[GRASS-user] Working with USA Public Land Survey System

I have a set of surveyed-section boundaries* for northern California
from the United States Public Land Survey System and would like to use
GRASS to find geometric fractions of these roughly square sections.
For example, I would like to divide a particular section into equal
quarters by bisecting it east-west and north-south and then save the
northwest quarter for further analysis. Can anyone suggest a method to
do this acurately?

* Used for legal descriptions of parcels given in terms of townships and
  ranges.

--
Henry House
+1 530 753 3361 ext. 13
Please don't send me HTML mail! My mail system frequently rejects it.
The unintelligible text that may follow is a digital signature.
See <http://hajhouse.org/pgp&gt; to find out how to use it.
My OpenPGP key: <http://hajhouse.org/hajhouse.asc&gt;\.

Henry House wrote:

I have a set of surveyed-section boundaries* for northern California
from the United States Public Land Survey System and would like to use
GRASS to find geometric fractions of these roughly square sections.
For example, I would like to divide a particular section into equal
quarters by bisecting it east-west and north-south and then save the
northwest quarter for further analysis. Can anyone suggest a method to
do this acurately?

* Used for legal descriptions of parcels given in terms of townships and
  ranges.

perhaps,

g.region vect=boundaries
v.mkgrid grid=2,2

or "g.region -p" then set "g.region n= e=" by hand and v.in.region?

?

Hamish

On Wednesday 30 August 2006 18:14, Henry House wrote:

I have a set of surveyed-section boundaries* for northern California
from the United States Public Land Survey System and would like to use
GRASS to find geometric fractions of these roughly square sections.
For example, I would like to divide a particular section into equal
quarters by bisecting it east-west and north-south and then save the
northwest quarter for further analysis. Can anyone suggest a method to
do this acurately?

* Used for legal descriptions of parcels given in terms of townships and
  ranges.

Hi Henry,

I think that the approach suggested by Hamish will work, but only when using a
projection where the PLSS sections area oriented _exactly_ NS and EW. For
example, looking at the PLSS data in the AEA projection that we use for many
things, the sections are _not_ oriented as such:

http://169.237.35.250/~dylan/temp/plss1.png

However, there is an 'angle' operator in the v.mkgrid module, which may be
able to account for this- although I cannot think of an _automated_ approach
to deriving this angle.

I have extracted a single section, marked red in the above image, like this:

v.extract in=pls out=pls1 list=80800

where 80800 is the cat, or feature id, of the section of interest. Zooming to
the extents of this section:

g.region vect=pls1

http://169.237.35.250/~dylan/temp/plss2.png

looking at the options for v.mkgrid:

Parameters:
       map name of vector map
      grid number of ROWS and COLUMNS in grid
  position Where to place the grid:
        region - current region
        coor - use 'coor' and 'box' options
             options: region,coor
             default: region
      coor lower left EASTING and NORTHING coordinates of map
       box WIDTH and HEIGHT of boxes in grid
     angle angle of rotation (in degrees counter-clockwise)
             default: 0

.... it looks like we might be able to define the grid in terms of a
lower-left point, and the width and height of grid cells, and an angle of
rotation.

this will require some math, but might easily be accomplished with some right
triangle-based trig.

fitting the region to _exactly_ that of the bounding box of our extracted
section:
g.region `v.info -g pls1 | awk ' {gsub("north","n"); gsub("south","s") ;
gsub("east","e") ; gsub("west","w"); gsub("top","t") ; gsub("bottom","b")}
$1 !~ /b|t/ {print $0}' | tr "\n" " "` -p

extracting vertices of selected section: can do this with v.out.ascii and awk,
or with v.to.points

will post some more ideas later.

good luck!

cheers,

Dylan

--
Dylan Beaudette
Soils and Biogeochemistry Graduate Group
University of California at Davis
530.754.7341

On 8/31/06, Dylan Beaudette <dylan.beaudette@gmail.com> wrote:

On Wednesday 30 August 2006 18:14, Henry House wrote:
> I have a set of surveyed-section boundaries* for northern California
> from the United States Public Land Survey System and would like to use
> GRASS to find geometric fractions of these roughly square sections.
> For example, I would like to divide a particular section into equal
> quarters by bisecting it east-west and north-south and then save the
> northwest quarter for further analysis. Can anyone suggest a method to
> do this acurately?

.... it looks like we might be able to define the grid in terms of a
lower-left point, and the width and height of grid cells, and an angle of
rotation.

This would work reasonably well if all of your PLSS sections are
perfectly square. Having dealt with plss in northern california, I can
tell you that the sections in some rural and mountainous areas are not
always regular or even resembling a square. ( good quick example :
http://www.sco.wisc.edu/plss/plss_graphics/section_nosquare_200.jpg )

You might want to go to the county assessors office and see if you can
drum up the official data. Otherwise any attempt at trying to
"calculate" what are legally defined boundaries may get you in
trouble.

--
Matt Perry
perrygeo@gmail.com
http://www.perrygeo.net

On 8/30/06, Henry House <hajhouse@houseag.com> wrote:

I have a set of surveyed-section boundaries* for northern California
from the United States Public Land Survey System and would like to use
GRASS to find geometric fractions of these roughly square sections.
For example, I would like to divide a particular section into equal
quarters by bisecting it east-west and north-south and then save the
northwest quarter for further analysis. Can anyone suggest a method to
do this acurately?

* Used for legal descriptions of parcels given in terms of townships and
  ranges.

--
Henry House
+1 530 753 3361 ext. 13
Please don't send me HTML mail! My mail system frequently rejects it.
The unintelligible text that may follow is a digital signature.
See <http://hajhouse.org/pgp&gt; to find out how to use it.
My OpenPGP key: <http://hajhouse.org/hajhouse.asc&gt;\.

I can not offer any technical solutions to your questions, but as a
Professional Land Surveyor, I do want to stave off any potential
misconceptions about the US Public Land Survey System (PLSS). It is
not, and was never intended to be, a regular Cartesian coordinate grid
like e.g. UTM and using processing algorithms that assume it is a
regular grid will usually lead to faulty results.

The PLSS was developed more than 200 years ago to mark points on the
ground and distribute real property. It is not a geodetic reference
system. The PLSS accommodates measurement errors (that were larger 200
years ago than they are now!) along with "errors" due to convergence
of meridians, and distributes those errors in places that can not be
mathematically modeled. Legally, the only way to divide a section
involves extensive field measurements.

The US Bureau of Land Management (BLM) has a digital product called
the Geographic Coordinate Database (GCDB) that if some areas includes
divisions of sections. This is still not a legal division of the
section, but attempts to follow the legal principles (clear as mud,
huh?). I suggest that you might Google on "California GCDB" for a
while before investing too much time a purely mathematical approach.

Regards,
Rich

--
Richard Greenwood
richard.greenwood@gmail.com
www.greenwoodmap.com

Henry House wrote:
> I have a set of surveyed-section boundaries* for northern California
> from the United States Public Land Survey System and would like to
> use GRASS to find geometric fractions of these roughly square
> sections. For example, I would like to divide a particular section
> into equal quarters by bisecting it east-west and north-south and
> then save the northwest quarter for further analysis. Can anyone
> suggest a method to do this acurately?
>
> * Used for legal descriptions of parcels given in terms of townships
> and ranges.

Dylan Beaudette wrote:

I think that the approach suggested by Hamish will work, but only when
using a projection where the PLSS sections area oriented _exactly_ NS
and EW. For example, looking at the PLSS data in the AEA projection
that we use for many things, the sections are _not_ oriented as such:

http://169.237.35.250/~dylan/temp/plss1.png

However, there is an 'angle' operator in the v.mkgrid module, which
may be able to account for this- although I cannot think of an
_automated_ approach to deriving this angle.

I have extracted a single section, marked red in the above image, like
this:

v.extract in=pls out=pls1 list=80800

where 80800 is the cat, or feature id, of the section of interest.
Zooming to the extents of this section:

g.region vect=pls1

http://169.237.35.250/~dylan/temp/plss2.png

looking at the options for v.mkgrid:

Parameters:
       map name of vector map
      grid number of ROWS and COLUMNS in grid
  position Where to place the grid:
        region - current region
        coor - use 'coor' and 'box' options
             options: region,coor
             default: region
      coor lower left EASTING and NORTHING coordinates of map
       box WIDTH and HEIGHT of boxes in grid
     angle angle of rotation (in degrees counter-clockwise)
             default: 0

.... it looks like we might be able to define the grid in terms of a
lower-left point, and the width and height of grid cells, and an angle
of rotation.

this will require some math, but might easily be accomplished with
some right triangle-based trig.

fitting the region to _exactly_ that of the bounding box of our
extracted section:
g.region `v.info -g pls1 | awk ' {gsub("north","n");
gsub("south","s") ;
gsub("east","e") ; gsub("west","w"); gsub("top","t") ;
gsub("bottom","b")} $1 !~ /b|t/ {print $0}' | tr "\n" " "` -p

extracting vertices of selected section: can do this with v.out.ascii
and awk, or with v.to.points

If true N-S E-W grid is wanted, why not just run v.mkgrid in a lat-lon
location and reproject that to the target location with v.proj?

IIRC, v.mkgrid breaks the line ~ 3 times per box, so results can look
quite nice even when "curved". I think this is how Markus made this
screenshot?

http://grass.ibiblio.org/grass60/screenshots/images/etopo2_grass_laea_9_48N_0E.jpg

Hamish

On Wednesday 30 August 2006 18:14, Henry House wrote:

I have a set of surveyed-section boundaries* for northern California
from the United States Public Land Survey System and would like to use
GRASS to find geometric fractions of these roughly square sections.
For example, I would like to divide a particular section into equal
quarters by bisecting it east-west and north-south and then save the
northwest quarter for further analysis. Can anyone suggest a method to
do this acurately?

* Used for legal descriptions of parcels given in terms of townships and
  ranges.

You might consider creating a dwg from you vector coverage and using CAD to
create the partitions. In most CADs there should be a tool that permits
ratio splits of line segments and polygons. You can then bring that drawing
back to GRASS and then proceed with the GIS work.

JWDougherty