Observations of the Labrador Sea eddy field

This paper is an observational study of small-scale coherent eddies in the Labrador Sea, a region of dense water formation thought to be of considerable importance to the North Atlantic overturning circulation. Numerical studies of deep convection emphasize coherent eddies as a mechanism for the lateral transport of heat, yet their small size has hindered observational progress. A large part of this paper is therefore devoted to developing new methods for identifying and describing coherent eddies in two observational platforms, current meter moorings and satellite altimetry. Details of the current and water mass structure of individual eddy events, as they are swept past by an advecting flow, can then be extracted from the mooring data. A transition is seen during mid-1997, with long-lived boundary current eddies dominating the central Labrador Sea year-round after this time, and convectively formed eddies similar to those seen in deep convection modeling studies apparent prior to this time. The TOPEX / Poseidon altimeter covers the Labrador Sea with a loose “net” of observations, through which coherent eddies can seem to appear and disappear. By concentrating on locating and describing anomalous events in individual altimeter tracks, a portrait of the spatial and temporal variability of the underlying eddy field can be constructed. The altimeter results reveal an annual “pulsation” of energy and of coherent eddies originating during the late fall at a particular location in the boundary current, pinpointing the time and place of the boundary current-type eddy formation. The interannual variability seen at the mooring is reproduced, but the mooring site is found to be within a localized region of greatly enhanced eddy activity. Notably lacking in both the annual cycle and interannual variability is a clear relationship between the eddies or eddy energy and the intensity of wintertime cooling. These eddy observations, as well as hydrographic evidence, suggest an active role for boundary current dynamics in shaping the energetics and water mass properties of the interior region.     

Vorticity and intermittency within the pre-breaking region of spilling breakers

This paper presents measurements and analysis of fluid velocity within the context of spilling waves. The data have been collected using 2-D Laser Doppler Velocimetry in pre-breaking monochromatic waves generated in a wave tank. The analysis is performed using orthogonal wavelets and, in addition to the classical criterion adopted in applying Taylor's hypothesis, a new algorithm is proposed for the eduction of eddies at different length scales. The contribution of different scale vortices is computed, and phase is resolved. Microvortices (smaller than the breaker height but larger than the dissipative vortices) and mid-size vortices (with length ranging from the breaker height to the wave length) carry out most turbulence energy under wave crest. The phase average vorticity and strain rate is computed at different wave lengths, with the analysis of intermittence. The intermittency factor shows spikes in the wave crest, especially for turbulence in small vortices.     

一维波动方程的奇性反演与小波

利用线性化的技巧及Ｇ．Ｂｅｙｌｋｉｎ引进的奇性反演的概念，使波动方程非均匀背景场的反演问题有了实质性的进展，但在进行线性化简时，往往会将数值小但奇性高的项略去，因而使反演结果失真，本文利用小波变换这一工具，在化简时保留了奇性的主要部分，从而使反演所得的结果从奇性分析的观点看来更为。     

Identifying linear and non-linear behaviour in reduced complexity modelling output using surrogate data methods

Validation of model output is an important issue in the environmental sciences. This is particularly the case for reduced complexity modelling approaches where verification of the underlying equations is often problematic. Hence, methods that go beyond validation based on average values or the histogram of model output, are clearly advantageous. In this paper we show that a validation method based on the serial properties of time–space data, and developed in geomorphology, is a useful alternative but is nevertheless still insensitive to certain asymmetric characteristics of the signal. Hence, use of this method for validation may be enhanced by the adoption of an accompanying test for asymmetry in the model output.     

Revising the paradigm of tidal analysis – the uses of non-stationary data

Surface elevation and current records contain non-tidal variance, often dismissed as noise. The processes responsible for the non-tidal component may also modulate the tidal signal, altering its strength and frequency structure. Because of their manner of generation and propagation, internal tides are inherently irregular. The non-stationary character of these and other tidal processes provides an integral and useful property of tidal records, because it provides an opportunity to obtain insights into tidal dynamics and the interaction of tidal and non-tidal processes. It is, moreover, productive to use multiple approaches in analyzing coastal and estuarine tidal processes so that both the time-varying and average frequency content are determined. Only by confronting the causes of non-stationary behaviour in this way can some of the remaining challenges in tidal analysis and prediction be overcome, e.g. shelf and estuarine currents, river tides, internal tides, tide-surge interactions and tidally influenced ecological processes. Several examples illustrate the utility of non-stationary tidal analysis methods.Responsible Editor: Jens Kappenberg     

The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers

The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1σ).     

Wavelet imaging cleaning method for atmospheric Cherenkov telescopes

We present a new method of image cleaning for imaging atmospheric Cherenkov telescopes. The method is based on the utilization of wavelets to identify noise pixels in images of gamma-ray and hadronic induced air showers. This method selects more signal pixels with Cherenkov photons than traditional image processing techniques. In addition, the method is equally efficient at rejecting pixels with noise alone. The inclusion of more signal pixels in an image of an air shower allows for a more accurate reconstruction, especially at lower gamma-ray energies that produce low levels of light. We present the results of Monte Carlo simulations of gamma-ray and hadronic air showers which show improved angular resolution using this cleaning procedure. Data from the Whipple Observatory's 10-m telescope are utilized to show the efficacy of the method for extracting a gamma-ray signal from the background of hadronic generated images.     

一维有耗散波动方程的奇性分析与小波

对系数有强奇性（间断）的波动方程,用通常的线性化简的方法时往往会将数值小但奇性强的项略去,导致结果严重失真。利用小波变换这一工具,可以在化简时保留奇性的主要部分,使所得的结果从奇性分析的观点看来更为精确。此方法曾被用来处理系数有间断的一维波动方程,得到了与精确解的奇性主部完全一致的解．在本文中,我们改进了用小波变换作奇性化简的方法,对系数有间断的一维有耗散波动方程求得了与精确解奇性主部完全一致的解。这说明利用小波分析作奇性化简的方法对高频近似及奇性分析问题是普遍适用的．     

The multiresolution character of collocation

 An interesting theoretical connection between the statistical (non-stochastic) collocation principle and the multiresolution/wavelet framework of signal approximation is presented. The rapid developments in multiresolution analysis theory over the past few years have provided very useful (theoretical and practical) tools for approximation and spectral studies of irregularly varying signals, thus opening new possibilities for `non-stationary' gravity field modeling. It is demonstrated that the classic multiresolution formalism according to Mallat's pioneering work lies at the very core of some of the general approximation principles traditionally used in physical geodesy problems. In particular, it is shown that the use of a spatio-statistical (non-probabilistic) minimum mean-square-error criterion for optimal linear estimation of deterministic signals, in conjunction with regularly gridded data, always gives rise to a generalized multiresolution analysis in the Hilbert space L <sup>2</sup>(R), under some mild constraints on the spatial covariance function and the power spectrum of the unknown field under consideration. Using the theory and the actual approximation algorithms associated with statistical collocation, a new constructive framework for building generalized multiresolution analyses in L <sup>2</sup>(R) is presented, without the need for the usual dyadic restriction that exists in classic wavelet theory. The multiresolution and `non-stationary' aspects of the statistical collocation approximation procedure are also discussed, and finally some conclusions and recommendations for future work are given. Received: 26 January 1999 / Accepted: 16 August 1999     

A wavelet for predicting the time-domain response of vertically tethered systems

The response wavelets for tether tension and the displacement of a package on the end of a tether are derived from a linear, frequency-domain model of vertically tethered systems using inverse fourier transform techniques. These wavelets are convolved with a record of ship displacement to predict the instantaneous tension and displacement to an accuracy of better than 20% for a typical system. Although snap loads are non-linear and the response cannot be calculated while the tether is slack, the onset of zero tension — a precursor to snap loads — is predicted by the wavelet. Thus, extreme and potentially hazardous conditions are foreseeable with the wavelet and this information can be used in real-time to guide operations at sea.