A formal framework for the representation of stack-based terrains

Graciano, Alejandro; Rueda, Antonio J.; Feito, Francisco R.

doi:10.1080/13658816.2018.1475671

Cited by 5 publications

(2 citation statements)

References 71 publications

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“…Terrain‐based flow algebra integrates topography and a set of algebraic rules to calculate flow quantities, but is not spatially dynamic (Tarboton & Baker, 2008; Tarboton, Schreuders, Watson, & Baker, 2009; Tesfa et al., 2011); She and Li's (2016) directed flow network focuses on tracing network neighborhood functions rather than spatially dynamic changes related to adding or subtracting materials within the network. Graciano, Rueda, and Feito (2018) do incorporate positional relationships built through a geo‐dipole, which connect two geospatial locations with a property and the value of that property. This data structure is useful for directed flow relationships, but lacks the ability to account for the overall position in the network and thus is not well suited for spatially dynamic flows.…”

Section: Introductionmentioning

confidence: 99%

A spatially dynamic network algebra

Wentz

Shook

Merson

2021

Transactions in GIS

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Map algebras are used for the manipulation of spatial data and form the basis for many types of spatial analyses and modeling efforts. The most basic form of a map algebra applies the same function (e.g., addition, subtraction) across the study area. To account for local variation of modeling parameters, we present a spatially dynamic map algebra to demonstrate the need for and utility of algebraic functions where the function is determined based on a specific and relative location. The need for such an algebra comes from the growth of complex models where the values of variables or parameters are not fixed across space. Locally derived parameters are not new, as shown by geographically weighted regression. This type of algebra is needed in cases of complex models, such as those found in flow networks, where network dynamics vary across space. This includes hydrologic processes, movement of people and goods, and the transmission of ideas. We test the approach on a case study of nitrogen flow in the Niantic River watershed, Connecticut. Findings show that the results from a spatially dynamic map algebra can differ from a fixed function. Fixed functions can result in model outputs that under‐ or overestimate by up to 50%.

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Section: Introductionmentioning

confidence: 99%

A spatially dynamic network algebra

Wentz

Shook

Merson

2021

Transactions in GIS

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“…Building on these pioneer works on map algebra, several new and domainspecific algebra have been proposed in the literature [2][5] [15] [32]. However none of initial and new map algebra are suitable to spatial multicriteria modelling.…”

Section: Introductionmentioning

confidence: 99%

Preference Learning Based Decision Map Algebra: Specification and Implementation

Abubahia

Chakhar²,

Cocea

2019

Advances in Intelligent Systems and Computing

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Decision Map Algebra (DMA) is a generic and context independent algebra, especially devoted to spatial multicriteria modelling. The algebra defines a set of operations which formalises spatial multicriteria modelling and analysis. The main concept in DMA is decision map, which is a planar subdivision of the study area represented as a set of non-overlapping polygonal spatial units that are assigned, using a multicriteria classification model, into an ordered set of classes. Different methods can be used in the multicriteria classification step. In this paper, the multicriteria classification step relies on the Dominance-based Rough Set Approach (DRSA), which is a preference learning method that extends the classical rough set theory to multicriteria classification. The paper first introduces a preference learning based approach to decision map construction. Then it proposes a formal specification of DMA. Finally, it briefly presents an object oriented implementation of DMA.

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