Archetypal Analysis: Mining Weather and Climate Extremes

Conventional analysis methods in weather and climate science (e.g., EOF analysis) exhibit a number of drawbacks including scaling and mixing. These methods focus mostly on the bulk of the probability distribution of the system in state space and overlook its tail. This paper explores a different method, the archetypal analysis (AA), which focuses precisely on the extremes. AA seeks to approximate the convex hull of the data in state space by finding “corners” that represent “pure” types or archetypes through computing mixture weight matrices. The method is quite new in climate science, although it has been around for about two decades in pattern recognition. It encompasses, in particular, the virtues of EOFs and clustering. The method is presented along with a new manifold-based optimization algorithm that optimizes for the weights simultaneously, unlike the conventional multistep algorithm based on the alternating constrained least squares. The paper discusses the numerical solution and then applies it to the monthly sea surface temperature (SST) from HadISST and to the Asian summer monsoon (ASM) using sea level pressure (SLP) from ERA-40 over the Asian monsoon region. The application to SST reveals, in particular, three archetypes, namely, El Niño, La Niña, and a third pattern representing the western boundary currents. The latter archetype shows a particular trend in the last few decades. The application to the ASM SLP anomalies yields archetypes that are consistent with the ASM regimes found in the literature. Merits and weaknesses of the method along with possible future development are also discussed

Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices

We show that negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heat can be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.Comment: RevTeX 11 pages + epsfig embedded figures. Submitted to Phys. Rev.

Crossover from directed percolation to compact directed percolation

We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical exponents switch from the compact directed percolation class to ordinary directed percolation. We conclude that the nonuniversality observed in models with multiple absorbing configurations cannot be explained as a simple surface effect.Comment: 4 pages, Revtex, 5 figures postscrip

A spin polarized disc

We present a solution to the gravitational field equations in a Riemann-Cartan spacetime. The solution describes a disc of infinite radius and finite thickness. The solution has three forms which depend on the size of the acceleration. The matter content of the disc is a rotating spin fluid with a constant z acceleration and a spin density polarized along the axis of rotation. The fluid has zero axial and tangential pressures. There is a radial pressure. The energy density and pressure are finite within the disc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44467/1/10714_2005_Article_BF02109124.pd