You can directly use the GDAL contour polygons tool. It is available from GDAL version 2.4.0. To see which GDAL version your QGIS installation uses go to Menu Help / About, see screenshot. If installed, it looks like this:
If you have GDAL >= 2.4.0, but the entry contour polygons does not appear in the QGIS processing toolbox, you can use the "...
As your DEM seems to be in a geographic CRS ( EPSG:4326 ; WGS84), the unit of measurement is in degrees, not in meters. So measurements of length do not make sense: your cellsize is 0.0002777 degrees.
Reproject your DEM to a projected CRS to have meters as measurement unit.
Problem is that contour lines may not be closed, so it's hard to create the polygons.
Simplest GDAL way seems to me classify the raster and then polygonize it.
gdal_calc.py --calc='(A<=30)*30+(A>30)*A//5*5' --outfile=classified.tif -A input.tif
The calc expression turns all values less than 30 to 30, and greater values are rounded to the floor ...
The output extend you defined is quite weird:
'TARGET_USER_XMIN TARGET_USER_XMAX TARGET_USER_YMIN TARGET_USER_YMAX' : '-93.137700000,-93.137400000,45.008800000,45.009000000 [EPSG:26915]'
You use EPSG:26915 (NAD83 / UTM zone 15N), but your coordinates seem to be in EPSG:4326. The coordinates -93.137700000,45.008800000 in EPSG:26915 are located somewhere in ...
Create a polygon named delete for the region you want to delete from the raster (unneeded region, in orange on the screenshot below).
Create a polygon extent (red outline polygon) that covers the extent of your raster using Menu Processing / Toolbox / Create layer from extent and set the raster as input.
Cut out shape of delete from the polygon extent ...
Get a polygon layer of the water surface, for example from OpenStreetMaps (OSM). See here how to download: https://gis.stackexchange.com/a/368774/88814. Another option is to use the QuickOSM plugin. You can use the OpenStreetMap tags natural=water (red on the screenshot) and natural=bay (blue).
You will get many very small water features, so probably you ...
I found a solution for this in R:
I created a uniform raster with all cells at elvetion 1
Using the function "xyFromcell" in the "raster" package I created separate rasters of latitude and of longitude of the uniform raster
I conducted a raster calculation of the form [f(x) = mx + b] using the slope and the intercept from the line ...