Evaluation of seven European aerosol optical depth retrieval algorithms for climate analysis

Satellite data are increasingly used to provide observation-based estimates of the effects of aerosols on climate. The Aerosol-cci project, part of the European Space Agency's Climate Change Initiative (CCI), was designed to provide essential climate variables for aerosols from satellite data. Eight algorithms, developed for the retrieval of aerosol properties using data from AATSR (4), MERIS (3) and POLDER, were evaluated to determine their suitability for climate studies. The primary result from each of these algorithms is the aerosol optical depth (AOD) at several wavelengths, together with the Ångström exponent (AE) which describes the spectral variation of the AOD for a given wavelength pair. Other aerosol parameters which are possibly retrieved from satellite observations are not considered in this paper. The AOD and AE (AE only for Level 2) were evaluated against independent collocated observations from the ground-based AERONET sun photometer network and against “reference” satellite data provided by MODIS and MISR. Tools used for the evaluation were developed for daily products as produced by the retrieval with a spatial resolution of 10 × 10 km2 (Level 2) and daily or monthly aggregates (Level 3). These tools include statistics for L2 and L3 products compared with AERONET, as well as scoring based on spatial and temporal correlations. In this paper we describe their use in a round robin (RR) evaluation of four months of data, one month for each season in 2008. The amount of data was restricted to only four months because of the large effort made to improve the algorithms, and to evaluate the improvement and current status, before larger data sets will be processed. Evaluation criteria are discussed. Results presented show the current status of the European aerosol algorithms in comparison to both AERONET and MODIS and MISR data. The comparison leads to a preliminary conclusion that the scores are similar, including those for the references, but the coverage of AATSR needs to be enhanced and further improvements are possible for most algorithms. None of the algorithms, including the references, outperforms all others everywhere. AATSR data can be used for the retrieval of AOD and AE over land and ocean. PARASOL and one of the MERIS algorithms have been evaluated over ocean only and both algorithms provide good results.

Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

Effects of allometry, productivity and lifestyle on rates and limits of body size evolution

Body size affects nearly all aspects of organismal biology, so it is important to understand the constraints and dynamics of body size evolution. Despite empirical work on the macroevolution and macroecology of minimum and maximum size, there is little general quantitative theory on rates and limits of body size evolution. We present a general theory that integrates individual productivity, the lifestyle component of the slow–fast life-history continuum, and the allometric scaling of generation time to predict a clade's evolutionary rate and asymptotic maximum body size, and the shape of macroevolutionary trajectories during diversifying phases of size evolution. We evaluate this theory using data on the evolution of clade maximum body sizes in mammals during the Cenozoic. As predicted, clade evolutionary rates and asymptotic maximum sizes are larger in more productive clades (e.g. baleen whales), which represent the fast end of the slow–fast lifestyle continuum, and smaller in less productive clades (e.g. primates). The allometric scaling exponent for generation time fundamentally alters the shape of evolutionary trajectories, so allometric effects should be accounted for in models of phenotypic evolution and interpretations of macroevolutionary body size patterns. This work highlights the intimate interplay between the macroecological and macroevolutionary dynamics underlying the generation and maintenance of morphological diversity.

Fractal-to-Euclidean crossover of the isotropy restoration feature in a family of fractal resistor networks

Fractal with microscopic anisotropy shows a unique type of macroscopic isotropy restoration phenomenon that is absent in Euclidean space [M. T. Barlow et al., Phys. Rev. Lett. 75, 3042]. In this paper the isotropy restoration feature is considered for a family of two-dimensional Sierpinski gasket type fractal resistor networks. A parameter xi is introduced to describe this phenomenon. Our numerical results show that xi satisfies the scaling law xi similar to l(-alpha), where l is the system size and alpha is an exponent independent of the degree of microscopic anisotropy, characterizing the isotropy restoration feature of the fractal systems. By changing the underlying fractal structure towards the Euclidean triangular lattice through increasing the side length b of the gasket generators, the fractal-to-Euclidean crossover behavior of the isotropy restoration feature is discussed.

Aerosol direct radiative effect of smoke over clouds over the southeast Atlantic Ocean from 2006 to 2009

The aerosol direct radiative effect (DRE) of African smoke was analyzed in cloud scenes over the southeast Atlantic Ocean, using Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) satellite observations and Hadley Centre Global Environmental Model version 2 (HadGEM2) climate model simulations. The observed mean DRE was about 30–35 W m−2 in August and September 2006–2009. In some years, short episodes of high-aerosol DRE can be observed, due to high-aerosol loadings, while in other years the loadings are lower but more prolonged. Climate models that use evenly distributed monthly averaged emission fields will not reproduce these high-aerosol loadings. Furthermore, the simulated monthly mean aerosol DRE in HadGEM2 is only about 6 W m−2 in August. The difference with SCIAMACHY mean observations can be partly explained by an underestimation of the aerosol absorption Ångström exponent in the ultraviolet. However, the subsequent increase of aerosol DRE simulation by about 20% is not enough to explain the observed discrepancy between simulations and observations.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

Memory and burstiness in dynamic networks

A discrete-time random process is described, which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time t is given by a fixed probability x, is modified to include a memory effect where the event probability is increased proportionally to the number of events that occurred within a given amount of time preceding t. For small values of x the interevent time distribution follows a power law with exponent −2−x. We consider a dynamic network where each node forms, and breaks connections according to this process. The value of x for each node depends on the fitness distribution, \rho(x), from which it is drawn; we find exact solutions for the expectation of the degree distribution for a variety of possible fitness distributions, and for both cases where the memory effect either is, or is not present. This work can potentially lead to methods to uncover hidden fitness distributions from fast changing, temporal network data, such as online social communications and fMRI scans.

Gál-type GCD sums beyond the critical line

We prove that ∑k,ℓ=1N(nk,nℓ)2α(nknℓ)α≪N2−2α(logN)b(α) holds for arbitrary integers 1≤n1<⋯exponent b(α)b(α). This estimate complements recent results for 1/2≤α≤11/2≤α≤1 and shows that there is no “trace” of the functional equation for the Riemann zeta function in estimates for such GCD sums when 0<α<1/20<α<1/2.