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An Approach for Appraising the Accuracy of Suspended-Sediment Data

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An Approach for Appraising the Accuracy of Suspended-Sediment Data An Approach for Appraising the Accuracy of Suspended-sediment Data U.S. GEOLOGICAL SURVEY PROFESSIONAL PAl>£R 1383 An Approach for Appraising the Accuracy of Suspended-sediment Data By D. E. BURKHAM U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1333 UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON, 1985 DEPARTMENT OF THE INTERIOR DONALD PAUL MODEL, Secretary U.S. GEOLOGICAL SURVEY Dallas L. Peck, Director First printing 1985 Second printing 1987 For sale by the Books and Open-File Reports Section, U.S. Geological Survey, Federal Center, Box 25425, Denver, CO 80225 CONTENTS Page Page Abstract ........... 1 Spatial error Continued Introduction ....... 1 Application of method ................................ 11 Problem ......... 1 Basic data ......................................... 11 Purpose and scope 2 Standard spatial error for multivertical procedure .... 11 Sampling error .......................................... 2 Standard spatial error for single-vertical procedure ... 13 Discussion of error .................................... 2 Temporal error ......................................... 13 Approach to solution .................................. 3 Discussion of error ................................... 13 Application of method ................................. 4 Approach to solution ................................. 14 Basic data .......................................... 4 Application of method ................................ 14 Standard sampling error ............................. 4 Basic data ......................................... 14 Spatial error ............................................ 5 Analysis of data .................................... 15 Discussion of error .................................... 5 Standard temporal error ............................ 15 Introduction ........................................ 5 Sediment-discharge error ............................... 15 Multivertical procedure .............................. 9 Discussion of error ................................... 15 Single-vertical procedure ............................ 9 Approach to solution ................................. 17 Single-point procedure ............................... 9 Application of method ................................ 17 Approach to solution .................................. 10 Summary and conclusions .............................. 17 Multivertical procedure .............................. 10 References cited ........................................ 18 Single-vertical and single-point procedures ............ 10 ILLUSTRATIONS FIGURE 1. Schema of assumed true concentration at a vertical during Tz~T\, with nomenclature ......................... 2-4. Graphs showing: 2. Relation between standard sampling error and percentage sand in the sampled water-sediment mixture .. 3. A, Relation between the coefficient of variation and the percentage of the sampled water-sediment mixture that is sand; B, Relation between the coefficient of variation, the standard spatial error, and the number of verticals required to obtain the indicated standard spatial error ..................................... 12 4. Relation between standard temporal error in instantaneous concentration and the average elapsed time between samples for the two indicated sites .......................................................... 16 TABLE Page TABLE 1. Estimates of standard errors and information related to errors for selected sites along selected rivers and streams in California, Nebraska, Washington, Arizona, New Mexico, and Pennsylvania ............ III IV CONTENTS CONVERSION FACTORS For readers who may prefer to use metric units rather than inch-pound units, the conversion factors for the terms used in this report are listed below. Multiply By To obtain feet 0.3048 meters ft3/s (cubic feet per second) 0.02832 m3/s (cubic meters per second) mi2 (square miles) 2.590 km2 (square kilometers) tons, short 0.9072 megagrams AN APPROACH FOR APPRAISING THE ACCURACY OF SUSPENDED-SEDIMENT DATA By D. E. BURKHAM ABSTRACT sedimentation, general environmental impact assess­ ment, water treatment problems of sediment-associated Procedures are presented for appraising the accuracy of suspended- sediment data. The types of error involved are sampling error error nutrients and pollutants, and evaluation of the precise introduced in obtaining a value representing suspended-sediment impacts of humans. Because of the many important concentration for a sample taken at a single vertical during the potential uses of suspended-sediment data, it is essen­ sampling time; spatial error error in mean concentration that is tial that the reliability and accuracy of the data be determined from sampled concentration at verticals in a cross section known. Yet the data are published without analysis of for a point in time; temporal error error in computed values of suspended-sediment concentration for a cross section at any point in the bias or the precision of the facts presented, mainly time; and sediment-discharge error error in computed values of because a direct and exact technique for appraising the suspended-sediment discharge for a cross section at any point in accuracy of suspended-sediment data is not available. time. The standard error of estimate is the statistic used to represent Errors are introduced in the collection and tabula­ errors. Suspended-sediment data for 17 U.S. Geological Survey gaging tion of suspended-sediment data because, for any mea­ stations in Arizona, California, Nebraska, New Mexico, Pennsylva­ surement or computational scheme, the measurement nia, and Washington are used in applications of the procedures. For and sampling equipment, measurement and sampling the study sites, the magnitudes of the different types of error appar­ procedure, laboratory analysis, and computation proce­ ently vary directly with the percentage of the sediment-water mix­ dure do not give exact results. A change in the mea­ ture that is sand. Among the study sites, when the percentage of sand is relatively high, the magnitudes of the different types of error have surement and sampling equipment, the measurement a relatively wide range. and sampling procedure, the laboratory analysis, and For seven sites on the Sacramento River, California, and its tribu­ the computation procedure can result in a significant taries, the standard sampling error apparently can range from 2.5 deviation in the quality of the data. percent for periods when the percentage of the suspended sediment that is sand is relatively low to 20 percent when the percentage sand The accuracy requirement for the different uses of is relatively high. For 16 sites in Arizona, California, Nebraska, New suspended-sediment data is different. On the one hand, Mexico, and Pennsylvania, the coefficient of variation (ratio of stand­ a geomorphological study may require only a. "right ard deviation to cross-sectional mean) for concentration of suspended ball park" estimate of the suspended-sediment dis­ sediment across stream apparently can range from 2.5 percent for charge. On the other hand, an evaluation of the precise periods when percentage sand is relatively low to 70 percent when percentage sand is relatively high. impact of humans may require accurate information on suspended-sediment discharge. INTRODUCTION Generally, increasing sampling frequency increases PROBLEM the accuracy of a record of suspended-sediment dis­ charge until the accuracy reaches a maximum level. At The U.S. Geological Survey (USGS) and other Fed­ this point, deviations from true values represent ran­ eral, State, and local agencies obtain records of dom errors resulting from turbulent fluctuations in suspended-sediment discharge at many sites through­ streamflow and sediment movement and random and out the United States. The use of these records has systematic errors due to instrumentation, sampling greatly increased in recent years. Uses involve the technique, and computation. If funds were available, evaluation of sediment transport to the oceans, geo- unlimited data of a quality equal to the maximum level morphological studies of denudation and rates of ero­ of accuracy could be obtained; this approach could re­ sion, assessment of soil erosion and soil loss, reservoir sult in excessive expenditure of funds. AN APPROACH FOR APPRAISING THE ACCURACY OF SUSPENDED-SEDIMENT DATA A method that could be used to relate program objec­ standard sediment-discharge error depends on the tives and accuracy to sampling frequency, to document sampling procedure used to obtain the mean concen­ the maximum attainable accuracy at a site, and to tration for a section. For this report, the procedures readily appraise the accuracy of sediment records in for sampling to obtain the mean concentration are general would be a valuable tool in the design of an called "multivertical," "single vertical," and "single optimum sediment-sampling program. The develop­ point." ment of the method would be a step toward the im­ The standard error of estimate, representing only a provement of the quality control of suspended- random error, is a weighted measure of the difference sediment data. between computed and true values of a parameter. However, the total error in a computed value may en­ PURPOSE AND SCOPE compass both a random error and a bias error. The random error represents the randomly distributed de­ The primary purpose of this report is to present pro­ viations of computed values around the true value of a cedures that can be used to roughly appraise the accu­ parameter.
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