1998 URISA Metadata Workshop
Latitude and Longitude Resolution (CSDGM 4.1.1.1 and 4.1.1.2), Abscissa and Ordinate Resolutions (CSDGM 4.1.2.4.3.1 and 4.1.2.4.3.2), and Depth Resolution (CSDGM 4.2.2.2) can sometimes be frustrating to understand and apply to your own data sets. Hopefully, this discussion will help set the record straight about (1) why you should do this and (2) how to calculate these numbers for yourself.
Why Should I Do This?
"These are silly calculations. This is a waste of my time. So
why should I do this?" This is a good question. Answer:
We need to understand what is the smallest piece of earth you can distinguish
or represent in your digital data set.
Let me try to address the significance of these numbers.
Remember long ago when our maps were drawn on paper or sheepskin? Each of those physical objects implied a final "scale" for feature representation. Once we invented the photocopy machine, we could enlarge or reduce the physical map, but we could never change the representative thicknesses of the lines drawn on the original map.
With the advent of digital maps, we entered into the realms of "scaleless" maps (meaning that I can reproduce the map at any scale I choose) and lines as true one-dimensional objects (meaning that there is never any thickness to my lines, thus a major departure from hand-drawn maps). These two features of digital maps have caused a great deal of confusion over the last decade as we (1) have spent a great deal of time automating pre-existing paper maps that have scale and (2) have no consistent way to describe "scale"for digital geospatial data.
In comes RESOLUTION. This term implies the smallest distance we can distinguish between the closest two adjacent points. Woven into this term are factors that determine just what we can accurately measure from a digital data base. Latitude and Longitude Resolution, Abscissa and Ordinate Resolutions, and Depth Resolution are all critical pieces of information that help us understand the limits of what is physically discernible on the earth. These numbers work in conjunction with Horizontal and Vertical Positional Accuracy (CSDGM 2.4.1 and 2.4.2) and Source Scale Denominator (CSDGM 2.5.1.2) to determine the limits of digital geospatial data usefulness.
RESOLUTION of your data reflects:
X How the data were originally collected (Did I collect
information from paper sources or GPS readings? What were the paper maps'
source scales? What is the resolution of the GPS receiver?);
X How the data were then automated (Did I digitize witha
magnifying glass? How well can I reproduce my digitizing? Does my
digitizer have a fine enough grid to distinguish the difference between
two points .0001 inches apart?);
X How the data are stored digitally in my computer and/or
computer program (Did I set my GIS software to store enough decimal places
before I started digitizing? Did some other processing step truncate
decimal places? And just because I can store 14 digits after the decimal
point, which ones are significant?).
How to Calculate These Numbers
Let's calculate Abscissa and Ordinate Resolution (in most cases they
will be the same). I've digitized something from a USGS 7.5 minute
series quadrangle map sheet (scale = 1:24,000). I set my GIS software
to handle lots of decimal places (say, 14 significant places) and set my
digitizing parameters to distinguish digitizer puck clicks as close as.001
board inches. When I digitize, what's limiting the smallest thing
I could conceivably delineate? In this case, it's the combination
of source map scale and digitizing parameters (e.g., fuzzy tolerance for
ARC/INFO users), since I have the capacity to store numbers with many more
than 3 decimal places.
(Source Map Scale in Inches) * (Digitizer Board Inch Setting) = (Resolution)
If source scale is 1:24,000, then 1" = 24,000".
If 1" = 24,000 inches, then (.001 inch on the digitizing board) = 24
inches on the paper map (i.e., .001 * 24,000)
Since CSDGM asks that you represent this number in "planar distance
units of measure" (CSDGM 4.1.2.4.4), we may need to convert this number
into survey feet or meters. For feet: 24" * (1' / 12") = 2 feet.
For meters: 1" = 2.54 cm; 24" = (2.54 cm * 24) = 60.96 cm; 60.96 cm * (1
m / 100 cm ) = .61 meters
No matter how hard I try, with the above constraints, I can never digitize something on the earth smaller than 2-feet on a side.
Final Note
In the example above, I can digitize something no smaller than 2-feet
by 2-feet. Since I am using a USGS 7.5 minute series quadrangle map
sheet with a scale of 1:24,000, I know that the horizontal positional accuracy
for well-defined points is +/- 40 feet because it is defined this way under
the National Map Accuracy Standards. In this case, the resolution
of the data is better than the horizontal positional accuracy. I
can resolve something smaller than I can place it with certainty on the
earth's surface.
Additional Reading
Goodchild, M.F. and Gopal, S., 1989, "Preface". In Accuracy of
Spatial Databases, Goodchild, M.F. and Gopal, S. (eds.), pp xi-xv.(London:
Taylor & Francis).
"Coverage resolution", Help Topic, ESRI ARCDOC on-line help software
for ARC/INFO, version 7.2.1, ESRI, Redlands, CA.
"Fuzzy tolerance", Help Topic, ESRI ARCDOC on-line help software for
ARC/INFO, version 7.2.1, ESRI, Redlands, CA.
URISA 1998 Metadata Workshop, Sunday 19 July
1998 Page
Resolution
CSDGM numbers refer to data element numbers
as represented in the Content Standards for Digital Geospatial Metadata
Workbook (describing June 8, 1994 version of metadata standard), Workbook
Version 1.0, March 24, 1995.