Abstract
A low-resolution global spectral model truncated at zonal wavenumber 5 and meridional mode 15 is developed to simulate the low-frequency variability of planetary-scale atmospheric motions. The effects of unresolved time and space scales on the slow evolution of the flow are deduced by analyzing their contribution to the tendencies of low-pass-filtered planetary-scale modes in a higher-resolution (R15 truncation) version of the model. This unresolved forcing is parameterized by a quasi-stochastic method formulated on the transform grid of the low-resolution model. The deterministic component of the parameterization consists of a linear regression of the unresolved forcing on the resolved forcing, which represents the autonomous dynamics of the low-resolution model. The regression parameters vary spatially and with the dependent variable. The stochastic component of the parameterization consists of kth-order univariate autoregressive statistical models, AR(k), which simulate the residuals from the linear regression.
Measured against the spatially and temporally filtered flow from the R15 model, the skill exhibited by the low-resolution model without the parameterization, with the deterministic component only, and with the full parameterization using AR(2) and AR(4) models is determined from a set of 30-day simulators. The full parameterization with the AR(4) model demonstrates the greatest skill. For all dependent variables, rms errors are less than their respective saturation values out to 7–11 days. Northern Hemisphere anomaly correlations greater than 0.6 are produced out to 6–8 days, comparable to the low-frequency skill of operational models.
Although this range of skill is not sufficient to cover typical life cycles of persistent anomalies, the low-resolution model is used to investigate the spatial pattern of skill degradation during Atlantic positive persistent anomalies using Monte Carlo simulations. The white-noise component of the AR(k) model provides the dispersion of predictions during the 10-day Monte Carlo runs. The skill degrades most rapidly in regions of enhanced high-frequency transient eddy activity and in regions most sensitive to the stochastic component of the parameterization. Dispersion among the ensemble of predictions is small during the first 4–5 days, indicating that the autoregressive portion of the stochastic model (i.e., excluding the white noise) dominates the loss of skill. Formulating the stochastic model as a multivariate process could conceivably lead to increased skill.
