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William W. Hsieh

Abstract

From vertical normal mode decomposition, sea level and sea surface temperature (SST) are shown to be modally biased—higher modes are suppressed in sea level while lower modes are suppressed in SST data. Having been effectively “low passed” and “high passed” (with respect to mode number) by nature, sea level and SST contain complementary information which can in principle be combined to yield a relatively unbiased picture. The full potential of the sea level-SST pair is not appreciated in present remote sensing studies, where the two are used separately. A proposed “stereoscopic” method may in the future produce unbiased three-dimensional pictures from satellite-sensed two-dimensional pictures of sea level and SST. Modal bias in coastal trapped waves is studied in the Appendix.

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William W. Hsieh

Abstract

The low-frequency current fluctuations on the Oregon shelf changed dramatically from winter to spring, 1975. A much faster offshore energy decay occurred simultaneously with a sharp decrease in the alongshore propagation speed. Cross-shelf analysis in a frequency band around 0.16 cpd showed the emergence of the third-mode shelf wave, in spring from the predominantly first-mode motion in winter. At frequencies <0.1 cpd, the current fluctuations propagated southward in winter, opposite to the direction of shelf waves.

On the Oregon and Washington shelves during summer (and early fall) 1972, the location of moorings on irregular topography rendered data interpretation difficult. Nevertheless, the general cross-shelf and alongshore properties of the current fluctuations were consistent with the first-mode shelf wave, in contrast to the situation during summer 1973 when the second mode was excited.

The excitation of relatively high modes and the generally sharp concentration of energy in one particular mode are surprising and difficult to explain with the present shelf-wave generation theories. Nonlinear resonance between wind and current is proposed as a possible explanation.

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Yuval and William W. Hsieh

Abstract

A novel neural network (NN)–based scheme performs nonlinear model output statistics (MOS) for generating precipitation forecasts from numerical weather prediction (NWP) model output. Data records from the past few weeks are sufficient for establishing an initial MOS connection, which then adapts itself to the ongoing changes and modifications in the NWP model. The technical feasibility of the algorithm is demonstrated in three numerical experiments using the NCEP reanalysis data in the Alaskan panhandle and the coastal region of British Columbia. Its performance is compared with that of a conventional NN-based nonadaptive scheme. When the new adaptive method is employed, the degradation in the precipitation forecast skills due to changes in the NWP model is small and is much less than the degradation in the performance of the conventional nonadaptive scheme.

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William W. Hsieh

Abstract

Given equal amounts of kinetic energy near the coast, different shelf wave modes (at the same frequency) have different magnitudes of sea-level oscillations—the magnitudes decrease with increasing mode number. Hence, an intrinsic bias for the lowest mode is present when using sea-level data for shelf wave detection.

Shelf waves have many modal-dependent structures in their cross-shelf dimension, which can be used to accurately identify the excited modes in the current fluctuations. In addition to rotary spectral analysis, a new technique that involves fitting (at a particular frequency of interest) the theoretical current ellipses of various barotropic shelf wave modes to the observed current ellipses at stations spread across the continental shelf, is introduced. This technique shows how the current energy is distributed among the modes.

These techniques are illustrated using Oregon shelf data from the summer of 1973. The cross-shelf fitting shows that at frequencies below 0.45 cycles day−1, the current fluctuations on the Oregon shelf were completely dominated by the second mode. Furthermore, the observed alongshore phase speed also agreed very closely with the theoretical value for the second mode shelf wave. This is the clearest shelf wave identification achieved to date.

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William W. Hsieh

Abstract

Recent advances in neural network modeling have led to the nonlinear generalization of classical multivariate analysis techniques such as principal component analysis and canonical correlation analysis (CCA). The nonlinear canonical correlation analysis (NLCCA) method is used to study the relationship between the tropical Pacific sea level pressure (SLP) and sea surface temperature (SST) fields. The first mode extracted is a nonlinear El Niño–Southern Oscillation (ENSO) mode, showing the asymmetry between the warm El Niño states and the cool La Niña states. The nonlinearity of the first NLCCA mode is found to increase gradually with time. During 1950–75, the SLP showed no nonlinearity, while the SST revealed weak nonlinearity. During 1976–99, the SLP displayed weak nonlinearity, while the weak nonlinearity in the SST was further enhanced. The second NLCCA mode displays longer timescale fluctuations, again with weak, but noticeable, nonlinearity in the SST but not in the SLP.

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Zhengqing Ye and William W. Hsieh

Abstract

With data from 12 coupled models in the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), climate under year 2000 greenhouse gas (GHG) + aerosol forcing was compared with climate under preindustrial conditions. In the tropical Pacific, the warming in the mean sea surface temperatures (SST) was found to have an El Niño–like pattern, while both the equatorial zonal overturning circulation and the meridional overturning circulation weakened under increased GHG forcing.

For the El Niño–Southern Oscillation (ENSO), the asymmetry in the SST anomalies between El Niño and La Niña was found to be enhanced under increased GHG, for both the ensemble model data and the observed data (1900–99). Enhanced asymmetry between El Niño and La Niña was also manifested in the anomalies of the zonal wind stress, the equatorial undercurrent, and the meridional overturning circulation in the increased GHG simulations. The enhanced asymmetry in the model SST anomalies was mainly caused by the greatly intensified vertical nonlinear dynamic heating (NDH) anomaly (i.e., product of the vertical velocity anomaly and the negative vertical temperature gradient anomaly) during El Niño (but not during La Niña). Under increased GHG, the enhanced positive NDH anomalies during El Niño, when time averaged over the whole record, would change the SST mean state by an El Niño–like pattern.

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William W. Hsieh and Benyang Tang

Empirical or statistical methods have been introduced into meteorology and oceanography in four distinct stages: 1) linear regression (and correlation), 2) principal component analysis (PCA), 3) canonical correlation analysis, and recently 4) neural network (NN) models. Despite the great popularity of the NN models in many fields, there are three obstacles to adapting the NN method to meteorology–oceanography, especially in large-scale, low-frequency studies: (a) nonlinear instability with short data records, (b) large spatial data fields, and (c) difficulties in interpreting the nonlinear NN results. Recent research shows that these three obstacles can be overcome. For obstacle (a), ensemble averaging was found to be effective in controlling nonlinear instability. For (b), the PCA method was used as a prefilter for compressing the large spatial data fields. For (c), the mysterious hidden layer could be given a phase space interpretation, and spectral analysis aided in understanding the nonlinear NN relations. With these and future improvements, the nonlinear NN method is evolving to a versatile and powerful technique capable of augmenting traditional linear statistical methods in data analysis and forecasting; for example, the NN method has been used for El Niño prediction and for nonlinear PCA. The NN model is also found to be a type of variational (adjoint) data assimilation, which allows it to be readily linked to dynamical models under adjoint data assimilation, resulting in a new class of hybrid neural–dynamical models.

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Youmin Tang and William W. Hsieh

Abstract

The advent of the feed-forward neural network (N) model opens the possibility of hybrid neural–dynamical models via variational data assimilation. Such a hybrid model may be used in situations where some variables, difficult to model dynamically, have sufficient data for modeling them empirically with an N. This idea of using an N to replace missing dynamical equations is tested with the Lorenz three-component nonlinear system, where one of the three Lorenz equations is replaced by an N equation. In several experiments, the 4DVAR assimilation approach is used to estimate 1) the N model parameters (26 parameters), 2) two dynamical parameters and three initial conditions for the hybrid model, and 3) the dynamical parameters, initial conditions, and the N parameters (28 parameters plus three initial conditions).

Two cases of the Lorenz model—(i) the weakly nonlinear case of quasiperiodic oscillations, and (ii) the highly nonlinear, chaotic case—were chosen to test the forecast skills of the hybrid model. Numerical experiments showed that for the weakly nonlinear case, the hybrid model can be very successful, with forecast skills similar to the original Lorenz model. For the highly nonlinear case, the hybrid model could produce reasonable predictions for at least one cycle of oscillation for most experiments, although poor results were obtained for some experiments. In these failed experiments, the data used for assimilation were often located on one wing of the Lorenz butterfly-shaped attractor, while the system moved to the second wing during the forecast period. The forecasts failed as the model had never been trained with data from the second wing.

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William W. Hsieh and Lawrence A. Mysak

Abstract

From the inviscid, unforced, barotropic long-wave equations for a rotating system, it is shown that resonant interactions between three continental shelf waves can occur. Evolution equations governing the amplitude and the energy of individual waves in a resonant triad are derived. The nonlinearity in the governing equations allows energy to be transferred between the waves, but with the total energy conserved. While the shelf waves typically have periods of several days, the energy transfer has a time scale of order 12 days. Observational evidence of resonant shelf wave interactions on the Oregon shelf is found in the spectral analyses of Cutchin and Smith (1973) and Huyer et al. (1975), where their observed signals agree well with the resonant frequencies deduced from the theory. The good agreement between theory and observation suggests that nonlinear energy transfer may play a much more significant role in shelf wave dynamics than was previously realized.

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William W. Hsieh and V. T. Buchwald

Abstract

The scattering of an incident shelf wave by a long thin offshore barrier located parallel to the coast is solved for a general monotonically increasing depth profile, using the unforced, inviscid barotropic shallow water equations under rigid lid and alongshore geostrophy approximation. In particular, simple analytic formulas for the scattering coefficients are derived for the exponential shelf profile. In the channel between the barrier and the coast, much of the incident shelf wave energy is transferred to the zero (or Kelvin) mode. Seaward of the barrier, substantial energy transfer from an incident second-mode shelf wave to the first mode is possible. Downstream from the barrier, the incident mode may vanish, leaving a different mode to dominate.

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