Simulation of Systematic Error Effects and Their Reduction in a Simple Model of the Atmosphere

Abstract

Use general question considered in this is study is: To what extent does the maintenance of a correctly simulated quasi-stationary flow in a model influence the simulation of the transient part of the flow? and, in particular, the question. To what extent does the existence of systematic errors influence the growth of random errors? As an initial approach toward addressing this question, a simple model is used to generate a sequence of realizations. The model is based on the equivalent barotropic equation with orography, forcing and dissipation included and is applied to the whole globe with a spectral representation of the fields, truncated triangularly at T25. Dissipation is in the form of a Rayleigh friction term and a fourth-order dissipation term. The forcing is calculated from observed data in such a way as to balance the time-mean Jacobian term and the dissipation. The data from these relations are called the control data. A perturbation of the model is purposely introduced and integrations are made with this perturbed model starting from the same initial data point of each realization of the control run. The data from these realizations of the perturbed model are called the perturbed data. Comparison of statistics compiled from the two datasets reveals a drift of the climate of the perturbed model away from the climate of the control model. The difference between the perturbed and control runs constitutes the error field. The systematic part of this error field is used to correct another sequence of forecasts made with the perturbed model. The corrections are made in two ways. First, all the forecasts are corrected at each forecast lead time after the entire integration is made. Second, all the forecasts are corrected every 12 hours during the integration so that the quasi-stationary part of the flow is repeatedly adjusted back to the climatology of the control run. Both types of corrections practically wipe out the systematic error. The main result of this paper is that, for this model, the recurrent corrections are also able to decrease the growth of the random error substantially, which indicates that the transient part of the flow is quite sensitive to the accuracy with which the quasi-stationary flow is simulated. Possible mechanisms in the model responsible for this behavior are briefly discussed.