Stochastic simulation of the atmosphere with localized precision

In the conventional representation of the distribution of error in an estimate of the state of the atmosphere it is usual to assume, for the sake of computational economy, that error covariance is localized. There is less justification for this assumption than appears to be commonly supposed. For instance, an array of observations of wind, whose observational errors are independent of the “first guess” error and independent of each other, will actually spread the covariance of error in geopotential arbitrarily far, and increase the correlation of error in the geopotential to a maximum as the error in the wind observations tends toward zero. On the other hand, localized independent observations do not spread precision, which is the inverse of covariance. The coupling between wind and geopotential can be described by localized precision, so that there is the possibility of describing the entire problem in this way.

The stochastic-dynamic simulation problem is formulated in terms of precision, with a linearizing approximation for the evolution of small errors. It is concluded that the precision will be approximately localized if the simulation is driven by a sufficient amount of localized observations. A method of computing stochastic simulations is devised which allows drastic computational economies when precision is localized.

The precision formulation is demonstrated by experiments with a simple stationary model.