement for monthly CH4 flux retrievals, based on
the maximum correlation lengths of potential carbon and hydrological controls
on wetland CH4 emissions. The details of the Moran's I analysis are
fully described in Appendix A.
CH4 flux resolution
Our resolution requirement is based on a first-order assessment of the
process variable correlation length scales: we anticipate that retrieving
wetland CH4 fluxes at much finer scales may be redundant, while
retrieving fluxes at much coarser scales may hinder the potential to
investigate biogeochemical process controls on wetland CH4 emission
variability. We use an autocorrelative approach to identify the variability
length scales of potential CH4 emissions process controls (see
Appendix A). The spatial autocorrelation coefficients (Moran's I) of the
seven limiting process variables indicate coherent spatial structures
spanning up to ∼ 333–666 km across the Amazon River basin (Fig. 3):
process variables exhibit high autocorrelation at a
1∘ × 1∘ resolution
(L ∼ 111 km) and no significant spatial
correlation at 6∘ × 6∘ (L ∼ 666 km). Based
on our correlative analysis, we expect that wetland CH4 flux estimates
at 3∘ × 3∘ (L ∼ 333 km) will likely be
critical for a first-order distinction between the roles of carbon and water
processes on Amazon wetland CH4 emissions: we propose a ∼ 333 km
CH4 flux resolution as the spatial resolution required to determine the
role of process control variability on wetland CH4 emissions. For all
time-varying datasets (C1, C4, H1, H2 and H3), we conducted a lagged
Pearson's correlation analysis: the time-varying datasets indicate varying
levels of statistically significant 1-month autocorrelations across the study
region (percent of area exhibiting significant autocorrelations:
C1 = 98 %; C4 = 6 %; H1 = 47 %; H2 = 51 %;
H3 = 64 %), while virtually 0 % of the study region exhibits
significant 2-month temporal autocorrelations. For this study, we opt for a
monthly temporal resolution requirement; however, we note that
higher-temporal-resolution datasets (given their availability) can
potentially provide an improved assessment of the temporal correlation scales
of carbon and hydrological process controls.
CH4 flux precision
We next derive the CH4 flux precision required to distinguish between
hypothesized wetland CH4 process controls at a ∼ 333 km monthly
resolution. We derive the precision requirements assuming 1 continuous year
of CH4 flux retrievals. We formulate (a) spatial CH4 emission
hypotheses, where wetland CH4 emissions linearly co-vary with the
hypothesized processes at ∼ 333 km scales, and (b) temporal CH4
emission hypotheses, where wetland CH4 emissions linearly co-vary with
the hypothesized processes on monthly timescales. Our motivation for
evaluating both spatial and temporal hypotheses is that we do not necessarily
expect the spatial and temporal process controls on wetland CH4
emissions to be the same. For example, Amazon wetland CH4 emissions
could be spatially limited by carbon uptake (GPP) and temporally driven by
inundation. Each wetland hypothesis is scaled to an annual mean flux of
12 mg m-2 day-1, which corresponds to the Melack et al. (2004)
annual Amazon-wide wetland CH4 emission estimate
(29.3 Tg CH4 year-1 across 668 Mha). The explicit formulation
of spatial and temporal wetland CH4 emission hypotheses is described in
Appendix B.
Distinction confidence between Amazon basin spatial and temporal
wetland CH4 emission hypotheses against monthly ∼ 333 km CH4
flux precision. Spatial and temporal wetland CH4 emission hypotheses are
distinguishable with a 95 % confidence at a ≤ 10 mg m-2
day-1 precision. For this study we define our ∼ 333 km CH4
flux precision requirement as 10 mg m-2 day-1.
For a range of retrieved CH4 flux precisions across the Amazon basin
(spanning 1–100 mg m-2 day-1), we test whether each spatial and
temporal wetland CH4 emission hypothesis is statistically distinct from
alternative hypotheses and a “no variability” hypothesis (i.e., a null
hypothesis); the derivation of the statistical confidence in distinguishing
between hypotheses is described in Appendix B. The distinction confidence
(%) for spatial and temporal hypotheses is shown in Fig. 4: at a monthly
∼ 333 km resolution, both spatial and temporal wetland CH4
emission hypotheses are inter-distinguishable with > 95 % confidence
at a ≤ 10 mg m-2 day-1 CH4 flux precision.
CH4 requirements
Given the spatial and temporal variability of potential hydrological and
carbon controls, we define the following requirements for wetland CH4
flux retrievals:
∼ 333 km spatial resolution
monthly temporal resolution
10 mg CH4 m-2 day-1 precision.
Our resolution and precision requirements provide a first-order assessment of
the wetland CH4 emission biogeochemical process control variability. We
anticipate that satellite-based CH4 flux estimates meeting the
above-stated requirements will provide robust characterization of spatial
variation in Amazon wetland CH4 emissions on the scale of variation in
the major carbon and water controls, allowing forcing (hydrology and carbon)
and response (CH4 flux) to be related directly. Therefore, by retrieving
CH4 fluxes at the required resolution and precision, carbon and
hydrological process hypotheses on the dominant drivers of Amazon wetland
CH4 emissions can be adequately investigated. However, depending on the
nature of the scientific investigation, we recognize that the trade-off space
between spatial resolution, temporal resolution, precision and study duration
can be further explored to derive an optimal combination of CH4 flux
requirements.
Throughout the next subsections, we characterize the required satellite
column CH4 measurements needed to resolve CH4 flux with the
above-stated requirements. To quantify the sensitivity of our results to the
above-mentioned requirements, we repeat our analysis for a range of CH4
flux spatial resolution requirements (L=150–990 km) and we derive the
corresponding CH4 flux precision requirements.
CH4 observation requirements
We define the atmospheric CH4 observation requirements by retrieving
CH4 fluxes from a range of LEO and GEO OS simulated CH4 retrieved concentrations, or
“observations”. Our approach is three-fold: (a) we simulate LEO and GEO
CH4 observations for March 2007; (b) we derive the precision of CH4
measurement averaged at an L×L resolution (henceforth the
“cumulative CH4 measurement precision”); and (c) we employ an
idealized inversion to simulate CH4 flux retrieval uncertainty for March
2007 based on the cumulative CH4 measurement precision. We note that
wetland emissions are the largest and most uncertain source of CH4
within the Amazon River basin (Wilson et al., 2016; Melton et al., 2013). We
henceforth assume that the non-wetland CH4 contribution (namely fires
and anthropogenic CH4 sources) can be relatively well characterized
using ancillary datasets and global inventories (Bloom et al., 2015; Turner
et al., 2015, and references therein).
LEO and GEO CH4 observations
The advantage of LEO systems is a near-global coverage; for the TROPOMI
mission CH4 orbit and measurement parameters, this equates to a 1-day
maximum revisit period globally. While a GEO system can only view a fixed
area on the globe, revisit periods can be far shorter. To relate CH4
observation requirements to current technological capabilities, we explore
six OS configurations based on LEO and GEO OS parameters used to simulate the
upcoming GEOCAPE and TROPOMI missions' observations in North America by
Wecht et al. (2014) (Table 1). We note that, for regional CH4 emission
estimates, the GEO OS configurations are expected outperform LEO due to a
larger data volume: the fixed viewing area permits multiple revisits per day
(Wecht et al., 2014), and the smaller GEO footprint size typically leads to
lower cloud contamination (Crisp et al., 2004). Our aim here is not to
compare CH4 emission estimates from LEO and GEO CH4 retrievals.
Rather, our aim is to determine whether CH4 emission estimates from a
range of LEO and GEO OS configurations are able meet the wetland process
requirements outlined in Sect. 2.1.
Observation system characteristicsa.
Observation
Single sounding
Single CH4
Visits
system
footprint size
measurement
per day
precision
LEO
7 km × 7 km
0.6 % (10.8 ppb)
1
GEO
3 km × 3 km
0.6 % (10.8 ppb)
4
LEO+b
7 km × 7 km
0.42 % (7.6 ppb)
1
GEO×2
3 km × 3 km
0.6 % (10.8 ppb)
8
GEO-Z1
3 km × 3 km
0.6 % (10.8 ppb)
4c
GEO-Z2
3 km × 3 km
0.6 % (10.8 ppb)
4d
a LEO and GEO observation parameters are broadly consistent with TROPOMI
and GEOCAPE simulations by Wecht et al. (2014); to simplify comparisons, we
set GEO and LEO default single CH4 sounding precision to 0.6 %.
b Single measurement precision is a factor of 2 higher than
LEO; this is the equivalent to doubling the visits per day for LEO.
c 2 (6) visits per day in 0–50 percentile (50–100 percentile)
cloud-cover areas;
d 2 (10) visits per day in 0–75 percentile (75–100 percentile) cloud-cover areas.
Cloud cover is a major limiting factor in Amazon basin trace-gas retrievals.
Mean March 2007 cloud cover is 89 % – ranging from 38 to 98 % at a
1∘ × 1∘ resolution – throughout the Amazon River
basin (based on MODIS cloud-cover data; Fig. B1). We quantify the
data rejection due to cloud cover based on 1 km March 2007 MODIS cloud-cover
data. Based on four MODIS cloud-cover flags, we categorize
1 km × 1 km cloud-cover observations into “cloud-contaminated”
and “cloud-free” observations (see Appendix C). Any cloud-contaminated
3 km × 3 km (GEO) or 7 km × 7 km (LEO) CH4
measurement footprints are rejected; i.e., all accepted footprints are
100 % “cloud-free”.
To assess the relative importance of CH4 measurement density in high
cloud-cover areas, we test two additional geostationary configurations:
“GEO-Z1” carries out two visits per day and six visits per day in the top
50 % cloudiest areas; “GEO-Z2” carries out 2 visits per day and 10
visits per day in the top 25 % cloudiest areas (we note that these two
OSs would require targeting capabilities to optimize the sampling strategy
over the cloudiest area of the basin). We further explore OS space by testing
LEO with a 2 precision enhancement (“LEO+”) and GEO with
eight visits per day instead of four
(“GEO×2”).
Cumulative CH4 measurement precision
For each OS ω (“GEO”,”LEO”, etc.), OL,ω is the cumulative CH4 measurement precision at a L×L
resolution. OL,ω is an N×1 array,
where N is the number of Amazon River basin grid cells at resolution L×L. We derive the cumulative atmospheric CH4 precision within
each L×L grid cell i, Oi{L,ω} as follows:
Oi{L,ω}=σωaϕi{ω}nωL2,
where σω is the single observation precision (Table 1),
ϕi{ω}is the fraction of cloud-free observations at
location i, nω is the number of observations per
km2 per month for OS ω (based on Table 1 values) and a the
fraction of accepted cloud-free CH4 column retrievals (set to a=0.5). The derivation of ϕi{ω} is based on MODIS 1 km
cloud-cover data over the Amazon River basin in March 2007 (Appendix C). The
square of the denominator in (1) corresponds to the number of
cloud-free atmospheric column CH4
measurements per L×L grid cell. For all OSs, nω is calculated assuming continuous basin-wide coverage at the
single-sounding footprint resolution (see Table 1). We highlight that our
formulation of cumulative CH4 precision in Eq. (1) implies retrieved
CH4 errors are spatially and temporally uncorrelated.
OS-retrieved CH4 flux precision
We calculate the monthly retrieved CH4 flux precision for OS ω
at an L×L resolution – F{L,ω} – based on
OL,ω (Eq. 1). F{L,ω} is a N×1 array, where N is the number of Amazon basin grid cells at
resolution L×L. To calculate F{L,ω} we simulate
an ensemble of 1000 retrieved CH4 concentration vectors (c∗,nL,ω for n=1–1000) over the Amazon River
basin, where
c∗,nL,ω=cL,0+N0,1∘OL,ω.
cL,0 is a N×1 array of L×L
gridded unperturbed CH4 concentrations, and N(0,1) is an N×1 array of normally distributed random numbers with mean zero and
variance one (“∘” denotes element-wise multiplication). We relate
the concentrations cL,∗ to the underlying
CH4 fluxes fL,∗ as follows:
cL,∗=ALfL,∗,
where AL is the atmospheric transport operator
(the N×N matrix transforming fluxes to concentrations over the
Amazon River basin domain) and f{L,∗} is an N×1
array of surface CH4 fluxes. For the sake of brevity, we present a
summary of AL here and the complete derivation
of AL in Appendix D. We use a Lagrangian
Particle Dispersion Model (LPDM: Uliasz, 1994; Lauvaux and Davis, 2014) to
derive an “influence function” (or “column footprint”) relating
satellite-retrieved atmospheric CH4 concentrations to surface fluxes
(the inverse solution of the transport from the surface to higher altitudes)
at the center of the study area. We simulate 30 km × 30 km
CH4 transport – A30km – by
spatially translating the LPDM influence function throughout the domain. To
assess the robustness of the LPDM approach, we also simulated CH4 column
mixing ratios over the Amazon River basin at 30 km using the Weather
Research and Forecasting model (WRF v2.5.1; Skamarock and Klemp, 2008). The
WRF model March 2007 Amazon River basin concentrations and the corresponding
LPDM approximations are shown in Fig. D1. Finally, we used a Monte Carlo
approach to statistically construct AL based
on A30km. The LPDM, WRF and the
Monte Carlo derivation of A are fully described in Appendix D.
For each L, we simulate the flux uncertainty based on the inverse of
AL, (AL)-1
and simulated CH4 concentration vectors (c∗,n{L,ω}, Eq. 2). For the sake of simplicity, we set all unperturbed
concentrations – cL,0 in Eq. (2) – to be equal
to zero, since these do not influence our subsequent derivation of
F{L,ω}. The nth retrieved flux estimate –
f∗,n{L,ω} – is calculated as
f∗,n{L,ω}=(AL)-1c∗,n{L,ω}.
Finally, we calculate the flux precision F{L,ω} at grid
cell i as follows:
Fi{L,ω}=SDfi,∗{L,ω}.
Retrieved monthly ∼ 333 km CH4 cumulative
precision (i.e., the combined precision of monthly-averaged CH4
measurements) for LEO and GEO observing systems; the observing system configurations
are described in Table 1.
Residual CH4 bias simulation
Despite the implementation of CH4 bias correction methods based on
satellite CH4 retrieval comparison against ground measurements of total
column CH4 (Parker et al., 2011), spatial structures in residual
CH4 biases are a key limiting factor in top-down CH4 flux accuracy.
Here we quantify the role residual CH4 biases for each OS
configurations. We simulate a retrieved pseudo-random CH4 bias structure
with a spatial correlation of s=100 km and no temporal correlation,
which is consistent with the likely first-order predictors of retrieved
CH4 residual biases (Worden et al., 2016). Here we simulate a range of
pseudo-random bias distributions with standard deviations spanning b=0.5–50 ppb. For each b, we calculate the bias-influenced flux
uncertainty F{L,ω,b} based on Eqs. (4) and (5): to
incorporate spatially correlated biases, we adapt Eq. (2) to derive the
CH4 concentration vector c′∗,nL,ω,b as
c′∗,nL,ω,b=N0,1⋅OL,ω+N0,1⋅b⋅sLv,
where b represents the standard deviation of the pseudo-random CH4
bias and v represents the number of visits per month; for bias errors
correlated across spatial scales s, the scale factor sLv
accounts for the pseudo-random behavior of bias errorsbat a monthly L×L resolution. We assess the role CH4 biases on
F{L,ω,b} for the LEO and GEO OS configurations at L=∼333 km.
CH4 observations density (observations per unit area; y axis)
vs. retrievable ∼ 333 km flux precision (x axis) for six
CH4 observation systems (see Table 1 for details). The “observation
density” includes all attempted CH4 measurements, including accepted
(cloud-free) and rejected (cloudy) observations.
Results and discussion
Cumulative CH4 precision for mean monthly atmospheric column CH4
measurements is 0.10–0.98 ppb for the LEO OS (Fig. 5, left) and
0.02–0.20 ppb for the GEO OS (Fig. 5, right). The lowest CH4
concentration precision occurs in the eastern and central Amazon River basin. A
crucial advantage of the smaller GEO OS footprint is the 88–148 % higher
probability of cloud-free observations in the cloudiest regions of the Amazon
River basin (Fig. B1); the probability of acquiring cloud-free observations
in cloud-prone areas is further enhanced by the GEO OS ability to conduct
multiple visits per day (see Eq. 1).
Retrieved GEO and LEO flux precision for L=∼333 km with modeled pseudo-random residual bias error. See Table 1 for
details on GEO and LEO CH4 observing systems.
For L=∼333 km, median monthly retrieved CH4 flux precision for
the LEO OS (i.e., the median of F{L,ω}) is
17.0 mg CH4 m-2 day-1 (Fig. 6); increasing the single
sounding retrieval precision by 2 (from 0.6 to 0.42 ppb) for LEO
observations (LEO+) reduces the retrieved flux uncertainty to
11.9 mg CH4 m-2 day-1. This uncertainty reduction is
equivalent to a second LEO visit per day (see Table 1): the factor 3-to-10
lower uncertainties for cumulative GEO CH4 concentrations (Fig. 5) lead
to a 2.7 mg CH4 m-2 day-1 median uncertainty in the
retrieved flux (Fig. 6). Doubling the number of GEO visits per day
(GEO×2 OS) reduces the retrieved flux
uncertainty to 1.9 mg CH4 m-2 day-1. GEO-Z1 and GEO-Z2
uncertainties (2.4 and 2.0 mg CH4 m-2 day-1) are both
lower than GEO. These results indicate that – despite a lower number of
cloud-free observations – a higher
observation density in the high cloud-cover areas of the Amazon basin (and
lower observation density elsewhere) can be used to reduce the retrieved
CH4 flux uncertainty without increasing the number of observations per
day. Based on the LEO OS, we anticipate that missions similar to the ESA
TROPOMI observation configuration (Veefkind et al., 2012; Wecht et al., 2014)
will lead to lower-than-required information content for Amazon wetlands and
are unlikely to provide sufficient observational constraints to resolve the
dominant CH4 flux process controls.
Our bias CH4 analysis (Fig. 7) indicates that GEO-retrieved CH4
flux precisions at L=∼333 km are relatively unaffected by residual
CH4 biases < 1 ppb, while LEO-retrieved CH4 flux precisions are
relatively unaffected by residual CH4 biases < 5 ppb. We find that
the advantage of GEO CH4 flux precision over LEO diminishes from almost
1 order of magnitude at residual CH4 biases < 1 ppb, to roughly a
factor of 2 for residual biases > 20 ppb. Here we assume a residual
CH4 bias correlation scale of 100 km (Sect. 2.3); based on Eq. (6), we
expect a larger impact of residual CH4 biases on OS-retrieved CH4
flux precision for residual CH4 bias correlation lengths > 100 km or
for temporally correlated CH4 biases. Overall, the relative advantage of
GEO over LEO OSs is contingent on both the cumulative CH4 precision
(Fig. 5) as well as the anticipated spatiotemporal structure of residual
CH4 bias.
Estimates of fluxes at L=150–990 km show that median GEO-retrieved
CH4 flux uncertainty is consistently a factor of ∼ 5 lower than
the median LEO-retrieved CH4 flux uncertainty (Fig. 8); for a 10 ppb
residual pseudo-random bias, the median GEO-retrieved flux uncertainty is
consistently a factor of ∼ 3 lower than LEO-retrieved flux uncertainty.
GEO-derived CH4 fluxes meet the both the precision and resolution
requirements for L=∼180–333 km; for a 10 ppb residual bias,
GEO-derived CH4 fluxes meet both requirements at L=∼280–333 km. At the expense of the resolution requirement, both GEO
simulations meet the precision requirements for all L≥∼333 km.
Unbiased median LEO-derived CH4 fluxes meet the precision requirements
at L>500 km; LEO-derived CH4 fluxes with a 10 ppb pseudo-random
bias meet the precision requirement at L>800 km and partially meet the
precision requirement for 550 km > L > 800 km.
In our analysis we have assumed (i) no systematic biases in our atmospheric
inversion simulation and (ii) perfectly known boundary conditions.
Significant systematic atmospheric CH4 retrieval and transport model
biases can undermine the enhanced accuracy of geostationary OSs. For example,
we find that our LPDM-derived transport operator yields a conservative
estimate of the monthly mean CH4 gradient across the domain relative to
the WRF model simulation (Appendix D; Fig. D1). We assess the sensitivity of
our results to a factor of 1.5 increase in the LPDM-derived transport
operator (AL); OS CH4 flux precision results
exhibit an inversely proportional response, corresponding to a
∼ 33 % uncertainty reduction (median GEO flux precision of
1.8 mg CH4 m-2 day-1 and a LEO precision of
11.3 mg CH4 m-2 day-1). GEO missions are likely to provide
a higher volume of observations at the boundaries of the observation domain,
relative to LEO OS: therefore, boundary conditions are likely to reinforce
the potential of GEO OS compared to LEO. We recognize that further efforts
are required to fully assess the role of seasonal transport variability,
transport errors, boundary condition assumptions and atmospheric CH4
bias structures on the accuracy of GEO and LEO CH4 flux retrievals.
We note that a limiting factor in our analysis is the lack of data
constraints on diurnal cloud-cover variability (since the MODIS cloud-cover
dataset does not provide diurnal constraints). The March 2007 ERA-Interim
monthly mean 3 h cloud-cover dataset indicates a 7–80 % (median 29 %)
coefficient of variation of cloud-free fraction diurnal variability
throughout the Amazon basin. Given the nonlinear sensitivity of data yield
to synoptic cloud cover (Fig. B1), the cloud-free fraction coefficient of
variation may amount to an important component in assessing and optimizing
the performance of LEO and GEO OSs over the Amazon basin, as well as other
high cloud-cover regions across the globe.
Median retrieved LEO and GEO CH4 fluxes for L=150–990 km;
the dashed lines indicate precision and resolution requirements. See
Table 1 for details on GEO and LEO CH4 observing systems. The bias
value of 10 ppb indicates modeled systematic CH4 measurement biases
with 100 km spatial correlations (see Sect. 2.3).
Our CH4 flux resolution requirement (monthly L=∼333 km CH4 flux retrievals) is derived based on an assessment of
carbon and hydrological autocorrelation scales across the Amazon River
basin. Although our sensitivity analysis (Fig. 8) shows that GEO can
potentially distinguish between the hypothesized CH4 emission scenarios
at L > ∼ 333 km, we anticipate that additional biogeochemical
investigations – such as the second-order interactions between carbon and
hydrological drivers on wetland CH4 emissions – would likely be
increasingly challenging at coarser resolutions. We recognize that our
resolution requirement and our quantification of correlation scales is
specific to our study region: for example, quantification of greenhouse gas
measurement requirements for finer-scale studies would yield a unique set of
requirements, and supporting analyses may require higher-resolution datasets.
Our approach provides the means to examine trade-offs between spatial and
temporal resolutions. For example, further analyses can be conducted to
establish the space–time trade-offs to optimize biogeochemical investigations
and process uncertainty reduction. We also note that GEO OSs provide
unprecedented volume of observations: the enhanced sampling approach can
potentially be used at shorter timescales to optimally resolve source and
transport patterns. This approach could be particularly useful in instances
when
wetland CH4 emissions are densely focused in space or time. Finally, we
highlight the potential for combining multiple OSs (e.g., LEO and GEO systems)
to optimally constrain CH4 fluxes and biogeochemical process controls;
the potential of OS synergies undoubtedly requires further investigation.
In contrast to our approach, CH4 flux uncertainty requirements can
alternatively be derived by quantifying process-based wetland CH4
emission model uncertainty (Melton et al., 2013) or by characterizing the
CH4 flux uncertainty stemming from wetland CH4 model parametric
uncertainty (Bloom et al., 2012). An advantage of model-based requirements
is the ability to assess CH4 flux uncertainties associated with the
complex interactions between wetland CH4 processes (e.g., Riley et al.,
2011). Prior information on the magnitude and variability of fluxes can also
be introduced (e.g., in a Bayesian atmospheric transport and chemistry
inversion framework) to reassess posterior uncertainty estimates.
However, as outlined in Sect. 2.1, large unknowns preside over the processes
governing the spatial and temporal variability of wetland CH4 fluxes.
Moreover, wetland CH4 models often exhibit structural similarities
(Melton et al., 2013); for example, wetland CH4 emission models (Melton
et al., 2013) suggest major CH4 emissions along the main stem of the
Amazon River (Fig. 1). Since model spatiotemporal CH4 flux variations –
and their associated processes – have not been adequately assessed due to
insufficient in situ measurements (particularly in the tropics), the
introduction of prior spatial and temporal correlations in wetland CH4
flux estimates would hinder the potential to independently investigate
biogeochemical process controls on wetland CH4 emissions. To our
knowledge, our analysis provides a first quantification of the OS
requirements for confronting prior knowledge on CH4 fluxes at a
process-relevant resolution.