Cécile Penland

The optimal growth of tropical sea surface temperature anomalies

Abstract It is argued from SST observations for the period 1950–90 that the tropical Indo-Pacific ocean-atmosphere system may be described as a stable linear dynamical system driven by spatially coherent Gaussian white noise. Evidence is presented that the predictable component of SST anomaly growth is associated with the constructive interference of several damped normal modes after an optimal initial structure is set up by the white noise forcing. In particular, El Nino–Southern Oscillation (ENSO) growth is associated with an interplay of at least three damped normal modes, with periods longer than two years and decay times of 4 to 8 months, rather than the manifestation of a single unstable mode whose growth is arrested by nonlinearities. Interestingly, the relevant modes are not the three least damped modes of the system. Rather, mode selection, and the establishment of the optimal initial structure from which growth occurs, are controlled by the stochastic forcing. Experiments conducted with an empir...

Prediction of Niño 3 Sea Surface Temperatures Using Linear Inverse Modeling

Abstract Linear inverse modeling is used to predict sea surface temperatures (SSTS) in the Nino 3 region. Predictors in three geographical locations are used: the tropical Pacific Ocean, the tropical Pacific and Indian oceans, and the global tropical oceans. Predictions did not depend crucially on any of these three domains, and evidence was found to support the assumption that linear dynamics dominates most of the record. The prediction model performs better when SST anomalies are rapidly evolving than during warm events when large anomalies persist. The rms prediction error at a lead time of 9 months is about half a degree Celsius.

Changes of Probability Associated with El Niño

Abstract Away from the tropical Pacific Ocean, an ENSO event is associated with relatively minor changes of the probability distributions of atmospheric variables. It is nonetheless important to estimate the changes accurately for each ENSO event, because even small changes of means and variances can imply large changes of the likelihood of extreme values. The mean signals are not strictly symmetric with respect to El Nino and La Nina. They also depend upon the unique aspects of the SST anomaly patterns for each event. As for changes of variance and higher moments, little is known at present. This is a concern especially for precipitation, whose distribution is strongly skewed in areas of mean tropospheric descent. These issues are examined here in observations and GCM simulations of the northern winter (January–March, JFM). For the observational analysis, the 42-yr (1958–99) reanalysis data generated at NCEP are stratified into neutral, El Nino, and La Nina winters. The GCM analysis is based on NCEP atmo...

A stochastic model of IndoPacific sea surface temperature anomalies

Abstract It is often desirable to represent a rapidly varying physical process as stochastic forcing of some slower dynamical system. A review of this approximation is presented. The white-noise limit of rapidly varying processes reduces the dynamical description of the affected slower systems to stochastic differential equations, the properties of which are summarized. As an application of stochastic differential equations, we review the evidence that IndoPacific sea surface temperature anomalies (SSTAs) can be represented as a stable linear process driven by spatially coherent stochastic forcing. An “inversemodeling” approach is used. That is, the relevant parameters of the best-fit stable linear process are obtained from observations and, given these parameters, the assumptions of stability and linearity are subsequently tested. An “optimal initial structure” for growth, predicted by the model, is found to occur approximately seven months before most of the major warm and cold (El Nino/La Nina) events in the data record. The optimal structure preferentially occurs in the boreal spring, with the mature phase of the extreme event occurring in the subsequent late fall/winter. The best model to fit the observations, including the dependence of the dynamical system on the annual cycle, is driven by stochastic forcing with periodic statistics. These statistics are inferred using a time-dependent fluctuation-dissipation relation. The variation of the stochastic forcing with the annual cycle is not the same as that of the optimal initial structure. Yet, when a linear numerical model is driven with the derived stochastic forcing, the optimal structure, including its variation with the annual cycle, is recovered. This implies that deterministic dynamics play an important role in setting up the optimal structure and, therefore, a mature phase of El Nino may be predicted before the optimal structure actually appears.

Random Forcing and Forecasting Using Principal Oscillation Pattern Analysis

Abstract The effects of random forcing and deterministic feedback are combined in a measured multivariate time series. It is shown here how the characteristics of the driving noise can be found after the deterministic effects have been identified by the principal oscillation pattern (POP) analysis. In addition, the POP analysis is extended to enable the prediction of the most probable meteorological pattern at some future time when the present pattern is known, and the conditional probability of finding the process at any location within a range of values given the value of the process at another location at an earlier time. Estimates of how well these predictions can be trusted are also given. The basic assumption of POP analysis is that the system can be optimally modeled by a linear Markov process.

Prediction of Tropical Atlantic Sea Surface Temperatures Using Linear Inverse Modeling

The predictability of tropical Atlantic sea surface temperature on seasonal to interannual timescales by linear inverse modeling is quantified. The authors find that predictability of Caribbean Sea and north tropical Atlantic sea surface temperature anomalies (SSTAs) is enhanced when one uses global tropical SSTAs as predictors compared with using only tropical Atlantic predictors. This predictability advantage does not carry over into the equatorial and south tropical Atlantic; indeed, persistence is a competitive predictor in those regions. To help resolve the issue of whether or not the dipole structure found by applying empirical orthogonal function analysis to tropical Atlantic SSTs is an artifact of the technique or a physically real structure, the authors combine empirically derived normal modes and their adjoints to form ‘‘influence functions,’’ maps highlighting the geographical areas to which the north tropical Atlantic and the south tropical Atlantic SSTs are most sensitive at specified lead times. When the analysis is confined to the Atlantic basin, the 6-month influence functions in the north and south tropical Atlantic tend to be of the opposite sign and evolve into clear dipoles within 6 months. When the analysis is performed on global tropical SSTs, the 6-month influence functions are connected

Multiplicative Noise and Non-Gaussianity: A Paradigm for Atmospheric Regimes?

Abstract Atmospheric circulation statistics are not strictly Gaussian. Small bumps and other deviations from Gaussian probability distributions are often interpreted as implying the existence of distinct and persistent nonlinear circulation regimes associated with higher-than-average levels of predictability. In this paper it is shown that such deviations from Gaussianity can, however, also result from linear stochastically perturbed dynamics with multiplicative noise statistics. Such systems can be associated with much lower levels of predictability. Multiplicative noise is often identified with state-dependent variations of stochastic feedbacks from unresolved system components, and may be treated as stochastic perturbations of system parameters. It is shown that including such perturbations in the damping of large-scale linear Rossby waves can lead to deviations from Gaussianity very similar to those observed in the joint probability distribution of the first two principal components (PCs) of weekly av...

A balance condition for stochastic numerical models with application to the El Nino-Southern Oscillation

Abstract Stochastic forcing due to unresolved processes adds energy to a measurable system. Although this energy is added randomly in time, conservation laws still apply. A balance condition for stochastically driven systems is discussed. This “fluctuation-dissipation relation” may be used either to deduce the geographical properties of the stochastic forcing from data given a model for the evolution of the macroscopic variables or to diagnose energy conservation in a stochastic numerical model. The balance condition in its first role was applied to sea surface temperatures (SSTs) in the Indo-Pacific basin. A low-dimensional empirical dynamical model of SSTs was generated in such a way that observed statistical properties of the field are preserved. Experiments varying the stochastic forcing in this model indicated how the geographical characteristics of the forcing affect the distribution of variance among the various normal modes thereby determining the dominant timescales of the SST field. These result...

Stochastic Forcing of the Wintertime Extratropical Flow

Abstract This study is concerned with assessing the extent to which extratropical low-frequency variability may be viewed as a response to geographically coherent stochastic forcing. This issue is examined with a barotropic model linearized about the long-term mean wintertime 300-mb flow with zonal and meridional structure. The perturbation eigenfunctions of the model are stable (i.e., decaying) for a realistic 5-day drag, so transient eddy activity can be maintained against the drag only with forcing. In a statistical steady state, a fluctuation–dissipation relation (FDR) links the covariance structure of the eddy vorticity to the covariance structure of the forcing. This relation is used in a forward sense to determine the covariance of eddy vorticity for a specified covariance of forcing. It is also used in a backward sense to infer the covariance of forcing required to maintain the observed covariance of eddy vorticity. The focus is on explaining the observed variability of 10-day running mean anomali...

How Important Is Air–Sea Coupling in ENSO and MJO Evolution?

Abstract The effect of air–sea coupling on tropical climate variability is investigated in a coupled linear inverse model (LIM) derived from the simultaneous and 6-day lag covariances of observed 7-day running mean departures from the annual cycle. The model predicts the covariances at all other lags. The predicted and observed lag covariances, as well as the associated power spectra, are generally found to agree within sampling uncertainty. This validates the LIM’s basic premise that beyond daily time scales, the evolution of tropical atmospheric and oceanic anomalies is effectively linear and stochastically driven. It also justifies a linear diagnosis of air–sea coupling in the system. The results show that air–sea coupling has a very small effect on subseasonal atmospheric variability. It has much larger effects on longer-term variability, in both the atmosphere and the ocean, including greatly increasing the amplitude of ENSO and lengthening its dominant period from 2 to 4 years. Consistent with these...