Backward trajectory analyses

The implication of backward error analysis is that the convergence order is still directly relevant in molecular simulations, even when the accuracy of trajectories (described by the convergence theorem) cannot be verified. We can think of the modified energy surface as a rippled version of the original. The order determining the allowed magnitude of the fiuctuation. 

A realistic simulation of real data was achieved using the model with a 56-km horizontal resolntion and 32 layers in the vertical. Numerical simulation for the forward trajectories was initialized at 0000 UTC April 18, and at 2100 UTC April 19, for the backward trajectory using ECMWF (European Centre for Medium-Range Weather Forecasts) analysis as the initial conditions. Initial fields of geopotential height, wind components and specific humidity, at ten standard pressure levels, were obtained by bihnear interpolation from the ECMWF operational initialized analyses. Time-dependent lateral boundary values were taken from the ECMWF analyses, linearly interpolated between the analyzed fields available at 6 h intervals. They were used at the outermost boundary points only. The row next to the outer boundary is a blend (four-point space interpolation) of the outer row and the third row inside, which is the outermost integration row of the model. 

The measured ammonia and ammonium concentrations at the Finnish EMEP measurement stations of Virolahti and Ahtari show a maximum on March 21, 1989 this time corresponds to computed arrival times. However, such maximum values are not uncommon in springtime. A detailed analysis of backward trajectories, computed for these measurement stations, and the measured concentrations do not show conclusively that the measured maximum values would have been caused by the accident (Kukkonen et al., 1993). Most of the NH due to the accident may have escaped the available measurement stations. 

Summarizing, from a mathematical point of view, both forward and backward analysis lead to the insight that long term trajectory simulation should be avoided even with symplectic discretizations. Rather, in the spirit of multiple as opposed to single shooting (cf. Bulirsch [4, 18]), only short term trajectories should be used to obtain reliable information. 

The MD trajectories contain the clues that should allow sense to be made from the complex chemistry of energetic materials. Thus each time a molecule is formed we can go backward in time to see which the key reactions were. Such analysis indicates complex (multi-molecular) processes for p = 4 km/s, we find (at 4 ps) a large percentage of the final molecules were formed by multimolecular processes 80% for HONO, 60% for OH, 20% for N2, 10% for NO and 5% for NO2. 

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