The following note is a preliminary draft and may be updated; watch this space.
GEODETICS OF SUPERK R. J. Wilkes, 8/24/96 * Our GPS receiver in the radon hut says its coordinates are lat 36 deg 24 min 31.2 sec N long 137 deg 18 min 30.5 sec E alt 389 meters ASL (GPS coordinates are essentially equivalent to WGS-84 coordinates which are the current geophysical standard) These values result from averaging 90,000 gps fixes. Histograms of recent individual fixes are consistent with this estimate (see below). * At this location: one minute of latitude = 1852.8m one min of longitude = 1491.3m The least-count of the GPS receiver is 0.1 sec, which = 3.09 m in latitude = 2.49 m in longitude. The GPS system provides nominal accuracy of 100 m in the C-code mode we use. Note that this is not a statistical error, but a deliberate corruption of precision by US-DOD. Averaging over a 24 hr period as we do, the ranging error is about 15 m. With a mean PDOP (Positional Dilution of Precision) factor of 4.04, we get a positioning error of about 60m, corresponding to 1.9 sec in latitude and 2.4 sec in longitude. We should be able to reduce this with repeated long-term averaging. * Mr. Fujii of the Kamioka Mining Co. kindly provided detailed maps of the mine. We scanned these and used Photoshop to measure distances at the pixel level. Resulting offsets from the centerline of the Atotsu tunnel mouth: to SK tank center: 1864.6 meters N, 393.4 m E to the roadway outside the tank entrance: 1823.7 m N, 344.7 m E These measurements should be taken with +/- 5 m precision (accuracy of the map is unknown, but it is the best available information). * Hans Berns measured the offset from the tunnel mouth centerline to the GPS antenna on the radon hut: 17.6 m along roadway centerline extended 8.1 m perpendicular to extended centerline 5.2 m above level of centerline at mouth. The roadway centerline makes an angle of 10.7 deg E of north. So the N and E components of the above vectors are: N1 = 17.6*cos(10.7deg) E1=17.6*sin(10.7) = 17.29m S = 3.26m W N2 = 8.1*sin 10.7deg) E2=8.1*cos(10.7deg) = 1.50 m S =7.95m E so the net offset of the antenna from the tunnel mouth centerline is N1+N2 = 18.79 m S W1+W2 = 4.69 m E I do not have information on the slope of the road, but although water flows nicely through the ditch, the road seems nearly level. Therefore I will take the tank top level to be the same as the tunnel mouth level. The SK origin is 20m below the tank top. Adding these to the map coordinates gives total offsets from antenna to tank: N: 1883.37m E: 388.69m Z: -25.2m * As noted above, at this location, one minute of latitude = 1852.8m one min of longitude = 1491.3m so the offsets given above are: N: 1.0165 min = 1 min 1.0 sec E: 0.2606 min = 0 min 15.6 sec Z: -25.2 m * The Superk standard coordinate system has conventional right-handed Cartesian coordinates with origin at the nominal center of the tank, +X axis pointing toward String 1 of PMTs, and the -Y axis 42.5 deg west of North. (see diagram below). Kai Martens confirms that his figure in the 11/95 Collaboration Meeting notes is mislabelled, and this direction is geographic, not magnetic, North. However, I am not yet certain whether the N direction indicated on the mine maps is magnetic or geographic north. The declination (deviation of a magnetic compass from geographic North) at Mozumi can be read off from a US-CGS map dated 1990. I read 7.2 deg W (increasing at the rate of 1.5 min/year, so translated to 1996 we get 7.35 deg W). I have asked Mr. Fujii for details, and also for a more precise declination value if he has one. If the direction indicated is in fact magnetic north, it means the -Y axis points 49.85 deg W of geographic North. Otherwise, the offset is 42.5 deg. * CONCLUSION: the SuperK tank coordinate origin is thus at geodetic coordinates: latitude: 36 deg 25 min 32.2 sec N longitude: 137 deg 18 min 46.1 sec E altitude: 363.8 m above WGS-84 ellipsoid (nominal sea level). Assuming the mine maps follow convention and are plotted relative to geographic (rather than magnetic) north, the -Y axis points 42.5 deg west of North. (I will update this note if Mr. Fujii tells me otherwise)Fig. 1: histograms of recent GPS fixes compared to 90,000-sample averages. Fig. 2: map of mine supplied by Mr. Fujii. Fig. 3: diagram of SuperK coordinate system.
Correspondence between RJW and H. Nuomi on GPS surveying of SK:
****Note: following is Noumi's view of the difference between magnetic,
"true" and dai-7-kei (surveyors' statutory) north:
"I hear that the deviation between magnetic and true north is 6 deg 54 min
52 sec West, and one between "Dai-7-kei Y axis(north)" and true north is 5
min 8 sec East."
Date: Thu, 5 Sep 1996 20:33:43 +0900
From: noumi@kekps.kek.jp
To: wilkes@sukip02.icrr.u-tokyo.ac.jp
Subject: geographic coordinate of ...
Dear Dr. Wilkes,
Prof. Nakamura asked me to inform you the geograhic coordinate of the SK
center and the Atotsu entrance. We carried out a GPS survey last year.
We took a point and put a small pile to place a GPS antena near the
Atotsu entrance. Maybe, the pile is still there. Mr. Fujii of Kamioka-mine co.
knows the position. We made an optical survey from the entrance to the SK tank.
As GPS usually employs the WGS-84 coordinate system, our measurement also
follows the system. WGS-84 is different from the geographic coorniate system
we usually use in Japan. (Particularly, you can find a large deviation in
height.)
ATOTSU SK
latitude(phi) 36~24'31.1391" 36~25'32.6155"
longitude(lam) 137~18'29.8702" 137~18'37.0929"
ellipsoidal height(H) 384.0555m 371.5146m
You can easily obtain the coordinate in the 3-D (XYZ) system as follows.
X = (N + H)cos{phi}cos{lam},
Y = (N + H)cos{phi}sin{lam},
Z = (N(1-e**2) + H)sin{phi},
where
N = a/sqrt{1-(e*sin{phi})**2}, e**2 = f(2-f),
a = 6378137 m,
f=1/298.257223.
Regards,
H. Noumi
From wilkes@dumand.phys.washington.eduFri Oct 11 16:44:34 1996
Date: Wed, 11 Sep 1996 17:08:29 -0700 (PDT)
From: "R. Jeffrey Wilkes"
To: "H. Noumi"
Cc: Young-Ken , Hans Berns
Subject: Re: geographic coordinate of ... (fwd)
Dr. Noumi:
thank you very much for your message (and please extend my thanks
to Prof. Nakamura also).
As you can see below, our measurements for the tunnel mouth and tank
location are in agreement within C-code errors. (The coordinates I give at
the beginning of the note below are for our antenna on the radon hut). I
will add your calculation of the offset from tunnel mouth to tank center
to my note (see below) on the WWW
(=http:/www.phys.washington.edu/~superk/data/location.html)
I have a few further questions:
1. I presume that what you mean by "SK" is the origin of the standard SK
coordinate system?
2. Were your measurements made with a differential GPS system?
3. How many readings did you average?
4. Finally, most important:
Mr. Fujii told me his maps actually show *magnetic* north, which means my
calculation of SK coordinates should be in error (and disagree with
yours). He said that the deviation between magnetic and true north is 6.69
deg W (but said this number is many years old, so my estimate of the
deviation is probably closer due to the time variation), and 6.78 deg W of
"Dai-7-Ken North" which i assume is a Japanese legal surveyors standard.
Can you help me resolve this? Did you also make the assumption that the
direction marked "N" on SK diagrams is true (WGS-84) North? If so, perhaps
you should speak to Mr. Fujii and see if I misunderstood him.
I plan to make properly DOP-weighted averages of long series to refine the
antenna position as nicely as possible, unless you have already used a
differential system to maximum precision.
From noumi@kekpsa.kek.jpFri Oct 11 16:44:01 1996
Date: Thu, 12 Sep 1996 21:24:27 +0900
From: noumi@kekpsa.kek.jp
To: wilkes@dumand.phys.washington.edu
Subject: Re: geographic coordinate of ... (fwd)
Dr. Wilkes,
>1. I presume that what you mean by "SK" is the origin of the standard SK
>coordinate system?
I don't know what is the origin of the standard SK coordinate.
"SK" is the point 21.6 meter below the center of the "roof" of the tank,
which is the center of the water tank we assumed.
>2. Were your measurements made with a differential GPS system?
Yes, they were. We took the statistic method with using at least 4 fixes
in a measurement.
>3. How many readings did you average?
Typically, it takes 1-2 hours per measurement for a local(within 20 km between
fixes) GPS survey. (Data acquisition interval is 30 sec.)
>4. Finally, most important:...
I hear that the deviation between magnetic and true north is 6 deg 54 min 52
sec West, and one between "Dai-7-kei Y axis(north)" and true north is 5 min 8
sec East.
We did a long baseline survey between Kamioka and Tsukuba last year to obtain
the relative position of SK to KEK PS directly. The coordinate I sent you
is given from the reference point in KEK where the coordinate is given in
Tokyo Datum (Japan standard). We estimate precision of the survey is ~30cm and
~90cm in horizontal and vertical plane at SK.
At that time we set 7 fixes in Kamioka area for the survey. Two of them are
located at around the Mozumi tunnel mouth, and another two are at around the
Atotsu mouth. The other 3 fixes are set around the "triangle point" in Kamioka
town, where the geographic coordinate is given by the Geographical Survey
Institute. To obtain the SK position, we made two sets of traverse survey
from Atotsu fixes and Mozumi fixes to SK. (Actually, to do this traverse
survey, we measured two points at each tunnel mouth with GPS.) So, our
measurement is independent of the map of the Kamioka-mine.
Regards,
H. Noumi