Barry Saltzman and the Theory of Climate

Barry Saltzman was a giant in the fields of meteorology and climate science. A leading figure in the study of weather and climate for over 40 yr, he has frequently been referred to as the "father of modern climate theory." Ahead of his time in many ways, Saltzman made significant contributions to our understanding of the general circulation and spectral energetics budget of the atmosphere, as well as climate change across a wide spectrum of time scales. In his endeavor to develop a unified theory of how the climate system works, lie played a role in the development of energy balance models, statistical dynamical models, and paleoclimate dynamical models. He was a pioneer in developing meteorologically motivated dynamical systems, including the progenitor of Lorenz's famous chaos model. In applying his own dynamical-systems approach to long-term climate change, he recognized the potential for using atmospheric general circulation models in a complimentary way. In 1998, he was awarded the Carl-Gustaf Rossby medal, the highest honor of the American Meteorological Society "for his life-long contributions to the study of the global circulation and the evolution of the earth's climate." In this paper, the authors summarize and place into perspective some of the most significant contributions that Barry Saltzman made during his long and distinguished career. This short review also serves as an introduction to the papers in this special issue of the Journal of Climate dedicated to Barry's memory.

A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.