How do rasters store geolocation information

A zero-order polynomial is used to shift your data. This is commonly used when your data is already georeferenced, but a small shift will better line up your data. Only one link is required to perform a zero-order polynomial shift. It may be a good idea to create a few links and then choose the one that looks the most accurate.

Use a first-order or affine transformation to shift, scale, and rotate a raster dataset. This generally results in straight lines on the raster dataset mapped as straight lines in the warped raster dataset. Thus, squares and rectangles on the raster dataset are commonly changed into parallelograms of arbitrary scaling and angle orientation. With a minimum of three links, the mathematical equation used with a first-order transformation can exactly map each raster point to the target location.

Any more than three links introduces errors, or residuals, that are distributed throughout all the links. However, you should add more than three links, because if one link is inaccurate, it has a much greater impact on the transformation. Thus, even though the mathematical transformation error may increase as you create more links, the overall accuracy of the transformation will increase as well.

The higher the transformation order, the more complex the distortion that can be corrected. However, transformations higher than third order are rarely needed.

Higher-order transformations require more links and, thus, will involve progressively more processing time. In general, if your raster dataset needs to be stretched, scaled, and rotated, use a first-order transformation. If, however, the raster dataset must be bent or curved, use a second- or third-order transformation. The spline transformation is a true rubber sheeting method and optimizes for local accuracy but not global accuracy.

It is based on a spline function—a piecewise polynomial that maintains continuity and smoothness between adjacent polynomials. Spline transforms the source control points exactly to target control points; the pixels that are a distance from the control points are not guaranteed to be accurate.

This transformation is useful when the control points are important, and it is required that they be registered precisely. Adding more control points can increase overall accuracy of the spline transformation. Spline requires a minimum of 10 control points. The adjust transformation optimizes for both global LSF and local accuracy.

It is built on an algorithm that combines a polynomial transformation and triangulated irregular network TIN interpolation techniques. The adjust transformation performs a polynomial transformation using two sets of control points and adjusts the control points locally to better match the target control points using a TIN interpolation technique. Adjust requires a minimum of three control points.

The projective transformation can warp lines so that they remain straight. In doing so, lines which were once parallel may no longer remain parallel. The projective transformation is especially useful for oblique imagery, scanned maps, and for some imagery products such as Landsat and Digital Globe.

A minimum of four links are required to perform a projective transformation. When only four links are used, the root mean square RMS error will be zero. When more points are used, the RMS error will be slightly above zero. The similarity transformation is a first-order transformation that tries to preserve the shape of the original raster.

The header defines the extent via the number of columns, the number of rows and the cell size resolution. Hence, starting from the origin, we can easily access and modify each single cell by either using the ID of a cell Figure 2. This matrix representation avoids storing explicitly the coordinates for the four corner points in fact it only stores one coordinate, namely the origin of each cell corner as would be the case for rectangular vector polygons.

This and map algebra Section 4. However, in contrast to vector data, the cell of one raster layer can only hold a single value. The value might be numeric or categorical Figure 2. Raster maps usually represent continuous phenomena such as elevation, temperature, population density or spectral data Figure 2. Of course, we can represent discrete features such as soil or land-cover classes also with the help of a raster data model Figure 2.

Consequently, the discrete borders of these features become blurred, and depending on the spatial task a vector representation might be more suitable. The terra package supports raster objects in R. It provides an extensive set of functions to create, read, export, manipulate and process raster datasets. Aside from general raster data manipulation, terra provides many low-level functions that can form the basis to develop more advanced raster functionality.

In this case, terra provides the possibility to divide the raster into smaller chunks, and processes these iteratively instead of loading the whole raster file into RAM. For the illustration of terra concepts, we will use datasets from the spDataLarge. For example, srtm. Typing the name of the raster into the console, will print out the raster header dimensions, resolution, extent, CRS and some additional information class, data source, summary of the raster values :.

Similar to the sf package, terra also provides plot methods for its own classes. There are several other approaches for plotting raster data in R that are outside the scope of this section, including:.

The SpatRaster class represents rasters object in terra. The easiest way to create a raster object in R is to read-in a raster file from disk or from a server Section 7. The terra package supports numerous drivers with the help of the GDAL library. Rasters from files are usually not read entirely into RAM, with an exception of their header and a pointer to the file itself. Rasters can also be created from scratch using the same rast function. This is illustrated in the subsequent code chunk, which results in a new SpatRaster object.

The resulting raster consists of 36 cells 6 columns and 6 rows specified by nrows and ncols centered around the Prime Meridian and the Equator see xmin , xmax , ymin and ymax parameters. This means the unit of the resolution is in degrees which we set to 0. Values vals are assigned to each cell: 1 to cell 1, 2 to cell 2, and so on.

Remember: rast fills cells row-wise unlike matrix starting at the upper left corner, meaning the top row contains the values 1 to 6, the second 7 to 12, etc. For other ways of creating raster objects, see? The SpatRaster class also handles multiple layers, which typically correspond to a single multispectral satellite file or a time-series of rasters. For multi-layer raster objects, layers can be selected with terra::subset.

The opposite operation, combining several SpatRaster objects into one, can be done using the c function:. Vector and raster spatial data types share concepts intrinsic to spatial data. Perhaps the most fundamental of these is the Coordinate Reference System CRS , which defines how the spatial elements of the data relate to the surface of the Earth or other bodies. CRSs are either geographic or projected, as introduced at the beginning of this chapter see Figure 2.

This section will explain each type, laying the foundations for Section 6 on CRS transformations. Longitude is location in the East-West direction in angular distance from the Prime Meridian plane. Latitude is angular distance North or South of the equatorial plane.

Distances in geographic CRSs are therefore not measured in meters. This has important consequences, as demonstrated in Section 6. The surface of the Earth in geographic coordinate systems is represented by a spherical or ellipsoidal surface. Spherical models assume that the Earth is a perfect sphere of a given radius — they have the advantage of simplicity but, at the same time, they are inaccurate: the Earth is not a sphere!

Ellipsoidal models are defined by two parameters: the equatorial radius and the polar radius. These are suitable because the Earth is compressed: the equatorial radius is around Ellipsoids are part of a wider component of CRSs: the datum.

You can see examples of these two types of datums in Figure 2. In a local datum , shown as a purple dashed line, the ellipsoidal surface is shifted to align with the surface at a particular location. This can be seen in Figure 2. Both datums in Figure 2. Image of the geoid is adapted from the work of Ince et al. All projected CRSs are based on a geographic CRS, described in the previous section, and rely on map projections to convert the three-dimensional surface of the Earth into Easting and Northing x and y values in a projected CRS.

Projected CRSs are based on Cartesian coordinates on an implicitly flat surface right panel of Figure 2. They have an origin, x and y axes, and a linear unit of measurement such as meters. This transition cannot be done without adding some deformations. A projected coordinate system can preserve only one or two of those properties.

Projections are often named based on a property they preserve: equal-area preserves area, azimuthal preserve direction, equidistant preserve distance, and conformal preserve local shape. There are three main groups of projection types - conic, cylindrical, and planar azimuthal. Distortions are minimized along the tangency lines and rise with the distance from those lines in this projection. We can use the bins argument to increase the number of bins for the histogram.

To render a final, three band, colored image in Python, we again turn to the plot. The colored pixels at the edges between white black result from there being no data in one or two channels at a given pixel. While this plot tells us where we have no data values, the color scale look strange, because our plotting function expects image values to be normalized between a certain range or When the range of pixel brightness values is closer to 0, a darker image is rendered by default.

We can stretch the values to extend to the full range of potential values to increase the visual contrast of the image. When the range of pixel brightness values is closer to , a lighter image is rendered by default. It is possible to perform a custom stretch when plotting multi-band rasters with imshow by using the keyword arguments vmin and vmax.

We can confirm this by accessing the NoData value directly:. This is not a bug! There are so many that the NoData value is the 2nd percentile.

We can check how many of the values in the array are NoData values. This plots the figure correctly:. Or by using the built-in dir function. The methods and attributes of each are the same because they are the same type of object, xarray. Individual bands within a DataArray can be accessed, analyzed, and visualized using the same plot function as single bands.

Plot summary pixel values using pandas. Convert character data to datetime format. This episode continues our discussion of shapefile attributes and covers how to work with shapefile attributes in Python. It covers how to identify and query shapefile attributes, as well as how to subset shapefiles by specific attribute values. Finally, we will learn how to plot a shapefile according to a set of attribute values. We will continue using the geopandas , and rioxarray and matplotlib.

Make sure that you have these packages loaded. We will continue to work with the three shapefiles that we loaded in the Open and Plot Shapefiles in R episode.

Note that the geometry is just another column and counts towards the total. We can explore individual values stored within a particular attribute.

Comparing attributes to a spreadsheet or a data frame, this is similar to exploring values in a column. We did this with the gapminder dataframe in an earlier lesson. We can see the contents of the TYPE field of our lines shapefile:. To see only unique values within the TYPE field, we can use the np. We can use the filter function from dplyr that we worked with in an earlier lesson to select a subset of features from a spatial object in Python, just like with data frames.

Once we subset out this data, we can use it as input to other code so that code only operates on the footpath lines. Our subsetting operation reduces the features count to 2. We can plot only the footpath lines:. There are two features in our footpaths subset. Why does the plot look like there is only one feature? Subset out all woods road from the lines layer and plot it. We adjusted line color by applying an arbitrary color map earlier.

If we want a unique line color for each attribute category in our GeoDataFrame , we can use the following argument, column , as well as some style arguments to improv ethe visuals. Our map is starting together, in the next lesson we will add our Canopy Height Model that we calculated in an earlier episode. First we read in the data and check how many levels there are in the region column:. A GeoDataFrame in geopandas is similar to standard pandas data frames and can be manipulated using the same functions.

Almost any feature of a plot can be customized using the various functions and options in the matplotlib package. This lesson is in the early stages of development Alpha version. Toggle navigation Home. This lesson is part of The Carpentries Incubator , a place to share and use each other's Carpentries-style lessons.

This lesson has not been reviewed by and is not endorsed by The Carpentries. Teaching: 15 min Exercises: 10 min. Questions What format should I use to represent my data? What are the main data types used for representing geospatial data? What are the main attributes of raster data? Objectives Describe the difference between raster and vector data. Describe the strengths and weaknesses of storing data in raster format. Teaching: 10 min Exercises: 5 min. Questions What are the main attributes of vector data?

Objectives Describe the strengths and weaknesses of storing data in vector format. Describe the three types of vectors and identify types of data that would be stored in each.

Questions What is a coordinate reference system and how do I interpret one? Objectives Name some common schemes for describing coordinate reference systems. Interpret a PROJ4 coordinate reference system description.

Teaching: 10 min Exercises: 0 min. Questions What programs and applications are available for working with geospatial data? Objectives Describe the difference between various approaches to geospatial computing, and their relative strengths and weaknesses.

Name some commonly used GIS applications. Name some commonly used Python packages that can access and process spatial data. Teaching: 40 min Exercises: 20 min. Questions What is a raster dataset? How do I work with and plot raster data in Python? How can I handle missing or bad data values for a raster? Objectives Describe the fundamental attributes of a raster dataset. Explore raster attributes and metadata using Python. EPSG The imshow function in the pyplot module of the matplotlib library is used to display data as an image.

Teaching: 60 min Exercises: 20 min. Questions How do I call a DataArray to print out its metadata information? How do I work with raster data sets that are in different projections? Objectives Reproject a raster in Python using rasterio.

Accomplish the same task with rioxarray and xarray. DataArray band: 1, y: , x: array [[[ Questions How do I subtract one raster from another and extract pixel values for defined locations?

Reclassify a continuous raster to a categorical raster using the CHM values. DataArray band: 1, y: , x: array [[[ 1. Teaching: 20 min Exercises: 10 min.

Questions How can I distinguish between and visualize point, line and polygon vector data? Objectives Know the difference between point, line, and polygon vector elements. Questions How can I create map compositions with custom legends using geopandas?

How can I plot raster and vector data together? Objectives Plot multiple shapefiles in the same plot. Apply custom symbols to spatial objects in a plot. Create a multi-layered plot with raster and vector data. Learners will have these data and libraries loaded from earlier episodes import rioxarray import geopandas as gpd import matplotlib.

Now that we have visualized the area of the CHM we want to subset, we can perform the cropping operation. We are going to create a new object with only the portion of the CHM data that falls within the boundaries of the AOI.

The plot above shows that the full CHM extent plotted in green is much larger than the resulting cropped raster. Our plot location extent is not the largest but is larger than the AOI Boundary.

It would be nice to see our vegetation plot locations plotted on top of the Canopy Height Model information. Crop the Canopy Height Model to the extent of the study plot locations. Plot the vegetation plot location points on top of the Canopy Height Model. One is situated on the blank space to the left of the map.

A modification of the first figure in this episode is below, showing the relative extents of all the spatial objects. Notice that the extent for our vegetation plot layer black extends further west than the extent of our CHM raster bright green. Thus, the extent of our vegetation plot layer will still extend further west than the extent of our cropped raster data dark green.

Define an Extent So far, we have used a shapefile to crop the extent of a raster dataset. This creates a new object of class extent. Extract Raster Pixels Values Using Vector Polygons Often we want to extract values from a raster layer for particular locations - for example, plot locations that we are sampling on the ground.

We can extract all pixel values within 20m of our x,y point of interest. These can then be summarized into some value of interest e. This is optional, the default is to return a list, NOT a data frame. These values help us better understand vegetation at our field site.

It appears that the mean height value, extracted from our LiDAR data derived canopy height model is By default, the units of the buffer are the same units as the data's CRS. All pixels that are touched by the buffer region are included in the extract.

Objectives Import. Export a spatial object to a. Objectives Plot vector objects with different CRSs in the same plot.

Questions How can I crop raster objects to vector objects, and extract the summary of raster pixels? Objectives Crop a raster to the extent of a vector layer Extract values from a raster that correspond to a vector file overlay with rasterstats.

Questions How can I visualize individual and multiple bands in a raster object? Objectives Identify a single vs. Questions How can I calculate, extract, and export summarized raster pixel data? Objectives Extract summary pixel values from a raster.

Save summary values to a. Compare NDVI values between two different sites. Questions How can I view and and plot data for different times of the year?

Objectives Understand the format of a time series raster dataset. Work with time series rasters. Import a set of rasters stored in a single directory. Create a multi-paneled plot. Questions How can I compute on the attributes of a spatial object?

Objectives Query attributes of a spatial object. Subset spatial objects using specific attribute values. Plot a shapefile, colored by unique attribute values. The most common geospatial file type.

This has become the industry standard. The three required files are: SHP is the feature geometry. On the other hand, networks are line data sets but they are often considered to be different. This is because linear networks are topologically connected elements. They consist of junctions and turns with connectivity. If you were to find an optimal route using a traffic line network, it would follow set rules.

For example, it can restrict turns and movement on one-way streets. When you join a set of vertices in a particular order and close it, this is now a vector polygon feature. When you create a polygon, the first and last coordinate pairs are the same. Cartographers use polygons to show boundaries and they all have an area.

For example, a building footprint has a square-footage, and agricultural fields have acreage. Raster data is made up of pixels also referred to as grid cells. Rasters often look pixelated because each pixel has its own value or class. Each pixel value in a satellite image has a red, green and blue value.

Alternatively, each value in an elevation map represents a specific height. It could represent anything from rainfall to land cover. Raster models are useful for storing data that varies continuously. For example, elevation surfaces , temperature and lead contamination.

Discrete rasters have distinct themes or categories. For example, one grid cell represents a land cover class or a soil type. Each class can be discretely defined where it begins and ends. In other words, each land cover cell is definable and it fills the entire area of the cell.

Discrete data usually consists of integers to represent classes. For example, the value 1 might represent urban areas, the value 2 represents forest, and so on. Continuous rasters non-discrete are grid cells with gradual changing data such as elevation, temperature or an aerial photograph.

A continuous raster surface can be derived from a fixed registration point. For example, digital elevation models use sea level as a registration point.