Raster Data

Raster Data is actually a kind of Sample data of a area, the area will be divided in regular grids (equally sized rectangles). The typical raster data like elevation is already the most important data for many spatial-based research fields. The raster form is also the important form for meteorological data, in order the area-value (e.g. Temperature and Presentation) to represent. But for the application e.g. in the Hydrology need we some statistical values for specific research regions, especially the Average.

Therefore we need the operate EXTRACT.

Extract from Raster

The basic Data are like:

The example Data

two Raster data
two Regions shape files

For the operate EXTRACT, we need basically the raster data and the regions (shape files). Before this we must confirm that, the both data are in the same CRS (coordinate reference system). In this Blog we discuss only the theories and ideas about EXTRACT. There will show total four methods:

1. Rough with original resolution

The first method we just use the original Raster with original resolution. But when the resolution not so fine, it will occur to that the selected grids have the big difference than the region. This is one very typical Problem in meteorological data, they have not so gut space resolution because the time resolution is always finer than the common geological data. In order to balance the data size, we must reduce the space resolution.

Illustration of Mask with “Touch” oder “Centerpoint”

For the SELECT, there are two familiar methods Touch and Center-point:

Touch: all the grids, who touched by the region, will be selected
Center-point: only the grids, who’s Center-point is with in the region, will be selected

For the both SELECT methods there some implausible cases:

when we use Touch method, it will select some grids, who has only a little area within the region, like Cell 4
Cell 5: only an eighth of the area within the region, but it counts as a “whole cell” just because its center is in the region
Cell 18: with three quarters of the area in the region, but is not selected, just because the center is not in the region

Summary we can say: the original resolution can be used, only when the deviation between the grids and region is not so big and

Touch includes all grid cells that are touched, so can be used for some extreme statistical value (e.g. Max or Min)
Center-point can be used for the average value and actually the deviation maybe reduced, due to the surplus of selected grids and deficit of not selected grids in the boundary.

2. Refine resolution

The second method is one simplest method, we need only refine our data in higher resolution, like resolution in 10 times finer and the grids will in 100 times more.

Essentially there is no difference as 1. method, but the problem will be solved. This method is pointed, just because I must use Matlab processing the data, but there is no spatial Analyse Toolbox in Matlab. Therefore this is fast the only Answer, just because the Refine needs no supply from spatial Analyse Toolbox, we can easily repeat the data 10 more in row and 10 more in column.

Illustration of Mask with “Touch” oder “Centerpoint” after Disaggregation

Like the figure shows: the accuracy is gut improvement, the deviation should lay under the 1%.

3. Exact with Area

The weighted mean is always exacter than the numerical average. The important Point for the weighted mean is the weights, in the spatial analyse it’s the portion of the area. So, the main task in third method is calculate the area of every value, that within one region.

In order to calculate the area, we need actually convert the raster grids into shape, for the convert we have also two methods:

the same value as one Polygon (this method should more convenient for the categories data with only several value)
every grid as a rectangle polygon, then calculate the portion of the area, where is located within the region (this method is use in R::terra package, but there is also a small deviation, when the CRS lie in lon-lat. The portion of one grid will be not equal to the portion of the region, because the grid area one to one is already different.)

Illustration von Extract mit Wert-Polygon

In the Illustration is every value as the same polygon converted.

4. Exact with scale product

This method is designed only for the meteorological data, those have the big mange on time scalar. It’s also the most effective method in the practice.

The theory and the formal is just like:

\[ \vec{\Omega}_{[time,region]} = \vec{A}_{[time,grid]} \cdot \vec{W}_{[grid,region]} \]

\(\vec{\Omega}_{[time,region]}\) = Region-value of every region

\(\vec{A}_{[time,grid]}\) = all Value in the matrix [time, grid]

\(\vec{W}_{[grid,region]}\) = Weights of every grid to every region in the matrix [grid,region]

Weight-Matrix

For the Weight-Matrix calculate we just the portion of the grid area only that within the region to the whole region area (but not the whole grid), then divide the area of the region.

One example weight_grid:

            [R1]      [R2]
 [G1]      0.000      0.00
 [G2] 134364.119 189431.77
 [G3] 212464.416      0.00
 [G4]   2747.413      0.00
 [G5] 150176.618      0.00
 [G6]      0.000  45011.22

G for Grid and R for Region

Value-Matrix

One example mat_value:

     [G1] [G2] [G3] [G4] [G5] [G6] 
[T1]    2    1    3    4    1    1  
[T2]    3    1    2    4    1    1

T for Time

The end.

Extract values from Raster Data