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314
A Practical Guide to Wavelet Analysis
, 1998
"... A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finitelength t ..."
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Cited by 869 (3 self)
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A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finitelength time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmller, crosswavelet spectra, and coherence are described. The statistical significance tests are used to give a qu...
Hydrologic Data Assimilation with the Ensemble Kalman Filter
, 2002
"... Soil moisture controls the partitioning of moisture and energy fluxes at the land surface and is a key variable in weather and climate prediction. The performance of the ensemble Kalman filter (EnKF) for soil moisture estimation is assessed by assimilating Lband (1.4 GHz) microwave radiobrightnes ..."
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Cited by 90 (7 self)
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Soil moisture controls the partitioning of moisture and energy fluxes at the land surface and is a key variable in weather and climate prediction. The performance of the ensemble Kalman filter (EnKF) for soil moisture estimation is assessed by assimilating Lband (1.4 GHz) microwave radiobrightness observations into a land surface model. An optimal smoother (a dynamic variational method) is used as a benchmark for evaluating the filter's performance. In a series of synthetic experiments the effect of ensemble size and nonGaussian forecast errors on the estimation accuracy of the EnKF is investigated. With a state vector dimension of 4608 and a relatively small ensemble size of 30 (or 100; or 500), the actual errors in surface soil moisture at the final update time are reduced by 55% (or 70%; or 80%) from the value obtained without assimilation (as compared to 84% for the optimal smoother). For robust error variance estimates, an ensemble of at least 500 members is needed.
The interpretation of short climate records, with comments on the North Atlantic and
, 1999
"... This pedagogical note reminds the reader that the interpretation of climate records is dependent upon understanding the behavior of stochastic processes. In particular, before concluding that one is seeing evidence for trends, shifts in the mean, or changes in oscillation periods, one must rule out ..."
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Cited by 73 (7 self)
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This pedagogical note reminds the reader that the interpretation of climate records is dependent upon understanding the behavior of stochastic processes. In particular, before concluding that one is seeing evidence for trends, shifts in the mean, or changes in oscillation periods, one must rule out the purely random fluctuations expected from stationary time series. The example of the North Atlantic oscillation (NAO) is mainly used here: the spectral density is nearly white (frequency power law ≈ s −0.2) with slight broadband features near 8 and 2.5 yr. By generating synthetic but stationary time series, one can see exhibited many of the features sometimes exciting attention as being of causal climate significance. Such a display does not disprove the hypothesis of climate change, but it provides a simple null hypothesis for what is seen. In addition, it is shown that the linear predictive skill for the NAO index must be very slight (less than 3% of the variance). A brief comparison with the Southern Oscillation shows a different spectral distribution, but again a simulation has long periods of apparent systematic sign and trends. Application of thresholdcrossing statistics (Ricean) shows no contradiction to the assumption that the Darwin pressure record is statistically stationary. 1.
Mental representations for musical meter
 Journal of Experimental Psychology: Human Perception and Performance
, 1990
"... Investigations of the psychological representation for musical meter provided evidence for an internalized hierarchy from 3 sources: frequency distributions in musical compositions, goodnessoffit judgments of temporal patterns in metrical contexts, and memory confusions in discrimination judgments. ..."
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Cited by 73 (9 self)
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Investigations of the psychological representation for musical meter provided evidence for an internalized hierarchy from 3 sources: frequency distributions in musical compositions, goodnessoffit judgments of temporal patterns in metrical contexts, and memory confusions in discrimination judgments. The frequency with which musical events occurred in different temporal locations differentiates one meter from another and coincides with musictheoretic predictions of accent placement. Goodnessoffit judgments for events presented in metrical contexts indicated a multileveled hierarchy of relative accent strength, with finer differentiation among hierarchical levels by musically experienced than inexperienced listeners. Memory confusions of temporal patterns in a discrimination task were characterized by the same hierarchy of inferred accent strength. These findings suggest mental representations for structural regularities underlying musical meter that influence perceiving, remembering, and composing music. Perception of music, speech, and other complex human behaviors requires the processing of structured information over time. Psychological theories of serially ordered behaviors often reveal hierarchical principles of mental processing and
2006: Tropical intraseasonal variability in 14 IPCC AR4 climate models. Part I: Convective signals
 J. Climate
"... Abstract This study evaluates the tropical intraseasonal variability, especially the fidelity of The results show that current stateoftheart GCMs still have significant problems and display a wide range of skill in simulating the tropical intraseasonal variability. The total intraseasonal (2128 ..."
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Cited by 64 (1 self)
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Abstract This study evaluates the tropical intraseasonal variability, especially the fidelity of The results show that current stateoftheart GCMs still have significant problems and display a wide range of skill in simulating the tropical intraseasonal variability. The total intraseasonal (2128 day) variance of precipitation is too weak in most of the models. About half of the models have signals of convectively coupled equatorial waves, with Kelvin and MRGEIG waves especially prominent. However, the variances are generally too weak for all wave modes except the EIG wave, and the phase speeds are generally too fast, being scaled to excessively deep equivalent depths. An interesting result is that this scaling is consistent within a given model across modes, in that both the symmetric and antisymmetric modes scale similarly to a certain equivalent depth. Excessively deep equivalent depths suggest that these models may not have a large enough reduction in their "effective static stability" due to diabatic heating. 3 The MJO variance approaches the observed value in only two of the 14 models, but is less than half of the observed value in the other 12 models. The ratio between the eastward MJO variance and the variance of its westward counterpart is too small in most of the models, which is consistent with the lack of highly coherent eastward propagation of the MJO in many models. Moreover, the MJO variance in 13 of the 14 models does not come from a pronounced spectral peak, but usually is associated with an overreddened spectrum, which in turn is associated with a too strong persistence of equatorial precipitation. The two models that arguably do best at simulating the MJO are the only ones having convective closures/triggers linked in some way to moisture convergence. 4
A comparison of techniques for magnetotelluric response estimation
 J. Geophys. Res
, 1989
"... Spectral analysis of the timevarying horizontal magnetic and electric field components yields the magnetotelluric (MT) impedance tensor. This frequency dependent 2x2 complex tensor can be examined for details which axe diagnostic of the electrical conductivity distribution in the Eaxth within the r ..."
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Cited by 61 (25 self)
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Spectral analysis of the timevarying horizontal magnetic and electric field components yields the magnetotelluric (MT) impedance tensor. This frequency dependent 2x2 complex tensor can be examined for details which axe diagnostic of the electrical conductivity distribution in the Eaxth within the relevant (frequency dependent) inductive scale length of the surface observation point. As such, precise and accurate determination of this tensor from the electromagnetic time series is fundamental to successful interpretation of the derived responses. In this paper, several analysis techniques are applied to the same data set from one of the EMSLAB Lincoln Line sites. Two subsets of the complete data set were selected, on the basis of geomagnetic activity, to test the methods in the presence of differing signaltonoise ratios for varying signals and noises. Illustrated by this comparison are the effects of both statistical and bias errors on the estimates from the diverse methods. It is concluded that robust processing methods should become adopted for the analysis of MT data, and that whenever possible remote reference fields should be used to avoid bias due to runcorrelated noise contributions. 1.
A dynamic factor model for the analysis of multivariate time series
 Psychometrika
, 1985
"... As a method to ascertain the structure of intraindividual variation, Ptechnique has met difficulties in the handling of a lagged covariance structure. A new statistical technique, coined dynamic factor analysis, is proposed, which accounts for the entire lagged covariance function of an arbitrary ..."
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Cited by 49 (8 self)
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As a method to ascertain the structure of intraindividual variation, Ptechnique has met difficulties in the handling of a lagged covariance structure. A new statistical technique, coined dynamic factor analysis, is proposed, which accounts for the entire lagged covariance function of an arbitrary second order stationary time series. Moreover, dynamic factor analysis is shown to be applicable to a relatively short stretch of observations and therefore is considered worthwhile for psychological research. At several places the argumentation is clarified through the use of examples. The statistical analysis of time series has many ramific~/tions, only some of which have so far become fashionable in psychology. In this article, attention will be drawn to a branch of time series analysis pertaining to dynamic factor modelling of the lagged covariance structure of a vectorvalued time series. In order to simplify any introduction to the dynamic factor model, it may be useful to first take a look at a rather wellknown precursor. Several decades ago, Cattell (1952) suggested the analysis of an observed trajectory of a vectorvalued time series, i.e., repeated measurements on a single subject across many occasions, by means of the usual factor model. Cattell proposed the special application of
R.: Extended versus ensemble Kalman filtering for land data assimilation
 J. Hydrometeor
"... The performance of the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation. In a twin experiment for the southeastern United States synthetic observations of nearsurface soil moisture are assimilated once every 3 days, neglecting horizontal e ..."
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Cited by 47 (0 self)
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The performance of the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation. In a twin experiment for the southeastern United States synthetic observations of nearsurface soil moisture are assimilated once every 3 days, neglecting horizontal error correlations and treating catchments independently. Both filters provide satisfactory estimates of soil moisture. The average actual estimation error in volumetric moisture content of the soil profile is 2.2 % for the EKF and 2.2 % (or 2.1%; or 2.0%) for the EnKF with 4 (or 10; or 500) ensemble members. Expected error covariances of both filters generally differ from actual estimation errors. Nevertheless, nonlinearities in soil processes are treated adequately by both filters. In the application presented herein the EKF and the EnKF with four ensemble members are equally accurate at comparable computational cost. Because of its flexibility and its performance in this study, the EnKF is a promising approach for soil moisture initialization problems. 1.