ALBERT

Description: We perform a series of observing system simulation experiments (OSSEs) to quantify how well surface CO2 fluxes may be estimated using column-integrated CO2 data from the Orbiting Carbon Observatory (OCO), given the presence of various error sources. We use variational data assimilation to optimize weekly fluxes at 2°×5° (lat/lon) using simulated data averaged only across the ~33 s that OCO takes to cross a typical 2°×5° model grid box. Grid-scale OSSEs of this sort have been carried out before for OCO using simplified assumptions for the measurement error. Here, we more accurately describe the OCO measurements in two ways. First, we use new estimates of the single-sounding retrieval uncertainty and averaging kernel, both computed as a function of surface type, solar zenith angle, aerosol optical depth, and pointing mode (nadir vs. glint). Second, we collapse the information content of all valid retrievals from each grid box crossing into an equivalent multi-sounding measurement uncertainty, factoring in both time/space error correlations and data availability due to clouds and thick aerosols (calculated from MODIS data). Finally, we examine the impact of three types of systematic errors: measurement biases due to aerosols, transport errors, and errors caused by assuming incorrect error statistics. When only random measurement errors are considered, both nadir- and glint-mode data give error reductions of ~50% over the land for the weekly fluxes, and ~65% for seasonal fluxes. Systematic errors reduce both the magnitude and extent of these improvements by up to a factor of two, however. Flux improvements over the ocean are significant only when using glint-mode data and are smaller than those over land; when the assimilation is mistuned, slow convergence makes even these improvements difficult to achieve. The OCO data may prove most useful over the tropical land areas, where our current flux knowledge is weak and where the measurements remain fairly accurate even in the face of systematic errors.

Description: We explore the use of a fixed-lag Kalman smoother for sequential estimation of atmospheric carbon dioxide fluxes. This technique takes advantage of the fact that most of the information about the spatial distribution of sources and sinks is observable within a few months to half of a year of emission. After this period, the spatial structure of sources is diluted by transport and cannot significantly constrain flux estimates. We therefore describe an estimation technique that steps through the observations sequentially, using only the subset of observations and modeled transport fields that most strongly constrain the fluxes at a particular time step. Estimates of each set of fluxes are sequentially updated multiple times, using measurements taken at different times, and the estimates and their uncertainties are shown to quickly converge. Final flux estimates are incorporated into the background state of CO2 and transported forward in time, and the final flux uncertainties and covariances are taken into account when estimating the covariances of the fluxes still being estimated. The computational demands of this technique are greatly reduced in comparison to the standard Bayesian synthesis technique where all observations are used at once with transport fields spanning the entire period of the observations. It therefore becomes possible to solve larger inverse problems with more observations and for fluxes discretized at finer spatial scales. We also discuss the differences between running the inversion simultaneously with the transport model and running it entirely off-line with pre-calculated transport fields. We find that the latter can be done with minimal error if time series of transport fields of adequate length are pre-calculated.

Description: We quantify how well column-integrated CO2 measurements from the Orbiting Carbon Observatory (OCO) should be able to constrain surface CO2 fluxes, given the presence of various error sources. We use variational data assimilation to optimize weekly fluxes at a 2°×5° resolution (lat/lon) using simulated data averaged across each model grid box overflight (typically every ~33 s). Grid-scale simulations of this sort have been carried out before for OCO using simplified assumptions for the measurement error. Here, we more accurately describe the OCO measurements in two ways. First, we use new estimates of the single-sounding retrieval uncertainty and averaging kernel, both computed as a function of surface type, solar zenith angle, aerosol optical depth, and pointing mode (nadir vs. glint). Second, we collapse the information content of all valid retrievals from each grid box crossing into an equivalent multi-sounding measurement uncertainty, factoring in both time/space error correlations and data rejection due to clouds and thick aerosols. Finally, we examine the impact of three types of systematic errors: measurement biases due to aerosols, transport errors, and mistuning errors caused by assuming incorrect statistics. When only random measurement errors are considered, both nadir- and glint-mode data give error reductions over the land of ~45% for the weekly fluxes, and ~65% for seasonal fluxes. Systematic errors reduce both the magnitude and spatial extent of these improvements by about a factor of two, however. Improvements nearly as large are achieved over the ocean using glint-mode data, but are degraded even more by the systematic errors. Our ability to identify and remove systematic errors in both the column retrievals and atmospheric assimilations will thus be critical for maximizing the usefulness of the OCO data.

Description: Top-down estimates of the spatiotemporal variations in emissions and uptake of CO2 will benefit from the increasing measurement density brought by recent and future additions to the suite of in situ and remote CO2 measurement platforms. In particular, the planned NASA Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) satellite mission will provide greater coverage in cloudy regions, at high latitudes, and at night than passive satellite systems, as well as high precision and accuracy. In a novel approach to quantifying the ability of satellite column measurements to constrain CO2 fluxes, we use a portable library of footprints (surface influence functions) generated by the WRF-STILT Lagrangian transport model in a regional Bayesian synthesis inversion. The regional Lagrangian framework is well suited to make use of ASCENDS observations to constrain fluxes at high resolution, in this case at 1° latitude × 1° longitude and weekly for North America. We consider random measurement errors only, modeled as a function of mission and instrument design specifications along with realistic atmospheric and surface conditions. We find that the ASCENDS observations could potentially reduce flux uncertainties substantially at biome and finer scales. At the 1° × 1°, weekly scale, the largest uncertainty reductions, on the order of 50%, occur where and when there is good coverage by observations with low measurement errors and the a priori uncertainties are large. Uncertainty reductions are smaller for a 1.57 μm candidate wavelength than for a 2.05 μm wavelength, and are smaller for the higher of the two measurement error levels that we consider (1.0 ppm vs. 0.5 ppm clear-sky error at Railroad Valley, Nevada). Uncertainty reductions at the annual, biome scale range from ∼40% to ∼75% across our four instrument design cases, and from ∼65% to ∼85% for the continent as a whole. Our uncertainty reductions at various scales are substantially smaller than those from a global ASCENDS inversion on a coarser grid, demonstrating how quantitative results can depend on inversion methodology. The a posteriori flux uncertainties we obtain, ranging from 0.01 to 0.06 Pg C yr−1 across the biomes, would meet requirements for improved understanding of long-term carbon sinks suggested by a previous study.

Description: We explore the use of a fixed-lag Kalman smoother for sequential estimation of atmospheric carbon dioxide fluxes. This technique takes advantage of the fact that most of the information about the spatial distribution of sources and sinks is observable within a 5 few months to half of a year of emission. After this period, the spatial structure of sources is diluted by transport and cannot significantly constrain flux estimates. We therefore describe an estimation technique that steps through the observations sequentially, using only the subset of observations and modeled transport fields that most strongly constrain the fluxes at a particular time step. Estimates of each set of fluxes 10 are sequentially updated multiple times, using measurements taken at different times, and the estimates and their uncertainties are shown to quickly converge. Final flux estimates are incorporated into the background state of CO2 and transported forward in time, and the final flux uncertainties and covariances are taken into account when estimating the covariances of the fluxes still being estimated. The computational demands 15 of this technique are greatly reduced in comparison to the standard Bayesian synthesis technique where all observations are used at once with transport fields spanning the entire period of the observations. It therefore becomes possible to solve larger inverse problems with more observations and for fluxes discretized at finer spatial scales. We also discuss the differences between running the inversion simultaneously with the 20 transport model and running it entirely off-line with pre-calculated transport fields. We find that the latter can be done with minimal error if time series of transport fields of adequate length are pre-calculated.

Description: We present a method for translating modeled terrestrial net ecosystem exchange (NEE) fluxes of carbon into the corresponding seasonal cycles in atmospheric CO2. The method is based on the pulse-response functions from the Transcom 3 Level 2 (T3L2) atmospheric tracer transport model (ATM) intercomparison. The new pulse-response method is considerably faster than a full forward ATM simulation, allowing CO2 seasonal cycles to be computed in seconds, rather than the days or weeks required for a forward simulation. Further, the results provide an estimate of the range of transport uncertainty across 13 different ATMs associated with the translation of surface NEE fluxes into an atmospheric signal. We evaluate the method against the results of archived forward ATM simulations from T3L2. The latter are also used to estimate the uncertainties associated with oceanic and fossil fuel influences. We present a regional breakdown at selected monitoring sites of the contribution to the atmospheric CO2 cycle from the 11 different T3L2 land regions. A test case of the pulse-response code, forced by NEE fluxes from the Community Land Model, suggests that for many terrestrial models, discrepancies between model results and observed atmospheric CO2 cycles will be large enough to clearly transcend ATM uncertainties.

Description: Top–down estimates of the spatiotemporal variations in emissions and uptake of CO2 will benefit from the increasing measurement density brought by recent and future additions to the suite of in situ and remote CO2 measurement platforms. In particular, the planned NASA Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) satellite mission will provide greater coverage in cloudy regions, at high latitudes, and at night than passive satellite systems, as well as high precision and accuracy. In a novel approach to quantifying the ability of satellite column measurements to constrain CO2 fluxes, we use a portable library of footprints (surface influence functions) generated by the Stochastic Time-Inverted Lagrangian Transport (STILT) model in combination with the Weather Research and Forecasting (WRF) model in a regional Bayesian synthesis inversion. The regional Lagrangian particle dispersion model framework is well suited to make use of ASCENDS observations to constrain weekly fluxes in North America at a high resolution, in this case at 1° latitude × 1° longitude. We consider random measurement errors only, modeled as a function of the mission and instrument design specifications along with realistic atmospheric and surface conditions. We find that the ASCENDS observations could potentially reduce flux uncertainties substantially at biome and finer scales. At the grid scale and weekly resolution, the largest uncertainty reductions, on the order of 50%, occur where and when there is good coverage by observations with low measurement errors and the a priori uncertainties are large. Uncertainty reductions are smaller for a 1.57 μm candidate wavelength than for a 2.05 μm wavelength, and are smaller for the higher of the two measurement error levels that we consider (1.0 ppm vs. 0.5 ppm clear-sky error at Railroad Valley, Nevada). Uncertainty reductions at the annual biome scale range from ~40% to ~75% across our four instrument design cases and from ~65% to ~85% for the continent as a whole. Tests suggest that the quantitative results are moderately sensitive to assumptions regarding a priori uncertainties and boundary conditions. The a posteriori flux uncertainties we obtain, ranging from 0.01 to 0.06 Pg C yr−1 across the biomes, would meet requirements for improved understanding of long-term carbon sinks suggested by a previous study.

Description: This paper describes real-time attitude determination results for the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX), a gyroless spacecraft, using a Kalman filter/Euler equation approach denoted the real-time sequential filter (RTSF). The RTSF is an extended Kalman filter whose state vector includes the attitude quaternion and corrections to the rates, which are modeled as Markov processes with small time constants. The rate corrections impart a significant robustness to the RTSF against errors in modeling the environmental and control torques, as well as errors in the initial attitude and rates, while maintaining a small state vector. SAMPLEX flight data from various mission phases are used to demonstrate the robustness of the RTSF against a priori attitude and rate errors of up to 90 deg and 0.5 deg/sec, respectively, as well as a sensitivity of 0.0003 deg/sec in estimating rate corrections in torque computations. In contrast, it is shown that the RTSF attitude estimates without the rate corrections can degrade rapidly. RTSF advantages over single-frame attitude determination algorithms are also demonstrated through (1) substantial improvements in attitude solutions during sun-magnetic field coalignment and (2) magnetic-field-only attitude and rate estimation during the spacecraft's sun-acquisition mode. A robust magnetometer-only attitude-and-rate determination method is also developed to provide for the contingency when both sun data as well as a priori knowledge of the spacecraft state are unavailable. This method includes a deterministic algorithm used to initialize the RTSF with coarse estimates of the spacecraft attitude and rates. The combined algorithm has been found effective, yielding accuracies of 1.5 deg in attitude and 0.01 deg/sec in the rates and convergence times as little as 400 sec.

Description: Attitude determination algorithms that requires only the earth's magnetic field will be useful for contingency conditions. One way to determine attitude is to use the time derivative of the magnetic field as the second vector in the attitude determination process. When no gyros are available, however, attitude determination becomes difficult because the rates must be propagated via integration of Euler's equation, which in turn requires knowledge of the initial rates. The spacecraft state to be determined must then include not only the attitude but also rates. This paper describes a magnetometer-only attitude determination scheme with no a priori knowledge of the spacecraft state, which uses a deterministic algorithm to initialize an extended Kalman filter. The deterministic algorithm uses Euler's equation to relate the time derivatives of the magnetic field in the reference and body frames and solves the resultant transcendental equations for the coarse attitude and rates. An important feature of the filter is that its state vector also includes corrections to the propagated rates, thus enabling it to generate highly accurate solutions. The method was tested using in-flight data from the Solar, Anomalous, and Magnetospheric Particles Explorer (SAMPEX), a Small Explorer spacecraft. SAMPEX data using several eclipse periods were used to simulate conditions that may exist during the failure of the on-board digital sun sensor. The combined algorithm has been found effective, yielding accuracies of 1.5 deg in attitude (within even nominal mission requirements) and 0.01 degree per second (deg/sec) in the rates.