# Vector and Raster Geospatial Data

Handouts for this lesson need to be saved on your computer. Download and unzip this material into the directory (a.k.a. folder) where you plan to work.

## Lesson Objectives

- Meet the key R packages for geospatial analysis
- Learn basic wrangling of vector and raster data
- Distinguish “scriptable” tasks from desktop GIS needs

## Specific Achievements

- Create, load and plot vector data types, or “features”
- Filter features based on associated data or on space
- Perform geometric operations on polygons
- Load, manipulate and extract raster data

## R Packages

The key R packages for this lesson are

### OSGeo Dependencies

In addition to the common case of depending on other R packages, these two have dependencies on system libraries.

- GDAL for read/write in geospatial data formats
- GEOS for geometry operations
- PROJ.4 for cartographic projections

System libraries cannot be installed by R’s `install.packages()`

, but can be
bundled with these packages and for private use by them. Either way, the
necessary libraries are maintained by the good people at the Open Source
Geospatial Foundation for free and easy distribution.

### Vector Data

The US Census website distributes county polygons (and much more) that are provided with the handouts. The sf package reads shapefiles (“.shp”) and most other vector data:

```
library(sf)
shp <- 'data/cb_2016_us_county_5m'
counties <- st_read(shp, stringsAsFactors = FALSE)
```

The `counties`

object is a `data.frame`

that includes a `sfc`

, which stands for
“simple feature column”. This special column is usually called “geometry” or
“geom”.

```
> head(counties)
```

```
Simple feature collection with 6 features and 9 fields
geometry type: MULTIPOLYGON
dimension: XY
bbox: xmin: -114.7556 ymin: 29.26116 xmax: -81.10192 ymax: 38.77443
epsg (SRID): 4269
proj4string: +proj=longlat +datum=NAD83 +no_defs
STATEFP COUNTYFP COUNTYNS AFFGEOID GEOID NAME LSAD
1 04 015 00025445 0500000US04015 04015 Mohave 06
2 12 035 00308547 0500000US12035 12035 Flagler 06
3 20 129 00485135 0500000US20129 20129 Morton 06
4 28 093 00695770 0500000US28093 28093 Marshall 06
5 29 510 00767557 0500000US29510 29510 St. Louis 25
6 35 031 00929107 0500000US35031 35031 McKinley 06
ALAND AWATER geometry
1 34475567011 387344307 MULTIPOLYGON (((-114.7556 3...
2 1257365642 221047161 MULTIPOLYGON (((-81.52366 2...
3 1889993251 507796 MULTIPOLYGON (((-102.042 37...
4 1828989833 9195190 MULTIPOLYGON (((-89.72432 3...
5 160458044 10670040 MULTIPOLYGON (((-90.31821 3...
6 14116799068 14078537 MULTIPOLYGON (((-109.0465 3...
```

### Geometry Types

Like any `data.frame`

column, the `geometry`

column is comprised of a single
data type. The “MULTIPOLYGON” is just one of several standard geometric data
types.

Common Types | Description |
---|---|

POINT | zero-dimensional geometry containing a single point |

LINESTRING | sequence of points connected by straight, non-self intersecting line pieces; one-dimensional geometry |

POLYGON | sequence of points in closed, non-intersecting rings; the first denotes the exterior ring, any subsequent rings denote holes |

MULTI* | set of * (POINT, LINESTRING, or POLYGON) |

The spatial data types are built upon eachother in a logical way: lines are built from points, polygons are built from lines, and so on.

We can create any of these spatial objects from coordinates.
Here’s a `sfc`

object with a single “POINT”, corresponding to SESYNC’s postition
in WGS84 degrees lat and degrees lon.

```
sesync <- st_sfc(st_point(
c(-76.503394, 38.976546)),
crs = st_crs(counties))
```

### Coordinate Reference Systems

A key feature of a **geo**spatial data type is its associated CRS, stored as an
EPSG ID and an equivalent PROJ.4 string.

```
> st_crs(counties)
```

```
Coordinate Reference System:
EPSG: 4269
proj4string: "+proj=longlat +datum=NAD83 +no_defs"
```

### Bounding Box

A bounding box for all featurs in a `sf`

data frame is generated by `st_bbox()`

.

```
> st_bbox(counties)
```

```
xmin ymin xmax ymax
-179.14734 -14.55255 179.77847 71.35256
```

The bounding box is not a static attribute—it is determined on-the-fly for the entire table or any subset of features.

```
library(dplyr)
counties_md <- filter(
counties,
STATEFP == '24')
```

```
> st_bbox(counties_md)
```

```
xmin ymin xmax ymax
-79.48765 37.91172 -75.04894 39.72312
```

### Grid

A bounding box summarizes the limits, but is not itself a geometry (not a POINT or POLYGON), even though it has a CRS attribute.

```
> st_crs(st_bbox(counties_md))
```

```
Coordinate Reference System:
EPSG: 4269
proj4string: "+proj=longlat +datum=NAD83 +no_defs"
```

A rectangular grid made over a `sf`

object is a geometry—by default, a POLYGON.

```
grid_md <- st_make_grid(counties_md,
n = 4)
```

```
> grid_md
```

```
Geometry set for 16 features
geometry type: POLYGON
dimension: XY
bbox: xmin: -79.48765 ymin: 37.91172 xmax: -75.04894 ymax: 39.72312
epsg (SRID): 4269
proj4string: +proj=longlat +datum=NAD83 +no_defs
First 5 geometries:
```

```
POLYGON ((-79.48765 37.91172, -78.37797 37.9117...
```

```
POLYGON ((-78.37797 37.91172, -77.26829 37.9117...
```

```
POLYGON ((-77.26829 37.91172, -76.15862 37.9117...
```

```
POLYGON ((-76.15862 37.91172, -75.04894 37.9117...
```

```
POLYGON ((-79.48765 38.36457, -78.37797 38.3645...
```

### Plot Layers

Spatial objects defined by sf are compatible with the `plot`

function. Setting the `plot`

parameter `add = TRUE`

allows an existing plot to
serve as a layer underneath the new one, so long as the CRS lines up.

```
plot(grid_md)
plot(counties_md['ALAND'],
add = TRUE)
plot(sesync, col = "green",
pch = 20, add = TRUE)
```

But note that the `plot`

function won’t prevent you from layering up geometries
with different coordinate systems: you must safegaurd your own plots from this
mistake. The arguments `col`

and `pch`

, by the way, are graphical parameters
used in base R, see `?par`

.

### Spatial Subsetting

An object created with `st_read`

is a `data.frame`

, which is why the `dplyr`

function `filter`

used above on the **non**-geospatial column named “STATEFP”
worked normally. The equivalent of a filtering operation on the “geometry”
column is called a spatial “overlay”.

```
> st_within(sesync, counties_md)
```

```
Sparse geometry binary predicate list of length 1, where the predicate was `within'
1: 5
```

It can be seen as a type of subsetting based on spatial (rather than numeric or
string) matching. Matching is implemented with functions like `st_within(x, y)`

.
The output implies that the 1^st^ (and only) point in `sesync`

is within the 5th
element of `counties_md`

.

- Question
- What was the message issued by the last command all about?
- Answer
- It is a reminder that all geometric calculations are performed as if the coordinates (in this case longitutde and latitude) are Cartesian x,y coordinates.

The overlay functions in the sf package follow the pattern
`st_predicate(x, y)`

and perform the test “x [is] predicate y”. Some key
examples are:

st_intersects | boundary or interior of x intersects boundary or interior of y |

st_within | interior and boundary of x do not intersect exterior of y |

st_contains | y is within x |

st_overlaps | interior of x intersects interior of y |

st_equals | x has the same interior and boundary as y |

### Coordinate Transforms

For the next part of this lesson, we import a new polygon layer corresponding to the 1:250k map of US hydrological units (HUC) downloaded from the United States Geological Survey.

```
shp <- 'data/huc250k'
huc <- st_read(shp, stringsAsFactors = FALSE)
```

Compare the coordinate reference systems of `counties`

and `huc`

, as given by
their Proj4 strings.

```
> st_crs(counties_md)$proj4string
```

```
[1] "+proj=longlat +datum=NAD83 +no_defs"
```

```
> st_crs(huc)$proj4string
```

```
[1] "+proj=aea +lat_1=29.5 +lat_2=45.5 +lat_0=23 +lon_0=-96 +x_0=0 +y_0=0 +datum=NAD27 +units=m +no_defs"
```

The Census data uses unprojected (longitude, latitude) coordinates, but `huc`

is
in an Albers equal-area projection (indicated as “+proj=aea”).

The function `st_transform()`

converts a `sfc`

between coordinate reference
systems, specified with the parameter `crs = x`

. A numeric `x`

must be a valid
EPSG code; a character `x`

is interpretted as a PROJ.4 string.

```
prj <- '+proj=aea +lat_1=29.5 +lat_2=45.5 \
+lat_0=23 +lon_0=-96 +x_0=0 +y_0=0 \
+ellps=GRS80 +towgs84=0,0,0,0,0,0,0 \
+units=m +no_defs'
```

Proj4 strings contain a reference to the type of projection, this one is another Albers Equal Area, along with numeric parameters associated with that projection. An additional important parameter that may differ between two coordinate systems is the “datum”, which indicates the standard by which the irregular surface of the Earth is approximated by an ellipsoid in the coordinates themselves.

Use `st_transform()`

to assign the two layers to a common projection string
(`prj`

). This takes a few moments, as it requires re-calculating coordinates for
every vertex of every polygon in the `sfc`

.

```
counties_md <- st_transform(
counties_md,
crs = prj)
huc <- st_transform(
huc,
crs = prj)
sesync <- st_transform(
sesync,
crs = prj)
```

```
plot(counties_md$geometry)
plot(huc$geometry,
border = 'blue', add = TRUE)
plot(sesync, col = 'green',
pch = 20, add = TRUE)
```

### Geometric Operations

The data for a map of watershed boundaries within the state of MD is all here;
in the country-wide `huc`

and in the state boundary “surrounding” all of
`counties_md`

. To get just the huc in a MD outline:

- remove the internal county boundaries within the state
- clip the hydrological areas to their intersection with the state

The first step is a spatial **union** operation: we want the resulting object to
combine the area covered by all the multipolygons in `counties_md`

.

```
state_md <- st_union(counties_md)
plot(state_md)
```

To perform a union of all sub-geometries in a single `sfc`

, we use the
`st_union()`

function with a single argument. The output, `state_md`

, is a new
`sfc`

that is no longer a column of a data frame. Tabular data can’t safely
survive a spatial union and is discarded.

The second step is a spatial **intersection**, since we want to limit the
polygons to areas covered by both `huc`

and `state_md`

.

```
huc_md <- st_intersection(
huc,
state_md)
```

```
Warning: attribute variables are assumed to be spatially constant
throughout all geometries
```

```
plot(state_md)
plot(huc_md, border = 'blue',
col = NA, add = TRUE)
```

The `st_intersection()`

function intersects its first argument with the second.
The individual hydrological units are preserved but any part of them (or any
whole polygon) lying outside the `state_md`

polygon is cut from the output. The
attribute data remains in the corresponding records of the `data.frame`

, but (as
warned) has not been updated. For example, the “AREA” attribute of any clipped
HUC does not reflect the new polygon.

The GEOS library provides many functions dealing with distances and areas. Many of these are accessible through the sf package, including:

`st_buffer`

: to create a buffer of specific width around a geometry`st_distance`

: to calculate the shortest distance between geometries`st_area`

: to calculate the area of polygons

Keep in mind that all these functions use **planar** geometry equations and thus
become less precise over larger distances, where the Earth’s curvature is
noticeable. To calculate geodesic distances that account for that curvature,
checkout the geosphere package.

## Raster Data

Raster data is a matrix or cube with additional spatial metadata (e.g. extent,
resolution, and projection) that allow its values to be mapped onto geographical
space. The raster package provides the eponymous `raster()`

function
for reading the many formats of such data.

The National Land Cover Database is ‘.GRD’ format data, a lot of it. The file provided in this lesson is cropped and reduced to a lower resolution in order to speed processing.

```
library(raster)
nlcd <- raster("data/nlcd_agg.grd")
```

By default, raster data is *not* loaded into working memory, as you can confirm
by checking the R object size with `object.size(nlcd)`

. This means that unlike
most analyses in R, you can actually process raster datasets larger than the RAM
available on your computer; the raster package automatically loads pieces of the
data and computes on each of them in sequence.

The default print method for a raster object is a summary of metadata contained in the raster file.

```
> nlcd
```

```
class : RasterLayer
dimensions : 2514, 3004, 7552056 (nrow, ncol, ncell)
resolution : 150, 150 (x, y)
extent : 1394535, 1845135, 1724415, 2101515 (xmin, xmax, ymin, ymax)
coord. ref. : +proj=aea +lat_1=29.5 +lat_2=45.5 +lat_0=23 +lon_0=-96 +x_0=0 +y_0=0 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
data source : /nfs/public-data/training/nlcd_agg.grd
names : nlcd_2011_landcover_2011_edition_2014_03_31
values : 0, 95 (min, max)
attributes :
ID COUNT Red Green Blue Land.Cover.Class Opacity
from: 0 7854240512 0 0 0 Unclassified 1
to : 255 0 0 0 0 0
```

The plot method interprets the pixel values of the raster matrix according to a pre-defined color scheme.

```
> plot(nlcd)
```

The `crop()`

function trims a raster object to a given spatial “extent” (or
range of x and y values).

```
extent <- matrix(st_bbox(huc_md), nrow=2)
nlcd <- crop(nlcd, extent)
plot(nlcd)
plot(huc_md, col = NA, add = TRUE)
```

The extent can be extracted from sp package objects with `extent`

,
but must be created “from scratch” for an `sfc`

. Here, we crop the `nlcd`

raster
to the extent of the `huc_md`

polygon, then display both layers on the same map.
Also note that the transformed raster is now loaded in R memory, as indicated by
the size of `nlcd`

. We could have also saved the output to disk by specifying an
optional `filename`

argument to `crop`

; the same is true for many other
functions in the raster package.

A raster is fundamentally a data matrix, and individual pixel values can be
extracted by regular matrix subscripting. For example, the value of
the *bottom*-left corner pixel:

```
> nlcd[1, 1]
```

```
41
```

The meaning of this number is not immediately clear. For this particular dataset, the mapping of values to land cover classes is described in the data attributes:

```
> head(nlcd@data@attributes[[1]])
```

```
ID COUNT Red Green Blue Land.Cover.Class Opacity
1 0 7854240512 0 0.0000000 0 Unclassified 1
2 1 0 0 0.9764706 0 1
3 2 0 0 0.0000000 0 1
4 3 0 0 0.0000000 0 1
5 4 0 0 0.0000000 0 1
6 5 0 0 0.0000000 0 1
```

The `Land.Cover.Class`

vector gives string names for the land cover type
corresponding to the matrix values. Note that we need to add 1 to the raster
value, since these go from 0 to 255, whereas the indexing in R begins at 1.

```
nlcd_attr <- nlcd@data@attributes
lc_types <- nlcd_attr[[1]]$Land.Cover.Class
```

```
> levels(lc_types)
```

```
[1] "" "Barren Land"
[3] "Cultivated Crops" "Deciduous Forest"
[5] "Developed, High Intensity" "Developed, Low Intensity"
[7] "Developed, Medium Intensity" "Developed, Open Space"
[9] "Emergent Herbaceuous Wetlands" "Evergreen Forest"
[11] "Hay/Pasture" "Herbaceuous"
[13] "Mixed Forest" "Open Water"
[15] "Perennial Snow/Ice" "Shrub/Scrub"
[17] "Unclassified" "Woody Wetlands"
```

### Raster Math

Mathematical functions called on a raster gets applied to each pixel. For a
single raster `r`

, the function `log(r)`

returns a new raster where each pixel’s
value is the log of the corresponding pixel in `r`

.

Likewise, addition with `r1 + r2`

creates a raster where each pixel is the sum of the
values from `r1`

and `r2`

, and so on. Naturally, spatial attributes of rasters
(e.g. extent, resolution, and projection) must match for functions that operate
pixel-wise on multiple rasters.

Logical operations work too: `r1 > 5`

returns a raster with pixel values `TRUE`

or `FALSE`

and is often used in combination with the `mask()`

function.

```
pasture <- mask(nlcd, nlcd == 81,
maskvalue = FALSE)
plot(pasture)
```

A pasture raster results from unsetting pixel values where the mask (`nlcd == 81`

)
is false (`maskvalue = FALSE`

).

To further reduce the resolution of the `nlcd`

raster, the `aggregate()`

function combines values in a block of a given size using a given function.

```
nlcd_agg <- aggregate(nlcd,
fact = 25, fun = modal)
nlcd_agg@legend <- nlcd@legend
plot(nlcd_agg)
```

Here, `fact = 25`

means that we are aggregating blocks 25 x 25 pixels and ```
fun =
modal
```

indicates that the aggregate value is the mode of the original pixels
(averaging would not work since land cover is a categorical variable).

## Crossing Rasters with Vectors: Prelude

Presently, to mix raster and vectors, we must convert needed `sf`

objects
to their counterpart `Spatial*`

objects:

```
sesync <- as(sesync, "Spatial")
huc_md <- as(huc_md, "Spatial")
counties_md <- as(counties_md, "Spatial")
```

The creation of geospatial tools in R has been a community effort, and not necessarilly a well-organized one. One current stumbling block is that the raster package, which is tightly integrated with the sp package, has not caught up to the sf package. The still-under-development stars package aims to remedy this problem and others.

## Crossing Rasters with Vectors

The `extract`

function allows subsetting and aggregation of raster values based
on a vector spatial object.

```
plot(nlcd)
plot(sesync, col = 'green',
pch = 16, cex = 2, add = TRUE)
```

When extracting by point locations (i.e. a *SpatialPoints* object), the result
is a vector of values corresponding to each point.

```
sesync_lc <- extract(nlcd, sesync)
```

```
> lc_types[sesync_lc + 1]
```

```
[1] Developed, Medium Intensity
18 Levels: Barren Land Cultivated Crops ... Woody Wetlands
```

When extracting with a polygon, the output is a vector of all raster values for pixels falling within that polygon.

```
county_nlcd <- extract(nlcd_agg,
counties_md[1,])
```

```
> table(county_nlcd)
```

```
county_nlcd
11 21 22 23 24 41
3 1 4 5 2 1
```

To get a summary of raster values for **each** polygon in a `SpatialPolygons`

object, add an aggregation function to `extract`

via the `fun`

argument. For
example, `fun = modal`

gives the most common land cover type for each polygon in
`huc_md`

.

```
modal_lc <- extract(nlcd_agg,
huc_md, fun = modal)
huc_md$modal_lc <- lc_types[modal_lc + 1]
```

```
> head(huc_md)
```

```
AREA PERIMETER HUC250K_ HUC250K_ID HUC_CODE
903 6413577966 454290.2 904 916 02050306
915 1982478663 292729.7 916 927 02040205
937 5910074657 503796.5 938 948 02070004
956 3159193443 506765.4 957 968 02060002
966 4580816836 433034.1 967 978 05020006
975 2502118608 252945.8 976 987 02070009
HUC_NAME REG SUB ACC CAT modal_lc
903 Lower Susquehanna 02 0205 020503 02050306 Deciduous Forest
915 Brandywine-Christina 02 0204 020402 02040205 Hay/Pasture
937 Conococheague-Opequon 02 0207 020700 02070004 Hay/Pasture
956 Chester-Sassafras 02 0206 020600 02060002 Cultivated Crops
966 Youghiogheny 05 0502 050200 05020006 Deciduous Forest
975 Monocacy 02 0207 020700 02070009 Cultivated Crops
```

## Resources

- raster package vignette.
- R.S. Bivand, E.J. Pebesma and V. Gómez-Rubio (2013) Applied Spatial Data Analysis with R. UseR! Series, Springer.
- R. Lovelace et al., Geocomputation with R
- F. Rodriguez-Sanchez. Spatial data in R: Using R as a GIS.
- CRAN Task View: Analysis of Spatial Data

## Exercises

### Exercise 1

Produce a map of Maryland counties with the county that contains SESYNC colored in red.

### Exercise 2

Use `st_buffer`

to create a 5km buffer around the `state_md`

border and plot it as a dotted line (`plot(..., lty = 'dotted')`

) over the true state border. **Hint**: check the layer’s units with `st_crs()`

and express any distance in those units.

### Exercise 3

The function `cellStats`

aggregates accross an entire raster. Use it to figure out the proportion of `nlcd`

pixels that are covered by deciduous forest (value = 41).

## Solutions

### Solution 1

```
> plot(counties_md$geometry)
> overlay <- st_within(sesync, counties_md)
> counties_sesync <- counties_md[overlay[[1]], 'geometry']
> plot(counties_sesync, col = "red", add = TRUE)
> plot(sesync, col = 'green', pch = 20, add = TRUE)
```

## Solution 2

```
> bubble_md <- st_buffer(state_md, 5000)
> plot(state_md)
> plot(bubble_md, lty = 'dotted', add = TRUE)
```

### Solution 3

```
> cellStats(nlcd == 41, "mean")
```

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