scholarly journals A strong statistical link between aerosol indirect effects and the self-similarity of rainfall distributions

2021 ◽  
Author(s):  
Kalli Furtado ◽  
Paul Field
Keyword(s):  
Indirect Effects ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Cloud Droplet ◽  
Aerosol Concentration ◽  
The Self ◽  
Rainfall Distribution ◽  
Aerosol Indirect Effects ◽  
Self Similar ◽  
Similar Density

Abstract. We use convective-scale simulations of monsoonal clouds to reveal a self-similar probability density function that underpins surface rainfall statistics. This density is independent of cloud-droplet number concentration and is unchanged by aerosol perturbations. It therefore represents an invariant property of our model with respect to cloud-aerosol interactions. For a given aerosol concentration, if the dependence of at least one moment of the rainfall distribution on cloud-droplet number is a known input parameter, then the self-similar density can be used to reconstruct the entire rainfall distribution to a useful degree of accuracy. In particular, we present both single-moment and double-moment reconstructions that are able to predict the responses of the rainfall distributions to changes in aerosol concentration. In doing so we show that the seemingly high-dimensional space of possible aerosol-induced rainfall-distribution transformations can be parametrized by a surprisingly small (at most three) independent “degrees of freedom”: the self-similar density, and auxiliary information about two moments of the rainfall distribution. This suggests that, although aerosol-indirect effects on any specific hydro-meteorological system may be multifarious in terms of rainfall changes and physical mechanisms, there may, nevertheless, be a universal constraint on the number of independent degrees of freedom needed to represent the dependencies of rainfall on aerosols.

scholarly journals Investigation of aerosol indirect effects on monsoon clouds using ground-based measurements over a high-altitude site in Western Ghats

2016 ◽  
Author(s):  
V. Anil Kumar ◽  
G. Pandithurai ◽  
P. P. Leena ◽  
K. K. Dani ◽  
P. Murugavel ◽  
...  
Keyword(s):  
High Altitude ◽  
Indirect Effects ◽  
Cloud Droplet ◽  
Droplet Size Distribution ◽  
Liquid Water Content ◽  
Number Concentration ◽  
Effective Radius ◽  
Aerosol Indirect Effects ◽  
Cloud Droplet Number Concentration ◽  
Aerosol Effects

Abstract. The effect of aerosols on cloud droplet number concentration and droplet effective radius are investigated from ground-based measurements over a high-altitude site where in clouds pass over the surface. First aerosol indirect effect AIE estimates were made using i) relative changes in cloud droplet number concentration (AIEn) and ii) relative changes in droplet effective radius (AIEs) with relative changes in aerosol for different LWC values. AIE estimates from two different methods reveal that there is systematic overestimation in AIEn as compared to that of AIEs. Aerosol indirect effects (AIEn and AIEs) and Dispersion effect (DE) at different liquid water content (LWC) regimes ranging from 0.05 to 0.50 gm-3 were estimated. The analysis demonstrates that there is overestimation of AIEn as compared to AIEs which is mainly due to DE. Aerosol effects on spectral dispersion in droplet size distribution plays an important role in altering Twomey’s cooling effect and thereby changes in climate. This study shows that the higher DE in the medium LWC regime which offsets the AIE by 30%.

Aerosol Indirect Effects in Marine Stratocumulus: The Importance of Explicitly Predicting Cloud Droplet Activation

2019 ◽  
Vol 46 (6) ◽  
pp. 3473-3481 ◽  
Author(s):  
I. Bulatovic ◽  
A. M. L. Ekman ◽  
J. Savre ◽  
I. Riipinen ◽  
C. Leck
Keyword(s):  
Indirect Effects ◽  
Cloud Droplet ◽  
Marine Stratocumulus ◽  
Aerosol Indirect Effects ◽  
Droplet Activation

scholarly journals Investigation of aerosol indirect effects on monsoon clouds using ground-based measurements over a high-altitude site in Western Ghats

2016 ◽  
Vol 16 (13) ◽  
pp. 8423-8430 ◽  
Author(s):  
Vasudevan Anil Kumar ◽  
Govindan Pandithurai ◽  
Parakkatt Parambil Leena ◽  
Kundan K. Dani ◽  
Palani Murugavel ◽  
...  
Keyword(s):  
High Altitude ◽  
Indirect Effects ◽  
Cloud Droplet ◽  
Droplet Size Distribution ◽  
Number Concentration ◽  
Effective Radius ◽  
Aerosol Indirect Effects ◽  
Spectral Dispersion ◽  
Cloud Droplet Number Concentration ◽  
Aerosol Effects

Abstract. The effect of aerosols on cloud droplet number concentration and droplet effective radius is investigated from ground-based measurements over a high-altitude site where clouds pass over the surface. First aerosol indirect effect (AIE) estimates were made using (i) relative changes in cloud droplet number concentration (AIEn) and (ii) relative changes in droplet effective radius (AIEs) with relative changes in aerosol for different cloud liquid water contents (LWCs). AIE estimates from two different methods reveal that there is systematic overestimation in AIEn as compared to that of AIEs. Aerosol indirect effects (AIEn and AIEs) and dispersion effect (DE) at different LWC regimes ranging from 0.05 to 0.50 g m−3 were estimated. The analysis demonstrates that there is overestimation of AIEn as compared to AIEs, which is mainly due to DE. Aerosol effects on spectral dispersion in droplet size distribution play an important role in altering Twomey's cooling effect and thereby changes in climate. This study shows that the higher DE in the medium LWC regime offsets the AIE by 30 %.

Cancellation of Aerosol Indirect Effects in Marine Stratocumulus through Cloud Thinning

2007 ◽  
Vol 64 (7) ◽  
pp. 2657-2669 ◽  
Author(s):  
Robert Wood
Keyword(s):  
Time Scales ◽  
Environmental Conditions ◽  
Indirect Effects ◽  
Marine Boundary Layer ◽  
Cloud Condensation Nuclei ◽  
Cloud Droplet ◽  
Cloud Base ◽  
Aerosol Indirect Effects ◽  
Surface Precipitation ◽  
Cloud Thickness

Abstract Applying perturbation theory within a mixed layer framework, the response of the marine boundary layer (MBL) cloud thickness h to imposed increases of the cloud droplet concentration Nd as a surrogate for increases in cloud condensation nuclei (CCN) concentrations is examined. An analytical formulation is used to quantify the response and demonstrate theoretically that for the range of environmental conditions found over the subtropical eastern oceans, on time scales of less than a day, the cloud thickness feedback response is largely determined by a balance between the moistening/cooling of the MBL resulting from the suppression of surface precipitation, and the drying/warming resulting from enhanced entrainment resulting from increased turbulent kinetic energy. Quantifying the transient cloud response as a ratio of the second to the first indirect effects demonstrates that the nature of the feedback is critically dependent upon the nature of the unperturbed state, with the cloud-base height zcb being the single most important determinant. For zcb < 400 m, increasing Nd leads to cloud thickening in accordance with the Albrecht hypothesis. However, for zcb > 400 m, cloud thinning occurs, which results in a feedback effect that increasingly cancels the Twomey effect as zcb increases. The environmental conditions favoring an elevated cloud base are relatively weak lower-tropospheric stability and a dry free troposphere, although the former is probably more important over the subtropical eastern oceans. On longer time scales an invariable thickening response is found, and thus accurate quantification of the aerosol indirect effects will require a good understanding of the processes that control the time scale over which aerosol perturbations are modified.

scholarly journals Influence of Turbulent Fluctuations on Cloud Droplet Size Dispersion and Aerosol Indirect Effects

2018 ◽  
Vol 75 (9) ◽  
pp. 3191-3209 ◽  
Author(s):  
K. K. Chandrakar ◽  
W. Cantrell ◽  
R. A. Shaw
Keyword(s):  
Droplet Size ◽  
Indirect Effects ◽  
Stochastic Theory ◽  
Cloud Droplet ◽  
Droplet Size Distribution ◽  
Cloud Chamber ◽  
Relative Dispersion ◽  
Number Density ◽  
Aerosol Indirect Effects ◽  
Removal Time

Abstract Cloud droplet relative dispersion, defined as the standard deviation over the mean cloud droplet size, is of central importance in determining and understanding aerosol indirect effects. In recent work, it was found that cloud droplet size distributions become broader as a result of supersaturation variability and that the sensitivity of this effect is inversely related to cloud droplet number density. The subject is investigated in further detail using an extensive dataset from a laboratory cloud chamber capable of producing steady-state turbulence. An extended stochastic theory is found to successfully describe properties of the droplet size distribution, including an analytical expression for the relative dispersion. The latter is found to depend on the cloud droplet removal time, which in turn increases with the cloud droplet number density. The results show that relative dispersion decreases monotonically with increasing droplet number density, consistent with some recent atmospheric observations. Experiments spanning fast to slow microphysics regimes are reported. The observed dispersion is used to estimate time scales for autoconversion, demonstrating the important role of the turbulence-induced broadening effect on precipitation development. An initial effort is made to extend the stochastic theory to an atmospheric context with a steady updraft, for which autoconversion time is the controlling factor for droplet lifetime. As in the cloud chamber, relative dispersion is found to increase with decreasing cloud droplet number density.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

scholarly journals Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

2020 ◽  
pp. 1-31
Author(s):  
Balázs Bárány ◽  
Károly Simon ◽  
István Kolossváry ◽  
Michał Rams
Keyword(s):  
Hausdorff Measure ◽  
Similar Case ◽  
Iterated Function Systems ◽  
The Self ◽  
Dimensional Hausdorff Measure ◽  
Assouad Dimension ◽  
Iterated Function ◽  
Self Similar ◽  
Weak Separation ◽  
Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

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