Introduction.

Spatial sampling.

Spatial interpolation.

Spatial autocorrelation Measure.

Introduction

Our live may be infinitesimally small compared with the geographic extent and history of the world, but they are nevertheless very intricate in detail . In terms of GIS application, these are respectively examples of the operational and strategic decisions discussed in sec 1.1 . Principle objective of geographic analysis is to understand how both types of decisions are structured over space. For example, how do people structure the searches they make for new housing when they move, and how can that

information systems to help them ?

" Our behavior in geographic space often reflects past patterns of behavior".

" Some geographic phenomena vary smoothly across space, while others can exhibit extreme

irregularity, in violation of Tablers laws "

The scale or level of detail at which we seek to represent reality often determines whether spatial and temporal phenomena appear regular or irregular. Every one would recognize the extreme differences of landscapes between such regions as the Antarctic, the Nile delta the Sahara desert or the Amazon basin. The real -world GIS application described in book variously share practical goal of operational and strategic problem- solving. Is an appropriate scale or level of detail at which to build representation for particular application? How might we generalize from our measurements in order to identify spatial structure of given application in a GIS?

The fundamental problem revisited:

There are some clues that we can develop from Hager strand time geography , since unevenness in the spatio-temporal outcome of human activities presents special and temporal processes in natural and artificial (human made) environment.

“ Area objects have the two dimensions of length and breadth, but not depth. They may be used to represent natural objects such as agriculture fields. The classification of spatial phenomena into object type is fundamentally dependent upon

scale .”

Spatial autocorrelation and scale is determined both by similarities in position, and by similarities in attributes. Unfortunately the word scale has acquired too many meaning in the course of time. Scale is also used by scientist

to talk about the geographic extent or scope of project" .

Spatial Sampling the quest to represent the myriad complexity of the real world requires us to abstract or sample, events and occurrences from a sample frame defined as the

universe of eligible elements of interests .

Spatial Sampling

- A spatial sampling frame might be bounded by the extent of a field of interest.

- We can think of sampling as the process of selecting points from a continuous field of selecting some of these objects while discarding others.

- remote sensing, for example, in which each pixel value is a spatially averaged reflectance value calculated at the spatial resolution characteristic of the sensor. 

* Geographic data are only as good as the sampling scheme used to create them…

-Random sampling is integral to probability theory, and this enables us to use the distribution of values in our sample to tell us something about the likely distribution of values in the parent population from which the sample was drawn. 

*Stratified sampling designs attempt to allow for the unequal abundance of different phenomena on the Earth's surface.

Spatial Interpolation:

-It means abstracting, or sampling, part of reality to hold within our representation, it follows that judgment is required to fill in the gaps between the observations that make up a representation

 -This requires understanding of the likely attenuating

effect of distance between the sample observations, and thus of the nature of geographic data .

Measure of spatial autocorrelation:

-Similarity among attributes.-Similarity of location.

Establishing dependence in space:

-Regression analysis.

Spatial Autocorrelation Measure

A straight line or linear distance relationship is the easiest assumption to make and analyze, but it may not be the correct one.

Generalization is the process of reasoning from the nature of a sample to the nature of a larger group.

The assumption of zero spatial autocorrelation that is made by many methods of statistical inference is in direct contradiction to Tobler's Law.

It is almost imagine that two maps of different phenomena over the same area would not reveal some similarities.

In a self-similar object, each part has the same nature as the whole.