Abstract

A multivariate empirical model is used to show that predictability of the dominant patterns of tropical and North Pacific oceanic variability, El Niño–Southern Oscillation (ENSO), and the Pacific decadal oscillation (PDO), is mostly limited to little more than a year, despite the presence of spectral peaks on decadal time scales. The model used is a linear inverse model (LIM) derived from the observed simultaneous and 1-yr lag correlation statistics of July–June-averaged SST from the Hadley Centre Global Sea Ice and Sea Surface Temperature (HadISST) dataset for the years 1900–2002. The model accurately reproduces the power spectra of the data, including interannual and interdecadal spectral peaks that are significant relative to univariate red noise. Eigenanalysis of the linear dynamical operator yields propagating eigenmodes that correspond to these peaks but have very short decay times and, thus, limited predictability.

Longer-term predictability does exist, however, due to two stationary eigenmodes that are more weakly damped. These eigenmodes do not strongly correspond to the canonical ENSO and PDO patterns. Instead, one is similar to the 1900–2002 trend and might represent anthropogenic effects, while the second represents multidecadal fluctuations of a pattern that potentially represents natural decadal variability; however, neither attribution can be made unambiguously with the analysis presented in this paper. Predictability of these two stationary eigenmodes is significantly enhanced by tropical–North Pacific coupling. Neither stationary eigenmode is well captured in the control run of any coupled GCM in the CMIP-3 project of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), perhaps because in all of the GCMs tropical SST decadal variability is too weak and North Pacific SSTs are too independent of the Tropics.

A key implication of this analysis is that the PDO may represent not a single physical mode but rather the sum of several phenomena, each of which represents a different red noise with its own autocorrelation time scale and spatial pattern. The sum of these red noises can give rise to apparent PDO “regime shifts” and seeming characteristics of a long memory process. Such shifts are not predictable beyond the time scale of the most rapidly decorrelating noise, less than two years, although the expected duration of regimes may be determined from the relative amplitudes of different eigenmodes.

Abstract

The suitability of a linear inverse model (LIM) as a benchmark for decadal surface temperature forecast skill is demonstrated. Constructed from the observed simultaneous and 1-yr lag covariability statistics of annually averaged sea surface temperature (SST) and surface (2 m) land temperature global anomalies during 1901–2009, the LIM has hindcast skill for leads of 2–5 yr and 6–9 yr comparable to and sometimes even better than skill of the phase 5 of the Coupled Model Intercomparison Project (CMIP5) model hindcasts initialized annually over the period 1960–2000 and has skill far better than damped persistence (e.g., a local univariate AR1 process). Over the entire post-1901 record, the LIM skill pattern is similar but has reduced amplitude. Pronounced similarity in geographical variations of skill between LIM and CMIP5 hindcasts suggests similarity in their sources of skill as well, supporting additional evaluation of LIM predictability. For forecast leads above 1–2 yr, LIM skill almost entirely results from three nonorthogonal patterns: one corresponding to the secular trend and two more, each with about 10-yr decorrelation time scales but no trend, that represent most of the predictable portions of the Atlantic multidecadal oscillation (AMO) and Pacific decadal oscillation (PDO) indices, respectively. As found in previous studies, the AMO-related pattern also contributes to multidecadal variations in global mean temperature, and the PDO-related pattern has maximum amplitude in the west Pacific and represents the residual after both interannual and decadal ENSO variability are removed from the PDO time series. These results suggest that current coupled model decadal forecasts may not yet have much skill beyond that captured by multivariate, predictably linear dynamics.

Abstract

The basic effect of extratropical atmosphere–ocean thermal coupling is to enhance the variance of both anomalous sea surface temperatures (SSTs) and air temperatures (AIRT) due to a decreased energy flux between the atmosphere and ocean, called reduced thermal damping. In this paper it is shown that rapidly varying surface winds, through their influence upon the turbulent surface heat fluxes that drive this coupling, act to effectively weaken the coupling and thus partially counteract the reduced thermal damping. In effect, rapid fluctuations in wind speed somewhat insulate the atmosphere and ocean from each other.

The nonlinear relationship between the rapidly varying wind speed anomalies and SST and AIRT anomalies results in a rapidly varying component of the surface heat fluxes. The clear separation between the dynamical time scales of the ocean and atmosphere allows this rapidly varying flux to be simply approximated by a stochastic process in which rapidly varying wind speed is represented as Gaussian white noise whose amplitude is modulated by the more slowly evolving thermal anomalies. Such state-dependent (multiplicative) noise can alter the dynamics of atmosphere–ocean coupling because it induces an additional heat flux term, the noise-induced drift, that effectively acts to weaken both coupling and dissipation. Another key implication of the outlined theory is that air–sea coupling includes both deterministic and stochastic components.

The theory is tested by examining daily observations during extended winter (November–April) at several ocean weather stations (OWSs). Two important results are found. First, multiplicative noise at OWS P effectively decreases the coupling by about one-third, with about a 10% (20%) decrease in the damping of SST (AIRT). This suggests that multiplicative noise may be responsible for roughly half of the AIRT variability at OWS P on subseasonal time scales. Second, OWS observations reveal that joint probability distribution functions of daily averaged SST and AIRT anomalies are significantly non-Gaussian. It is shown that treating the rapidly varying boundary layer heat fluxes as state-dependent noise can reproduce this observed non-Gaussianity. It is concluded that the effect of state-dependent noise is crucial to understand and model atmosphere–ocean coupling.

Abstract

The upper-tropospheric circulation is investigated for the three months of April, May, and June 1988 during which the Great Plains region of the United States experienced one of its most severe droughts in history. It is found that during this period the April–June (AMJ) seasonal-mean anomaly was not representative of the variability of 10-day low-pass anomalies. Rather, over North America large fluctuations on monthly and shorter timescales occurred, with the dominant streamfunction anomalies not strongly anticyclonic until June. In fact, the AMJ anomaly was dominated by two episodes of rapidly developing, intense anomalous anticyclones in early and late June.

Examination of the daily 10-day low-pass streamfunction anomalies at 300 mb suggests that propagating Rossby waves originating in the west Pacific played a dominant role in the initiation of these intense anomalous anticyclones. Numerical experiments with a linear, time-dependent, barotropic model also support this hypothesis. These results suggest that the AMJ anomaly, which has been characterized as a wave train seemingly forced in the east Pacific, may not provide a useful picture of the circulation associated with the drought. Instead, the drought may be better studied not as a single seasonal event, but rather as a succession of events that together produced a serious hydrological deficit.

Abstract

The impact of the climatological seasonally varying 300-mb flow on the North Pacific/North American response to remote anomalous forcing is considered in the context of a linear barotropic model. WKB theory suggests that the total wavenumber of stationary Rossby waves over the Pacific increases from about 7 in January to 8.5 by June, with the reverse occurring during fall. This change is accompanied by monthly changes in the location and shape of the Rossby waveguide itself. Using a diagnostic tool called the influence function, it is shown that the most sensitive area of forcing for producing a large response over the United States shifts from the east Pacific in late winter to the west Pacific by late spring. As spring progresses, there is also a marked increase in the sensitivity to smaller-scale forcing in both of these regions, particularly the west Pacific. The amplitude of the forced response can potentially be larger in June than any other month of the year. These results suggest that the evolution of extreme springtime weather events over North America may depend critically upon the precise timing and geographical structure of forcing anomalies over both the east and the west Pacific.

In this model, low-frequency variability within and downstream of the Rossby waveguide is sensitive to the annual cycle of the ambient flow. This suggests that the impact of the annual cycle must be taken into account in any complete theory of low-frequency variability. The impact is large enough to raise the possibility of significant interactions across timescales. In other words, it is possible for a steady forcing to produce an unsteady response and, equally, for an unsteady forcing to produce a seasonal-mean response. In such situations, particularly during the northern spring and fall seasons, investigating low-frequency anomalies as departures from three-month seasonal climatologies may lead to confusion and may not be useful.

Abstract

The relative impacts of tropical diabatic heating and stratospheric circulation anomalies on wintertime extratropical tropospheric variability are investigated in a linear inverse model (LIM) derived from the observed zero lag and 5-day lag covariances of 7-day running mean departures from the annual cycle. The model predicts the covariances at all other lags. The predicted and observed lag covariances are generally found to be in excellent agreement, even at the much longer lag of 21 days. This validates the LIM’s basic premise that the dynamics of weekly averages are effectively linear and stochastically driven, which justifies further linear diagnosis of the system.

Analysis of interactions among the LIM’s variables shows that tropical diabatic heating greatly enhances persistent variability over most of the Northern Hemisphere, especially over the Pacific Ocean and North America. Stratospheric effects are largely confined to the polar region, where they ensure that the dominant pattern of sea level pressure variability is the annular Arctic Oscillation rather than the more localized North Atlantic Oscillation. Over the North Atlantic, both effects are important, although some of the stratospheric influence is ultimately traceable to tropical forcing. In general, the tropically forced anomalies extend through the depth of the troposphere and into the stratosphere, whereas stratospherically generated anomalies tend to be largest at the surface and relatively weak at midtropospheric levels. Some persistent variability is, however, found even in the absence of these “external” forcings, especially near the amplitude maxima of the leading eigenmodes of the internal extratropical tropospheric evolution operator. One of these eigenmodes has a circumglobal zonal wavenumber-5 structure with maxima over the Arabian Sea and the central Pacific, and two others are associated with north–south dipole variations across the North Atlantic jet. Overall, tropical influences are generally found to be larger than stratospheric influences on extratropical tropospheric variability and have a pronounced impact on the persistent, and therefore the potentially predictable, portion of that variability.

Abstract

An assessment is made of the ability of the singular value decomposition (SYD) technique to recover the relationship between two variables x and y from a time series of their observations. It is shown that SVD is rigorously successful only in the special cases when either (i) the transformation linking x and y is orthogonal or (ii) the covariance matrix of either x or y is the identity matrix. The behavior of the method when theSE conditions are not met is also studied in a simple two-dimensional case.

That this caveat can be relevant in a meteorological context is demonstrated by performing an SVD analysis of a time series of global upper-tropospheric streamfunction and vorticity fields. Although these fields are linked by the two-dimensional Laplacian operator on the sphere, it is shown that the pairs of singular patterns resulting from the SVD analysis are not so related. The problem is apparent even for the first SVD pair and generally becomes worse for succeeding pairs These results suggest that any physical interpretation of SVD pairs may be unjustified.

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 anomalies of the 300-mb flow in the northern winters of 1985–93.

When used in the backward sense described above, the FDR yields a forcing covariance matrix that is not quite positive definite. This immediately implies that the low-frequency variability cannot be rigorously viewed as a linear barotropic response to white noise forcing. Nonetheless, retaining only the positive definite part of the forcing matrix and using the forward FDR gives a reasonable approximation to the observed vorticity covariance. The approximation can be improved by specifying a stronger drag in the barotropic model. However, the simulation of the 5-day lag covariance of vorticity, which is poor using the 5-day drag, is made worse with the stronger drag. In other words this model cannot correctly simulate the time development of low-frequency variability. Thus extratropical low-frequency variability cannot be understood as a linear barotropic response to geographically coherent white noise forcing.

A slightly red stochastic forcing, with a decorrelation timescale of 1–2 days, produces only a modest improvement in the 5-day lag results. A very red forcing, with a decorrelation timescale of 20 days, gives better results at 0- and 5-day lags, but not at 10- or 20-day lags. Modeling the forcing separately as a first-order Markov process, with the model parameters estimated from observations, gives almost perfect results at 0- and 5-day lags. However, further analysis shows this to be an artifact of comparing the empirical–dynamical model simulations with dependent data. When the noise model parameters estimated from one-half of the data record are used to explain low-frequency variability in the other, the results are again poor. It is concluded that extratropical low-frequency variability cannot be viewed as randomly forced barotropic Rossby waves evolving on a zonally and meridionally varying climatological 300-mb flow. The spatial and temporal structure of the observed variability cannot be explained without also taking into account the detailed spatial and temporal structure of the forcing, respectively.

Abstract

The observed profile of heating through the troposphere in the Madden–Julian oscillation (MJO) is found to be very top heavy: more so than seasonal-mean heating and systematically more so than all of the seven models for which intraseasonal heating anomaly profiles have been published. Consistently, the Tropical Rainfall Measuring Mission (TRMM) precipitation radar shows that stratiform precipitation (known to heat the upper troposphere and cool the lower troposphere) contributes more to intraseasonal rainfall variations than it does to seasonal-mean rainfall. Stratiform rainfall anomalies lag convective rainfall anomalies by a few days. Reasons for this lag apparently include increased wind shear and middle–upper tropospheric humidity, which also lag convective (and total) rainfall by a few days.

A distinct rearward tilt is seen in anomalous heating time–height sections, in both the strong December 1992 MJO event observed by the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE) and a composite MJO constructed from multiyear datasets. Interpretation is aided by a formal partitioning of the COARE heating section into convective, stratiform, and radiative components. The tilted structure after the maximum surface rainfall appears to be largely contributed by latent and radiative heating in enhanced stratiform anvils. However, the tilt of anomalous heating ahead of maximum rainfall is seen within the convective component, suggesting a change from shallower to deeper convective heating as the wet phase of the MJO approached the longitude of the observations.

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 averaged 750-hPa streamfunction data for the past 52 winters. A closer examination of the Fokker–Planck probability budget in the plane spanned by these two PCs shows that the observed deviations from Gaussianity can be modeled with multiplicative noise, and are unlikely the results of slow nonlinear interactions of the two PCs. It is concluded that the observed non-Gaussian probability distributions do not necessarily imply the existence of persistent nonlinear circulation regimes, and are consistent with those expected for a linear system perturbed by multiplicative noise.