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Adam H. Monahan

Abstract

A nonlinear generalization of principal component analysis (PCA), denoted nonlinear principal component analysis (NLPCA), is implemented in a variational framework using a five-layer autoassociative feed-forward neural network. The method is tested on a dataset sampled from the Lorenz attractor, and it is shown that the NLPCA approximations to the attractor in one and two dimensions, explaining 76% and 99.5% of the variance, respectively, are superior to the corresponding PCA approximations, which respectively explain 60% (mode 1) and 95% (modes 1 and 2) of the variance. It is found that as noise is added to the Lorenz attractor, the NLPCA approximations remain superior to the PCA approximations until the noise level is so great that the lower-dimensional nonlinear structure of the data is no longer manifest to the eye. Finally, directions for future work are presented, and a cinematographic technique to visualize the results of NLPCA is discussed.

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Adam H. Monahan

Abstract

The statistical predictability of wintertime (December–February) monthly-mean sea surface winds (both vector wind components and wind speed) in the subarctic northeast Pacific off the west coast of Canada is considered, in the context of surface wind downscaling. Predictor fields (zonal wind, meridional wind, wind speed, and temperature) are shown to carry predictive information on the large scales (both vertical and horizontal) that are well simulated by numerical weather prediction and global climate models. It is found that, in general, the monthly mean vector wind components are more predictable by indices of the large-scale flow than by the monthly mean wind speed, with no systematic vertical variation in predictive skill for either across the depth of the troposphere. The difference in predictive skill between monthly-mean vector wind components and wind speed is interpreted in terms of an idealized model of the vector wind speed probability distribution, which demonstrates that for the conditions in the subarctic northeast Pacific, the sensitivity of mean wind speed to the standard deviations of vector wind component fluctuations (which are not well predicted) is greater than that to the mean vector wind components. It is demonstrated that this sensitivity is state dependent, and it is suggested that monthly mean wind speeds may be inherently more predictable in regions where the sensitivity to the vector wind component means is greater than that to the standard deviations. It is also demonstrated that daily wind fluctuations (both vector wind and wind speed) are generally more predictable than monthly-mean variability, and that monthly averages of the predicted daily winds generally represent the monthly-mean surface winds better than the predictions directly from monthly mean predictors.

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Adam H. Monahan

Abstract

The statistical predictability of wind speed using Gaussian predictors, relative to the predictability of orthogonal vector wind components, is considered. With the assumption that the vector wind components are Gaussian, analytic expressions for the correlation-based wind speed prediction skill are obtained in terms of the prediction skills of the vector wind components and their statistical moments. It is shown that

  • at least one of the vector wind components is generally better predicted than the wind speed (often much more so);

  • wind speed predictions constructed from the predictions of vector wind components are more skillful than direct wind speed predictions; and

  • the linear predictability of wind speed (relative to that of the vector wind components) decreases as the variability in the vector wind increases relative to the mean.

These idealized model results are shown to be broadly consistent with linear predictive skills assessed using observed sea surface wind from the SeaWinds scatterometer. Biases in the model predictions are shown to be related to the degree to which vector wind variations are non-Gaussian.

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Adam H. Monahan

Abstract

The temporal autocorrelation structures of sea surface vector winds and wind speeds are considered. Analyses of scatterometer and reanalysis wind data demonstrate that the autocorrelation functions (acf) of surface zonal wind, meridional wind, and wind speed generally drop off more rapidly in the midlatitudes than in the low latitudes. Furthermore, the meridional wind component and wind speed generally decorrelate more rapidly than the zonal wind component. The anisotropy in vector wind decorrelation scales is demonstrated to be most pronounced in the storm tracks and near the equator, and to be a feature of winds throughout the depth of the troposphere. The extratropical anisotropy is interpreted in terms of an idealized kinematic eddy model as resulting from differences in the structure of wind anomalies in the directions along and across eddy paths. The tropical anisotropy is interpreted in terms of the kinematics of large-scale equatorial waves and small-scale convection. Modeling the vector wind fluctuations as Gaussian, an explicit expression for the wind speed acf is obtained. This model predicts that the wind speed acf should decay more rapidly than that of at least one component of the vector winds. Furthermore, the model predicts a strong dependence of the wind speed acf on the ratios of the means of vector wind components to their standard deviations. These model results are shown to be broadly consistent with the relationship between the acf of vector wind components and wind speed, despite the presence of non-Gaussian structure in the observed surface vector winds.

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Adam H. Monahan

Abstract

The component of the sea surface wind in the along-mean wind direction is known to display pronounced skewness at many locations over the ocean. A recent study by Proistosescu et al. found that the skewness of daily 850-hPa air temperature measured by radiosondes is typically reduced by bandpass filtering. This behavior was also shown to be characteristic of correlated additive–multiplicative (CAM) noise, which has been proposed as a generic model for non-Gaussian variability in the atmosphere and ocean. The present study shows that if the cutoff frequency is not too low, the skewness of the along-mean wind component is enhanced by low-pass filtering, particularly in the equatorial band and in the midlatitude storm tracks. The filter time scale beyond which skewness is systematically reduced by filtering is of the daily to synoptic scale, except in a narrow equatorial band where it is of subseasonal to seasonal time scales. This behavior is reproduced in an idealized stochastic model of the near-surface winds, in which key parameters are the characteristic time scales of the nonlinear dynamics and of the noise. These results point toward more general approaches for assessing the relative importance of multiplicative noise or dynamical nonlinearities in producing non-Gaussian structure in atmospheric and oceanic fields.

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Julie Alexander
and
Adam H. Monahan

Abstract

Generalized linear stability theory is used to calculate the optimal initial conditions that result in transient amplification of the thermohaline circulation (THC) in a zonally averaged single-basin ocean model. The eigenmodes of the tangent linear model verify that the system is asymptotically stable, but the nonnormality of the system permits the growth of perturbations for a finite period through the interference of nonorthogonal eigenmodes. It is found that the maximum amplification of the THC anomalies occurs after 6 yr with both the thermally and salinity-driven components playing major roles in the amplification process. The transient amplification of THC anomalies is due to the constructive and destructive interference of a large number of eigenmodes, and the evolution over time is determined by how the interference pattern evolves. It is found that five of the most highly nonnormal eigenmodes are critical to the initial cancellation of the salinity and temperature contributions to the THC, while 11 oscillating modes with decay time scales ranging from 2 to 6 yr are the major contributors at the time of maximum amplification. This analysis demonstrates that the different dynamics of salinity and temperature anomalies allow the dramatic growth of perturbations to the THC on relatively short (interannual to decadal) time scales.

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Adam H. Monahan
and
John C. Fyfe

Abstract

Dipolar structures arise as empirical orthogonal functions (EOFs) of extratropical tropospheric zonal-mean zonal wind in observations, in idealized dynamical models, and in complex general circulation models. This study characterizes the conditions under which dipoles emerge as EOFs of a jet of fixed shape f (x), which takes a unique localized extremum and is smooth but is otherwise arbitrary, characterized by fluctuations in strength, position, and width of arbitrary distribution. It is shown that the factors that influence the extent to which a dipolelike structure will arise as an EOF are (i) the skewness of position fluctuations, (ii) the dependence of position fluctuations on strength and width fluctuations, and (iii) the relative strength of the position and width fluctuations. In particular, the leading EOF will be a dipole if jet position fluctuations are not strongly skewed, not strongly dependent on strength and width fluctuations, and sufficiently large relative to strength and width fluctuations. Because these conditions are generally satisfied to a good approximation by observed and simulated tropospheric eddy-driven jets, this analysis provides a simple explanation of the ubiquity of dipolar jet EOFs.

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Adam H. Monahan
and
John C. Fyfe

Abstract

This study considers the relation of the annular mode to the kinematics of a fluctuating jet in zonal-mean zonal wind and to the zonal index, using an idealized model of fluctuations in the eddy-driven jet. When the sphericity of the domain is accounted for, observed and numerically simulated annular modes for the Southern Hemisphere summertime are found to be in excellent agreement. In particular, the annular mode and zonal index mode are shown to be related but distinct. Although the annular mode is strongly (but not identically) related to fluctuations in jet position, fluctuations in jet strength and width are shown to also be important for its simulation. When the sphericity of the domain is neglected, analytic expressions for the leading empirical orthogonal function (EOF) modes of zonal-mean geopotential for the cases of individual fluctuations in jet strength, position, and width can be obtained. None of these EOF modes have the characteristics of the annular mode. In the presence of simultaneous fluctuations in jet strength and position, the leading zonal-mean geopotential EOF mode (strongly resembling the annular mode) is shown to mix the zonal index mode of zonal-mean zonal wind with other EOF modes, demonstrating why the annular mode and zonal index mode are related but distinct. The greater sensitivity to domain size of EOF modes of geopotential relative to the EOF modes of zonal-mean zonal wind is also discussed. This study focuses on the Southern Hemisphere summertime, which is characterized by a single, eddy-driven jet; the generality of the results presented suggest that the conclusions should be qualitatively unchanged in the presence of both subtropical and eddy-driven jets.

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Adam H. Monahan
and
John C. Fyfe

Abstract

Analytic results are obtained for the mean and covariance structure of an idealized zonal jet that fluctuates in strength, position, and width. Through a systematic perturbation analysis, the leading empirical orthogonal functions (EOFs) and principal component (PC) time series are obtained. These EOFs are built of linear combinations of basic patterns corresponding to monopole, dipole, and tripole structures. The analytic results demonstrate that in general the individual EOF modes cannot be interpreted in terms of individual physical processes. In particular, while the dipole EOF (similar to the leading EOF of the midlatitude zonal mean zonal wind) describes fluctuations in jet position to leading order, its time series also contains contributions from fluctuations in strength and width. No simple interpretations of the other EOFs in terms of strength, position, or width fluctuations are possible. Implications of these results for the use of EOF analysis to diagnose physical processes of variability are discussed.

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