Introduction

This notebook provides examples of:

Dependencies

This notebook requires a number of packages:

# tidyverse packages
library(dplyr)       # data cleaning
library(ggplot2)     # static mapping
library(readr)       # read/write tabular data

# spatial packages
library(mapview)     # preview spatial data
library(sf)          # spatial data tools
library(tigris)      # access TIGER/line data

# other packages
library(here)        # file path management
library(measurements) # unit conversion
library(naniar)     # missing data

Load Data

This notebook requires one set of data:

sluPlaces <- read_csv(here("data", "example-data", "sluPlaces.csv"))
Rows: 6 Columns: 4
── Column specification ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): name
dbl (3): id, lng, lat

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Data Cleaning Notes

Make sure your x and y coordinate variables are numeric or double:

str(sluPlaces)
spec_tbl_df [6 × 4] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
 $ id  : num [1:6] 1 2 3 4 5 6
 $ name: chr [1:6] "Morrissey Hall" "Starbucks" "Simon Rec" "Pius Library" ...
 $ lng : num [1:6] -90.2 -90.2 -90.2 -90.2 -90.2 ...
 $ lat : num [1:6] 38.6 38.6 38.6 38.6 38.6 ...
 - attr(*, "spec")=
  .. cols(
  ..   id = col_double(),
  ..   name = col_character(),
  ..   lng = col_double(),
  ..   lat = col_double()
  .. )
 - attr(*, "problems")=<externalptr> 

If they are not, use mutate() with as.numeric() to convert them.

Next, we need to make sure there are no missing data in our coordinate columns. This will cause errors when we go to project these data.

miss_var_summary(sluPlaces)

Great! We have no missing data in lng and lat. If we did, we would need to use filter() from dplyr to remove those missing values. Also be aware of coordinates that are set to 0,0. These can sometimes be used to identify missing data as well.

sluPlaces %>%
  filter(lng == 0 | lat == 0)

Again, excellent, no missing data!

Identifying Coordinates

Identifying the coordinate system that lng and lat represent can be challenging:

Once we have candidates for projecting our points, we need to identify the CRS/EPSG values (or, alternatively, the Proj4 strings) that correspond to our coordinate system candidate(s). For this, we’ll use websites like EPSG.io and Spatial Reference.

Project Data

First, we want to convert these data to from a tibble to an sf object with st_as_sf(). We use the lng variable as our x variable and lat as our y variable, and use 4269 for our crs argument since these data are in decimal degrees and this corresponds to the likely coordinate system we identified above:

sluPlaces_sf <- st_as_sf(sluPlaces, coords = c("lng", "lat"), crs = 4269)

Next, we want to confirm that this worked:

mapview(sluPlaces_sf)

Excellent!

Transform Our Projection

We’ve already used st_transform(), but now can do so with purpose. For example, to convert our data to State Plane (meters). We’ll use the data based on the 2007 update to NAD 1983:

sluPlaces_statePlane <- st_transform(sluPlaces_sf, crs = 3601)

If we need our data in feet, there are also options. However, these are ESRI products that are not included in the sf package. How do we know? We can use the EPSG value 102696.

st_transform(sluPlaces_sf, crs = 102696)

Note that error includes this language - GDAL Error 1: PROJ: proj_create_from_database: crs not found. Even so, we can still use the coordinate system by specifying the Proj4 string value instead of the CRS number:

sluPlaces_statePlane_ft <- st_transform(sluPlaces_sf, crs = "ESRI:102696")

Sometimes this doesn’t work, and so it is also useful to know how to apply Proj4 strings as well.

sluPlaces_statePlane_ft <- st_transform(sluPlaces_sf, crs = "+proj=tmerc +lat_0=35.83333333333334 +lon_0=-90.5 +k=0.9999333333333333 +x_0=250000 +y_0=0 +ellps=GRS80 +datum=NAD83 +to_meter=0.3048006096012192 +no_defs ")

This should give us correctly projected data. Using this trick with the Proj4 strings also works, by the way, with st_as_sf() as well.

Write Data

Finally, we’ll write our data:

st_write(sluPlaces_statePlane, here("data", "example-data", "clean-data", "sluPlaces.shp"), delete_dsn = TRUE)
Deleting source `/Users/prenercg/GitHub/slu-soc5650/module-3-projections/data/example-data/clean-data/sluPlaces.shp' using driver `ESRI Shapefile'
Writing layer `sluPlaces' to data source 
  `/Users/prenercg/GitHub/slu-soc5650/module-3-projections/data/example-data/clean-data/sluPlaces.shp' using driver `ESRI Shapefile'
Writing 6 features with 2 fields and geometry type Point.

The st_write() function identifies the file type from what you include at the end of the here() statement. If I am working solely in R, I tend to use .geojson because:

  1. It does not impose limits on column names or data types.
  2. It is an open standard for storing data that is plain text.
  3. It can be previewed live on GitHub.com (where I share most my data).

However, if you are going to be working in the ESRI ecosystem, saving data as shapefiles is suggested. Note that #1 above needs to be addressed - keep variable names short (8 characters or less) and convert big numbers to strings or remove them completely before saving.

Using Projections to Calculate Area

One final task we have when working with projections is to use them as the basis for making calculations. Often, this entails calculating area so that we can use it for normalizing our data. Sometimes our data come with measurements, but we don’t know what those units are. Other times, we don’t have an area measure at all. Consider these data from tigris:

moCounties <- counties(state = 29) %>%
  select(GEOID, NAMELSAD, ALAND, AWATER)

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There are both ALAND and AWATER columns, but it isn’t immediately clear what their units are (they are in meters, FYI). If we want the total area of these units, we can combine a few functions from sf, dplyr, and measurements to achieve a few different outcomes. First, we’ll re-calculate the area based on a projected coordinate system. We need to move from the current coordinate system to a projected coordinate system. To get a sense of our starting place, we’ll use st_crs():

st_crs(moCounties)
Coordinate Reference System:
  User input: NAD83 
  wkt:
GEOGCRS["NAD83",
    DATUM["North American Datum 1983",
        ELLIPSOID["GRS 1980",6378137,298.257222101,
            LENGTHUNIT["metre",1]]],
    PRIMEM["Greenwich",0,
        ANGLEUNIT["degree",0.0174532925199433]],
    CS[ellipsoidal,2],
        AXIS["latitude",north,
            ORDER[1],
            ANGLEUNIT["degree",0.0174532925199433]],
        AXIS["longitude",east,
            ORDER[2],
            ANGLEUNIT["degree",0.0174532925199433]],
    ID["EPSG",4269]]

This confirms that we are using a geographic coordinate system (this is typical for TIGER/Line data). We’ll switch to Albers Equal Area Conic for the contiguous United States:

moCounties <- st_transform(moCounties, crs = "ESRI:102003")
# moCounties <- st_transform(moCounties, crs = "+proj=aea +lat_1=29.5 +lat_2=45.5 +lat_0=37.5 +lon_0=-96 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs")

I’ve also included the Proj4 string, but it is commented out. Notice how +units=2 appears in the Proj4 string. This means are data are in meters. If we wanted to recalculate our area units meters, we can use the st_area() function and the geometry column to do so:

moCounties %>%
  select(-c("ALAND", "AWATER")) %>%
  mutate(sq_m = as.numeric(st_area(geometry)), .after = NAMELSAD) %>%
  mutate(sq_km = conv_unit(sq_m, from = "m2", to = "km2"), .after = sq_m) -> moCounties

We can do the same thing if we want to convert to square miles:

moCounties <- mutate(moCounties, sq_mi = conv_unit(sq_m, from = "m2", to = "mi2"), .after = sq_km)

Writing the sq_m column to shapefile might be tricky, so its best to do these conversions and then remove the source column before saving!

Symbolizing Points

One thing I wanted to share quickly this week is how we can approach displaying points with ggplot2, since we happen to have some point data to work with. We’ll use the shape and size arguments to make simple adjustments:

ggplot() +
  geom_sf(data = sluPlaces_sf, shape = 18, size = 4)

Some point symbols - those with values 21 through 25 - can be customized with fills and colors as well:

ggplot() +
  geom_sf(data = sluPlaces_sf, shape = 22, size = 6, fill = "#9d4a9d", color = "#5d92e5")

---
title: "Meeting Examples, Completed"
author: "Christopher Prener, Ph.D."
date: '(`r format(Sys.time(), "%B %d, %Y")`)'
output: 
  github_document: default
  html_notebook: default 
always_allow_html: true
---

## Introduction
This notebook provides examples of:

  * working with projections with `st_transform()`, 
  * projecting points with `st_as_sf()`,
  * saving geometric data with `st_read()`,
  * calculating area with `st_area()` and the `measurements` package,
  * and use the `shape` and `size` arguments with `ggplot2`.

## Dependencies
This notebook requires a number of packages:

```{r load-packages}
# tidyverse packages
library(dplyr)       # data cleaning
library(ggplot2)     # static mapping
library(readr)       # read/write tabular data

# spatial packages
library(mapview)     # preview spatial data
library(sf)          # spatial data tools
library(tigris)      # access TIGER/line data

# other packages
library(here)        # file path management
library(measurements) # unit conversion
library(naniar)     # missing data
```

## Load Data
This notebook requires one set of data:

```{r load-data}
sluPlaces <- read_csv(here("data", "example-data", "sluPlaces.csv"))
```

## Data Cleaning Notes
Make sure your `x` and `y` coordinate variables are numeric or double:

```{r class}
str(sluPlaces)
```

If they are not, use `mutate()` with `as.numeric()` to convert them.

Next, we need to make sure there are no missing data in our coordinate columns. This will cause errors when we go to project these data.

```{r missing}
miss_var_summary(sluPlaces)
```

Great! We have no missing data in `lng` and `lat`. If we did, we would need to use `filter()` from `dplyr` to remove those missing values. Also be aware of coordinates that are set to 0,0. These can sometimes be used to identify missing data as well.

```{r zero-coords}
sluPlaces %>%
  filter(lng == 0 | lat == 0)
```

Again, excellent, no missing data!

## Identifying Coordinates
Identifying the coordinate system that `lng` and `lat` represent can be challenging:

  * Sometimes, the "metadata" that your tabular data come with (if they come with any at all) will state what coordinate system was used. This is not typical, however.
  * Decimal degrees are one common way that we represent points. It's helpful to know roughly the longitude and latitude of the area you are working in. For example, St. Louis is roughly located at 38 degrees north and 90.2 degrees west. When I see `-90.2` in the longitude column, this immediately suggests to me that we have decimal degrees data here. If the data originate in the United States, they're typically encoded using NAD 1983. If they are international data, they'll use WGS 1984.
  * Another common way to represent data are with State Plane coordinate systems. There isn't an intuitive way to identify these coordinates. It's also important to know that the State Plane system ships with both feet and meters measurement options. Points encoded in Missouri State Plane East, for example, will either be encoded using feet or meters. Unfortunately, the `x,y` pairs for State Plane meters do not correspond to State Plane feet. So, we need to experiment here. Many local municipalities rely on State Plane for mapping out of tradition, and it's therefore common to run into both the feet and meters versions when working with local data.
  * It's also worth remember that some users may encode their points using UTM zones. This is not nearly as common as State Plane. 
  
Once we have candidates for projecting our points, we need to identify the CRS/EPSG values (or, alternatively, the Proj4 strings) that correspond to our coordinate system candidate(s). For this, we'll use websites like [EPSG.io](https://epsg.io/) and [Spatial Reference](https://spatialreference.org/).

## Project Data
First, we want to convert these data to from a `tibble` to an `sf` object with `st_as_sf()`. We use the `lng` variable as our `x` variable and `lat` as our `y` variable, and use `4269` for our `crs` argument since these data are in decimal degrees and this corresponds to the likely coordinate system we identified above:

```{r project}
sluPlaces_sf <- st_as_sf(sluPlaces, coords = c("lng", "lat"), crs = 4269)
```

Next, we want to confirm that this worked:

```{r preview}
mapview(sluPlaces_sf)
```

Excellent!

## Transform Our Projection
We've already used `st_transform()`, but now can do so with purpose. For example, to convert our data to State Plane (meters). We'll use the data based on the 2007 update to NAD 1983:

```{r convert-to-state-plane-m}
sluPlaces_statePlane <- st_transform(sluPlaces_sf, crs = 3601)
```

If we need our data in feet, there are also options. However, these are ESRI products that are not included in the `sf` package. How do we know? We can use the EPSG value `102696`.

```r
st_transform(sluPlaces_sf, crs = 102696)
```

Note that error includes this language - `GDAL Error 1: PROJ: proj_create_from_database: crs not found`. Even so, we can still use the coordinate system by specifying the `Proj4` string value instead of the CRS number:

```{r convert-to-state-plane-ft}
sluPlaces_statePlane_ft <- st_transform(sluPlaces_sf, crs = "ESRI:102696")
```

Sometimes this doesn't work, and so it is also useful to know how to apply `Proj4` strings as well.

```{r convert-to-state-plane-ft-string}
sluPlaces_statePlane_ft <- st_transform(sluPlaces_sf, crs = "+proj=tmerc +lat_0=35.83333333333334 +lon_0=-90.5 +k=0.9999333333333333 +x_0=250000 +y_0=0 +ellps=GRS80 +datum=NAD83 +to_meter=0.3048006096012192 +no_defs ")
```

This should give us correctly projected data. Using this trick with the `Proj4` strings also works, by the way, with `st_as_sf()` as well.

## Write Data
Finally, we'll write our data:

```{r write-data}
st_write(sluPlaces_statePlane, here("data", "example-data", "clean-data", "sluPlaces.shp"), delete_dsn = TRUE)
```

The `st_write()` function identifies the file type from what you include at the end of the `here()` statement. If I am working solely in `R`, I tend to use `.geojson` because:

  1. It does not impose limits on column names or data types.
  2. It is an open standard for storing data that is plain text.
  3. It can be previewed live on GitHub.com (where I share most my data).

However, if you are going to be working in the ESRI ecosystem, saving data as shapefiles is suggested. Note that #1 above needs to be addressed - keep variable names short (8 characters or less) and convert big numbers to strings or remove them completely before saving.

## Using Projections to Calculate Area
One final task we have when working with projections is to use them as the basis for making calculations. Often, this entails calculating area so that we can use it for normalizing our data. Sometimes our data come with measurements, but we don't know what those units are. Other times, we don't have an area measure at all. Consider these data from `tigris`:

```{r}
moCounties <- counties(state = 29) %>%
  select(GEOID, NAMELSAD, ALAND, AWATER)
```

There are both `ALAND` and `AWATER` columns, but it isn't immediately clear what their units are (they are in meters, FYI). If we want the total area of these units, we can combine a few functions from `sf`, `dplyr`, and `measurements` to achieve a few different outcomes. First, we'll re-calculate the area based on a **projected** coordinate system. We need to move from the current coordinate system to a projected coordinate system. To get a sense of our starting place, we'll use `st_crs()`:

```{r}
st_crs(moCounties)
```

This confirms that we are using a geographic coordinate system (this is typical for TIGER/Line data). We'll switch to Albers Equal Area Conic for the contiguous United States:

```{r}
moCounties <- st_transform(moCounties, crs = "ESRI:102003")
# moCounties <- st_transform(moCounties, crs = "+proj=aea +lat_1=29.5 +lat_2=45.5 +lat_0=37.5 +lon_0=-96 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs")
```

I've also included the `Proj4` string, but it is commented out. Notice how `+units=2` appears in the `Proj4` string. This means are data are in meters. If we wanted to recalculate our area units meters, we can use the `st_area()` function and the `geometry` column to do so:

```{r}
moCounties %>%
  select(-c("ALAND", "AWATER")) %>%
  mutate(sq_m = as.numeric(st_area(geometry)), .after = NAMELSAD) %>%
  mutate(sq_km = conv_unit(sq_m, from = "m2", to = "km2"), .after = sq_m) -> moCounties
```

We can do the same thing if we want to convert to square miles:

```{r}
moCounties <- mutate(moCounties, sq_mi = conv_unit(sq_m, from = "m2", to = "mi2"), .after = sq_km)
```

Writing the `sq_m` column to shapefile might be tricky, so its best to do these conversions and then remove the source column before saving!

## Symbolizing Points
One thing I wanted to share quickly this week is how we can approach displaying points with `ggplot2`, since we happen to have some point data to work with. We'll use the `shape` and `size` arguments to make simple adjustments:

```{r symbolize-points}
ggplot() +
  geom_sf(data = sluPlaces_sf, shape = 18, size = 4)
```

Some point symbols - those with values 21 through 25 - can be customized with fills and colors as well:

```{r symbolize-points-custom}
ggplot() +
  geom_sf(data = sluPlaces_sf, shape = 22, size = 6, fill = "#9d4a9d", color = "#5d92e5")
```



```{r move-to-docs, include=FALSE}
# you do need to include this in any notebook you create for this class
fs::file_copy(here::here("examples", "meeting-3-1-examples-complete.nb.html"), 
              here::here("docs", "index.nb.html"), 
              overwrite = TRUE)
```

