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Brian J. Hoskins
and
Prashant D. Sardeshmukh

Abstract

Virtually all investigations of transient-eddy effects on the large-scale mean vorticity start from the premise that only the rotational transient motion need be considered. In this paper, the seasonal mean vorticity balance at 250 mb is examined, with particular emphasis on those transient term that are associated with the horizontally divergent transient motion. The largest transient terms are, in fact, found to be the advection of vorticity by the divergent flow and the stretching term. These am only a factor of 2 smaller than the mean flow terms. However, these transient term have a strong mutual cancellation. Their residual, the convergence of the vorticity flux associated with the divergent motion, although much smaller, is comparable on the planetary scale with the similar term associated with the rotational motion. These properties are interpreted using simple models. It is concluded that a representation of the vorticity flux by the transient divergent flow may be necessary in an accurate parameterization of transient eddies in global-scale climate models, and that any analysis of transient effects must include the divergent motions in a consistent manner.

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Prashant D. Sardeshmukh
and
Philip Sura

Abstract

While it is obvious that the mean diabatic forcing of the atmosphere is crucial for maintaining the mean climate, the importance of diabatic forcing fluctuations is less evident in this regard. Such fluctuations do not appear directly in the equations of the mean climate but affect the mean indirectly through their effects on the time-mean transient-eddy fluxes of heat, momentum, and moisture. How large are these effects? What are the effects of tropical phenomena associated with substantial heating variations such as ENSO and the MJO? To what extent do variations of the extratropical surface heat fluxes and precipitation affect the mean climate? What are the effects of the rapid “stochastic” components of the heating fluctuations? Most current climate models misrepresent ENSO and the MJO and ignore stochastic forcing; they therefore also misrepresent their mean effects. To what extent does this contribute to climate model biases and to projections of climate change?

This paper provides an assessment of such impacts by comparing with observations a long simulation of the northern winter climate by a dry adiabatic general circulation model forced only with the observed time-mean diabatic forcing as a constant forcing. Remarkably, despite the total neglect of all forcing variations, the model reproduces most features of the observed circulation variability and the mean climate, with biases similar to those of some state-of-the-art general circulation models. In particular, the spatial structures of the circulation variability are remarkably well reproduced. Their amplitudes, however, are progressively underestimated from the synoptic to the subseasonal to interannual and longer time scales. This underestimation is attributed to the neglect of the variable forcing. The model also excites significant tropical variability from the extratropics on interannual scales, which is overwhelmed in reality by the response to tropical heating variability. It is argued that the results of this study suggest a role for the stochastic, and not only the coherent, components of transient diabatic forcing in the dynamics of climate variability and the mean climate.

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Prashant D. Sardeshmukh
and
Philip Sura

Abstract

Linear stochastically forced models have been found to be competitive with comprehensive nonlinear weather and climate models at representing many features of the observed covariance statistics and at predictions beyond a week. Their success seems at odds with the fact that the observed statistics can be significantly non-Gaussian, which is often attributed to nonlinear dynamics. The stochastic noise in the linear models can be a mixture of state-independent (“additive”) and linearly state-dependent (“multiplicative”) Gaussian white noises. It is shown here that such mixtures can produce not only symmetric but also skewed non-Gaussian probability distributions if the additive and multiplicative noises are correlated. Such correlations are readily anticipated from first principles. A generic stochastically generated skewed (SGS) distribution can be analytically derived from the Fokker–Planck equation for a single-component system. In addition to skew, all such SGS distributions have power-law tails, as well as a striking property that the (excess) kurtosis K is always greater than 1.5 times the square of the skew S. Remarkably, this KS inequality is found to be satisfied by circulation variables even in the observed multicomponent climate system. A principle of “diagonal dominance” in the multicomponent moment equations is introduced to understand this behavior.

To clarify the nature of the stochastic noises (turbulent adiabatic versus diabatic fluctuations) responsible for the observed non-Gaussian statistics, a long 1200-winter simulation of the northern winter climate is generated using a dry adiabatic atmospheric general circulation model forced only with the observed long-term winter-mean diabatic forcing as a constant forcing. Despite the complete neglect of diabatic variations, the model reproduces the observed KS relationships and also the spatial patterns of the skew and kurtosis of the daily tropospheric circulation anomalies. This suggests that the stochastic generators of these higher moments are mostly associated with local adiabatic turbulent fluxes. The model also simulates fifth moments that are approximately 10 times the skew, and probability densities with power-law tails, as predicted by the linear theory.

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Matthew Newman
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Prashant D. Sardeshmukh

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.

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Prashant D. Sardeshmukh
and
Brant Liebmann

Abstract

Any discussion of intraseasonal and interannual variability in the atmosphere must presume a reliable assessment of the observed variability. In spite of continued improvements in observing systems, quality control techniques, and data analysis schemes, however, and also because of them, this assessment remains difficult in the tropics.

In this paper the authors examine the mean tropical circulation during two Januarys, 1988 and 1989, as described by the circulation analyses produced at two weather prediction centers, the National Meteorological Center (NMC) in Washington, D.C., and the European Center for Medium-Range Weather Forecast (ECMWF) in Reading, England. In particular, the authors’ focus is on the change in the circulation between 1988 and 1989 as estimated by these two sets of analyses, especially the change in the 200-mb wind divergence associated with organized deep convection. The authors find that in many regions the discrepancy between thew estimates is of the order of the change itself. A comparison with maps of the outgoing longwave radiation (OLR) is not quantitatively useful in this regard.

One way out of this dilemma is to derive divergence fields that are consistent with the 200-mb vorticity balance. The authors do so by solving the “chi problem” of Sardeshmukh and Hoskins. Because the large-scale vorticity fields generated by NMC and ECMWF are highly correlated (∼98%), the divergence fields derived in this manner are also better correlated than the analyzed fields and enable a more reliable assessment of the observed change between these two periods.

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Cécile Penland
and
Prashant D. Sardeshmukh

Abstract

The first-order perturbation technique is reviewed as a tool for investigating the error and sensitivity of results obtained from the eigenanalysis of geophysical systems. Expressions are provided for the change in a system's eigenfunctions (e.g., normal modes) and their periods and growth rates associated with a small change δL in the system matrix L. In the context of data analysis, these expressions can be used to estimate changes or uncertainties in the eigenstructure of matrices involving the system's covariance statistics. Their application is illustrated in the problems of 1) updating a subset of the empirical orthogonal functions and their eigenvalues when more data become available, 2) estimating uncertainties in the growth rate and spatial structure of the singular vectors of a linear dynamical system, and 3) estimating uncertainties in the period, growth rate, and spatial structure of the normal modes of a linear dynamical system. The linear system considered in examples 2 and 3 is an empirical stochastic-dynamic model of tropical sea surface temperature (SST) evolution derived from 35 years of SST observations in the tropical Indo-Pacific basin. Thus, the system matrix L is empirically derived. Estimates of the uncertainty in L, required for estimating the uncertainties in the singular vectors and normal modes, are obtained from a long Monte Carlo simulation. The analysis suggests that the singular vectors, which represent optimal initial structures for SST anomaly growth, am more reliably determined from the 35 years of observed data than are the individual normal modes of the system.

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Cécile Penland
and
Prashant D. Sardeshmukh

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 Niño–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 empirical stochastic-dynamical model show that stochastic forcing not only adds energy to the system, but also plays a role in setting up the optimal structure.

It is shown that growth from modal interference can occur for as long as 18 months, which within the confines of this model defines a predictability limit for growth events. Growth associated with the stochastic forcing is also possible, but is unpredictable. The timescale on which the predictable and unpredictable components of SST growth become comparable to each other gives a more conservative predictability limit of 15 months.

The above scenario is based on empirical evidence obtained from SST anomalies alone. From the results of several tests based on statistical properties of linear and nonlinear dynamical systems, one may conclude that much of the ENSO cycle in nature is dominated by stable, forced dynamics.

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Gilbert P. Compo
and
Prashant D. Sardeshmukh
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Gilbert P. Compo
and
Prashant D. Sardeshmukh

Abstract

An important question in assessing twentieth-century climate change is to what extent have ENSO-related variations contributed to the observed trends. Isolating such contributions is challenging for several reasons, including ambiguities arising from how ENSO itself is defined. In particular, defining ENSO in terms of a single index and ENSO-related variations in terms of regressions on that index, as done in many previous studies, can lead to wrong conclusions. This paper argues that ENSO is best viewed not as a number but as an evolving dynamical process for this purpose. Specifically, ENSO is identified with the four dynamical eigenvectors of tropical SST evolution that are most important in the observed evolution of ENSO events. This definition is used to isolate the ENSO-related component of global SST variations on a month-by-month basis in the 136-yr (1871–2006) Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST). The analysis shows that previously identified multidecadal variations in the Pacific, Indian, and Atlantic Oceans all have substantial ENSO components. The long-term warming trends over these oceans are also found to have appreciable ENSO components, in some instances up to 40% of the total trend. The ENSO-unrelated component of 5-yr average SST variations, obtained by removing the ENSO-related component, is interpreted as a combination of anthropogenic, naturally forced, and internally generated coherent multidecadal variations. The following two surprising aspects of these ENSO-unrelated variations are emphasized: 1) a strong cooling trend in the eastern equatorial Pacific Ocean and 2) a nearly zonally symmetric multidecadal tropical–extratropical seesaw that has amplified in recent decades. The latter has played a major role in modulating SSTs over the Indian Ocean.

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Joseph J. Barsugli
and
Prashant D. Sardeshmukh

Abstract

The sensitivity of the global atmospheric response to sea surface temperature (SST) anomalies throughout the tropical Indian and Pacific Ocean basins is investigated using the NCEP MRF9 general circulation model (GCM). Model responses in January are first determined for a uniform array of 42 localized SST anomaly patches over the domain. Results from the individual forcing experiments are then linearly combined using a statistically based smoothing procedure to produce sensitivity maps for many target quantities of interest, including the geopotential height response over the Pacific–North American (PNA) region and regional precipitation responses over North America, South America, Africa, Australia, and Indonesia.

Perhaps the most striking result from this analysis is that many important targets for seasonal forecasting, including the PNA response, are most sensitive to SST anomalies in the Niño-4 region (5°N–5°S, 150°W–160°E) of the central tropical Pacific, with lesser and sometimes opposite sensitivities to SST anomalies in the Niño-3 region (5°N–5°S, 90°–150°W) of the eastern tropical Pacific. However, certain important targets, such as Indonesian rainfall, are most sensitive to SST anomalies outside both the Niño-4 and -3 regions.

These results are also relevant in assessing atmospheric sensitivity to changes in tropical SSTs on decadal to centennial scales associated with natural as well as anthropogenic forcing. In this context it is interesting to note the surprising result that warm SST anomalies in one-third of the Indo-Pacific domain lead to a decrease of global mean precipitation.

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