Properties of sand waves formed by subcritical unidirectional water currents are investigated by statistical analyses of records of streambed profiles. Records of bed elevation y as a function of distance x along the channel, y = y(x), and time records at a fixed point of the channel, y = y(t), were collected in three laboratory flumes that were 8 inches, 2 ft and 8 ft wide and in a straight alluvial channel that was 55 ft wide. For all cases, the bed material was fine sand. The continuous analogue records were converted to discrete data points and were analyzed by digital computer.
The analyses show that both types of records, y(x) and y(t), can be approximately represented as stationary Gaussian processes. When the data are standardized and the length or distance are expressed as ratios of the mean duration between zero-crossings of y, the statistical properties of all the flume data are similar, with no distinguishing characteristics that can be attributed to size of flume or to whether the bed forms were ripples or dunes. The field data, however, reflect the influence of large alternate bars that were not present in the flumes.
The Gaussian assumption, together with the spectral properties of the records as expressed by a dimensionless parameter, 6, permit predicting the distributions of maximum and minimum values of y between successive zeros of y. These distributions represent the probability distributions of the depth of local scour and fill due to the formation and migration of sand waves, and the parameters that specify the distributions relate approximately to flow velocity and depth.
Observed values of the number of zero and h-level crossings, the mean duration between zero crossings, and the mean duration of upward excursions of the process y(t) above the fixed level h compared reasonably well with theoretical values for the Gaussian model. The distribution of the duration of upward excursions is the conditional probability distribution of the rest period of a particle, given that it is deposited on the downstream face of a ripple or dune at the level h. Observed distributions of these durations can be approximated by a gamma distribution with parameters that relate to h, where h is measured in units of standard deviation from the mean bed level. These distributions and other probability distributions that enter into stochastic models of sediment transport can be determined either from the theoretical model or empirically from the observed data. The results of the study ,-show that even though the bed elevation deviates somewhat from the postulated normal distribution, reasonable estimates of many properties of the bed profiles can be derived from fairly simple statistical models.
","language":"English","publisher":"U.S. Geological Survey","doi":"10.3133/ofr68201","usgsCitation":"Nordin, C., 1968, Statistical properties of dune profiles: U.S. Geological Survey Open-File Report 68-201, xiv, 137 p., https://doi.org/10.3133/ofr68201.","productDescription":"xiv, 137 p.","costCenters":[],"links":[{"id":491571,"rank":2,"type":{"id":11,"text":"Document"},"url":"https://pubs.usgs.gov/of/1968/0201/report.pdf","linkFileType":{"id":1,"text":"pdf"}},{"id":184022,"rank":1,"type":{"id":24,"text":"Thumbnail"},"url":"https://pubs.usgs.gov/of/1968/0201/report-thumb.jpg"}],"noUsgsAuthors":false,"publicationStatus":"PW","scienceBaseUri":"4f4e49dde4b07f02db5e1e3f","contributors":{"authors":[{"text":"Nordin, C.F. Jr.","contributorId":100852,"corporation":false,"usgs":true,"family":"Nordin","given":"C.F.","suffix":"Jr.","affiliations":[],"preferred":false,"id":254388,"contributorType":{"id":1,"text":"Authors"},"rank":1}]}} ,{"id":43770,"text":"ofr6873 - 1968 - Geologic map of the Yucaipa quadrangle, California","interactions":[],"lastModifiedDate":"2021-09-21T17:56:58.65276","indexId":"ofr6873","displayToPublicDate":"1994-01-01T00:00:00","publicationYear":"1968","noYear":false,"publicationType":{"id":18,"text":"Report"},"publicationSubtype":{"id":5,"text":"USGS Numbered Series"},"seriesTitle":{"id":330,"text":"Open-File Report","code":"OFR","onlineIssn":"2331-1258","printIssn":"0196-1497","active":true,"publicationSubtype":{"id":5}},"seriesNumber":"68-73","title":"Geologic map of the Yucaipa quadrangle, California","docAbstract":"No abstract available.
","language":"English","publisher":"U.S. Geological Survey","doi":"10.3133/ofr6873","usgsCitation":"Dibblee, T.W., 1968, Geologic map of the Yucaipa quadrangle, California: U.S. Geological Survey Open-File Report 68-73, 1 Plate: 22.07 × 27.39 inches, https://doi.org/10.3133/ofr6873.","productDescription":"1 Plate: 22.07 × 27.39 inches","costCenters":[],"links":[{"id":81310,"rank":400,"type":{"id":17,"text":"Plate"},"url":"https://pubs.usgs.gov/of/1968/0073/plate-1.pdf","linkFileType":{"id":1,"text":"pdf"}},{"id":162068,"rank":0,"type":{"id":24,"text":"Thumbnail"},"url":"https://pubs.usgs.gov/thumbnails/usgs_thumb.jpg"},{"id":101861,"rank":700,"type":{"id":36,"text":"NGMDB Index Page"},"url":"https://ngmdb.usgs.gov/Prodesc/proddesc_113.htm","linkFileType":{"id":5,"text":"html"},"description":"113"}],"scale":"24000","country":"United States","state":"California","otherGeospatial":"Yucaipa quadrangle","geographicExtents":"{\n \"type\": \"FeatureCollection\",\n \"features\": [\n {\n \"type\": \"Feature\",\n \"properties\": {},\n \"geometry\": {\n \"type\": \"Polygon\",\n \"coordinates\": [\n [\n [\n -117.125,\n 34\n ],\n [\n -117,\n 34\n ],\n [\n -117,\n 34.125\n ],\n [\n -117.125,\n 34.125\n ],\n [\n -117.125,\n 34\n ]\n ]\n ]\n }\n }\n ]\n}","noUsgsAuthors":false,"publicationStatus":"PW","scienceBaseUri":"4f4e4ae3e4b07f02db688fbf","contributors":{"authors":[{"text":"Dibblee, T. W.","contributorId":30600,"corporation":false,"usgs":true,"family":"Dibblee","given":"T.","email":"","middleInitial":"W.","affiliations":[],"preferred":false,"id":228669,"contributorType":{"id":1,"text":"Authors"},"rank":1}]}} ,{"id":38818,"text":"pp543J - 1968 - Effects of the Alaska earthquake of March 27, 1964, on shore processes and beach morphology","interactions":[{"subject":{"id":38818,"text":"pp543J - 1968 - Effects of the Alaska earthquake of March 27, 1964, on shore processes and beach morphology","indexId":"pp543J","publicationYear":"1968","noYear":false,"chapter":"J","title":"Effects of the Alaska earthquake of March 27, 1964, on shore processes and beach morphology"},"predicate":"IS_PART_OF","object":{"id":70048225,"text":"pp543 - 1966 - The Alaska earthquake, March 27, 1964: regional effects","indexId":"pp543","publicationYear":"1966","noYear":false,"title":"The Alaska earthquake, March 27, 1964: regional effects"},"id":1}],"isPartOf":{"id":70048225,"text":"pp543 - 1966 - The Alaska earthquake, March 27, 1964: regional effects","indexId":"pp543","publicationYear":"1966","noYear":false,"title":"The Alaska earthquake, March 27, 1964: regional effects"},"lastModifiedDate":"2022-02-15T20:19:06.712305","indexId":"pp543J","displayToPublicDate":"1994-01-01T00:00:00","publicationYear":"1968","noYear":false,"publicationType":{"id":18,"text":"Report"},"publicationSubtype":{"id":5,"text":"USGS Numbered Series"},"seriesTitle":{"id":331,"text":"Professional Paper","code":"PP","onlineIssn":"2330-7102","printIssn":"1044-9612","active":true,"publicationSubtype":{"id":5}},"seriesNumber":"543","chapter":"J","title":"Effects of the Alaska earthquake of March 27, 1964, on shore processes and beach morphology","docAbstract":"Some 10,000 miles of shoreline in south-central Alaska was affected by the subsidence or uplift associated with the great Alaska earthquake of March 27, 1964. The changes in shoreline processes and beach morphology that were suddenly initiated by the earthquake were similar to those ordinarily caused by gradual changes in sea level operating over hundreds of years, while other more readily visible changes were similar to some of the effects of great but short-lived storms. Phenomena became available for observation within a few hours which would otherwise not have been available for many years.\n\nIn the subsided areas—including the shorelines of the Kenai Peninsula, Kodiak Island, and Cook Inlet—beaches tended to flatten in gradient and to recede shoreward. Minor beach features were altered or destroyed on submergence but began to reappear and to stabilize in their normal shapes within a few months after the earthquake. Frontal beach ridges migrated shoreward and grew higher and wider than they were before. Along narrow beaches backed by bluffs, the relatively higher sea level led to vigorous erosion of the bluff toes. Stream mouths were drowned and some were altered by seismic sea waves, but they adjusted within a few months to the new conditions.\n\nIn the uplifted areas, generally around Prince William Sound, virtually all beaches were stranded out of reach of the sea. New beaches are gradually developing to fit new sea levels, but the processes are slow, in part because the material on the lower parts of the old beaches is predominantly fine grained. Streams were lengthened in the emergent areas, and down cutting and bank erosion have increased.\n\nExcept at Homer and a few small villages, where groins, bulkheads, and cobble-filled baskets were installed, there has been little attempt to protect the postearthquake shorelines. The few structures that were built have been only partially successful because there was too little time to study the habits of the new shore features and to design appropriate protection measures. Emergence of large areas that were once below water and permanent submergence of once-useful land areas have led to many problems of land use and ownership in addition to the destruction or relocation of wildfowl, shellfish, and salmon habitats.","largerWorkType":{"id":18,"text":"Report"},"largerWorkTitle":"The Alaska earthquake, March 27, 1964: Regional effects (Professional Paper 543)","largerWorkSubtype":{"id":5,"text":"USGS Numbered Series"},"language":"English","publisher":"U.S. Government Printing Office","publisherLocation":"Washington, D.C.","doi":"10.3133/pp543J","usgsCitation":"Stanley, K.W., 1968, Effects of the Alaska earthquake of March 27, 1964, on shore processes and beach morphology: U.S. Geological Survey Professional Paper 543, vi, 21 p., https://doi.org/10.3133/pp543J.","productDescription":"vi, 21 p.","numberOfPages":"34","costCenters":[{"id":380,"text":"Menlo ParkCalif. Office-Earthquake Science Center","active":false,"usgs":true}],"links":[{"id":277850,"type":{"id":15,"text":"Index Page"},"url":"https://pubs.usgs.gov/pp/0543j/index.html"},{"id":395994,"rank":4,"type":{"id":36,"text":"NGMDB Index Page"},"url":"https://ngmdb.usgs.gov/Prodesc/proddesc_99033.htm"},{"id":65742,"rank":300,"type":{"id":11,"text":"Document"},"url":"https://pubs.usgs.gov/pp/0543j/pp543j_text.pdf","linkFileType":{"id":1,"text":"pdf"}},{"id":119822,"rank":0,"type":{"id":24,"text":"Thumbnail"},"url":"https://pubs.usgs.gov/pp/0543j/report-thumb.jpg"}],"country":"United States","state":"Alaska","geographicExtents":"{\n \"type\": \"FeatureCollection\",\n \"features\": [\n {\n \"type\": \"Feature\",\n \"properties\": {},\n \"geometry\": {\n \"type\": \"Polygon\",\n \"coordinates\": [\n [\n [\n -154.8193359375,\n 56.68037378950137\n ],\n [\n -145.72265625,\n 56.68037378950137\n ],\n [\n -145.72265625,\n 63.93737246791484\n ],\n [\n -154.8193359375,\n 63.93737246791484\n ],\n [\n -154.8193359375,\n 56.68037378950137\n ]\n ]\n ]\n }\n }\n ]\n}","noUsgsAuthors":false,"publicationStatus":"PW","scienceBaseUri":"4f4e4a27e4b07f02db6106c9","contributors":{"authors":[{"text":"Stanley, Kirk W.","contributorId":8900,"corporation":false,"usgs":true,"family":"Stanley","given":"Kirk","email":"","middleInitial":"W.","affiliations":[],"preferred":false,"id":220494,"contributorType":{"id":1,"text":"Authors"},"rank":1}]}} ,{"id":949,"text":"wsp1860 - 1968 - Electrical analog analysis of ground-water depletion in central Arizona","interactions":[],"lastModifiedDate":"2022-02-15T20:58:25.416238","indexId":"wsp1860","displayToPublicDate":"1994-01-01T00:00:00","publicationYear":"1968","noYear":false,"publicationType":{"id":18,"text":"Report"},"publicationSubtype":{"id":5,"text":"USGS Numbered Series"},"seriesTitle":{"id":341,"text":"Water Supply Paper","code":"WSP","active":false,"publicationSubtype":{"id":5}},"seriesNumber":"1860","title":"Electrical analog analysis of ground-water depletion in central Arizona","docAbstract":"The Salt River Valley and the lower Santa Cruz River basin are the two largest agricultural areas in Arizona. The extensive use of ground water for irrigation has resulted in the need for a thorough appraisal of the present and future ground-water resources. The ground-water reservoir provides 80 percent (3.2 million acre-feet) of the total annual water supply. The amount of water pumped greatly exceeds the rate at which the ground-water supply is being replenished and has resulted in water-level declines of as much as 20 feet per year in some places. The depletion problem is of economic importance because ground water will become more expensive as pumping lifts increase and well yields decrease. The use of electrical-analog modeling techniques has made it possible to predict future ground-water levels under conditions of continued withdrawal in excess of the rate of replenishment. The electrical system is a representation of the hydrologic system: resistors and capacitors represent transmissibility and storage coefficients. The analogy between the two systems is accepted when the data obtained from the model closely match the field data in this instance, measured water-level change since 1923. The prediction of future water-table conditions is accomplished by a simple extension of the pumping trends to determine the resultant effect on the regional water levels. \r\n\r\nThe results of this study indicate the probable depths to water in central Arizona in 1974 and 1984 if the aquifer characteristics are accurately modeled and if withdrawal of ground water continues at the same rate and under the tame areal distribution as existed between 1958 and 1964. The greatest depths to water in 1984 will be more than 700 feet near Stanfield and more than 650 feet in Deer Valley and northeast of Gilbert. South of Eloy and northwest of Litchfield Park, a static water level of more than 550 feet is predicted. The total water-level decline in the 20-year period 1964-84 at the deepest points of the major cones of depression will range from 150 to 300 feet, and the average decline in the entire central Arizona area will be about 100 feet.","language":"English","publisher":"U.S. Govt. Print. Off.,","doi":"10.3133/wsp1860","usgsCitation":"Anderson, T.W., 1968, Electrical analog analysis of ground-water depletion in central Arizona: U.S. Geological Survey Water Supply Paper 1860, Report: iii, 21 p.; 4 Plates: 44.69 × 26.00 inches or smaller, https://doi.org/10.3133/wsp1860.","productDescription":"Report: iii, 21 p.; 4 Plates: 44.69 × 26.00 inches or smaller","costCenters":[],"links":[{"id":396005,"rank":7,"type":{"id":36,"text":"NGMDB Index Page"},"url":"https://ngmdb.usgs.gov/Prodesc/proddesc_25084.htm"},{"id":25451,"rank":401,"type":{"id":17,"text":"Plate"},"url":"https://pubs.usgs.gov/wsp/1860/plate-2.pdf","linkFileType":{"id":1,"text":"pdf"}},{"id":25450,"rank":400,"type":{"id":17,"text":"Plate"},"url":"https://pubs.usgs.gov/wsp/1860/plate-1.pdf","linkFileType":{"id":1,"text":"pdf"}},{"id":25454,"rank":300,"type":{"id":11,"text":"Document"},"url":"https://pubs.usgs.gov/wsp/1860/report.pdf","linkFileType":{"id":1,"text":"pdf"}},{"id":25453,"rank":403,"type":{"id":17,"text":"Plate"},"url":"https://pubs.usgs.gov/wsp/1860/plate-4.pdf","linkFileType":{"id":1,"text":"pdf"}},{"id":25452,"rank":402,"type":{"id":17,"text":"Plate"},"url":"https://pubs.usgs.gov/wsp/1860/plate-3.pdf","linkFileType":{"id":1,"text":"pdf"}},{"id":138057,"rank":0,"type":{"id":24,"text":"Thumbnail"},"url":"https://pubs.usgs.gov/wsp/1860/report-thumb.jpg"}],"country":"United States","state":"Arizona","geographicExtents":"{\n \"type\": \"FeatureCollection\",\n \"features\": [\n {\n \"type\": \"Feature\",\n \"properties\": {},\n \"geometry\": {\n \"type\": \"Polygon\",\n \"coordinates\": [\n [\n [\n -112.4835205078125,\n 32.59773394005744\n ],\n [\n -111.3299560546875,\n 32.59773394005744\n ],\n [\n -111.3299560546875,\n 33.660353121928814\n ],\n [\n -112.4835205078125,\n 33.660353121928814\n ],\n [\n -112.4835205078125,\n 32.59773394005744\n ]\n ]\n ]\n }\n }\n ]\n}","noUsgsAuthors":false,"publicationStatus":"PW","scienceBaseUri":"4f4e4abbe4b07f02db672556","contributors":{"authors":[{"text":"Anderson, T. W.","contributorId":105686,"corporation":false,"usgs":true,"family":"Anderson","given":"T.","email":"","middleInitial":"W.","affiliations":[],"preferred":false,"id":142905,"contributorType":{"id":1,"text":"Authors"},"rank":1}]}} ,{"id":22416,"text":"ofr685 - 1968 - Some hydrologic effects of canal 111 near Homestead, Florida","interactions":[],"lastModifiedDate":"2012-02-02T00:08:07","indexId":"ofr685","displayToPublicDate":"1994-01-01T00:00:00","publicationYear":"1968","noYear":false,"publicationType":{"id":18,"text":"Report"},"publicationSubtype":{"id":5,"text":"USGS Numbered Series"},"seriesTitle":{"id":330,"text":"Open-File Report","code":"OFR","onlineIssn":"2331-1258","printIssn":"0196-1497","active":true,"publicationSubtype":{"id":5}},"seriesNumber":"68-5","title":"Some hydrologic effects of canal 111 near Homestead, Florida","language":"ENGLISH","publisher":"U.S. Dept. of the Interior, Geological Survey,","doi":"10.3133/ofr685","issn":"0094-9140","usgsCitation":"Barnes, H., Meyer, F., and Hartwell, J., 1968, Some hydrologic effects of canal 111 near Homestead, Florida: U.S. Geological Survey Open-File Report 68-5, 28 p. :ill., maps ;28 cm., https://doi.org/10.3133/ofr685.","productDescription":"28 p. :ill., maps ;28 cm.","costCenters":[],"links":[{"id":156632,"rank":0,"type":{"id":24,"text":"Thumbnail"},"url":"https://pubs.usgs.gov/thumbnails/usgs_thumb.jpg"}],"noUsgsAuthors":false,"publicationStatus":"PW","scienceBaseUri":"4f4e49e9e4b07f02db5e91ff","contributors":{"authors":[{"text":"Barnes, H.H. Jr.","contributorId":67916,"corporation":false,"usgs":true,"family":"Barnes","given":"H.H.","suffix":"Jr.","email":"","affiliations":[],"preferred":false,"id":188202,"contributorType":{"id":1,"text":"Authors"},"rank":1},{"text":"Meyer, F.W.","contributorId":25150,"corporation":false,"usgs":true,"family":"Meyer","given":"F.W.","email":"","affiliations":[],"preferred":false,"id":188201,"contributorType":{"id":1,"text":"Authors"},"rank":2},{"text":"Hartwell, J.H.","contributorId":98356,"corporation":false,"usgs":true,"family":"Hartwell","given":"J.H.","email":"","affiliations":[],"preferred":false,"id":188203,"contributorType":{"id":1,"text":"Authors"},"rank":3}]}} ,{"id":68135,"text":"ha255 - 1968 - Floods in McHenry Quadrangle, Northeastern Illinois","interactions":[],"lastModifiedDate":"2012-02-10T00:11:29","indexId":"ha255","displayToPublicDate":"1994-01-01T00:00:00","publicationYear":"1968","noYear":false,"publicationType":{"id":18,"text":"Report"},"publicationSubtype":{"id":5,"text":"USGS Numbered Series"},"seriesTitle":{"id":318,"text":"Hydrologic Atlas","code":"HA","active":false,"publicationSubtype":{"id":5}},"seriesNumber":"255","title":"Floods in McHenry Quadrangle, Northeastern Illinois","language":"ENGLISH","doi":"10.3133/ha255","usgsCitation":"Mycyk, R.T., and Walter, G.L., 1968, Floods in McHenry Quadrangle, Northeastern Illinois: U.S. Geological Survey Hydrologic Atlas 255, 1 col. map ;58 x 43 cm., on sheet 80 x 122 cm., https://doi.org/10.3133/ha255.","productDescription":"1 col. map ;58 x 43 cm., on sheet 80 x 122 cm.","costCenters":[],"links":[{"id":186678,"rank":0,"type":{"id":24,"text":"Thumbnail"},"url":"https://pubs.usgs.gov/thumbnails/usgs_thumb.jpg"},{"id":89436,"rank":400,"type":{"id":17,"text":"Plate"},"url":"https://pubs.usgs.gov/ha/255/plate-1.pdf","linkFileType":{"id":1,"text":"pdf"}}],"scale":"24000","geographicExtents":"{ \"type\": \"FeatureCollection\", \"features\": [ { \"type\": \"Feature\", \"properties\": {}, \"geometry\": { \"type\": \"Polygon\", \"coordinates\": [ [ [ -88.36749999999999,42.25 ], [ -88.36749999999999,42.3675 ], [ -88.25,42.3675 ], [ -88.25,42.25 ], [ -88.36749999999999,42.25 ] ] ] } } ] }","noUsgsAuthors":false,"publicationStatus":"PW","scienceBaseUri":"4f4e49e5e4b07f02db5e7010","contributors":{"authors":[{"text":"Mycyk, Roman T.","contributorId":58331,"corporation":false,"usgs":true,"family":"Mycyk","given":"Roman","email":"","middleInitial":"T.","affiliations":[],"preferred":false,"id":277708,"contributorType":{"id":1,"text":"Authors"},"rank":1},{"text":"Walter, Gerald L.","contributorId":59880,"corporation":false,"usgs":true,"family":"Walter","given":"Gerald","email":"","middleInitial":"L.","affiliations":[],"preferred":false,"id":277709,"contributorType":{"id":1,"text":"Authors"},"rank":2}]}} ,{"id":58078,"text":"wdrCO671 - 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","language":"English","publisher":"U.S. Fish and Wildlife Service","usgsCitation":"Spaulding, W., and Ogden, R.D., 1968, Effects of surface mining on the fish and wildlife resources of the United States: Resource Publication 68, iv, 51 p.","productDescription":"iv, 51 p.","costCenters":[],"links":[{"id":162909,"rank":0,"type":{"id":24,"text":"Thumbnail"},"url":"https://pubs.usgs.gov/thumbnails/usgs_thumb.jpg"}],"noUsgsAuthors":false,"publicationStatus":"PW","scienceBaseUri":"4f4e4ac9e4b07f02db67c901","contributors":{"authors":[{"text":"Spaulding, William M.","contributorId":32582,"corporation":false,"usgs":true,"family":"Spaulding","given":"William M.","affiliations":[],"preferred":false,"id":217754,"contributorType":{"id":1,"text":"Authors"},"rank":1},{"text":"Ogden, Ronald D.","contributorId":6499,"corporation":false,"usgs":true,"family":"Ogden","given":"Ronald","email":"","middleInitial":"D.","affiliations":[],"preferred":false,"id":217753,"contributorType":{"id":1,"text":"Authors"},"rank":2}]}} ,{"id":37253,"text":"rp64 - 1968 - Progress in sport fishery research, 1967","interactions":[],"lastModifiedDate":"2016-11-03T16:53:30","indexId":"rp64","displayToPublicDate":"1994-01-01T00:00:00","publicationYear":"1968","noYear":false,"publicationType":{"id":18,"text":"Report"},"publicationSubtype":{"id":1,"text":"Federal Government Series"},"seriesTitle":{"id":79,"text":"Resource Publication","active":false,"publicationSubtype":{"id":1}},"seriesNumber":"64","title":"Progress in sport fishery research, 1967","docAbstract":"No abstract available.
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