What are the greenhouse gas observing system requirements for reducing fundamental biogeochemical process uncertainty? Amazon wetland CH 4 emissions as a case study.

. Understanding the processes controlling terrestrial carbon fluxes is one of the grand challenges of climate science. 10 Carbon cycle process controls are readily studied at local scales, but integrating local knowledge across extremely heterogeneous biota, landforms and climate space has proven to be extraordinarily challenging. Consequently, top-down or integral flux constraints at process-relevant scales are essential to reducing process uncertainty. Future satellite-based estimates of greenhouse gas fluxes – such as CO 2 and CH 4 – could potentially provide the constraints needed to resolve biogeochemical process controls at the required scales. Our analysis is focused on Amazon wetland CH 4 emissions, which 15 amount to a scientifically crucial and methodologically challenging case study. We quantitatively derive the observing system requirements for testing wetland CH 4 emission hypotheses at a process-relevant scale. To capture the spatial and temporal patterns of the major hydrological and carbon controls over wetland CH 4 production, a satellite mission will need to resolve monthly CH 4 fluxes at a 300km resolution and with a 25% flux precision. We simulate a range of low-earth orbit (LEO) and geostationary orbit (GEO) CH 4 observing system configurations to evaluate the ability of these approaches to 20 meet the CH 4 flux requirements. Conventional LEO and GEO missions resolve monthly 300km × 300km Amazon wetland fluxes at a 186% and 33% median uncertainty level. Improving LEO CH 4 measurement precision by 2 would only reduce the median CH 4 flux uncertainty to 132%. A GEO mission with targeted observing capability could resolve fluxes at a 21-27% median precision by increasing the observation density in high cloud-cover regions at the expense of other parts of the domain. Process-driven greenhouse gas observing system simulations can enhance conventional uncertainty reduction assessments by providing the measurement needs for testing biogeochemical process hypotheses.


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 globalscale 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 CH 4 budget (Mitsch et al., 2010;Bloom et al., 2010;Melton et al., 2013).While we focus this analysis on CH 4 , we note that the models and methodology are equally applicable to other gases (such as CO 2 ), as well as other regions or mechanisms.

Wetland CH 4 emissions
Biogenic methane (CH 4 ) emission processes are one of the principal components of global carbon-climate interactions; CH 4 is a potent greenhouse gas (Myhre et al., 2013) and wetlands account for roughly 20-40 % of the global CH 4 source (Kirschke et al., 2013).The processes controlling the magnitude and temporal evolution of CH 4 outgassing from wetland environments remain largely unquantified on continental scales.As a result, global-scale wetland CH 4 emissions (Melton et al., 2013) and their role in the interannual growth of atmospheric CH 4 remain highly uncertain.
Global wetland CH 4 emissions largely depend on soil inundation, temperature and substrate carbon availability.The major sources of wetland CH 4 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 CH 4 emissions dominate both the magnitude and uncertainty of global wetland CH 4 emissions (Melton et al., 2013).Estimates of Amazon wetland CH 4 emissions range between 20 and 60 Tg CH 4 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 CH 4 source.Major uncertainties are also associated with the spatial and temporal variability of CH 4 emissions (Fig. 1).Uncertainties in tropical wetland CH 4 emission estimates largely stem from a lack of quantitative knowledge of process controls on wetland CH 4 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 CH 4 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 CH 4 flux estimates
Top-down constraints on CH 4 fluxes -from atmospheric CH 4 observations -are key to retrieving quantitative information on continental-scale CH 4 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 CH 4 concentrations for over a decade (Frankenberg et al., 2008;Crevoisier et al., 2009;Butz et al., 2011;Worden et al., 2012).In particular, column CH 4 retrievals from SCIAMACHY have proven sensitive to wetland and other CH 4 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 CH 4 concentrations, atmospheric inversion estimates of wetland CH 4 emissions remain exceedingly difficult, especially in the absence of wellcharacterized prior information on the magnitude, location and timing of emissions.
Atmospheric inverse estimates of CH 4 emissions are expected to improve with tropospheric CH 4 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 CH 4 emission es-  (Melton et al., 2013).Inset: WETCHIMP model total Amazon basin monthly CH 4 emissions.
timates (Wecht et al., 2014;Bousserez et al., 2016).Ultimately, the precision and sampling configuration of atmospheric CH 4 observations both determine the OS capability of retrieving surface CH 4 fluxes.It is currently unclear whether future CH 4 measurements will be sufficient to resolve key CH 4 fluxes -such as the Amazon basin wetlandsat a process-relevant resolution.
In this study we characterize the satellite observations required to quantify the biogeochemical process controls on Amazon wetland CH 4 emissions.Specifically, we identify and characterize the Amazon CH 4 emission processes (Sect.2.1), define the process-relevant CH 4 flux resolution and precision required to statistically distinguish between hypothesized wetland CH 4 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 CH 4 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 CH 4 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 CH 4 fluxes from Amazon basin (Fig. 2).Our OSSE involves the following three steps: we (1) characterize the variability of wetland CH 4 process controls, (2) define CH 4 flux resolution and precision requirements and (3) derive the atmospheric CH 4 concentration OS requirements.We define the atmospheric CH 4 OS requirement as the ability to meet the CH 4 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 process controls
Wetland CH 4 emissions are controlled by a range of biogeochemical processes: inundation is likely to be a first-order control of wetland emissions, as soil CH 4 production largely occurs in oxygen-depleted soils (Whalen, 2005).However, extensive studies of wetland CH 4 emissions suggest that inundation is not the sole determinant of spatial and temporal CH 4 emission dynamics.CH 4 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) (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 CH 4 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 CH 4 flux resolution and precision requirements based on the variability of potential tropical wetland CH 4 emissions process controls (namely carbon uptake, live biomass and dead organic matter stocks, inundation and precipitation).

Wetland CH 4 flux requirements
Here we define a set of wetland CH 4 flux precision and resolution requirements suitable for the formulation and testing of wetland CH 4 emissions process control hypotheses.Measurement and model-based analyses of Amazon wetland CH 4 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 CH 4 emissions remain virtually unknown.
Here, our aim is to provide a first-order, model-independent characterization of wetland CH 4 flux resolution and precision requirements based on the basin-wide variations in car-bon and hydrological processes.Our resolution requirement is based on the correlation lengths of hypothesized wetland CH 4 emission process controls.At the required resolution, our precision requirement is that wetland CH 4 emissions scenarios -derived from a range of hypothesized carbon and hydrological process controls -are (a) statistically interdistinguishable and (b) distinguishable from a spatiotemporally uniform wetland CH 4 flux (i.e., a null hypothesis).
Given our process-level understanding of wetland CH 4 emissions, we propose four carbon and three hydrological proxies as the dominant drivers of wetland CH 4 emission variability (C1-C4 and H1-H3 respectively).We use carbon stocks and fluxes as proxies for variation in C availability for wetland CH 4 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).

CH 4 flux resolution
Our resolution requirement is based on a first-order assessment of the process variable correlation length scales: we anticipate that retrieving wetland CH 4 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 CH 4 emission variability.We use an autocorrelative approach to identify the variability length scales of potential CH 4 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 CH 4 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 CH 4 emissions: we propose a ∼ 333 km CH 4 flux resolution as the spatial resolution required to determine the role of process control variability on wetland CH 4 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 auto- correlations: 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.

CH 4 flux precision
We next derive the CH 4 flux precision required to distinguish between hypothesized wetland CH 4 process controls at a ∼ 333 km monthly resolution.We derive the precision requirements assuming 1 continuous year of CH 4 flux retrievals.We formulate (a) spatial CH 4 emission hypotheses, where wetland CH 4 emissions linearly co-vary with the hypothesized processes at ∼ 333 km scales, and (b) temporal CH 4 emission hypotheses, where wetland CH 4 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 wet-land CH 4 emissions to be the same.For example, Amazon wetland CH 4 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 CH 4 emission estimate (29.3 Tg CH 4 year −1 across 668 Mha).The explicit formulation of spatial and temporal wetland CH 4 emission hypotheses is described in Appendix B.
For a range of retrieved CH 4 flux precisions across the Amazon basin (spanning 1-100 mg m −2 day −1 ), we test whether each spatial and temporal wetland CH 4 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 CH 4 emission hypotheses are inter-distinguishable with > 95 % confidence at a ≤ 10 mg m −2 day −1 CH 4 flux precision.

CH 4 requirements
Given the spatial and temporal variability of potential hydrological and carbon controls, we define the following requirements for wetland CH 4 flux retrievals: -∼ 333 km spatial resolution monthly temporal resolution -10 mg CH 4 m −2 day −1 precision.
Our resolution and precision requirements provide a firstorder assessment of the wetland CH 4 emission biogeochemical process control variability.We anticipate that satellitebased CH 4 flux estimates meeting the above-stated requirements will provide robust characterization of spatial variation in Amazon wetland CH 4 emissions on the scale of variation in the major carbon and water controls, allowing forcing (hydrology and carbon) and response (CH 4 flux) to be related directly.Therefore, by retrieving CH 4 fluxes at the required resolution and precision, carbon and hydrological process hypotheses on the dominant drivers of Amazon wetland CH 4 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 CH 4 flux requirements.
Throughout the next subsections, we characterize the required satellite column CH 4 measurements needed to resolve CH 4 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 CH 4 flux spatial resolution requirements (L = 150-990 km) and we derive the corresponding CH 4 flux precision requirements.

CH 4 observation requirements
We define the atmospheric CH 4 observation requirements by retrieving CH 4 fluxes from a range of LEO and GEO OS simulated CH 4 retrieved concentrations, or "observations".Our approach is three-fold: (a) we simulate LEO and GEO CH 4 observations for March 2007; (b) we derive the precision of CH 4 measurement averaged at an L × L resolution (henceforth the "cumulative CH 4 measurement precision"); and (c) we employ an idealized inversion to simulate CH 4 flux retrieval uncertainty for March 2007 based on the cumulative CH 4 measurement precision.We note that wetland emissions are the largest and most uncertain source of CH 4 within the Amazon River basin (Wilson et al., 2016;Melton et al., 2013).We henceforth assume that the non- wetland CH 4 contribution (namely fires and anthropogenic CH 4 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 CH 4 observations
The advantage of LEO systems is a near-global coverage; for the TROPOMI mission CH 4 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 CH 4 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 CH 4 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 CH 4 emission estimates from LEO and GEO CH 4 retrievals.Rather, our aim is to determine whether CH 4 emission estimates from a range of LEO and GEO OS configurations are able meet the wetland process requirements outlined in Sect.2.1.
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 • resolutionthroughout 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) CH 4 measurement footprints are rejected; i.e., all accepted footprints are 100 % "cloud-free".
To assess the relative importance of CH 4 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 CH 4 measurement precision
For each OS ω ("GEO","LEO", etc.), O {L,ω} is the cumulative CH 4 measurement precision at a L × L resolution.O {L,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 CH 4 precision within each L × L grid cell i, O {L,ω} i as follows: where σ ω is the single observation precision (Table 1), φ {ω} i is the fraction of cloud-free observations at location i, n {ω} is the number of observations per km 2 per month for OS ω (based on Table 1 values) and a the fraction of accepted cloud-free CH 4 column retrievals (set to a = 0.5).The derivation of φ {ω} i 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 CH 4 measurements per L × L grid cell.For all OSs, n {ω} is calculated assuming continuous basin-wide coverage at the single-sounding footprint resolution (see Table 1).We highlight that our formulation of cumulative CH 4 precision in Eq. ( 1) implies retrieved CH 4 errors are spatially and temporally uncorrelated.

OS-retrieved CH 4 flux precision
We calculate the monthly retrieved CH 4 flux precision for OS ω at an L × L resolution -F {L,ω} -based on O {L,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 CH 4 concentration vectors (c 15206 A. A. Bloom et al.: Amazon wetland CH 4 emissions as a case study distributed random numbers with mean zero and variance one ("•" denotes element-wise multiplication).We relate the concentrations c {L, * } to the underlying CH 4 fluxes f {L, * } as follows: where A {L} 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 CH 4 fluxes.For the sake of brevity, we present a summary of A {L} here and the complete derivation of A {L} 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 CH 4 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 CH 4 transport -A {30 km} -by spatially translating the LPDM influence function throughout the domain.To assess the robustness of the LPDM approach, we also simulated CH 4 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 A {L} based on A {30 km} .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 A {L} , (A {L} ) −1 and simulated CH 4 concentration vectors (c {L,ω} * ,n , Eq. 2).For the sake of simplicity, we set all unperturbed concentrations -c {L,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 Finally, we calculate the flux precision F {L,ω} at grid cell i as follows: . (5)

Residual CH 4 bias simulation
Despite the implementation of CH 4 bias correction methods based on satellite CH 4 retrieval comparison against ground measurements of total column CH 4 (Parker et al., 2011), spatial structures in residual CH 4 biases are a key limiting factor in top-down CH 4 flux accuracy.Here we quantify the role residual CH 4 biases for each OS configurations.We simulate a retrieved pseudo-random CH 4 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 CH 4 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 CH 4 concentration vector c {L,ω,b} * ,n where b represents the standard deviation of the pseudorandom CH 4 bias and v represents the number of visits per month; for bias errors correlated across spatial scales s, the scale factor s L √ v accounts for the pseudo-random behavior of bias errorsbat a monthly L × L resolution.We assess the role CH 4 biases on F {L,ω,b} for the LEO and GEO OS configurations at L =∼ 333 km.

Results and discussion
Cumulative CH 4 precision for mean monthly atmospheric column CH 4 measurements is 0.10-0.98ppb for the LEO OS (Fig. 5, left) and 0.02-0.20 ppb for the GEO OS (Fig. 5, right).The lowest CH 4 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).
For L =∼ 333 km, median monthly retrieved CH 4 flux precision for the LEO OS (i.e., the median of F {L,ω} ) is 17.0 mg CH 4 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 CH 4 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 CH 4 concentrations (Fig. 5) lead to a 2.7 mg CH 4 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 CH 4 m −2 day −1 .GEO-Z1 and GEO-Z2 uncertainties (2.4 and 2.0 mg CH 4 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 CH 4 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;Figure 5. Retrieved monthly ∼ 333 km CH 4 cumulative precision (i.e., the combined precision of monthly-averaged CH 4 measurements) for LEO and GEO observing systems; the observing system configurations are described in Table 1.  1 for details).The "observation density" includes all attempted CH 4 measurements, including accepted (cloud-free) and rejected (cloudy) observations.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 CH 4 flux process controls.
Our bias CH 4 analysis (Fig. 7) indicates that GEOretrieved CH 4 flux precisions at L =∼ 333 km are relatively unaffected by residual CH 4 biases < 1 ppb, while LEOretrieved CH 4 flux precisions are relatively unaffected by residual CH 4 biases < 5 ppb.We find that the advantage of GEO CH 4 flux precision over LEO diminishes from almost 1 order of magnitude at residual CH 4 biases < 1 ppb, to roughly a factor of 2 for residual biases > 20 ppb.Here we assume a residual CH 4 bias correlation scale of 100 km (Sect.2.3); based on Eq. ( 6), we expect a larger impact of residual CH 4 biases on OS-retrieved CH 4 flux precision for residual CH 4 bias correlation lengths > 100 km or for temporally correlated CH 4 biases.Overall, the relative advantage of GEO over LEO OSs is contingent on both the cumulative CH 4 precision (Fig. 5) as well as the anticipated spatiotemporal structure of residual CH 4 bias.
Estimates of fluxes at L = 150-990 km show that median GEO-retrieved CH 4 flux uncertainty is consistently a factor of ∼ 5 lower than the median LEO-retrieved CH 4 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.GEOderived CH 4 fluxes meet the both the precision and resolution requirements for L =∼ 180-333 km; for a 10 ppb residual bias, GEO-derived CH 4 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 CH 4 fluxes meet the precision requirements at L > 500 km; LEOderived CH 4 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 CH 4 retrieval and transport model biases can un-  dermine the enhanced accuracy of geostationary OSs.For example, we find that our LPDM-derived transport operator yields a conservative estimate of the monthly mean CH 4 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 LPDMderived transport operator (A {L} ); OS CH 4 flux precision results exhibit an inversely proportional response, corresponding to a ∼ 33 % uncertainty reduction (median GEO flux precision of 1.8 mg CH 4 m −2 day −1 and a LEO precision of 11.3 mg CH 4 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 CH 4 bias structures on the accuracy of GEO and LEO CH 4 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.
Our CH 4 flux resolution requirement (monthly L =∼ 333 km CH 4 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 CH 4 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 CH 4 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 CH 4 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 CH 4 fluxes and biogeochemical process controls; the potential of OS synergies undoubtedly requires further investigation.
In contrast to our approach, CH 4 flux uncertainty requirements can alternatively be derived by quantifying processbased wetland CH 4 emission model uncertainty (Melton et al., 2013) or by characterizing the CH 4 flux uncertainty stemming from wetland CH 4 model parametric uncertainty (Bloom et al., 2012).An advantage of model-based requirements is the ability to assess CH 4 flux uncertainties associated with the complex interactions between wetland CH 4 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 CH 4 fluxes.Moreover, wetland CH 4 models often exhibit structural similarities (Melton et al., 2013); for example, wetland CH 4 emission models (Melton et al., 2013) suggest major CH 4 emissions along the main stem of the Amazon River (Fig. 1).Since model spatiotemporal CH 4 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 CH 4 flux estimates would hinder the potential to independently investigate biogeochemical process controls on wetland CH 4 emissions.To our knowledge, our analysis provides a first quantification of the OS requirements for confronting prior knowledge on CH 4 fluxes at a process-relevant resolution.

Concluding remarks
Quantitative knowledge of biogeochemical processes controlling biosphere-atmosphere greenhouse gas fluxes remains highly uncertain.Optimally designed satellite greenhouse gas OSs can potentially resolve the processes controlling critical boreal and tropical greenhouse gas fluxes.In this study, we have characterized a satellite OS able to resolve the principal process controls on Amazon basin wetland CH 4 emissions.Conventional low-earth orbit satellite missions will likely be unable to resolve Amazon wetland CH 4 emissions at a process-relevant scale and precision.Observation density in time and space, and its reduction by cloud cover are the major limiting factors.Increasing the number of daily CH 4 measurements in cloudy regions at the expense of other measurements can further reduce the retrieved CH 4 flux precision from geostationary satellite CH 4 measurements.OSSEs based on reducing process uncertainty can inform observation requirements for future greenhouse gas satellite missions in a far more targeted way than simply quantifying overall flux uncertainty reduction for a given OS.

Figure 1 .
Figure 1.Mean annual wetland and rice CH 4 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 CH 4 emissions.

Figure 3 .
Figure 3. Spatial autocorrelation (Moran's I) for potential carbon controls (left column) and hydrological controls (right column) on wetland CH 4 emissions.The spatial variability of carbon controls are derived from satellite observations (biomass in Saatchi et al., 2011; solarinduced fluorescence in Joiner et al., 2013), the Harmonized World Soil Database (soil carbon; Hiederer and Köchy, 2011) and FLUXNETderived 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 CH 4 flux retrievals, based on the maximum correlation lengths of potential carbon and hydrological controls on wetland CH 4 emissions.The details of the Moran's I analysis are fully described in Appendix A.

Figure 4 .
Figure 4. Distinction confidence between Amazon basin spatial and temporal wetland CH 4 emission hypotheses against monthly ∼ 333 km CH 4 flux precision.Spatial and temporal wetland CH 4 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 CH 4 flux precision requirement as 10 mg m −2 day −1 .

Figure 7 .
Figure 7. Retrieved GEO and LEO flux precision for L =∼ 333 km with modeled pseudo-random residual bias error.SeeTable 1 for details on GEO and LEO CH 4 observing systems.

Figure 8 .
Figure 8. Median retrieved LEO and GEO CH 4 fluxes for L = 150-990 km; the dashed lines indicate precision and resolution requirements.See Table1for details on GEO and LEO CH 4 observing systems.The bias value of 10 ppb indicates modeled systematic CH 4 measurement biases with 100 km spatial correlations (see Sect. 2.3).

Figure D1 .
Figure D1.March 2007 simulations of atmospheric CH 4 concentration enhancements -based on 12 mg m −2 day −1 fluxes throughout the Amazon basin -derived using the WRF atmospheric transport model (a) and the LPDM influence function approach (b).The dashed line denotes our delineation of "northeast Amazon basin" and "southwest Amazon basin" regions (see Appendix C).

CH 4 emissions Quan8fying wetland CH 4 process controls Wetland CH 4 OSSE (this study)
4 fluxes from retrieved satellite CH 4 observations and (ii) resolving process parameters from retrieved CH 4 fluxes (middle column).The optimal satellite CH 4 observation requirements are a function of the flux resolution and precision required to resolve wetland CH 4 process controls (right column): OSSE steps 1-3 are described in Sects.2.1-2.3.

Table 1 .
Observation system characteristics a .
Table 1 for details on GEO and LEO CH 4 observing systems.