The Appearance and Disappearance of Ship Tracks on Large Spatial Scales

The 1-km advanced very high resolution radiometer observations from the morning, NOAA-12, and afternoon, NOAA-11, satellite passes over the coast of California during June 1994 are used to determine the altitudes, visible optical depths, and cloud droplet effective radii for low-level clouds. Comparisons are made between the properties of clouds within 50 km of ship tracks and those farther than 200 km from the tracks in order to deduce the conditions that are conducive to the appearance of ship tracks in satellite images. The results indicate that the low-level clouds must be sufficiently close to the surface for ship tracks to form. Ship tracks rarely appear in low-level clouds having altitudes greater than 1 km. The distributions of visible optical depths and cloud droplet effective radii for ambient clouds in which ship tracks are embedded are the same as those for clouds without ship tracks. Cloud droplet sizes and liquid water paths for low-level clouds do not constrain the appearance of ship tracks in the imagery. The sensitivity of ship tracks to cloud altitude appears to explain why the majority of ship tracks observed from satellites off the coast of California are found south of 358N. A small rise in the height of low-level clouds appears to explain why numerous ship tracks appeared on one day in a particular region but disappeared on the next, even though the altitudes of the low-level clouds were generally less than 1 km and the cloud cover was the same for both days. In addition, ship tracks are frequent when lowlevel clouds at altitudes below 1 km are extensive and completely cover large areas. The frequency of imagery pixels overcast by clouds with altitudes below 1 km is greater in the morning than in the afternoon and explains why more ship tracks are observed in the morning than in the afternoon. If the occurrence of ship tracks in satellite imagery data depends on the coupling of the clouds to the underlying boundary layer, then cloud-top altitude and the area of complete cloud cover by low-level clouds may be useful indices for this coupling.This work was supported in part by the Office of Naval Research and by the National Science Foundation through the Center for Clouds, Chemistry and Climate at the Scripps Institution of Oceanography, an NSF Science and Technology Center

Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere's three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere's vertical stratification and general circulation. Specifically, the new measure "cross-betweenness" identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective

Asymmetric correlation matrices: an analysis of financial data

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.Comment: Revised version; 11 pages, 13 figure