We derive regional-scale (∼104 km2) CO2 flux estimates for summer 2004 in the northeast United States and southern Quebec by assimilating extensive data into a receptor-oriented model-data fusion framework. Surface fluxes are specified using the Vegetation Photosynthesis and Respiration Model (VPRM), a simple, readily optimized biosphere model driven by satellite data, AmeriFlux eddy covariance measurements and meteorological fields. The surface flux model is coupled to a Lagrangian atmospheric adjoint model, the Stochastic Time-Inverted Lagrangian Transport Model (STILT) that links point observations to upwind sources with high spatiotemporal resolution. Analysis of CO2 concentration data from the NOAA-ESRL tall tower at Argyle, ME and from extensive aircraft surveys, shows that the STILT– VPRM framework successfully links model flux fields to regionally representative atmospheric CO2 data, providing a bridge between ‘bottom-up’ and ‘top-down’ methods for estimating regional CO2 budgets on timescales from hourly to monthly. The surface flux model, with initial calibration to eddy covariance data, produces an excellent a priori condition for inversion studies constrained by atmospheric concentration data. Exploratory optimization studies show that data from several sites in a region are needed to constrain model parameters for all major vegetation types, because the atmosphere commingles the influence of regional vegetation types, and even high-resolution meteorological analysis cannot disentangle the associated contributions. Airborne data are critical to help define uncertainty within the optimization framework, showing for example, that in summertime CO2 concentration at Argyle (107 m) is ∼0.6 ppm lower than the mean in the planetary boundary layer.
 Knowledge of trace gas fluxes at the land surface is essential for understanding the impact of human activities on the composition and radiative balance of the atmosphere. An ability to derive fluxes at the regional scale (on the order of 102–104 km2), at the scale of ecosystems and political borders, is crucial for policy and management responses. Lagrangian (“air mass-following”) aircraft experiments have potential for providing direct estimates of regional-scale fluxes by measuring concentration changes in air parcels as they travel over the landscape. Successful Lagrangian experiments depend critically on forecasts of air parcel locations, rate of dispersion of air parcels, and proper assessment of forecast errors. We describe an operational tool to forecast air parcel locations and dispersion and to guide planning of flights for air mass-following experiments using aircraft. The tool consists of a particle dispersion model driven by mesoscale model forecasts from operational centers. The particle model simulates time-reversed motions of air parcels from specified locations, predicting the source regions which influence these locations. Forecast errors are incorporated into planning of Lagrangian experiments using statistics of wind errors derived by comparison with radiosonde data, as well as the model-to-model spread in forecast results. We illustrate the tool’s application in a project designed to infer regional CO2 fluxes—the CO2 Budget and Rectification Airborne study, discuss errors in the forecasts, and outline future steps for further improvement of the tool.
The spatial and temporal gradients in atmospheric CO2 contain signatures of carbon fluxes, and as part of inverse studies, these signatures have been combined with atmospheric models to infer carbon sources and sinks. However, such studies have yet to yield finer-scale, regional fluxes over the continent that can be linked to ecosystem processes and ground-based observations. The reasons for this gap are twofold: lack of atmospheric observations over the continent and model deficiencies in interpreting such observations.
 We provide quantitative estimates for the spatial variability of CO2, crucial for assessing representativeness of observations. Spatial variability determines the mismatch between point observations and spatial averages simulated by models or observed from space-borne sensors. Such “representation errors” must be properly specified in determining the leverage of observations to retrieve surface fluxes or to validate space-borne sensors. We empirically derive the spatial variability and representation errors for tropospheric CO2 over the North American continent and the Pacific Ocean, using in-situ observations from extensive aircraft missions. The spatial variability and representation error of CO2 is smaller over the Pacific than the continent, particularly in the lowest altitudes, and decreases with altitude. Representation errors resulting from spatial variability in the summer continental PBL are as large as 1∼2 ppmv for typical grid resolutions used in current models for inverse analyses.
 We present a general framework for designing and analyzing Lagrangian-type aircraft observations in order to measure surface fluxes of trace gases on regional scales. Lagrangian experiments minimize uncertainties due to advection by measuring tracer concentrations upstream and downstream of the study region, assuring that observed concentration changes represent fluxes within the region. The framework includes (1) a receptor-oriented model of atmospheric transport, including turbulent dispersion, (2) an upstream tracer boundary condition, (3) a surface flux model that predicts the distribution of tracer fluxes in time and space, and (4) a Bayesian inverse analysis that combines a priori information with observations to yield optimal estimates of tracer fluxes by the flux model. We use a receptor-oriented transport model, the Stochastic Time-Inverted Lagrangian Transport (STILT) model, to simulate ensembles of particles representing air parcels transported backward in time from an observation point (receptor), linking receptor concentrations with upstream locations and surface inputs. STILT provides the capability to forecast flight tracks for Lagrangian experiments in the presence of atmospheric shear and dispersion. STILT may be used to forecast flight tracks that sample the upstream tracer boundary condition, or to analyze the data and provide optimized parameters in the surface flux model. We present a case study of regional scale surface CO2 fluxes using data over the United States obtained in August 2000 in the CO2 Budget and Rectification Airborne (COBRA-2000) study. STILT forecasts were obtained using the National Centers for Environmental Prediction Eta model to plan the flight tracks. Results from the Bayesian inversion showed large reductions in a priori errors for estimates of daytime ecosystem uptake of CO2, but constraints on nighttime respiration fluxes were weaker, due to few observations of CO2 in the nocturnal boundary layer. Derived CO2 fluxes from the influence-following analysis differed notably from estimates using a conventional one-dimensional budget (“Boundary Layer Budget”) on a typical day, due to time-variable contributions from forests and croplands. A critical examination of uncertainties in the Lagrangian analyses revealed that the largest uncertainties were associated with errors in forecasting the upstream sampling locations and with aggregation of heterogeneous fluxes at the surface. Suggestions for improvements in future experiments are presented.
 Quantitative models of deep convection play a central role to improve understanding of weather, trace gas distributions, and radiative regime of the upper troposphere. Cloud-resolving models of deep convection are useful tools to simulate relevant processes. Observations of tracers such as CO2 can provide critical constraints on mass transport within these models. However, such measurements do not span the entire four-dimensional domain in space and time. We introduce a new method to improve tracer constraints on such models, combining a Receptor-Oriented Atmospheric Modeling (ROAM) framework with airborne and ground-based CO2 data. We illustrate the application of ROAM in generating initial and boundary conditions of CO2 for cloud-resolving model simulations, for a case study in the CRYSTAL-FACE campaign. Observations and model results were compared for CO2 profiles from the surface up to 16 km, inside and outside of a deep convective cloud. ROAM generated concentration fields that agreed within 0.5 ppm (1σ) of observations outside the cloud. When ROAM-derived initial and boundary CO2 concentrations were fed to a state-of-the-art cloud-resolving model (DHARMA), the combined modeling system successfully reproduced observed concentration differences, 0.2–0.8 ppm, between in-cloud and out-of-cloud air at 9 ∼ 14 km. Results suggest that ∼25% of air at 14 km was lifted through the convective system from the PBL. This study demonstrates the potential of the receptor-oriented framework to constrain redistribution of air within convective systems using CO2, and it points to the need for better coordinated tracer measurements in future field missions.
 Ecosystem CO2 exchange and atmosphere boundary layer (ABL) mixing are correlated diurnally and seasonally as they are both driven by solar insulation. Tracer transport models predict that these covariance signals produce a meridional gradient of annual mean CO2 concentration in the marine boundary layer that is half as strong as the signal produced by fossil fuel emissions. This rectifier effect is simulated by most global tracer transport models. However, observations to constrain the strength of these covariance signals in nature are lacking. We investigate the covariance between ecosystem carbon dioxide exchange and ABL dynamics by comparing one widely cited transport model with observations in the middle of the North American continent. We measured CO2 flux and mixing ratio using an eddy-covariance system from a 447-m tower in northern Wisconsin, mixed layer depths using a 915-MHz boundary layer profiling radar near the tower, and vertical CO2 profiles from aircraft in the vicinity of the tower. We find (1) that simulated and observed net daily CO2 fluxes are similar; (2) the simulated maximum ABL depths were too shallow throughout year; (3) the simulated seasonal variability of the CO2 mixing ratio in the lowest layer of the free troposphere is 3 ppm smaller than that inferred from a mixed layer jump model and boundary layer observations; and (4) the simulated diurnal and seasonal covariance between CO2 flux and mixing ratio are weaker than the observed covariance. The comparison between model and observations is limited by the questionable representativeness of a single observing site and a bias towards fair weather observing conditions.
 We present an analysis framework and illustrate its potential to constrain terrestrial carbon fluxes at the regional scale using observations of CO2 and CO over North America acquired during the CO2 Budget and Rectification Airborne (COBRA) study in 2000. The COBRA data set, presented in detail in a companion paper [Gerbig et al., 2003] provides dense spatial coverage and extensive profiling in the lower atmosphere, revealing strong CO2 signatures of land surface fluxes in the active and relic mixed layers of the atmosphere. We introduce a “receptor-oriented” analysis framework designed to quantitatively interpret the atmospheric signatures of surface processes by linking concentrations at measurement locations (receptors) to surface fluxes in upwind regions. The framework incorporates three main components: (1) the Stochastic Time-Inverted Lagrangian Transport (STILT) model, driven with assimilated winds and running backward in time to map out the source-receptor relationship (footprint) at high temporal and spatial resolution; (2) an observation-based lateral boundary condition for CO2, resolving vertical and meridional gradients; and (3) a simple parameterization for biosphere-atmosphere fluxes that uses eddy covariance observations from the AmeriFlux network as prior estimates for fluxes. This framework allows quantitative comparison between the top-down constraint on fluxes from airborne observations of CO2 with the bottom-up constraint of eddy flux measurements in a Bayesian synthesis inversion. The model is used to investigate the observed representation error (mismatch between point measurements and grid-cell-averaged values in models), evaluated in the companion paper, showing that unresolved spatial variability of surface fluxes gives rise to most of the representation error over the continent. Thus the representation error reflects the effect of aggregation errors. Discrepancies between simulated and observed CO2 distributions are assessed to indicate where improvements are needed, including improved empirical representation of biosphere-atmosphere exchange process and better simulation of convective processes in atmospheric transport models.
 We analyze the spatial variability of CO2 measurements from aircraft platforms, including extensive observations acquired over North America during the CO2 Budget and Rectification Airborne (COBRA) study in 2000. The COBRA data set is unique in its dense spatial coverage and extensive profiling in the lower atmosphere. Strong signatures of CO2 fluxes at the land surface were observed in the active and relic mixed layers of the atmosphere (up to ∼20 ppm gradients). Free tropospheric CO2 exhibited significantly less variability except in areas affected by convective transport. Statistical analyses of the COBRA data indicate that CO2 mixed-layer averages can be determined from vertical profiles with an accuracy of approximately ±0.2 ppm, limited by atmospheric variance. Analysis of the associated representation error suggests that models require horizontal resolution smaller than ∼30 km to fully resolve spatial variations of atmospheric CO2 in the boundary layer over the continent. To provide a global context for these data, we analyzed the GLOBALVIEW marine boundary layer (MBL) reference CO2. Comparison of the MBL reference with extensive aircraft data extending over 20 years, covering the whole troposphere over the northern Pacific, shows significant seasonal biases of up to 2 ppm in the free troposphere, indicating that the MBL reference is a suitable boundary condition only for some applications. The spatial variability of CO2 revealed by the COBRA-2000 calls for a suitable analysis framework to derive regional and continental fluxes, presented in a companion paper. The problem requires boundary conditions constrained by both surface and upper tropospheric observations and constraints on terrestrial fluxes that exploit the information content of the highly variable CO2 distribution over land.
 Automated flask sampling aboard small charter aircraft has been proposed as a low-cost, reliable method to greatly increase the density of measurements of CO2 mixing ratios in continental regions in order to provide data for assessment of global and regional CO2 budgets. We use data from the CO2 Budget and Rectification-Airborne 2000 campaign over North America to study the feasibility of using discrete (flask) sampling to determine column mean CO2 in the lowest 4 km of the atmosphere. To simulate flask sampling, data were selected from profiles of CO2 measured continuously with an onboard (in situ) analyzer. We find that midday column means can be determined without bias relative to true column means measured by the in situ analyzer to within 0.15 and better than 0.10 ppm by using 10 and 20 instantaneously collected flask samples, respectively. More precise results can be obtained by using a flask sampling strategy that linearly integrates over portions of the air column. Using less than 8–10 flasks can lead to significant sampling bias for some common profile shapes. Sampling prior to the breakup of the nocturnal stable layer will generally lead to large sampling bias because of the inability of aircraft to probe large CO2 gradients that often exist very close to the ground at night and during the early morning.
 We introduce a tool to determine surface fluxes from atmospheric concentration data in the midst of distributed sources or sinks over land, the Stochastic Time-Inverted Lagrangian Transport (STILT) model, and illustrate the use of the tool with CO2 data over North America. Anthropogenic and biogenic emissions of trace gases at the surface cause large variations of atmospheric concentrations in the planetary boundary layer (PBL) from the “near field,” where upstream sources and sinks have strong influence on observations. Transport in the near field often takes place on scales not resolved by typical grid sizes in transport models. STILT provides the capability to represent near-field influences, transforming this noise to signal useful in diagnosing surface emissions. The model simulates transport by following the time evolution of a particle ensemble, interpolating meteorological fields to the subgrid scale location of each particle. Turbulent motions are represented by a Markov chain process. Significant computational savings are realized because the influence of upstream emissions at different times is modeled using a single particle simulation backward in time, starting at the receptor and sampling only the portion of the domain that influences the observations. We assess in detail the physical and numerical requirements of STILT and other particle models necessary to avoid inconsistencies and to preserve time symmetry (reversibility). We show that source regions derived from backward and forward time simulations in STILT are similar, and we show that deviations may be attributed to violation of mass conservation in currently available analyzed meterological fields. Using concepts from information theory, we show that the particle approach can provide significant gains in information compared to conventional gridcell models, principally during the first hours of transport backward in time, when PBL observations are strongly affected by surface sources and sinks.
This chapter contains sections titled:
- Rectifier Effects
- Measurement Requirements
- Harvard Forest Data
- Amazon Data
- A Simple Boundary-Layer Model
- The Co2 Budget and Rectification Airborne Study