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Abstract
Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence.
Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided.
Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method—based on an empirical statistical model derived from a Monte Carlo simulation-is formulated, and shown to work very well.
Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Abstract
Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence.
Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided.
Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method—based on an empirical statistical model derived from a Monte Carlo simulation-is formulated, and shown to work very well.
Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Testing Atmospheric Oxidation in an Alabama ForestAbstract
The chemical species emitted by forests create complex atmospheric oxidation chemistry and influence global atmospheric oxidation capacity and climate. The Southern Oxidant and Aerosol Study (SOAS) provided an opportunity to test the oxidation chemistry in a forest where isoprene is the dominant biogenic volatile organic compound. Hydroxyl (OH) and hydroperoxyl (HO2) radicals were two of the hundreds of atmospheric chemical species measured, as was OH reactivity (the inverse of the OH lifetime). OH was measured by laser-induced fluorescence (LIF) and by taking the difference in signals without and with an OH scavenger that was added just outside the instrument’s pinhole inlet. To test whether the chemistry at SOAS can be simulated by current model mechanisms, OH and HO2 were evaluated with a box model using two chemical mechanisms: Master Chemical Mechanism, version 3.2 (MCMv3.2), augmented with explicit isoprene chemistry and MCMv3.3.1. Measured and modeled OH peak at about 106 cm−3 and agree well within combined uncertainties. Measured and modeled HO2 peak at about 27 pptv and also agree well within combined uncertainties. Median OH reactivity cycled between about 11 s−1 at dawn and about 26 s−1 during midafternoon. A good test of the oxidation chemistry is the balance between OH production and loss rates using measurements; this balance was observed to within uncertainties. These SOAS results provide strong evidence that the current isoprene mechanisms are consistent with measured OH and HO2 and, thus, capture significant aspects of the atmospheric oxidation chemistry in this isoprene-rich forest.
Abstract
The chemical species emitted by forests create complex atmospheric oxidation chemistry and influence global atmospheric oxidation capacity and climate. The Southern Oxidant and Aerosol Study (SOAS) provided an opportunity to test the oxidation chemistry in a forest where isoprene is the dominant biogenic volatile organic compound. Hydroxyl (OH) and hydroperoxyl (HO2) radicals were two of the hundreds of atmospheric chemical species measured, as was OH reactivity (the inverse of the OH lifetime). OH was measured by laser-induced fluorescence (LIF) and by taking the difference in signals without and with an OH scavenger that was added just outside the instrument’s pinhole inlet. To test whether the chemistry at SOAS can be simulated by current model mechanisms, OH and HO2 were evaluated with a box model using two chemical mechanisms: Master Chemical Mechanism, version 3.2 (MCMv3.2), augmented with explicit isoprene chemistry and MCMv3.3.1. Measured and modeled OH peak at about 106 cm−3 and agree well within combined uncertainties. Measured and modeled HO2 peak at about 27 pptv and also agree well within combined uncertainties. Median OH reactivity cycled between about 11 s−1 at dawn and about 26 s−1 during midafternoon. A good test of the oxidation chemistry is the balance between OH production and loss rates using measurements; this balance was observed to within uncertainties. These SOAS results provide strong evidence that the current isoprene mechanisms are consistent with measured OH and HO2 and, thus, capture significant aspects of the atmospheric oxidation chemistry in this isoprene-rich forest.
