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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 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 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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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 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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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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Carsten Abraham
and
Adam H. Monahan

Abstract

The evolution of profiles of meteorological state variables during nights with and without transitions in the nocturnal stably stratified boundary layer (SBL) between weakly stable (wSBL) and very stable (vSBL) regimes, as classified by a hidden Markov model, is examined at nine different tower sites. During wSBL-to-vSBL transitions, inversion strengths increase, near-surface winds decelerate, and atmospheric layers vertically decouple. Turbulence kinetic energy (TKE) steadily decreases before wSBL-to-vSBL transitions and fluctuations of the vertical velocity become weak. In contrast to land-based sites where wSBL-to-vSBL transitions are normally caused by surface cooling, at sea-based stations the transitions generally are initiated by advection of warm air aloft. The vSBL-to-wSBL transition is characterized by a fast breakdown of the inversion strength, acceleration of wind profiles, and a restored vertical coupling of the atmospheric flow. TKE recovers on time scales of minutes first in atmospheric levels between 50 and 100 m. Profiles of state variables for the two different regimes during very persistent nights (nights without SBL regime transitions) are clearly separated and similar to structures during nights with transitions away from transition times. During very persistent nights the wind conditions stay relatively steady. Similarly, the temperature is steady after an initial adjustment time at sunset (wSBL) or shortly after sunset (vSBL). Even though nights with and without transitions are a common feature of the SBL, there is no clear indicator in Reynolds-averaged mean variables that distinguishes very persistent nights from nights with transitions.

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Cangjie Sun
and
Adam H. Monahan

Abstract

The statistical prediction of local sea surface winds from large-scale, free-tropospheric fields is investigated at a number of locations over the global ocean using a statistical downscaling model based on multiple linear regression. The predictands (the mean and standard deviation of both vector wind components and wind speed) calculated from ocean buoy observations on daily, weekly, and monthly scales are regressed on upper-level predictor fields from reanalysis products. It is found that in general the mean vector wind components are more predictable than mean wind speed in the North Pacific and Atlantic, while in the tropical Pacific and Atlantic the difference in predictive skill between mean vector wind components and wind speed is not substantial. The predictability of wind speed relative to vector wind components is interpreted by an idealized model of the wind speed probability density function, which indicates that in the midlatitudes the mean wind speed is more sensitive to the vector wind standard deviations (which generally are not well predicted) than to the mean vector winds. In the tropics, the mean wind speed is found to be more sensitive to the mean vector winds. While the idealized probability model does a good job of characterizing month-to-month variations in the mean wind speed in terms of the vector wind statistics, month-to-month variations in the standard deviation of speed are not well modeled. A series of Monte Carlo experiments demonstrates that the inconsistency in the characterization of wind speed standard deviation is the result of differences of sampling variability between the vector wind and wind speed statistics.

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Carsten Abraham
and
Adam H. Monahan

Abstract

In a companion paper hidden Markov model (HMM) analyses have been conducted to classify the nocturnal stably stratified boundary layer (SBL) into weakly stable (wSBL) and very stable (vSBL) conditions at different tower sites on the basis of long-term Reynolds-averaged mean data. The resulting HMM regime sequences allow analysis of long-term (climatological) SBL regime statistics. In particular, statistical features of very persistent wSBL and vSBL nights, in which a single regime lasts for the entire night, are contrasted with those of nights with SBL regime transitions. The occurrence of very persistent nights is seasonally dependent and more likely in homogeneous surroundings than in regions with complex terrain. When transitions occur, their timing is not seasonally dependent, but transitions are enhanced close to sunset (for land-based sites). The regime event durations depict remarkably similar distributions across all stations with peaks in transition likelihood approximately 1–2 h after a preceding transition. At Cabauw in the Netherlands, very persistent wSBL and vSBL nights are usually accompanied by overcast conditions with strong geostrophic winds U geo or clear-sky conditions with weak U geo, respectively. In contrast, SBL regime transitions can neither be linked to magnitudes in U geo and cloud coverage nor to specific tendencies in U geo. However, regime transitions can be initiated by changes in low-level cloud cover.

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Elizabeth Ramsey
and
Adam H. Monahan

Abstract

The atmospheric stable boundary layer (SBL) is observed to display multiple regimes of stratification, flow, and turbulence. Transitions between weakly stable regimes of sustained turbulence and very stable regimes of weak turbulence are observed to occur abruptly. The understanding and predictability of turbulent recovery remains limited, reducing the accuracy of numerical weather prediction and climate projections. Idealized SBL models have related regimes to dynamically stable equilibria. Under conditions of weak energetic surface coupling, two stable branches separated by an unstable branch are predicted by these models. Such bifurcation structures are associated with rapid transitions. This work investigates the extent to which observed temperature inversion variability can be described by an empirical one-dimensional stochastic differential equation (SDE). The drift and diffusion coefficients of the SDE of observed inversion strength are approximated from statistics of their averaged time tendencies, conditioned on wind speed. Functional forms of the state dependence of these coefficients are estimated using Gaussian process regression. Probabilistic estimates of the system’s deterministic equilibria are found and used to create empirical bifurcation diagrams of inversion strength as a function of wind speed. These data-driven bifurcation structures are first obtained from idealized model simulations, then repeated for observations from several meteorological towers. It is found that the effective low-dimensional dynamics of observed temperature inversions is similar to that of the idealized model. Evidence of multiple equilibria and hysteresis is found at a single site, Dome C, Antarctica, but is not robust to variations in the analysis. Evidence of state-dependent noise consistent with intermittent turbulence under very stably stratified conditions is presented.

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