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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

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