The geography of the Antelope Valley

Location

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The Antelope Valley is an approximately 2,400-square-mile (6,200-square-kilometer)[1] arid desert region located at 34°45′05″N 118°15′08″W / 34.7513712°N 118.2522977°W / 34.7513712; -118.2522977 (Antelope Valley) in the northern part of Los Angeles County, the southeastern portion of Kern County, and the far western edge of San Bernadino County, California. It constitutes the western tip of the Mojave Desert, lying within the foothills of the San Gabriel Mountains to the southeast, Portal Ridge and the Sierra Pelona Mountains to the southwest, and the Tehachapi Mountain Range to the northwest.[2] The northern and eastern boundaries are not so easily defined, especially by noticeable geographic features such as mountains, but in 1911 a United States Geological Survey (USGS) Water-Supply Paper placed Rosamond "near the north margin of the valley".[3] It also noted a region of detrital rock that stretched for about ten miles between Cottonwood Creek in the Tehachapi Mountains and Rosamond Buttes where surface runoff on the northern and eastern sides of this area possibly drained towards the northeast and the town of Mojave.[4] On the southeastern edge of the AV another area of detritus was found to run along the San Gabriel Mountains and separate the region from Victor Valley in San Bernadino County. On the western side of this rock, the water from Little Rock Creek and Big Rock Creek was found to drain into the Antelope Valley; to the east, it was thought the water drained into the Mojave River.[4]

The USGS thus identified the northern edge of the Antelope Valley as being along the detritus from the Tehachapi Mountains and then following the BNSF railroad which loosely parallels State Route 58 Business to the north of Rogers Dry Lake, and the eastern border of the valley as lying about six miles east of Llano, through Black Butte and towards Haystack Butte along the LA County – San Bernadino County border.[5] A second USGS WSP published in 1929 included a map that altered the eastern border;[6] while most recent surveys show the valley extending as far north as to actually include Mojave, as well as California City and Boron.[7]

In a straight line, the AV is about 50 mi (80 km) north of Los Angeles.[8] Bakersfield is 60 mi (97 km) northwest of the Antelope Valley, and Las Vegas, Nevada is 200 mi (320 km) east of the valley.[9] The three cities in the Antelope Valley are Lancaster and Palmdale, both in LA County, and California City in Kern County. Three of the five highest populated census-designated places in the valley are also in LA County: Lake Los Angeles, Sun Village and Quartz Hill, California;[10] Rosamond and Mojave are in Kern County.[11]

Topography

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The Antelope Valley is a graben, the result of the surrounding mountains uplifting due to fault activity. The San Andreas Rift Zone enters the valley from the western tip at Gorman, and runs parallel to Portal Ridge and the Sierra Pelona range, forming a long, narrow basin in which lie Hughes Lake and Elizabeth Lake. The Fault Line continues through Soledad Canyon and along the foot of the San Gabriels out of the valley into San Bernadino County.[12] The valley floor decreases gently from an elevation of around 4,000 feet (1,200 meters) on the flanks of the Tehachapi Mountains, to an endorheic depression lying near the northwest corner of the valley where, at an elevation of 2,300 ft (700 m), the Rogers, Buckhorn, Rich and Rosamond Dry Lakes are found.[4] These playas are all bisected by the LA – Kern County boundary lines. Because the valley is a closed basin, all streams and rain water either sink into the ground or collect in the lower corner of the valley and evaporate.[13] The floor of the Antelope Valley is characterized by a broad plain of undulating alluvial fans,[14] throughout which scattered mountain peaks or buttes are found.[15] Examples of these are Fairmont Butte,[16] Antelope Buttes,[17] Quartz Hill,[18] Alpine Butte,[19] and Piute Butte.[20]

At 2,300 ft above sea level, the lowest elevation of the Antelope Valley is higher than most of the valleys on the other side of the mountains that surround it.[21] The highest point of the Fremont Valley is about the same,[22] but its lowest point is Koehn Lake at 1,900 ft (580 m);[23] the south-eastern edge of the San Joaquin Valley, which lies west of the Tehachapi Mountains, slopes upwards to 600 ft (180 m);[24] and the San Fernando Valley, on the south side of the San Gabriels, reaches a height of 1,400 ft (430 m).[25] Victor Valley and Mojave River Valley, both east of the AV, are the exceptions at 2,900 ft (880 m) and 2,500 ft (760 m) respectively.[26]

Hydrology

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The Antelope Valley is a part of the Environmental Protection Agency's Antelope-Fremont Valleys Watershed (Hydrological code 18090206),[27] a 3,376 sq mi (8,740 km2) area that is further divided into 24 subwatersheds.[28] There are a number of waterbodies and watercourses within the Antelope Valley, both natural and artificial, and the Antelope Valley Groundwater Basin has historically been the primary source of water for agricultural, municipal and industrial use in the valley.

Groundwater

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The Antelope Valley Groundwater Basin consists of two aquifers: the principal aquifer, which is unconfined; and the deep aquifer, which is confined. The two aquifers are separated by a layer of clay between 200 and 300 feet thick.[29] The principal aquifer is thickest in the southern area of the valley, and the deep aquifer is thickest in the northern part near the dry lakes.[30] The possibility of the existence of a third, or middle aquifer has being studied by the USGS.[31] The groundwater in the Antelope Valley is known to be contaminated with arsenic and other substances including fluoride, boron, lead and nitrates;[32] however, the water quality is well within the Maximum Contaminant Levels set by the Environmental Protection Agency.[citation needed]

Most of the extracted groundwater is from the principal aquifer. The volume of water obtained has differed greatly since the time the valley was permanently inhabited. The USGS estimate that in the early 1900s when groundwater pumping began, around 29,000 acre-feet (9.45 billion US gallons; 35.8 million cubic metres) per year was pumped,[33] and accounted for more than 90% of the water used in the valley.[34] The figure increased to 400,000 acre-feet (130 billion US gallons; 493 million cubic metres) per year in the 1950s,[35] and then decreased as farming in the area declined.[36] The introduction of the State Water Project (SWP) in the 1970s also reduced the need for groundwater pumping,[37] although the valley's increasing population and renewed agricultural industry soon increased the demand of water once again.[citation needed]

As such, groundwater is still an important source and continues to be pumped by the local water utility companies.[38] It now accounts for anywhere between 50% and 90% of annual total water usage in the valley, depending on the yearly demand and availability of surface water.[39] Palmdale Water District states that groundwater accounts for up to 60% of its annual water usage,[40] and it continues to be Littlerock Creek Irrigation District's (LCID) main source of water ahead of that from Littlerock Creek and the California Aqueduct. LCID owns five wells that pump groundwater; one is suitable for irrigation only, the other four wells provide potable water (suitable for drinking).[41]

The extended period of the pumping of groundwater has caused long-lasting issues within the Antelope Valley. For most of the first three-quarters of the 20th century, the amount of groundwater being pumped was more than that being recharged through the deep percolation of precipitation and runoff.[42] This overdrafting has resulted in the artesian wells that were present in the late 1800s and early 1900s to stop flowing,[43] the aquifers to compact, and the land to subside. Surveys conducted using Global positioning systems have determined that between 1930 and 1992, close to 7 ft (2.1 m) of subsidence occurred in the Antelope Valley, mostly around Lancaster (34°44′25″N 118°07′05″W / 34.74034°N 118.11796°W / 34.74034; -118.11796 and 34°44′44″N 117°58′21″W / 34.74556°N 117.97256°W / 34.74556; -117.97256). The USGS has stated that this sinking has resulted in "a loss of aquifer storage, increased flooding, cracks and fissures at land surface, and damage to man-made structures".[44]

Reservoirs

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The two main waterbodies in the Antelope Valley are reservoirs. The largest is Lake Palmdale, located about two miles south of Palmdale sandwiched between State Route 14 and the Union Pacific Railroad. It has previously been identified in literature and old USGS maps as Lake Yuna, Alpine Lake, Harold Lake, Harold Reservoir, Shoulder Lake, Palmdale Lake and Palmdale Reservoir.[45] The area of Lake Palmdale was originally the location of a natural depression along the San Andreas Rift Zone that often filled with water. It formed as either a sag pond or rift lake due to fault activity that caused the uplift of the land to close off drainage into the depression.[46] The development and operation of Lake Palmdale is intrinsically linked with that of Little Rock Reservoir (34°28′45″N 118°01′22″W / 34.4790947°N 118.0227466°W / 34.4790947; -118.0227466 (Little Rock Reservoir)) and its primary tributary, Little Rock Creek, 7.5 mi (12.1 km) away in the San Gabriel Mountains of the Angeles National Forest,[citation needed]

In the late 1880s, Nathan Cole Jr. purchased 1,960 acres (7.9 km2) of land east of where Little Rock Creek enters the Antelope Valley, and with his two brothers Charles and Zack, and Charles's son Burt, developed the area for agriculture and housing. Originally called Alpine Springs, they changed its name in 1892 to the Tierra Bonita Colony and then Little Rock the following year. The Coles persuaded the land owners in the area to petition the Los Angeles County Board of Supervisors to form an irrigation district under the Wright Act of 1887. The Little Rock Creek Irrigation District (LCID) was thus formed on March 28, 1892 to cover an area of 1,300 acres (5.3 km2) and use the water from Little Rock Creek.[47]

At around the same time as the LCID was formed, so too was the private – i.e., not a Wright Irrigation district – Palmdale Irrigation Company.[48] The Palmdale Irrigation Company, under the control of Nathan Cole Jr.,[49] dug an 8.5 mi (13.7 km) earthen ditch between Little Rock Creek and Palmdale, and installed a headgate on the Creek to divert water via the ditch.[50] A few years later the South Antelope Valley Irrigation District constructed a dam at Harold Lake to form a reservoir and dug a second unlined ditch, called the Palmdale Ditch, parallel to the first between the creek and the reservoir;[48] however, the reservoir had a capacity of only 3,000 acre-feet (0.978 billion US gallons; 3.70 million cubic metres), and in the winter when the surface runoff was at its greatest, the reservoir would overflow and a lose a large amount of water.[51]

At the turn of the century following a period of drought in the late 1890s,[49] it became clear that a dam needed to be installed on Little Rock Creek.[48] The Palmdale Irrigation District – now Palmdale Water District (PWD) – was formed as a public district in 1918 and purchased the rights of the existing private districts, and began working with the LCID to construct a concrete dam on the creek.[48] The Little Rock Dam was completed in June 1924[52] and can hold a maximum volume of 3,500 acre-feet (1.14 billion US gallons; 4.32 million cubic metres).[53] In the 1960s following Palmdale Irrigation District's contract with the State Water Project (SWP), Lake Palmdale was upgraded to hold a larger volume of water.[54] Following the expansion, Lake Palmdale's storage capacity increased to 4,129 acre-feet (1.35 billion US gallons; 5.09 million cubic metres).[53]

Over a hundred years after it was built, the Palmdale Ditch is still used to transport water from Littlerock Reservoir to Lake Palmdale.[53] It runs alongside the California Aqueduct but travels in the opposite direction. It was built with such accuracy that it runs downhill the entire route; gravity alone directs the flow, and pumps are not used at all.[55]

Aqueducts

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The California Aqueduct runs through the southern border of the region and is a third water supply source for the AV. It enters the valley at its westernmost edge at the mouth of Los Alamos Creek (34°50′01″N 118°42′41″W / 34.8335883°N 118.7114797°W / 34.8335883; -118.7114797 (Los Alamos Creek)) after tunneling through the Tehachapi Mountains.[56] It then bifurcates at the Tehachapi Afterbay (34°49′44″N 118°42′31″W / 34.8288664°N 118.7087017°W / 34.8288664; -118.7087017 (Tehachapi Afterbay)), and from here the West Branch and East Branch split. The West Branch heads southwest towards Oso Pumping Plant (34°48′37″N 118°43′10″W / 34.8102562°N 118.7195351°W / 34.8102562; -118.7195351 (Oso Pumping Plant)) and into Quail Lake, before being piped through the Sierra Pelonas into Pyramid Lake and out towards its terminus at Castaic Lake.[57]

The East Branch navigates along the entire southern edge of the valley in a concrete ditch.[58] From Alamo Powerplant (34°49′16″N 118°41′33″W / 34.82113°N 118.69251°W / 34.82113; -118.69251 (Alamo Powerplant)) it travels southeast along the foothills of Portal Ridge and the Sierra Pelonas before turning south into the San Andreas Rift Zone at Anaverde Valley (34°34′28″N 118°10′53″W / 34.57457°N 118.18130°W / 34.57457; -118.18130 (Anaverde Valley)), where it passes underneath State Route 14 and runs alongside Lake Palmdale, which is fed water from the Aqueduct.[40] The canal continues to head east along the southern border of Palmdale towards Littlerock and Pearblossom, where the Pearblossom Pumping Plant lifts the water 540 ft (160 m) to the top of Ward Butte, before it descends out of the valley to Silverwood Lake near Hesperia, San Bernadino County, and its terminus at Lake Perris in Riverside County.[59]

Three water companies in the AV have contracted to receive potable and irrigation water from the SWP until 2035:[60] LCID, PWD and the Antelope Valley-East Kern Water Agency (AVEK).[61] Other water districts in the area that have not contracted with the SWP purchase water from AVEK instead, such as Quartz Hill Water District, Rosamond Community Services District, and Los Angeles County Waterworks District No. 40.[62] The Antelope Valley's maximum entitlement of SWP water is about 160,000 acre-feet (52.1 billion US gallons; 197 million cubic metres) per year.[63]

The Los Angeles Aqueduct also passes through the Antelope Valley and serves to convey water to the City of Los Angeles from the Owens River in Inyo County.

Streams

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Many of the creeks and streams that enter the valley are ephemeral. About 10 miles[citation needed] east of Little Rock Creek is Big Rock Creek. Amargosa Creek enters the valley from Leona Valley, and Cottonwood Creek begins in the Tehachapi Mountains.

Wetlands

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Una Lake, Piute Ponds, Barrel Springs

Geology

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Climate

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Human development

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Settlements, farming and roads

(Use Lede from above History article)

Flora and fauna

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The vegetation of the Antelope Valley is limited to desert-type flora, and is in marked contrast to that found on the western side of the Tehachapis or the mountains in Los Angeles National Forest which are prevalent with oak, sycamore and willow trees, and grass-covered floor. Entering the valley from these ranges, the change in vegetation is sudden. The valley floor is covered in desert brush, while Eschscholzia californica (California poppy), Larrea tridentata (creosote bushes), Quercus berberidifolia (scrub oak), and Yucca brevifolia (Joshua trees) are the only other native flora fround in large quantities.[15] Except for junipers, true native arboreals are rare[15] (the Joshua tree is not really a tree as it is not woody, does not produce annual growth rings, and is closely related to agaves and lillies). The only other trees are those imported into the region by man, such as fruit trees during the late 1800s and early to mid-1900s and palm trees.

Birds

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Feiner, Aaron K. (2001). Birds of Apollo Park and Associated Areas of the Antelope Valley. Lancaster, California.{{cite book}}: CS1 maint: location missing publisher (link):

Feiner, Aaron K. (1998). Antelope Valley Birds. Lancaster, California.{{cite book}}: CS1 maint: location missing publisher (link):

Insects and arthropods

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Mollusks

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Lizards

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Snakes

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Mammals

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References

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  1. ^ "Executive Summary". Antelope Valley Integrated Regional Water Management Plan. Los Angeles County Department of Public Works. p. ES-xix. Retrieved January 3, 2012.
  2. ^ Thompson (1929) p. 289
  3. ^ Johnson (1911) p. 9
  4. ^ a b c Johnson, Harry Roland (1911). "Water Resources of Antelope Valley". United States Geological Survey Water-Supply Paper 278. United States Government Printing Office: 10. Retrieved June 24, 2011.
  5. ^ Johnson (1911) pp. 11-12
  6. ^ Thompson, David G (1929). "Antelope Valley". The Mohave Desert Region. United States Government Printing Office. Plate 19, p. 295. {{cite book}}: |journal= ignored (help)
  7. ^ Schmitt, Stephen J.; Milby Dawson, Barbara J.; Belitz, Kenneth (2009). "Introduction". Groundwater-Quality Data in the Antelope Valley Study Unit, 2008: Results from the California Groundwater Ambient Monitoring and Assessment Program: United States Geological Survey Data Series 479. United States Government Printing Office: 5.
  8. ^ Thompson (1929) p. 290
  9. ^ "Great Circle Distance Maps, Airport Routes, & Degrees/Minutes/Seconds Calculator". GPS Visualiser. Retrieved December 8, 2011.
  10. ^ "The Antelope Valley – Mapping L.A." Los Angeles Times. Retrieved 7 December 2011.
  11. ^ Durham, David L. (1998). California's Geographic Names: A Gazetteer of Historic and Modern Names of the State. Clovis, Calif.: Word Dancer Press. p. 1098. ISBN 1-884995-14-4.
       Durham, David L. (1998). California's Geographic Names: A Gazetteer of Historic and Modern Names of the State. Clovis, Calif.: Word Dancer Press. p. 1074. ISBN 1-884995-14-4.
  12. ^ http://geohazards.usgs.gov/cfusion/qfault/qf_web_disp.cfm?qfault_or=759&ims_cf_cd=cf&disp_cd=C
       http://geohazards.usgs.gov/cfusion/qfault/qf_web_disp.cfm?qfault_or=1524&ims_cf_cd=cf&disp_cd=C
  13. ^ Thompson (1929) p. 299
  14. ^ "Ground Water Atlas of the United States – Segment 1 California Nevada". USGS. Retrieved June 23, 2011.
  15. ^ a b c Merriam, John C (March 1915). "Extinct Faunas of the Mojave Desert". The Popular Science Monthly. 86 (15). Bonnier Corporation: 249. ISSN 0161-7370. Retrieved June 6, 2011.{{cite journal}}: CS1 maint: date and year (link)
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  17. ^ "Feature Detail Report for Antelope Buttes". Geographic Names Information System. January 19, 1981. Retrieved June 24, 2011.
  18. ^ "Feature Detail Report for Quartz Hill". Geographic Names Information System. January 19, 1981. Retrieved June 24, 2011.
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  20. ^ "Feature Detail Report for Piute Butte". Geographic Names Information System. January 19, 1981. Retrieved June 24, 2011.
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       Helendale Quadrangle – California – San Bernadino Co (Map). 1:24,000. 7.5-Minute Series (Topographic). United States Geological Survey. 1993 [1956].
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  28. ^ "My WATERS Mapper". Environmental Protection Agency. Retrieved January 16, 2012.
  29. ^ 2010 Integrated UWMP for the Antelope Valley (2011) p. 21
  30. ^ AVIRWM Plan, p. 10
  31. ^ AVIRMA Plan (2007), p. 1–4
       Leighton, Phillips (2003), p. 1
  32. ^ AVIRMA Plan (2007), p. 1–4
  33. ^ AVIRWM Plan (2007), p. ES-xx
  34. ^ Leighton, David A.; Phillips, Steven P. (2003). Simulation of Ground-water Flow and Land Subsidence, Antelope Valley Ground-Water Basin, California. Water–Resources Investigations Report 03-4016. Sacramento, California: United States Geological Survey: 2. {{cite journal}}: Missing or empty |title= (help)
  35. ^ AVIRWM Plan (2007), p. ES-xx
  36. ^ Leighton, Phillips (2003), p. Needed
  37. ^ 2010 Integrated UWMP for the Antelope Valley (2011) p. 10
  38. ^ "Your Water Supply". Palmdale Water District. Retrieved January 2, 2012.
       "Rosamond Community Services District Water Supply". Rosamond Community Services District. Retrieved January 2, 2012.
       "Palm Ranch Irrigation District History". Palm Ranch Irrigation District. Retrieved January 2, 2012.
       "Waterworks Districts FAQ". Los Angeles County Department of Public Works. Retrieved January 2, 2012.
       "2010 Integrated Regional Urban Water Management Plan for the Antelope Valley" (PDF). Los Angeles County Department of Public Works. May 31, 2011: 10. Retrieved January 3, 2012. {{cite journal}}: Cite journal requires |journal= (help)
  39. ^ Leighton, Phillips (2003), p. 88
  40. ^ a b "Your Water Supply". Palmdale Water District. Retrieved December 17, 2011.
       "2010 Consumer Confidence Report" (PDF). Palmdale Water District. Retrieved December 17, 2011. {{cite journal}}: Cite journal requires |journal= (help)
  41. ^ Semchuck, Alisha (June 27, 2009). "Water Rates Up, but Not for Littlerock". Antelope Valley Press.
  42. ^ AVIRWM Plan, p. ES-xx
       2010 Integrated UWMP for the Antelope Valley (2011) p. 10
  43. ^ AVIRWM Plan (2007), p. 2-10
  44. ^ Leighton, Phillips (2003), pp. 22–23
  45. ^ Gurba, Norma H.; West, Nicholas J. (2010). Images of America: Palmdale. Mount Pleasant, South Carolina: Arcadia Publishing. ISBN 978-0-7385-8122-4.
       Decisions on names in the United States and Puerto Rico, Decisions rendered in May, June, July, and August, 1959. Vol. Decision list no. 5903. Washington D.C.: United States Board on Geographic Names. United States Government Printing Office. 1960. p. 16.
  46. ^ Johnson (1910) p. 33
  47. ^ Gidney, Ray M. (1912). The Wright Irrigation Act in California. University of California, Berkeley. pp. 210–212.
       Adams (1917). "Appendix B". Irrigation districts in California, 1887–1915. Fifth Biennial Report. California Department of Engineering. p. 8.
  48. ^ a b c d Thompson (1929) p. 293
       RMC Water and Environment (June 2011). "Section 2: System Description" (PDF). Palmdale Water District 2010 Urban Water Management Plan. Palmdale Water District: 2-1. Retrieved January 15, 2012.
  49. ^ a b Gidney (1912) p. 244
  50. ^ Thompson (1929) p. 293
       Newell, F.H. (1895). Report on the Agriculture by Irrigation in the Western Part of the United States at the Eleventh Census: 1890. Washington D.C.: U.S. Census Office. Government Printing Office: 61. {{cite journal}}: Missing or empty |title= (help)
  51. ^ Thompson (1929) p. 293
  52. ^ Jackson, Donald Conrad (2005). Building the Ultimate Dam: John S. Eastwood and the Control of Water in the West. University of Oklahoma Press. p. 205. ISBN 0-8061-3733-9.
       Jackson, Donald Conrad (June 1, 1988). Great American Bridges and Dams. John Wiley and Sons. p. 75. ISBN 0-471-14385-5.
  53. ^ a b c "Section 3: Issues & Needs". Antelope Valley Integrated Regional Water Management Plan. Los Angeles County Department of Public Works. p. 3-4. Retrieved January 3, 2012.
  54. ^ RMC Water and Environment (June 2011). "Section 2: System Description" (PDF). Palmdale Water District 2010 Urban Water Management Plan. Palmdale Water District: 2-1. Retrieved January 15, 2012.
  55. ^ Bostwick, Charles F. (February 29, 1999). "Dumping Continues Along Water Channel". Los Angeles Daily News. MediaNews Group. {{cite news}}: Check date values in: |date= (help)
  56. ^ La Liebre Ranch Quadrangle – California (Map). 1:24,000. 7.5-Minute Series (Topographic). United States Geological Survey. 1995. ISBN 978-06079-1345-3.
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  58. ^ Cooke, Anne Z.; Haggerty, Steve (April 20, 1986). "Biking Along California Aqueduct". Los Angeles Times. Retrieved December 15, 2011.
  59. ^ "California State Water Project Today". California Department of Water Resources. Retrieved December 16, 2011.
       1:100,000-scale metric topographic map of Lancaster, California (Map). 1:100,000. 30×60-Minute Series (Topographic). United States Geological Survey. 1981. ISBN 978-06071-0393-9.
       1:100,000-scale metric topographic map of Victorville, California (Map). 1:100,000. 30×60-Minute Series (Topographic). United States Geological Survey. 1982. ISBN 978-06071-0002-0.
       1:100,000-scale metric topographic map of San Bernadino, California (Map). 1:100,000. 30×60-Minute Series (Topographic). United States Geological Survey. 1982.
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  61. ^ "Water Contractors" (PDF). California Department of Water Resources. Retrieved December 18, 2011.
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  120. ^ Jaeger (1961) p. 49
  121. ^ Jaeger (1961) p. 58
  122. ^ Jaeger (1961) p. 70
  123. ^ Jaeger (1961) p. 73
  124. ^ Jaeger (1961) p. 77
  125. ^ Jaeger (1961) p. 79
  126. ^ Jaeger (1961) p. 79
  127. ^ a b Jaeger (1961) p. 81
  128. ^ Jaeger (1961) p. 90
  129. ^ Jaeger (1961) p. 91
  130. ^ Jaeger (1961) p. 94
  131. ^ Jaeger (1961) p. 104
  132. ^ Jaeger (1961) p. 110
  133. ^ Jaeger (1961) p. 118
  134. ^ Jaeger (1961) p. 130
  135. ^ Jaeger (1961) p. 135
  136. ^ Jaeger (1961) p. 145