Improvements in the perturbation simulations of the global reference atmospheric model

Abstract

The Global Reference Atmospheric Model (GRAM) program includes the capability for simulating pseudo-random perturbations in density, temperature, pressure, or wind components along a simulated reentry trajectory or other path through the atmosphere. Some concerns were expressed by GRAM users, however, that the mean-square perturbation gradients may be too large for small values of the vertical separation Delta z. The present GRAM perturbation simulations, based on a one-step autoregressive model, yield a power spectrum versus wavenumber k which is proportional to k sup -2 at high wavenumbers. This feature also produces mean-square perturbation differences which are directly proportional to Delta z, and mean-square perturbation gradients which are inversely proportional to Delta z. Thus, root-mean-square gradients, (Delta f/Delta z) sub rms, increase with decreasing Delta a as Delta z sup -1/2. A simple modification to GRAM is suggested which overcomes this problem, i.e., which produce root-mean-square gradient that remain bound as Delta z approaches zero. Possible applications of more sophisticated simulation approaches, e.g., second order autoregressive models, or fractal model techniques, were also explored briefly but found to yield improvements which appear too small to justify their considerable added complexity for use in the GRAM programs