Functional Map Algebra: Designing Local Operations for Ocean Zinc Models

Authors: Behzad Vahedi*, Department of Geography and Center for Spatial Studies, University of California Santa Barbara, Saeed Roshan, Department of Geography, University of California Santa Barbara, Werner Kuhn, Department of Geography and Center for Spatial Studies, University of California Santa Barbara
Topics: Geographic Information Science and Systems, Oceanography
Keywords: map algebra, local operations, field, ocean zinc models
Session Type: Paper
Day: 4/14/2018
Start / End Time: 2:00 PM / 3:40 PM
Room: Grand Chenier, Sheraton, 5th Floor
Presentation File: No File Uploaded


Geographical fields are often represented in two different ways, in a grid of same-sized and regularly shaped cells, or with a finite set of (measured) points, or location-value pairs, along with a function to calculate field values in locations other than those measured. The most famous example of the first group is a remotely sensed raster of sea surface temperatures, and an example of the second group is a field of ocean zinc, generated from measurements in the Pacific ocean. While there is a set of well established and widely used map algebraic operations for the first representation type, there is no implementation inherently designed for fields represented by point samples. In this research we present a first attempt to design map algebraic operations that can directly be applied on fields represented by point samples. We model ocean zinc field using a set of measured locations and an interpolation function generated using a neural network. Then re-design local map algebraic operations for the field function, that take not a raster cell, but a location inside the domain of the function as input. In this method, both the field and the map algebra operations are modeled as functions, so a local classification operation for instance, would be a composite function, a pointwise application of classification function to the field function.

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