QGIS 3.10: why is PCS project, loaded with a single PCS layer, showing only geographic (angular, lat/long) coordinates instead of linear ones

Question

[OP: my error, circle CRS in LR corner is Project's CRS, not layer's.] QGIS 3.10; Ubuntu 18.04

Glossary for new users: CRS-Coordinate reference system (one of two types, geographic or projected); GCS-geographic coord. system, on-the-globe, lat/long, angles; PCS-projected coordinate system, onto a 2D map, lengths

Here are my steps:

1. start QGIS and set Project->Properties->CRS to a PCS (EPSG:5070)
2. load a PCS raster file as a layer (saved from a previous GCS raster layer, as in this thread)
3. verify that the layer's CRS is identical to the project's
4. note that the coordinates displayed below the layer view are still GCS, lat/long, only.

Another thread advises to edit the attribute table, but that applies to vector layers only.

I know I've expressed a considerable amount of thickness regarding how to handle mixed layers of GCS and PCS coordinates over some years, but it's beginning to feel like I'm closing in on it.

Q. Is there a 'toggle' between displaying GCS and PCS in the main QGIS window? No, but discussion follows.

Response to @Ian Turton's request for 'gdalinfo layer-file'

    grdn36w112_1$ gdalinfo w001001.adf 
Driver: AIG/Arc/Info Binary Grid
Files: .
       ./sta.adf
       ./log
       ./w001001.adf
       ./hdr.adf
       ./prj.adf
       ./metadata.xml
       ./dblbnd.adf
       ./w001001x.adf
Size is 3612, 3612
Coordinate System is:
GEOGCS["NAD83",
    DATUM["North_American_Datum_1983",
        SPHEROID["GRS 1980",6378137,298.257222101,
            AUTHORITY["EPSG","7019"]],
        TOWGS84[0,0,0,0,0,0,0],
        AUTHORITY["EPSG","6269"]],
    PRIMEM["Greenwich",0,
        AUTHORITY["EPSG","8901"]],
    UNIT["degree",0.0174532925199433,
        AUTHORITY["EPSG","9122"]],
    AUTHORITY["EPSG","4269"]]
Origin = (-112.001666666700004,36.001666666664136)
Pixel Size = (0.000277777777778,-0.000277777777778)
Corner Coordinates:
Upper Left  (-112.0016667,  36.0016667) (112d 0' 6.00"W, 36d 0' 6.00"N)
Lower Left  (-112.0016667,  34.9983333) (112d 0' 6.00"W, 34d59'54.00"N)
Upper Right (-110.9983333,  36.0016667) (110d59'54.00"W, 36d 0' 6.00"N)
Lower Right (-110.9983333,  34.9983333) (110d59'54.00"W, 34d59'54.00"N)
Center      (-111.5000000,  35.5000000) (111d30' 0.00"W, 35d30' 0.00"N)
Band 1 Block=256x4 Type=Float32, ColorInterp=Undefined
  Min=1079.405 Max=3847.728 
  NoData Value=-3.4028234663852886e+38

Answer 1

Is there a 'toggle' between displaying GCS and PCS in the main QGIS window?

When the map reference system is geographic, you can only see geographic coordinates. But when the map system is projected, you can see the geographic coordinates referring to the base geographic system from which the projection is made, instead of the projected plane coordinates.

From the Project Properties, in the General tab, change the Coordinates and Bearing Display options:

So, since your map is defined in a projected reference system, you can see longitudes and latitudes in the coordinates.

---

If you're displaying the projected plane coordinates and they look like geographic ones, it's a strong indication that you've changed the layer reference system without reprojecting it. Don't do that, because you are changing the geolocation of the data.

Reload the source raster file in a new layer and export it to your desired reference system.

Change the map reference system to the same projected reference system of the projected layer if you want to see the projected coordinates.

---

A raster layer is always a rectangle of rows and columns of pixels, but when you reproject them to a system with a meridian convergence, you can see triangles of no-data pixels in the corners. If you want to remove them, you need to draw a rectangle in the same reference system and just clip the raster with the rectangle mask, or clip the raster with an extent defined inside the raster.

If you want to see all the raster data which was provided in a rectangle of geographic coordinates, but reprojected in a system which have a 10 degrees of meridian convergence in that location, in a rectangular map without being the raster inclined 10 degrees, and the raster placed in its correct geolocation, it is just not possible.

Answer 2

[I leave my answer rather than delete it because it expresses I think a level of confusion and misconception shared by a lot of newcomers to QGIS. I insert footnote {numbers} and comment on them below.]

This is a practical answer of sorts. I conclude a) that how layers finally appear do depend on the choice of project CRS{1}, and that similarly named proj. coord. sys. do not necessarily give similar results{2}, and b) that sometimes the obvious thing to do is precisely wrong{3}.

I post three images. In the first two, the Project's CRS is 5070 (NAD83-Conus-Albers{1}). In the third, it is 3742 (NAD83 UTM 12N{2}). In all three cases, the same, single NAD83 raster layer, 4269, is loaded and displayed.

In the first image, the layer does show UTM coordinates, as expected from a projected coord system, but it is rotated{1}. This rotation is a problem because I wish to measure and crop rectangular areas.

In the second image, the layer's CRS has been changed to match the project's, which caused it to disappear{4}, requiring "Zoom to layer." Although unrotated now, the coord. values, in meters no doubt, are apparently merely copies of the geographic coords. in the original NAD83 layer, and thus useless for measuring.

Note that in the third image, I appear to get what I quest: an unrotated image with UTM coordinates{2}. A new project has been created with CRS set to 3742 before the NAD83 raster layer is added.

Note: recalling discussions that "defining" a layer's CRS is completely distinct from "projecting" it, I went back to the situation in the first image; namely, Project 5070, Layer 4269. I then exported that layer to a file with a 5070 CRS and loaded it back in. It came back in rotated{1}: unusable for my purposes. For completeness' sake, I repeated that with 3742 as the project CRS, saving and reloading the 4269 layer as a 3742 file. It came back without rotation, and displaying UTM coords{2}.