SPSS Syntax Calculating Distance using Latitude and Longitude

[Björn Türoque]

I was wondering if anyone has some SPSS Syntax to calculate the distance
between two places with latitude and longitude coordinates. I have looked up
the formulas, but have been unable to get the calculations to work.

I currently have latitude and longitude stored in "Decimal degrees" but not
the formula of HH:mm:ss that needs to be put into the formula. Does anyone
have any suggestions about data transformations or have a formula that works
to find distance using "decimal degrees." I am not sure, but this could also
have to do with the difference between radians and degrees as well. Any help
would be appreciated.

Example Data:
Zipcode Latitude  Longitude
    78540 26.30178 -98.15952 78541 26.29592 -98.164071 78543 26.297908
-97.992486

Don

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[Peck, Jon]

In the extendedTransforms.py programmability module on SPSS Developer Central (www.spss.com/devcentral) there are two functions for this: sphDist and ellipseDist.

They take latitude and longitude values in degrees or in radians and calculate the distance.
sphDist uses a spherical approximation to the earth and ellipseDist uses an ellipsoidal approximation, which is a bit more accurate.  Result is returned in miles.

HTH,
Jon Peck

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Don Asay
Sent: Monday, August 11, 2008 11:47 AM
To: [hidden email]
Subject: [SPSSX-L] SPSS Syntax Calculating Distance using Latitude and Longitude

I was wondering if anyone has some SPSS Syntax to calculate the distance
between two places with latitude and longitude coordinates. I have looked up
the formulas, but have been unable to get the calculations to work.

I currently have latitude and longitude stored in "Decimal degrees" but not
the formula of HH:mm:ss that needs to be put into the formula. Does anyone
have any suggestions about data transformations or have a formula that works
to find distance using "decimal degrees." I am not sure, but this could also
have to do with the difference between radians and degrees as well. Any help
would be appreciated.

Example Data:
Zipcode Latitude  Longitude
    78540 26.30178 -98.15952 78541 26.29592 -98.164071 78543 26.297908
-97.992486

Don

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[Richard Ristow]

At 01:46 PM 8/11/2008, Don Asay wrote:

>I was wondering if anyone has some SPSS Syntax to calculate the distance
>between two places with latitude and longitude coordinates.

Jon Peck has pointed out that there's Python code
available on Developer Central. It can also be
done in native SPSS code; see below. It's
slightly less than what's on Developer Central,
accurate, because it ignores the Earth's
deviation from sphericity.(1)  It's from an
earlier posting(2), edited some, not tested.

*  Initialize constants  ............  .
DO IF $CASENUM EQ 1.
*  #EarthRad is the Earth's radius in whatever units you please; .
*  the calculated distance will be in those units. Radius (3):   .
*              6,372.7976 km,
*              3,959.873  statute miles,
*              3,441.035  nautical miles.
.  COMPUTE
    #EarthRad = 6,372.7976 /* km */.

*  #AngleCvt is the number of your angle units (degrees) in      .
*  one of SPSS's angle units (radians). It uses that ARCTAN(1)  .
*  is PI/4 radians.                                              .
    #AngleCvt =  360  /* Number of input units in a full circle */.
               /(8*ARCTAN(1)).

END IF.


*  Compute distance between points with coordinates              .
*  (lat1,lon1) and (lat2,lon2)                                   .

compute distance = #EarthRad*
                     arcos(sin(lat1/#AngleCvt)*sin(lat2/#AngleCvt)
                         + cos(lat1/#AngleCvt)*cos(lat2/#AngleCvt
                           *cos(lon2/#AngleCvt-lon1/#AngleCvt)).
...............................................
(1)
>fromloc = (41.90, 87.65)
>toloc   = (41.73, 71.43)
>[...]
>Using these  coordinates (Chicago, IL to
>Providence, RI), the ellipsoidal and spherical
>results are 836.2705 and 834.0903 miles.
(Jon Peck, "Re: Function for arc cosine", Thu, 7 Jun 2007 09:53:06 -0500)

(2) Richard Ristow, "Re: Function for arc
cosine", Thu, 31 May 2007 11:35:53 -0400, taken
in turn from posting by Seumas Rogan, Thu, 3 Jul 2003 16:23:18 -0700

(3) From http://en.wikipedia.org/wiki/Earth_radius:
Quadratic mean radius: Qr

The ellipsoidal quadratic mean radius provides
the best approximation of Earth's average
transverse meridional radius and radius of
curvature ... This is the equivalent spherical
"great-circle" radius of the ellipsoid).
For Earth, Qr equals 6,372.7976 km (˜3,959.873 mi; ˜3,441.035 nmi).

See also http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html)

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD