Phytoplankton Scales of Variability in the California Current System: 1. Interannual and Cross-Shelf Variability

In the California Current System, strong mesoscale variability associated with eddies and meanders of the coastal jet play an important role in the biological productivity of the area. To assess the dominant timescales of variability, a wavelet analysis is applied to almost nine years (October 1997 to July 2006) of 1-km-resolution, 5-day-averaged, Sea-viewing Wide Field-of-view Sensor (SeaWiFS) chlorophyll a (chl a) concentration data. The dominant periods of chlorophyll variance, and how these change in time, are quantified as a function of distance offshore. The maximum variance in chlorophyll occurs with a period of similar to 100-200 days. A seasonal cycle in the timing of peak variance is revealed, with maxima in spring/summer close to shore (20 km) and in autumn/winter 200 km offshore. Interannual variability in the magnitude of chlorophyll variance shows maxima in 1999, 2001, 2002, and 2005. There is a very strong out-of-phase correspondence between the time series of chlorophyll variance and the Pacific Decadal Oscillation (PDO) index. We hypothesize that positive PDO conditions, which reflect weak winds and poor upwelling conditions, result in reduced mesoscale variability in the coastal region, and a subsequent decrease in chlorophyll variance. Although the chlorophyll variance responds to basin-scale forcing, chlorophyll biomass does not necessarily correspond to the phase of the PDO, suggesting that it is influenced more by local-scale processes. The mesoscale variability in the system may be as important as the chl a biomass in determining the potential productivity of higher trophic levels.

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.