Experimenting with Google Earth

Kriging

Today, I will look at some of the assumptions underlying kriging, and important exploratory data analysis summaries, that should be obtained when performing kriging. As you know, Kriging is a geostatistical technique used to interpolate surfaces. It is similar to IDW in that the Z-values are weighted by some parameter. In IDW, Z-values are weighted by the inverse of the distance between the points. In kriging, z-values are weighted by the rate at which variance between sample points changes over space, that is, by the spatial autocorrelation between sample points.


Assumptions
Kriging should only be applied if the following underlying assumptions are met:

1. The data shows existence of second-order stationarity, i.e., at a minimum the mean and variance of the sample data should remain invariant in space. If the mean and variance of the samples are not stationary, then kriging may not be the best interpolation technique to apply.

2. The data represents one single homogenous domain.

3. A sufficient number of sample points should exist. Approximately 40 samples are needed to reasonably define and model a variogram, which can be used to produce an acceptable kriged
estimate.

EDA Output
In ArcGIS, before running kriging interpolation, you should explore the data before modeling the surface. Some things that should be explored include:
1. The number of sample points.
2. The minimum and maximum values in the distribution.
3. The variability of the distribution (variance and standard deviation)
4. The histogram of the distribution with coefficients of skewness and kurtosis,
5. Quantile-quantile (QQ) plots.
6. The semi-variogram cloud and fitted model. An example of a semi-variogram model is shown below:


1. At locations close to the origin, the semi-variances are low values, implying high levels of autocorrelation.
2. As distance (h) increases, variance also increases but levels off with increasing distance from the origin.
3. A constant variogram values imply that the variance between values does not change with distance.

In ArcGIS, the researcher can choose to fit one of several models to the variogram cloud in order to best capture the overall trend in the data (see illustration below). The best fit line can then be used to obtain values for all distance values (h). Alternative models include:

• Linear - a straight line with a positive slope.
• Spherical - rises rapidly then curves to the sill.
• Exponential – rises more gradually and is asymptotic to the sill.
• Gaussian – parabolic near the origin, then rises steeply toward the sill.

ArcGIS.com Viewer

ArcGIS.com viewer helps you to quickly create maps using a basemap from ESRI and additional layers found in ArcGIS.com. When creating these maps, one can set your area of interest, save the maps, and share them with others over the internet. These maps can be embedded in web pages to support themes on your webpage, or they can function as separate web applications. ESRI has created several templates that can be used to create these simple web applications. Visit ArcGIS.com at http://www.arcgis.com/home/webmap/viewer.html and follow the simple tutorial to start creating your own applications.


Here is a map of Guyana's ecumene from ArcGIS.com Viewer


View Larger Map. You can also use a hyperlink to access the map.

Kernel Density

Kernel density analysis is a type of cluster analysis. It helps us to detect areas where there are increased intensity of a phenomenon. This link provides instructions on how to calculate kernel densities. Usually, the main issue is with the search radius. Often the default search radius does not give recognizable clusters, so you may have to increase the search radius. Feel free to play around with the search radius until your clusters look smooth and realistic. The image below provides an idea of what clusters looks like after running a kernel density or hot spot analysis.

(Image source: http://jratcliffe.net/hsd/).

Using Relative Paths Rather Than Full Paths to Save Your Files

Full path

Suppose at school you saved your project as S:\Lab3\Michigan.mxd. Your data were also stored in the same folder, i.e., S:\Lab3\washtenaw.shp. At the end of class, you go home and want to continue working, so you copied your data to D:\Lab3 on your home computer. Since you used the full path convention for saving your data, when you open your project file (Michigan.mxd) at home, ArcMap would not be able find your data. Instead of seeing your data, you will see a red exclamation mark near to the name of the map layer in your project. The reason for this is that ArcMap is still looking for your map layer in the s:\Lab3\ because this information was hard-coded into the .mxd file. However, your data are now in D:\Lab3\. To automatically point ArcMap to your data folder, you should use relative paths to store your data and project file.

Relative path

An example of a relative path is: \Lab3\Boundary.shp.

Relative paths in a map specify the location of the data contained in your project relative to the current location on disk of the map document (.mxd file) itself. As relative paths do not contain drive names, they enable the map and its associated data to be moved to any disk drive without the map having to be repaired. As long as the same directory structure is used at the new location, the map will still be able to find its data by traversing the relative paths.

Data referenced by a relative path can be in the same folder as the map or in a folder above or below the folder containing the map. Using relative paths allows you to smoothly move maps that you made with data on your S:\ drive to any drive on another computer.

How to store relative pathnames to data for a map in ArcMAP

1. Click the File menu and click Document Properties.
2. Click Data Source Options.
3. Click Store relative pathnames and click OK on all dialog boxes.
4. Save the map.

Tip

If you want all new maps that you create stored with relative paths, go to the File > Document Properties dialog box and click the Data Source Options button. Check the option to make relative paths the default for new map documents. This setting is stored in the registry. If this box is not checked, the default is absolute paths.