Abstract
This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a three-layer quasigeostrophic model. This model climate has reasonable approximations of the North Atlantic Oscillation (NAO) and Pacific–North America (PNA) patterns. The systematic strategy consists first of the identification of slowly evolving climate modes and faster evolving nonclimate modes by use of an empirical orthogonal function (EOF) decomposition in the total energy metric. The low-order stochastic climate model predicts the evolution of these climate modes a priori without any regression fitting of the resolved modes. The systematic stochastic mode reduction strategy determines all correction terms and noises with minimal regression fitting of the variances and correlation times of the unresolved modes. These correction terms and noises account for the neglected interactions between the resolved climate modes and the unresolved nonclimate modes. Low-order stochastic models with 10 or less resolved modes capture the statistics of the original model very well, including the variances and temporal correlations with high pattern correlations of the transient eddy fluxes. A budget analysis establishes that the low-order stochastic models are highly nonlinear with significant contributions from both additive and multiplicative noise. This is in contrast to previous stochastic modeling studies. These studies a priori assume a linear model with additive noise and regression fit the resolved modes. The multiplicative noise comes from the advection of the resolved modes by the unresolved modes. The most straightforward low-order stochastic climate models experience climate drift that stems from the bare truncation dynamics. Even though the geographic correlation of the transient eddy fluxes is high, they are underestimated by a factor of about 2 in the a priori procedure and thus cannot completely overcome the large climate drift in the bare truncation. Also, variants of the reduced stochastic modeling procedure that experience no climate drift with good predictions of both the variances and time correlations are discussed. These reduced models without climate drift are developed by slowing down the dynamics of the bare truncation compared with the interactions with the unresolved modes and yield a minimal two-parameter regression fitting strategy for the climate modes. This study points to the need for better optimal basis functions that optimally capture the essential slow dynamics of the system to obtain further improvements for the reduced stochastic modeling procedure.
Corresponding author address: Dr. Christian Franzke, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012. Email: franzke@cims.nyu.edu
