U.S. Department of 

U.S. Geological Su

Standar

of Surfa

Using E

Water-Res

U.S. Department of the Interior

U.S. Geological Survey

Water-Resources Investigations Report 01–4044
U.S. Geological Survey, Reston, Virginia: 2002

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

For more information about the USGS and its products:

Telephone: 1-888-ASK-USGS

World Wide Web: http://www.usgs.gov/

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

Although this report is in the public domain, it contains copyrighted materials that are noted in the text. 

Permission to reproduce those items must be secured from the individual copyright owners.

Library of Congress Cataloging-in-Publication Data

Suggested Citation: Sauer, V.B., 2002, Standards for the Analysis and Processing of Surface-Water Data and 

ation Using Electronic Methods: U.S. Geological Survey Water-Resources Investigations Report 01–4044, 91 
3.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3.2 Gage-Height Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.3 Velocity Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.4 Control Structure Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.5 Discharge Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.6 Field Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.7 Accuracy, Precision, and Significant Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4. Entry of Data to the Electronic Processing System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1 Unit Value Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1.1 Sources of Unit Value Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1.2 Unit Value Recording Time Interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.1.3 Time System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.1.4 Standard Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2 Field Measurement Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2.1 Discharge Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.2.1.1 Discharge Measurement Entry Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.2.1.2 Numbering Discharge Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.2 Gage Datum Leveling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.3 Crest-Stage Gage Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2.4 Channel and Control Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2.5 Miscellaneous Field Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5. Verification and Editing of Unit Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.1 Times and Dates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2 Time Corrections and Adjustments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2.1 Clock Error Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2.2 Universal Coordinated Time (UTC) Adjustments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.3 Parameter Value Verifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.3.1 Threshold Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.3.2 Rating Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.3.3 Direct Reading Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.3.4 Graphical Comparisons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.4 Parameter Value Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.4.1 Datum Adjustments and Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.4.1.1 Adjustments For Gage Datum Error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.4.1.2 Conversion to NGVD or Other Datum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.4.2 Instrument Error Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.4.2.1 Constant Value Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.4.2.2 Parameter Variable Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6.1.2 Logic and Consistency Checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.3 Computation of Measurement Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.4 Shift Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.4.1 Shifts for Stage-Discharge Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.4.2 Shifts for Slope Ratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.4.3 Shifts For Rate-of-Change In Stage Ratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.4.4 Shifts for Velocity-Index Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5 Special Procedures for Other Types of Discharge Measurements . . . . . . . . . . . . . . . . 

6.1.5.1 Ice Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.2 Measurements With Vertical Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.3 Moving Boat Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.3.1 Moving Boat Measurement, Manual Type. . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.3.2 Moving Boat Measurement, Automatic Type . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.4 Acoustic Doppler Current Profiler (ADCP) Measurements . . . . . . . . . . . . . . . . 

6.1.5.5 Indirect Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.6 Portable Weir and Flume Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.7 Tracer-Dilution Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.8 Volumetric Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.5.9 Discharge Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.6 Rounding and Significant Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.1.7 Summary of Discharge Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.2 Gage Datum Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.2.1 Established Elevations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.2.2 Datum Error Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.2.2.1 Base Benchmark Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.2.2.2 Alternate Benchmark Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.2.2.3 Rounding and Significant Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.2.2.4 Gage Datum Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.3 Crest-Stage Gage Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.3.1 Arithmetic Checking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.3.2 Logic and Consistency Comparisons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.3.3 Rounding and Significant Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.3.4 Summary of Crest-Stage Gage Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.4 Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.4.1 Logic and Consistency Checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.4.2 Graphical Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6.4.3 Computation of Cross-Section Hydraulic Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
7.4 Rating Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7.4.1 Interpolation Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7.4.2 Rating Table Precision and Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

7.4.3 Rating Table Smoothness Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

7.4.4 Other Rating Table Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

7.5 Rating Curve Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

7.6 Updating and Renumbering Existing Rating Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.7 Rating Curve Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.7.1 Reversal of Ordinate and Abscissa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.7.2 Electronic Processing System Monitor Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.7.3 Paper Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.7.4 Plotting Forms for Paper Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.7.5 Linear Scale Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.7.5.1 Linear Scale Selection Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7.7.5.2 Linear Scale Breaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7.7.6 Logarithmic Scale Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7.7.6.1 Logarithmic Scale Selection Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7.7.6.2 Scale Offsets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7.7.6.2.1 Scale Offset Limitations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7.7.6.2.2 Determination of Best Scale Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7.7.6.3 Rating Curve Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.7.7 Mathematical Fitting of Rating Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.7.8 Measurement Plotting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.7.8.1 Selection of Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.7.8.2 Selection of Independent Variable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7.7.8.3 Selection of Dependent Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7.7.8.4 Identification of Measurements on Rating-Curve Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.7.8.5 Other Rating-Curve Plot Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.8 Rating Curve Development Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.8.1 Stage-Discharge Ratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.8.1.1 Section Control Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.8.1.2 Channel Control Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.8.1.3 Step-Backwater Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.8.2 Slope Ratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.8.3 Index Velocity Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.8.4 Rate-of-Change-in-Stage Ratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

8. Shift Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
8.4.1 Individual Shift Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

8.4.2 Multiple Shift Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

8.4.3 Additive Shift Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

8.4.4 Shift Interpolation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

8.4.5 Rounding and Significant Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

8.4.6 Unit Value Graphical Comparisons of Shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

8.4.7 Shift Curve Tracking Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9. Primary Computations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1 Unit Value Computations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.1 Stage-only Stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.2 Stage-Discharge Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.3 Velocity Index Stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.4 Slope Stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.5 Rate-of-Change-in-Stage Stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.6 Reservoir Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.7 Tide Stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.8 Hydraulic Structure Stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.1.9 BRANCH Model Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.2 Daily Value Computations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.2.1 Daily Mean Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.2.2 Daily Minimum and Maximum Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.2.3 Daily Values at Selected Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.2.4 Daily Values for Tidal Stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.3 Summary of Primary Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.3.1 Unit Values Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.3.2 Primary Computations Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.3.3 Diagnostics Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.3.4 Daily Values Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9.3.5 Unit Values and Discharge Measurement Comparison Table . . . . . . . . . . . . . . . . . . . . . 

10. Hydrograph Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

10.1 Unit Values Hydrographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

10.2 Daily Values Hydrographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

10.3 Supplementary Hydrograph Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

11. Computation of Extremes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

11.1 Annual Peak Stage and Discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

11.2 Secondary Peak Stages and Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

11.3 Annual Minimum Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
13.1.2 Discharge Ratio Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

13.1.3 Regression Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

13.1.4 Water-Budget Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

13.1.5 Mathematical Translation Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

13.1.6 Flow Routing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

13.2 Estimating Gage Height and Other Hydrologic Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

13.3 Comparison of Estimation Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

13.4 Flagging and Archival of Estimation Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

14. Monthly and Annual Value Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

14.1 Monthly and Annual Values of Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

14.2 Monthly and Annual Values of Discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

14.3 Monthly and Annual Values for Reservoirs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

14.4 Monthly and Annual Values for Tidal Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

15. Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

15.1 Record Processing Notebook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

15.2 Station Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

15.3 Station Analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

15.4 Station Manuscripts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

16. Review, Approval, and Finalization of Records. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

17. Status of Data and Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

17.1 Original Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

17.2 Working Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

17.3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

17.4 Approval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

17.5 Publication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

18. Archiving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

19. Quality Assurance and Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

20. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

21. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7. Typical rating curve, shift curve, shift table, and optional shift diagram . . . . . . . . . . . . . . . . . . . . 

8. Example of shift-analysis table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

9. Example plot of time-series stage and shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

10. Example of a historical primary output of primary computations table. . . . . . . . . . . . . . . . . . . . . 

11. Example of a standard primary output of primary computations table . . . . . . . . . . . . . . . . . . . . . 

12. Basic navigation path requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Tables

1. Normal precision of measurements of surface water and related parameters . . . . . . . . . . . . 

2. Standard significant figures for surface-water data and information (English units) . . . . . . . 

3. Standard and daylight savings time zones of the United States and possessions. . . . . . . . . . 

4. Items to be entered to the electronic processing system from a discharge measurement 

front sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

5. Items to be entered to the electronic processing system from the inside body of a discharg

measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

6. Items that may be entered to an electronic processing system from level notes. . . . . . . . . . . 

7. Items that may be entered to an electronic processing system from crest-stage gage note

8. Items that may be entered to an electronic processing system from cross-section notes . 

9. Items that may be entered to an electronic processing system from miscellaneous field no

10. Discharge measurement items that should be shown in U.S. Geological Survey long-form 

and in short-form output (historical form 9-207) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

11. Crest-stage gage items that should be shown in the summary output form . . . . . . . . . . . . . . . 

12. Summary of calculated cross-section properties that should be listed in tabular format. . . 

13. Rating curve characteristics, limitations, and requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

14. Parameters requiring daily maximum and minimum values computed for various station ty

15. Items required for primary output tables for various gaging station types. . . . . . . . . . . . . . . . . . 

16. Items required for diagnostics tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
mile (mi) 1.609x100 kilometer (km)

Area

acre 4.047x103 square meter (m2

)

acre 4.047x10-1 square hectometer (hm2

)

acre 4.047x10-3 square kilometer (km2

)

square foot (ft2

) 9.290x10-2 square meter (m2)

square mile (mi2

) 2.590x100 square kilometer (km2)

Volume

cubic foot (ft3

) 2.832x101 cubic decimeter (dm3)

cubic foot (ft3

) 2.832x10-2 cubic meter (m3)

cubic foot per second day [(ft3

/s)d] 2.447x103 cubic meter (m3)

cubic foot per second day [(ft3

/s)d] 2.447x10-3 cubic hectometer (hm3)

acre-foot (acre-ft) 1.233x103 cubic meter (m3

)

acre-foot (acre-ft) 1.233x10-3 cubic hectometer (hm3

)

acre-foot (acre-ft) 1.233x10-6 cubic kilometer (km3

)

Flow rate

cubic foot per second (ft3

/s) 2.832x101 liter per second (l/s)

cubic foot per second (ft3

/s) 2.832x101 cubic decimeter per second (dm3/s)

cubic foot per second (ft3

/s) 2.832x10-2 cubic meter per second (m3/s)

Velocity

foot per second (ft/s) 3.048x10-1 meter per second (m/s)

foot per hour (ft/hr) 3.048x10-1 meter per hour (m/hr)

foot per hour (ft/hr) 2.54x101 millimeter per hour (mm/hr)

Sea level: In this report, “sea level” refers to the National Geodetic Datum of 1929 (NGVD of 

1929)—a geodetic datum derived from a general adjustment for the first-order level nets of both 

the United States and Canada, formerly called Sea Level Datum of 1929.

Abstract

Surface-water computation methods and procedures are 

described in this report to provide standards from which a completely automated electronic processing system can be developed. To the greatest extent possible, the traditional U. S. Geological Survey (USGS) methodology and standards for 

streamflow data collection and analysis have been incorporated 

into these standards. Although USGS methodology and standards are the basis for this report, the report is applicable to 

other organizations doing similar work. The proposed electronic processing system allows field measurement data, 

including data stored on automatic field recording devices and 

data recorded by the field hydrographer (a person who collects 

streamflow and other surface-water data) in electronic field 

notebooks, to be input easily and automatically. A user of the 

electronic processing system easily can monitor the incoming 

data and verify and edit the data, if necessary. Input of the computational procedures, rating curves, shift requirements, and 

other special methods are interactive processes between the 

user and the electronic processing system, with much of this 

processing being automatic. Special computation procedures 

are provided for complex stations such as velocity-index, slope, 

control structures, and unsteady-flow models, such as the 

Branch-Network Dynamic Flow Model (BRANCH). Navigation paths are designed to lead the user through the computational steps for each type of gaging station (stage-only, stagedischarge, velocity-index, slope, rate-of-change in stage, reservoir, tide, structure, and hydraulic model stations). The proposed electronic processing system emphasizes the use of interactive graphics to provide good visual tools for unit values 

editing, rating curve and shift analysis, hydrograph comparisons, data-estimation procedures, data review, and other needs. 

Documentation, review, finalization, and publication of records 

are provided for with the electronic processing system, as well 

as archiving, quality assurance, and quality control.

1. Introduction

The U.S. Geological Survey (USGS), Water R

Division (WRD), has been using automated data-pr

methods to compute, analyze, and publish surface-

records since about 1963. Surface-water records, by 

generally include stage and streamflow of rivers, cr

other streams; reservoir stage and contents; and tid

and near the mouths of coastal streams. Prior to 1963

streamflow data were processed by hand and deskt

tors. After 1963, some of the processing steps, such 

rating curves, were accomplished by hand methods 

ferred to the computer by keying in the necessary v

first nationally used computer program for process

flow data was installed in 1972 and was part of the 

Water Data Storage and Retrieval System, referred 

STORE (Hutchinson, 1977). In about 1983, a secon

referred to as the New Jersey District Automatic Da

(ADR) Processing System, or WRD Interim System

nationally and essentially replaced the WATSTOR

The New Jersey System was installed for use on th

Computers and was intended only for interim use u

program, the Automated Data Processing System, A

(Dempster, 1990), could be completed and installed

was installed nationally in 1985 and is part of the N

Water Information System (NWIS). In 1996–97, A

converted to run on the Data General computer supe

Prime computer, and has since been further convert

the Sun computer that superseded the Data General 

Instrumentation for the collection and field rec

time-series data has attempted to keep pace with co

capabilities for processing the data; however, a not

has resulted. The evolution of data-collection metho

progression from analog, or graphic, recorders to di

ers, and finally to electronic data loggers and data-c

platforms. Even so, many digital recorders still are i

mary instruments, and many graphic recorders are 

backup instruments. Part of the reason for this is a 

development and acceptance of electronic data logg

of the reason is lack of funds to support a full conve

a mixture of instrumentation still in use, it becomes 
Traditionally, streamflow information is produced primarily 

through the use of stage-discharge relations, with adjustments 

to these relations for shifting controls. For some stations, more 

complex computation procedures are used to account for variable backwater and rate-of-change in stage. Structures, such as 

dams, spillways, and turbines, are used at some stations to measure streamflow. The use of electromagnetic velocity meters 

and acoustic velocity meters has increased our abilities to continuously monitor stream velocity, and, thereby, provide an 

index of variable backwater. Unsteady-flow models, such as the 

Branch-Network Dynamic Flow Model (BRANCH), by Schaffrannek and others (1981), also have been accepted as viable 

methods to compute streamflow records. An unsteady-flow 

model uses detailed hydraulic characteristics of a stream reach, 

and has the capability to provide streamflow information at virtually every location in the stream reach, which may extend for 

many miles. This capability is a distinct advantage over the traditional gaging station that provides information at only one 

location.

Another aspect of streamgaging and the production of 

streamflow records is the increased need for streamflow information on a real-time, or near-real-time, basis. This aspect has 

led to remote sensing and transmitting systems where data are 

received in the office within minutes, or at the most hours, of the 

time of occurrence. These data usually are processed immediately upon reception in the office using automated computer 

systems. In many instances, these same data are received by 

agencies other than the USGS. Data and information of this type 

should be classified as operational, having more uncertainty 

than data and information that are subjected to verification, 

interpretation, and review. Operational data and information 

should not be considered the final answer for publication and 

archiving.

The changing technologies of data collection and data processing require changes in computer software. There is no 

doubt that this will be a continuing process as new and better 

computer technologies become available. In order to produce an 

accurate and consistent data base, it is important that certain 

procedures be standardized. The traditional hand methods, and 

some of the more recent computer methods, have been 

described in various USGS manuals, publications, and policy 

memorandum. Probably the oldest and most well known of the 

publications is Water Supply Paper 888 (Corbett and others, 

1943). A recent update of that report is Water Supply Paper 

ment and establish a standard set of techniques for sur

water data analysis and processing using electronic m

2. Purpose and Scope

The purpose of this report is to describe the standa

used in the automated processing of surface- water rec

computer. Although these standards are intended for u

rily by the USGS, they may be used by other organiza

doing similiar work. By definition, surface-water reco

include reservoir, stage-only, tide, and streamflow rec

streamflow computation methods, including stage-dis

relations, slope station method, index-velocity method

change in stage method, control structure methods, an

unsteady-flow model methods are described in this rep

emphasis of the report concerns automated, electronic 

ing and analysis, but by necessity, user interaction is re

provide the necessary interpretation and quality contro

3. Surface-Water Data and Informatio

Surface-water data and information are compose

number of measured and computed variables. This sec

the report will describe some of these, and will define 

the terminology used throughout the report. These def

should become part of the standards, just as the method

part of the standards.

3.1 Definitions

The words data and information, as used in this re

intended to have special meanings. The term data is use

results obtained from the measurement of a basic varia

which cannot be repeated. Data can be accepted, quali

rejected, but they cannot be modified without compro

their identity as data. Any change or modification of a 

value converts that value into information. For examp

original measurement of gage height is corrected for s

error (such as drift related to time, gage height, temper

other factors), the new value of gage height is informa
parameters, such as velocity, tend to fluctuate rapidly and a true 

instantaneous value would be difficult to use in the analysis and 

processing of the records. Some instruments are designed to 

take frequent (for example, every second) readings, temporarily 

store these readings, and then compute and store a mean value 

for a short time period. For these situations, the field instruments should be programmed to record mean unit values for 

very short time intervals (1 to 2 minutes) so they can be considered for practical purposes to be instantaneous unit values.

Daily values are measured or computed values of a parameter for a specific date only. The time of the daily value is not 

required, although for certain daily values, time sometimes is 

stated. Examples of daily values are daily mean value, maximum instantaneous value for a day, and minimum instantaneous value for a day. In the case of maximum and minimum 

instantaneous values for a day, the time of the value usually is 

stated.

A hydrographer is defined for purposes of this report to be 

a person who collects streamflow and other surface-water data 

in the field. A user is a person who uses the electronic processing system to input data, analyze data, and process streamflow 

and other surface-water data and information. In many cases, 

the hydrographer and user may be the same person, but sometimes may be different persons.

3.2 Gage-Height Data

The height of the surface of a water feature, such as a 

stream, reservoir, lake, or canal, usually is referred to as gage 

height, stage, or elevation. For a streamgaging station, gage 

height is the more appropriate terminology, but the more general term “stage” is sometimes used interchangeably (Langbein 

and Iseri, 1960). For lakes, reservoirs and tidal streams, the 

height of the water surface usually is referred to as elevation. 

Gage height (also stage) is measured above an arbitrary gage 

datum, whereas elevation is measured above National Geodetic 

Vertical Datum (NGVD). Gage heights and elevations are principal data elements in the collection, processing, and analysis of 

surface-water data and information. Gage heights and elevations are measured in various ways, such as by direct observation of a gaging device, or by automatic sensing through the use 

of floats, transducers, gas-bubbler manometers, and acoustic 

methods. Gage heights and elevations should be measured and 

vane gage, the electromagnetic velocity meter, and 

velocity meter. The methods for using each of these 

stream discharge will be described in section 9.1.3. 

poses of definition, the deflection vane gage readin

simply an index of stream velocity, whereas the ele

netic and acoustic meters provide actual velocity re

Deflection vane gage readings are instantaneous va

tromagnetic and acoustic velocity readings usually a

as an average of a number of instantaneous reading

aging period should be short, on the order of 1 or 2 m

recording interval is determined by the site charact

the flashiness of the stream. For example, a typical 

netic or acoustic gage setup may compute 1 minute 

stream velocity every 15 minutes and record these 

neous readings. The instrument would be active for 

and idle for 14 minutes.

3.4 Control Structure Data

Control structures, for the purpose of this repo

defined as manmade structures that are used to cont

of water in a river or stream. These structures are loc

at dams. A number of devices, such as free-flow sp

gated spillways, sluice gates, turbines, pumps, siph

navigation locks convey flow through, over, and/or 

structure. In many cases, these can be instrumented 

brated so that the stream discharge can be accurate

mined. At a control-structure streamgage site, instr

may be required to record unit values of headwater g

tailwater gage height, gate openings, turbine pressu

ages, and other variables that relate to the flow thro

structure. A control structure is frequently a very co

system requiring numerous instruments and sensor

rately measure the flow. A special computer progra

the control-structure system and is used to process t

data and compute discharge.

3.5 Discharge Information

A very important element, and frequently the u

in streamgaging, is the determination of stream disc

charge cannot be measured directly, but must be com

other measured variables such as gage height, strea
taneous unit values of discharge. This method differs from 

some of the methods used in the past where daily mean values 

of discharge were computed from daily mean values of gage 

height. It also differs from procedures where mean values of 

gage height for subdivided parts of a day were used to compute 

discharge. The procedure for computing daily mean values of 

discharge from instantaneous unit values is described in section 

9.2.

3.6 Field Measurements

Various kinds of data and information that are needed for 

the calibration and maintenance of a streamgaging station are 

obtained from field measurements. Most notable of these field 

measurements is the current meter measurement that is obtained 

periodically to define and check the discharge rating curve. 

Other types of field measurements include gage-datum leveling, indirect discharge measurements, and crest-stage gage 

measurements. Various measurements, other than discharge, 

and gage inspection notes sometimes are made and reported on 

field note sheets. For some stations with special methods for 

determining discharge, field measurements will be made of 

stream cross sections, estimates of stream roughness coefficients, and details of structures such as spillways, gates, and 

others. It is beyond the scope of this report to describe the 

details of most field measurements, but the surface-water analysis and processing system must provide an efficient method for 

entry and use of the field data and information.

3.7 Accuracy, Precision, and Significant Figures

Accuracy, precision, and significant figures are terms that 

are often confused and misinterpreted. This section of the report 

will describe the meanings of these terms, and provide a standard for use with surface-water data and information.

Accuracy is defined as the closeness or agreement of a 

measurement to the absolute or true value. Precision, refers to 

the closeness or agreement of repeated measurements to each 

other. Thus, precision also refers to the degree of refinement 

with which a measurement is made and repeated. An accurate 

measurement also is a precise measurement, but a precise measurement is not necessarily an accurate measurement. For 

example, a person making a measurement of gage height by 

low values may be more precise than a gage reading a

values because the water surface may have more surgi

wave action at high values. Accuracy also may be diff

between high and low values because gage-datum sett

other gage errors, may be different at high and low va

Another way of expressing accuracy and precisio

a statistical point of view. If an observer makes a num

readings of a gage over a very short time period (minu

during a time when the stream stage is not changing, th

retically the same gage height is measured each time th

read, assuming the equipment is in perfect working or

including the observer’s ability to read the gage. Becau

ment and people are not perfect, the gage readings wil

always be the same. A statistical measure of the dispe

scatter of the gage readings is defined as precision. Ge

the statistical measure used is the standard deviation, o

spread of about two-thirds of the readings. Precision, o

precision, is a random error having both plus and minu

tions. Averages of individual readings usually have les

than individual readings. Thus, the precision can be in

by averaging readings. However, averaging does not t

eliminate scatter and, thus, even the average has limite

sion.

The preciseness of a gage reading, as described a

not the sole measure of the accuracy of the reading. Fo

ple, if the cable of a wire-weight gage is longer or sho

because of an uncorrected temperature difference, then 

error affects all gage readings during the short time pe

question. Averaging does not remove this error, becau

the gage readings are affected by it with exactly the sa

nitude and sign. Such errors, which do not change dur

series of repeated gage readings, and that are not redu

averaging, are called systematic errors or biases.

Accuracy is expressed in terms of the difference 

a measurement result (whether a single measurement 

mean of various measurements) and the true gage heig

measurement result can differ from the true value beca

random errors (precision) or systematic errors (bias), o

Accuracy, or more properly, its obverse, uncertainty, n

is expressed as the square root of the sum of squares of 

deviation of random errors plus the sum of squares of e

systematic errors. A discussion of accuracy is given al

Rantz and others (1982).
Parameter

Precision of Measurements

English Units Metric Un

Gage height or elevation of water surface 0.01 ft 0.001 meter

Gage height of zero flow, natural channel .1 ft .01 meter

Gage height of zero flow, manmade control structure .01 ft .001 meter

Gage height of gage features .01 ft .001 meter

Velocity (Electromagnetic meter (EM), ultrasonic velocity meter (UVM), Price 

current meter)

.01 ft/s .001 meters p

Depth (uneven streambed, deep streams) .1 ft .01 meter

Depth (smooth streambed, shallow streams) .01 ft .001 meter

Width (wading measurements, narrow cross sections) .1 ft .01 meter

Width (bridge, cable, boat, wide cross sections) 1 ft .1 meter

Ground elevation (cross section) .1 ft .01 meter

Reference and benchmarks .001 ft .001 meter
Table 2. Standard significant figures for surface-water data and information (English units)

[x = significant figure, 0 = nonsignificant figure]

Data or Information Value Significant Figures

Water-surface gage height and elevation .0x, .xx, x.xx, xx.xx, xxx.xx, xxxx.xx

Stream depth .0x, .xx, x.x, xx.x xxx.

Stream width .xx, x.x, xx., xxx., xxxx., xxxx0.

Cross-section area .xx, x.x, xx.x, xxx., xxx0., xxx00., xxx000.

Cross-section conveyance x., xx., xxx., xxx0., xxx00., xxx000., xxx0000.

Stream velocity (mean or instantaneous) .0x, .xx, x.xx, xx.xx

Velocity adjustment factor (index-velocity) .0x, .xx, x.xx

Boyer factor (1/USc) .0x, .xx, x.xx

Reservoir contents xxxx., xxxx0., xxxx00., xxxx000., and so forth

Stream discharge (daily mean) .0x, .xx, x.x, xx., xxx., xxx0., xxx00., xxx000., xxx0000.

Stream discharge (measurement) .0xx, .xx, x.xx, xx.x, xxx., xxx0., xxx00., xxx000., xxx0000.

Water-surface fall (slope stations) .0x, .xx, x.xx, xx.xx

Fall ratio (slope stations) .0x, .xx, x.xx

Discharge ratio (slope stations) .0x, .xx, x.xx

Gage height of zero flow .0x, x.xx, xx.xx

Gage height of high water marks .xx, x.xx, xx.xx, xxx.xx

Gage height of gage features .xx, .xx, x.xx, xx.xx, xxx.xx

Reference and benchmark elevations .00x, .0xx, .xxx, x.xxx, xx.xxx, xxx.xxx, xxxx.xxx

Control structure elevations and gage heights .0x, .xx, x.xx, xx.xx, xxx.xx

Natural ground elevations and gage heights .x, x.x, xx.x, xxx.x
4.1 Unit Value Data

The recording of unit value data has evolved from simple 

hand written notes, to analog recorders, to digital recorders, to 

sophisticated programmable data loggers, and to direct data 

transmission to the computer by radio, telephone, or satellite. 

Although the trend today is toward the use of programmable 

data loggers and direct data transmission, digital recorders still 

are widely used, and some use of analog recorders and hand 

written observer records. Therefore, the electronic processing 

system must accommodate each of these types of data formats.

Preparation of unit value data for electronic processing 

should follow a basic sequence. However, because different 

methods are available for collecting and recording field data, 

there may be instances where the preferred sequence cannot be 

followed. The following sequence is advised:

1. A copy of the original, unedited unit values should be 

stored (archived) before any editing, conversions, or computations are made. All editing, conversions, and computations should be performed using an electronic copy of the 

original data.

2. The unit values should be translated into a standard format 

(see section 4.1.4).

3. The unit value times should be corrected for clock errors, 

if applicable (see section 5.2).

4. Conversions to UTC time should be made (see section 5.2) 

so that all unit value data can be related to standard time or 

daylight savings time, as required.

5. The unit values prepared in this manner then can be used 

for all further computations, analysis, and archiving, as 

described in this report.

Various types of unit value data can be entered into the 

electronic processing system. These data include unit values of 

gage height (stage or elevation), velocity or velocity index, 

spillway gate opening or index, turbine pressures, navigation 

lockages, and other readings associated with structures. For 

some gage sites, multiple data sets of unit values may be available for a given parameter. For instance, a stream affected by 

backwater may have two gages at different locations for the pur

y g, 

date and time of the reading, on a preprinted form. 

ings may be used as the primary set of unit values for 

or they may be used only for backup and verificatio

measuring and recording method. The hand written 

made by an observer must be entered into the elect

cessing system by direct keyboard entry. The date 

must be entered for each unit value, and the time zo

tion must be entered for each set of unit values.

Analog recorders—Analog, or graphical, reco

frequently used to record the gage height, or other p

as sensed by a float, pressure system, or other measu

connected to the recorder. Analog recorders provid

ous trace of the measurements on a graphical chart th

by a clock to provide a time scale. Unit value data 

charts are entered to the electronic processing syste

the use of an automatic, or hand operated, digitizer

tizer enters unit values from the chart at time interva

by the user. Beginning and ending dates and times, a

zone designation, must be entered for each segment 

is digitized. Analog records may be used as the prim

values for a station, but are more frequently used for 

verification of unit values collected with a differen

Automated digital recorders—The automated 

recorder (ADR) is a device that records data on a na

strip by punching a series of holes that digitally are 

represent the unit value reading. The paper strip adv

each punch and data are recorded at a specified tim

commonly 5, 15 or 60 minutes. Other time interval

used in some instances, but the time interval is unifo

gage. Unit value data are entered to the electronic p

system by passing the paper strip through a digital 

Starting and ending dates and times, and the time zo

tion, must be entered for each processing period. A

quently are used as the primary recording instrumen

site, but also are used as backup and verification for 

of instruments.

Electronic data loggers—Various types of ele

loggers are in use for recording unit value data. Th

receive data from a sensing instrument and record th

in electronic memory. Data are extracted from the d

either by removing the memory chip or by reading d

memory into an external storage module or field co

Because of the many configurations and types of d
interval, the starting and ending date and time must be entered 

for the period of record being processed. Electronic data loggers 

frequently are used for the primary recording instrument, but in 

some cases they may be used only for backup and verification.

Data-collection platforms—Data-collection platforms 

(DCP's) are field systems whereby data are stored electronically 

for a relatively short time (from 2 to 4 hours) and then transmitted by radio, telephone, or satellite to an office computer. For 

some types of DCP's, storage may be comparable to an electronic data logger and the data can be retrieved in similar fashion. DCP's are frequently operated in conjunction with an electronic data logger, ADR, or analog recorder. A variety of gage 

and recorder configurations is possible. Where two or more 

recorders are used, one should be designated the primary instrument, and the DCP frequently is given that distinction. In some 

instances, the DCP is the only instrument used and the primary 

record is received directly in the office. Unit value data transmitted and received by satellite automatically are tagged with 

date and time, which is determined from Universal Coordinated 

Time (UTC).

Other—Unit value data that are stored on other computer 

systems can be transferred to the electronic processing system 

by use of card images or other standard data formats.

One of the recorder types described above usually is designated as the primary recorder for computing the primary 

records of gage height, discharge, reservoir contents, or other 

parameters. Frequently, a second recorder is operated in conjunction with the primary recorder, and is designated the 

backup recorder. In the event of the malfunction of the primary 

recorder, the electronic processing system should allow the 

entry of unit values from the backup recorder as a substitute for 

g p

interval can be based on the value of the parameter be

recorded, the time length since the last recording, the r

change of the parameter value being recorded, the valu

of change of some other parameter, or some combinat

these. The electronic processing system can accommo

either method of data recording, constant or variable ti

val.

4.1.3 Time System Requirements

The time system used in most field data-collection 

is based on the local time in use at each gaging locatio

most parts of the United States, the local time is a chang

system where the clock is advanced 1 hour in the spring

back 1 hour in the fall. The time during the summer per

monly is referred to as daylight savings time, and the re

of the year as standard time. The advent of the satellite 

lection platforms (DCP) has required the use of Univer

dinated Time (UTC) for DCP field instruments. Addit

some gage sites are operated year around on local stand

without making the change for daylight savings time. 

quently, there is a mixture of time systems being used 

lection and recording of surface-water data. The surfa

electronic processing system must accommodate the e

data in any of the time systems. Therefore, all data ent

include a designation of the time system at which the d

recorded. Time system designations will be an acrony

on the time zone, or time system, to which the gage is o

Standard and daylight savings time zones, and the UT

for the United States and possessions are shown in tab
All times, both for time series data and for measurement 

data, automatically will be converted to UTC time for storage 

within the electronic processing system. Therefore, time adjustments for the 1-hour daylight savings time offset automatically 

will be accounted for when times are converted to UTC. The 

user will be able to perform computations, such as for daily 

mean values of streamflow, using any specified time system. 

The electronic processing system automatically will make the 

necessary time conversions, including changes between standard and daylight savings times, prior to making the computations. Likewise, unit values of gage height, discharge, or other 

parameters, would be retrieved using a time system of the user's 

choice.

4.1.4 Standard Format

All unit value data stored in the electronic processing 

system should conform to a standard unit value format. This 

format essentially means that the electronic process

should convert all unit values to engineering units, 

decimal, and assign times and dates based on the ti

used for field recording of data. Time adjustments 

pose of converting the unit value times to standard 

are made automatically. Time corrections made for 

should be made after the data are converted to a sta

mat. Parameter value corrections are made on the b

instructions after data are entered to the electronic p

system. Additional details regarding time and para

rections are described in section 5.

4.2 Field Measurement Data

Various types of field measurements are made 

water gaging stations, each providing various kinds 

information. These include measurements of stream 

leveling for gage datum checking, crest-stage gage 

EDST Eastern Daylight Savings Time + 4

CST Central Standard Time + 6

CDST Central Daylight Savings Time + 5

MST Mountain Standard Time + 7

MDST Mountain Daylight Savings Time + 6

PST Pacific Standard Time + 8

PDST Pacific Daylight Savings Time + 7

YST Yukon Standard Time + 9

YDST Yukon Daylight Savings Time + 8

AHST Alaska-Hawaii Standard Time +10

BST Bering Standard Time +11

BDST Bering Daylight Savings Time +10

1

Time zone names and designations not defined for the United States Trust Territory west of 

the international date line, where UTC offsets vary from -10 to -12 hours.

2

UTC offsets are added to the standard and daylight savings local times to obtain Universal 

Coordinated Time (UTC)
matically.

4.2.1 Discharge Measurements

The electronic processing system should have the capability to receive and store essentially all of the data and information recorded on discharge measurement note sheets. This 

capability would include the information shown on the front 

sheet of the notes and the detailed measurement data shown in 

the body of the notes. In the case where discharge measurements and associated information are recorded in electronic 

field computers, the electronic processing system would receive 

the data and information automatically through an interface.

Although the electronic processing system should be able 

to receive all data (front sheet and inside body) from a discharge 

measurement recorded on paper forms, it is not mandatory that 

the inside body data and information be entered. This part of the 

measurement is not normally used in the processing of daily 

discharge records. The main purpose for entering the data and 

information from the inside body would be for computational 

checking (see section 6.1), and for special studies.

The original measurement is either the data and information recorded on paper notes, or the data and information 

recorded in an electronic field notebook. If the measurement 

was recorded on paper, those original paper notes are saved for 

archival. If the measurement was recorded electronically, the 

first electronic copy entered to the electronic processing system 

becomes the archival copy. For this reason, it is mandatory that 

the entire measurement recorded in an electronic field note

3. moving boat measurements (manual and automate

4. acoustic Doppler profiler measurements (ADCP), 

5. tracer-dilution measurements,

6. portable weir and flume measurements, 

7. indirect measurements (slope area, contracted ope

culvert, stepbackwater, and critical depth),

8. surface velocity measurements (timing of floats o

optical, and others),

9. volumetric measurements, and 

10. simple estimates of discharge.

The input forms presented to the user with the ele

processing system should be designed to conform with 

surement method. That is, the input form for measurem

mary information for a specific method of measureme

example, portable flume) would have input items spec

that method of measurement, and would omit input ite

are not applicable to that method of measurement. Da

requirements for entry of summary information for dis

measurements, according to the method of measureme

listed in table 4.

The specific measurement data on the inside of th

charge measurement, although not mandatory, would 

entered on separate input forms. The data and informa

required for these forms are listed in table 5. For some 

ment methods the inside data may require multiple en

some items.
Standar

Moving Boat (M

Acoustic Do

Dy

Portabl

Surf

V

1

1 Station identification number XXXXXXXXX

1

2 Station name (Obtain from site file, if 

available)

X X X X X X X X X 

1

3 Measurement type1 XXXXXXXXX

1

4 Measurement sequence number X X X X X X X X X

1

5 Party XXXXXXXXX

1

6 Start date (date of flood for indirects) X X X X X X X X X 

7 End date XXXXXX XX

8 Start time X X X X X X X X 

9 End time XXXXXX XX

10 Time zone X X X X X X X X X 

11 Gage readings (table) XXXXXX XX

1

12 Mean gage height, Inside Gage X X X X X X X X X 

13 Mean gage height, Outside Gage XXXXXXXXX

14 Gage-height change X X X X X X X X 

15 Gage-height change time XXXXXX XX

16 Mean index velocity X X X X X X X X X 

17 Mean auxiliary gage height XXXXXXXXX

18 Stream width X X X X X

19 Stream area XXXX X

20 Mean velocity X X X X X

21 Number of sections XXXX X

1

22 Measured discharge X X X X X X X X X 

23 Channels measured XXXXXXXXX

24 Adjusted discharge X X X X X X
25 Adjustment method 2 XXXXX X

26 Measurement location 2 X X X X X X X X X 

27 Current meter type 2 XXX X

28 Current meter number X X X X

29 Initial current meter inspection X X X X

30 Final current meter inspection X X X X

31 Suspension method 2 XX X

32 Observation method 2 X X X

33 Description of measuring section XXXXX X 

34 Flow conditions 2 X X X X X X X

35 Horizontal angle coefficient X X X

36 Method coefficient 2 X X X X

37 Suspension coefficient 2 X X

38 Average time for point velocities X X X

39 Accuracy rating 2 XXXXXXXXX

40 Computed accuracy X

41 Control description 2 XXXXXXXXX

42 Control conditions 2 X X X X X X X X X 

43 Control cleaned X X X X X 

44 Time of control cleaning X X X X X 

45 Gage-height change from cleaning X X X X X 

46 Maximum stage indicator X X X X X X X X 

47 Minimum stage indicator XXXXXX XX

48 Highwater marks 2 X X X X X X X X X 

49 Air temperature XXXXXX XX

Stan

Moving Bo

Acoustic 

Por
Table 5. Items to be entered to the electronic processing system from the inside body of a discharge measurement 

Discharge Measurement Method

Item

Number Measurement Item

Standard Current Meter

Ice

Moving Boat (Manual Only)1

Acoustic Doppler current profiler1

Dye Dilution2

Portable Weir orFflume

Indirect2

Surface Velocity

Volumetric

3

1 Station identification number X X X X X X

3

2 Station Name X X X X X X

3

3 Measurement sequence number X X X X X X

4 Channel number or name X X X X X X

5 Distance from initial point X X X X

6 Subsection width X X X

7 Horizontal angle coefficient X X X

8 Depth, water surface to streambed X X X X

50 Water temperature X X X X X X X X 

51 Base flow 2 X XX X

52 Gage height of zero flow X X X X X 

53 Gage height of zero flow accuracy X X X X X 

54 Remarks, written comments X X X X X X X X X 

1

Mandatory.

2

Requires supplementary table or menu selections.

Stan

Moving Bo

Acoustic 

Por
9 Velocity observation depth(for example, .2, 

.6, .8, Surface)

XX X

10 Current meter revolutions X X X

11 Time of current meter revolutions X X X

12 Velocity at point X X X

13 Mean velocity in vertical X X X X

14 Subsection area X X X

15 Depth, water surface to bottom of ice X

16 Effective depth X X

17 Air line distance (for vertical angle corrections)X

18 Vertical angle X

19 Horizontal angle, manual moving boat X

20 Pulses per second X

21 Boat travel distance X

22 Vector velocity X

23 Sine of horizontal angle X

24 Subsection discharge X X X

25 Surface velocity measuring distance X

26 Surface velocity travel time X

27 Surface velocity X

28 Total container volume X

29 Starting volume X

30 Ending volume X

31 Flow volume (difference of start and end 

volumes

X

32 Fill time X

St

Mov

Acoust

Po
33 Total volume (sum of flow volumes) 

34 Total time (sum of fill times) 

35 Subsection number (items 35-39 for volumetric-incremental method)

36 Subsection width 

37 Sample width 

38 Subsection/sample width ratio 

39 Subsection discharge 

40 Head X

41 Average head X

42 Total width X X X X

43 Total area X X X X

44 Total discharge X X X X X 

1

Inside notes are entered electronically for automated moving boat and accoustic Doppler current profiler (ADCP).

2

Inside notes not required.

3

These items may not require direct entry. They should correspond to the front sheet entries for the given measurement, and may be provided di

electronic processing system.

St

Mov

Acoust

Po
measurements should be discouraged.

Table 6. Items that may be entered to an electronic processing system from level notes

[Note—Items 4–9, 11–21, and 23–24 may require more than one entry. For example, more than one reference mark, such as RM2, RM 3, RM 4, and o

be present.]

1

1.

1

2.

1

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

Station identification number

Date of leveling 

Party—initials and last name of each person 

Benchmark number (Benchmark, or Reference mark, that is used for the base should be separately identified)

Benchmark elevation, as found by levels

Reference mark number

Reference mark elevation, as found by levels

Reference point number

Reference point elevation, as found by levels

Electric tape reference point elevation, as found by levels

Inside gage reference point elevation, as found by levels

Inside gage reference point elevation, as read on gage

Outside gage reference point elevations, as found by levels

Outside gage reference point elevation, as read on gage

Wire-weight elevation (bottom of weight), as found by levels

Wire-weight elevation, as read on dial and corresponding to above item

Wire-weight check bar elevation, as found by levels

Wire-weight check bar elevation, as read on dial

Outside water surface elevation, as read on outside reference gage

Inside water surface elevation, as read on inside reference gage

Time of reading outside and inside gages, for two above items

Base (primary reference gage) correction, as found by levels

Highwater mark elevation

Crest-stage gage reference point elevation, (top of rod/stick, bottom pin, etc), as found by levels

Orifice elevation, by levels

Point of zero flow elevation, as found by levels

Remarks—written comments from level notes

1

Mandatory.
4.2.4 Channel and Control Cross Sections

Data defining cross sections of the stream channel and/or 

control are useful in rating curve analysis. Also, unsteady-flow 

model methods of computing stream discharge must have 

cross-section data at intervals along the stream reach for which 

the model is defined. The electronic processing system should 

allow input of items necessary for defining the cross-section 

location and the descriptors for each cross section. In addition, 

Manning roughness coefficients may be required and should be 

variable, both horizontally and vertically. For some cross sections that are considered section controls, a weir coe

should be an optional entry, which also may be var

stage. Transverse stationing for cross sections shou

the left bank of the stream and increase from left to 

survey data are entered with transverse stationing th

from right to left, the electronic processing system 

vide an automatic conversion of the data to the left-

mat. The electronic processing system also should a

input of cross-section data that were collected and r

electronically. A listing of data that should be allow

for cross sections is listed in table 8.

 4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

Crest-stage gage identification (for example, upstream gage, downstream gage, and others)

Elevation of crest-stage gage reference point (top of rod/stick or bottom pin), as given in station description

Distance measured from crest-stage gage reference point to high water mark on rod/stick

Highwater mark elevation, as calculated from two above items

Highwater mark elevation, as determined from marks outside the crest-stage gage

Estimated date of highwater mark

Gage height of current water surface

Gage read to obtain corresponding item 10 above (staff gage, wire weight, tape down, or other)

Time of gage reading

Time zone

Remarks—written comments from notes

1

Mandatory.

Table 8. Items that may be entered to an electronic processing system from cross-section notes

[Multiple cross sections may be entered. For items 7–14 multiple entries may be entered]

1

1.

1

2.

1

3.

1

4.

1

5.

1

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

Station identification number

Date of survey

Party—initials and last name of each person

Cross-section ID number—an alpha-numeric ID unique for each cross section.

A descriptive identification of the cross section, such as "section control" or "typical channel control section".

Longitudinal stationing, in ft, that locates the section relative to the gage. Positive stationing increases in the downstream 

and negative stationing increases in the upstream direction. The gage is station 0.

Transverse stationing along the cross section, with the initial point beginning on the left bank.

Ground elevation for each transverse station.

Sub-area breakpoint station (rightmost transverse station of a sub-area).

Sub-area low elevation breakpoint for roughness coefficients.

Sub-area high elevation breakpoint for roughness coefficients.

Sub-area low elevation roughness coefficient, Manning’s n.

Sub-area high elevation roughness coefficient, Manning’s n.

Cross-section weir coefficient, C, if applicable (can be variable with stage).

Remarks

1

Mandatory.
5. Verification and Editing of Unit Values

Unit values for the various parameters, such as gage height 

and velocity, must be carefully checked and verified before 

used in further analysis. Erroneous or suspicious data may 

require editing and appending special identification codes 

(flags) to individual values. Before any editing is performed, the 

original unit values should be set aside for archiving. Details of 

archiving requirements are described in another part of this 

report. This section of the report describes techniques for verification and editing, which includes time corrections, unit value 

corrections, datum adjustments, various comparisons and crosschecking, and flagging requirements. All verification, editing, 

and time corrections must be performed on a copy of the original data, and not on the original. This copy will become the 

work file, and also will be archived following completion and 

finalization of the records.

5.1 Times and Dates

Unit values of gage height and other streamflow parameters generally are recorded in field instruments at a fixed time 

interval, such as every 15 minutes, 1 hour, and so forth. The 

time and date associated with each unit value are not always 

recorded, but are determined on the basis of the initial time and 

date, and the recording time interval. Times and dates are 

recorded for each unit value when field recorders are programmed for variable time-interval data. Field instrument 

clocks are fairly reliable, but occasionally clock errors will 

result. True times and dates are those noted by the hydrographer 

using his watch and calendar at the time the field instrument is 

serviced. Servicing would be at the beginning and end of a 

record period, and occasionally at intermediate points of a 

record period. Also, the hydrographer should note the 

system designation, such as CST, CDST, PST, and oth

whenever the time and date are noted. Times, dates, an

system designations noted by hydrographers will be us

basis for making time corrections, standard and daylig

ings time adjustments, and conversion to UTC of the u

data.

Data acquired by satellite DCP installations will h

times and dates assigned automatically. These times a

are considered accurate and do not need adjustment or 

tion.

5.2 Time Corrections and Adjustments

Time corrections to account for clock errors may 

sary for unit value data recorded in the field. In addition

value times must be adjusted to UTC time for purpose

archiving. These time corrections and adjustments do n

to data collected by way of a satellite DCP because th

are considered correct as collected.

5.2.1 Clock Error Corrections

The simplest case of clock error is where the beg

time and date are correct and the ending time and date a

rect by a known amount. Lacking any evidence of inte

clock or recorder problems, it usually is assumed that t

error is a gradual and uniform error. The correction for 

of error should be prorated uniformly throughout the r

period.

A somewhat more complex case involves a clock 

recorder malfunction somewhere in the middle of the 

period, or where the clock was set wrong at the beginn

5.

6.

7.

8.

9.

10.

Gage read to obtain corresponding item 4 above (IG, OG, Tape, WW, recorder dial, other)

Time of gage reading

Time zone

Highwater mark elevation

Gage height of zero flow as determined from field measurement

Remarks—written comments from notes

1

Mandatory.
field notes when the gage was visited but the record was not 

removed. The electronic processing system should automatically retrieve dates and times from the field note entries for 

checking clock performance. This requires that the unit value 

file has been marked or tagged in some way so the user can 

identify the place in the record where the correct times and dates 

apply. Such readings would be treated the same as described 

above, and corrections would be made by linear proration 

between adjacent readings.

Past methods for making time corrections, such as used in 

ADAPS, provide a method referred to as the "historical" 

method, whereby occasional unit values are dropped, or added, 

in order to account for a time error. This method is not considered as good as the linear proration method and should not be 

used.

The standard time-correction method, or linear proration 

method, described herein will result in unit values of gage 

height (or velocity, or other parameter) that will not be on the 

even hour, or 15 minutes, or other even time. This is not considered detrimental to the record. If unit values of gage height (or 

other parameter) are needed on the even hour or other even time 

interval, they can be obtained by interpolation between the 

time-adjusted values.

Time differences caused by a change into or out of daylight 

savings time should not be treated the same as a clock error. If 

a clock error exists during a period of record where the time 

changed because of daylight savings time, the clock error 

should first be prorated by assuming a uniform time designation 

for all of the period of record being processed. The electronic 

processing system should adjust times and dates input from 

field notes to the same time designation. The clock error is then 

corrected according to the user's instructions. After clock error 

corrections are made, the record is automatically converted with 

the electronic processing system to UTC time for storage and 

archiving. No unit values would be dropped or artificially added 

because of the daylight savings time change.

5.2.2 Universal Coordinated Time (UTC) Adjustments

All data and information should be stored and archived 

with Universal Coordinated Time (UTC). Therefore, following 

the standard time-correction method for making clock error 

adjustments, the electronic processing system should automati

dard time is illustrated in figure 1. Also shown are 

that would be used for computing daily values for d

change between standard time and daylight savings 

that all unit values are used in the computations, an

dropped or artifically added. The day when time ch

daylight savings time will contain 23 hours, and the 

time changes out of daylight savings time will conta

5.3 Parameter Value Verifications

Unit values of gage height and other paramete

been automatically measured and recorded by field 

always should be carefully inspected and verified b

accepting them for further analysis and computatio

methods are available in electronic data processing t

task relatively easy. The most frequently used meth

threshold comparisons, rating comparisons, direct r

parisons, and graphical methods. Of these, graphic

are the most versatile and can be easily adapted to 

other methods.

5.3.1 Threshold Comparisons

A threshold is a minimum or maximum value t

detect unit values that might be erroneous. Thresho

compared directly to unit values, or to differences b

adjacent unit values. Testing a period of record aga

thresholds is performed automatically with the elec

cessing system. The user is alerted whenever a unit 

exceeds the threshold value. Thresholds can be esta

the user, or they can be automatically computed ba

period of record.

The set of thresholds should consist of (1) a hi

threshold, (2) a low-value threshold, (3) a maximum 

threshold, and (4) a flat-spot threshold (maximum t

stant values). Thresholds should be used to detect v

are unusual and outside the normal expected range 

For instance, an ADR punch recorder malfunctions a

additional holes in the paper tape, which translates 

values outside of the expected range of values. The 

check should alert the user to this condition. Maxim

minimum threshold values should be set at or near 

mum and minimum values actually experienced dur
3 to 5 years of record. The difference threshold also should be 

set at or near the largest valid difference during the past 3 to 5 

years.

Selection of threshold values should be based, if possible, 

on an analysis of the observed record for the past 3 to 5 years. 

This analysis should be performed with the electronic processing system and should furnish listings of the 20 highest peak 

unit values, and the 20 lowest trough unit values during the 

period. The electronic processing system also should provide 

the 20 greatest differences between consecutive unit values, and 

the 20 longest time periods during which there was no change 

in unit values (flat spots). This type of analysis would provide 

data for the user to use in selecting appropriate thresholds and 

would be performed every three years, or whenever it is desired 

to change thresholds.

Threshold checking, if used primarily for the purpose of 

identifying unit values that are outside the range of most experience, is a very valuable tool for identifying erroneous 

ues. However, caution should be exercised if high-valu

olds are set too low, or low-value thresholds set too hig

many unit values within the range of experience are id

by the threshold test. In this case, the user always shou

other methods to verify, or disqualify, unit values that 

failed the threshold test.

5.3.2 Rating Comparisons

A simple comparison, similar to threshold compa

the rating comparison. This comparison identifies all u

values that exceed the high end or fall below the low e

rating currently in use. This comparison can be perform

matically with the electronic processing system, becaus

are stored in the electronic processing system. This tes

 xxxx 0800 1200 xxxx 0600 1100

 xxxx 0900 1300 xxxx 0700 1200

 xxxx 1000 1400 xxxx 0800 1300

 xxxx 1100 1500 xxxx 0900 1400

 xxxx 1200 1600 xxxx 1000 1500

 xxxx 1300 1700 xxxx 1100 1600

 xxxx 1400 1800 xxxx 1200 1700

 xxxx 1500 1900 xxxx 1300 1800

 xxxx 1600 2000 xxxx 1400 1900

 xxxx 1700 2100 xxxx 1500 2000

 xxxx 1800 2200 xxxx 1600 2100

 xxxx 1900 2300 xxxx 1700 2200

 xxxx 2000 2400 xxxx 1800 2300

 xxxx 2100 0100 xxxx 1900 2400

 xxxx 2200 0200 xxxx 2000 0100

 xxxx 2300 0300 xxxx 2100 0200

 xxxx 04/04 2400 0400 xxxx 2200 0300

 xxxx 04/05 0100 0500 xxxx 2300 0400

 xxxx 0200 0600 xxxx 10/25 2400 0500

 xxxx 0300 0700 xxxx 10/26 0100 0600

 xxxx 04/05 0400 0800 EDST xxxx 10/26 0200 0700 EST

24 unit values used to compute daily value for April 4 26 unit values used to compute daily value for October 25

Figure 1. Comparison of time system examples where daylight savings time is used. [UTC, Coordinated Universal Time; 

EST, Eastern Standard Time; EDST, Eastern Standard Daylight Savings Time.]
g yy py

junction with the unit values being verified.

At some gaging stations auxiliary and/or backup gages are 

operated in conjunction with the primary gage. In many cases, 

the records from these gages can be used as an independent 

check, or comparison, to the primary record.

5.3.4 Graphical Comparisons

Graphics can be the most important and easily used 

method to verify a period of unit values. All of the methods 

described in sections 5.3.1 through 5.3.3 should be incorporated 

into a graphic system to automatically scan and review a period 

of record for the purpose of verification. The primary record of 

unit values should be plotted as a time series, with a unit-values 

scale that allows the user to see each value clearly and that does 

not distort the general shape of the record. The time scale should 

automatically default to the time zone normally used for the station, but there should be provision for the user to change to any 

other time zone. A basic plot of unit values can be used to identify erroneous data by an experienced user. With the addition to 

the plot of thresholds, rating limits, observer and hydrographer 

gage readings, high water marks, maximum and minimum indicator readings, and auxiliary gage records, much more can be 

done to verify the primary record.

The primary record of recorded unit values should be plotted and considered the base plot. The processing system should 

plot all direct gage readings by observers and streamgagers at 

the correct time on the base plot. High and low thresholds, high 

and low rating limits, highwater mark readings, maximum and 

minimum indicator readings, and crest-stage gage readings 

should be plotted at their respective elevations as a horizontal 

line that extends throughout the period of record being verified. 

This process will allow the user to compare these readings to 

peaks and troughs in the primary record. Auxiliary and backup 

records should be plotted as a time series for comparison to the 

primary record. The plotting system should use different colors 

and symbols to easily distinguish the various components. Unit 

values that trigger the difference threshold and the flat spot 

threshold also should be easily identified by color or symbol.

those errors resulting from a malfunction, an incorr

an incorrect calibration, or other problem with the r

instrument. An instrument error usually can be dete

comparing a recorded parameter value with a corre

reference gage reading. Datum errors, on the other 

those errors resulting from a change in the referenc

apply only to gage heights or elevations. A datum e

can be detected only by running levels to the refere

using a stable benchmark of known elevation as a r

Another distinction between datum errors and 

errors, is that datum errors generally occur over a lon

time (many months or years), whereas instrument er

are short term (a few days or weeks). Consequently, 

for datum errors and instrument errors usually are m

rately. However, correction for datum errors should 

same methods as those used for instrument errors, a

in section 5.4.2 below for instrument error correctio

When a parameter value, or series of values, h

determined to be erroneous, it may be corrected, or e

user has a sufficient basis for doing so. Editing of i

unit values should be allowed with the electronic p

system at any of the verification steps, including th

display. In the graphical display, the user should be 

edit unit values directly on the graph, or in a supplem

of unit values. In addition to correcting and editing 

the electronic processing system also should allow 

flag unit values in such a way that they will not be 

ther analysis.

5.4.1 Datum Adjustments and Conversions

The gage datum of a gage site usually is an arb

datum, unique and specifically selected as a conven

ing reference for each gage site. The datum frequent

at a level just below the lowest expected gage heigh

below the gage height of zero flow. For some statio

at reservoirs and coastal streams, the gage datum m

arbitrary, but is established to be the same as sea lev

known and common datum. In any case, there are t

datum adjustments must be made to correct a datum 

there are some stations for which it is necessary to 

arbitrary datum to a known datum, such as sea level

described in sections 5.4.1.1 and 5.4.1.2.
that are correct in relation to the original gage datum. Gage 

movement, relative to gage datum, is quantitatively measured 

by leveling from stable reference marks or benchmarks of 

known elevation. Leveling procedures for surface-water gaging 

stations are well established and are described by Kennedy 

(1990).

Datum errors should be carefully analyzed to determine 

the best method to make corrections. Frequently, it cannot be 

determined when a datum error occurred, and the best method 

of correction is to prorate it uniformly throughout the period in 

question. If a specific time of occurrence can be defined, then 

the correction can be made starting at that time and carrying the 

correction forward until the datum is restored. As a general rule, 

corrections for gage-datum errors of 0.02 ft or less are not 

applied, except in cases where smaller gage-datum errors are 

critical in correctly defining another parameter, such as for reservoir contents computations. Small errors of this kind usually 

are absorbed by ratings and rating shifts.

5.4.1.2 Conversion to NGVD or Other Datum

In addition to making datum adjustments for the purpose 

of correcting gage-height values that are incorrect because of a 

change of the base (reference) gage, it is sometimes necessary 

to convert recorded gage heights to a different datum. The most 

common conversion is where the recorded values must be converted to National Geodetic Vertical Datum (NGVD), sometimes referred to as mean sea level. This type of conversion 

requires that a constant value be added to, or subtracted from, 

the recorded gage heights throughout the record period. A gage 

datum adjustment for gage movement, as described in section 

5.4.1.1, also may be needed at times. In such cases, two simultaneous adjustments would be needed.

5.4.2 Instrument Error Corrections

Recording instruments and parameter sensors may, at 

times, produce erroneous gage readings for a number of reasons. For example, float tapes may slip, recorders may punch 

incorrectly, gage drawdown because of high velocity may occur 

at some stages, stage or velocity sensors may drift because of 

temperature or other reason, and the recorder even may be set 

wrong by the user. These, and numerous other causes, will 

sible, each of these types of corrections should be defi

the same entry form or graphical interface. In addition, 

methods and entry form should be applicable to datum 

corrections.

5.4.2.1 Constant Value Corrections

Constant value corrections are simply the additio

traction of a constant value from a sequence of unit val

user should be able to specify the constant value corre

be used, and the dates and times for which the correct

be applied. The electronic processing system then shou

the correction automatically.

5.4.2.2 Parameter Variable Corrections

Certain types of parameter errors may vary accor

the value of the parameter. For instance, for some gag

tions the stage measurements may not reflect actual riv

because of drawdown caused by high flow velocity ne

gage intake or orifice. The resulting stage error is dire

related to the velocity, which in turn is often related to t

A relation between stage and stage-correction can some

defined that is reasonably consistent for long time per

can be used to determine the gage-height correction on 

of the recorded stage.

Parameter variable corrections require a relation 

the parameter and the correction. The user should be a

input this relation to the electronic processing system, 

with a starting date and time, and if needed an ending 

time. The electronic processing system should calcula

apply the corrections automatically. When a correction 

of this type is entered, and no ending date and time are 

fied, then it should be continued in use until such time 

ending date and time are specified.

A parameter variable correction relation should be 

by entering point pairs of parameter and correspondin

tions for as many points as necessary through the intend

of correction. The processing system should automatic

interpolate corrections that are needed between the inpu

If parameter values occur below the lowest point of th

tion relation, then the correction value for the lowest po

relation should be used for all corrections below this p

Likewise, the correction values above the highest poin

correction relation should be the same as the highest co
apply to singular correction values and to parameter variable 

correction relations. Likewise, time variable corrections should 

apply to datum corrections as well as instrument error corrections.

Corrections that do not vary with parameter value are considered a singular correction for a given point in time. However, 

such a correction may vary with time. For example, at the 

beginning of a time series of unit values, a correction of +0.15 

ft is defined, which does not vary with stage. At a subsequent 

date and time, a correction of +0.10 ft is defined, which likewise 

does not vary with stage. The electronic processing system 

should allow the user to make a linear, time proration between 

these two correction values and defined times.

Corrections that vary with parameter value (as defined by 

a parameter variable correction relation) sometimes gradually 

may change shape or position with time. The electronic processing system should allow time proration between two consecutive parameter variable correction relations. Time proration 

between two correction relations should be made on the basis of 

equal parameter values. For example, assume that a correction 

relation is entered with a date and time. A second correction 

relation is entered with a subsequent date and time. At some 

intermediate date and time, assume that the gage height is 4.23 

ft. Correction values are determined from each of the two correction relations for a gage height of 4.23 ft, resulting in two 

correction values, one at the start of the proration period, and 

one at the end of the proration period. The correction that 

applies to the intermediate date and time, for the gage height of 

4.23 ft., is determined by time interpolation between the two 

correction values.

5.4.3 Numbering Correction Relations

Parameter variable correction relations should be numbered for ease of identification, reuse, and archiving. A simple 

consecutive number sequence for each year is preferred, such as 

1997.1, 1997.2, 1997.3, and so forth.

5.4.4 Additive Corrections

Sometimes, more than one correction for the same period 

of unit values may be needed. For instance, a datum correction 

may be needed during the same period of time that a parameter 

The electronic processing system should prov

option to identify the separate corrections entered by 

is recommended that a standard group of correction 

defined as (1) instrument error, (2) datum error, (3) 

adjustment, (4) velocity drawdown error, and (5) oth

correction is entered by the user, one of these types 

selected to describe the correction. Each type shoul

vision to enter additional descriptive text, if necess

5.4.6 Flagging of unit values

Corrections cannot always be determined for u

and in fact, corrections are not always desired for u

For certain situations it is recommended that daily 

estimated rather than attempting to correct, or estim

ues. In these situations, the user should be able to m

specific unit values to specify the reason they are no

flags also will be an indicator in other parts of the e

processing system, such as the primary computation

the unit values for certain kinds of computations. Th

flags are recommended.

• Affected—This flag is for unit values that 

and representative of the true stage (or othe

ter), but because of some irregular conditio

is severely affected and may not be applicab

should be used for severe conditions of back

irregular downstream conditions, backwate

and other conditions. The flag should not b

normal shifting control conditions.

• Erroneous—This flag is for incorrect unit v

instance, the float is resting on mud in the s

and the recorded unit values do not represe

in the stream.

• Missing—This flag is reserved for situation

values were expected, but because of some m

of equipment where no data were recorded

• Estimated—This flag is used for estimated 

It should be automatically attached to unit 

are changed by the user.

The first three types of flags defined above are 

primarily for the original, archivable, unit values. T

will document, for historical purposes, the evaluatio
y

Measurement Data

Field measurement data and information that are entered 

into the electronic processing system include discharge measurements, gage datum leveling measurements, crest-stage gage 

data, channel and control cross-section data, and miscellaneous 

field notes. All of these data usually are entered by keyboard, 

except that some discharge measurements are entered from 

electronic field computers. Various computations and comparisons should be made to verify the accuracy and insure the consistency of the information. Sections 6.1.1 through 6.1.3 

describe some of the verification, computations, and cross 

checking that should be performed with the electronic processing system. Errors resulting from data entry and incorrect computation should be corrected by the user.

It is important to emphasize that measurement data should

not be deleted or erased from the original notes, which in most 

cases are the paper note sheets. Editing of data that are entered 

from paper notes to the electronic processing system is permitted, provided the data were entered by keyboard. This editing 

allows for correction of keyboard entry errors without compromising the integrity of the original paper notes. On the other 

hand, data entered electronically, such as from an electronic 

field computer, should not be edited, changed, or deleted 

because once they are entered to the electronic processing 

system they become the original copy which will be used for 

archiving. It is assumed that no errors occur during an electronic 

transfer. All information in measurement notes (for example, 

computed values such as area, velocity, width, discharge, and 

others) may be edited and changed regardless of the entry 

method. Obviously, these values should be arithmetically correct and based on the original data.

6.1 Discharge Measurement Analysis

All discharge measurements should be checked wherever 

possible for arithmetic errors, logic errors, and other inconsistencies, with the electronic processing system. In addition, the 

electronic processing system should compute the standard error 

for regular current meter measurements. If a rating is available 

for the gaging station, the electronic processing system should 

compute the shift, or deviation, of the measurement from the 

y f

Most of these numbers are computed from the field m

ment data, that are part of the inside body of the measu

For discharge measurements recorded on paper forms, 

putations are made by the hydrographer in the field w

culator. If an electronic field notebook was used for re

the discharge measurement data, then the computation

made automatically by the field notebook, and little or 

metic checking is required.

When original computations are made on paper fo

following checks of the inside part of the measuremen

be made with the electronic processing system:

• Subsection width—The width for a subsection 

puted as one-half the distance between the pre

vertical stationing and the succeeding vertical 

ing. For verticals at the edge of a channel or bri

the subsection width is computed as one-half 

tance to the adjacent vertical.

• Point velocities—If a current meter rating or e

has been entered for the current meter used in 

the discharge measurement, then each point v

should be checked.

• Mean velocity for each vertical—The mean v

for each vertical is computed as follows:

For the one-point method, the mean velocity is 

the point velocity at the 0.6 depth. If the point 

was measured at a depth other than the 0.6 dep

the mean velocity for the vertical is computed 

tiplying the point velocity by the method coeffi

a method coefficient has not been entered for 

cal, then the electronic processing system shou

the hydrogapher and provide an opportunity to 

method coefficient. The user can choose to ign

warning.

For the two-point method, the mean velocity is 

a mean of the point velocities for the 0.2 and 

depths.

For the three-point method, the mean velocity 

to a weighted mean of the 0.2 depth velocity, 

depth velocity, and the 0.8 depth velocity, wher

depth velocity is given double weight.
and the subsection mean velocity.

• Total width—The total width for each channel is computed by summing the subsection widths.

• Total area—The total area for each channel is computed by summing the subsection areas.

• Total discharge—The total discharge for each channel 

is computed by summing the subsection discharges.

• Total number of verticals—The total number of verticals for a measurement is simply a count of the number 

of verticals, and includes the beginning and ending 

points where depth often is equal to zero.

• Average velocity—The average velocity for each channel is computed by dividing the total discharge by the 

total area.

• Totals for multiple channels—When the discharge 

measurement has two or more channels, such as for a 

braided stream, or a flood measurement that has a main 

channel and one or more overflow channels, the grand 

total of width, area, discharge, and number of verticals 

is computed. These grand totals are the values used to 

summarize the discharge measurement on the front

sheet. The average velocity for the measurement is the 

grand total of discharge divided by the grand total of 

area.

6.1.2 Logic and Consistency Checking

Information entered to the electronic processing system 

from one part of the discharge measurement notes should be 

automatically compared and cross checked with information 

from other parts of the measurement to verify that it is logical 

and consistent. The electronic processing system should alert 

the user when inconsistencies occur and provide an opportunity 

to make a change. In addition, when specific information items 

are entered, the electronic processing system then should limit 

the entry of other items so that the choices are consistent among 

themselves. For instance, if the type of measurement is entered 

as a wading measurement, then the choices for equipment entry 

would be limited to the various types of wading rods. A listing 

of some of the possible logic and consistency checks are given 

below:

the gage heights at the start and end of the 

measurement.

• Compare gage-height change time to start 

time—The gage-height change time should 

ference between the start and end time of th

measurement.

• Compare stream width on summary input t

width for inside note input—The stream w

summary input should be exactly the same 

stream width computed and entered for the 

input. For multiple channels the stream wid

the sum of individual channel widths.

• Compare stream area on summary input to 

for inside note input—The stream area on th

input should be exactly the same as the are

and entered for the inside note input. For mu

nels the stream area should be the sum of th

channel areas.

• Check mean velocity—The mean velocity 

checked by dividing the measured discharg

stream area.

• Compare number of sections on summary 

number of section for inside note input—T

of sections should be the total number of ve

for making the discharge measurement. Th

includes each end section of the measurem

though depth and velocity at these points m

For multiple channels, the number of section

the sum of the sections for individual chan

• Check adjusted discharge—If an adjusted 

entered, the electronic processing system s

pute an adjusted discharge based on the adj

method, if stated. This computed value sho

pared to the entered value.

• Check average time of point velocities—Th

time of point velocities on the summary inp

agree with the average of the time of curren

olutions entered for the inside note input.

• Compare gage height of zero flow to gage 

ings—The gage height of zero flow should 

the mean gage height of the discharge mea
, g

depth, average velocity, number of verticals, horizontal angle 

information, and velocity measurement method (one-point, 

two-point, and so forth). Much of this information is part of the 

regular entry of discharge measurement data. The discharge 

measurement entry form should allow for the entry of any missing items of information, and when all requirements are met the 

electronic processing system should automatically compute the 

measurement standard error and display it on the measurement 

entry form.

The standard error computation described above only can 

be used for regular open-water, current-meter discharge measurements, according to the limitations described by Sauer and 

Meyer (1992). It should not be used for ice measurements, 

moving boat measurements, and acoustic velocity measurements, indirect measurements, portable flume measurements, 

dye dilution measurements, volumetric measurements, and discharge estimates.

6.1.4 Shift Analysis

Discharge measurements are used primarily to check 

rating curves to insure that currently used rating curves still are 

applicable and have not changed. The electronic processing 

system should automatically compute the shift information for 

each discharge measurement The shift information should, by 

default, be computed on the basis of the rating curve applicable 

for the time and date of the discharge measurement; however, 

the user should be allowed to specify a different rating curve for 

which the shift information is computed. If, at a later date, a new 

rating curve is prepared, then the shift information should be 

automatically updated for all measurements that fall within the 

period of time that the new rating is applicable. Shift information, as noted in sections 6.1.4.1 through 6.1.4.4, should be displayed as part of the output for each discharge measurement.

Sections 6.1.4.1 through 6.1.4.4, respectively, describe the 

methods of computing shift information for discharge measurements made at stage-discharge stations, slope stations, rate-ofchange in stage stations, and velocity-index stations. Shifts are 

not computed or used for structure stations and BRANCH 

model stations. Definition of shift curves, use of partial or average shifts, and other aspects of shift application are described in 

section 8.

between the gage height, Gr

, that corresponds 

rating curve discharge for the measurement, a

gage height, Gm, of the discharge measuremen

resulting algebraic sign should be observed. T

tion is 

• Measurement percent difference, D%—This i

cent difference between the measured dischar

and the rating curve discharge, Qr, that corresp

the gage height of the discharge measurement

represents the difference between the measure

charge and rating discharge if no shift is appli

equation is 

D% = 100 (Qm – Qr)/Qr 

• Shifts for the gage height of zero flow, S0—If 

height of zero flow, G0, is determined either wh

ular discharge measurement is made, or indep

during a visit to the gaging station, then it is po

compute a shift for that gage height if the ratin

is defined down to zero flow. This information 

very useful as an aid in defining the low end o

curve. The equation for computing the shift for 

height of zero flow is similar to equation 1 for 

ing the rating shift, and is

Because the discharge corresponding to G0 is by d

zero, it is not possible to compute a measurement perce

ence.

6.1.4.2 Shifts for Slope Ratings

Slope ratings usually are referred to as complex r

because they involve two sites for measuring gage hei

base gage and an auxiliary gage) and three individual r

different parameters. The required ratings are (1) a sta

charge rating, (2) a stage-fall rating, and (3) a fall ratio

charge ratio rating. The use of these ratings for compu

charge are described in section 9.1.4. The purpose of t

section is to describe how shift information is comput

S r Gr Gm = –

S 0 Gr G0 = –
the observed stages at the base gage and the auxiliary gage, the 

observed fall, which is the difference between the two observed 

stages, and the defined rating curves. This adjusted discharge is 

used for comparison to the rating discharge, Qr, to determine 

shift information. If no shift is present, then Qadj and Qr will be 

equal. The method for computing Qadj and shift information is 

given in the following paragraphs.

• Adjusted discharge, Qadj—Compute the measured fall, 

Fm, as the difference between the observed mean gage 

height for the measurement at the base gage, Gb, and 

the auxiliary gage, Ga. The equation is

(4)

1. If the auxiliary gage is upstream from the base gage, 

reverse the order of Gb and Ga in equation 4.

2. Determine the rating fall, Fr, that corresponds to the base 

gage height, Gb, from the stage-fall rating.

3. Compute the fall ratio, Rf, of the measured fall to the 

rating fall. The equation is

(5)

4. Determine the discharge ratio, Rq, corresponding to Rf

from the ratio rating.

5. Compute the adjusted discharge, Qadj, based on the 

measured discharge, Qm, and the discharge ratio, Rq, is

(6)

• Stage-discharge rating shift, Sr—Determine the gage 

height, Gr, corresponding to the adjusted discharge, 

Qadj, from the stage-discharge rating.

Compute the shift, Sr, based on the observed gage 

height, Gb, for the base gage and the rating gage height, 

Gr. The equation is

(7)

• Measurement percent difference, D%—The percent 

difference, D%, between the adjusted discharge, Qadj,

and the rating discharge, Qr, also should be computed. 

This percentage represents the error of the adjusted dis

The term 1/USc is a measure of floodwave velocity

constant discharge stream slope, Sc. This term usua

defined empirically from the discharge measureme

greatest effect of changing stage occurs on streams 

tively mild slopes, and rapid changes in discharges. 

this effect will happen when the flow regime of a s

been changed artificially, such as below a dam whe

are made quickly, or in urban areas where basin de

causes rapid increases in flow rates for a stream tha

ously sluggish.

Shift information for Boyer ratings should be 

only for the stage-discharge rating. The rating of st

should not be shifted. If this rating changes, then a 

should be prepared. The shift and percent differenc

based on the rating discharge, Qr, and the adjusted 

Qadj.

The method for computing the adjusted discha

shift information for Boyer ratings is as follows.

• Adjusted discharge, Qadj—Compute the ch

stage, dG, for the discharge measurement a

ence between the ending gage height, Ge, a

ing gage height, Gs. For rising stages the d

positive, and for falling stages the differenc

tive. The equation is

1. Compute the elapsed time, dt, for the discharge 

ment as the difference between the ending time

starting time, ts. The equation is

2. Compute the rate-of-change in stage, dG/dt, fo

discharge measurement.

3. Determine the factor, 1/USc, for the mean gage 

the discharge measurement, from the stage-1/U

4. Compute the adjustment factor, Fadj, using

. 

5. Compute the adjusted discharge, Qadj, as

Fm Gb Ga = –

R f Fm Fr = ⁄

Qadj Qm Rq = ⁄

Sr Gr Gb = –

dG Ge Gs = –

dt te ts = –

Fadj 1 1

USc

〈 〉 --------- dG

dt = + 〈 〉 -------
(13)

• Measurement percent difference, D%—Determine the 

rating discharge, Qr, from the stage-discharge rating 

using the measured mean gage height, Gm.

Compute the percent difference, D%, between the 

adjusted discharged, Qadj, and the rating discharge, Qr,

as

D% = 100(Qadj – Qr)/Qr (14)

This percent difference represents the error between the 

Boyer adjusted discharge and the rating discharge if no shift 

adjustment is applied.

6.1.4.4 Shifts for Velocity-Index Stations

Ratings at gaging stations with velocity index as part of the 

rating system are considered complex ratings, and in some 

cases can be extremely complex if two or more velocity meters 

are in use. Stream channels may be subdivided either vertically 

or horizontally, with each subdivision having a specific set of 

ratings, or in some cases the individual meters may be averaged 

for use with one set of ratings. Also, for some stations discharge 

measurements may be made so that only the total discharge is 

computed, with no accurate method of subdividing the measured discharge into the various rating components. Because of 

this variability in the way velocity-index stations are processed, 

it is not possible to describe all of the ways that rating shifts are 

computed. The electronic processing system should provide an 

interactive mode that allows the user to define the shifts and the 

shifting method.

Shift information for a basic velocity-index rating is 

described in the following paragraphs. A basic velocity-index 

rating includes a single rating of stage and cross-section area, a 

single rating of index velocity and mean velocity, and in some 

cases an optional rating of stage and a velocity correction factor. 

The rating discharge, Qr, is computed by multiplying the crosssection area, Ar, from the area rating, times the mean velocity, 

Vr, from the velocity rating, and times the velocity correction 

factor, Kr, from the stage-factor rating. If the velocity correction factor is not used, it is set to a default value of 1.00. The 

basic velocity-index equation for discharge is

ent section. All computations should be related to and 

the standard cross section. For instance, the mean strea

ity, as used for rating purposes, should be computed by 

the measured discharge by the cross-section area deter

from the stage-area rating of the standard cross section

mean stream velocity is the velocity that should be use

check or define the velocity rating, and the one to be u

plotting purposes on the velocity rating, for those sites 

stage-factor rating is not used. If a stage-factor rating 

then this velocity should be adjusted by dividing it by t

cable factor before using it to check or define the velo

ing.

The order of computations for shift determination

important because two, and in some cases three, rating

involved. The following step-by-step procedure should 

Standard cross-section area, Ar—Determine the 

sectional area, Ar, of the standard cross section from t

area rating, using the mean gage height, Gm, of the dis

measurement.

Velocity correction factor, Kr—Determine the ve

correction factor, Kr, from the rating of stage and velo

rection factor, using the mean gage height, Gm, of the d

measurement. If this rating is not used, then set the velo

rection factor to a default value of 1.00.

Adjusted mean stream velocity, Vm—Compute th

stream velocity, adjusted for the velocity correction fa

the standard cross section using

, 

where Qm is the measured discharge, and the oth

ables are as previously defined.

Rating index velocity, Vir—Determine the rating 

velocity from the rating of index velocity and mean st

velocity, by entering the rating with the adjusted mean 

velocity, Vm, as computed in equation 16.

Index velocity shift, Sv—Compute the index veloc

as the difference between the rating index velocity, Vir

mean measured index velocity, Vim, for the discharge 

ment. The shift, Sv, is defined by

 . 

Sr Gr Gm = –

Vm

Qm

Ar × Kr

= -----------------

Sv Vir Vim = –
Then determine the rating mean velocity, Vr

, corresponding to the index velocity observed for the discharge measurement. If a factor rating is used for the 

site, determine the rating factor, Kr, corresponding to 

the observed stage of the discharge measurement. If a 

factor rating is not used for the site, the rating factor 

defaults to 1.00. Finally, compute the rating discharge, 

Qr, using equation 15.

The measurement percent difference is computed as

D%= 100(Qm – Qr)/Qr . (18)

6.1.5 Special Procedures for Other Types of Discharge 

Measurements

Some discharge measurements are made under conditions 

that require computational procedures that are different than the 

standard open-water, current-meter discharge measurement 

described in preceding sections. In some cases, the differences 

are minor, but in other cases the measurement method is completely different. Also, some measurement methods use highly 

specialized equipment and recording methods that differ 

entirely from those of standard discharge measurements. The 

following sections describe some of the verification, editing, 

and computations that should be performed with the electronic 

processing system for each of the various types of measurements.

6.1.5.1 Ice Measurements

Ice measurements, in most respects, are the same as a standard open-water discharge measurement. All of the same arithmetic checking, logic and consistency checking, and shift analysis should be performed on ice measurements. Differences 

between computations for a standard discharge measurement 

and an ice measurement are listed below:

• Computation of effective depth—The inside body of 

the discharge measurement notes for ice measurements 

contains two additional columns of data and information. One of the extra data columns is a field measurement of the vertical distance between the free water 

surface and the bottom of the ice (solid or slush ice). 

These measurements should be compared to the total 

• Computation of subsection area—The area 

subsection is computed by multiplying the 

width times the effective depth, de, of the v

• Velocity coefficient—For verticals where th

method is used to observe velocity, it is freq

essary to apply a velocity coefficient to cor

ice effect on the vertical velocity distributio

velocity coefficient is similar to the use of 

coefficient for computing the mean velocit

cal, as described in section 6.1.1 on arithm

ing. The mean velocity in the vertical is co

multiplying the velocity coefficient times t

velocity observed at the 0.6 depth. If a velo

cient is not given, then it should default to 

two-point method (0.2 depth/0.8 depth) is u

observe velocity, then no velocity coefficie

sary.

• Shift computations—Shifts are not usually 

for ice measurements, but in some cases m

desired. The user should have the option to 

shifts should be computed, and if so, they s

computed just as they are for a regular open

surement.

• Percent difference from rating curve—The 

in percent, between the measured discharg

rating curve should be computed for all ice 

ments, based on the same method as descri

tion 6.1.4.1 for standard discharge measure

• Discharge ratio—For some gaging station

charge-ratio method is used for computing 

The user should have the option to specify 

tation of the ratio if it is used. The electronic 

system then should compute the ratio, Ki

, f

measurement as the ratio of the measured d

Qm, to the open-water rating discharge, Qr

sponds to the mean gage height of the mea

 . 

Ki Qm Qr = ⁄
ally are not recorded in the field notes, account for an airline 

correction and a wet-line correction of the sounding cable. In 

some cases, such as when sounding line tags are used, the airline correction may be eliminated or reduced to a negligible 

amount.

The electronic processing system should contain the airline correction table and the wet-line table so that the computed 

vertical depth can be checked. These tables are given by Rantz 

and others (1982), which also provides a detailed description of 

the computation methods. A brief summary of the procedure is 

listed below.

1. Determine the air-line correction based on the observed airline vertical distance between the sounding equipment and 

the water surface, the observed vertical angle, and the airline correction table.

2. Subtract the air-line correction (if used) from the 

uncorrected observed depth of water. This subtraction 

must be made before determining the wet-line correction.

3. Determine the wet-line correction based on the air-line 

corrected observed depth, the observed vertical angle, and 

the table of wet-line corrections.

4. Compute the true vertical depth by subtracting the wet-line 

correction from the air-line corrected observed depth.

5. Air-line and wet-line corrections should be interpolated 

from their respective tables to the nearest tenth of a foot.

All other computations and checking are essentially the 

same for measurements with vertical angles as they are for standard discharge measurements, including the computation of 

measurement standard error.

matic method, almost all data collection, data recordin

computations are performed by an on-board computer

manual method is still in use at the time of this report 

however, it is rapidly being replaced by the automatic 

Also, some moving boat measurements now utilize an 

Doppler current profiler (ADCP) for measurement of 

velocity. This method is described in section 6.1.5.5.

6.1.5.3.1 Moving Boat Measurement, Manual Type

The discharge measurement front sheet (summary

manual type of moving boat measurement is different 

standard current meter front sheet, but the differences a

and for practical purposes can be considered the same

fore, entry of summary data and information for a man

of moving boat measurement should use the same entry 

the standard current meter measurement (see table 4). 

special items that show on the front sheet can be entere

of the inside of the measurement described below.

The inside notes of the manual type of moving bo

surement are considerably different than those of a stan

charge measurement. A typical inside note sheet is sho

figure 2. The data columns required are as follows.

• Angle, α—The horizontal angle of the current 

read visually from an angle indicator as the bo

progresses across the stream.

• Depth—Depths at each vertical are taken from 

acoustic sounding chart.

• Pulses per second—These readings are instan

values of current meter response, related to ve

taken visually from the rate indicator at each v

• Remarks—The remarks column provides data 

information that relate to the individual vertic

subsections.
25 33.1 100.1 48.2 39.0 340 6.09 .423 2.58 1880 4850 (

30 63.2 163.3 63.5 38.0 370 6.62 .500 3.31 2410 7980

29 63.8 227.1 60.2 37.5 340 6.09 .485 2.95 2260 6670

39 56.7 283.8 56.3 37.0 340 6.09 .629 3.83 2080 7970

40 55.9 339.7 57.8 35.0 330 5.91 .643 3.80 2020 7680

35 59.8 399.5 57.8 35.5 330 5.91 .574 3.39 2050 6950

40 55.9 455.4 52.4 33.0 330 5.91 .643 3.80 1730 6570

48 48.8 504.2 48.8 32.5 350 6.27 .743 4.66 1590 7410

48 48.8 553.0 50.6 32.0 340 6.09 .743 4.52 1620 7320

44 52.5 605.5 50.2 31.5 340 6.09 .695 4.23 1580 6680

49 47.9 653.4 48.4 31.0 320 5.74 .755 4.33 1500 6500

48 48.8 702.2 52.4 30.0 330 5.91 .743 4.39 1570 6890

40 55.9 758.1 53.8 28.5 320 5.94 .643 3.69 1530 5650

45 51.6 809.7 52.5 26.5 300 5.38 .707 3.80 1390 5280

43 53.4 863.1 54.2 27.0 330 5.91 .682 4.03 1460 5880

41 55.1 918.2 50.5 27.0 350 6.27 .656 4.11 1360 5590

51 45.9 964.1 51.3 26.0 330 5.91 .777 4.59 1330 6100

39 56.7 1020.8 55.0 25.0 320 5.74 .629 3.61 1380 4980

43 53.4 1074.2 54.6 25.0 320 5.74 .682 3.91 1360 5320

40 55.9 1130.1 57.4 25.0 330 5.91 .643 3.80 1440 5470

36 59.0 1189.1 51.4 24.5 330 5.91 .588 3.48 1260 4380

53 43.9 1233.0 48.2 23.5 320 5.74 .799 4.59 1130 5190

44 52.5 1285.5 53.8 22.5 320 5.74 .695 3.99 1210 4830

41 55.1 1340.6 58.8 22.5 330 5.91 .656 3.88 1320 5120

31 62.6 1403.2 60.8 22.0 330 5.91 .515 3.04 1340 4070

36 59.0 1462.2 55.4 22.5 320 5.74 .588 3.38 1250 4220

19 51.8 1514.0 55.4 12.0 340 6.09 .326 1.99 665 1320 (3

REW 59.0 1573.0 29.5 0 0

FP 1596.0 REW 

1545.0 1544.7 42,039 157,369

x1.022 x1.022 W

Width/Area Adjustment Coefficient: 1579 1545=1.022 A

43,000 160,831

x .91 Ve

146,000

Figure 2. Discharge measurement inside notes for manual type of moving boat measurement.
for the determination of Lb values at the beginning and 

end of each run. The first Lb value, corresponding to the 

first measured angle, is an actual field measurement of 

the distance from the edge of water to the float marker. 

This measurement is a field data value, and should not 

be changed. The second Lb value, corresponding to the 

second measured angle, always is entered as one-half of 

the table value. The next-to-last Lb value is entered on 

the basis of the proportion shown in the remarks 

column of the field notes. The last Lb value is an actual 

field measurement, and should not be changed. All Lb

values between the two points at each end of the measurement are determined directly from the look-up 

table. The total boat travel distance should be computed 

as the sum of all subsection distances.

• Distance from initial point—These distances mostly 

are computed values, and should begin at the edge of 

water on one side of the stream and end at the edge of 

water at the other side of the stream. The water edges 

usually are designated LEW (left edge of water) and 

REW (right edge of water). All distances are referenced 

to an initial point (IP), which usually is designated as 

having a distance of zero (0). A final point (FP) also is 

included in the notes. The distance for the edge of water 

at the beginning of the measurement is based on the 

actual field measurement of the distance from the IP to 

the edge of water. All other distances are computed by 

adding Lb to the preceding distance.

• Width—These are incremental widths for each subsection, and are computed just as they are in a standard current meter measurement, based on one-half the distance 

from the preceding vertical to one-half the distance to 

the next vertical. The total width should be computed as 

the sum of all subsection widths.

• Vector velocity, Vv—These are instantaneous vector 

velocities, and are determined from the rating table (or 

equation) for the current meter, and correspond to the 

pulses per second recorded for each vertical.

• Sine of angle, Sine α—These values are the sine function values corresponding to the angle, α, for each vertical.

justed discharge also should be computed as th

all unadjusted subsection discharges.

A number of individual data items and computati

included in the inside note sheet, and should be entere

electronic processing system and/or checked for comp

accuracy. These items and computations are listed bel

grouped as data items and computations.

Data items:

• Run number—This number indicates the run n

for a series of runs.

• Control panel range number—This number i

determine the correct look-up table for determ

• Measured width—This is the total measured w

the stream, water's edge to water's edge.

• Velocity adjustment coefficient, kv—This is the 

velocity coefficient used to adjust the total disc

the effect of velocity measurements taken nea

stream surface.

• Distance from IP to beginning edge of water—

a measured distance.

• Distance from ending edge of water to FP—T

measured distance.

• Distance from beginning edge of water to init

float—This is a measured distance.

• Distance from final float to ending edge of wate

is a measured distance.

Computations:

• Width/area adjustment coefficient, kb—This c

cient is a computed value equal to the ratio of 

sured stream width to the computed stream w

• Total adjusted area—The total adjusted area 

puted by multiplying the total unadjusted area t

coefficient, kb.

• Total adjusted discharge—The total adjusted 

charge is computed by multiplying the total un

discharge times the coefficient, kb, and times t

ficient, kv.
meter measurement, should be used (see table 4).

6.1.5.4 Acoustic Doppler Current Profiler (ADCP) Measurements

The ADCP is used to define the complete (or nearly complete) velocity profile in a stream vertical. This velocity profile 

provides a much more accurate measure of the mean stream 

velocity than other techniques where only one or two measuring 

points are used, and sometimes adjusted by velocity coefficients. The ADCP can be incorporated into the moving boat 

method of measurement, providing a fast, accurate type of discharge measurement for wide and deep streams. This type of 

measurement is fully computerized, with all data collected and 

computed automatically.

Data and information from the ADCP measurement should 

be transferred to the electronic processing system through an 

interface. These data and information become the original, 

archivable record. Summary information for the measurement 

is much the same as for a regular discharge measurement and 

can be entered using the same entry form (table 4).

6.1.5.5 Indirect Measurements

Indirect discharge measurements include slope area, contracted opening, critical depth, culvert, step backwater, and 

flow over dams and embankments. These types of measurements are almost always made after a flood event, rather than at 

the time of the flood event. Data collection, recording of field 

notes, and computation procedures are appreciably different 

than standard measurements made during a flood event. For 

most indirect measurements, special computer programs are 

used for the computations and detailed reports are prepared. 

Entry of information from indirect measurements to the electronic processing system should include only the summary 

information. The same entry form can be used as for a standard 

discharge measurement (table 4).

6.1.5.6 Portable Weir and Flume Measurements

Measurements of low discharge can be made using a portable weir or flume. Various types of weirs and flumes are available for these measurements and usually are rated in the laboratory so that coefficients and discharge ratings are defined for 

each. Field setup and measuring methods are described by 

Rantz and others (1982), and are relatively simple and easy to 

and the determined discharge. Some hydrographers 

information on the front sheet of the measurement, 

in the inside body. Regardless of where these notes 

recorded, the electronic processing system should p

form for entering the basic data and computations, 

check the computations. The data and information r

as follows.

• Head measurements—These are the indivi

vations of head. The recommended number 

tions is about seven, one observation every 

for a period of 3 minutes. However, this nu

vary and in some cases only one observatio

recorded. The electronic processing system 

allow for at least 10 entries.

• Average head, h—This is an unweighted av

individual head observations. The electronic 

system should calculate the average head, h

pare it to the entered value. If the two value

ent, a message to this effect should be given 

The user should be allowed to select the av

value for use in computing discharge.

• Discharge, Q—The discharge should be ca

either from a rating table or from an equati

tables and/or equations for standard weirs a

should be included in the electronic process

However, if they are not directly available, 

should be allowed to enter one.

Entry of front-sheet information for weir and f

surements greatly is abbreviated from that of a stan

charge measurement and is described in table 4.

6.1.5.7 Tracer-Dilution Measurements

Tracer-dilution discharge measurements are h

cialized techniques that utilize one of a number of di

ers, different types of measurement equipment, and 

measurement methods. Data collection, recording, 

tion of measurement information varies depending 

method and tracer used. Details of each type of trac

measurement are described by Rantz and others (19

Although the methods are well standardized, it is n

mended that complete details of tracer-dilution mea

be entered to the electronic processing system. Sum
measurement. The discharge, in cubic feet per second, is com

puted by dividing the total volume (sum of the volume measurements from each repetitive run), in cubic feet, by the total time 

of diversion (sum of the time measurements from each repetitive run), in seconds.

Data entry from the inside field notes includes the following:

• Total container volume, in cubic feet.

• Starting volume, in cubic feet, for each repetitive 

run—This value should be equal to or greater than zero, 

but less than the total container volume.

• Ending volume, in cubic feet, for each repetitive 

run—This value should be greater than the starting volume, and equal to or less than the total container volume.

• Flow volume, in cubic feet, for each repetitive 

run—This is the difference between the ending volume 

and the starting volume, and must be equal to or less 

than the total container volume.

• Fill time, in seconds, for each repetitive run.

• Total volume, in cubic feet—This is a summation of the 

individual flow volumes of each repetitive run.

• Total time, in seconds—This is a summation of the 

individual fill times of each repetitive run.

• Discharge, in cubic feet per second—This is the total 

volume divided by the total time.

The electronic processing system should make the checks 

and computations indicated above, and report any discrepancies.

The procedure described above is used where the total 

flow can be easily diverted into a container. In some cases, such 

at a broad-crested weir or dam the flow may be too shallow to 

measure using conventional methods, but volumetric measurements may be applicable to small segments (samples) of the 

flow. This is the volumetric-incremental sampling method. In 

this method, volumetric flow measurements are made as 

described in the preceding paragraphs at 5-10 subsections along 

the weir or dam. The flow rate of each sample is increased by 

the ratio of the subsection width to the sampled width to obtain 

a flow rate for each subsection. The total flow of the stream is 

the summation of the discharge rates of each subsection. The 

they generally cannot be checked or verified, and the p

notes are considered the original archivable record. A s

of the measurement can be entered using the standard d

measurement entry form (see table 4), but abbreviated 

erably to accommodate only the information pertinent 

estimate.

6.1.6 Rounding and Significant Figures

All data (actual field measurements) for discharg

surements should be entered to the electronic processin

with the same precision and significant figures as reco

the field notes. Table look-up values and calculated va

should be rounded to standard significant figures (tabl

unless specified otherwise by the user. Exceptions to t

dard significant figures are required for calculations of 

section values of width, area, and discharge in the insi

of the field notes, as follows.

• Subsection width—The width of each subsect

should be used and displayed as an unrounded 

• Subsection area—Each subsection area shoul

rounded and displayed with one additional sig

figure from that of the expected total area. For 

if the total area is expected to be between 10.0 

ft2, the individual subsection areas should be r

and displayed to hundredths of a square foot.

• Subsection discharge—Each subsection disch

should be rounded and displayed with one add

significant figure over that of the expected tot

charge, similar to that described above for sub

area. For instance, if the total discharge is exp

be between 100 and 999, then each subsection 

charge should be rounded and displayed to the 

0.1 ft3/s.

All summary information for discharge measurem

should be rounded and displayed with significant figu

conform to those listed in table 2, unless specified othe

the user.
(9-207)

Station identification number X X

Station name X X

Measurement sequence number X X

Date of measurement X X

Mean time of measurement X X

Time zone X X

Party X X

Mean gage height, inside gage X X

Mean gage height, outside gage X

Gage-height change X X

Gage-height change time X X

Stream width X X

Stream area X X

Mean velocity X X

Number of sections X X

Measured discharge X X

Rating number X X

Shift adjustment X X

Percent difference X X

Adjusted discharge X X

Adjustment method X X

Number of channels measured X

Measurement type X

Measurement location X

Observation method X X

Accuracy rating (field assigned) X X

Computed accuracy X X
6.2 Gage Datum Analysis

The gages at streamgaging stations are referenced to a permanent datum (zero level) that must be maintained as accurately as possible throughout the lifetime of the station. In order 

to maintain this accuracy, leveling is performed periodically to 

check the gages and reference marks for vertical movement, so 

that if appreciable movement is detected, corrections can be 

made. Generally, leveling at gaging stations is performed once 

every 2 to 4 years, but the time frame varies according to gage 

stability conditions and other factors. For complete details of 

leveling procedures for gaging stations, see Kennedy (1990).

Complete gage levels are recorded on paper field notes that 

include all turning point elevations, instrument setup heights, 

elevations of gage reference marks, and other miscellaneous 

gage features. These notes also may include various adjustments required to account for instrument error and closure 

error. In some instances, the field notes may include more than 

one level circuit, and a summary field note sheet is included that 

shows average elevations for benchmarks, reference marks, and 

other gage features. These paper field notes are the original leveling notes, and are archived as part of the permanent record. It 

is not required that the complete field notes be entered to the 

electronic processing system.

The electronic processing system should provide 

entry of a summary of the field notes for gage- datum l

Data and information that should be entered to the ele

processing system from leveling notes are listed in tab

addition, established elevations should be entered for 

benchmark, reference mark, and other gage feature for 

ence and comparison purposes. For each set of level n

electronic processing system should perform datum er

parisons as described in section 6.2.2.

6.2.1 Established Elevations

All benchmarks, reference marks, reference poin

features, and other permanent points that may be refer

the gage datum should be included in a gage datum re

list. Each mark, feature, and point should be given a sh

abbreviated name that conforms with the usual surveyi

nology, such as BM1 (Benchmark No. 1), BM2 (Benc

No. 2), RM1 (Reference Mark No. 1), WWCB (Wire 

Check Bar), IGRP (Inside Staff Gage Reference Point

OGRP (Outside Staff Gage Reference Point). For each 

station, the list will be different and the user should be 

to establish the initial list and add new points at any ti

Maximum stage indicator X

Minimum stage indicator X

Air temperature (degrees Celsius) X

Water temperature (degrees Celsius) X X

Base flow (Yes or No) X

Gage height of zero flow X X

Gage height of zero flow accuracy X X

Mean index velocity X

Mean auxiliary gage height X

Remarks X X
times found that the elevation of a point or feature may have 

changed so that the new elevation is considered reasonably permanent. The user should be allowed to make a change to the 

established elevation, but the electronic processing system 

should maintain a history of all elevation changes, along with 

dates of change, and names of persons making the change. An 

optional "remarks" entry should be allowed for the purpose of 

describing the reason for making an established elevation 

change. Established elevations should be maintained as permanent "known,” or "given" elevations, and changes should not be 

made arbitrarily. These elevations become the basis for datum 

error comparisons, as described in section 6.2.2, and are the 

basis for making datum corrections to gage readings.

6.2.2 Datum Error Comparisons

One of the permanent benchmarks or reference marks at a 

gaging station usually is defined and referred to as the base

benchmark. This is the benchmark at the station considered to 

be the most stable of the various marks that may be used for leveling purposes. Leveling at the station usually will start at this 

benchmark, using it as the base, and all other elevations are 

computed from that base. The base benchmark should be maintained as a permanent base so long as it remains stable.

For each set of levels, comparisons should be made 

between established elevations and elevations determined by 

leveling, for each benchmark, reference mark, reference point, 

and gage feature. The first, and primary, comparison should use 

the base benchmark as the starting point for all computations.

6.2.2.1 Base Benchmark Comparisons

The first, and sometimes the only, comparison between 

established elevations and elevations determined by leveling is 

made using the established base benchmark as the starting point 

to compute the elevations of other benchmarks, reference 

marks, reference points, and gage features. This method of 

comparison almost always conforms to the way the levels were 

run, and the way level data are entered to the electronic processing system. The electronic processing system should compute 

the difference between the established elevation and the elevation found by leveling, for each benchmark, reference mark, 

reference point, and gage feature. These differences should be 

6.2.2.2 Alternate Benchmark Comparisons

Instances may result where comparative eleva

alternate benchmarks as a base, are desired, even th

designated base benchmark is still being used. The 

be allowed to designate an alternate benchmark as 

the electronic processing system should compute an

other elevations on this basis. These elevations sho

sidered temporary, or work-sheet computations for c

analysis only. If such comparisons reveal that a diff

mark should be designated as a new base, then the 

be allowed to make the change, and the elevations 

using this new base should be retained.

Recomputation of elevations cannot be made 

original rod readings and instrument heights becau

not entered to the electronic processing system. Th

recomputation must be based on relative difference

the entered elevations of each benchmark, referenc

other feature.

6.2.2.3 Rounding and Significant Figures

All elevations of benchmarks, reference mark

features usually are shown to thousandths of a foot 

notes and level-note front sheets. This degree of pre

not be justified for some gage features, gage height

flow, and ground elevations. It is recommended tha

sion and significant figures conform to the common

values shown in tables 4 and 5; however, the precis

nificant figures are optional and the electronic proc

system should retain the precision and significant f

entered by the user.

6.2.2.4 Gage Datum Summary

A historical summary of benchmarks, referenc

and gage features should be maintained with the ele

cessing system. This summary should include the n

abbreviation of each feature, a designation for the b

mark, the original established elevations for all benc

features, the elevations determined by leveling for 

levels, the difference between the established eleva

elevation determined by leveling, and remarks for e

The summary should be updated each time a new s

is entered, showing the date of leveling, and the na
99111100 Example creek near Timbucktoo, SC

(Station ID Number) (Station name)

[B=Base benchmark; (xxx)=Difference from gage reading; R=Gage reset; BM=Benchmark; RM=Reference mark; RP=Reference point; OG=Outsid

IG=Inside gage; WWT=Wire-weight gage; Elev.=Elevation; —=No data]

Date of levels 10-12-42 06-18-44 03-21-47

Party DJS, VBS VBS, MBS JDC, DJS

Benchmarks Original Elev. Elevation Elevation Elevation Elevation Elevation El

 BM1 12.235 12.240 12.242

 RM1 2.468 (B) 2.468 (B) 2.468 (B)

 RM2 2.992 2.990 2.994

 RP1 15.334 15.333 15.331

 USC&GS 275 25.451 25.448 25.449

 Other...

Gage Features

 Instrument shelf 16.43 16.44 16.43

 Bottom of well 0.34 0.37 0.33

 Lower door sill 5.89 5.89 5.88

 Lower intake 0.75 0.76 0.76

 Upper intake 1.79 1.79 1.80

 Point of zero flow 0.23 0.30 0.20

 Orifice —

Gages

 OG 3.3 - 6.8 4.500 (-0.002) 4.501 (+.001) 4.530(+.030)

4.504(+.004)R

 IG 0.0 - 6.8 3.480 (+0.004) 3.492 (+.012) 3.478 (-.002)

 WWT check bar 19.673 19.660 19.662

 Elec. tape index 16.532 16.532 16.530

 Steel tape RP 16.687 16.691 16.688

 Other...

Remarks Gage establ. OG reset

History and summary of gaging station levels

measurements, either from the top of the rod/stick or the bottom 

of the rod/stick to the line of cork dust, can be used to compute 

the peak stage. Sometimes, more than one peak will occur 

Figure 3. Example of a streamflow station datum summary.
should be alerted so that changes can be made, if necessary.

6.3.2 Logic and Consistency Comparisons

The electronic processing system should make the following comparisons to confirm that the data and information 

entered for each crest mark are consistent and logical for the 

given gage setup.

• Date comparison—The date estimated for the crest 

mark normally should fall between the date of the previous and current gage visit. The electronic processing 

system should make this comparison, and if the estimated date does not fall between the two visits, the user 

should be alerted and given the opportunity to make a 

change. It is not mandatory that the estimated date fall 

between the two visits. Circumstances may result to 

cause the apparent discrepancy.

• Maximum gage-height comparison—The computed 

crest-gage height should be compared to the maximum 

possible gage height for the crest-stage gage. If the 

computed gage height is greater, the user should be 

alerted and given the opportunity to make necessary 

changes.

• Minimum gage-height comparison—The computed 

crest-gage height should be compared to the minimum 

possible gage height for the crest-stage gage. If the 

computed gage height is less than the minimum, the 

user should be alerted and given the opportunity to 

make necessary changes.

• Crest sequence comparisons—The cork dust marks 

that are deposited on the rod/stick are fairly fragile, and 

can be erased by subsequent peaks that exceed a mark. 

When two or more marks are entered from one set of 

field notes, the electronic processing system should 

make a sequence comparison. The highest crest-gage 

height should have the earliest estimated date of occurrence, the second highest crest-gage height should have 

an estimated date that is later than the highest crestgage height, and the third highest crest-gage height 

should be later than the previous one. The lowest crestgage height in the sequence should have the latest estimated date. Although the previous description is the 

, p

marks should be retained as entered to the electronic 

system.

6.3.4 Summary of Crest-Stage Gage Measur

A summary of all crest-stage gage measureme

be listed in chronological order, and grouped by wat

summary listing should include all items shown in 

6.4 Cross Sections

Cross-section data have various uses, but are p

intended as an aid in rating-curve analysis. One or 

sections may be entered with specific identifying in

that make them unique to a particular gage site. Th

information entered for each cross section are listed 

Some of the checking and computations that should 

formed with the electronic processing system are li

tions 6.4.1 through 6.4.3.

6.4.1 Logic and Consistency Checking

Cross-section entry consists mainly of transve

ing along the line of the cross section, and ground e

each station. Station distances are measured from a

point located on the left bank of the stream. The ele

cessing system should check that each station dista

to or greater than the preceding station distance. Th

processing system also should insure that ground ele

provided for each station. Negative values of statio

ground elevations are acceptable.

6.4.2 Graphical Review

The user should be required to view a graphic

each cross section to review and edit for inconsiste

data-entry errors. The plot should be drawn to a sca

horizontal to 1 vertical, with an option to change th

necessary. The plot should include all ground point

subdivision boundaries, if entered, horizontal rough

aries, if entered, and Manning roughness coefficien

entered. A typical cross-section plot is shown in fig
10.

11.

12.

13.

14.

15.

Elevation of creststage gage reference point (top of rod/stick, bottom pin, and others)

Measured distance from crest-stage gage reference point to high watermark

Highwater mark elevation (calculated from items 9 and 10)

Highwater mark elevation, determined from outside highwater marks

Estimated date of highwater mark

Remarks

+

+

+

+ +

+

+

+

+

+ ++

+

+

Left bank Right bank

n=Manning roughness coefficient

n=0.03

n=0.045 n=0.04

n=prorated n=prorated

n=0.06 n=0.06

Horizontal distance (not to scale)

Vertical distance (not to scale)

Figure 4. Typical stream cross-section plot.
6.4.4 Rounding and Significant Figures

All data entered for cross sections should conform to the 

precision given in table 1, and all computed information for 

cross sections should be rounded to the precision given in table 

2. The user should have the option to change the standard precision, as required, and numbers entered with a non-standard 

precision should be retained as entered.

7. Rating Curves

Rating curves are relations between dependent and independent variables. For instance, a rating curve expressing the 

mathematical or graphical relation between stage (independent 

variable) and discharge (dependent variable) is referred to as a 

stage-discharge relation. The processing of most surface-water 

records requires the application of one or more rating curves. 

This section of this report will describe the various types of 

rating curves, the methods of rating curve development, the 

methods of rating curve entry to the electronic processing system, and other related aspects of rating curves as they apply to 

the electronic processing system.

Rating curves are an integral part of the comp

most streamflow records, and become a part of the 

records for each station. However, the electronic pr

system also should allow the entry, development, an

rating curves independent of computing streamflow 

specific gaging stations. That is, the user should be 

use the rating curve aspects of the electronic proces

and choose any one of the rating types listed below f

editing, developing, refining, and experimenting w

7.1 Types of Rating Curves

A number of rating curve types are available f

cessing of surface-water records. Following is a bri

tion of each type.

• Stage-discharge relation—This type of rat

most common rating used for the processin

water records. It is a relation between wate

gage height and the rate of flow of the strea

the descriptive information about rating cu

follow in this report will be discussed in ter

discharge relations; however, many of the b

ples, entry procedures, plotting procedures

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

Station identification number

Station name

Date of cross-section survey

Party

Cross-section identification number (a sequential number unique for each cross section)

Location of cross section (longitudinal stationing, in feet, relative to the gage)

Type of control that cross section represents, if applicable (for example, section control or channel control)

Gage height, incremented according to user specifications (for example, 0.5 ft intervals, 1.0 ft intervals, 2.0 ft intervals)

Number of sub-areas

Total cross-section top width

Total cross-section area

Total cross-section conveyance

Wetted perimeter

Hydraulic radius

Critical discharge

Maximum depth (for natural sections), or head (for weirs and flumes).

Mean depth

Remarks

NOTE—For each cross section, items 8–12 should be arranged in tabular format, beginning with the lowest specified gage height and incremented at the specified interval to the highest specified gage height.
• Velocity-index and mean velocity relation—This is a 

relation between an index velocity (electromagnetic, 

acoustic, and others) and the mean velocity for a standard cross section of the stream. This type of rating 

commonly is used for velocity-index methods of computing discharge. The mean velocity usually increases 

as the index velocity increases, but sometimes may 

decrease. Negative values of either parameter, the 

velocity index or the mean velocity, are permitted; most 

velocity ratings of this type will extend into the negative range. For this reason, logarithmic ratings are 

seldom used for this type of rating.

• Stage and velocity factor relation—This is a relation 

between gage height and an adjustment factor used in 

the velocity-index method of computing discharge. The 

adjustment factor almost always increase as stage 

increases, but in some instances it will decrease. It 

always should be a positive value.

• Stage-fall relation—This is a relation between gage 

height and the water-surface fall between the base gage 

and an auxiliary gage. This relation is used in the slope 

method of computing discharge. Fall may increase or 

decrease as stage increases, but it always should be a 

positive value. Negative values of fall should not be 

allowed.

• Fall ratio and discharge ratio relation—This is a relation between the fall ratio, Fm/Fr

, and discharge ratio, 

Qm/Qr, as used in the slope method of computing dis

relation between the water-surface elevation o

voir and the contents of the reservoir. The rese

contents always should increase as elevation in

and always should be a positive value. The mi

allowable value for reservoir contents is zero. 

rating should allow for large numbers, with re

contents sometimes exceeding 4,000,000 acre

elevation sometimes exceeding 6,000 ft above 

Elevation usually is shown to a precision of hu

of a foot (for example, 2,345.67).

Gaging stations at control structures such as dam

a number of different rating curves and rating equation

spillways, gates, turbines, and other flow conveyances

ratings specifically are designed for each individual st

and are a part of the structure computation program, a

described by Collins (1977).

The BRANCH model method for computation of 

flow records does not require the use of individual rat

curves. That model has internal calibration procedures 

described by Schaffrannek and others (1981).

All ratings may be defined as logarithmic plots, l

plots, or equations. A summary of rating curve charac

limitations, and requirements is given in table 13. All 

should be tested with the requirements and limitations 

table 13.
7.2 Rating Selection Default Procedure

When a user is working on a specific gaging station with a 

specific computation method defined, and where ratings may, 

or may not, already be defined, the electronic processing system 

automatically should default to the rating type applicable to the 

defined computation method. For instance, if the computation 

method is stage-discharge, then the electronic processing 

system should default to a stage-discharge rating, or if a slope 

computation method is required, then the electronic processing 

system should default to the three rating types applicable to 

slope stations (stage-discharge, stage-fall, and fall ratio-discharge ratio ratings). The electronic processing system should 

not allow a rating type to be entered for a gaging station other 

than those applicable to the defined computation method for 

that station.

Stage-discharge ratings are the most commonly used ratings, and should, therefore, be the default rating of choice when 

the rating procedure is used independently; that is, not in conjunction with a specific gaging station.

7.3 Entry of Rating Curve Information

Rating curve information required for defining 

between the independent and dependent variables, s

heights and discharges, can be entered into the elec

cessing system using various methods, including ta

tion, and graphical methods. Tabular entry is the us

of descriptor data pairs, each representing a specific 

the rating curve. Equation entry is the use of a math

expression to define the rating curve algebraically. 

entry is a method whereby a series of points are ente

on a rating curve plot displayed on the computer m

the electronic processing system automatically eva

points, connects the points, and displays the rating 

Tabular entry and graphical entry are similar i

utilize user-defined descriptor points. The primary d

that tabular entry is based on descriptor points that 

picked from a paper rating curve plot, whereas grap

is based on descriptor points defined on the comput

thus, negating the need for a paper plot. An individ

curve can be entered by using only one or the other o

entry modes, or in combination. However, the elec

cessing system should not allow either of these entr

area

Area Abscissa Zero No limit No

Index velocity 

and mean 

velocity

Index velocity Ordinate No limit No limit Yes Ye

Mean velocity Abscissa No limit No limit Yes

Stage and 

velocity

factor

Gage height Ordinate No limit No limit Yes Ye

Velocity factor Abscissa Zero No limit No

Slope1 Stage—fall Gage height Ordinate No limit No limit Yes Ye

Water-surface fall Abscissa Zero No limit No

Fall ratio and

Q ratio

Fall ratio Abscissa Zero 1.5 No No

Discharge ratio Ordinate Zero 1.5 No

Change in stage1 Stage—1/USc Gage height Ordinate No limit No limit Yes Ye

Factor, 1/USc Abscissa Zero No limit No

Reservoir Elevation—

contents

GHt or elevation Ordinate No limit No limit Yes No

Reservoir contents Abscissa Zero No limit No

1

Requires a stage-discharge rating in addition to rating types shown. 
pp

Point pairs always should be entered in ascending order of the 

independent variable, starting with the lowest point on the 

rating curve. If the user incorrectly enters a point pair in which 

the independent variable is not ascending, the electronic processing system immediately should issue a warning message to 

alert the user that an entry error was made. This checking 

method also should be used for the dependent variable for those 

ratings where the dependent variable is not allowed to decrease. 

A similar warning message also should be given if negative 

values are entered for ratings where they are not allowed.

Rating curves that are entered as linear scale ratings will 

require only the table of point pairs. No other descriptive information is needed for either plotting or expanding (interpolating) 

a linear scale rating.

Rating curves entered as logarithmic scale ratings will 

require entry of scale offset information, in addition to the table 

of point pairs. A scale offset is a value that is subtracted from 

the independent variable before interpolating between point 

pairs of the rating. It is important that the scale offset entered at 

this point is the same as the one used for the plotted rating curve. 

Because there is no way to verify that the offset used for a paper 

plot and the entered offset are the same, the electronic processing system should include a reminder at the point of offset entry, 

that states, “Offsets entered here must be identical to offsets 

used for the rating curve plot to provide exact duplication in the 

rating table.” If the user does not enter a scale offset for a logarithmic rating, the electronic processing system should not 

accept the rating, and should prompt the user that an offset is 

required.

The electronic processing system should allow one, two, 

or three scale offset values for each logarithmic rating curve, 

with each respective offset applicable to a designated range, or 

segment, of the rating. The offsets should be entered starting 

with the lowest rating curve segment and progressing upward, 

with a defined breakpoint between successive offsets. The 

breakpoint is the value (usually gage height) of the independent 

variable above which the succeeding offset should be used. The 

following combinations of offsets and breakpoints are allowable.

• One offset, no breakpoints—In this case, a single offset 

is used throughout the range of the rating.

• Two offsets, one breakpoint—In this case, the first 

offset is used for all values of the independent variable 

gp

A point pair entry in the table of point pairs is req

each breakpoint of the rating. If the user omits the poi

corresponding to a breakpoint, the electronic processin

should issue a warning message and should not accept t

unless this requirement is met. The point pair at each br

is used as the ending point for the rating-curve segmen

the breakpoint, and the beginning point for the rating-c

ment above the breakpoint This process insures contin

the rating-curve segments. Scale offsets are described 

detail in section 7.7.6.2.

7.3.2 Equation Entry

Some ratings may be easily expressed in equation 

and if so, they may be entered to the electronic proces

system as a mathematical expression. Such ratings usu

of simple form, consisting of a smooth curve or straig

with no unusual shapes or sharp bends. For all equation 

a basic format as given in equation 21 should be used.

where

Y = dependent variable (usually discharge),

X = independent variable (usually gage height),

a = equation constant (default value is zero),

b = multiplier (default value is 1),

e = scale offset (default value is zero),

c = exponent (default is 1).

Equation 21 can be used for rating curves interpo

either linearly or logarithmically. Other types of equatio

as parabolic equations, are not recommended for surfa

rating curves.

Upper and lower equation limits also should be req

part of the input for equation ratings. These limits sho

default, be in terms of the independent variable; howe

user should have the option to specify the limits in term

dependent variable. When extrapolation of equation r

needed, and can be justified, a modification of the app

limits should be allowed. The electronic processing sy

automatically should not extrapolate the equation beyo

approved specified limits.

Y a bX e ( ) – c = +
tion entry, and before application of the equations.

When multiple equations are used to define a rating curve, 

a lower limit should be specified for the lower equation, and an 

upper limit should be specified for the upper equation. The 

same rules and guidelines apply to these limits as stated previously for single equation limits.

7.3.3 Graphical Entry

Graphical input of rating curves is presently the most automated and preferred method of entering a rating curve to the 

electronic processing system. Historically, rating curves have 

been drawn manually on paper work sheets, and descriptor 

points visually are read from the plot. The electronic processing 

system should provide a method whereby the user can automatically plot, from the electronic processing system files, selected 

discharge measurements and other rating curve information on 

the computer monitor, and then fit a rating curve to the plotted 

points directly on the monitor. The fitting process will be done 

by specifying a series of descriptor points, either directly on the 

computer monitor or in a table displayed on the monitor. After 

the user is satisfied with the accuracy and smoothness of the 

rating curve, the electronic processing system should automatically transform the plotted rating curve into a rating table.

7.4 Rating Tables

The rating table is primarily for the purpose of displaying 

values of the dependent variable for the complete range of the 

independent variable. Rating tables should be generated with 

the electronic processing system for all rating curves. The tables 

are populated by interpolating values of the dependent variable 

for the complete range of the independent variable, at intervals 

equal to the stated precision of the independent variable or other 

user-defined interval. For instance, if the independent variable 

is gage height, and its stated precision is hundredths of a foot, 

then values of the dependent variable (for example, discharge) 

would be computed for every hundredth of a foot of gage height 

for the full range of gage height defined by the limits of the rating. The interpolation methods and other requirements of producing rating tables are described in sections 7.4.1 through 

7.4.5.

defined with two or three scale offsets, then each o

should be applied within the range defined by the r

breakpoints.

It is very important that the interpolation proc

same offset, or offsets, that are used for the develop

rating curve plot, so that the resulting rating table p

duplicates the plotted curve. If the rating is plotted 

tronic processing system monitor, the rating curve 

cally is converted to a rating table, and the offset w

ically be the same for both the plotted curve and th

table. If the rating curve is entered as a table of des

points, then the interpolation method must use the s

or offsets, entered with the descriptor points. The us

sible for insuring that the offsets are identical.

Note that the subtraction of the scale offset fro

pendent variable is made only for the purpose of tran

and interpolation. The subtraction should not alter 

values of the independent variable that are displaye

rating table or plotted on rating curve plots.

The dependent variable (for example, discharg

rating curves has a minimum value of zero, which th

cannot be transformed to a logarithm. A simple line

lation between the zero point and the next larger inp

the dependent variable should be used for logarithm

beginning with zero. To avoid appreciable distortio

end of the rating, it is recommended that the input v

dependent variable that follows the zero input value 

or less than 0.1. The electronic processing system s

a warning message to the user if 0.1 is exceeded, and 

opportunity to make changes.

The independent variable (for example, gage h

sometimes be zero or negative at the low end of a r

This value is permissible only when subtraction of 

offset from the independent variable results in a po

ber. See section 7.7.6.2.1 for additional details.

Rating curves defined by one or more equatio

should be transformed into rating tables. This is a s

method of computing the dependent variable for th

range of each equation, as defined by the breakpoin

limits.
7.4.3 Rating Table Smoothness Analysis

One method of analyzing the smoothness of a rating curve 

and/or rating table can be done by studying the differences 

between successive values of the dependent variable. To make 

this task easy for the user, the rating table should display the 

computed differences (traditionally referred to as first differences) of the dependent variable between every tenth value of 

the independent variable displayed in the rating table. For 

instance, if gage height is incremented every 0.01 ft in the rating 

table, then the difference between discharges corresponding to 

gage heights at 0.1 ft intervals should be computed and displayed.

7.4.4 Other Rating Table Information

The rating table should include descriptive information 

that identifies the gaging station, type of rating, period of use, 

and other items that are unique for that rating. At a minimum, 

the following items should be included in the table.

• Station number—The downstream order number that 

identifies the station.

• Station name—The official name of the station.

• Rating table number—The unique number assigned to 

identify the rating table.

• Processing information—The time and date the rating 

was entered, and name of the person making the entry. 

If the rating is edited (minor changes only) or extrapolated and the rating number is not changed, then additional times, dates, and names should be shown that 

identify when these changes were made. Information 

explaining a change, or extrapolation, can be given in 

the narrative rating description (see descriptions 

below).

• Type of rating—The rating type, such as stage-discharge, stage-area, and others. This rating type also will 

identify the input parameter (independent variable) and 

the output parameter (dependent variable). The units of 

measurement (for example, feet, cubic feet per second, 

square foot, and so forth) should be shown for the independent and dependent variables.

• Period of use—The date, time, and time zone t

tifies the beginning and ending of the period of 

which the rating is to be used. If the rating is sti

then the ending date, time, and time zone shou

open.

• Rating description (optional)—A narrative de

of the rating definition. This is an optional ent

which point the user can describe how the rati

defined, the number of measurements used, str

weak points of the rating, how the rating was 

lated (if done), use of theoretical methods in de

the rating, and any other information that migh

the rating.

• Significant figures—The use, or non-use, of e

precision should be identified.

• Input values—If the rating was entered using d

points, each of the entered points should be ide

the body of the table. This traditionally has be

by flagging each entered point with an asterisk 

An example of an expanded rating table for a log

stage-discharge rating curve is shown in figure 5. This 

rating table illustrates the header information and a typ

arrangement of table information.

7.5 Rating Curve Numbers

Every rating curve for a specific gaging station sh

identified with a number. The preferred numbering sy

should be a simple, consecutive number, with the earl

rating as number 1, the next rating number 2, and so f

Although not recommended, alpha-numeric numbers s

permitted, as well as decimal number combinations suc

or 4.2b. Gaging stations with long periods of record m

old ratings that either are identified only by dates of us

secutive numbers. These older ratings may no longer b

and in many cases may not be entered to the electronic 

ing system. It is recommended, however, that the old n

be retained whenever possible, and that newer ratings 

entered to the electronic processing system be number

same sequence. Changing original rating numbers, brea

numbering sequence, or using duplicate numbers for d

ratings at a gaging station, should be avoided, if possib
(FEET)

.00 .01 .02 .03 .04 .05 .06 .07 .08 .09

3.00

3.10

3.20

3.30

3.40

2.000*

2.998

4.337

6.346

8.346

2.086

3.115

4.493

6.294

8.602

2.175

3.236

4.653

6.501

8.864

2.267

3.360

4.817

6.713

9.132

2.362

3.489

4.985

6.930

9.406

2.460

3.620

5.158

7.152

9.687

2.561

3.756

5.336

7.379

9.974

2.666

3.895

5.518

7.613

10.27

2.773

4.039

5.705

7.851

10.57

2.884

4.186

5.896

8.096

10.87

3.50

3.60

3.70

3.80

3.90

11.19

14.71

19.03

24.26

30.52

11.51

15.11

19.51

24.84

31.21

11.83

15.51

20.00

25.43

31.91

12.17

15.92

20.50

26.02

32.62

12.51

16.34

21.01

26.63

33.34

12.86

16.77

21.53

27.25

34.08

13.21

17.20

22.05

27.88

34.83

13.58

17.65

22.59

28.53

35.59

13.95

18.10

23.14

29.18

36.36

14.33

18.56

23.69

29.84

37.15

4.00

4.10

4.20

4.30

4.40

37.95

46.68

56.88

68.69

82.30

38.76

47.63

57.98

69.97

83.76

39.58

48.60

59.10

71.26

85.25

40.42

49.58

60.24

72.58

86.75

41.28

50.58

61.40

73.91

88.28

42.14

51.59

62.57

75.26

89.83

43.02

52.61

63.76

76.63

91.39

43.92

53.66

64.97

78.02

92.98

44.82

54.71

66.19

79.42

94.59

45.75

55.79

67.43

80.85

96.22

4.50

4.60

4.70

7.80

4.90

97.87

115.6

135.7

158.4

183.8

99.54

117.5

137.8

160.8

186.5

101.2

119.4

140.0

163.2

189.2

103.0

121.4

142.2

165.7

192.0

104.7

123.3

144.4

168.2

194.8

106.5

125.3

146.7

170.7

197.6

108.2

127.4

149.0

173.3

200.5

110.0

129.4

151.3

175.9

203.4

111.9

131.5

153.6

178.5

206.3

113.7

133.6

156.0

181.1

209.3

5.00

5.10

5.20

5.30

5.40

212.3

244.0

279.2

318.1

361.1

215.3

247.3

282.9

322.2

365.7

218.3

250.7

286.6

326.4

370.2

221.4

254.1

290.4

330.6

374.8

224.5

257.6

294.3

334.8

379.5

227.7

261.1

298.2

339.1

384.2

230.9

264.6

302.1

343.4

389.0

234.1

268.2

306.0

347.8

393.8

237.3

271.8

310.0

352.2

398.6

240.6

275.5

314.1

356.6

403.5

5.50

5.60

5.70

5.80

5.90

408.4

460.3

517.1

579.1

646.6

413.4

465.8

523.1

585.6

653.7

418.4

471.3

529.1

592.1

660.8

423.5

476.8

535.1

598.8

668.0

428.6

482.4

541.3

605.4

675.2

433.8

488.1

547.4

612.1

682.6

439.0

493.8

553.6

618.9

689.9

444.2

499.5

559.9

625.8

697.3

449.5

505.3

566.3

632.7

704.8

454.9

511.2

572.7

639.6

712.4

6.00

6.10

6.20

6.30

6.40

720.0*

780.8

845.1

913.0

984.6

725.9

787.1

851.7

920.0

992.0

731.9

793.4

858.4

927.0

999.4

737.9

799.7

865.1

934.1

1007

743.9

806.1

871.8

941.2

1014

750.0

812.5

878.6

948.3

1022

756.1

819.0

885.4

955.5

1029

762.2

825.4

892.2

962.7

1037

768.4

832.0

899.1

970.0

1045

774.6

838.5

906.0

977.3

1052

6.50

6.60

6.70

1060*

1140

1223

1068

1148

1232

1076

1156

1241

1083

1164

1249

1091

1173

1258

1099

1181

1267

1107

1189

1276

1115

1198

1284

1123

1206

1293

1131

1215

1302

Figure 5. Example of expanded precision rating table.
own sequence of numbers, and consequently, in many cases 

each of the three ratings would have the same number. The ratings would be distinguished by rating type and rating number,

not only by number.

7.6 Updating and Renumbering Existing Rating Curves

Rating curves occasionally may require updating, or revision. Updates usually are composed of extrapolating either the 

low end or the high end of the rating. If no change is made to the 

available part of the rating, and it is simply extrapolated (either 

end, or both ends), then the electronic processing system should 

retain the rating with no change in the rating number. However, 

the user should have the option to renumber the rating, if 

desired. Revisions to an existing rating, or to a segment of an 

existing rating, require renumbering, and revision of the period 

of use. In effect, a new rating is established.

All updating and revisions of rating curves should be made 

a part of the record processing notebook, as described in 

section14.1. The date, users name, nature of the update, and 

reason for updating should be required input to the log.

7.7 Rating Curve Plots

A graphical presentation of a rating curve is useful to the 

user. Rating curves plotted on paper graphs traditionally have 

been used for studying the relation between parameters (mainly 

gage height and discharge), and very high standards have been 

established for this purpose. For the relation between stage and 

discharge, for instance, the hydraulics of the stream and control 

are expressed in the rating curve plot. Therefore, the user can 

make basic interpretations regarding the stream hydraulics if 

the plot is made by observing specific guidelines. Details of 

rating curve analysis and interpretation can be found in various 

reports, and specifically by Rantz and others (1982), and by 

Kennedy (1984).

Rating curves may be plotted either to linear scales or logarithmic scales. Certain types of ratings are better plotted with 

linear scales, whereas other rating types are best plotted with 

logarithmic scales. Preferences are frequently subjective, with 

either type of plot as acceptable. The most frequently used 

rating is the stage-discharge, and for hydraulic analysis purposes the working plot should be done with logarithmic scales.

gggp, 

height always is plotted as the ordinate, and the depend

able as the abscissa. This designation allows gage heigh

is measured in a vertical direction, to be plotted in a v

direction. The rating curve slope for this method of pl

defined as a horizontal distance divided by a vertical d

The plotting scale preference for other ratings is given 

13.

7.7.2 Electronic Processing System Monitor Plo

The electronic processing system should provide 

ting of rating curves on the electronic processing syste

tor with interaction by the user to manipulate, draw, an

ratings electronically. The requirements for electronic 

ing system monitor plots are essentially the same as fo

plots, as described in sections 7.7.3 through 7.7.8. The

tor plots should be a highly flexible part of the electro

cessing system and also should provide the capability 

duce a paper plot of the same rating, if required.

7.7.3 Paper Plots

The electronic processing system should be able 

duce a paper plot of rating curves that are entered either 

the use of descriptor points or equations. Paper plots als

be producible from system monitor plots. Requiremen

paper plots are described in sections 7.7.4 through 7.7

7.7.4 Plotting Forms for Paper Plots

The electronic processing system should develop 

the entire plotting form for a paper plot. It should print 

as well as the rating curve and other rating curve infor

Preprinted plotting forms are not advised. The combin

linear and log-log plotting form that traditionally has b

for stage-discharge ratings (see fig. 6) should be inclu

paper plot option.

7.7.5 Linear Scale Plots 

An arithmetically divided, linear, plotting scale is 

plest type of rating curve plot. Linear scale plots are co
to use and easy to read. Zero values can be plotted on the arithmetic scale, whereas these values cannot be plotted on logarithmic scales. For this reason, linear scale plots frequently are used 

for analyzing the low end of stage-discharge ratings. However, 

for detailed hydraulic analysis linear scale plots have little or no 

advantage over logarithmic scale plots. A stage-discharge relation plotted to a linear scale is almost always a curved line, concave downward, which can be difficult to shape correctly if only 

a few discharge measurements are available. Logarithmic scale 

plots, on the other hand, have a number of analytical advantages 

as described in section 7.7.6.

Linear scale plots are excellent for displaying a rating 

curve. Usually, a rating curve is first drawn on a logarithmic 

scale plot for shaping and analysis, then transferred to a linear 

scale plot for display, (usually a paper plot). The electronic processing system should make this process simple and easy.

7.7.5.1 Linear Scale Selection Procedure

 Linear scale subdivisions should be established to cover 

the complete range of the independent and dependent variables, 

or a selected range. If only part of the rating is to be plotted, the 

user should specify the range of either the independent variable 

or the dependent variable for the desired plot. The electronic 

processing system should make an initial determina

scales, subdivided in uniform, even increments that 

read and interpolate. The scales also should be cho

the plotted rating curve is not very steep or very fla

the curve should follow a slope of between 30 and 

The user should be able to change the scales easily 

so that various plots can be viewed. The electronic 

system should replot all measurements and rating c

mation each time a scale change is made.

7.7.5.2 Linear Scale Breaks

If the range of the variables is large, it may be n

break the plotting scale and plot the rating curve in t

segments to provide scales that are easily read with 

sary precision. This method may result in separate 

low water, medium water, and high water. Althoug

three separate curves are plotted, they should be plo

the same plotting form, if possible. The electronic p

system should arrange the individual plots on the fo

they are separate and distinct, properly scaled, and 

ping. Optionally, the separate curves could be plott

rate forms.

Figure 6. Linear and log-log combination plotting form.
The electronic processing system should plot rating curves 

and rating curve information to logarithmic scales, by default, if 

the rating is defined as a logarithmic rating. Ratings defined as 

linear ratings, or equation ratings, may be plotted to logarithmic 

scales at the users option. The initial plot should cover the full 

range of the rating, or a selected range if defined. A normal logarithmic scale (no offset) always should be used for the 

abscissa, or dependent variable. However, the ordinate scale 

should be adjusted, by default, by an amount equal to the offset 

defined for the primary rating being plotted. If multiple offsets 

are defined with this rating, and the user chooses to plot a continuous rating for the complete range of all segments, then the 

electronic processing system should default to the offset corresponding to the lowest segment of the rating to make the initial 

plot. If this is a plot for a new rating, where no other rating is to 

be plotted, then the electronic processing system should define 

the ordinate scale as a normal log scale (no offset), or use an 

offset selected by the user. Although default scale selections 

and offsets are prescribed, the user should be allowed to override the defaults and provide his/her own selections.

Generally, it is advised that full log cycles be used for logarithmic scale plots; however, the user should have the option 

to set lower and/or upper limits so that only partial log cycles 

are used at each end of the scales. The setting of scales should 

be highly flexible and easily changed so the user can plot and 

position the rating to the best advantage.

Logarithmic scale cycles always should be square. That is, 

the linear measurement of a log cycle, both horizontally and 

vertically, must be equal. Unless this requirement is met, it is 

impossible to hydraulically analyze the resulting plot of the rating.

7.7.6.2 Scale Offsets

Many rating curves, and especially stage-discharge rating 

curves, are analyzed and drawn on logarithmic scale plots, 

using a scale offset for the ordinate, or gage-height scale. A 

scale offset is a constant value that, when subtracted from the 

independent variable (gage height), changes the plotting relation between the dependent and independent variables. The 

results are a change to the curvature of the line of relation. If the 

offset value is too large, the line will plot as a curve concave 

downward. Conversely, if the offset value is too small, the 

curve will plot concave upward. Theoretically, a segment of a 

rating curve that is controlled by a specific cross section, or spe

stage-discharge rating curves, where three major segm

present; (1) the extreme low water segment that usuall

trolled by a section control, (2) the within bank segmen

be either a section control or channel control, and (3) 

bank segment that usually is channel control. Short tra

curves that join major rating segments usually are curv

that will not plot as a straight line, regardless of the sca

7.7.6.2.1 Scale Offset Limitations

Scale offsets must be limited to values that are less 

lowest value of the independent variable for the rating 

segment of a curve, being defined. Otherwise, the math

would produce zero or negative results, for which loga

cannot be determined. The electronic processing system 

not accept scale offsets that are equal to or greater tha

lowest value of the independent variable for the range 

the offset applies.

Negative scale offsets are acceptable. A negative o

the low segment of a stage-discharge relation would in

that the gage height of zero flow is negative. Although 

condition usually is not advised, this condition can res

some gaging stations.

7.7.6.2.2 Determination of Best Scale Offset

When drawing a new rating curve, or rating curv

ment, the best value for the scale offset is not always a

A trial-and-error procedure usually is used, and theref

electronic processing system should provide an easy m

change the scale offset and quickly produce a new plo

measurements and rating curve. In this way, the user c

with different scale offsets to find the one best suited f

rating curve in question. Three or four trials usually ar

cient to find the best offset, but the electronic processin

should not limit the number of trials.

The electronic processing system should provide a

to compute a scale offset. The computation method is 

defined by Johnson (1952), and is further described by K

(1984) and Rantz and others (1982). The following com

steps are required for the procedure.

1. Choose two points on the rating curve segment for 

computation of the scale offset, e, is desired. One 

chosen points should be near the lower end of the s
 . (23)

5. Round the resulting value of the scale offset, e, to one that 

easily is used for the logarithmic plot.

7.7.6.3 Rating Curve Shaping

Stage-discharge rating curves usually are shaped by fitting 

a curve or straight line to a series of plotted discharge measurements. For paper plots, this fitting is easily performed by hand 

with straight edges and preformed plastic curves. For electronic 

processing system monitor plots, a method, or methods, should 

be provided whereby the user similarly can fit a smooth curve 

or straight line to points plotted on the electronic processing 

system monitor. This should be a highly interactive process 

between the electronic processing system and the user.

Certain helps should be made available for electronic processing system plots to ensure that stage-discharge ratings are 

hydraulically correct. One such help is to plot a theoretical 

rating based on the control properties and the governing hydraulic equations. The computations and plotting of theoretical ratings should be performed with the electronic processing system, 

but will require interaction with the user. Methods of computing 

theoretical ratings will be described in more detail in section 

7.8. The theoretical ratings are used primarily for defining the 

rating shape, and not necessarily for locating the rating position. 

The user must use such ratings with caution, and should make 

discharge measurements to verify these ratings whenever possible.

Another help, when working with logarithmic scale ratings 

for stage-discharge stations, is to measure the slope of straight 

line rating segments for comparison to theoretical slopes that 

correspond to various control conditions. Rating slope computations should be done automatically with the electronic processing system on command. The user first should designate the 

end points of the segment of rating where slope is to measured. 

The electronic processing system should check to be sure the 

selected rating curve segment is reasonably close to a straightline segment. This checking can be done by computing percentage differences of discharge between the actual rating and the 

straight line defined by the selected end points, at intermediate 

points along the rating segment. If any difference exceeds + or 

- 1 percent (default value), the rating segment should be considered curvilinear and the slope should not be computed. The 

run and rise are measured as linear distances on log

plotting scales. They should not be measured in ter

independent and dependent variables, but rather in t

logarithms of these variables. For a straight-line se

points [(Q1, G1) and (Q2, G2)] on the segment can 

compute the slope using

, 

where

c = the rating curve slope, and

e = the scale offset for the independent variab

7.7.7 Mathematical Fitting of Rating Curves

As previously stated, rating curves are hydraul

that should conform to the laws of hydraulics. For 

rating curves should not be defined with statistical 

such as regression techniques, or by fitting curves w

matical methods such as quadratic equations. All me

used in a mathematical or statistical derivation are 

lie on the same rating curve. Frequently, this is an i

assumption, especially for streams with shifting co

7.7.8 Measurement Plotting

Selected field measurements and other compu

ters should be plotted with the electronic processing 

rating curve plots. The rating type will govern the pa

be plotted. For each respective rating, these may be 

ments of stage and discharge, stage and fall, index v

mean velocity, stage and area, or elevation and rese

tents. Computed parameters such as discharge ratio 

ratio for slope ratings, velocity factor and stage for 

ity ratings, and 1/USc and stage for change-in-stage 

should be plotted as required.

7.7.8.1 Selection of Measurements

The user should have considerable flexibility 

tion of measurements and computed parameters to 

The selection criteria should be based on measurem

measurement date, independent variable, dependen

e

G1 G2 2G3 + – = -----------------------------------

c

logQ2 Q1 – log

Y2 log( ) – e Y1 – log( ) – e = ------------------------------------------------------------
date, prior to a specified date, and (or) between two 

specified dates.

3. Plot all measurements where the independent variable 

exceeds a specified value, is less than a specified value, or 

between two specified values.

4. Plot all measurements where the dependent variable 

exceeds a specified value, is less than a specified value, or 

between two specified values.

Plot combinations of the above selection criteria as follows:

1. Combinations of (1) and (3).

2. Combinations of (1) and (4).

3. Combinations of (2) and (3).

4. Combinations of (2) and (4).

Other combinations of plotting criteria are not recommended.

For each of the above selection criteria and combinations, 

the user should be allowed to select various types of measurements, namely selected control conditions and measurement 

method.

7.7.8.2 Selection of Independent Variable

Gage height is used as the independent variable for most of 

the rating curve types, such as gage height and discharge, or 

gage height and area. For these rating types, the selection of 

inside or outside gage height becomes an important consideration for rating curve plots. It is common practice that both an 

inside gage reading and an outside gage reading will be measured. Frequently, these readings are identical, and either gage 

height can be used. However, the inside and outside gages do 

not read the same at some stations, sometimes by small amounts 

of only .01 or .02 ft, but in other cases where drawdown is 

present the difference could be large.

The electronic processing system should, by default, select 

the inside gage height for those ratings that use gage height as 

the independent variable. The user should have the option to 

change the default to outside gage height, if desired. Rating 

curve plots clearly should label the gage-height scale as “Inside 

surement as the independent variable.

7.7.8.3 Selection of Dependent Variable

The dependent variable is selected according to th

rating being plotted, as indicated in table 13. The depe

variable for each rating type is given below.

• Stage-discharge rating—Discharge is the depe

variable and should be plotted for all discharg

surements. For discharge measurements wher

sured discharge and an adjusted discharge are 

in the discharge measurement file, they both s

plotted, but with different symbols. A connect

between the measured discharge and the adjus

charge, as indicated below, should be shown o

rating to indicate that the two discharges are f

same measurement.

• Stage-area rating—The area measured at the s

cross section is the dependent variable.

• Index velocity-mean velocity rating—The me

ity in the standard cross section at the time of 

charge measurement is the dependent variable

• Stage-velocity factor rating—The mean veloc

adjustment factor is the dependent variable.

• Stage-fall rating—The mean fall between the b

and the auxiliary gage at the time of the discha

surement is the dependent variable.

• Fall ratio-discharge ratio rating—The comput

charge ratio, Qm/Qr

, at the time of the dischar

surement is the dependent variable.

• Stage-1/USc rating—The flood wave factor, 1

the dependent variable.

• Elevation-contents rating—The reservoir cont

the dependent variable.

Connecting line

Measured

discharge

Adjusted

discharge
7.7.8.5 Other Rating-Curve Plot Information

The rating curve plot should include information that identifies the gaging station by number and name, the rating type, 

the period of use for each rating plotted, the selection criteria of 

the plotted measurements, the date of rating development and 

approval for each plotted rating, the name of the user responsible for developing each plotted rating, and the name of the 

person approving each rating. Each rating shown on the plot 

should be clearly identified by rating number. Scales should be 

labeled with the correct parameter name, and the units of measurement for the parameter.

The rating plot sheet should contain a disclaimer statement 

that alerts the user that direct application of the rating may lead 

to errors if undefined shifts and/or backwater occur. The wording of the disclaimer statement should be designed to fit the specific gaging station and the type of rating. A typical statement 

for a stage-discharge rating is 

“This rating curve is applicable only for stream conditions unaffected by backwater, ice, debris, scour, 

and other undefined changes to the control.”

7.8 Rating Curve Development Procedures

Rating curves traditionally have been developed by hand 

plotting of measurements and manually drawing curves of best 

fit. Complex ratings, such as slope ratings and velocity-index 

ratings, have been developed through a combination of hand 

calculations and plotting methods. All of these methods are 

time-consuming and tedious. The computer development methods that can assist the user in rating curve shaping and definition 

are given in Sections 7.8.1 through 7.8.4.

7.8.1.1 Section Control Methods

Rating segments that are controlled by a specif

tion of the stream, such as a sand bar, rock outcrop

made weir, or other stream feature, can be approxim

flow computations based on a surveyed cross sectio

trol and the weir equation. The input of cross-sectio

the computation of cross-section properties are give

6.4.

Flow computations can be made for the section 

using the cross-section properties, a coefficient of d

and the weir equation. For purposes of defining the 

rating shape (not exact rating position), the method d

is simplified and some of the more detailed intricac

computations are not accounted for in the method.

The general form for the weir equation to be u

tion control computations is as follows:

, 

where

Q = discharge, in cubic feet per second,

C = the discharge coefficient,

L = the top width, in feet, of the water surface 

trol section and for the gage height of intere

h = the head, in feet, (difference between the g

and lowest point of the control section).

The discharge coefficient, C, used in the weir 

may be input directly by the user at the time the cro

data are entered. A value of C should be required fo

limit of gage height for the computations and for the 

of computations. Optionally, C- values may be spe

intermediate gage heights. The electronic processin

should use linear interpolation, based on gage heig

mediate values of C.

For control sections where C is not known, the 

choose to obtain estimates of the C values compute

charge measurement data. The electronic processin

should allow the user to designate specific discharg

ments for which a C value would be computed, bas

gage height and discharge of the measurement, the 

tion, and the weir equation. The computation of C w

based on the weir equation

-0.04

123

Q CLh1.5 =
section should be specified by defining the lower and upper 

limit gage height. Intermediate computations should be spaced 

at 0.1 intervals of gage height. The theoretical rating curve 

should be plotted on the rating curve plot, and clearly identified 

as theoretical.

7.8.1.2 Channel Control Methods

Rating curve segments that are controlled by channel conditions such as cross-section area, channel slope, channel shape, 

and roughness of the bed and banks, can be defined by theoretical computations using the Manning equation and a typical 

cross section near the gage. Such computations can define the 

correct hydraulic shape of the rating, but not necessarily the correct position of the rating. Computations of this type have been 

historically referred to as the conveyance-slope method as 

described by Rantz and others (1982).

The Manning equation is

, (27)

where

Q = discharge, in cubic feet per second,

n = the Manning roughness coefficient,

A = the cross-section area, in square feet,

R = the hydraulic radius, in feet, computed as the area, A, 

divided by the wetted perimeter of the cross section, 

and

S = the energy slope, in feet/feet.

The first part of the equation, consisting of the n, A, and R 

terms, commonly is referred to as channel conveyance, K, and 

can be computed from the channel cross section and visual estimates of the roughness coefficient, n. The equation for conveyance, K, is

. (28)

Some cross sections may be subdivided into two or more 

subsections because of channel shape and (or) roughness variability. For such cross sections, the conveyance, K, should be 

computed for each subsection, and a total conveyance, K determined as a summation of the individual subsection K’s. Points 

of subdivision are defined at the time the channel cross-section 

data are entered.

input at the lower and upper limits of the conveyance-

computations. The electronic processing system shoul

linear interpolation to determine intermediate values o

The electronic processing system should provide a

for the user to plot the computed values of slope and gag

so that a curve of relation can be drawn. This curve the

be used to determine values of S for the conveyance-sl

putations.

The range of theoretical computations for a given 

section using the conveyance-slope method should be s

by defining the lower and upper limit gage height. Inte

computations should be spaced at 0.5 ft intervals of gag

by default. The user should be allowed to specify other 

if desired. The theoretical rating curve should be plotte

rating curve plot, and clearly identified as theoretical.

7.8.1.3 Step-Backwater Method

Step-backwater is a water-surface profile comput

method that requires a minimum of two cross sections

erally four or more cross sections are required to produ

rate results. The details of the method are described by 

man (1990) and will not be discussed in this report. It 

excellent method to define the shape, and position of t

curve, and sometimes is used instead of discharge mea

ments when they are difficult to obtain. Cross-section 

other information necessary for step-backwater compu

are entered in the step-backwater program.

The step-backwater method computes water-surf

vations at each cross section in the stream reach down

from the gage. The computation depends on a given d

in the reach and on an assumed water-surface elevatio

downstream end of the reach. Two or more downstrea

tions are used to verify that the results at the gage will 

unique stage-discharge relation. The electronic proces

system should provide an option to plot the profiles of 

surface elevations for the various starting elevations fo

selected discharge. This type of plot is referred to as a 

gence plot that is useful in evaluating the accuracy of 

backwater results.

The electronic processing system should have a d

to the step-backwater software so that results can be tra

easily to the rating analysis for a gaging station. Gene

series of discharges is selected and for each discharge 

Q 1.486

n -------------AR2 3⁄ S

1 2⁄ =

K 1.486

n -------------AR2 3⁄ =
charge on the rating plot. This is an additional method to define 

the shape of a rating where section control is effective.

7.8.2 Slope Ratings

Slope ratings are used for stations with channel controls 

where variable stream slope downstream from the base gage 

affects the position of the stage-discharge relation. Variable 

stream slope usually is caused by a downstream condition, such 

as a reservoir, tributary stream, or overbank storage. In reality, 

the term “slope rating” is a misnomer, because these ratings do 

not use actual stream slope as a rating parameter. Instead, an 

index of stream slope is used, which usually is the water-surface 

fall measured between the base gage and an auxiliary gage 

downstream from the base gage. For some slope stations, the 

auxiliary gage may be located upstream from the base gage, but 

a better index of stream slope can be obtained if the auxiliary 

gage is located downstream from the base gage.

The rating method for slope stations involves a complex 

relation of three separate rating curves, (1) stage-discharge, (2) 

stage-fall, and (3) fall ratio-discharge ratio. These ratings are 

described in section 7.1, and a detailed description of slope ratings can be found in Kennedy (1984) and Rantz and others 

(1982). Slope ratings usually are classified into three specific 

types: (1) unit fall ratings, (2) constant fall ratings, and (3) limiting fall ratings. Although these different fall ratings are treated 

separately in the literature, they can be treated as one rating for 

computational purposes. This treatment is accomplished by 

defining the stage-fall rating to fit the specific fall rating type. 

For instance, if a unit fall rating is desired, then the fall rating is 

defined so that fall equals 1 ft for all gage heights. If a constant 

fall rating is desired, for a fall other than unity, then the fall 

rating is defined so that the desired constant fall is computed for 

all gage heights. Finally, if a limiting fall rating is desired, then 

the stage-fall rating is defined so that a variable fall is computed, which is dependent on gage height.

The development of slope ratings must be defined empirically, using discharge measurements, simultaneous measurements of fall, and a trial-and-error method to position and shape 

the individual rating curves. This procedure traditionally has 

been done by hand plotting and hand computing methods, a 

slow and tedious process. The electronic processing system 

should provide an interactive process, whereby the user makes 

ggg ggg 

where index-velocity ratings are used. Instead, ratin

developed for index velocity and mean stream velo

height and cross-section area, and gage height and 

factor (optional). Each of these ratings are develope

dard cross section of the stream. Development of th

fairly straight forward, but may require some amou

and -error fitting, especially if the stage and velocit

rating is used. The electronic processing system sho

an interactive process that allows the user to fit and 

ings so that the best combination of ratings can be 

The methods described here for index velocity 

refer to a single channel rating situation. However, 

ods can be used where the stream is subdivided into 

subsections, either horizontally or vertically. In such 

subsection has its own set of ratings, and is comput

rately. The total discharge is the sum of the subsect

charges.

7.8.4 Rate-of-Change-in-Stage Ratings

Rate-of-change-in-stage ratings sometimes are 

gaging stations where changing discharge causes a 

stream slope. These ratings are used for stations wi

tion frequently referred to as loop ratings. The Boye

Water Supply Paper 2175 (Rantz and others, 1982) 

used to determine the rating at a station with this con

method requires two ratings: (1) a stage-discharge 

(2) a stage-1/USc rating. An empirical, trial-and-err

is used to develop these ratings, and requires a num

charge measurements. Like other complex ratings, 

traditionally has been done using hand computation

plotting methods. The electronic processing system 

vide an interactive method so the user can quickly 

develop a Boyer rating. The user should be allowed 

test trial ratings until the best combination is attain

8. Shift Adjustments

Shifts are gage-height adjustments used to acc

temporary changes to rating curves, without having 

the rating curve. The method for computing shift in
tational purposes. It does not permanently alter the input unit 

value.

Although most shifts will apply to stage-discharge ratings, 

they also may be defined and applied to the index velocity and 

mean velocity rating for index-velocity stations. Shifts should 

not be allowed for any other types of rating curves except stagedischarge ratings and index velocity and mean velocity ratings. 

Because shifts are predominantly used for stage-discharge ratings, the shift discussions in this section will relate to that type 

of rating.

Shifts usually are applied only when discharge measurements deviate from a rating curve by more than a specified percentage. The specified percentage frequently is based on the 

accuracy of discharge measurements that can be made at the 

gaging station. For instance, if discharge measurements can be 

made with 5 percent or better accuracy, then shifts will be used 

only when measurements deviate more than 5 percent from the 

rating. Otherwise, if more than 2 or 3 consecutive discharge 

measurements consistently plot on one side of the rating a shift 

curve may be used for these measurements even though they are 

within the specified shift percentage. See the following section 

(Shift Curves) for methods for defining shift curves.

8.1 Shift Curves

Shift-variation diagrams (a plot of gage height and shift, 

and commonly known as V-diagrams) that have been used in 

previous computing systems, such as in the Water Data Storage 

and Retrieval System, WATSTORE, (Hutchinson and others, 

1977), or the Automated Data Processing System, ADAPS, 

(Dempster, 1990), should not be considered the primary method 

of defining and applying shifts. Shift curves, as defined here, 

become the primary method of defining and applying shifts. 

Shift-variation diagrams and tables are not eliminated from the 

system, but used more for an evaluative tool as described in subsequent sections.

A shift curve is defined as a shifted-rating curve, and has 

all of the basic characteristics of a rating curve. A few common 

characteristics of shift curves are

• Shift curves have the same independent and dependent 

variables as the parent rating curve.The parent rating 

curve is defined as the original, primary rating curve 

that is being shifted.

example, section control) of the rating usually 

only to that segment of the rating. For exampl

curve defined for a low-water section control s

merged with the parent rating at or near the tran

a channel control segment of the rating, unles

charge measurements or other information sho

wise.

• Shift curves may be time-interpolated as desc

section 8.4.4.

8.1.1 Input of Shift Curves

Shift curves should be an integral part of rating cu

may be defined graphically or by tabular input, using as 

a screen displayed plot of the current rating curve, the 

shift curve, and selected discharge measurements. The 

tronic processing system should allow the user to draw 

shape a shift curve on the screen in a similar manner to 

and shaping rating curves on the screen. The current, o

rating curve should be displayed, by default, at the tim

curves are defined. However, the user should be allow

play any other defined rating curve or previously used 

curves, simultaneously or individually.

8.1.2 Shift Curve Tables and Diagrams

For each shift curve defined graphically, a summ

of the independent variable (usually gage height) and 

sponding shift should be produced automatically with 

tronic processing system. The user may choose to enter 

the table prior to defining a shift curve graphically. Th

the tabular entries automatically should be displayed a

curve on the rating plot. This table will aid the user in 

and smoothing the shift curve. The table should begin 

lowest gage height of the shift curve and end with the 

gage height of the shift curve. The tabular listing should 

all points along the shift curve that were specified by t

during the process of defining the shift curve.

A plot of gage height and shift, or shift-variation 

for all points in the shift curve table should be an optio

diagram should not be considered the basic method of 

a shift curve, but it can be useful in evaluating the shif

tions and applications.
Figure 7. Typical rating curve, shift curve, shift table, and optional shift diagram.

8.1.3 Period of Use for Shift Curves

Each shift curve must be given a starting date and time. An 

ending date and time may or may not be required, depending on 

how the shift curve is to be applied. When both starting and 

ending dates, and times are given for a specific shift curve, then 

that shift curve will be applied directly throughout the defined 

period of time.

If an ending date and time for a specified shift curve is not 

given, then that shift curve will be time-interpolated to the succeeding shift curve, if one is given. If a succeeding shift curve 

is not given, then the last specified shift curve will be used 

directly until it is terminated either with an ending date and 

time, or with a succeeding shift curve. Additional details on 

time-interpolation of shift curves are given in section 8.4.

8.1.4 Extrapolation of Shift Curves

Shift curves should be extrapolated parallel to the parent 

rating curve below their lowest defined gage height and above 

their highest defined gage height. For example, if the shift curve 

is 0.20 ft above the parent rating curve at the highest defined 

gage height of the shift curve, then a constant shift of 0.20 ft 

should be used for all gage heights greater than the highest 

defined gage height of the shift curve. Likewise, a shift equal to 

referenced to the rating curve for which the shift cu

A two part number is recommended, with the first pa

rating curve number, and the second part a sequent

curve number that is determined in the order that th

curves are defined. Shift curves should retain its nu

assigned, and not be renumbered. The two parts of 

curve number should be separated by a colon (:). Fo

two examples of shift curve numbers.

1. The second shift curve defined for rating numb

be numbered 5:0002.

2. The third shift curve defined for rating number 

would be numbered 12b.2:0003.

8.3 Shift Curve Error Analysis

An error analysis should be performed with th

processing system for each discharge measurement 

effects of shifting or not shifting. In effect, this ana

extension of the computations described in section 

Analysis). The error analysis should show the optim

and the percent difference of the discharge measure

out shifting, as described in section 6.1.4. Also, th

should show the percent difference between the me

charge and the discharge computed by using the opt

In addition, it should show the shift actually applied 

date and time of the discharge measurement based 

defined shift curve and the interpolation method, if 

should show the percent difference between the me

charge and the discharge computed on the basis of 

shift. The shift analysis also should show the range 

tainty for each discharge measurement, based on th

accuracy of the measurements. This range of uncer

referred to as the uncertainty bars for a measureme

The electronic processing system should produ

discharge measurements showing the results of the 

sis and identifying information about each discharg

ment, such as measurement number, date, gage hei

sured discharge, and measurement accuracy. The ta

normally should cover the period of time for a wate

Shift

Diagram

Shift

Shift Curve 5:0003

Rating No. 5

 x.xx x.xx

 x.xx x.xx

 x.xx x.xx

 x.xx x.xx

Log of Discharge (-) 0 (+)

1

The water year is the period of time from October 1 through the following September 30.
Measurement

Rating Shift Analysis Uncertainty Bars

Applie

Optimum Shift Without Shift Low

Optimum

Shift

High

Number Date Stage Discharge RTD

PCT

UNC

(+/-)

Shift Discharge % Diff Discharge % Diff Shift Discharge Shift Discharge Shift Disch

213 09/15/1992 2.18 115.0 P 10.0 -0.03 116.1 -0.9 123.3 -6.7 -0.08 103.5 -0.03 0.01 126.5 -0.02 118

214 10/01/1992 2.40 178.0 F 8.0 -0.01 177.5 0.3 180.2 -1.2 -0.06 163.8 -0.01 0.04 192.2 -0.01 177

215 11/02/1992 1.91 60.40 F 8.0 -0.03 60.94 -0.9 65.84 -8.3 -0.06 55.57 -0.03 0.00 65.23 -0.01 63.

216 03/23/1993 1.63 24.60 F 8.0 -0.01 25.10 -2.0 26.15 -5.9 -0.03 22.63 -0.01 0.00 26.57 -0.01 25.

217 04/29/1993 2.08 93.50 F 8.0 -0.03 92.95 0.6 99.72 -6.2 -0.06 86.02 -0.03 0.01 101.0 -0.02 95.

218 05/18/1993 3.58 563.0 F 8.0 -0.04 561.2 0.3 576.7 -2.4 -0.15 518.0 -0.04 0.08 608.0 -0.04 561

219 06/29/1993 2.79 276.0 F 8.0 -0.06 276.9 -0.3 295.8 -6.7 -0.13 253.9 -0.06 0.01 298.1 -0.04 283

220 08/11/1993 2.09 99.80 F 8.0 -0.01 99.72 0.1 102.0 -2.2 -0.05 91.82 -0.01 0.03 107.8 -0.01 99.

221 10/22/1993 1.78 44.40 F 8.0 -0.01 44.24 0.4 45.79 -3.0 -0.03 40.85 -0.01 0.01 47.95 -0.01 44.

polation, and a combination of time and stage interpolation.

8.4.1 Individual Shift Curves

An individual shift curve can be used when it is desired to 

apply a constant shift, or a shift varied with stage for a period of 

time without varying the shift curve. The individual shift curve 

can be applied to a specified period of time by defining the starting date and time, and the ending date and time. If an ending 

date and time are not defined, then the shift curve will be used 

indefinitely until such time as an ending date and time are 

defined.

A constant shift that does not vary with stage or time can 

be accomplished by defining an individual shift curve with a 

single point. When a single point on a shift curve is used to 

define that shift curve, the shift will automatically be extrapolated below and above the specified gage height using the same 

shift entered for the specified gage height. This sometimes is 

referred to as a shift curve parallel to the rating curve. It is considered parallel because the shift is constant throughout the 

range of application.

An individual shift curve also can be used to apply shifts 

that are varied by stage only (not varied by time). This method 

defines an individual shift curve drawn so that it will have dif

ent constant shift (not varied with stage), then the elec

processing system will interpolate between these two 

based on time only. This procedure commonly is refer

time interpolation of shifts.

If two consecutive shift curves are entered so tha

both of them have shifts that vary by stage, then the el

processing system will interpolate shifts based on both 

and time for all unit values between the two assigned 

curves. The interpolation method is described in sectio

Two or more consecutive shift curves entered with 

dates and times only (no ending dates and times) will 

polated for intermediate dates and times. In this mann

user can vary shifts by stage and time, or time only, fr

shift curve to another, and even between a shift curve 

base rating.

8.4.3 Additive Shift Curves

The electronic processing system should not allow 

more shift curves to be added. If overlapping dates and 

entered for two shift curves, the electronic processing 

should issue a warning message to this effect, and req

corrections be made.

Figure 8. Example of shift-analysis table [RTD, measurement rating; P, poor; F, fair; G, good; E, excellent; PCT UNC, percent unc

%DIFF, percent difference].
values should be determined by interpolation, and not those outside the range of recorded unit values. Likewise, the interpolation process should be continuous in time, so that a shift interpolation is performed for each unit value to which shifts are to 

be applied.

The interpolation procedure is described in the following 

step-by-step example.

1. Two shift curves, 001 and 002, are defined graphically for 

use at dates and times, t1 and t2, respectively.

2. An interpolated shift, Sn, is required for unit value, Gn, at 

an intermediate date and time, tn.

3. The electronic processing system computes the shifts, S1

and S2, corresponding to the unit value, Gn, from each of 

the shift curves, 001 and 002, respectively.

4. The electronic processing system performs an unweighted, 

linear time interpolation of shifts S1 at time t1, and S2 at 

time t2, to obtain the shift, Sn, at time tn.

5. The same interpolation procedure is used to estimate shifts 

for all other unit values resulting between times, t1 and t2.

8.4.5 Rounding and Significant Figures

All computed shifts and interpolated shifts should be 

rounded to two significant figures to the right of the decimal 

(for example, all shifts should be rounded to hundredths). 

Rounding should be performed before any application process.

8.4.6 Unit Value Graphical Comparisons of Shifts

Shifts that are applied to a time series of unit values should 

be displayed with the electronic processing system in a graphical plot. The graphical comparison should show a time-series 

plot of the unit values of gage height (or other independent variable) and a superimposed plot of the unit values of shifts. Scales 

for the two plots should be used so that each plot is easily discernible and readable. The user should have the option to 

change either or both of the scales. An example plot is shown in 

figure 9.

include only defined information, not extrapolated 

shift curve. The table should be accessible at any tim

include, at a minimum, the following items for each 

• Shift curve number

• Beginning date and time

• Ending date and time (if used)

• Minimum gage height

• Shift corresponding to minimum gage heig

• Maximum gage height

• Shift corresponding to maximum gage heig

• Name of user

• Date shift curve entered

9. Primary Computations

Primary computations are the functions that co

data, such as gage height, velocity index, and other 

data, into time series of unit values, daily values, m

ues, and annual values of discharge, mean velocity

contents, and other output parameters. The convers

is dependent on the type of gaging station and, exce

only stations, always will require the use of at least 

Stage

Shift

Time

+

0

_

Figure 9. Example plot of time-stage and series shift
gage height and velocity index, are entered to the electronic pro

cessing system as described in section 4.1. Also, specific information such as parameter correction diagrams, shift curves, and 

rating curves are entered as described previously. The primary 

computations should produce additional unit values files of specific output parameters, dependent on the station type. These 

unit values and their associated time tags are saved for the purpose of computing daily mean values, various statistics, and for 

archiving. The unit values files that should be computed for 

each type of station are described in sections 9.1.1 and 9.1.9.

Most gaging stations use gage height as the input parameter, however, some stations use elevation above NGVD as the 

input parameter (for example, reservoir and tide stations). For 

some of these stations, the original data are recorded as gage 

heights above an arbitrary datum, and then converted to elevation as described in section 5.4.1.2. The computations in terms 

of either gage height or elevation, depending on the most 

common usage at each type of gage are described in sections 

9.1.1 through 9.1.9.

Rating curves are used extensively in the conversion of 

input parameters to unit value files of output parameters. Occasionally, the range of the input parameter may exceed the range 

of the defined rating. In such cases, the electronic processing 

system should not automatically extrapolate the rating curve, 

but rather, should insert a flag at points in the unit values file 

where the rating is exceeded to alert the user. The user then may 

make necessary extrapolations, and perform a new primary 

computation to complete the files.

9.1.1 Stage-Only Stations

Stage-only stations are those stations where unit and daily 

mean values of gage height, and associated statistics, are 

required. For this type of station, only the unit values files of 

gage-height data and the gage-height correction information are 

needed. Primary computations should create the following unit 

values files. Unless otherwise noted, each unit value file should 

be saved for further use, and for archiving.

• Gage-height corrections—The electronic processing 

system should evaluate and compute the gage-height 

correction that corresponds to each input value of gage 

height. gage-height corrections include instrument 

errors, gage datum errors, and gage datum conversions 

(for example, conversion to NGVD), as described in 

hundredths of a foot, unless specified otherwis

using them in further calculations. The resulti

series of cumulative gage-height correction va

should be saved as a working file, and for late

archiving.

• Corrected gage heights—A unit values file of c

gage heights should be computed by adding th

lative gage-height correction (see above) to th

unit values of gage height for each time step. 

of corrected gage heights is considered the fin

most accurate, gage-height record for the gagi

tion. The file also should be saved for further c

tions, and for archiving.

9.1.2 Stage-Discharge Stations

Stage-discharge stations are those stations where 

daily values of discharge are computed, based on unit v

gage height and a stage-discharge rating curve. This s

the most common type of gaging station, and requires 

values files of gage height and information defining g

height corrections and shift adjustments. Unless other

noted, each unit value file should be saved for further 

for archiving.

• Gage-height corrections—A file of unit value

cumulative gage-height corrections should be 

puted and saved for each unit value of gage he

described for stage-only stations in section 9.

• Corrected Gage Heights—A file of unit value

rected gage heights should be computed and s

described for stage-only stations in section 9.

• Shift Adjustments—Unit values of shifts shou

computed for each unit value of corrected gag

These shifts should be based on the shift curve

by the user, and for the applicable time period

lation of shifts by time and stage should be pe

with the electronic processing system, accordi

method described in section 8.4.4. All unit val

shifts should be rounded to standard gage-heig

sion, usually hundredths of a foot, before using 

further computations. The computed unit valu
g, , , 

archiving.

For the low end of the rating, and if the rating is defined to zero 

discharge, all shift-adjusted gage heights that are lower than the 

gage height of zero flow will be assigned a unit value discharge 

of zero. If the rating is not defined to zero flow, and a shift 

adjusted gage height is below the lowest gage height of the rating, a flag should be set indicating the rating was exceeded on 

the low end. Rating extrapolations can be made by the user at a 

later point in the processing.

9.1.3 Velocity Index Stations

Velocity index stations are those stations where unit values 

of discharge are computed on the basis of unit values of gage 

height, cross-section area, an index velocity, mean stream 

velocity, and a velocity adjustment factor (optional). At least 

two rating curves are required, (1) a stage-area rating, and (2) an 

index velocity and mean stream velocity rating. A third rating 

sometimes is used, relating stage to a velocity adjustment factor. Information defining gage-height corrections, index-velocity corrections, and index-velocity shift adjustments also are 

required.

Two unit value input files are used for velocity index stations, (1) an input file of unit values of gage height, and (2) an 

input file of unit values of index velocity. For various reasons, 

these files may not have corresponding and simultaneous time 

steps, which is required for the unit value computations of discharge. If the time steps for the two files do not correspond, the 

electronic processing system should automatically interpolate 

each file to provide estimated unit values corresponding to all 

recorded times of both files. That is, the gage-height file should 

be interpolated so that an estimated gage height is available for 

all time steps of the index velocity file, and conversely, the 

index velocity file should be interpolated so that an index velocity is available for all time steps of the gage-height file. Therefore, this method doubles the size of each of the input unit 

values files. The electronic processing system should flag, save, 

and archive all estimated unit values, together with the recorded 

unit values.

Unit value files should be computed with the electronic 

processing system for the following parameters. Unless otherwise noted, each unit value file should be saved for further use, 

and for archiving.

station, a velocity adjustment factor should 

puted from that rating for each unit value o

gage height. Shift adjustments are not appl

height for use with the velocity adjustment 

ing. If a velocity factor rating is not used for 

then the velocity adjustment factor of 1.00 

all gage heights. Velocity adjustment factor

rounded to two decimal places for applicat

poses.

• Cross-Section Area—The cross-sectional a

be computed for each unit value of gage he

the stage-area rating.

• Index Velocity Correction—Correction valu

be computed for each input value of index 

(including estimated values), based on the 

ity correction value diagrams, and the meth

polation described in section 5.4. All index 

correction values should be rounded to stan

ity precision, usually hundredths of a foot p

• Corrected Index Velocity—Each input valu

velocity should be corrected by adding the 

ity correction value to the corresponding v

input index velocity.

• Index Velocity Shifts—Shifts for each value 

rected index velocity should be computed b

velocity shift curves, and the interpolation 

described in section 8.4. All velocity shifts 

rounded to standard velocity precision, usu

dredths of a foot per second, before applyin

computations.

• Mean Rating Velocity—The mean rating ve

should be computed for each shift adjusted 

corrected index velocity by using the rating 

velocity and mean velocity.

• Mean Stream Velocity—The mean stream v

should be computed for each time step by m

the mean rating velocity times the velocity 

factor.

• Discharge—The unit values of discharge s

computed by multiplying each unit value o

tional area times the corresponding value o

stream velocity.
dures are possible, depending on the gage configuration and the 

number of index velocity gages that are used. The electronic 

processing system should provide for user-defined equations to 

compute average index velocity. The ratings for such a station 

are based on the average index velocity. All other aspects of 

computing unit values of discharge for the stream are the same 

as described above.

9.1.4 Slope Stations

Slope stations are those stations where discharge is computed on the basis of a stage-discharge relation that is adjusted 

for variable water-surface slope. Water-surface slope cannot be 

measured directly, so the water-surface fall between the base 

gage and an auxiliary gage is used as an indicator of slope. The 

auxiliary gage preferably is located downstream from the base 

gage, at a distance that provides a measurable fall but does not 

introduce hydraulically appreciable channel changes or tributary inflow. For some sites, the auxiliary gage may be located 

upstream, but this is not advised because the water-surface 

slope in the upstream reach is not as representative of backwater 

conditions as it is in the downstream reach.

Computation of discharge at a slope station requires unit 

values of gage height at the base gage and the auxiliary gage. 

Three ratings are required: (1) stage-discharge, (2) stage-fall, 

and (3) fall ratio and discharge ratio. Information defining gageheight corrections for the base gage and the auxiliary gage, and 

shift adjustments for the base gage, also are required.

Timing accuracy of unit-value data is very important at 

each gage, because water-surface fall computations require that 

time synchronous stage data be available for the base gage and 

the auxiliary gage. Even with the best timers and time-correction methods, it is not always possible to obtain this kind of 

accuracy, and stage data will sometimes be recorded and/or 

time corrected to different time steps for the two gages. For such 

situations, the stage data for the base gage should be interpolated so that estimated stage values are available for each corresponding stage value at the auxiliary gage. Likewise, the stage 

data at the auxiliary gage should be interpolated so that estimated stage values are available for each corresponding stage 

value at the base gage. This procedure effectively doubles the 

number of stage values at each gage, half of which are measured 

values, and half are estimated values. The electronic processing 

specific range in stage. The user should be allowe

designate the lower and upper limits of the slope r

entering a minimum gage height and a maximum 

height, below and above which the slope rating pro

should not be used. Discharge should be compute

directly from the stage-discharge rating for gage h

that are outside these limits.

3. Slope ratings may, in some situations, have maxim

constraints. That is, for measured fall values exce

designated amount, or for measured fall exceeding 

from the stage-fall rating, no slope adjustments sh

applied. The user should be allowed to enter a ma

fall so that when measured falls exceed this value

adjustments will not be made. Likewise, the user 

be allowed to designate that when measured fall e

the rating fall slope adjusted computations will no

made. For both of these situations, unit values of d

should be computed by direct application of the s

discharge rating.

4. For some slope stations, constraints 2 and 3 both 

apply, and should be checked.

Unit value files should be computed with the elec

processing system for the following parameters, subje

above constraints. Unless otherwise noted, each unit v

should be saved for further use and archiving.

• Gage-height Corrections, Base Gage—A file 

values of cumulative gage-height corrections 

base gage should be computed and saved for e

responding unit value of gage height (includin

mated values), as described for stage-only stat

section 9.1.1.

• Corrected Gage Heights, Base Gage—A file 

values of corrected gage heights for the base g

should be computed by adding the gage-heigh

tions for the base gage to the corresponding un

of gage heights.

• Gage-height Corrections, Auxiliary Gage—A 

unit values of cumulative gage-height correcti

the auxiliary gage should be computed and sa

each corresponding unit value of gage height (i

estimated values), as described for stage-only 

in section 9.1.1.
g gggy gg

height.

• Shift Adjustments—For slope stations, shift adjustments are used only for the stage-discharge rating for 

the base gage. A unit values file of shift adjustments 

should be computed for each base gage height, including estimated values, by using the defined shift curves 

and the time/stage interpolation procedures described 

in section 8.4. If shift curves are not applicable for specific time periods, shifts should default to zero for that 

time period.

• Rating Discharge—Unit values of rating discharge are 

computed for each unit value of shift adjusted gage 

height for the base gage, using the stage-discharge 

rating for the base gage. The rating discharge is an 

unadjusted discharge value, and does not represent the 

true discharge of the stream.

• Rating Fall—Unit values of rating fall are computed 

for each unit value of gage height (not shift adjusted) 

for the base gage, using the stage-fall rating for the base 

gage.

• Fall Ratio—Unit values of fall ratio are computed by 

dividing the measured water-surface fall by the rating 

fall.

• Discharge Ratio—Unit values of the discharge ratio 

are computed using the rating curve of fall ratio and discharge ratio.

• Discharge—Unit values of discharge are computed by 

multiplying the rating discharge times the discharge 

ratio. The resulting discharge represents the true discharge of the stream.

9.1.5 Rate-of-Change-in-Stage Stations

Rate-of-change-in-stage stations are those stations where 

discharge is computed on the basis of a stage-discharge relation 

that is adjusted for variable rates of change in stage. Computation of discharge is based on the Boyer Method and requires 

unit values of gage height. Two ratings are required, (1) a stagedischarge rating, and (2) a stage-1/USc rating. Information 

defining gage-height corrections and shift adjustments also are 

required.

2. Rate-of-change-in-stage computations are freq

made when the Boyer adjustment factor result

small change of the rating discharge. The elect

processing system should use default values of 

1.04 as the range of Boyer adjustment factors f

adjustments would not be made.The user shou

allowed to change these values, if necessary (f

to achieve smoothness of the computed unit va

discharge).

Unit value files should be computed with the e

processing system for the parameters listed below, 

the above constraints. Unless otherwise noted, each 

file should be saved for further use and archiving.

• Gage-height Corrections—A file of unit va

cumulative gage-height corrections should 

puted and saved for each corresponding un

gage height, as described for stage-only sta

tion 9.1.1.

• Corrected Gage Heights—A file of unit va

rected gage heights should be computed by 

gage-height corrections to the correspondin

values of gage heights.

• Rate of Change in Stage—A rate-of-chang

(dG/dt) should be computed for each unit v

rected gage height that is within the range 

heights defined by the minimum and maxim

straint. First, the difference in stage is com

subtracting the previous unit value of corre

height from the next unit value of the corre

height. This difference in gage height is co

the rate-of-change in stage, in feet per hour, 

it by the time difference of the previous an

values. This method of computation provid

age rate-of-change-in-stage for the time pe

ing one time interval before and one time in

the current unit value of gage height. The alg

of the computed rate-of-change-in-stage sh

retained as computed. A positive sign indic

stage, and a negative sign indicates a fallin

• Shift Adjustment—For rate-of-change-in-st

tions, shift adjustments are used only for th

charge rating. A unit values file of shift adj

should be computed for each corrected gag
computed for each corrected gage height (not shift 

adjusted) that is within the range of gage heights 

defined by the minimum and maximum constraint, by 

application of the stage-1/USc rating.

• Discharge Adjustment Factor—Unit values of the discharge adjustment factor, Fadj, are computed based on 

the Boyer Factor and the rate-of-change-in-stage, by 

using the following equation. Discharge adjustment 

factors should be computed only for gage heights that 

are within the range of gage heights defined by the minimum and maximum constraint as

. (30)

• Discharge—Unit values of discharge are computed by 

multiplying the rating discharge times the discharge 

adjustment factor. All unit values of discharge that are 

based on adjustment factors from 0.96 to 1.04, by 

default, should not be used unless overridden or otherwise specified by the user. Instead, the rating discharges 

based on the shift adjusted gage heights should be used 

directly.

9.1.6 Reservoir Stations

Reservoir stations are those stations where unit and daily 

values of reservoir elevation and reservoir contents are 

required. If only reservoir elevation is required, no rating is 

needed. However, if reservoir contents are required, then a 

rating of reservoir elevation and contents is needed. Input 

requires unit values of elevation and information defining elevation corrections. Generally, for reservoir stations, the term 

elevation is used rather than gage height because the elevation 

above National Geodetic Vertical Datum (NGVD) is used for 

many reservoir gages. However, gage heights are allowed and 

used at many reservoir stations. Unit values files should be 

computed with the electronic processing system for the parameters listed below. Unless otherwise noted, each unit value file 

should be saved for further use and archiving.

• Elevation Correction—A file of unit values of cumulative elevation corrections should be computed and 

saved for each corresponding unit value of elevation, as 

described for stage-only stations in section 9.1.1.

along tidal affected rivers and streams to provide the da

mation on diurnal and/or semi-diurnal variations of su

water levels in those areas. Tide stations may be set to 

trary datum or to an elevation based on the National G

Vertical Datum (NGVD). When an arbitrary datum is u

values of elevation are determined by adding a constan

conversion to the unit values of gage height. No other 

sions to other parameters are required, therefore, no ra

required. Information defining gage height or elevatio

tions also is required. Each unit value file should be sa

further use and archiving.

• Gage-Height or Elevation Correction—A file 

values of cumulative gage height or elevation 

tions should be computed and saved for each 

sponding unit value of gage height or elevatio

described for stage-only stations in section 9.

correction value is separate from the datum-co

value used to convert gage height to NGVD.

• Corrected Gage Height or Elevation—A file 

values of corrected gage heights or elevations s

computed by adding the gage-height or elevat

rections to the unit values of gage heights or el

9.1.8 Hydraulic Structure Stations

Hydraulic structure stations are those stations wh

and daily values of discharge are computed using specia

and equations for spillways, gates, turbines, pumps, si

and other controlled conveyances. A special software 

developed by C.L. Sanders, USGS, South Carolina Di

(written communication, 1997) is available for this pu

The basic theory and concepts are described by Collin

Input data may include unit values of headwater gage 

tailwater gage heights, individual gate openings for ea

conveyance, turbine pressures, lockages, and other var

required for a specific site. Hydraulic structure gaging 

are extremely complex and may have many sub-units 

ual gates, turbines, and others) for which unit values o

charge are computed. Unit values of total discharge ar

puted as a summation of the individual subunits. Becau

complexity and variability of hydraulic structure gages

of unit values files will not be given here. However, th

Fadj 1 1

USc

---------     dG

dt

-------     = +
gggp

gaged reach. Details of calibration and computation are given 

by Schaffrannek and others (1981). Primary computations 

require unit values of gage height at the upstream and downstream ends of the reach, as given below. Information defining 

gage-height corrections for the upstream and downstream gages 

is required.

• Gage-height Corrections, Upstream Gage—A file of 

unit values of cumulative gage-height corrections for 

the upstream gage should be computed and saved for 

each corresponding unit value of gage height (including 

estimated values), as described for stage-only stations 

in section 9.1.1.

• Corrected Gage Heights, Upstream Gage—A file of 

unit values of corrected gage heights for the upstream 

gage should be computed by adding the gage-height 

corrections for the upstream gage to the corresponding 

unit values of gage heights.

• Gage-height Corrections, Downstream Gage—A file 

of unit values of cumulative gage-height corrections for 

the downstream gage should be computed and saved for 

each corresponding unit value of gage height (including 

estimated values), as described for stage-only stations 

in section 9.1.1.

• Corrected Gage Heights, Downstream Gage—A file of 

unit values of corrected gage heights for the downstream gage should be computed by adding the gageheight corrections for the downstream gage to the corresponding unit values of gage heights.

BRANCH model gages have a unique characteristic, in 

that the parameters of gage height, mean stream velocity, and 

discharge are computed for each cross-section location, as well 

as at the upstream and downstream gage locations. For this reason, unit values of each of these parameters, for each cross section, can be saved for future use and archiving, if desired. The 

electronic processing system should allow the user to designate 

which output parameters, and for which cross sections and gage 

sites, should be saved for future use and archiving.

9.2 Daily Value Computations

Various kinds of daily values are computed for each 

station type, and are based on the unit values files 

requiring that they be saved and archived. Such file

values could be used for review and comparisons b

ization of the records.

9.2.1 Daily Mean Values

Daily mean values, frequently referred to as d

consist of a time-weighted arithmetic mean of selec

ters, and are computed from the files of unit values. 

values may be computed for the following paramet

• Gage height

• Discharge

• Cross-section area (index velocity stations

• Index velocity

• Mean stream velocity

• Fall (slope stations)

• Elevation (reservoir and tide stations)

• Contents (reservoir stations)

A file of all computed daily mean values shou

for future use and archiving.

The time-weighted arithmetic method of comp

mean values is referred to as the trapezoidal metho

ezoidal method is a mathematical integration of the 

hydrograph and provides an accurate computation o

parameter value. With a large number of instantane

for each day, the trapezoidal method closely approx

actual integration.

The trapezoidal method assumes that all unit v

instantaneous values, and that each unit value has a 

designated time of occurrence. The time interval be

values may be constant or variable. The file of unit 

for the computation of the daily mean value by the 

method must include a unit value at the midnight ti

day. If actual values are not recorded for the midni

unit value should be interpolated based on the reco

values on either side of the midnight time. These in

midnight values should be flagged as interpolated, 

be retained in the unit values file for future use and 

The equation for the trapezoidal method is

Q

q0 q1 +

2 ----------------     t1 t0 ( ) – q1 q2 +2 ----------------     + t2 t1 ( )... – q( ) n – 1 qn +2 ---------------------------     + tn t( 

n – 

( –

tn t0 – = -----------------------------------------------------------------------------------------------------------------------------------------------------------------
time,

t1, t2......, t(n-1) = consecutive times corresponding to the 

parameter unit values during the day, and

tn = midnight time at the end of the day, or 24.00 hour 

time. Note that all times must be expressed in hours and 

decimal parts of a hour.

Daily values will not be computed for days when time gaps 

exceed a value specified as the abort interval. The abort interval, 

by default, is 2 hours; however, the user should be allowed to 

change this interval to any other value less than 24 hours.

9.2.2 Daily Minimum and Maximum Values

The minimum and maximum values for some of the 

parameters are required for each day. These values are determined from the unit value files for the various parameters, and 

the selection process should consider all recorded and interpolated unit values for each day, including the midnight values at 

the beginning and end of each day. For some parameters, corresponding values of other parameters also should be determined.

The parameters requiring maximum and minimum values 

for each day and for each station type, and the corresponding 

unit values required for each maximum and minimum are 

shown in table 14. Not all tidal stations are included in table 14. 

Tidal stations require special computations to determine peak 

and trough elevations for semi-diurnal, diurnal, and mixed tidal 

cycles. The computation procedures for determinations at tidal 

stations are described in section 9.2.4.

9.2.3 Daily Values at Selected Times

Some stations require additional daily values at selected 

times for some parameters. For instance, reservoir stations 

sometimes require daily elevation and contents at specific 

qy g

tides for each day for semi-diurnal fluctuations. The pr

for computing daily values for tidal stations also recog

diurnal and mixed fluctuations when they occur. The fo

discussion is excerpted from Hutchinson and others (1

“In order to find true tidal peaks and troughs whi

occur once or twice in relation to the lunar day rat

than the solar day, the record is NOT broken up i

groups of observations in a calendar day before p

cessing. Instead, the whole record is scanned con

uously for successive peaks and troughs within 

periods of given length following the time of the 

vious extreme. After each extreme is found, the c

endar day in which it occurred and time is 

determined. This completely eliminates any conf

sion with inclusion or exclusion of extremes occu

ring just before or just after midnight.

“The method of finding successive tidal peaks an

troughs is to look for an opposite extreme in a 

selected time period (normally 10-1/2 hours) foll

ing each recognized peak or trough. That is, whe

tidal peak is found (and its date and time are store

search is made for the lowest stage in the selected 

time period following the time of the previous tid

peak. Then having found the time of this tidal trou

a search is made for the highest stage in the selec

time period following the time of the previous tid

trough. Comparison of two peaks found within a 

endar day and two troughs found within the same 

calendar day are used to assign each as a HIGHHIGH, a LOW-HIGH, a HIGH-LOW, or a LOWLOW for the day.
Corrected velocity index Index velocity correction, index velocity shift

Mean stream velocity —

Discharge —

Slope Corrected base gage height Gage-height correction, shift, measured fall, ra

fall ratio, discharge ratio, discharge

Corrected auxiliary gage height Gage-height correction

Measured fall —

Discharge —

Rate-of-change in stage Corrected gage height Gage-height correction, shift, rate-of-change, B

tor, discharge adjustment factor, rating dischar

charge

Discharge —

Reservoir Corrected elevation Elevation correction

Contents —

Hydraulic structure Corrected headwater gage height Gage-height corrections for headwater

Corrected tailwater gage height Gage-height corrections for tailwater

Discharge —

BRANCH Corrected upstream gage height Gage-height corrections for upstream gage

Corrected downstream gage height Gage-height corrections for downstream gage

Discharge —

“Although the normal tide on most of the United 

States coastline is semi-diurnal, at a few places the 

tides are diurnal or are mixed semi-diurnal. This program tries to give meaningful results in a situation by 

the following logic. Starting each search for a peak or 

trough, a normal, semi-diurnal tidal cycle is assumed 

and the length of the selected time period for the 

search is set at about 10-1/2 hours (0.44 day). This 

length of the search period was picked so as to be 

long enough to include the normal time of occurrence 

of the next peak or trough for a semi-diurnal tide 

(which should occur about 6-1/2 hours after th

ceding trough or peak) and short enough to av

confusion with the advance side of the next fol

tidal wave if the two tidal waves are of greatly 

ent magnitude. (If a 12-hour search period wer

confusion could occur such as when the secon

wave of the day is so much higher than the firs

the water level 12 hours after the previous tida

trough is rapidly rising and already higher than 

at the time of the first real peak which occurred 

6-1/2 hours after the previous tidal trough).
results used as the next peak or trough. However, 

after finding the next tidal peak or trough, the following search is again made for an initial period of 10-

1/2 hours so that a change back from a diurnal tide to 

a semi-diurnal tide is not missed.”

The daily values of HIGH-HIGH, LOW-HIGH, HIGHLOW, and LOW-LOW determined in the above procedure 

should be saved for further use, and for archiving. In addition, 

the cumulative elevation correction values corresponding to 

each of the peak and trough elevations should be saved and 

archived. The daily mean gage height and/or elevation also may 

be computed for a tidal station, as is done for a stage only station, and these values should be saved and archived.

9.3 Summary of Primary Computations

Primary computations include the determination of unit 

values and daily values for numerous parameters, as described 

in sections 9.1 and 9.2. It is important and necessary to summarize the results in tables that can be used for review, analysis, 

and for publication. Standard formatted tables include unit values, primary computations, diagnostics, and daily value tables. 

The electronic processing system should allow for the design of 

other summary tables, as needed, and as specified by the user.

9.3.1 Unit Values Tables

The electronic processing system should provide a flexible 

array of unit values tables to allow for the analysis and review 

of individual parameters, or selected groups of parameters. For 

9.3.2 Primary Computations Tables

Primary computations involve the application of 

user instructions to derive the final discharge record (o

parameter such as reservoir contents, tide, and others) 

gaging station. These instructions include gage-height 

tions, shifts, and rating curves. The computations shou

played in a table that shows input data, and various co

information so that they can be easily reviewed. Tradi

two formats have been utilized for displaying primary 

tations, (1) the historical format, and (2) the standard f

Selection of either format is optional.

The main difference between the historical forma

standard format of a primary computation is that the h

format shows hourly values of input data (for example

heights). The standard format provides more informat

the historical format regarding the computations. Othe

ences are present between the formats, but these are m

the arrangement of the data and information.

Each gaging station type, such as stage-discharge

velocity-index, and others, will have primary output fo

specifically designed for the station type. A listing of i

station type, that should be included in a primary com

form, is shown in table 15. Arrangement of the inform

not critical. A slightly modified version of a traditiona

cal primary output is shown in figure 10, and a standar

is shown in figure 11, each for a stage-discharge statio

mary computation tables for other gaging station type

be similarly designed.
Name of responsible user X X X X X X X X 

List of ratings used X X X X X

Unit value recording interval X X X X X X X X 

Station type (for example, processing 

method)

X X XXX XXX 

Datum conversion (if applicable) X X X X X X X X 

Tabular Information

Date X X X X X X X X 

Hourly gage heights for base gage X X X X X

Daily maximum gage height X X X X X X 

Time of maximum gage height X X X X X X 

Shift corresponding to maximum gage 

height

X X X

Gage-height correction corresponding to 

maximum gage height

X X XXX X 

Daily minimum gage height X X X X X X 

Time of minimum gage height X X X X X X 

Shift corresponding to minimum gage 

height

X X X

Gage-height correction corresponding to 

minimum gage height

X X XXX X 

Daily mean gage height X X X X X X 

Daily maximum discharge X X X X X 

Time of maximum discharge X X X X X 

Daily minimum discharge X X X X X 

Time of minimum discharge X X X X X 

Daily mean discharge X X X X X 

Hourly discharges X X X 

Daily maximum index velocity X

Time of maximum index velocity X

Shift corresponding to maximum index 

velocity

X

Index velocity correction for maximum 

index velocity

X

Daily minimum index velocity X

Time of minimum index velocity X
Daily minimum cross-section area X

Time of minimum cross-section area X

Daily mean cross-section area X

Daily maximum stream velocity X

Time of maximum stream velocity X

Daily minimum stream velocity X

Time of minimum stream velocity X

Daily mean stream velocity X

Daily maximum reservoir contents X

Time of maximum reservoir contents X

Daily minimum reservoir contents X

Time of minimum reservoir contents X

Daily mean reservoir contents X

Reservoir gage height at specified time X

Gage-height correction at specified time X

Reservoir contents at specified time X

Daily high-high gage height without 

datum conversion

X

Daily high-high gage height with datum 

conversion

X

Time of daily high-high gage height X

Correction for daily high-high gage height X

Daily low-high gage height without 

datum conversion

X

Daily low-high gage height with datum 

conversion

X

Time of daily low-high gage height X

Correction for daily low-high gage height X

Daily high-low gage height without 

datum conversion

X

Daily high-low gage height with datum 

conversion

X

Time of daily high-low gage height X

Correction of daily high-low gage height X
Correction for daily low-low gage height X

Daily mean tide gage height without 

datum conversion

X

Daily mean tide gage height with datum 

conversion

X

Daily maximum gage height at auxiliary 

gage

X 

Time of maximum daily gage height X 

Gage-height correction corresponding to 

maximum auxiliary gage height

X 

Daily minimum gage height at auxiliary 

gage

X 

Time of daily minimum gage height X 

Gage-height correction corresponding to 

minimum auxiliary gage height

X 

Daily mean gage height at auxiliary gage X 

Daily maximum fall X

Time of daily maximum fall X

Daily minimum fall X

Time of daily minimum fall X

Maximum rate-of-change in stage X

Time of maximum rate-of-change in stage X

Maximum adjustment factor X

Time of maximum adjustment factor X

Minimum adjustment factor X

Time of minimum adjustment factor X

Figure 11. Example of a 
Stage

Header Information

Station identification number X X X X X XX X 

Station name X X X X X X X X 

Water year information X X X X X XX X 

Date of primary processing X X X X X X X X 

List of ratings used XXXXX X

Station type (for example, processing 

information)

X X X X X X X X 

Tabular information

Date X X X X X XX X 

Time X X X X X X X X 

Base gage height, without corrections or 

adjustments

X X X X X XX X 

Base gage-height correction X X X X X X X X 

Base gage-height datum adjustment X X X X X XX X 

Base gage height, with corrections and 

adjustments

X X X X X X X X 

Base gage-height shift X X X

Index velocity, without correction X

Index velocity correction X

Index velocity, with correction X

Index velocity shift X

Index velocity adjustment factor X

Mean stream velocity X 

Cross-section area X 

Discharge (mean stream velocity times 

cross-section area)

X

Auxiliary gage height, without correction or adjustmentX X 
Auxiliary gage height with correction 

and adjustment

X X

Measured Fall X

Rating Fall X

Fall ratio X

Discharge ratio (from ratio rating) X

Rating discharge X X X

Discharge, adjusted for slope X

Rate-of-change in stage X

Factor 1/USc X

Discharge adjustment factor X

Discharge, adjusted for rate-of-changein-stageX

Reservoir contents X

Number of gates X

Discharge through gates X

Number of turbines X

Discharge through turbines X

Spillway discharge X

Weir discharge X

Pump discharge X

Siphon discharge X

Lockage discharge X

Leakage discharge X

Other discharge X

Total discharge, hydraulic structure stationX

Discharge computed by BRANCH 

model

1For structures’ gaging stations, base gage is headwater gage and auxiliary gage is tailwater gage.
appropriate. See section 13 for computation of monthly and 

annual values.

9.3.5 Unit Values and Discharge Measurement 

Comparison Table

A table where primary computation unit values are compared to measured discharge should be produced for all gaging 

stations where discharge measurements are made. This table 

will be used to review the final results after the primary computations are completed, and to verify that all shifts, corrections, 

and adjustments were applied correctly. The comparison should 

be made using the mean time of the discharge measurement. At 

a minimum, this table should include the following items.

• Date of discharge measurement

• Mean time of discharge measurement

• Measured discharge

• Computed unit value of discharge for same date and 

time (interpolated, if necessary)

• Difference between measured discharge and computed 

unit value discharge, (Qm - Quv)

• Percent difference of measured discharge and computed unit value discharge, 100(Qm - Quv)/Quv

10. Hydrograph Plots

Hydrographs are useful for graphical viewing, verification, editing, and comparisons of streamflow information, 

including most of the basic information that contributes to the 

primary computation of streamflow records. Hydrograph plots 

of unit values of discharge, along with comparative plots of 

other parameters, such as gage height, velocity, and shifts, and 

supplementary data such as peak discharge, peak stage, and discharge measurements, provide an excellent means of reviewing 

and editing the primary computations. Likewise, hydrograph 

plots of daily discharge records can be combined with 

hydrograph plots of other station records, precipitation records, 

and temperature records for review and editing purposes, as 

well as providing a graphical summary of the records for visual 

presentation and publication. Hydrograph requirements for 

10.1 Unit Values Hydrographs

The electronic processing system should allow th

choose any of the unit values files for hydrograph plott

erally, hydrographs showing unit values of discharge w

most interest, but other unit values hydrographs, such 

height, elevation, and reservoir contents also may be r

Other unit values files of supplementary information, 

for shifts, gage-height corrections, auxiliary gage info

and others should be superimposed on the same plot if 

additional parameter plots are specified. Also, unit val

mation from other gaging stations, precipitation statio

temperature stations should be superimposed on the sa

as specified by the user.

When more than one unit values file is shown on 

values hydrograph plot, each should be clearly identif

distinctive plotting symbol. Individual scales should b

for each parameter, labeled with the correct parameter n

units of measurement.

The abscissa scale for a unit values hydrograph p

time scale, with hours being the primary unit of subdiv

Each day, month, and year are shown as secondary su

sions. The ordinate scale should conform to the parame

plotted. Discharge scales should default to logarithmic

should be changeable to linear if specified. All other s

such as for gage height, elevation, shifts, rainfall, temp

and others, should default to linear scales. The range of 

nate scale should default to one that will include the fu

of the plotted unit values file, but should be changeabl

specified range.

10.2 Daily Values Hydrographs

A daily values hydrograph is a traditional USGS 

for displaying the results of streamflow computations 

gaging station. This hydrograph usually is an annual p

ing the daily values for a water year, but can be for an

period of time as selected by the user. Daily value hyd

usually are plots of daily mean discharge for a gaging 

with comparative hydrograph plots of daily mean disch

one or more nearby gaging stations. For some stations, 

values hydrograph also may include daily values of pr

tion and/or temperature. Daily values hydrographs als
linear scales. The range of the ordinate scale for the primary 

parameter should default to one that will include the full range 

of the daily values for the time period being plotted.

10.3 Supplementary Hydrograph Information

A few items of supplementary information are required, or 

are optional, for both unit value and daily value hydrograph 

plots. These include hydrograph identification information 

(required), discharge measurement data (optional), and peak 

information (optional).

• Station Number and Name—Each hydrograph plot 

should include a heading that shows the station number 

and name of the parameter of primary interest. If supplementary hydrographs are plotted on the same plot, 

they should be identified separately within the grid 

area, using an explanation.

• Time Period of Hydrograph—The hydrograph heading 

should state the time period covered by the plot. For 

instance, water year 1996, calendar year 1996, January 

1996 through June 1996, and others. The same period 

of time is identified on the abscissa scale.

• Discharge Measurements—All discharge measurements made during the time period of the hydrograph 

plot should be plotted if specified by the user. Discharge measurements should be plotted at the mean 

time of each discharge measurement. The measured 

discharge always should be plotted, and the adjusted 

discharge also should be plotted if one is available. Discharge measurements should be plotted as a small open 

circle and identified with the measurement number 

adjacent to the circle. Adjusted discharges should be 

plotted with a distinctive symbol.

• Peak Measurements—For unit value stage and elevation hydrographs, peak stages and/or elevations (from 

crest-stage gages and high water marks) may be plotted 

if specified by the user. Peak stage values should be 

shown as a short horizontal line at the estimated time 

and date, and at the stage or elevation of the peak, and 

identified as CSG or HWM.

For daily value discharge hydrographs, each instantaneous 

peak discharge that is greater than the base discharge should be 

charges, and the minimum discharge be computed 

water year. The maximum peak stage and discharg

minimum discharge, are referred to as the annual p

annual minimum. Guidelines for these computation

in sections 11.1 through 11.4.

11.1 Annual Peak Stage and Discharge

The annual peak stage and discharge are defin

highest instantaneous (unit value) gage height and 

associated with the highest flood peak that occurred 

water year. The annual peak stage and discharge, a

ciated date and time, should be determined with the 

processing system. If the highest gage height and dis

at the beginning or end of the water year as a result 

sion from or rise to a peak that occurred in the prev

lowing water year, they should not be included as a

For some gaging stations, the user may designate th

imum daily discharge be used rather than the maxim

taneous discharge.

The annual instantaneous maximum gage heig

sometimes occur at a different time than the annual 

neous maximum discharge. In these cases, the annua

instantaneous discharge should be determined, and 

gage height corresponding (at the same date and tim

discharge. In addition, the annual maximum instanta

height should be determined, and also the discharg

sponding (at the same date and time) to this gage he

and times for both pairs of values should be determ

11.2 Secondary Peak Stages and Discharge

Secondary peak stages and discharges are thos

are less than the annual peak stage and discharge, b

than a specified base discharge. Furthermore, the se

peaks must conform to guidelines that insure their 

dence. That is, to provide reasonable certainty that 

not been influenced, or affected, by another peak. T

lines are described by Novak (1985), and are given 

“Two peaks are considered independent if the 

hydrograph recedes to a well-defined trough be

the peaks. Publish both peaks if the instantane

discharge of the trough is equal to or less than 
teria. Identification of each distinct period of melting 

is largely a matter of individual judgment, but the 

principle as explained in paragraph 1 above for 

instantaneous discharges can be applied to daily discharges as an identification guide.”

All secondary peak stages and discharges should be determined with the electronic processing system. In addition, the 

date and time for each secondary peak should be determined.

11.3 Annual Minimum Discharge

The annual minimum discharge is defined as the lowest 

instantaneous (unit value) discharge that results during the 

water year. For some gaging stations, the user may specify that 

the lowest daily discharge be determined as the annual minimum discharge. In either case, the electronic processing system 

should determine the annual minimum discharge, and the associated date and time (if applicable), for the water year.

11.4 Summary of Annual Extremes

A tabular listing of the annual peak gage height and discharge, secondary peak gage heights and discharges, annual 

minimum discharge, and all associated dates and times should 

be produced with the electronic processing system. The user 

should review this report on the system monitor, and select 

items from it for publication and other applications.

12. Navigation Paths

This report describes the individual processes required for 

the computation and analysis of gaging station records. A navigation path, as described here, is a concept whereby the electronic processing system would lead the user through the processing routines that are specific to the various gaging station 

types. The user would be prompted for input and decisions 

along the way, but much of the information transfer and record 

processing would be automatic. As each processing step is completed, the electronic processing system automatically would go 

to the next step defined for that particular gaging station type. 

The electronic processing system tracks the progress through 

search for data and information, reduces the likelihood 

errors, and increases the probability that all relevant d

information will be used.

12.1 Basic Navigation Path

Navigation paths for the various types of gaging 

are similar in many, but not all, respects. The basic pr

steps required for a navigation path are shown in figur

Some steps must be repeated for each parameter type, a

steps will not apply for certain station types.The speci

gation path for each station type should be derived fro

basic steps shown in figure 12.

The same basic steps shown above would be used 

gaging station type, but with some modification. For i

an index velocity station would do steps 5 through 9 fo

values file of stage and the unit values file of index ve

The index velocity station also would require a shift a

and shift application (steps 10 and 11) for the index ve

mean velocity rating.

The choice of the correct navigation path to use f

cific gaging station should be automatic. When a gagin

initially is created in the electronic processing system, 

method of processing (for example, stage-discharge, s

index-velocity, and others) is defined, which automati

should establish the appropriate navigation path to use

quent access to the processing routines for that station 

use that same navigation path. If the station is multi-pu

that various parameters are measured, such as streamf

water quality, and/or sediment, then the user would ne

specify the parameter that is to be processed so that th

navigation path is used.

12.2 Navigating Through a Navigation Path

The user should be allowed to enter a navigation 

any point, as well as to back-track, if necessary. New 

would be entered by starting at the initial point of the na

path. If a period of record has not been completely pro

the user should be able to start at the point where proc

ended during the prior processing session. Finally, the 

should be able to enter or back-track to a step in the na

path that already has been processed, and do a recomp
analyses, and publication manuscripts. The functions also 

include definition and analysis of rating curves, estimation of 

missing records, computation of various statistics, qualityassurance reports, and data archival. All of these functions are 

described in other sections of this report.

13. Estimating Missing Records

Complete records of daily discharges, and other parameters, are necessary in order to compute monthly and annual 

totals and other statistics. Complete records also are needed to 

compute total runoff from a drainage basin, to calibrate runoff 

the USGS annual data reports and to those paramete

be required for the purpose of computing a publish

ter. For example, in some cases it may be reasonable 

unit values of gage height for the purpose of compu

values of discharge, provided the gage heights can b

with reasonable accuracy. The electronic processin

should provide estimating methods that commonly 

accepted, but the user must be able to interact and a

site specific information and procedures in order to 

best estimate of missing records.

Also, it is important that only one estimate of d

other hydrologic parameter) be saved and archived

the user may make various preliminary estimates fo

and comparison purposes, only the best estimate sh

saved.

13.1 Estimating Discharge Records

A number of methods potentially are available 

user in estimating discharge for periods of missing 

such methods that can be adapted to computer appl

described in sections13.1.1 through13.1.6. The elec

cessing system should allow the use of one or more 

methods, as well as other site specific methods, to m

compare discharge estimates.

13.1.1 Hydrographic and Climatic Compariso

The hydrographic and climatic comparison me

described by Rantz and others (1982), is the most c

method used to estimate discharge during periods o

record and ice-affected periods. A semilogarithmic 

of daily discharge is plotted, encompassing the per

ing record, and valid records for periods prior to an

missing record period. Other data and information, 

below, may be superimposed on this plot to aid in the 

procedure.

• Hydrographs of nearby stations (reference 

• Hydrographs based on the direct applicatio

affected gage heights to the rating (without 

for ice-induced backwater)

• Daily or hourly precipitation Figure 12. Basic navigation path requirements.

Data entry

1. Discharge measurements

2. Crest-stage gage data

3. Highwater marks

4. Miscellaneous notes

5. Unit values

Verification and editing

6. Start/end dates and times

7. Define time corrections

8. Verify and edit

Computation and analysis

9. Define data (datum) correction

10. Perform shift analysis

11. Define shift curves and

application method

12. Primary computations

Review

13. User review

• Stage discharge

• Index velocity/

mean velocity

• Base stage or elevation

• Auxilliary stage

• Index velocity
g , pg p

may need to be performed various times, each time for a different segment of the missing period. Values of daily mean discharge are then estimated by using the reference site as a guide 

and drawing a hydrograph for the missing period, whereas 

taking into account all of the other available data and information, such as the discharge measurements, climatic data, and 

notes. This estimation process is performed by the user on the 

electronic processing system monitor, using a mouse or other 

suitable device. After the estimated hydrograph segment is 

completed and accepted by the user, the electronic processing 

system automatically should determine the daily values of discharge, flag the values as estimated, and insert them into the 

daily values file.

A period of missing record resulting during an unbroken 

recession can be estimated by connecting the adjacent periods 

of good record with a straight line or a smooth recession curve 

on a semilogarithmic plot. This procedure is improved if recession curves, within the range of discharge to be estimated, are 

available for the station in question to superimpose on the plot. 

Recessions also may vary by season; therefore, it is useful to 

categorize the recession curves by season of the year. The user 

should be able to re-position the recession curves vertically and 

horizontally to obtain the best fit of the recession curves. The 

electronic processing system should allow for the storage, and 

later recall, of recession curve data for this purpose.

13.1.2 Discharge Ratio Method

The discharge ratio method is used for estimating discharge during ice-affected periods, and is described by Rantz 

and others (1982). For this method, the equivalent open-water 

daily mean discharge is multiplied by a variable correction factor, K, to produce a discharge corrected for the effects of backwater from ice. The correction factor, K, is computed for each 

discharge measurement as the ratio of measured discharge, Qm,

to the open water discharge, Qr. As changes occur in the ice 

cover throughout a winter period, the value of K for each day 

also will change, and intermediate values should be determined 

with the electronic processing system by time interpolation 

between K values determined from consecutive discharge measurements. Climatic data, such as temperature and precipitation, 

should be used to as a guide to modify the simple time interpolation procedure, as necessary.

13.1.3 Regression Method

Multiple, stepwise, regression is a useful method 

ing time series discharge data of one gaging station to 

rent time series discharge data of one or more nearby r

gages. Regression equations can be developed for spe

ranges of discharge, for instance, low flows, medium 

and/or high flows. They also can be developed for sea

periods and for ice-affected periods. The electronic pr

system should provide a flexible method of developin

sion equations, allowing the user to specify reference 

records, time periods, and discharge ranges. The regre

equations should include the ability to time-lag referen

records, and to use transformations of discharges (for e

logarithmic). Also, developed regression equations an

associated limitations, should be documented and arch

later use, if desired.

A regression equation can be applied to provide e

discharges for periods of missing record. In addition, t

regression equation should be used to compute discharg

for short time periods adjacent to the estimated period 

discharges are known. These adjacent periods sometim

used for verifying the accuracy of the regression results

adjusting the estimated discharges during the period of 

record to more closely fit the adjacent known records.

13.1.4 Water-Budget Method

A gaging station located just upstream from a rese

the purpose of measuring inflow to the reservoir, can h

ing discharge records estimated using the water-budge

if accurate records are available for the outflow from t

voir and the change in contents of the reservoir. The d

inflow to the reservoir is equal to the daily outflow plu

minus the change in reservoir contents. In some cases

the flow at the inflow station may not represent the tota

to the reservoir, an adjustment may be required. The ad

may be simply the application of a drainage area ratio, 

multiplication factor supplied by the user. The adjustm

factor can also be estimated by applying the water-bud

tion during periods when inflow, outflow and storage 

are all available. The water-budget method is

Q , 

i K Qo = ( ∆ + C)
13.1.5 Mathematical Translation Method

The mathematical translation method is a set of various 

mathematical functions that can be used to translate streamflow 

records for other gaging stations (referred to as reference gages) 

into estimates of streamflow for the gage.site where missing 

records result. Some of these functions are similar to the regression method described in section13.1.3, but are defined independently from regression methods. The selection of reference 

gages to use for making an estimate is important because the 

reference stations should be hydrologically related to the station 

for which estimates are made. For this reason, reference stations 

usually are nearby stations, have similar runoff characteristics, 

and are sometimes stations on the same stream. The user should 

use considerable care and judgment in selecting stations to use 

with the mathematical translation method. This method 

includes the following mathematical functions.

• Combining two streamflow records by addition, subtraction, multiplication, or division.

• Transforming a streamflow record into a different 

record using

, (33)

where

Qe = estimated discharge,

Qr = discharge at reference gage, and

a, b, c, and d, are constants defined by the user.

• Offsetting a reference gage record by a specified time 

period. The offset record can be mathematically combined with another reference record, or can be transformed by an equation. Two or more reference records 

can be offset with the same, or different, offsets.

• Transformation of reference gage records into log10, 

and inverse log10. These transformations can be made 

prior to performing any of the above mathematical 

functions.

13.1.6 Flow Routing Methods

Various flow routing models can be used to route a streamflow record from a reference gage to a downstream location on 

Discharge is the primary parameter for most g

tions, and discharge estimates usually are made for 

periods so that a complete record is available for ea

Complete records of other secondary, hydrologic p

such as gage height or stream velocity, are not alwa

and estimates are not usually made when missing rec

However, in some cases estimates of these seconda

ters are necessary.

Gage height (or elevation) can be reliably esti

for short periods of missing record, and even then, 

gage-height changes are small during the period. Th

recommended that gage-height (or elevation) recor

estimated, unless specifically required for publicati

computation of another parameter when no other re

method of estimating that parameter is available. F

it usually is easier and more accurate to make direc

of discharge than it is to estimate gage height for the 

computing discharge.

When gage-height record must be estimated, s

judgment and interpolation between periods of goo

should be used. The user should use all available in

such as miscellaneous gage readings, peak and min

information, and comparison with nearby gage site

estimation process.

13.3 Comparison of Estimation Results

It is important that all estimated discharge rec

other parameter estimates be compared with known 

with estimates made by various methods for the sam

period. The best method of comparison is by plottin

hydrograph that includes the estimated records. In t

estimated records can be compared visually to the o

records on either side of the estimated period. Likew

more estimated records for the same period can be 

visually for consistency and accuracy. The compar

dure should allow the user to make changes and revi

estimated record as appropriate. Finally, the user sh

the best estimate for incorporation of the records in

base.

Qe a b + Qr ( ) + c

d =
“computed from estimated values of _____.” The wording of 

this flag should be varied to fit the situation.

14. Monthly and Annual Value 

Computations

Monthly and annual values of stage, elevation, discharge, 

runoff, reservoir contents, and tidal lows and highs should be 

computed for each station as required or as designated. The 

required and designated monthly and annual values will vary 

with station type and with specific stations. All computations 

of monthly values should be based on the rounded results of 

daily values, and all computations of annual values should be 

based on rounded results of either daily or monthly values, as 

indicated. This results in consistent agreement of the daily, 

monthly, and annual values.

At least two sets of annual values should be computed for 

each gaging station, (1) for the calendar year, January through 

December, and (2) for the water year, October through September. In special cases, the user may designate additional or alternative types of years, such as the climatic year, April through 

March.

14.1 Monthly and Annual Values of Stage

Monthly and annual values of stage should be computed 

for those stations where stage routinely is measured for defining 

the gage-height fluctuations of a stream. For some stations, the 

stage may be the primary end product, such as for a stage-only 

station. In other instances the stage may be measured for the 

purpose of computing other parameters, such as discharge.

The monthly stage values that should be computed are the 

following.

• Monthly mean stage, in feet—The arithmetic mean of 

all daily mean stages for each month.

• Monthly minimum daily stage, in feet—The lowest 

daily mean stage for each month.

• Monthly maximum daily stage, in feet—The highest 

daily mean stage for each month.

Monthly and annual values of discharge should b

puted for gaging stations where daily discharge is rout

computed, such as for a stage-discharge station, a slope 

a velocity-index station, or other station types where s

flow is the parameter of primary interest. Some of the 

and annual values are required, whereas others are optio

are computed only for specific gaging stations. The op

computations generally are designated on the basis of 

flow conditions, drainage basin size, natural runoff co

degree of regulation, and other factors that may affect 

hydrologic value and need for the computed paramete

The monthly discharge values that are required ar

lowing.

• Monthly total discharge, in cubic feet per sec

days—Total of all daily mean discharges for e

month.

• Monthly mean discharge, in cubic feet per sec

ond—The mean of all daily mean discharges 

month, and is computed by dividing the mont

discharge by the number of days in the month

• Monthly minimum daily discharge, in cubic fe

second—The lowest daily mean discharge for 

month.

• Monthly maximum daily discharge, in cubic f

second—The highest daily mean discharge fo

month.

The monthly discharge values that are optional ar

lows.

• Monthly runoff volume, in acre-feet—This is 

monthly total discharge, converted to a volume

feet, and represents the total number of acres th

be covered to a uniform depth of 1 ft by the to

charge for that month. The monthly runoff vo

acre-feet, is computed by multiplying the mon

discharge, in cubic feet per second-days, times 

version constant, 1.983471.

• Monthly runoff depth, in inches—The monthl

discharge volume, converted to a depth, in inc

would uniformly cover the drainage basin. The 

total runoff depth, in inches, is computed by m

ing the monthly total discharge, in cubic feet p
lows.

• Annual total discharge, in cubic feet per seconddays—The total of all daily mean discharges for the 

year.

• Annual mean discharge, in cubic feet per second—The

mean of all daily mean discharges for the year, and is 

computed by dividing the annual total discharge by 

365, or by 366 for leap years.

• Annual minimum daily discharge, in cubic feet per second—The lowest daily mean discharge for the year.

• Annual maximum daily discharge, in cubic feet per second—The highest daily mean discharge for the year.

The annual discharge values that are optional are as follows.

• Annual runoff volume, in acre-feet—The annual total 

runoff volume, in acre-feet, is computed by summing 

the monthly values of runoff volume for the year.

• Annual runoff depth, in inches—The annual total 

runoff depth, in inches, is computed by summing the 

monthly values of runoff depth for the year.

• Annual mean unit runoff, in cubic feet per second per 

square mile—The annual mean runoff, in cubic feet per 

second per square mile, is computed by dividing the 

annual mean discharge, in cubic feet per second, by the 

drainage area, in square miles.

14.3 Monthly and Annual Values for Reservoirs

The computation of monthly and annual values for reservoir stations is varied and highly dependent on the type of daily 

values that are used for the station. Reservoir stations may 

require daily mean elevations, daily mean contents, elevation at 

a specific time (for example, at 0800, 1200, 2400, or other 

time), or contents at a specific time. The choice of daily values 

that are used, and published, for a reservoir station is dependent 

on user requirements, and consequently, the monthly values 

that should be computed will be based on these same requirements. The list of monthly and annual values that can be computed is fairly long (see below), but generally only a few of 

these values will be chosen for a given reservoir station. The 

choice will be partially based on the daily values used for the 

• daily maximum elevation

• daily maximum contents

• daily minimum gage height

• daily minimum elevation

• daily minimum contents

• daily gage height at a specified time

• daily elevation at a specified time

• daily contents at a specified time

The full parameter name is formed by precedi

selected name(s) by “monthly minimum”; for exam

“monthly minimum daily maximum elevation.”

• Monthly maximum value—The highest val

the month of selected parameters. The poss

are the same as listed above for monthly m

ues, and the full parameter name is formed a

above.

• Monthly mean value—The mean of all dai

during the month of one or more of the fol

parameters:

• daily mean gage height

• daily mean elevation

• daily mean contents

The full parameter name is simply monthly m

height, elevation, or contents.

• End of month contents—The reservoir cont

2400 hours of the last day of the month.

• Monthly change in contents—The change 

contents during the month. It is computed b

ing the end of month contents for the previ

from the end of month contents for the cur

The change in contents may be shown in u

feet, cubic feet, or in units of equivalent cu

second, or all three. Equivalent cubic feet p

computed by dividing the change in conten

feet, by the number of seconds in the mont

The annual reservoir values that may be comp

lows.
• End of year contents—The reservoir contents at time 

2400 hours of the last day of the year.

• Yearly change in contents—The change in reservoir 

contents during the year. It is computed by subtracting 

the end of year contents for the previous year from the 

end of year contents for the current year. The change in 

contents may be shown in units of acre feet, cubic feet, 

or in units of equivalent cubic feet per second, or all 

three. Equivalent cubic feet per second is computed by 

dividing the change in contents, in cubic feet, by the 

number of seconds in the year.

14.4 Monthly and Annual Values for Tidal Stations

Tidal stations require the computation of various monthly 

and annual values as described below. For tidal stations that use 

an arbitrary gage-height datum and a datum-conversion constant to convert the gage heights to NGVD, the monthly and 

annual values should be computed for both datums.

The monthly tide values that may be computed as follows.

• Monthly mean stage and/or elevation, in feet—The

mean of all daily mean stages and/or elevations for each 

month.

• Monthly mean high tide, in feet—The mean of all daily 

HIGH-HIGH tide stages and/or elevations for each 

month.

• Monthly mean low tide, in feet—The mean of all daily 

LOW-LOW tide stages and/or elevations for each 

month.

• Monthly minimum low tide, in feet—The lowest of all 

daily LOW-LOW tide stages and (or) elevations for 

each month.

• Monthly maximum high tide, in feet—The highest of all 

daily HIGH-HIGH tide stages and (or) elevations for 

each month.

The annual tide values that may be computed as follows.

• Annual mean stage and/or elevation, in feet—The

mean of all daily mean stages and (or) elevations for the 

year.

• Annual mean high tide, in feet—The mean of all daily 

HIGH-HIGH tide stages and/or elevations for the year.

The operation and maintenance of gaging stations

analysis and publication of gaging station records, req

number of documents to describe each gage and to do

the records for that gage. In an automated electronic pr

system these documents can be easily prepared using pr

formats, automatic transfer of information, and a word

ing system. Four basic documents, (1) record processi

book, (2) station description, (3) station analysis, and (4

manuscript should be incorporated and formatted for e

face-water record. Additional, miscellaneous documen

as the documentation of an indirect measurement, can 

pared, as needed, using the word-processing system.

15.1 Record Processing Notebook 

The record processing notebook is an open comm

that can be accessed at any point during the processing 

gaging station record. The notebook provides the user a 

record comments pertaining to the data and informatio

reasoning for various analytical steps such as shifts, dat

tions, rating changes, and others, and other informatio

should be retained for future use. One of the main use

notebook is the preparation of the annual station analy

(described in section15.3) where it will allow quick an

recall of the analytical steps used during the preceding 

comments recorded in the notebook automatically sho

categorized into defined subjects, patterned primarily a

to the format of the station analysis. In addition, all co

should be dated automatically according to the date of 

and automatically signed with the name of the user ma

entry. All processing steps should fit into one of the co

categories listed below.

• Equipment—All comments pertaining to field 

ment such as recorders, gage structures, artific

trols, cableways, and other field measuring de

should be saved as an equipment category. Mo

ments in this category will be derived from fie

such as discharge measurements, level notes, 

stage gage notes, and miscellaneous notes.

• Unit values data—All comments pertaining to 

values of gage height, elevation, index velocit

other unit values field data should be saved in 
() 

recorded, the method of making corrections, and 

changes in gage datum. Most comments for this category will come from the parameter value corrections 

processing step and the gage datum analysis step.

• Rating analysis—Comments in this category will relate 

to all phases of rating analysis, including the development of new ratings, revision of old ratings, use of 

cross-section data to define ratings, control conditions, 

shift analysis, shift application, rating curve plots, shift 

curve plots, and any other aspect of rating curve analysis.

• Discharge computations—Comments in this category 

will relate to the methods of producing unit and daily 

discharge records. These comments will include methods of direct computation and methods of estimating 

record during periods of missing record, ice, backwater, 

and other conditions. Comments for this category 

should be derived during the primary computation 

phase and missing record estimation phase of record 

processing.

• Quality assurance and accuracy—Comments in this 

category will relate to any phase of record processing 

that provides special applications of quality control and 

quality assurance. Comments also should be included 

for any condition that may affect the accuracy of the 

records. Comments for this category may be derived at 

any point during the process of producing a streamflow 

record from the initial entry of field data through the 

final computation steps.

• Miscellaneous—Comments in this category will be 

miscellaneous comments that do not fit in any of the 

other categories.

15.2 Station Descriptions

The station description is a narrative of the features and 

characteristics of a gaging station. A basic format containing 

specified topics is used for most station descriptions; however, 

deviations from the basic format sometimes are needed to 

describe special gaging station installations. Most of the input 

for preparing or editing a station description is supplied by the 

user. Some items, however, should be supplied automatically 

ever, minor changes or changes to one or two featu

tion may occur from time to time, and the station d

should be edited to reflect these changes. The elect

cessing system should provide an easy and flexible 

making such changes. In addition, the date of editin

name of the person making the change, automaticall

attached to each change. Automatic updating, made 

electronic processing system, should be footnoted a

The following items are suggested for most st

descriptions; however, some of these may not appl

cific gaging station and should not be used. On the 

additional items may be required for some gaging s

Also, some stations (such as slope stations) may hav

gages and will require multiple entries for some ite

Kennedy (1983) for additional details.

• Station name

• Station ID

• Location and road log

• Establishment

• Drainage area

• Gage

• History

• Reference and benchmarks

• Channel and control

• Discharge measurements

• Floods

• Gage height of zero flow

• Winter flow

• Regulation and diversions

• Accuracy

• Cooperation

• Purpose of record and gage classification

• Land ownership

• Indirect measurement site

• Sketch

• Photographs

• Observer
The station analysis for a gaging station usually is written 

and finalized at the end of each water year, however, parts of it 

may be written at any time during the year as information 

becomes available. The record processing notebook described 

in section 15.1 should be utilized to the fullest extent as an aid 

in writing the station analysis. The electronic processing system 

automatically should transfer information from the record processing notebook to the appropriate paragraphs of the station 

analysis.

The electronic processing system also should automatically transfer information from other parts of the electronic processing system to the station analysis phase to assist the user. 

Specific transfer items should include the following.

• Level and datum information should be transferred 

from the most recent level summary. This information 

should include the date of the latest levels, and information about datum differences of the various gages at the 

station.

• All periods (dates) of missing record, and the total 

number of days of missing record, should be transferred from the unit values files.

• The minimum and maximum gage heights recorded 

during the water year should be transferred from the 

unit values files.

• The number of discharge measurements made during 

the water year, and their corresponding sequence numbers, should be transferred from the measurement file. 

In addition, the lowest and highest measured gage 

height and discharge should be transferred from the 

measurement file.

• The comparison of measured discharges to computed 

unit values of discharge should be transferred from the 

table described in section 9.3.5.

• Methods of estimating missing records and ice records 

should be transferred from the electronic processing 

system documentation of estimating missing records 

for the water year.

• The listing of records used for hydrograph comparisons 

should be transferred from the electronic processing 

system documentation of hydrograph comparisons 

used for the water year. This listing should include sta

cessing system, then can be used to write the station a

The station analysis should include, at a minimum, the 

ing items and paragraphs. For some gaging stations, ot

graphs may be required in order to adequately describe 

putation methods. See Kennedy (1983) for additional 

• Station name

• Station ID

• Water year

• Equipment

• Gage-height record

• Gage-height and datum corrections

• Rating

• Discharge

• Quality assurance and control

• Remarks

• Recommendations

The name of the user who writes the station analy

the date of preparation, automatically should be attach

end of the station analysis. Also, the name of the revie

section 16) automatically should be attached, along w

date of review completion.

15.4 Station Manuscripts

The station manuscript is the narrative part of the 

lished page for each gaging station record for each wa

A standard format is used that consists of paragraphs, 

required, taken from the following list.

• A heading consisting of the basin name, statio

ber, and station name

• Location

• Drainage area

• Period of record

• Revised records

• Gage

• Remarks (includes statement on accuracy)

• Cooperation
ggg , p

are included, such as separate summaries before and after regulation by a major reservoir. The final station manuscript is variable among gaging stations depending on the period of record, 

the parameter of interest, the statistical presentation, and other 

characteristics of each individual station. For details of station 

manuscript preparation, see Novak (1985).

A copy of the previous year's manuscript (if available) 

should be recalled for use as a guide and starting point for the 

preparation of the current year's manuscript. Information used 

for completion of some parts of the station manuscript automatically should be computed and transferred from other parts of 

the electronic processing system. The electronic processing 

system automatically should highlight any differences of information between the previous and the current manuscript.

16. Review, Approval, and Finalization of 

Records

Gaging station records are reviewed at various points 

during the process of entering, analyzing, interpreting, and 

computing the streamflow information. These records generally 

are referred to as working reviews that usually are made by the 

user as the records are processed. This report refers to a number 

of places during the process of producing a streamflow record 

where such reviews should be made. Working reviews are a 

normal function of the record production process, and the electronic processing system provides the user with numerous aids 

to make this process as easy as possible.

A formal review should be made after the records have 

been processed and the user is satisfied that the records are complete and accurate. This final review should be made by a senior 

reviewer who is designated to make such reviews. This review 

ultimately results in the approval and finalization of the records 

for publication and archival if the reviewer finds that the records 

are complete and accurate. If this review reveals deficiencies in 

the records, the reviewer can return the records to working 

status (see section 17.2).

The formal review should have access to all of the same 

review functions that are used in the record processing steps. 

These review functions would include all output tables, such as 

the discharge measurement summary tables, the level summary 

records as approved and ready for publication and 

Records that are flagged as approved should be pro

any further changes or revisions. In the event that a c

approved record is required, the records must be se

working status (see section 17.2).

17. Status of Data and Information

All data and information will progress through 

of processing steps. These steps include (1) origina

working data, (3) review, (4) approval, and (5) publi

cific processing functions that pertain to each of th

have been described in previous parts of this report

of the data and information as they progress through 

are described in sections 17.1 through 17.5.

17.1 Original Data

Original data are defined as direct measuremen

parameter such as gage height, velocity, depth, wid

station variable. Direct field measurements are cons

those made by the hydrographer while at the gage s

include all measurements required to make a stream

surement, direct visual readings of gages, determin

highwater marks and crest-stage gage readings, lev

and other data collected during the course of servici

Historically, these notes and measurements were re

paper field notes. Presently (2002), paper field note

accepted media by the USGS. Paper field notes are 

the original data, and should be preserved even thou

the data and information from these notes will be e

ually to the electronic processing system.

Electronic field notebooks presently are in the 

ational stages for the purpose of recording direct fie

ments. It is expected that these notebooks will be u

sively within the next 5 to 10 years, and may elimin

for some or all of the paper note recording. All fiel

ments recorded in electronic format should be elect

transferred to the electronic processing system. The 

fer of this type becomes the original data and shoul

served without alteration. Any supplemental paper 

should be preserved separately as original data.
ing records. Both the primary and backup original unaltered 

data should be set aside for archiving.

Various types of automatic field recorders are currently in 

use by the USGS, each having unique characteristics that relate 

to the definition of original data, as well as to the format and 

method by which the data will be preserved. The following text 

describe these characteristics.

• Analog recorders—Analog recorders are graphical 

recorders that record a pencil or pen trace on a paper 

chart. This chart is the original record and should be 

preserved. Various mechanical and electronic methods 

are available that can be used to digitize the graphical 

record into an electronic record suitable for entry to the 

electronic processing system. The digitized record is 

not considered an original record, and should be used 

only as a working record (see section 17.2 for a definition of working data).

• Automated digital recorders—Automated digital 

recorders record data as punched holes in a paper tape. 

These tapes cannot be read easily by eye, and usually 

are translated into an electronic format by paper tape 

readers. The first electronic unaltered translation of the 

tape is considered the original record and should be permanently preserved.

• Electronic data loggers—Electronic data loggers 

record data in various formats that must frequently be 

translated to engineering units through the use of special algorithms. The first translation to engineering 

units is considered to be the original record and should 

be preserved as such. 

• Data-collection platforms—Data-collection platforms 

are systems whereby data are transmitted from the field 

site to an office by radio, telephone, or satellite. In addition, the data frequently are recorded at the field site by 

a data logger or other backup recorder. The primary 

original record may be either the field recorded data or 

the transmitted data, depending on the individual gage 

setup, or the specific policy of the office collecting the 

data. In either case, the designated primary original 

data and the designated backup record should be preserved.

by interactive input by the user. Data and information 

working status generally follow a specific navigation p

section 12) of transformations and computations that ul

result in a record of discharge, reservoir contents, or o

parameter that is published or used for various project 

While in the working status, data and information may 

changed as deemed appropriate by the user, reworked 

sary at any point in the working process, and even com

deleted so that processing can be restarted. At some po

ever, when the user is satisfied that the computations a

plete and accurate, the working files are moved to a re

tus. At this point, changes can no longer be made unless 

files are moved back to working status at the direction 

ignated reviewer.

17.3 Review

The process of review has been described in sect

Review status is the point where a senior reviewer rev

records and either accepts the records and recommends 

approval, or rejects the records and recommends a com

partial reworking. Records that are in the review status 

be changed or altered in any way. If the review reveals 

for changes, the records must be moved back to worki

as described in section 17.2.

17.4 Approval

The approval status is the step following review, 

results from the final approval of records as described i

17.3. Records that are approved are considered ready f

cation.

17.5 Publication

The publication status refers to records that are p

in USGS annual data reports, released as approved rec

public access, or released for public use in an electron

such as CD ROM or the World Wide Web. Published 

may be revised, but the original published values mus

retained and flagged as superseded. The new, revised 

must be flagged as revised. Revisions to approved and 
become increasingly difficult to define the method by which 

these records should be archived. A study group in the early 

1990's addressed the problems of data archiving, and made recommendations that are given by Hubbard (1992). That report 

provides a comprehensive set of recommendations for the management and retention (archiving) of hydrologic data, both for 

hard copy and electronic data and information, and should be 

used as the basis for permanent archiving of all hydrologic data 

and information. Only a brief summary of the archiving recommendations for electronic data and information will be given 

here, as taken from Hubbard (1992).

The following list of electronic data and information is not 

all inclusive, but at a minimum these items should be placed in 

permanent electronic archives.

• All original data for automated data-collection sites, as 

defined in section17.1.

• Records of algorithms used to convert field values to 

conventional engineering units.

• All non-automated data collected in electronic format, 

such as discharge measurement notes, as defined in section 4.2.

• All approved files of edited and calculated data, such as 

unit values and daily values of gage height, velocity, 

correction values, shift adjustments, discharge, reservoir contents, and other parameters resulting from the 

processing of the gaging station records.

• All approved algorithms, rating curves, shift curves, 

and other transformation information required for the 

processing of the records.

• All documents specific to a gaging station, such as station descriptions, station analyses, station manuscripts, 

level summaries, and comment files.

19. Quality Assurance and Quality Control

Quality assurance and quality control (QA/QC) is the process of performing specific tasks that ensure that the input data, 

algorithms, transformations, computations, and final results are 

complete and accurate to the greatest extent possible. Much of 

the QA/QC process is automatic in that many arithmetic checks, 

cross checks, and logic checks are programmed into the elec

equally is important that the QA/QC process and fi

documented. For streamflow and other surface-wat

stations, the documentation traditionally has been k

annual station analysis. The preparation of a station 

described in section 15.3. Automation and electronic 

provides an easy and efficient means by which data 

mation can be supplied to the writer of the station a

number of different reports and information items t

used for this purpose are described in the station an

tion (15.3). Some of these reports may be useful as Q

umentation.

In summary, the quality-assurance and quality-

cess is a continuous process that starts when data a

in the field, and continues throughout the data and i

processing procedure. This section of the report doe

specific QA/QC tasks because these are imbedded 

of the many steps required to produce a surface-wa

20. Summary

The USGS has been using automated data-pro

methods in various electronic systems to process su

records since about 1963. This report describes stan

the processing, computation, and analysis of stream

records using modern electronic computer methods

tional USGS methodology for streamflow data coll

analysis has been incorporated into these standards 

est extent possible. Although these standards are in

use primarily by the USGS, they may be used by o

zations doing similar work. In addition, the high sp

satility of present-day computers allow for the desig

tronic processing system that offers many new oppo

expand and improve on the ways that some traditio

methods have been applied.

Surface-water data and surface-water informa

defined for this report to distinguish between a vari

measured and cannot be repeated (data), and a vari

computed or changed in some way (information). F

a measurement of gage height or a measurement of 

considered data. Whereas, a computed value of dis

cross-section area is considered information. The te

value is defined as data or information that is assoc
and store all times in Universal Coordinated Time (UTC). Field 

measurement data and information, such as discharge measurements, gage datum leveling, crest-stage gage data, and crosssection data also must be entered to the electronic processing 

system. These data and information may require manual entry 

from paper field notes or from electronic field notebooks.

All unit values entered to the electronic processing system 

should be verified and edited, if necessary. However, an electronic copy of the original values should be archived, and all 

data processing should be performed on a copy of the original 

values. Times and dates should be verified, and corrections and 

adjustments made, as necessary, to account for clock errors. 

UTC adjustments should be made following the time and date 

corrections. Parameter values, such as gage height, should be 

verified by making various comparisons such as threshold comparisons, rating-curve comparisons, direct-reading comparisons, and graphical comparisons. Corrections to parameter 

values should be made for any datum or instrument errors that 

may have occurred.

Field measurement data and information that are entered to 

the electronic processing system require various checks to 

verify correctness. Some field measurements also require special analyses for use in other parts of the electronic processing 

system. Discharge measurements should be checked for arithmetic errors, and for logic and consistency. The standard error 

of discharge measurements should be computed if applicable 

methods can be used. Shift analysis should be made according 

to the methods defined for stage-discharge ratings, slope ratings, rate-of-change-in-stage ratings, and velocity-index ratings. Special procedures for verification and analysis apply to 

some measurements, such as ice measurements, measurements 

with vertical angles, moving boat measurements, acoustic Doppler current profiler measurements, indirect measurements, 

weir and flume measurements, tracer-dilution measurements, 

volumetric measurements, and discharge estimates. Specific 

rounding and significant figures are defined for all discharge 

measurements.

Rating curves are an integral part of the computation of 

most streamflow records. The electronic processing system 

should accommodate the use of various rating curve types, 

including stage-discharge, stage-area, velocity-index, stagevelocity factor, stage-fall, fall ratio and discharge, stage-1/USc,

and elevation-reservoir contents. In addition, control structures 

require a number of different rating curves and equations. Rat

require temporary adjustments, called shift corrections

ings to which shifts may be applied are stage-discharg

velocity-index. All other ratings should be redrawn.

Primary computations are the functions that conv

data, such as gage height or velocity data into unit, da

monthly, and annual values of discharge or other outpu

eters.This part of the process should be carried out by 

tronic processing system with minimal user interaction

should produce tables, graphs, and files of information 

commonly are referred to as primary output. Each stat

has a specific primary computation process that produ

cific information. However, the primary output for mos

stations is to calculate stream discharge (unit, daily, m

and annual values) and some related information such 

or velocity. Primary computations for reservoir station

duce reservoir elevation and contents. Primary compu

for tide stations produce various tidal statistics such as 

low tide elevations.

Other functions that the electronic processing sys

should provide to the user include hydrograph plotting 

daily and unit values, and automatic determination of 

values such as maximum and minimum stages and dis

for a water year and calendar year. The electronic proc

system should provide navigation paths that guide the 

through routine computation and analysis of the stream

records for the various gage types. In order to produce c

records of daily streamflow and other parameters, esti

methods such as the hydrograph and climatic compari

method, discharge-ratio method, regression method, w

budget method, mathematical translation method, and 

routing method are functions of the electronic process

tem.

Various monthly and annual statistics should be c

for streamflow stations, reservoir stations, and tide sta

tions.These statistics should conform to the traditional 

that currently are published in USGS annual data repo

electronic processing system should provide the user a 

enter and archive documents such as the record process

book, station descriptions, station analyses, and station 

scripts. Quality assurance and control should be a con

process in the electroic processing system from data c

to archiving. Finally, the electronic processing system 

allow easy access to the computed records for review, a

finalization, and archiving.
Dempster, George R., Jr., National water information system 

user’s manual, v. 2, chap. 3, Automated data processing system: U.S. Geological Survey Open-File Report 90–116.

Fulford, J.M. (1993), User’s guide to hydraulic information 

exchange program: A computer program for hydraulic properties computations. On file with the U.S. Geological Survey, 

at Stennis Space Center, MS 39529.

Hubbard, E.F., 1992, Policy recommendations for management 

and retention of hydrologic data of the U.S. Geological Survey: U.S. Geological Survey Open-File Report 92–56, 32 p.

Hutchison, N.E., and others, 1977, WATSTORE user's guide, 

v. 5, chapters I–IV: U.S. Geological Survey Open-File 

Report 77–729–I, 230 p.

Johnson, L.H., 1952, Nomography and empirical equations: 

New York, John Wiley, 150 p.

Kennedy, E.J., 1983, Computations of continuous records of 

streamflow: U.S. Geological Survey Techniques of WaterResources Investigation Report, book 3, chap. A13, 53 p.

individual discharge measurements: U.S. Geolog

Open-File Report 92–144, 21 p.

Schaffrannek, R.W., Baltzer, R.A., and Goldberg, D

A model for simulation of flow in singular and in

nected channels: U.S. Geological Survey Techni

Water Resources Investigation Report, book 7, c

110 p.

Shearman, J.O., 1990, User's manual for WSPRO—

model for water surface profile computa tions: Fe

way Administration Publication No. FHWA–IP–

177 p.