Data Series 247

Summary of Percentages of Zero Daily Mean Streamflow for 712 U.S. Geological Survey Streamflow-Gaging Stations in Texas Through 2003

By William H. Asquith, Joseph Vrabel, and Meghan C. Roussel


Abstract

Analysts and managers of surface-water resources might have interest in the zero-flow potential for U.S. Geological Survey (USGS) streamflow-gaging stations in Texas. The USGS, in cooperation with the Texas Commission on Environmental Quality, initiated a data and reporting process to generate summaries of percentages of zero daily mean streamflow for 712 USGS streamflow-gaging stations in Texas. A summary of the percentages of zero daily mean streamflow for most active and inactive, continuous-record gaging stations in Texas provides valuable information by conveying the historical perspective for zero-flow potential for the watershed. The summaries of percentages of zero daily mean streamflow for each station are graphically depicted using two thematic perspectives: annual and monthly. The annual perspective consists of graphs of annual percentages of zero streamflow by year with the addition of lines depicting the mean and median annual percentage of zero streamflow. Monotonic trends in the percentages of zero streamflow also are identified using Kendall’s τ. The monthly perspective consists of graphs of the percentage of zero streamflow by month with lines added to indicate the mean and median monthly percentage of zero streamflow. One or more summaries could be used in a watershed, river basin, or other regional context by analysts and managers of surface-water resources to guide scientific, regulatory, or other inquiries of zero-flow or other low-flow conditions in Texas.

Introduction

Analysts and managers of surface-water resources might have interest in the zero-flow potential for U.S. Geological Survey (USGS) streamflow-gaging stations in Texas. To facilitate information transfer, this report provides a historical perspective of zero-flow potential for most of the active and inactive, continuous-record streamflow-gaging stations in Texas. Zero-flow potential refers to the proportion of daily mean streamflow values equal to zero; an alternative interpretation is that the proportion is the probability of zero flow. However, for purposes of this report the zero-flow potential is best interpreted as the percentage of zero daily mean streamflow for a given time period.

A graphical and statistical history of the percentages of zero daily mean streamflow for gaging stations in Texas provides valuable information by conveying the historical perspective for zero-flow potential for a given watershed, in particular, and Texas, in general. Therefore, in 2006 the USGS, in cooperation with the Texas Commission on Environmental Quality (TCEQ), initiated a data and reporting process to generate station-specific summaries of percentages of zero daily mean streamflow in Texas. This report includes graphical depictions of percentages of zero daily mean streamflow for 712 USGS streamflow-gaging stations in Texas with at least 1 year of record through water year 2004 (fig. 1).

Streamflow-gaging stations that monitor spring flow or stage (water level) only were not used. Further, partial-record streamflow-gaging stations were not used because the full range of streamflow at each station was needed. Partial-record streamflow-gaging stations are sites where discrete measurements of streamflow are obtained over a period of time without continuous data being recorded. These stations intrinsically do not monitor the entire range of streamflow. The 712 stations considered in this report were analyzed in Asquith and others (2006) for an evaluation of the drainage-area ratio method in Texas. A listing of the station numbers, station names, and ancillary information is available in Asquith and others (2006, table 1). A companion report (Asquith and others, 2007) considers four selected annual statistics of daily mean streamflow for the same stations and streamflow data.

The data for the 712 stations were obtained from the USGS National Water Information System (U.S. Geological Survey, 2005). The stations have at least 1 year of daily mean streamflow record through the 2004 water year. A water year is the 12-month period between October 1 and September 30. A water year is designated as the calendar year in which it ends. Thus, the year ending September 30, 2004, is called the "2004 water year." The earliest year of streamflow record is 1898. The data were trimmed to the last complete calendar year (2003). For the analysis reported here the calendar year context is used for statistical computations. Therefore, the last date of daily mean streamflow is December 31, 2003. The total number of daily values processed is 7,748,449.

Summary of Percentages of Zero Daily Mean Streamflow for Texas

The summary of percentages of zero daily mean streamflow for each of the 712 stations is provided in figures 2--713 (at end of report). Each figure consists of two thematic perspectives: annual and monthly. The annual perspective is shown in the top graph of each the figure, and the monthly perspective is shown in the bottom graph. The monthly perspective facilitates seasonal interpretations of zero-flow potential for a given watershed. Above each figure is the text annotation "U.S. Geological Survey streamflow-gaging station #," where # is the eight-digit station identification number. This annotation is included to confirm that the pairing of the two graphs and the figure caption are correct. Some stations have substantial gaps (measured in years) such as those shown in figure 588 on page 592. No special treatment of the streamflow data was applied for stations with gaps in the period of record.

Annual Perspective of Percentages of Zero Streamflow

The annual perspective consists of four components. First, the annual percentages of zero streamflow are plotted as n open circles (n represents the number of data points) in the top graph in figures 2--713. Each percentage was computed by totaling the number of zero-flow days for the year and dividing by the number of days of observed record for the calendar year. For a full year of record, the number of days for the year was 365 (or 366 for leap years). For the summaries reported here, incomplete years are plotted as well with requisite change in sample size. Second and third, the mean annual percentage and median annual percentage of zero streamflow of the n data points were computed and are illustrated as solid and dashed horizontal lines, respectively. The numeric values of mean and median annual percentage of zero streamflow are shown in the explanation of the graph. The fourth component is the assessment of a monotonic trend in the data.

For the fourth component, Kendall’s τ was computed using an integrated statistical computing environment (The MathWorks, 2006) for the n annual percentages of zero streamflow. The p-value for τ also is shown. Hollander and Wolfe (1973, p. 185--199) and Helsel and Hirsch (1992, p. 212 and 216) provide the background and details of computation. Both τ and the p-value are shown in figures 2--713 to three significant figures, except when there is a perfect decreasing or increasing monotonic relation, in which case the exact τ value of -1 or 1, respectively, is given. P-values less than .001 are expressed as <.001.

Kendall’s τ measures the strength of the monotonic relation between time and annual percentage of zero streamflow. Kendall’s τ is nonparametric, meaning that the statistic is based on the ranks of the data and not the actual data values. Positive τ values indicate that occurrences of zero streamflow increase with time for the period of record, and negative τ values indicate that occurrences of zero streamflow decrease with time for the period of record. Perfect monotonically decreasing relations result in τ values of exactly -1; conversely, perfect monotonically increasing relations result in τ values of exactly 1. The p-value is a measure of the strength or statistical significance of the relation; small p-values (p-value ≤ .02 in this report) indicate a strong relation. If all the data values are equal, such as exactly 0 or 100 percent, then τ and the p-value are listed as "--". Kendall’s τ and the p-value also are listed as "--" for stations with only 1 year of record.

For stations for which Kendall’s τ has a p-value less than or equal to 0.02, a Theil trend line is superimposed on the top graph as a solid grey line. Thus, the Theil line is not drawn on all the top graphs of the figures. The Theil line, as discussed by Hollander and Wolfe (1973, p. 205) and Helsel and Hirsch (1992, p. 266), is a robust estimator of the slope of a linear relation between time and annual percentage of zero flow. The slope is estimated as the median of all unique (n x (n - 1)/2) slopes between individual data points. The purpose of the Theil line is to provide a visual cue that a statistically significant trend in annual percentage of zero streamflow was detected. For many stations on small watersheds or in generally dry parts of Texas, such as station 07227500 (fig. 3 on page 7), the Theil line is drawn, but not visible--it is masked by the mean annual percentage of zero streamflow line (solid horizontal line). The masking occurs because the median pairwise slope is precisely zero.

In regards to the Theil line, the line could represent an over simplification of the relation between time and annual percentage of zero streamflow for individual watersheds. The actual temporal changes in annual percentage of zero streamflow for individual watersheds could indicate curvilinear or even cyclical variations caused by natural or anthropogenic sources.

Monthly Perspective of Percentages of Zero Streamflow

The monthly perspective (bottom graph in figs. 2--713) consists of three components. First, the percentage of zero streamflow for the indicated month for an individual year (calendar year) is shown as a grey circle. Considerable overplotting of these symbols can occur if the percentages of zero flow in a given month are 0 or 100 percent. For example, if the period of record contains 15 months of August, then 15 grey circles are plotted. The percentage for each month was computed by totaling the number of zero-flow days for that month for the period of record and dividing by the number of days of observed record for that month. For the summaries in this report, incomplete months are plotted as well with the requisite change in sample size. The second and third components are the mean and median monthly percentage of zero streamflow for each month and are indicated by the solid and dashed "steps," respectively.

General Discussion

The number of stations summarized in this report is too large for effective discussion and commentary of station-specific results. Conceptually, numerous attributes or factors of a watershed influence the potential for zero daily mean streamflow. These include attributes such as watershed size, climatic setting, geology and soils, and upstream water use or regulation. As a result, specific causes for zero flow for a given station are beyond the scope of this report. However, some general comments can be made to guide analysts.

Some streamflow-gaging stations, such as those with large watersheds or in parts of the State with abundant rainfall, have few or no occurrences of zero daily mean streamflow (for example, the station in fig. 202 on page 206). Other stations, such as those with small drainage areas or in climatically dry parts of the State, consistently experience zero flow (for example, the station in fig. 48 on page 52). Some stations have definite patterns in monthly zero-flow potential (for example, the station in fig. 316 on page 320 or fig. 453 on page 457), whereas other stations do not (fig. 459 on page 463).

Some stations have a statistically significant downward trend in percentage of zero daily mean streamflow, which is indicated by the negatively sloped Theil line (for example, the station in fig. 158 on page 162). Other stations have a statistically significant upward trend, which is indicated by the positively sloped Theil line (for example, the station in fig. 56 on page 60). Although trends are not always indicated, the daily mean streamflow at some stations appears to have been driven toward perennial conditions (such as that in fig. 131 on page 135) or conversely toward ephemeral conditions (such as that in fig. 6 on page 10).

The number of stations with statistically significant positive trends, an increase in the percentage of zero streamflow (drier conditions), is 22 (about 3 percent). The number of stations with statistically significant negative trends, a decrease in the percentage of zero streamflow (wetter conditions), is 60 (about 8 percent). No statistically significant trends were detected for 630 stations (about 89 percent).

Finally, each summary provides a compact visual description of the history of zero-flow potential of daily mean streamflow for the watershed monitored by the USGS streamflow-gaging station. Station-specific discussion of climatic, hydrologic, anthropogenic, and other processes potentially influencing the percentages of zero flow can be made. One or more summaries could be used in a watershed, river basin, or other regional context by analysts and managers of surface-water resources to guide scientific, regulatory, or other inquiries of zero-flow or other low-flow conditions in Texas.

References

Asquith, W.H., Roussel, M.C., and Vrabel, Joseph, 2006, Statewide analysis of the drainage-area ratio method for 34 streamflow percentile ranges in Texas: U.S. Geological Survey Scientific Investigations Report 2006--5286, 34 p., 1 appendix. Available Online

Asquith, W.H., Vrabel, Joseph, and Roussel, M.C., 2007, Summary of annual mean, maximum, minimum, and L-scale statistics of daily mean streamflow for 712 U.S. Geological Survey streamflow-gaging stations in Texas through 2003: U.S. Geological Survey Data Series 248, 721 p. Available Online

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in water resources---Studies in environmental science 49: Amsterdam, Elsevier, 529 p.

Hollander, Myles, and Wolfe, D.A., 1973, Nonparametric statistical methods: New York, John Wiley, 503 p.

The MathWorks, 2006, MATLAB version 7.2.0.232 (R2006a): Natick, Mass.

U.S. Geological Survey, 2005, National Water Information System: accessed in July 2005 at http://nwis.waterdata.usgs.gov/nwis/discharge


For additional information contact:
Director, Texas Water Science Center
U.S. Geological Survey
8027 Exchange Drive
Austin, Texas 78754-4733
 
World Wide Web: http://tx.usgs.gov/
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Last modified: Thursday, 10-May-2007 11:42:33 EDT