Dynamical model and nonextensive statistical mechanics of liquid water path fluctuations in stratus clouds
|
|
- Lorraine Byrd
- 5 years ago
- Views:
Transcription
1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006jd007493, 2007 Dynamical model and nonextensive statistical mechanics of liquid water path fluctuations in stratus clouds K. Ivanova, 1 H. N. Shirer, 1 T. P. Ackerman, 2 and E. E. Clothiaux 1 Received 9 May 2006; revised 25 January 2007; accepted 8 February 2007; published 22 May [1] The shape and tails of the probability distribution functions of the liquid water path in stratus clouds are expressed through a model encompassing Tsallis nonextensive statistics. A model originally proposed to describe turbulent flows describes the behavior of the normalized increments of the liquid water path, at both small and large timescales, provided that the distribution of the local variability of the normalized increments can be sufficiently well fitted with a c 2 distribution. The transition between the small-timescale model of a nonextensive process and the large-scale Gaussian extensive homogeneous fluctuation model is found to be at around 24 h. Citation: Ivanova, K., H. N. Shirer, T. P. Ackerman, and E. E. Clothiaux (2007), Dynamical model and nonextensive statistical mechanics of liquid water path fluctuations in stratus clouds, J. Geophys. Res., 112,, doi: /2006jd Introduction [2] In recent years, the formalism of nonextensive statistical mechanics, first introduced by Tsallis [1988] and later further developed by others [Abe, 2000; Abe et al., 2001; Tsallis et al., 1998], has gained considerable interest [Beck, 2000, 2001a, 2001b, 2001c, 2002a, 2002b, 2002c, 2004; Arimitsu and Arimitsu, 2000a, 2000b, 2001, 2002, 2006; Wilk and Wlodarczyk, 2000; Daniels et al., 2004]. The new theoretical approach is suitable to treat physical systems of sufficient complexity that cannot maximize the usual Boltzmann-Gibbs-Shannon (BGS) entropy, the latter leading to the usual statistical mechanics. In such a case, the system maximizes some other, more general entropy measure, such as the Tsallis entropies S q, which have the BGS as a limit. Various reasons may cause some physical systems not to maximize the BGS entropy, for example, long-range correlations, multifractality [Lyra and Tsallis, 1998; Campos Velho et al., 2001; Meson and Vericat, 2002; Arimitsu and Arimitsu, 2000a, 2000b, 2006], or simply the fact that the system is not in equilibrium owing to some external forcing [Tsallis and Bukman, 1996]. Recently it has been shown that nonextensive statistical mechanics is particularly useful in describing two-dimensional Eulerian turbulence [Boghosian, 1996] and the stochastic properties of fully developed turbulent flows [Beck, 2000, 2001a, 2001b, 2001c, 2002a, 2002c, 2004; Beck et al., 2001; Arimitsu and Arimitsu, 2000a, 2000b, 2001; Ramos et al., 2001a; Bolzan et al., 2002], including dislocation motion in defect turbulence in inclined layer convection [Daniels et al., 2004]. 1 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania, USA. 2 Department of Atmospheric Sciences, University of Washington, Seattle, Washington, USA. Copyright 2007 by the American Geophysical Union /07/2006JD [3] In this study, we apply the Beck dynamical model [Beck, 2000, 2001a, 2002a] to liquid water path fluctuations in stratus clouds in the framework of nonextensive statistical mechanics. As introduced to describe fully developed turbulence, the Beck dynamical model aims neither to solve the turbulence problem nor to reproduce fully the spatiotemporal dynamics of the Navier-Stokes equations, but rather to provide a simple model that captures some of the most important statistical properties of the phenomena in an analytically tractable manner [Beck, 2004]. [4] Stratus overcast conditions are associated with a neutral boundary layer. The turbulence in such a layer is generated predominately by shear production from the atmosphere toward the Earth s surface. In classical studies, the phenomenology of turbulence has been described by self-similar cascades, in which an identical, scale-invariant step is repeated from large scales to small ones, as the small ones produce even smaller ones until the turbulent flow energy gets dissipated on the smallest scale [Mandelbrot, 1974]. More realistic description of turbulence is achieved by generalization of this approach to anisotropic scaling and multiplicative cascade models [Schertzer and Lovejoy, 1987]. Cascade processes generically give rise to multifractals. The resulting multifractal behavior of a random variable is scale invariant and can be determined either by the scaling of its probability distribution functions or by the scaling of its structure functions. In hydrodynamics, the velocity structure functions are expected to exhibit multiaffine scaling, for example, nonlinear scaling of the structure function exponents [Frisch, 1995]. [5] In contrast, the probability distribution functions that are obtained within the nonextensive statistical mechanics approach are not scale invariant [Tsallis, 1988]. The Beck dynamical model in the framework of Tsallis statistics describes the evolution of the time-dependent probability distribution functions of a random variable for different delay times [Beck, 2000, 2001a]. The purpose of this study is to 1of6
2 for the Southern Great Plains site, that allows us to analyze a high resolution and unusually long time series of 25,772 data points. [9] In this study, we are concerned with the distribution of the normalized increments of the liquid water path signal y(t) for various values of the time lag Dt. Normalized increments are calculated as Z(t, Dt) =(y(t) hyi Dt )/s Dt, where hyi Dt and s Dt are the mean and the standard deviation of y(t) for time lag Dt, respectively. Figure 1. Probability distribution function p Dt (Z) of normalized increments Z(t, Dt) of liquid water path (LWP) data measured at the ARM SGP site on 9 14 January 1998, for Dt = 40 s (circles). Normalized increments are calculated as Z(t, Dt) =(y(t) hyi Dt )/s Dt, where hyi Dt and s Dt are the mean and standard deviation of y(t) for time lag Dt. The solid curve represents a Gaussian distribution. The probability distribution function of normalized increments Z(t, Dt) of shuffled liquid water path signal is denoted by the crosses. Note that the fat tails disappear in the shuffled case. present empirical evidence that the probability distribution functions of the liquid water path fluctuations in stratus clouds are time-dependent and their evolution can be sufficiently well described in the framework of Tsallis statistics. 2. Data Analyzed [6] The data used in this study are the liquid water path (LWP) time series measured with the microwave radiometer at the Southern Great Plains (SGP) site of the US Department of Energy Atmospheric Radiation Measurements (ARM) program. The microwave radiometer (Radiometrics, Model WVR-1100) measures the radiances, expressed as brightness temperatures, at the frequencies of 23.8 and 31.4 GHz from which the vertical column amounts of cloud liquid water and water vapor are retrieved [Westwater, 1993]. [7] The microwave radiometer measures the downwelling atmospheric radiance and records the data as brightness temperatures at Dt 0 = 20 s intervals. The microwave radiometer is equipped with a Gaussian-lensed microwave antenna whose small-angle receiving cone is steered with a rotating flat mirror ( The field of view of the microwave radiometer is 5.7 at 23.8 GHz and 4.6 at 31.4 GHz. The brightness temperature is measured with a radiance error of ±0.5 K. The atmosphere is not optically thick at these two microwave radiometer frequencies during cloudy conditions. Hence these two frequencies can be used to retrieve the total column amounts of water vapor and cloud liquid water. The error for the liquid water path retrieval is estimated to be less than about g/cm 2 [Liljegren et al., 2001]. [8] We consider a 6-day stratus cloud event, 9 14 January 1998, which is an exceptionally long-lasting cloudy period 3. Conventional Analysis [10] The distribution of the normalized increments Z(t, Dt) of the liquid water path signal for the period 9 14 January 1998 for Dt = 40 s is plotted in Figure 1. A fit is attempted first with a Gaussian distribution (solid curve in Figure 1) for small values of the increments, i.e., the central part of the distribution. Even for small values of the increments, however, the probability distribution function (PDF) is not fit well with a Gaussian curve. [11] To illustrate that the correlations of the fluctuations of the liquid water path signal are expressed in the tails of the probability distribution function, we shuffle the LWP signal by randomly changing the order of the measurements in the time series. The PDF of the normalized increments of the shuffled signal is plotted with crosses in Figure 1. The so-called fat tails, for example, tails of the PDF showing probabilities higher than the Gaussian distributions would predict, almost vanish. [12] To test the tails of the PDF further, we calculate the probability that the increment is larger than jzj; that is, we calculate the cumulative probability distribution (cpdf) of the increments P > (jzj) for the different values of the time lag Dt = 40 s, 80 s, 320 s, 10 min, 1 h, 12 h, and 89,200 s (24 h 46 min 40 s). These cumulative distributions are Figure 2. Cumulative probability distribution functions of normalized increments jz(t, Dt)j of liquid water path signal for Dt = 40 s, 80 s, 320 s, 10 min, 1 h, 12 h, and 24 h (24 h 46 min 40 s). In the asymptotic regime of large values of the normalized increments jzj, the cpdf of small delay times Dt = 40 s, 80 s, 320 s, and 10 min scale as a power law. The solid line indicates a power law dependence with an exponent k = of6
3 plotted in Figure 2. In the asymptotic regime for large values of the increments jzj > 4, the cumulative distributions for small values of the time lag Dt = 40 s, 80 s, 320 s, and 10 min decay as a power law P > (jzj) jzj k with k 4, as shown by the solid line in Figure 2. The cpdf of the liquid water path data for larger values of the time lag approach Gaussian behavior. [13] Previous empirical studies of the tropical atmospheric boundary layer report values of the exponent k 5for wind velocity in the vertical [Lazarev et al., 1994], k 7 for wind velocity in the horizontal [Chigirinskaya et al., 1994], and k 7 for the time series of wind velocity at the finest available resolution [Schmitt et al., 1994]. In contrast, the cumulative probability distribution of hourly rainfall data in Valentia, Ireland, at the resolution of the data set is found to scale with an exponent k =4[Kiely and Ivanova, 1999], and the value of the scaling exponent is equal to k = 3.5 for daily rainfall accumulations in France [Ladoy et al., 1991]. The value of the exponent k obtained in this study is closer to its value for rainfall probably because the liquid water path in stratus clouds is quantitatively closely related to precipitation. 4. Nonextensive Statistical Approach [14] The fat tails in the liquid water path distributions and long-range temporal correlations [Davis et al., 1994; Marshak et al., 1997; Ivanova et al., 2000, 2002] indicate that nonextensive statistical mechanics may offer an appropriate framework to quantify the corresponding statistics. At present, the most consistent one seems to be the one based on the generalized entropies given by Z 1 S q ¼ k q 1 1 pðx; tþ q dx ; ð1þ as postulated by Tsallis [1988]. In equation (1), q is a parameter and k is a normalization constant. The main ingredient in equation (1) is the time-dependent probability distribution p(x, t) of the stochastic variable x. The functional S q is reduced to the classical extensive Boltzmann-Gibbs- Shanon form in the limit of q! 1. The Tsallis parameter q characterizes the nonextensivity of the entropy. Subject to certain constraints, the functional in equation (1) yields a probability distribution function of the form [Beck, 2001a, 2002a; Ramos et al., 2001a, 2001b] ( ) pðxþ ¼ 1 1 þ Cb 02aðq 1Þjxj 2a 1 ðq 1Þ Z q 2a ðq 1Þ for the stochastic variable x, where 1 ¼ a Cb 02aðq 1Þ Z q 2a ðq 1Þ ð2þ 1=2a G 1 q 1 ; ð3þ G 1 G 1 2a q 1 1 2a in which G is the gamma function, C is a constant, and 0 < a 1 is the power law exponent of the potential U(x) =Cjxj 2a that provides the restoring force F(x) in the Beck model of turbulence [Beck, 2001a, 2001b; Beck et al., 2001]. The latter is described by a Langevin equation dx dt ¼ gfðxþþsrðtþ where g and s are parameters and R(t) is a Gaussian white noise. A nonzero value of g corresponds to providing energy to (or draining from) the system [Sattin, 2003]. The parameter b 0 in equations (2) and (3) is the mean of the fluctuating variability b, i.e., the local standard deviation of x over a certain window of size n [Ramos et al., 2001a, 2001b]. [15] Although the nonextensive formalism originally was suggested to have physical applications to equilibrium systems with long-range interactions, it has been suggested recently that the nonextensive formalism is of particular physical relevance for nonequilibrium systems with fluctuating temperature [Wilk and Wlodarczyk, 2000] or fluctuating energy dissipation [Beck, 2001a, 2001c, 2002a, 2002b]. Beck [2002a] showed that the nonextensive behavior is a consequence of integrating over all possible values of the fluctuating variable b, provided that b is c 2 -distributed with degree v: f Dt ðbþ 1 n n=2 b n=2 1 exp nb ; n > 2 ð5þ Gðn=2Þ 2b 0 2b 0 where G is the Gamma function and b 0 = hbi with average taken over the entire data series for that specific b. The number of degrees of freedom n can be found from n ¼ 2hbi2 hb 2 i hbi 2 The Tsallis parameter q satisfies [Beck, 2001a] q 1 þ 2a an þ 1 Significantly, equation (1) is obtained exactly for systems that are governed by the nonlinear Langevin equation (4) for which parameters g and s fluctuate in such a way that b = g/s 2 is c 2 -distributed with degree n (equation (5) [Beck, 2002a]). [16] We use the Beck model assuming that the normalized increments Z(t, Dt) represent the stochastic variable x, as in equation (1). We search whether equation (2) is obeyed for x Z(t, Dt), thus studying p(x) p Dt (Z) for various time lags Dt. [17] In order to test if the distribution of the local variability of the normalized increments Z(t, Dt) is of the form of a c 2 distribution, we have checked the distribution of the normalized increments of the liquid water path signal for the different values of the time lag Dt = 40 s, 80 s, 320 s, 10 min, 1 h, 12 h, and 89,200 s (24 h 46 min 40 s). We have calculated the standard deviation of the normalized incre- ð4þ ð6þ ð7þ 3of6
4 Figure 3. Probability distribution function f Dt (b) of the local variability b [equation (8)] in terms of standard deviation of the normalized increments Z(t, Dt) of the liquid water path signal for box size n = 5 min for different time lags (symbols) (a-f): Dt = 40 s, 80 s, 320 s, 10 min, 1 h, and 89,200 s (24 h 46 min 40 s). Solid curves: c 2 distribution as given by equation (5). ments within various nonoverlapping windows of size n, ranging from 10Dt 0 to 100Dt 0 : vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! u jþn 1 1 X bð jþ ¼ Z n 2 ðiþ 1 jþn 1 2 X t ZðiÞ n i¼j j ¼ 1; 2;...; N n þ 1 where N is the length of the time series. [18] In doing so, we have considered different various numbers of nonoverlapping windows for various time lags Dt, and we have searched for the most efficient size of the window in order not to lose data points and therefore information. The resulting empirically obtained distributions of the local variability [equation (8)] of normalized increments for the different time lags of interest are plotted in Figure 3 for an intermediate case n =15Dt 0 = 5 min. The values of the degree n of the c 2 distribution then are obtained using equation (6). The spread [b min, b max ] of the local variability b decreases with increasing time lag, as is expected from a c 2 distribution function because of the exponential function in equation (5) for large values of the degrees of freedom n. On the basis of these results, for example, Figure 3, we accept that the b distributions of the increments Z(t, Dt) for each of the Z(t, Dt) obtained for the different values of the time lag can be sufficiently well fitted for our purpose with a c 2 distribution, thereby justifying the initial assumption used to obtain equation (5). [19] The impact of the a parameter on the tail behavior of the Tsallis-type distribution function for fixed q and the impact of q at fixed a are investigated elsewhere [Ausloos and Ivanova, 2003] and find as expected that the tails of i¼j ð8þ the distribution functions approach a Gaussian type when q approaches 1. [20] Next, we calculate the probability distributions of the normalized increments of the liquid water path signal Figure 4. Probability distribution function of normalized increments Z(t, Dt) of liquid water path signal (symbols) and the Tsallis-type distribution function (solid curves) for Dt = 40 s, 80 s, 320 s, 10 min, 1 h, 12 h, and 24 h (24 h 46 min 40 s). The last value of Dt is chosen such that at least the PDF for the positive value of the increments converges to a Gaussian distribution (dashed curve). The PDFs (symbols and curves) for each Dt are displaced by 0.1 with respect to the previous one; the top curve for Dt = 40 s is not moved. The values of the parameters for the Tsallis-type distribution function for each Dt are summarized in Table 1. 4of6
5 Table 1. Values of the Parameters Characterizing the Liquid Water Path Signal in the Nonextensive Thermostatistics Approach a Dt, s q a Cb 0 w =2a/(q 1) K r d KS a For the definition of the Kolmogorov-Smirnov distance d KS, see the text. for the different values of the time lag Dt =40s,80s, 320 s, 10 min, 1 h, 12 h, and 89,200 s (24 h 46 min 40 s). They are shown in Figure 4 together with the curves representing the best fit to the Tsallis type of distribution function. In Table 1, the statistical parameters related to the Tsallis type of distribution function are summarized, including a criterion for the goodness of the fit, i.e., the Kolmogorov-Smirnov distance d KS, which is defined as the maximum Euclidean distance between the cumulative probability distributions of the data and the fitting curves. Note that the flatness coefficient K r (see Table 1) for the Tsallis type of distribution function, given by K r ¼ K L ð5 3qÞ ð7 5qÞ where K L = 3 for a Gaussian process, is positive for all values of q < 7/5 as expected because the positiveness of K r is related directly to the occurrence of intermittency [Sreenivasan and Antonia, 1997; Ramos et al., 2001a, 2001b]. Moreover, the limit q < 7/5 also implies that the second moment of the Tsallis-type distribution function will always remain finite, as necessarily due to the type of phenomena studied here. [21] In order to obtain an estimate for the value of the scale at which the distribution converges to Gaussian, we observe that equation (2) fits well the normalized increments for Dt = 24 h 46 min 40 s and q = 1.03 (Table 1 and Figure 4). The a parameter (a = 0.7) in this case plays an important role in controlling the tails such that the Tsallis-type distribution function for the negative values of Z fits the data whose probability distribution function still deviates from Gaussian. We consider that Dt L = 24 h 46 min 40 s is a good estimate for the time lag at which the PDF converges to Gaussian (dashed curve in Figure 4), based on the limited duration of the stratus cloud event. This result indicates where the transition occurs between the small-timescale model of a nonextensive, intermittent process and the large-scale Gaussian extensive homogeneous fluctuation model [Ramos et al., 2001a, 2001b; Tsallis, 1988]. [22] One can explore the theoretically predicted Tsallis type of the probability distribution function equation (2) in two limits. For small values of the normalized increments Z, the probability distribution function converges to the form p Dt ðzþ 1 exp Cb 02a Z q 2a ðq 1Þ jzj2a ð9þ ð10þ Therefore the Tsallis-type distribution function converges to a Gaussian, i.e., a! 1, for small values of the normalized increments, for any Dt investigated here (see Figure 4). [23] In the limit of large values of normalized increments Z, i.e., the tails of the probability distribution function, the Tsallis-type distribution converges to a power law p Dt ðzþ 1 Z q ðq 1ÞCb 0 2a 1 q 1 2a ðq 1Þ jzj2a jzj w ð11þ with an exponent w =2a/(q 1) (see Table 1). The value of w at small scales is 5 that is in good agreement with the values of the slope of the cumulative probability distributions (Figure 2) k = w 1 4. At larger scales, the tail exponent w increases to 10. A similar trend though different values of the tail exponent is found experimentally in the case of fully developed turbulence. In the highprecision measurements during experimentally observed fully developed turbulence [Beck et al., 2001], the tail exponent was estimated to be 9 for very small spatial scales, increasing to 15 at medium scales. Different values of the tail exponent w for the liquid water path data versus those for fully developed turbulence are understood to be owing to the differences that occur when analyzing vector versus passive scalar quantities related to atmospheric turbulence [Sreenivasan and Antonia, 1997]. 5. Conclusion [24] We present here a method that provides the evolution of the time-dependent probability distribution functions of the liquid water path observed in stratus clouds. We apply the Beck dynamical model that encompasses Tsallis nonextensive statistics to liquid water path data after testing that their local variability is c 2 -distributed. The model describes well the shape and the tails of the probability distribution functions. We find that the transition between the smalltimescale model of a nonextensive process and the largescale Gaussian extensive homogeneous fluctuation model is found to be at around 24 h. In the limit of large values of the normalized increments, the values of the exponent of the PDF tails given by the model theoretical predictions are found to be in agreement with the slopes of the cumulative probability distribution functions. The model thus can provide a useful framework for treating liquid water path in global circulation models. [25] Acknowledgments. KI, HNS, and EEC were supported by the Office of Biological and Environmental Research of the US Department of Energy under contracts DE-FG02-04ER63773 and DE-FG02-90ER TPA was supported by the Office of Biological and Environmental Research of the US Department of Energy under contract DE-AC06-76RL01830 to the Pacific Northwest National Laboratory as part of the Atmospheric Radiation Measurement Program. The Pacific Northwest National Laboratory is operated by Battelle for the US Department of Energy. References Abe, S. (2000), Axioms and uniqueness theorem for Tsallis entropy, Phys. Lett. A, 271, 74. Abe, S., S. Martinez, F. Pennini, and A. Plastino (2001), Nonextensive thermodynamic relations, Phys. Lett. A, 281, 126. Arimitsu, T., and N. Arimitsu (2000a), Analysis of fully developed turbulence in terms of Tsallis statistics, Phys. Rev. E, 61, of6
6 Arimitsu, T., and N. Arimitsu (2000b), Tsallis statistics and fully developed turbulence, J. Phys. A Math. Gen., 33, L235 L241. Arimitsu, T., and N. Arimitsu (2001), Analysis of fully developed turbulence by a generalized statistics, Prog. Theor. Phys., 105, 355. Arimitsu, T., and N. Arimitsu (2002), Tsallis statistics and turbulence, Chaos Solitons Fractals, 13(3), Arimitsu, T., and N. Arimitsu (2006), Multifractal PDF analysis for intermittent systems, Physica A, 365, Ausloos, M., and K. Ivanova (2003), Dynamical model and nonextensive statistical mechanics of a market index on large time windows, Phys. Rev. E, 68, Beck, C. (2000), Application of generalized thermostatistics to fully developed turbulence, Physica A, 277, Beck, C. (2001a), Dynamical foundations of nonextensive statistical mechanics, Phys. Rev. Lett., 87, Beck, C. (2001b), Scaling exponents in fully developed turbulence from nonextensive statistical mechanics, Physica A, 295, Beck, C. (2001c), On the small-scale statistics of Lagrangian turbulence, Phys. Lett. A, 287, Beck, C., G. S. Lewis, and H. L. Swinney (2001), Measuring nonextensitivity parameters in a turbulent Couette-Taylor flow, Phys. Rev. E, 63, Beck, C. (2002a), Generalized statistical mechanics and fully developed turbulence, Physica A, 306, Beck, C. (2002b), Non-additivity of Tsallis entropies and fluctuations of temperature, Europhys. Lett., 57, Beck, C. (2002c), Non-extensive statistical mechanics approach to fully developed hydrodynamic turbulence, Chaos Solitons Fractals, 13, Beck, C. (2004), Superstatistics in hydrodynamic turbulence, Physica D, 193, Boghosian, B. M. (1996), Thermodynamic description of the relaxation of two-dimensional turbulence using Tsallis statistics, Phys. Rev. E, 53, Bolzan, M. J. A., F. M. Ramos, L. D. A. Sa, C. R. Neto, and R. R. Rosa (2002), Analysis of fine-scale canopy turbulence within and above an Amazon forest using Tsallis generalized thermostatistics, J. Geophys. Res., 107(D20), 8063, doi: /2001jd Campos Velho, R. F., F. M. Ramos, R. R. Rosa, F. M. Ramos, R. A. Pielke, G. A. Degrazia, C. Rodrigues Neto, and A. Zanandrea (2001), Multifractal model for eddy diffusivity and counter-gradient term in atmospheric turbulence, Physica A, 295, Chigirinskaya, Y., D. Schertzer, S. Lovejoy, A. Lazarev, and A. Ordanovich (1994), Unified multifractal atmospheric dynamics tested in the tropics: Part I, horizontal scaling and self criticality, Nonlinear Process. Geophys., 1, Daniels, K. E., C. Beck, and E. Bodenschatz (2004), Defect turbulence and generalized statistical mechanics, Physica D, 193, Davis, A., A. Marshak, W. Wiscombe, and R. Cahalan (1994), Multifractal characterizations of nonstationarity and intermittency in geophysical fields, observed, retrieved or simulated, J. Geophys. Res. Atmos., 99, Frisch, U. (1995), Turbulence: the Legacy of A. N. Kolmogorov, Cambridge Univ. Press, New York. Ivanova, K., M. Ausloos, E. E. Clothiaux, and T. P. Ackerman (2000), Break-up of stratus cloud structure predicted from non Brownian motion liquid water and brightness temperature fluctuations, Europhys. Lett., 52, Ivanova, K., E. E. Clothiaux, H. N. Shirer, T. P. Ackerman, J. C. Liljegren, and M. Ausloos (2002), Evaluating the quality of ground-based microwave radiometer measurements and retrievals using detrended fluctuation and spectral analysis methods, J. Appl. Meteorol., 41, Kiely, G., and K. Ivanova (1999), Multifractal analysis of hourly precipitation, Phys. Chem. Earth, 24, Ladoy, P., S. Lovejoy, and D. Schertzer (1991), Extreme fluctuations and intermittency in climatological temperatures and precipitation, Scaling, fractals, and non-linear variability in geophysics, edited by D. Schertzer and S. Lovejoy, pp , Springer, New York. Lazarev, A., D. Schertzer, S. Lovejoy, and Y. Chigirinskaya (1994), Unified multifractal atmospheric dynamics tested in the tropics: Part II, vertical scaling and generalized scale invariance, Nonlinear Process. Geophys., 1, Liljegren, J. C., E. E. Clothiaux, G. G. Mace, S. Kato, and X. Dong (2001), A new retrieval for cloud liquid water path using a ground-based microwave radiometer and measurements of cloud temperature, J. Geophys. Res., 106(D13), 14,485 14,500. Lyra, M. L., and C. Tsallis (1998), Nonextensivity and multifractality in low-dimensional dissipative systems, Phys. Rev. Lett., 80, Mandelbrot, B. B. (1974), Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier, J. Fluid Mech., 62, Marshak, A., A. Davis, W. Wiscombe, and R. Cahalan (1997), Scale invariance in liquid water distributions in marine stratocumulus. Part II: Multifractal properties and intermittency issues, J. Atmos. Sci., 54, Meson, A. M., and F. Vericat (2002), On the Kolmogorov-like generalization of Tsallis entropy, correlation entropies and multifractal analysis, J. Math Phys., 43, Ramos, F. M., R. R. Rosa, C. Rodrigues Neto, M. J. A. Bolzan, L. D. Abreu Sa, and H. F. Campos Velho (2001a), Non-extensive statistics and threedimensional fully developed turbulence, Physica A, 295, Ramos, F. M., R. R. Rosa, C. Rodrigues Neto, M. J. A. Bolzan, and L. D. Abreu Sa (2001b), Nonextensive thermostatistics description of intermittency in turbulence and financial markets, Nonlinear Anal., 47, Sattin, F. (2003), Non-Gaussian probability distribution functions from maximum-entropy-principle considerations, Phys. Rev. E, 68, 32,102 32,105. Schertzer, D., and S. Lovejoy (1987), Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, J. Geophys. Res., 92(D8), Schmitt, F., D. Schertzer, S. Lovejoy, and Y. Brunet (1994), Empirical study of multifractal phase transitions in atmospheric turbulence, Nonlinear Process. Geophys., 1, Sreenivasan, K. R., and R. A. Antonia (1997), The phenomenology of small-scale turbulence, Annu. Rev. Fluid Mech., 29, Tsallis, C. (1988), Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52, 479. Tsallis, C., and D. J. Bukman (1996), Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis, Phys. Rev. E, 54, R2197 R2200. Tsallis, C., R. S. Mendes, and A. R. Plastino (1998), The role of constraints within generalized nonextensive statistics, Physica A, 261, Westwater, E. R. (1993), Ground-based microwave remote sensing of meteorological variables, in Atmospheric Remote Sensing by Microwave Radiometry, edited by M. A. Janssen, pp , John Wiley, Hoboken, N. J. Wilk, G., and Z. Wlodarczyk (2000), Interpretation of the nonextensivity parameter q in some applications of Tsallis statistics and Lvy distributions, Phys. Rev. Lett., 84, T. P. Ackerman, Department of Atmospheric Sciences, University of Washington, Seattle, WA 98195, USA. E. E. Clothiaux, K. Ivanova, and H. N. Shirer, Department of Meteorology, The Pennsylvania State University, University Park, PA 16802, USA. (ivanova@psu.edu) 6of6
From time series to superstatistics
From time series to superstatistics Christian Beck School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E 4NS, United Kingdom Ezechiel G. D. Cohen The Rockefeller University,
More informationEvaluating the Quality of Ground-Based Microwave Radiometer Measurements and Retrievals Using Detrended Fluctuation and Spectral Analysis Methods
56 JOURNAL OF APPLIED METEOROLOGY Evaluating the Quality of Ground-Based Microwave Radiometer Measurements and Retrievals Using Detrended Fluctuation and Spectral Analysis Methods K. IVANOVA, E.E.CLOTHIAUX,
More informationSuperstatistics: theory and applications
Continuum Mech. Thermodyn. (24) 6: 293 34 Digital Object Identifier (DOI).7/s6-3-45- Original article Superstatistics: theory and applications C. Beck School of Mathematical Sciences, Queen Mary, University
More informationEnvironmental Atmospheric Turbulence at Florence Airport
Environmental Atmospheric Turbulence at Florence Airport Salvo Rizzo, and Andrea Rapisarda ENAV S.p.A. U.A.A.V Firenze, Dipartimento di Fisica e Astronomia and Infn sezione di Catania, Università di Catania,
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 24 May 2000
arxiv:cond-mat/0005408v1 [cond-mat.stat-mech] 24 May 2000 Non-extensive statistical mechanics approach to fully developed hydrodynamic turbulence Christian Beck School of Mathematical Sciences, Queen Mary
More informationarxiv:physics/ v1 [physics.flu-dyn] 28 Feb 2003
Experimental Lagrangian Acceleration Probability Density Function Measurement arxiv:physics/0303003v1 [physics.flu-dyn] 28 Feb 2003 N. Mordant, A. M. Crawford and E. Bodenschatz Laboratory of Atomic and
More informationarxiv: v1 [cond-mat.stat-mech] 6 Mar 2008
CD2dBS-v2 Convergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models Burhan Bakar and Ugur Tirnakli Department of Physics, Faculty of Science, Ege University, 35100 Izmir, Turkey
More informationIn Situ Comparisons with the Cloud Radar Retrievals of Stratus Cloud Effective Radius
In Situ Comparisons with the Cloud Radar Retrievals of Stratus Cloud Effective Radius A. S. Frisch and G. Feingold Cooperative Institute for Research in the Atmosphere National Oceanic and Atmospheric
More informationLogarithmic scaling in the near-dissipation range of turbulence
PRAMANA c Indian Academy of Sciences Vol. 64, No. 3 journal of March 2005 physics pp. 315 321 Logarithmic scaling in the near-dissipation range of turbulence K R SREENIVASAN 1 and A BERSHADSKII 1,2 1 The
More informationarxiv:cond-mat/ v2 28 Jan 2002
Multifractal nature of stock exchange prices M. Ausloos 1 and K. Ivanova 2 arxiv:cond-mat/0108394v2 28 Jan 2002 1 SUPRAS and GRASP, B5, University of Liège, B-4000 Liège, Euroland 2 Pennsylvania State
More informationWind and turbulence experience strong gradients in vegetation. How do we deal with this? We have to predict wind and turbulence profiles through the
1 2 Wind and turbulence experience strong gradients in vegetation. How do we deal with this? We have to predict wind and turbulence profiles through the canopy. 3 Next we discuss turbulence in the canopy.
More informationarxiv:cond-mat/ v1 3 Aug 2001
Some Statistical Physics Approaches for Trends and Predictions in Meteorology Kristinka Ivanova 1, Marcel Ausloos 2, Thomas Ackerman 3, Hampton Shirer 1, and Eugene Clothiaux 1 arxiv:cond-mat/0108056v1
More informationPassive Scalars in Stratified Turbulence
GEOPHYSICAL RESEARCH LETTERS, VOL.???, XXXX, DOI:10.1029/, Passive Scalars in Stratified Turbulence G. Brethouwer Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden E. Lindborg Linné Flow Centre,
More informationarxiv: v1 [cond-mat.stat-mech] 3 Apr 2007
A General Nonlinear Fokker-Planck Equation and its Associated Entropy Veit Schwämmle, Evaldo M. F. Curado, Fernando D. Nobre arxiv:0704.0465v1 [cond-mat.stat-mech] 3 Apr 2007 Centro Brasileiro de Pesquisas
More informationPassive scalars in stratified turbulence
GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L06809, doi:10.1029/2007gl032906, 2008 Passive scalars in stratified turbulence G. Brethouwer 1 and E. Lindborg 1 Received 5 December 2007; accepted 29 February 2008;
More informationRepresenting intermittency in turbulent fluxes: An application to the stable atmospheric boundary layer
Physica A 354 (25) 88 94 www.elsevier.com/locate/physa Representing intermittency in turbulent fluxes: An application to the stable atmospheric boundary layer Haroldo F. Campos Velho a,, Reinaldo R. Rosa
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 1 Aug 2001
Financial Market Dynamics arxiv:cond-mat/0108017v1 [cond-mat.stat-mech] 1 Aug 2001 Fredrick Michael and M.D. Johnson Department of Physics, University of Central Florida, Orlando, FL 32816-2385 (May 23,
More informationLogarithmically modified scaling of temperature structure functions in thermal convection
EUROPHYSICS LETTERS 1 January 2005 Europhys. Lett., 69 (1), pp. 75 80 (2005) DOI: 10.1209/epl/i2004-10373-4 Logarithmically modified scaling of temperature structure functions in thermal convection A.
More informationLagrangian intermittency in drift-wave turbulence. Wouter Bos
Lagrangian intermittency in drift-wave turbulence Wouter Bos LMFA, Ecole Centrale de Lyon, Turbulence & Stability Team Acknowledgments Benjamin Kadoch, Kai Schneider, Laurent Chevillard, Julian Scott,
More informationDimensionality influence on energy, enstrophy and passive scalar transport.
Dimensionality influence on energy, enstrophy and passive scalar transport. M. Iovieno, L. Ducasse, S. Di Savino, L. Gallana, D. Tordella 1 The advection of a passive substance by a turbulent flow is important
More informationHow the Nonextensivity Parameter Affects Energy Fluctuations. (Received 10 October 2013, Accepted 7 February 2014)
Regular Article PHYSICAL CHEMISTRY RESEARCH Published by the Iranian Chemical Society www.physchemres.org info@physchemres.org Phys. Chem. Res., Vol. 2, No. 2, 37-45, December 204. How the Nonextensivity
More informationarxiv:cond-mat/ v1 8 Jan 2004
Multifractality and nonextensivity at the edge of chaos of unimodal maps E. Mayoral and A. Robledo arxiv:cond-mat/0401128 v1 8 Jan 2004 Instituto de Física, Universidad Nacional Autónoma de México, Apartado
More informationMulti-Scale Modeling of Turbulence and Microphysics in Clouds. Steven K. Krueger University of Utah
Multi-Scale Modeling of Turbulence and Microphysics in Clouds Steven K. Krueger University of Utah 10,000 km Scales of Atmospheric Motion 1000 km 100 km 10 km 1 km 100 m 10 m 1 m 100 mm 10 mm 1 mm Planetary
More informationPeter Molnar 1 and Paolo Burlando Institute of Environmental Engineering, ETH Zurich, Switzerland
Hydrology Days 6 Seasonal and regional variability in scaling properties and correlation structure of high resolution precipitation data in a highly heterogeneous mountain environment (Switzerland) Peter
More informationThe applications of Complexity Theory and Tsallis Non-extensive Statistics at Space Plasma Dynamics
The applications of Complexity Theory and Tsallis Non-extensive Statistics at Space Plasma Dynamics Thessaloniki, Greece Thusday 30-6-2015 George P. Pavlos Democritus University of Thrace Department of
More informationReynolds Averaging. Let u and v be two flow variables (which might or might not be velocity components), and suppose that. u t + x uv ( ) = S u,
! Revised January 23, 208 7:7 PM! Reynolds Averaging David Randall Introduction It is neither feasible nor desirable to consider in detail all of the small-scale fluctuations that occur in the atmosphere.
More informationJ12.4 SIGNIFICANT IMPACT OF AEROSOLS ON MULTI-YEAR RAIN FREQUENCY AND CLOUD THICKNESS
J12.4 SIGNIFICANT IMPACT OF AEROSOLS ON MULTI-YEAR RAIN FREQUENCY AND CLOUD THICKNESS Zhanqing Li and F. Niu* University of Maryland College park 1. INTRODUCTION Many observational studies of aerosol indirect
More informationScaling properties of fine resolution point rainfall and inferences for its stochastic modelling
European Geosciences Union General Assembly 7 Vienna, Austria, 5 April 7 Session NP.: Geophysical extremes: Scaling aspects and modern statistical approaches Scaling properties of fine resolution point
More informationTsallis non - Extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar Flares dynamics
Tsallis non - Extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar Flares dynamics L.P. Karakatsanis [1], G.P. Pavlos [1] M.N. Xenakis [2] [1] Department of
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 15 Jan 2003
arxiv:cond-mat/31268v1 [cond-mat.stat-mech] 15 Jan 23 Deterministic and stochastic influences on Japan and US stock and foreign exchange markets. A Fokker-Planck approach Kristinka Ivanova 1, Marcel Ausloos
More informationarxiv:nlin/ v1 [nlin.cd] 29 Jan 2004
Clusterization and intermittency of temperature fluctuations in turbulent convection A. Bershadskii 1,2, J.J. Niemela 1, A. Praskovsky 3 and K.R. Sreenivasan 1 1 International Center for Theoretical Physics,
More informationarxiv:cond-mat/ v1 [cond-mat.dis-nn] 3 Apr 2002
arxiv:cond-mat/0204076v1 [cond-mat.dis-nn] 3 Apr 2002 In: M. Suzuki and N. Kawashima (eds.) Coherent Approaches to Fluctuations (Proc. Hayashibara Forum 95), pp. 59-64, World Scientific (singapore, 1995).
More informationPARCWAPT Passive Radiometry Cloud Water Profiling Technique
PARCWAPT Passive Radiometry Cloud Water Profiling Technique By: H. Czekala, T. Rose, Radiometer Physics GmbH, Germany A new cloud liquid water profiling technique by Radiometer Physics GmbH (patent pending)
More informationAPPLICATIONS WITH METEOROLOGICAL SATELLITES. W. Paul Menzel. Office of Research and Applications NOAA/NESDIS University of Wisconsin Madison, WI
APPLICATIONS WITH METEOROLOGICAL SATELLITES by W. Paul Menzel Office of Research and Applications NOAA/NESDIS University of Wisconsin Madison, WI July 2004 Unpublished Work Copyright Pending TABLE OF CONTENTS
More informationSuperstatistics and temperature fluctuations. F. Sattin 1. Padova, Italy
Superstatistics and temperature fluctuations F Sattin 1 Padova, Italy Abstract Superstatistics [C Beck and EGD Cohen, Physica A 322, 267 (2003)] is a formalism aimed at describing statistical properties
More informationANALYSIS AND SIMULATIONS OF MULTIFRACTAL RANDOM WALKS. F. G. Schmitt, Y. Huang
3rd European Signal Processing Conference (EUSIPCO) ANALYSIS AND SIMULATIONS OF MULTIFRACTAL RANDOM WALKS F. G. Schmitt, Y. Huang CNRS Lab of Oceanology and Geosciences UMR LOG, 8 av Foch 693 Wimereux,
More informationarxiv:cond-mat/ v1 10 Aug 2002
Model-free derivations of the Tsallis factor: constant heat capacity derivation arxiv:cond-mat/0208205 v1 10 Aug 2002 Abstract Wada Tatsuaki Department of Electrical and Electronic Engineering, Ibaraki
More informationShortwave spectral radiative forcing of cumulus clouds from surface observations
GEOPHYSICAL RESEARCH LETTERS, VOL. 38,, doi:10.1029/2010gl046282, 2011 Shortwave spectral radiative forcing of cumulus clouds from surface observations E. Kassianov, 1 J. Barnard, 1 L. K. Berg, 1 C. N.
More informationScaling properties of fine resolution point rainfall and inferences for its stochastic modelling
European Geosciences Union General Assembly 7 Vienna, Austria, 5 April 7 Session NP3.4: Geophysical extremes: Scaling aspects and modern statistical approaches Scaling properties of fine resolution point
More informationarxiv: v1 [q-fin.st] 5 Apr 2007
Stock market return distributions: from past to present S. Drożdż 1,2, M. Forczek 1, J. Kwapień 1, P. Oświȩcimka 1, R. Rak 2 arxiv:0704.0664v1 [q-fin.st] 5 Apr 2007 1 Institute of Nuclear Physics, Polish
More informationLocality of Energy Transfer
(E) Locality of Energy Transfer See T & L, Section 8.2; U. Frisch, Section 7.3 The Essence of the Matter We have seen that energy is transferred from scales >`to scales
More informationOn the (multi)scale nature of fluid turbulence
On the (multi)scale nature of fluid turbulence Kolmogorov axiomatics Laurent Chevillard Laboratoire de Physique, ENS Lyon, CNRS, France Laurent Chevillard, Laboratoire de Physique, ENS Lyon, CNRS, France
More informationarxiv: v1 [nlin.cd] 22 Feb 2011
Generalising the logistic map through the q-product arxiv:1102.4609v1 [nlin.cd] 22 Feb 2011 R W S Pessoa, E P Borges Escola Politécnica, Universidade Federal da Bahia, Rua Aristides Novis 2, Salvador,
More information1/f Fluctuations from the Microscopic Herding Model
1/f Fluctuations from the Microscopic Herding Model Bronislovas Kaulakys with Vygintas Gontis and Julius Ruseckas Institute of Theoretical Physics and Astronomy Vilnius University, Lithuania www.itpa.lt/kaulakys
More informationarxiv:chao-dyn/ v1 5 Mar 1996
Turbulence in Globally Coupled Maps M. G. Cosenza and A. Parravano Centro de Astrofísica Teórica, Facultad de Ciencias, Universidad de Los Andes, A. Postal 26 La Hechicera, Mérida 5251, Venezuela (To appear,
More informationISSN Article. Tsallis Entropy, Escort Probability and the Incomplete Information Theory
Entropy 2010, 12, 2497-2503; doi:10.3390/e12122497 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Tsallis Entropy, Escort Probability and the Incomplete Information Theory Amir
More informationStatistics of wind direction and its increments
PHYSICS OF FLUIDS VOLUME 12, NUMBER 6 JUNE 2000 Statistics of wind direction and its increments Eric van Doorn, Brindesh Dhruva, and Katepalli R. Sreenivasan a) Mason Laboratory, Yale University, New Haven,
More informationPreferred spatio-temporal patterns as non-equilibrium currents
Preferred spatio-temporal patterns as non-equilibrium currents Escher Jeffrey B. Weiss Atmospheric and Oceanic Sciences University of Colorado, Boulder Arin Nelson, CU Baylor Fox-Kemper, Brown U Royce
More informationStatistical studies of turbulent flows: self-similarity, intermittency, and structure visualization
Statistical studies of turbulent flows: self-similarity, intermittency, and structure visualization P.D. Mininni Departamento de Física, FCEyN, UBA and CONICET, Argentina and National Center for Atmospheric
More informationThreshold radar reflectivity for drizzling clouds
Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L03807, doi:10.1029/2007gl031201, 2008 Threshold radar reflectivity for drizzling clouds Yangang Liu, 1 Bart Geerts, 2 Mark Miller, 2
More informationPower law distribution of Rényi entropy for equilibrium systems having nonadditive energy
arxiv:cond-mat/0304146v1 [cond-mat.stat-mech] 7 Apr 2003 Power law distribution of Rényi entropy for equilibrium systems having nonadditive energy Qiuping A. Wang Institut Supérieur des Matériaux du Mans,
More informationLecture 2. Turbulent Flow
Lecture 2. Turbulent Flow Note the diverse scales of eddy motion and self-similar appearance at different lengthscales of this turbulent water jet. If L is the size of the largest eddies, only very small
More informationA Longwave Broadband QME Based on ARM Pyrgeometer and AERI Measurements
A Longwave Broadband QME Based on ARM Pyrgeometer and AERI Measurements Introduction S. A. Clough, A. D. Brown, C. Andronache, and E. J. Mlawer Atmospheric and Environmental Research, Inc. Cambridge, Massachusetts
More informationComparison of Convection Characteristics at the Tropical Western Pacific Darwin Site Between Observation and Global Climate Models Simulations
Comparison of Convection Characteristics at the Tropical Western Pacific Darwin Site Between Observation and Global Climate Models Simulations G.J. Zhang Center for Atmospheric Sciences Scripps Institution
More informationThe Importance of Three-Dimensional Solar Radiative Transfer in Small Cumulus Cloud Fields Derived
The Importance of Three-Dimensional Solar Radiative Transfer in Small Cumulus Cloud Fields Derived from the Nauru MMCR and MWR K. Franklin Evans, Sally A. McFarlane University of Colorado Boulder, CO Warren
More informationFractal interpolation of rain rate time series
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi:10.1029/2004jd004717, 2004 Fractal interpolation of rain rate time series Kevin S. Paulson Radio Communications Research Unit, Rutherford Appleton Laboratory,
More informationNote the diverse scales of eddy motion and self-similar appearance at different lengthscales of the turbulence in this water jet. Only eddies of size
L Note the diverse scales of eddy motion and self-similar appearance at different lengthscales of the turbulence in this water jet. Only eddies of size 0.01L or smaller are subject to substantial viscous
More informationPower law distribution of Rényi entropy for equilibrium systems having nonadditive energy
arxiv:cond-mat/030446v5 [cond-mat.stat-mech] 0 May 2003 Power law distribution of Rényi entropy for equilibrium systems having nonadditive energy Qiuping A. Wang Institut Supérieur des Matériaux du Mans,
More informationINVERSE FRACTAL STATISTICS IN TURBULENCE AND FINANCE
International Journal of Modern Physics B Vol. 17, Nos. 22, 23 & 24 (2003) 4003 4012 c World Scientific Publishing Company INVERSE FRACTAL STATISTICS IN TURBULENCE AND FINANCE MOGENS H. JENSEN, ANDERS
More informationChristian Sutton. Microwave Water Radiometer measurements of tropospheric moisture. ATOC 5235 Remote Sensing Spring 2003
Christian Sutton Microwave Water Radiometer measurements of tropospheric moisture ATOC 5235 Remote Sensing Spring 23 ABSTRACT The Microwave Water Radiometer (MWR) is a two channel microwave receiver used
More informationInstrument Cross-Comparisons and Automated Quality Control of Atmospheric Radiation Measurement Data
Instrument Cross-Comparisons and Automated Quality Control of Atmospheric Radiation Measurement Data S. Moore and G. Hughes ATK Mission Research Santa Barbara, California Introduction Within the Atmospheric
More informationOn the statistics of wind gusts
On the statistics of wind gusts F. Boettcher, Ch. Renner, H.-P. Waldl and J. Peinke Department of Physics, University of Oldenburg, D-26111 Oldenburg, Germany Phone: +49 (0)441 798-3007 +49 (0)441 798-3536
More informationImage thresholding using Tsallis entropy
Pattern Recognition Letters 25 (2004) 1059 1065 www.elsevier.com/locate/patrec Image thresholding using Tsallis entropy M. Portes de Albuquerque a, *, I.A. Esquef b, A.R. Gesualdi Mello a, M. Portes de
More informationInvestigating anomalous absorption using surface measurements
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D24, 4761, doi:10.1029/2003jd003411, 2003 Investigating anomalous absorption using surface measurements M. Sengupta 1 and T. P. Ackerman Pacific Northwest
More informationThe weather and climate as problems in physics: scale invariance and multifractals. S. Lovejoy McGill, Montreal
The weather and climate as problems in physics: scale invariance and multifractals S. Lovejoy McGill, Montreal McGill April 13, 2012 Required reading for this course The Weather and Climate Emergent Laws
More informationPower-law behaviors from the two-variable Langevin equation: Ito s and Stratonovich s Fokker-Planck equations. Guo Ran, Du Jiulin *
arxiv:22.3980 Power-law behaviors from the two-variable Langevin equation: Ito s and Stratonovich s Fokker-Planck equations Guo Ran, Du Jiulin * Department of Physics, School of Science, Tianjin University,
More informationLagrangian particle statistics in turbulent flows from a simple vortex model
PHYSICAL REVIEW E 77, 05630 2008 Lagrangian particle statistics in turbulent flows from a simple vortex model M. Wilczek,, * F. Jenko, 2 and R. Friedrich Institute for Theoretical Physics, University of
More informationPreferential concentration of inertial particles in turbulent flows. Jérémie Bec CNRS, Observatoire de la Côte d Azur, Université de Nice
Preferential concentration of inertial particles in turbulent flows Jérémie Bec CNRS, Observatoire de la Côte d Azur, Université de Nice EE250, Aussois, June 22, 2007 Particle laden flows Warm clouds Plankton
More informationIntermittency in two-dimensional turbulence with drag
Intermittency in two-dimensional turbulence with drag Yue-Kin Tsang, 1,2 Edward Ott, 1,2,3 Thomas M. Antonsen, Jr., 1,2,3 and Parvez N. Guzdar 2 1 Department of Physics, University of Maryland, College
More informationFragmentation under the scaling symmetry and turbulent cascade with intermittency
Center for Turbulence Research Annual Research Briefs 23 197 Fragmentation under the scaling symmetry and turbulent cascade with intermittency By M. Gorokhovski 1. Motivation and objectives Fragmentation
More informationBuoyancy Fluxes in a Stratified Fluid
27 Buoyancy Fluxes in a Stratified Fluid G. N. Ivey, J. Imberger and J. R. Koseff Abstract Direct numerical simulations of the time evolution of homogeneous stably stratified shear flows have been performed
More informationPALM - Cloud Physics. Contents. PALM group. last update: Monday 21 st September, 2015
PALM - Cloud Physics PALM group Institute of Meteorology and Climatology, Leibniz Universität Hannover last update: Monday 21 st September, 2015 PALM group PALM Seminar 1 / 16 Contents Motivation Approach
More informationMultifractals and Wavelets in Turbulence Cargese 2004
Multifractals and Wavelets in Turbulence Cargese 2004 Luca Biferale Dept. of Physics, University of Tor Vergata, Rome. INFN-INFM biferale@roma2.infn.it Report Documentation Page Form Approved OMB No. 0704-0188
More informationEXACT SOLUTIONS TO THE NAVIER-STOKES EQUATION FOR AN INCOMPRESSIBLE FLOW FROM THE INTERPRETATION OF THE SCHRÖDINGER WAVE FUNCTION
EXACT SOLUTIONS TO THE NAVIER-STOKES EQUATION FOR AN INCOMPRESSIBLE FLOW FROM THE INTERPRETATION OF THE SCHRÖDINGER WAVE FUNCTION Vladimir V. KULISH & José L. LAGE School of Mechanical & Aerospace Engineering,
More informationGeneralized Huberman-Rudnick scaling law and robustness of q-gaussian probability distributions. Abstract
Generalized Huberman-Rudnick scaling law and robustness of q-gaussian probability distributions Ozgur Afsar 1, and Ugur Tirnakli 1,2, 1 Department of Physics, Faculty of Science, Ege University, 35100
More informationTurbulent velocity fluctuations need not be Gaussian
J. Fluid Mech. (1998), vol. 376, pp. 139 147. Printed in the United Kingdom c 1998 Cambridge University Press 139 Turbulent velocity fluctuations need not be Gaussian By JAVIER JIMÉNEZ School of Aeronautics,
More informationEffects of Forcing Scheme on the Flow and the Relative Motion of Inertial Particles in DNS of Isotropic Turbulence
Effects of Forcing Scheme on the Flow and the Relative Motion of Inertial Particles in DNS of Isotropic Turbulence Rohit Dhariwal PI: Sarma L. Rani Department of Mechanical and Aerospace Engineering The
More informationStability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: A basis for q-exponential distributions
PHYSICAL REVIE E 66, 4634 22 Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: A basis for -exponential distributions Sumiyoshi Abe Institute of Physics, University
More informationScale-free network of earthquakes
Scale-free network of earthquakes Sumiyoshi Abe 1 and Norikazu Suzuki 2 1 Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan 2 College of Science and Technology, Nihon University, Chiba
More informationLocal flow structure and Reynolds number dependence of Lagrangian statistics in DNS of homogeneous turbulence. P. K. Yeung
Local flow structure and Reynolds number dependence of Lagrangian statistics in DNS of homogeneous turbulence P. K. Yeung Georgia Tech, USA; E-mail: pk.yeung@ae.gatech.edu B.L. Sawford (Monash, Australia);
More information6A.3 Stably stratified boundary layer simulations with a non-local closure model
6A.3 Stably stratified boundary layer simulations with a non-local closure model N. M. Colonna, E. Ferrero*, Dipartimento di Scienze e Tecnologie Avanzate, University of Piemonte Orientale, Alessandria,
More informationFlow Complexity, Multiscale Flows, and Turbulence
Invited Paper for 2006 WSEAS/IASME International Conference on Fluid Mechanics Miami, FL, January 18-20, 2006 Flow Complexity, Multiscale Flows, and Turbulence Haris J. Catrakis Iracletos Flow Dynamics
More informationCritical phenomena in atmospheric precipitation Supplementary Information
Critical phenomena in atmospheric precipitation Supplementary Information Ole Peters and J. David Neelin Contents Supplementary Figures and Legends See sections in which supplementary figures are referenced.
More informationarxiv:chao-dyn/ v1 30 Jan 1997
Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing Yoshiki Kuramoto and Hiroya Nakao arxiv:chao-dyn/9701027v1 30 Jan 1997 Department of Physics,
More informationConvective scheme and resolution impacts on seasonal precipitation forecasts
GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 20, 2078, doi:10.1029/2003gl018297, 2003 Convective scheme and resolution impacts on seasonal precipitation forecasts D. W. Shin, T. E. LaRow, and S. Cocke Center
More informationAn Introduction to Theories of Turbulence. James Glimm Stony Brook University
An Introduction to Theories of Turbulence James Glimm Stony Brook University Topics not included (recent papers/theses, open for discussion during this visit) 1. Turbulent combustion 2. Turbulent mixing
More informationarxiv: v2 [cond-mat.stat-mech] 6 Jun 2010
Chaos in Sandpile Models Saman Moghimi-Araghi and Ali Mollabashi Physics department, Sharif University of Technology, P.O. Box 55-96, Tehran, Iran We have investigated the weak chaos exponent to see if
More informationCascades and statistical equilibrium in shell models of turbulence
PHYSICAL REVIEW E VOLUME 53, UMBER 5 MAY 1996 Cascades and statistical equilibrium in shell models of turbulence P. D. Ditlevsen and I. A. Mogensen The iels Bohr Institute, Department for Geophysics, University
More informationSimultaneously retrieving cloud optical depth and effective radius for optically thin clouds
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110,, doi:10.1029/2005jd006136, 2005 Simultaneously retrieving cloud optical depth and effective radius for optically thin clouds Qilong Min and Minzheng Duan Atmospheric
More informationSmall-Scale Drop-Size Variability: Empirical Models for Drop-Size-Dependent Clustering in Clouds
FEBRUARY 2005 M A R S H A K E T A L. 551 Small-Scale Drop-Size Variability: Empirical Models for Drop-Size-Dependent Clustering in Clouds ALEXANDER MARSHAK Climate and Radiation Branch, NASA Goddard Space
More informationOn the Asymptotic Convergence. of the Transient and Steady State Fluctuation Theorems. Gary Ayton and Denis J. Evans. Research School Of Chemistry
1 On the Asymptotic Convergence of the Transient and Steady State Fluctuation Theorems. Gary Ayton and Denis J. Evans Research School Of Chemistry Australian National University Canberra, ACT 0200 Australia
More informationSpatio-temporal multifractal comparison of 4 rainfall events at various locations: radar data and meso-scale simulations
Spatio-temporal multifractal comparison of 4 rainfall events at various locations: radar data and meso-scale simulations A Gires 1, I. Tchiguirinskaia 1, D. Schertzer 1, S. Lovejoy 2 1 LEESU, Ecole des
More informationDiurnal cycles of precipitation, clouds, and lightning in the tropics from 9 years of TRMM observations
GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L04819, doi:10.1029/2007gl032437, 2008 Diurnal cycles of precipitation, clouds, and lightning in the tropics from 9 years of TRMM observations Chuntao Liu 1 and Edward
More informationChapter 2 Analysis of Solar Radiation Time Series
Chapter 2 Analysis of Solar Radiation Time Series Abstract In this chapter, various kinds of analysis are performed by using solar radiation time series recorded at 12 stations of the NREL database. Analysis
More informationEffects of Forcing Scheme on the Flow and the Relative Motion of Inertial Particles in DNS of Isotropic Turbulence
Effects of Forcing Scheme on the Flow and the Relative Motion of Inertial Particles in DNS of Isotropic Turbulence Rohit Dhariwal and Vijaya Rani PI: Sarma L. Rani Department of Mechanical and Aerospace
More informationNew Technique for Retrieving Liquid Water Path over Land using Satellite Microwave Observations
New Technique for Retrieving Liquid Water Path over Land using Satellite Microwave Observations M.N. Deeter and J. Vivekanandan Research Applications Library National Center for Atmospheric Research Boulder,
More informationTheoretical Advances on Generalized Fractals with Applications to Turbulence
Proceedings of the 5th IASME / WSEAS International Conference on Fluid Mechanics and Aerodynamics, Athens, Greece, August 25-27, 2007 288 2007 IASME/WSEAS 5 th International Conference on Fluid Mechanics
More information3-Fold Decomposition EFB Closure for Convective Turbulence and Organized Structures
3-Fold Decomposition EFB Closure for Convective Turbulence and Organized Structures Igor ROGACHEVSKII and Nathan KLEEORIN Ben-Gurion University of the Negev, Beer-Sheva, Israel N.I. Lobachevsky State University
More informationOn the Interpretation of Shortwave Albedo-Transmittance Plots
On the Interpretation of Shortwave Albedo-Transmittance Plots H. W. Barker Atmospheric Environment Service of Canada Downsview, Ontario, Canada Z. Li Canada Centre for Remote Sensing Ottawa, Canada Abstract
More informationModeling by the nonlinear stochastic differential equation of the power-law distribution of extreme events in the financial systems
Modeling by the nonlinear stochastic differential equation of the power-law distribution of extreme events in the financial systems Bronislovas Kaulakys with Miglius Alaburda, Vygintas Gontis, A. Kononovicius
More information