#Velocity Data for Byrd Glacier # #Source of Data: #Brecher, Henry H. 1982. Photogrammetric determination of surface velocities # and elevations on Byrd Glacier. Antarctic Journal of the U.S., # XVII(5): 79-81. # #Brecher, Henry H. 1986. Surface velocity determination on large polar # glaciers by aerial photogrammetry. Annals of Glaciology, VIII: 22-26. # #Van der Veen, C.J., and I.M. Whillans. 1989a. Force Budget: I. Theory # and numerical methods. Journal of Glaciology, 35(119): 53-60. # #Van der Veen, C.J., and I.M. Whillans. 1989b. Force Budget: # II. Application to two-dimensional flow along the Byrd Station Strain # Network, Antarctica. Journal of Glaciology, 35(119): 61-67. # #Whillans, I.M., Y.H. Chen, C.J. van der Veen, and T.J. Hughes. 1989c. # Force Budget: III. Application to Three-Dimensional Flow of Byrd # Glacier, Antarctica. Journal of Glaciology, 35(119): 68-80. # #DESCRIPTION AND ERROR ESTIMATES (Summary of notes provided by Henry Brecher) #Surface velocities and elevations of Byrd Glacier were determined by #photogrammetric methods (bundle block aerial triangulation) from two sets #of aerial photographs (scale about 1:48,000) taken on 6 December 1978 and #31 January 1979. The data were reported as three-dimensional coordinates #of points at these two epochs. Velocities were calculated from the two #positions of the same surface points and the time interval between the #two flights. # #Natural features, such as crevasses, seracs, or dunes, were identified #and marked on both sets of photographs. Seventy-one fixed points on rock #outcrops at the glacier's lateral margins were also identified and marked #in the same way. 13 control points on the perimeter of the area were #established by ground survey. All these points were measured on the #photographs by a stereo comparator, and their elevations and planimetric #terrain coordinates were determined analytically by a rigorous #least-squares adjustment of the two blocks of photographs. This yielded #coordinates of 1467 terrain points from 6738 image points (13,476 photo #coordinate measurements) on 322 photographs. # #The average spacing between points on the glacier surface is about 2.5 #km. Surface velocities of 601 common moving points, of which 472 are on #the main ice stream, were determined from the differences of planimetric #coordinates and the time interval of 56 days (56/365 year) between the #photo flights. The standard deviation of the photo coordinate #measurements is 16.3 micrometers which is equivalent to 0.8 m in #planimetry and 1.8 m in elevation at the average scale of the #photographs. This appears to be a reasonable indication of the precision #of the photogrammetric work. The number of points measured on a #photograph is more than twice as large as in a usual block adjustment (21 #points on an average photo instead of 9) which results in significantly #higher than normal redundancy, coordinate residuals approximate a normal #distribution very well and only 154 (1.1%) residuals are larger than #three standard deviations. It is difficult to give a satisfactory #estimate of accuracy, however, because no unambiguous checks are #available. From various indirect approaches it appears that both #planimetry and elevation are accurate to a few meters. Taking 5 m as a #conservative estimate of position accuracy yields errors of about 5% for #the highest velocities and up to 15% for the low velocities near the #glacier edge. Clock times of day of the photo flights were not available #but rough measurements of shadows indicate that Flight 1 was flown about #2 2/3 hours earlier than Flight 2. This makes the time interval between #flights negligibly (about 1/500) different from the nominal 56-day period #used. Velocities from this work agree very well with those reported by #Swithinbank for a transect across the mouth of the glacier over a 348-day #period during the years 1960-1962. Values taken from a graphical profile #(published at a larger scale as Figure 3 in Swithinbank 1964) and one #numerical value given for "middle of glacier" with probable error of 1% #(Swithinbank 1963) agree with values presented here within better than 3% #over virtually the whole transect. Where direct comparisons are possible #with independently determined velocities from ground surveys in 1978-79 #(Hughes and Fastook 1981) all agree within 4% and the vast majority within 2%. # #ADDITIONAL REMARKS #In response to a request by Terry Hughes in November 2000 I provided new #copies of all the Byrd Glacier results to him. While assembling the data #on that occasion I found some "anomalies". Planimetric (x,y) coordinates #in the BYRDGLAC.RES and BYRDVELO.GRD files are derived from a "map #projection" which I cooked up from an empirical fit to the USGS #1:250,000 topo map with the x axis aligned arbitrarily approximately in #the downglacier direction. Map coordinates in the BYRDPLST.ALL file are #intended to be easting, northing in the polar stereographic projection #used for the USGS 1:250,000 map. (Note that numbers are entirely #different because the two coordinate systems have different origins). Of #course, DIFFERENCES OF COORDINATES should be identical. Unfortunately #they are not. In several comparisons which I made, however, I found #differences between "correct" values (computed on the ellipsoid) and #those derived from either system to be negligible over short distances #(including the point with the largest motion, namely 1611, which moved #134.2 m). The distance between two points at the two extreme ends of the #area, about 103 km apart, was 17.2 m too short (about 1 part in 6,000) in #the BYRDGLAC.RES file coordinate system and 26.5 m too short (about 1 #part in 3,900) in the BYRDPLST.ALL file system. Long after finishing the #Byrd Glacier work I found an error in my programming of equations for the #polar stereographic projection and this may be the source of the errors. #Of course, the map projection itself introduces some unavoidable #distortion but I have been unable to determine a numerical value for #this. I should add that the 103 km distance computed from the latitude, #longitude, elevation positions agrees to 3.6 m (about 1 part in 28,500) #with the distance computed from the Cartesian coordinate system in which #the photogrammetric measurements were made. # #REFERENCES (cited above) #Hughes, T. and J.L. Fastook. 1981. Byrd Glacier: 1978-1979 field #results. Antarctic Journal of the U. S., XVI(5): 86-89. # #Swithinbank, Charles W. 1963. Ice movement of valley glaciers flowing #into the Ross Ice Shelf, Antarctica. Science, 141(3580): 523-524. # #Swithinbank, Charles 1964. To the valley glaciers that feed the Ross Ice #Shelf. The Geographical Journal, 130(I): 32-48. # #A NOTE ON POINT NUMBERS (Henry Brecher) #This explanation of the point numbering scheme is included in case it is #found desirable to re-compute motion from the two positions given in the #BYRDPLST.ALL file. It may not seem that way but there actually IS a #system. It has gone through several stages and there are some oddities #but it is consistent nevertheless. Note that I started out without ever #intending to adjust the two flights simultaneously and therefore #originally planned the point numbering so that the same point in the two #flights would have the same number, regardless of whether it was #stationary or moving. When I ultimately did an adjustment of the two #flights together I, of course, had to assign different identification to #two different points in space; i.e. moving points had to have two #different numbers. (The block adjustment program limited point #identifiers to 4 characters and this was a consideration). I #"rationalized" all the numbers so that all ended in the digits 0, 1, 2, 3 #or 4 and then I added 5 to all MOVING point numbers in Flight 1. So, all #MOVING points in Flight 2 and all STATIONARY points have numbers ending #in 0 to 4 and MOVING points in Flight 1 have numbers correspondingly #ending in 5 to 9. Thus, if motion of a point is to be computed, the #position of that point in Flight 2 and that of a point with a point #number which is 5 larger in Flight 1 must be used; for example, the #positions of point numbers 1206 and 1201 are to be used to calculate #motion of point 1201. All ground control points are two or three digit #numbers ending in 0. (Note, however, that 120 and 140 are labeled 125 #and 145 in Flight 1 because they are moving points). There are some #other point numbers of two or three digits ending in 0, originally #attempts to establish additional "pseudo control" which were abandoned, #which should be considered simply as additional photogrammetrically #determined points. Targeted motion markers which were also surveyed in #the field are given four digit numbers beginning with 9. # #All data may be freely released to anyone who is interested. # #Questions may be directed to: Henry H. Brecher Byrd Polar Research Center #Ohio State University 1090 Carmack Road Columbus, OH 43210-1002, U.S.A. #e-mail: brecher.1@osu.edu # # #NOTES: # 1. Error in speed and error in bearing are reported below as -1. # The actual errors are discussed above. # # Lat Long Speed Bearing ErrSp ErrBr Date1 Date2 Label Notes # (m/a) (degrees) (m/a) (degrees) #--------------------------------------------------------------------------------------------------------------------- -80.5479664 156.1754784 386.7 56.1 -1 -1 1978-12-06 1979-01-31 "1208--1203" #1 -80.5317742 156.3585335 428.5 54.8 -1 -1 1978-12-06 1979-01-31 "1218--1213" #1 -80.5150653 156.3353786 317.6 57.2 -1 -1 1978-12-06 1979-01-31 "1747--1742" #1 -80.5350200 156.1363835 267.0 56.7 -1 -1 1978-12-06 1979-01-31 "1757--1752" #1 -80.5153897 156.1413228 61.7 117.8 -1 -1 1978-12-06 1979-01-31 "4798--4793" #1 -80.4996947 156.3388168 117.8 56.1 -1 -1 1978-12-06 1979-01-31 "4808--4803" #1 -80.5184268 156.3329135 339.8 58.8 -1 -1 1978-12-06 1979-01-31 "5626--5621" #1 -80.5362451 156.1447210 294.2 56.3 -1 -1 1978-12-06 1979-01-31 "5636--5631" #1 -80.5639026 156.2500285 484.2 55.2 -1 -1 1978-12-06 1979-01-31 "5866--5861" #1 -80.5456569 156.4362974 524.0 51.9 -1 -1 1978-12-06 1979-01-31 "5876--5871" #1 -80.6686344 156.7614282 215.1 42.6 -1 -1 1978-12-06 1979-01-31 "117--112" #1 -80.6521203 156.9373417 166.9 48.2 -1 -1 1978-12-06 1979-01-31 "127--122" #1 -80.6617143 156.9561738 23.7 2.9 -1 -1 1978-12-06 1979-01-31 "2478--2473" #1 -80.6567551 156.8476539 247.7 47.1 -1 -1 1978-12-06 1979-01-31 "3479--3474" #1 -80.6699386 156.7221953 247.7 45.7 -1 -1 1978-12-06 1979-01-31 "3977--3972" #1 -80.5154274 156.5293921 466.4 55.3 -1 -1 1978-12-06 1979-01-31 "1228--1223" #1 -80.4989631 156.5058374 357.8 53.6 -1 -1 1978-12-06 1979-01-31 "1737--1732" #1 -80.5804594 156.6046877 600.2 50.7 -1 -1 1978-12-06 1979-01-31 "1996--1991" #1 -80.5591615 156.6585299 599.8 50.8 -1 -1 1978-12-06 1979-01-31 "3267--3262" #1 -80.5789732 156.4599726 585.1 50.2 -1 -1 1978-12-06 1979-01-31 "3279--3274" #1 -80.4998990 156.5227252 380.7 54.7 -1 -1 1978-12-06 1979-01-31 "5616--5611" #1 -80.5917750 156.5187171 592.1 49.6 -1 -1 1978-12-06 1979-01-31 "5879--5874" #1 -80.5293599 156.6214307 565.8 54.3 -1 -1 1978-12-06 1979-01-31 "5886--5881" #1 -80.5743057 156.7179109 604.9 51.0 -1 -1 1978-12-06 1979-01-31 "5888--5883" #1 -80.6129111 156.7835013 544.9 51.4 -1 -1 1978-12-06 1979-01-31 "125--120" #1 -80.6177813 156.7986966 536.4 50.5 -1 -1 1978-12-06 1979-01-31 "2476--2471" #1 -80.5940633 156.7028309 584.0 49.6 -1 -1 1978-12-06 1979-01-31 "2477--2472" #1 -80.6366578 156.6175668 519.0 48.1 -1 -1 1978-12-06 1979-01-31 "2486--2481" #1 -80.6109433 156.5342162 575.2 51.4 -1 -1 1978-12-06 1979-01-31 "2487--2482" #1 -80.5942193 156.8244405 575.9 51.9 -1 -1 1978-12-06 1979-01-31 "3266--3261" #1 -80.6201551 156.9113880 499.2 51.5 -1 -1 1978-12-06 1979-01-31 "3268--3263" #1 -80.6218217 156.5998173 564.6 48.6 -1 -1 1978-12-06 1979-01-31 "3276--3271" #1 -80.5785065 156.4586095 573.5 49.9 -1 -1 1978-12-06 1979-01-31 "3277--3272" #1 -80.6440607 156.7104618 455.1 45.3 -1 -1 1978-12-06 1979-01-31 "3278--3273" #1 -80.6103442 156.6943480 571.2 49.9 -1 -1 1978-12-06 1979-01-31 "3477--3472" #1 -80.5912140 156.5149695 583.0 49.8 -1 -1 1978-12-06 1979-01-31 "5878--5873" #1 -80.4747251 156.5248345 42.1 56.8 -1 -1 1978-12-06 1979-01-31 "4818--4813" #1 -80.6441058 157.0053197 167.3 45.7 -1 -1 1978-12-06 1979-01-31 "3486--3481" #1 -80.4697511 156.5503902 22.7 66.8 -1 -1 1978-12-06 1979-01-31 "1236--1231" #1 -80.6318218 157.1696682 85.4 51.8 -1 -1 1978-12-06 1979-01-31 "137--132" #1 -80.6291640 157.1423221 158.4 51.3 -1 -1 1978-12-06 1979-01-31 "3957--3952" #1 -80.4993696 156.7164578 536.1 54.2 -1 -1 1978-12-06 1979-01-31 "1238--1233" #1 -80.4818008 156.6894600 420.3 54.7 -1 -1 1978-12-06 1979-01-31 "1727--1722" #1 -80.5343929 156.6987006 582.9 53.6 -1 -1 1978-12-06 1979-01-31 "1736--1731" #1 -80.5619576 156.8027924 618.4 52.7 -1 -1 1978-12-06 1979-01-31 "2006--2001" #1 -80.5424120 156.8673663 634.5 52.2 -1 -1 1978-12-06 1979-01-31 "3257--3252" #1 -80.4816256 156.7089992 432.7 54.4 -1 -1 1978-12-06 1979-01-31 "5606--5601" #1 -80.5114347 156.8126335 597.7 53.3 -1 -1 1978-12-06 1979-01-31 "5896--5891" #1 -80.5561911 156.9242167 651.7 54.4 -1 -1 1978-12-06 1979-01-31 "5898--5893" #1 -80.6017294 156.9859217 538.8 54.9 -1 -1 1978-12-06 1979-01-31 "2466--2461" #1 -80.5761563 156.9110367 618.7 55.2 -1 -1 1978-12-06 1979-01-31 "2467--2462" #1 -80.5775057 157.0002274 611.4 55.7 -1 -1 1978-12-06 1979-01-31 "3256--3251" #1 -80.6074638 157.1221132 471.8 56.1 -1 -1 1978-12-06 1979-01-31 "3258--3253" #1 -80.4630921 156.7281182 300.7 55.3 -1 -1 1978-12-06 1979-01-31 "4828--4823" #1 -80.5832464 157.1739907 573.1 55.0 -1 -1 1978-12-06 1979-01-31 "2456--2451" #1 -80.6223011 157.3135718 51.4 52.3 -1 -1 1978-12-06 1979-01-31 "2458--2453" #1 -80.6437923 157.1058871 10.4 -19.3 -1 -1 1978-12-06 1979-01-31 "2468--2463" #1 -80.5984022 157.2537259 470.8 56.6 -1 -1 1978-12-06 1979-01-31 "3496--3491" #1 -80.5716507 157.1544573 608.8 55.0 -1 -1 1978-12-06 1979-01-31 "3497--3492" #1 -80.6177204 157.3203057 109.6 59.5 -1 -1 1978-12-06 1979-01-31 "3947--3942" #1 -80.4511428 156.7210812 7.4 34.4 -1 -1 1978-12-06 1979-01-31 "1246--1241" #1 -80.4804328 156.8885067 569.6 56.4 -1 -1 1978-12-06 1979-01-31 "1248--1243" #1 -80.4625367 156.8687239 472.0 56.5 -1 -1 1978-12-06 1979-01-31 "1717--1712" #1 -80.5172685 156.8800549 626.1 52.5 -1 -1 1978-12-06 1979-01-31 "1726--1721" #1 -80.5462432 156.9963199 665.9 54.4 -1 -1 1978-12-06 1979-01-31 "2016--2011" #1 -80.5193403 157.0629517 685.2 58.0 -1 -1 1978-12-06 1979-01-31 "3247--3242" #1 -80.4615438 156.8984095 490.1 56.6 -1 -1 1978-12-06 1979-01-31 "5596--5591" #1 -80.4943765 157.0196520 660.7 57.8 -1 -1 1978-12-06 1979-01-31 "5906--5901" #1 -80.5371860 157.1225006 692.7 56.6 -1 -1 1978-12-06 1979-01-31 "5908--5903" #1 -80.5558154 157.1030737 656.0 55.0 -1 -1 1978-12-06 1979-01-31 "2457--2452" #1 -80.5560110 157.2320814 653.7 56.5 -1 -1 1978-12-06 1979-01-31 "3246--3241" #1 -80.5864524 157.3379856 518.8 56.5 -1 -1 1978-12-06 1979-01-31 "3248--3243" #1 -80.6146611 157.3662317 93.8 59.1 -1 -1 1978-12-06 1979-01-31 "147--142" #1 -80.6101519 157.3641501 169.9 62.5 -1 -1 1978-12-06 1979-01-31 "3499--3494" #1 -80.4358744 156.8768649 8.1 57.2 -1 -1 1978-12-06 1979-01-31 "1256--1251" #1 -80.4727735 157.0101221 622.7 58.7 -1 -1 1978-12-06 1979-01-31 "1258--1253" #1 -80.4472100 156.9190278 423.7 51.0 -1 -1 1978-12-06 1979-01-31 "4838--4833" #1 -80.4410519 157.0936349 506.1 55.9 -1 -1 1978-12-06 1979-01-31 "1707--1702" #1 -80.4973847 157.0627903 682.6 58.9 -1 -1 1978-12-06 1979-01-31 "1716--1711" #1 -80.5299476 157.1752642 691.0 57.6 -1 -1 1978-12-06 1979-01-31 "2026--2021" #1 -80.4977563 157.2742063 715.5 59.5 -1 -1 1978-12-06 1979-01-31 "3237--3232" #1 -80.4454156 157.0814578 524.0 57.6 -1 -1 1978-12-06 1979-01-31 "5586--5581" #1 -80.4776901 157.1979392 685.2 59.3 -1 -1 1978-12-06 1979-01-31 "5916--5911" #1 -80.5181532 157.2979569 706.9 58.8 -1 -1 1978-12-06 1979-01-31 "5918--5913" #1 -80.6002047 157.5144174 91.3 58.2 -1 -1 1978-12-06 1979-01-31 "157--152" #1 -80.5616720 157.3796432 620.0 59.1 -1 -1 1978-12-06 1979-01-31 "2446--2441" #1 -80.6046582 157.5061945 31.5 59.4 -1 -1 1978-12-06 1979-01-31 "2448--2443" #1 -80.5461856 157.4254662 659.3 59.3 -1 -1 1978-12-06 1979-01-31 "3236--3231" #1 -80.5923844 157.5311244 179.5 53.2 -1 -1 1978-12-06 1979-01-31 "3937--3932" #1 -80.4142239 157.0515664 21.1 43.2 -1 -1 1978-12-06 1979-01-31 "1266--1261" #1 -80.4547974 157.1907560 638.5 58.9 -1 -1 1978-12-06 1979-01-31 "1268--1263" #1 -80.4290110 157.0715385 399.9 54.1 -1 -1 1978-12-06 1979-01-31 "4848--4843" #1 -80.5109176 157.3646060 701.5 59.2 -1 -1 1978-12-06 1979-01-31 "2036--2031" #1 -80.5372672 157.2940231 693.6 57.3 -1 -1 1978-12-06 1979-01-31 "2447--2442" #1 -80.5712325 157.5264953 460.5 51.9 -1 -1 1978-12-06 1979-01-31 "3238--3233" #1 -80.4405693 157.3467103 667.2 58.6 -1 -1 1978-12-06 1979-01-31 "1278--1273" #1 -80.4241792 157.2778421 530.5 57.4 -1 -1 1978-12-06 1979-01-31 "1697--1692" #1 -80.4786733 157.2449523 692.3 59.3 -1 -1 1978-12-06 1979-01-31 "1706--1701" #1 -80.4779224 157.4729765 719.0 58.6 -1 -1 1978-12-06 1979-01-31 "3227--3222" #1 -80.4265082 157.2729427 540.4 58.5 -1 -1 1978-12-06 1979-01-31 "5576--5571" #1 -80.4577857 157.3746681 700.3 59.8 -1 -1 1978-12-06 1979-01-31 "5926--5921" #1 -80.4969858 157.5229871 704.1 59.4 -1 -1 1978-12-06 1979-01-31 "5928--5923" #1 -80.5748596 157.6796890 152.5 52.9 -1 -1 1978-12-06 1979-01-31 "167--162" #1 -80.5844544 157.5804456 210.0 54.5 -1 -1 1978-12-06 1979-01-31 "3506--3501" #1 -80.4016500 157.2347551 161.0 56.3 -1 -1 1978-12-06 1979-01-31 "1276--1271" #1 -80.4136519 157.2365157 400.1 56.9 -1 -1 1978-12-06 1979-01-31 "4858--4853" #1 -80.4910585 157.5481763 709.4 58.8 -1 -1 1978-12-06 1979-01-31 "2046--2041" #1 -80.5281747 157.7307166 602.9 58.7 -1 -1 1978-12-06 1979-01-31 "2048--2043" #1 -80.5437636 157.5675949 599.9 54.7 -1 -1 1978-12-06 1979-01-31 "2436--2431" #1 -80.5132738 157.4861863 678.4 58.6 -1 -1 1978-12-06 1979-01-31 "2437--2432" #1 -80.5200074 157.6662714 654.8 58.7 -1 -1 1978-12-06 1979-01-31 "3226--3221" #1 -80.5472431 157.7674407 401.3 57.1 -1 -1 1978-12-06 1979-01-31 "3228--3223" #1 -80.3855586 157.3820493 160.1 67.1 -1 -1 1978-12-06 1979-01-31 "1286--1281" #1 -80.3963543 157.4170132 411.9 61.1 -1 -1 1978-12-06 1979-01-31 "4868--4863" #1 -80.4253122 157.5085062 703.8 59.8 -1 -1 1978-12-06 1979-01-31 "1288--1283" #1 -80.4060149 157.4566116 553.6 61.0 -1 -1 1978-12-06 1979-01-31 "1687--1682" #1 -80.4592993 157.4279756 720.7 59.3 -1 -1 1978-12-06 1979-01-31 "1696--1691" #1 -80.4410981 157.5709509 739.8 57.9 -1 -1 1978-12-06 1979-01-31 "5936--5931" #1 -80.4836018 157.6768656 741.0 56.0 -1 -1 1978-12-06 1979-01-31 "5938--5933" #1 -80.4625299 157.5602908 738.6 56.7 -1 -1 1978-12-06 1979-01-31 "6277--6272" #1 -80.4646493 157.5458302 737.9 56.7 -1 -1 1978-12-06 1979-01-31 "9129--9124" #1 -80.5506511 157.9233990 120.0 62.1 -1 -1 1978-12-06 1979-01-31 "3917--3912" #1 -80.4408020 157.6117958 760.1 57.8 -1 -1 1978-12-06 1979-01-31 "1686--1681" #1 -80.3891503 157.4906042 432.0 63.2 -1 -1 1978-12-06 1979-01-31 "4878--4873" #1 -80.4722829 157.7415456 770.5 53.6 -1 -1 1978-12-06 1979-01-31 "2056--2051" #1 -80.5082490 157.9207951 626.0 57.4 -1 -1 1978-12-06 1979-01-31 "2058--2053" #1 -80.5306157 157.8172930 559.9 59.3 -1 -1 1978-12-06 1979-01-31 "2426--2421" #1 -80.4936718 157.7009851 731.2 56.3 -1 -1 1978-12-06 1979-01-31 "2427--2422" #1 -80.4946313 157.8491047 711.4 54.3 -1 -1 1978-12-06 1979-01-31 "3216--3211" #1 -80.4593481 157.6959554 784.2 53.9 -1 -1 1978-12-06 1979-01-31 "3217--3212" #1 -80.5242657 157.9500438 493.3 59.9 -1 -1 1978-12-06 1979-01-31 "3218--3213" #1 -80.5400883 158.0374657 124.0 54.7 -1 -1 1978-12-06 1979-01-31 "187--182" #1 -80.5237700 158.0124424 433.9 57.4 -1 -1 1978-12-06 1979-01-31 "3526--3521" #1 -80.4944714 157.9148063 693.5 54.7 -1 -1 1978-12-06 1979-01-31 "3527--3522" #1 -80.5367614 158.0463529 197.5 55.4 -1 -1 1978-12-06 1979-01-31 "3529--3524" #1 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