0. What Is Isarithmic Map?

Isarithmic map

Reading: Slocum chapter 14

0. What is isarithmic map?

It depicts continuous and smooth phenomenon

e.g. temperature map in TV weather forecast

1. Two kinds of isarithmic map

1) Isometric map: constructed from true point data

e.g. toxic level map is constructed from the point data at sampled location

2) Isopleth map: constructed from perceptual point data

e.g. demographic trends map is constructed from the point data at centroid of enumeration unit

It is important to note that isopleth map should be created from standardized data such as proportion, rate, or average (don’t use isopleth map for raw data, but justifiable to use isopleth map for derived value such as population density or median income given that enumeration units are fairly small – census tract than county)

2. Three spatial interpolation methods

Spatial interpolation estimates unknown values from known values; thus transforms point data to continuous surface

Two kinds of spatial interpolation methods:

1)point data to regular gridded form – includes inverse distance and Kriging

2)point data to irregular form – includes triangulation

Inverse distance (IDW)

The interpolated value is calculated as a function of z-value of control points nearby, and the value is weighted by inverse distance to control points

Kriging

Same as inverse distance (in that it produces gridded form as output, and the weight is determined by inverse distance), but the weight is determined in a way that it takes into account overall trends captured by semivariogram

Semivariogram shows how semivariance in y-axis varies by lag distance in x-axis (The higher lag distance, the higher semivariance, which is indicative of spatial autocorrelation)

Semivariance measures how values are dissimilar from values in a certain neighborhood defined by a lag distance (see the text for formula).

You should specify the model that presumably fits the observation well

Then the weight (used for spatial interpolation like IDW) is determined such that the difference between observation and model is minimized. In other words, the weight is optimized rather than determined only by the distance to control points nearby like IDW.

Triangulation

Different from inverse distance and Kriging in that it honors control points; in other words, the interpolation is based on the Delaunay triangle directly constructed from control points rather than data values at grid points like inverse distance and Kriging.