Record-breaking statistics for random walks in the presence of measurement error and noise

We address the question of distance record-setting by a random walker in the presence of measurement error, $\delta$, and additive noise, $\gamma$ and show that the mean number of (upper) records up to $n$ steps still grows universally as $\sim n^{1/2}$ for large $n$ for all jump distributions, including L\'evy flights, and for all $\delta$ and $\gamma$. In contrast to the universal growth exponent of 1/2, the pace of record setting, measured by the pre-factor of $n^{1/2}$, depends on $\delta$ and $\gamma$. In the absence of noise ($\gamma=0$), the pre-factor $S(\delta)$ is evaluated explicitly for arbitrary jump distributions and it decreases monotonically with increasing $\delta$ whereas, in case of perfect measurement $(\delta=0)$, the corresponding pre-factor $T(\gamma)$ increases with $\gamma$. Our analytical results are supported by extensive numerical simulations and qualitatively similar results are found in two and three dimensions

CALIPSO Observations of Transatlantic Dust: Vertical Stratification and Effect of Clouds

CALIOP nighttime measurements of lidar backscatter, color and depolarization ratios during the summer of 2007 are used to study transatlantic dust properties downwind of Saharan sources, and to examine the interaction of clouds and dust. We discuss the following findings: (1) while lidar backscatter doesn't change much with altitude in the Saharan Air Layer (SAL), depolarization and color ratios both increase with altitude in the SAL; (2) lidar backscatter and color ratio increase as dust is transported westward in the SAL; (3) the vertical lapse rate of dust depolarization ratio increases within SAL as plumes move westward; (4) nearby clouds barely affect the backscatter and color ratio of dust volumes within SAL but not so below SAL. Finally, (5) the odds of CALIOP finding dust below SAL next to clouds are about 2/3 of those far away from clouds. This feature, together with an apparent increase in depolarization ratio near clouds, indicates that particles in some dusty volumes lose asphericity in the humid air near clouds, and cannot be identified by CALIPSO as dust

Global association of aerosol with flash density of intense lightning

A global scale study of the association between aerosol loading and lightning production was conducted, using a full year’s data for 2012 (as well as seasonal data) of the cloud-to-ground lightning record from the world wide lightning location network and aerosol optical depth measured by MODIS. 70% of all grid squares examined and 94% of the statistically significant ones had higher flash densities under polluted conditions than the clean ones. This trend is evident for large continental regions in North, Central and South America, Europe, southern Africa and north-east Australia. A detailed examination of the link to the meteorology was performed for four continental regions: the Amazon, North America, southern Africa and the Maritime Continent. The findings showed a similar trend under different meteorological conditions (defined by subsets of specified CAPE values and pressure velocity at 400 hPa). The results of this study suggest a route to association between aerosol loading and lightning-production rates in thunderclouds

ON REYNOLDS NUMBER DEPENDENCE OF TURBULENCE INTENSITIES IN FREE SHEAR FLOWS (CASCADE, ANISOTROPY).

ON REYNOLDS NUMBER DEPENDENCE OF TURBULENCE INTENSITIES IN FREE SHEAR FLOWS (CASCADE, ANISOTROPY)

Real-time C-band radar observations of 1992 eruption clouds from Crater Peak, Mount Spurr Volcano, Alaska

Repeated aircraft hazards in Alaska related to volcanic clouds have resulted in the use of a mobile C-band radar devoted to volcanic-cloud monitoring. The radar is located at Kenai, in range of several volcanoes in the Cook Inlet area. Three significant eruptions from the Crater Peak vent of Mount Spurr volcano (about 80 km from Kenai) in 1992 provided the first tests of the radar. The system constructs maps of the eruption columns and the drifting ash clouds for short periods (as long as 30 minutes) after eruption. The radar gives direct information about active eruptions in any weather conditions and allows estimates of the altitude of the column, which are useful for three-dimensional trajectory models of ash-cloud transport. It also allows an estimate of the eruption rate based on the ash-column height. However, such estimates may be lower than the true values because the very top of the eruption column, which may not contain coarse ash, may not be detected by the radar. We conclude that the radar detects mainly ash particles, sized from about 1 millimeter to a few centimeters on the basis of three sources-the brief duration of the reflected radar signal, data from independent ground observations on the mass and size of particles which fell out of the reflected cloud, and the intensity of the reflected signal. The most intense reflections come from ash clouds with particles that range from 2 to 20 mm in diameter and with a total particle mass concentration of less than .O1 to 1 g/m3. The data are useful for constructing models of ash columns and deposition of coarse tephra. Radars are not .useful for long-term volcanic cloud tracking because the large ash particles, that provide for strong radar signals fall out soon after an eruption. The radar does not detect smaller

Bounds on Spectral Dispersion from Fermi-Detected Gamma Ray Bursts

Data from four Fermi-detected gamma-ray bursts (GRBs) is used to set limits on spectral dispersion of electromagnetic radiation across the universe. The analysis focuses on photons recorded above 1 GeV for Fermi detected GRB 080916C, GRB 090510A, GRB 090902B, and GRB 090926A because these high-energy photons yield the tightest bounds on light dispersion. It is shown that significant photon bunches in GRB 090510A, possibly classic GRB pulses, are remarkably brief, an order of magnitude shorter in duration than any previously claimed temporal feature in this energy range. Although conceivably a $>3 \sigma$ fluctuation, when taken at face value, these pulses lead to an order of magnitude tightening of prior limits on photon dispersion. Bound of $\Delta c / c < 6.94$ x $10^{-21}$ is thus obtained. Given generic dispersion relations where the time delay is proportional to the photon energy to the first or second power, the most stringent limits on the dispersion strengths were $k_1 <$ 1.61 x $10^{-5}$ sec Gpc$^{-1}$ GeV$^{-1}$ and $k_2 <$ 3.57 x $10^{-7}$ sec Gpc$^{-1}$ GeV$^{-2}$ respectively. Such limits constrain dispersive effects created, for example, by the spacetime foam of quantum gravity. In the context of quantum gravity, our bounds set $M_1 c^2$ greater than 525 times the Planck mass, suggesting that spacetime is smooth at energies near and slightly above the Planck mass.Comment: 4 pages, 1 figure, accepted to PR