Windowed and Wavelet Analysis of Marine Stratocumulus Cloud Inhomogeneity

Gollmer, Steven M.; Harshvardhan, _; Cahalan, Robert F.; Snider, J. B.

doi:10.1175/1520-0469(1995)052<3013:wawaom>2.0.co;2

Cited by 13 publications

(6 citation statements)

References 28 publications

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“…Single‐point histograms of satellite, radar, and lidar measurements of optical depth or liquid water/ice path can, in principal, be used to constrain the e PDF at the 10 to 200 km spatial scales typical of mesoscale and climate model grids [ Smith and Del Genio , 2002; Carlin et al , 2002; Jeffery and Austin , 2003]. However, across this range of scales, the two‐point statistics (in particular, the scalar spectra and the structure functions) of cloud radiance or optical depth measurements typically satisfy a power law relation with a scale‐invariant exponent which indicates the presence of long‐range correlations [e.g., Cahalan and Snider , 1989; Lovejoy et al , 1993; Barker and Davies , 1992; Gollmer et al , 1995; Davis et al , 1999]. Such a power law relation implies a statistical symmetry that is usually referred to simply as “scaling.” Determining the nature and extent of this scaling is important both because the prognostic equations for the PDF moments require estimates of the unresolved statistics and because establishing the extent of long‐range correlations is a prerequisite to obtaining reliable estimates of the one‐point statistics.…”

Section: Introductionmentioning

confidence: 99%

Spatial statistics of marine boundary layer clouds

2004

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[1] An analysis is presented of the structure functions and scalar spectra for 25 satellitederived marine stratocumulus cloud optical depth fields. The scenes, which cover a horizontal domain of 58 Â 58 km at a resolution of 28.5 m, are partitioned into two ensembles on the basis of cloud fraction. For the fully cloudy scenes, although there is wide scene-to-scene variability, both the average isotropic scalar spectrum and the average isotropic second-order structure function exhibit power law behavior over approximately two decades, with scale-invariant exponents equal to those expected for inertial-subrange passive tracer fluctuations. Higher-order structure functions show anomalous scaling that closely matches that observed for wind tunnel temperature fluctuations and for other fully cloudy observations. The partly cloudy scenes, while scaling, show different behavior. The average isotropic second-order structure function and average isotropic scalar spectrum have scale-invariant exponents that are significantly smaller than those of the fully cloudy scenes, and the analysis of the higher-order structure functions indicates that the field has much more intermittent fluctuations than the fully cloudy scenes. Fits to random cascade models for the fully cloudy scenes show that the increment statistics are consistent with an underlying log normal distribution. For the partly cloudy scenes a divergence of higherorder moments is predicted, indicating that the field fluctuations are necessarily derived from fat-tailed distributions and that there will be significant realization dependence of the measured statistics. In addition, the presence of long-range correlations in all the data predicts that single-point histograms of the field values will have significant scene-to-scene variability, or equivalently, the use of spatial averages in the approximation of the parameters of the single-point probability density function of the field will result in random fluctuations of the estimated parameters.

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Section: Introductionmentioning

confidence: 99%

Spatial statistics of marine boundary layer clouds

2004

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“…This gives rise to the paradigm that WT is merely a sophisticated procedure used by mathematics specialists for pure academic pursuit and therefore has limited practical application in climate research. Recently, wavelet analyses are beginning to make inroads into the traditional atmospheric and oceanographic literature (e.g., Gambis 1992;Kumar and Foufoula-Georgiou 1993;Gamage and Blumen 1993;Gao and Li 1993;Collineau and Brunet 1993;Meyers et al 1993;Weng and Lau 1994;Gollmer et al 1995). However, given the appeal of WT for the study of nonstationary geophysical processes, there is little doubt that WT is underused and underexplored for climate research.…”

Section: Introductionmentioning

confidence: 99%

Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing

Lau¹,

Weng²

1995

Bull. Amer. Meteor. Soc.

685

434

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In this paper, the application of the wavelet transform (WT) to climate time series analyses is introduced. A tutorial description of the basic concept of WT, compared with similar concepts used in music, is also provided. Using an analogy between WT representation of a time series and a music score, the authors illustrate the importance of local versus global information in the time-frequency localization of climate signals. Examples of WT applied to climate data analysis are demonstrated using analytic signals as well as real climate time series. Results of WT applied to two climate time series-that is, a proxy paleoclimate time series with a 2.5-Myr deep-sea sediment record of <5 18 0and a 140-yr monthly record of Northern Hemisphere surface temperature-are presented. The former shows the presence of a 40-kyr and a 100-kyr oscillation and an abrupt transition in the oscillation regime at 0.7 Myr before the present, consistent with previous studies. The latter possesses a myriad of oscillatory modes from interannual (2-5 yr), interdecadal (10-12 yr, 20-25 yr, and 40-60 yr), and century (-180 yr) scales at different periods of the data record. In spite of the large difference in timescales, common features in time-frequency characteristics of these two time series have been identified. These features suggest that the variations of the earth's climate are consistent with those exhibited by a nonlinear dynamical system under external forcings.

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“…These measurements have shown that for wavelengths above about 2-5 m, the spectrum follows the Kolmogorov law, but below this, there is a significant departure, with the spectral index becoming about unity. Microwave radiometry has been used to measure the columnaveraged liquid-water content as a time series (converting it to a space series with the wind velocity) [20]. They find that the spectral index is −1.75, which is not far from the Kolmogorov law.…”

Section: Measurements Of Atmospheric Turbulencementioning

confidence: 99%

Measurement of Correlation Functions and Power Spectra in Clouds Using the NRL WARLOC Radar

Fliflet

Manheimer

2006

IEEE Trans. Geosci. Remote Sensing

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The Naval Research Laboratory W-band Advanced Radar for Low Observable Control (WARLOC) is a highpower 94-GHz radar, with 3-10-kW average and 80-kW peak power, now set up on the western shore of the Chesapeake Bay. It has three orders of magnitude more power and sensitivity than other W-band radar systems. This enables cloud reflectivity to be measured with high signal-to-noise ratios and a resolution of about 15 m over a two (or three)-dimensional region, which can be as large as tens of kilometers on a side. This allows imaging of the internal structure of clouds over great distances in very great detail. At the shortest scale lengths, the structure has a speckle pattern indicating that it is governed at least in part by stochastic processes. The WARLOC data allow the reflectivity correlation function and its Fourier transform, which is the power spectrum, to be computed for scale lengths ranging from 30 m to 10 km. For measurements taken of cirrus clouds on several occasions as well as one case of a precipitating cloud, it was found that for small correlation distance r, the correlation function usually decreases as r 2/3 , or, equivalently, the wavenumber spectrum scales as k −5/3 , where k is the wavenumber. This suggests that fluid turbulence in the inertial range is playing a role; however, unlike classical fluid turbulence, the results suggest that the turbulence here is generally quite anisotropic. Furthermore, for longer scale lengths (the outer range according to the Kolmogorov theory), the reflectivity fluctuations usually show a wavelike behavior in the vertical direction but only occasionally in the horizontal direction.

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Windowed and Wavelet Analysis of Marine Stratocumulus Cloud Inhomogeneity

Abstract: To improve radiative transfer calculations for inhomogeneous clouds, a consistent means of modeling inhomogeneity is needed. One current method of modeling cloud inhomogeneity is through the use of fractal paramdemonstrate both the strengths and weaknesses of these models•

Cited by 13 publications

References 28 publications

Spatial statistics of marine boundary layer clouds

Spatial statistics of marine boundary layer clouds

Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing

Measurement of Correlation Functions and Power Spectra in Clouds Using the NRL WARLOC Radar

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