GIS Concepts

Kriging

The main GIS concept used in this process was kriging. Kriging was used to come up with a comprehensive spatial picture of the average monthly precipitation over a series of years and monthly temperature in 2009, the purpose of which was to compare with spatial pictures developed by the PRISM group at OSU. 

Kriging uses “Tobler’s first law of geography,” which is essentially that things that are close together should have similar geographical properties (Middleton 200 and Carr 2002). If it is known that the average temperature at a given point is 30 degrees Celsius, it can be assumed with almost complete certainty that a given point one or two yards away does not have a very different average temperature. The mathematical formulation for kriging is very complicated, so only a very superficial explanation will be given here. For more information, see the book Data Visualization in the Geosciences (Carr), cited in the references section. Kriging uses a mathematical tool called a variogram, which is computed using a method very similar to the method used to compute the variance of a group of data points. In both cases, a sum of the square of the differences from the mean is calculated, but in the variogram, spatial data is taken into account. It is in this way that, for instance, given any point on the map, the temperature can be determined by the distance from the surrounding weather stations and their temperatures. Close weather stations will be given more weight than farther weather stations. 

The three “advanced parameters” that one can vary while kriging are Major Range, Partial Sill, and Nugget. The nugget determines the maximum amount by which the resulting raster can disagree with the actual data. For instance, if the nugget is assigned a value of zero, then the raster will agree exactly with the weather station data at the location of the weather stations. The reason for having a nonzero nugget is that it creates a neater, smoother curve, especially if two stations are close together but have rather different values. The major range is a parameter which describes the maximum distance a pixel can be from a weather station while still being affected by the measurement at that weather station. For instance, if the major range is 500 m, and a pixel is located at a point which is 600 m away from a given weather station, the temperature at that weather station does not affect the pixel. If the pixel is located 500 m away or less, however, the temperature of the weather station is taken into account. The partial sill is the value given to any pixel outside the major range of any weather station. It is easy enough to calculate; it is the average of all the given values of each weather station.

 

Difficulty

The defaults were used for each krig except for two. The krigs for April and May had a very low major range, and they each essentially guessed that the entire study area would have the exact same amount of precipitation, except for areas which are very close to each weather station. To fix the problem, the partial sill, range, and nugget had to be manually entered. For each one, the nugget was set at zero, the partial sill was set at the average value of precipitation for each weather station for the given month, and the range was modified until the entire study area was covered. The hypothesis for why the major range was so low is that there were two weather stations that were very close together that had rather different values. The default settings assumed that, if two stations could be so close together but have such different values, then each individual station must not have much of an effect on points which are not close, because there was not a great deal of spatial autocorrelation between the two very differently valued points. This hypothesis is supported by the fact that there were indeed two points that were close together with very different values in those two months.

 

Projection

Projection is a systematic rendering of geographic coordinates that allows a sphere to be transformed to a planar surface with Cartesian coordinates(Theobald 2003). Datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth. The PRISM data did not have any metadata, but the source reported that it had a datum and projection of WGS 72 UTM zone 12N. The "define projection" tool was used to define the datum of the data as WGS 72. Then, the "project raster" tool was used to give the data the projection of UTM zone 12N. Finally, the "project raster" tool was used again to project the data as WGS 84 zone 12N to match the projection of the YPG data. Similar, the YPG data did not have any metadata either, and the source reported that it had a datum and projection of WGS 84 UTM zone 12N. The "define projection" tool was used to define the datum of the data as WGS 84. Then, the "project" tool was used to project the data as WGS 84 zone 12N.

 

Resampling

Resampling is needed when two raster datasets of different cell sizes are combined or overlaid (Theobald 2003). In this case, raster datasets from YPG and from PRISM were compared and as a result needed to have the same cell sizes. The PRISM datasets were resampled to the cell size of the YPG datasets.

 

Spatial Analyst

The spatial analyst tool allows manipulation, analysis, and modeling of raster-based data (Theobald 2003). It has an option called the raster calculator, which provides an interface in which map algebra expressions can be entered. The raster calculator was used to clip the maximum temperature and precipitation data to the YPG boundary, and in the case of the PRISM data it was also used to clip the data to a square that encompasses the YPG boundary (This was done because the PRISM data needed to be resampled and it processes faster when there is less data).

 

Classification

For raster datasets, quantitative data can be displayed using the classified option. The number in the value attribute table is displayed with a color. This option was used for the precipitation and maximum temperature raster datasets. As a result, different amounts of precipitation and maximum temperatures were displayed in different colors.