Mathematical geography

(geography) The branch of geography that deals with the features and processes of the earth, and their representations on maps and charts.

The branch of geography that examines human and physical activities on the Earth's surface using models and statistical analysis. The primary areas in which mathematical methods are used include the analysis of spatial patterns, the processes that are responsible for creating and modifying these patterns, and the interactions among spatially separated entities.

What sets geographic methods apart from other quantitative disciplines is geography's focus on place and relative location. Latitude and longitude provide an absolute system of recording spatial data, but geographic databases also typically contain large amounts of relative and relational data about places. Thus, geographers have devoted much effort to accounting for spatial interrelations while maintaining consistency with the assumptions of mathematical models and statistical theory. See also Geography; Model theory; Statistics.

Spatial pattern methodologies attempt to describe the arrangement of phenomena over space. In most cases these phenomena are either point or area features, though computers now allow for advanced three-dimensional modeling as well. Point and area analyses use randomness (or lack of pattern) as a dividing point between two opposite pattern types—dispersed or clustered.

An important innovation in geographic modeling has been the development of spatial autocorrelation techniques. Unlike conventional statistics, in which many tests assume that observations are independent and unrelated, very little spatial data can truly be considered independent. Soil moisture or acidity in one location, for example, is a function of many factors, including the moisture or acidity of nearby points. Because most physical and human phenomena exhibit some form of spatial interrelationships, several statistical methods, primarily based on the Moran Index, have been developed to measure this spatial autocorrelation. Once identified, the presence and extent of spatial autocorrelation can be built into the specification of geographical models to more accurately reflect the behavior of spatial phenomena.

The study of the earth's size and shape, of time zones, and of the motion of the earth.