U.S. Department of the Interior U.S. Geological Survey Rating Stability, and Frequency and Magnitude of Shifts, for Streamgages in Virginia Through Water Year 2013 Scientific Investigations Report 2017–5137 By Terence Messinger and Robert W. Burgholzer https://doi.org/10.3133/sir20175137 Abstract The U.S. Geological Survey, in cooperation with the Virginia Department of Environmental Quality, has quantified several measures of rating stability and the frequency and magnitude of changes to ratings through time for 174 real-time continuous streamgages active in Virginia as of September 30, 2013. Generalized additive models (GAMs) were fitted through all available flow measurements for all the streamgages in Virginia’s real-time network as of September 30, 2013, with at least 20 flow measurements with positive flow values. For each measurement with a positive flow value, residuals from the GAM curve were calculated. Time series of these residuals were used to identify major changes to the control (the stream feature or features which control the relation between stage and flow); the measurements in the periods of equilibrium between major changes were assigned to rating families. Of the 127 rating families that were identified as being distinct at sites, documented explanations were found for 67 of them. The most common reasons for the control to change enough to warrant a new rating family are moving the streamgage (28 times), floods (26 times), and construction activities (13 times). Provisional flow data from any streamgage that has recently experienced a major flood, regardless of historical stability, are more uncertain than usual until post-flood evidence emerges that the rating is stable, or if the rating has changed, until it is known to be well defined. A direct comparison between provisional flow data (those data originally displayed on the web in near-real time) and flow data approved for publication following subsequent flow measurements and review could not be made because provisional flow data have not been archived. As a substitute, alternative flow (AltFlow) tables were constructed for periods with complete records of shifts and ratings. Alternate flows consist of Qsame, the flow value from the shifted rating table used to compute the daily flow value at the time of the most recent flow measurement that corresponds to the gage height of each day’s daily flow value, and Qprev, the flow value from the shifted rating table in effect at the time of the previous flow measurement that corresponds to the gage height of each day’s daily flow value. Several metrics that summarize AltFlow tables were computed and evaluated; particular importance was given to how well the metrics agreed with the descriptive stability class developed from interviews with hydrographers. Of these stability metrics, at least four were determined to be meaningful and to represent different aspects of control stability that might be relevant to water managers: total root mean square error between log-transformed Qprev and Qsame, percentage of days when the difference between Qprev and Qsame is greater than (>) Qsame, the sum of absolute AltFlow error divided by total flow, and percentage of days with zero difference between Qprev and Qsame. Three other meaningful metrics of control stability or provisional flow-data quality were computed: R2 (coefficient of determination) of GAMs from the flow measurements, percentage of total estimated days, and percentage of estimated days in the winter. Correlations among metrics varied, indicating they responded to different aspects of control stability. Relations among the various stability metrics and quantitative basin and site characteristics were weak. Although quantitative relations between stability metrics and basin and site characteristics were all weak, some common patterns still emerged. Controls and ratings on large streams [>500-square mile (mi2) drainage area] and at high elevations (> 1,000 feet) were more likely to be stable than controls and ratings on small streams (less than (<) 100-mi2 drainage area) and at low elevations (<500 feet). There were exceptions to both generalizations, and streamgages that were intermediate in both characteristics varied widely in stability. Typical timing of record computation changed during water years 1991–2013. From 1991 through 2001, the median number of days between the start date of the shift and the date it was created fluctuated between about 240 and about 300 days and decreased by about 4 months from 2001 to 2002. Only in 2012 and 2013 did one-half of the shifts have a delay of about 60 days between start date and final modification. List of files Report Plates 1. A, Long-term stage-flow relations at selected streamgages in Virginia with a generalized additive model smoother, B, seasonal variation of relations between residual of flow and date with a LOESS smoother, and C, seasonal variation of relations between residual of flow and Julian date with a LOESS smoother.....................................................................................available online 2. Patterns of variation in, A, long-term stage-flow relations at selected streamgages in Virginia, B, residual of flow and date with a LOESS smoother, and C, residual of flow and Julian date with a LOESS smoother...........................................available online 3. AltFlow hydrographs for four selected streamgages in Virginia, water years 1991–2013.............................................................................................................available online 4. Matrix of proposed stability metrics developed using daily flow, shifted ratings, and flow measurements for streamgages in Virginia, water years 1991–2013.............................................................................................................available online 5. Scatterplot matrixes of stage-flow relation stability metrics in relation to selected basin characteristics for A, 64 plots and, B, 88 plots, for streamgages in Virginia, water years 1991–2013.......................................................................................available online Tables 8. Hydrographer descriptions of controls for streamgages in Virginia at which real-time flow data were collected as of September 30, 2013, and descriptions of associated features of interest....................................................................available online 20. Summary of selected rating stability metrics for streamgages in Virginia, water years 1991–2013.......................................................................................available online 24. Average of daily percent errors for flow in Virginia streams, by month and percentile range..........................................................................................available online 25. Root-mean-square error of AltFlows and number of days of record for streamgages on Virginia streams by month and percentile of monthly flow, water years 1991–2013.............................................................................................................available online 26. Proportion of days when the difference between Qprev and Qsame was zero at streamgages in Virginia, by month, 1990–2013..........................................available online Appendixes Appendix 1. Plots for real-time streamgages in Virginia is available online at https://doi.org/10.3133/sir20175137 Appendix 3. UNIX shell scripts used to develop AltFlow record is available online at https://doi.org/10.3133/sir20175137 Appendix 4. Plots showing daily time series of Qsame and Qprev is available online at https://doi.org/10.3133/sir20175137 For users who need to quickly locate graphs for particular stations provided in the PDF of the plates or appendixes, please use the "find" command (control-f on Windows or cmd-f on Mac) available in Adobe Acrobat or Adobe Acrobat Reader. Searching for either the station identifier or a (partial) station name will allow the program to quickly reposition the page near the required plot.