Pasayten Wilderness
Washington, United States, North America

Pasayten Wilderness

Page Type Page Type: Area/Range
Location Lat/Lon: 48.80000°N / 120.5°W
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Overview

More to come. Page was adopted on December 19, 2006.

The Pasayten Wilderness is one of the largest wildernesses in the state of Washington and one of the largest in the contiguous United States. It covers ____ acres in North-Central Washington. Here is a map showing its size and location:


The wilderness is characterized by rivers, creeks, divides, and spurs running in all sorts of directions but the predominate orientation of these are North-South. The "Pasayten Divide" runs East-West. Several notable rivers flow south of this divide, rivers such as the Chewuch.....

There are approximately ____ named or prominence peaks within the wilderness. The highest point is 9,066-ft Jack Mountain on the WSW boundary. The lowest point is ____ along the ____ River on the ___ boundary.

The northern tip of the Pacific Crest Trail runs through it....

Significant Peaks in the Pasayten

The Pasayten's 35-highest summits and 35-most-prominent summits.
Big Craggy (8470F, 3070P) lies just outside the wilderness boundary.
Desolation Peak (3222P) is just outside the wilderness in Ross Lake National Recreation Area.
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Highest Summits

Most-Prominent Summits

01 Jack Mountain (9066F)

01 Remmel Mountain (4365P)

02 Mt. Lago (8745F)

02 Jack Mountain (4186P)

03 Robinson Mountain (8726F)

03 Hozomeen Mountain (3966P)

04 Remmel Mountain (8685F)

04 Mt. Lago (3265P)

05 Ptarmigan Peak (8614F)

05 Castle Peak (3226P)

06 Cathedral Peak (8601F)

06 Three Fools Peak (2440P)

07 Mt. Carru (8595F)

07 "Daemon Peak" (2194P)

08 Monument Peak (8592F)

08 Sheep Mountain (2034P)

09 Osceola Peak (8587F)

09 Windy Peak (1771P)

10 Lost Peak (8464F)

10 Mt. Winthrop (1690P)

11 Blackcap Mountain (8397F)

11 Robinson Mountain (1686P)

12 Lake Mountain (8371F)

12 Nanny Goat Mountain (1660P)

13 West Craggy (8366F)

13 Pasayten Peak (1650P)

14 Amphitheater Mountain (8358F)

14 Lost Peak (1624P)

15 Windy Peak (8334F)

15 Andrew Peak (1581P)

16 Castle Peak (8306F)

16 Hozomeen, South Peak (1483P)

17 Andrew Peak (8301F)

17 Pk 7330 on Jack Mtn Quad (1330P)

18 Apex Mountain (8297F)

18 Buckskin Ridge (1295P)

19 Sheep Mountain (8274F)

19 Coleman Peak (1290P)

20 "Amos Peak" (8259F)

20 "Fool Hen Mountain" (1288P)

21 Many Trails Peak (8241F)

21 Jackita Ridge (1270P)

22 Dot Mountain (8220F)

22 Shull Mountain (1190P)

23 "Trailblazer" [south of Many Trails] (8211F)

23 Bauerman Ridge (1187P)

24 "Fool Hen Mountain" (8168F)

24 Pk 7040 on Castle Pk Quad (1160P)

25 Peepsight Mountain (8146F)

25 Osceola Peak (1147P)

26 Sunrise Peak (8144F)

26 Blizzard Peak (1142P)

27 Armstrong Mountain (8140F)

27 Island Mountain (1128P)

28 Wolframite Mountain (8137F)

28 Bald Mountain [Ashnola Pass Quad] (1091P)

29 Crater Mountain (8128F)

29 Monument Peak (1072P)

30 Three Pinnacles (8124F)

30 Armstrong Mountain (1053P)

31 McLeod Mountain (8099F)

31 Sunrise Peak (1024P)

32 Mt. Rolo (8096F)

32 Billy Goat Mountain (1033P)

33 Arnold Peak (8090F)

33 Holman Peak (1030P)

34 Devils Peak (8081F)

34 Tamarack Peak (1010P)

35 Freds Mountain (8080+F)

35 Pk 7838 on Ashnola Pass Quad (998P)


test


Calculate the distance to the center of the Earth
Enter an elevation, latitude, and longitude
Elevation: Meters Feet
Latitude:   Degrees (negative for S. Hemisphere)
Longitude:   Degrees (negative for W. Hemisphere direction)
   
  Adjust for Geoid Height Don't Adjust
  
 
Geoid Height:   Meters (above or below ellipsoid)
    Feet
  
Distance:   Meters (to the center of the Earth)
    Feet
  
Speed of Point:   km/hour (spin speed around axis)
    miles/hour
  

text


This is the explicit equation to determine the distance of any point on, below, or above the surface of the Earth to the center of the Earth.
This equation uses the WGS 84 ellipsoid as it is the most current for defining the oblate spheroid shape of the Earth. This ellipsoid defines nominal (mean) sea level for the world by way of the two ellipse parameters a and b, the semimajor and semiminor axes respectively.

The Equation


D = f(Φ,Z,G) = {(a4cos2Φ+ b4sin2Φ)/(a2cos2Φ + b2sin2Φ) + 2(Z + G)(a2cos2Φ + b2sin2Φ)½ + (Z + G)2}½
or, in a different HTML format... (if this doesn't show square root symbols, try another browser or just use the equation above)
D = f(Φ,Z,G) = a 4 cos 2 Φ + b 4 sin 2 Φ a 2 cos 2 Φ + b 2 sin 2 Φ + 2 (Z+G) a 2 cos 2 Φ + b 2 sin 2 Φ + (Z+G) 2
where,

D is the distance to the Center of the Earth
Φ is the latitude (the angle measured north or south from the Equator)
Z is the height above sea level (i.e., the elevation of the point on the Earth, such as a summit)
G is the geoid height above or below the ellipsoid (the user must also know the longitude of the point in question)
a is the semimajor axis (the Equatorial diameter of the Earth)
b is the semiminor axis (the pole-to-pole diameter)

The units must be consistent across the equation. If Z is in meters, a, b, and G must be in meters. If Z is in feet, a, b, and G must be in feet.

The WGS 84 ellipsoid defines a and b as:
a = 6,378,137.0 meters = 20,925,646.325 ft
b = 6,356,752.3 meters = 20,855,486.548 ft

The equation will solve for all zero (on the Equator), positive (Northern Hemisphere), and negative (Southern Hemisphere) latitude angles, Φ, within the range of +90 to -90 degrees; positive and negative values for longitude, λ, within the range of -360 + 360 degrees; and for zero, positive, and negative values of elevation Z and geoid height G. The geoid height must be obtained from an outside source (see below).

Microsoft Excel Format


D = SQRT((A1^4*(COS(L1*PI()/180))^2+B1^4*(SIN(L1*PI()/180))^2)/(A1^2*(COS(L1*PI()/180))^2+B1^2*(SIN(L1*PI()/180))^2)+2*(Z1+G1)*SQRT(A1^2*(COS(L1*PI()/180))^2+B1^2*(SIN(L1*PI()/180))^2)+(Z1+G1)^2)

where,

A1 = ellipse parameter a
B1 = ellipse parameter b
L1 = latitude, Φ, in degrees
Z1 = summit elevation above (or below) mean sea level
G1 = geoid height above or below the ellipsoid (i.e., positive or negative).

The cell numbers A1, B1, L1, Z1, and G1 are used as an example here only. Also, any units of measure will work (meters, feet, miles,…) as long as they are consistent across the equation.

The Geoid Height


The geoid height value, G, can be obtained from tabulated data that can be downloaded from the Internet or from websites that will do the calculation for you (A HREF=http://geographiclib.sourceforge.net/cgi-bin/GeoidEval>example). However, I have downloaded the most practical dataset I could use on this webpage (egm84). This data is a table (a grid) of geoid heights at 30-minute (half-degree) arc increments around the globe in the latitudinal and longitudinal directions. This means the table is 361 rows (latitudes) by 721 columns (longitudes) and therefore contains over 260,000 data points (geoid heights in meters). The next level of accuracy up is egm96, which is at 15-minute arc angle increments and therefore would contain over a million data points. In the future if I think Summitpost can handle it, or I can host the table elsewhere (not directly on this page), I may upgrade the calculator above to egm96. egm2008 is way too large of a datafile (it's not even available in ASCII format, that I can tell) and the small added level of accuracy we would get from it would probably not be useful for the scope of this page.

Bilinear interpolation (wiki) is used to obtain the geoid height at a discrete, user-input latitude and longitude that falls inside the square formed by four grid points. There are more sophisticated interpolation techniques that are more accurate such as Lagrangian, bicubic, or spline but these have not been used here due to their complexity. However, I may switch over to one of these in the future if I find the time to put the math to java script. For now, bilinear interpolation is acceptable and only yields an error compared to the other techniques of less than a meter. Besides, there is more error inherent in using egm84 vs. egm96 or egm2008. If the user wishes to use the geoid heights from these latter two, they can use the geographiclib link above.

Caveats


Two caveats to this equation must be addressed:

The first is that the WGS 84 ellipsoid defines mean sea level for the world over (the "ellipsoid") and therefore does not concern itself with continental bulges and their effect on the Earth's gravitational field. These bulges can induce a non-mean sea level (see here). That is, sea level in the region around the land mass can actually be a few tens of meters higher than the nominal sea level of the Earth. Fortunately, gravimetric geoid height evaluation projects have taken place at least three times since the 1980s. This data can be used to calculate the geoid height around the world to within a fair enough accuracy for purposes of comparing summits across the globe.

The second is for summits that have not been measured for a long time, they may have compared to a sea level that was considered the standard prior to WGS 84 resetting it (i.e., using an older geodetic system, such as WGS 66, that was in effect when the summit was last measured). The differences in semimajor and semiminor axes between these two surveys should be taken into account and the height of the summit adjusted accordingly. Without intimate knowledge of when a summit or summits were last surveyed, it may be impossible to know how to make this adjustment. We can take it on faith at this moment that the adjustment is negligible. Also, it is not really determinate, in my view, when looking at a map (or using an online mapping tool such as Acme Mapper, if the elevations shown thereon are in reference to the most current geoid, or even an older geoid, or if they were referenced to a sea level that is sufficiently distant from the summit such that that sea level point itself would have a significantly different geoid height than the summit’s geoid height. In short, when old survey methods were used to triangulate the height of a summit, what was their initial sea level datum? Is this known? Can it be determined?

--Paul Klenke

table

Here are some sample calculations using this equation courtesy of Rob (rgg). The notes at the bottom are from Rob with some modification from Klenke.
If you have javascript activated, you can swap between feet and meters, else you only get to see feet.

Select Units:  Meters Feet



Elevation Latitude Longitude Geoid
height
 Distance
to the
center		 Difference
with
Chimborazo
Chimborazo 20561 -1.469 -78.817 85.335 20946247 0
Huascarán Sur 22133 -9.122 -77.604 70.892 20946101 -132
Kilimanjaro 19341 -3.076 37.354 -64.639 20944722 -1375
Carstensz Pyramid 16024 -4.083 137.185 225.217 20941543 -4844
Everest 29035 27.988 86.925 -100.525 20939230 -6830
Aconcagua 22841 -32.653 -70.011 103.855 20928288 -17977
Elbrus 18510 43.353 42.439 51.552 20911290 -34922
Denali 20322 63.069 -151.007 48.268 20890345 -55865
Vinson 16050 -78.526 -85.617 -81.755 20874254 -71826
North Pole 0 90 n/a   42.969 20855530 -90675

Notes
  • The elevation at the Equator is assumed to be 0 with respect to the WGS 84 ellipsoid. However, the geoid height will probably be non-zero there. This same effect applies to the North Pole, and the sea ice covering the Arctic Ocean is not considered "land."
  • Some of the given mountain elevations are disputed, including that of Chimborazo.
  • All elevations in feet have been calculated from values in meters by dividing by 0.3048.
  • Small errors in latitude do not have a great effect on the calculations. Near the equator and the poles the effects are actually almost negligible: an error of 1º (one full degree!) translates to less than seven meters or less than 22 feet. Relatively speaking, an error around 45 degrees latitude would have the biggest effect, but it would still be small. As an example, if the latitude of Elbrus would be wrong by 1' (one arc-minute), that translates to just over six meters or 20 feet.

Additions and CorrectionsPost an Addition or Correction

Viewing: 1-4 of 4
Redwic

Redwic - Aug 12, 2009 3:47 pm - Voted 10/10

Apex, Wolframite, Bauerman

If you want to, you can now add links to your lists on this page: Apex Mountain and Wolframite Mountain on the "Highest" list. Bauerman Ridge on the "Prominence" list. I planned a trip in the area for this past weekend, and because Gimpilator agreed to accompany me I said he could create the Apex page as long as I could create the other two pages. Teamwork! :-)

Klenke

Klenke - Aug 12, 2009 5:28 pm - Hasn't voted

Re: Apex, Wolframite, Bauerman

I will add these to the Pasayten List i've got there. They won't go on the 100 Highest and 2kP Prominence lists because they don't apply to those.

Redwic

Redwic - Aug 12, 2009 6:45 pm - Voted 10/10

Re: Apex, Wolframite, Bauerman

I'm well aware of that, good buddy. I was only referring to the Pasayten page. :-)

Klenke

Klenke - Aug 12, 2009 7:17 pm - Hasn't voted

Re: Apex, Wolframite, Bauerman

Oh I got ya. Sorry, I read your post too fast...while slackin' at work.

Viewing: 1-4 of 4


Images

View Pasayten Wilderness Image Gallery - 55 Images

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Album32 Mountains & Rocks
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