Stream Gauge Data
Some sites exist where a series of stream flow observations have been made and stream gauge data obtained. You may use these data, with certain qualifications, to develop a peak discharge versus frequency relation for peak runoff from the watershed.
Peak Stream Flow Frequency Relation. Stream gauging stations recording annual peak discharges have been established at 936 stream flow-gauging stations around Texas. If the gauging record covers a sufficient period of time, it is possible to develop a peak stream- flow frequency relation by statistical analysis of the series of recorded annual maximum flows. You can then use such relationships productively in several different ways:
♦ If the facility site is near the gauging station on the same stream and watershed, you can use the discharge directly for a specific frequency (T-year discharge) from the peak stream flow frequency relationship.
♦ If the facility site is within the same basin but not proximate to the gauging station, transposition of gauge analysis results is possible.
♦ If the facility site is not within a gauged basin, you can develop the peak-flow flood- frequency from data from a group of several gauging stations based on either a hydrologic region (e.g., regional regression equations), or similar hydrologic characteristics (e.g., Texas Interactive Flood Frequency Method.)
Curve Development Stipulations. It is possible to develop a peak stream flow versus
frequency curve for a site by statistical means provided you meet the following stipulations:
♦ Sufficient peak discharge sample -- A sufficient statistical sample of annual peak discharges must be available. This usually means a minimum of eight years of data.
Some statisticians prefer a sample of 20 or more years. However, 20 years usually is not realistic for available observation periods, and fewer observations are often used as a basis for an analysis.
♦ No significant change in channel/basin -- No significant changes in the channel or basin should have taken place during the period of record. If significant changes did occur, the resulting peak-stream flow frequency relation could be flawed. The urbanization character of the watershed must not be likely to change enough to affect significantly the characteristics of peak flows within the total time of observed annual peaks and anticipated service life of the highway drainage facility. No means of accommodating future changed characteristics of a watershed within the statistical methods are used in highway hydrology.
♦ No physical flow regulations existing -- A series of observed data from a watershed within which there have been, are, or will be physical flow regulations is not a sound basis for a hydrologic analysis.
♦ Data representative of watershed -- The measured data must be representative of the subject watershed, either directly or by inference.
Stream Gauge Record Sources. Generally, for department application, the designer will need to acquire a record of the annual peak flows for the appropriate gauging station. The following sources provide stream gauge records:
♦ U.S Department of the Interior, United States Geological Survey Water Resources Data—Texas, Surface Water. These are prepared annually and contain records for one water year per publication. As a result, abstracting annual peaks for a long record is time-consuming
♦ International Boundary and Water Commission water bulletins
♦ the USGS web site
Applicability and Limitations. For highway drainage purposes, a statistical analysis of stream gauge data is typically applied only in those instances where there is adequate data from stream gauging stations. The definition of adequate data comes from U.S. Geological Survey (USGS) practice and is illustrated in the table below.
Recommended Minimum Stream Gauge Record Lengths
Desired Frequency (Years) Minimum Record Length (Years)
10 8
25 10
50 15
100 20
If adequate data are not available, base the design peak discharge on analyses of data from several stream flow-gauging stations.
In some cases, a site needing a design peak discharge is on the same stream and near an active or discontinued stream flow-gauging station with an adequate length of record (see the “Recommended Minimum Stream Gauge Record Lengths” table). Currently, the active and discontinued gauging station records for Texas are available for access on the USGS web site for Texas. See U.S. Geological Survey for more information.
Having determined that a suitable stream gauge record exists, you need to determine if any structures or urbanization may be affecting the peak discharges at the design site. Consider the following guidelines:
♦ Period of record similar to design site -- The period of record for the gauging station’s annual peak discharges should represent the same or similar basin conditions as that of the design site. Therefore, you should exclude from the analysis any gauged peak discharges not representing the basin conditions for the design site.
♦ Factors affecting peak discharge -- The most typical factors affecting peak discharges are regulation by urbanization and reservoirs. Densities of impervious cover less than 10 percent of the watershed area generally do not affect peak discharges. The existence in the watershed of a major reservoir or many smaller reservoirs or flood control structures can greatly affect the runoff characteristics.
♦ Length of record -- You should adjust the length of record to include only those records that have been collected subsequent to the impoundment of water by reservoirs and subsequent to any major urbanization. If the resulting records then become too short, do not use the procedures in this section.
Log Pearson Type III Distribution and Procedure
♦ Numerous statistical distribution methods establish peak discharge versus frequency relations. The Log Pearson Type III statistical distribution method has gained the most widespread acceptance and is recommended by the US Water Resources Council Bulletin #17B. An outline of this method follows; however, you are not limited to using only this method, especially if the resulting discharge frequency relation does not seem to fit the data.
The Log-Pearson Type III method for the statistical analysis of gauged flood data applies to just about any series of natural floods. Three statistical moments are involved in the
analysis.
♦ The mean is approximately equal to the logarithm of the two-year peak discharge. (See Equation 5-33)
♦ The standard deviation can be compared to the slope of the plotted curve. (Although, with the consideration of the third moment, skew, there is no single slope to the curve.
See Equation 5-34.)
♦ The skew represents the form of curvature to the plotted curve.
For a negative skew, the flood-frequency curve is concave (downward), and for a positive skew, the curve is convex (upward). If the skew is zero, the following occurs:
♦ the plotted relation forms a straight line
♦ the distribution is defined as normal
♦ the standard deviation becomes the slope of that straight line
The significance of the skew becomes especially important in the estimation of floods based upon extrapolated curves.
1,000 10,000 100,000
1 10 100
Return Interval (years)
Discharge (cfs)
Figure 5-15. Skew of Discharge versus Frequency Plots
Flooding is often erratic in Texas such that a series of observed floods may include annual- peak discharge rates that do not seem to belong to the population of the series. The values may be extremely large or extremely small with respect to the rest of the series of
observations. Such values may be “outliers” that you should possibly exclude from the set of data to be analyzed. Additionally, you can make adjustments to incorporate historical data.
The following steps outline the Log-Pearson type III analysis procedure:
1. Acquire and assess the annual peak discharge record. The record should comprise only one discharge (maximum) per year. Note that the USGS water year is October to September.
2. Calculate the logarithm of each discharge value.
3. Use Equation 5-33, Equation 5-34, and Equation 5-35 to calculate the statistics.
4. Use Equation 5-36 to calculate the logarithm of the discharge for each frequency.
5. Plot discharge versus frequency on standard log probability paper.
6. Consider adjusting the calculations to accommodate a weighted skew and accommodating outliers in the data.
Equation 5-33: Q = X
L ồN
Equation 5-34:
( )
S =
X - X N
L N -1
2 ồ
ỡồ
í ùù
ợ ùù
ü ý ùù
þ ùù
2 1
2
Equation 5-35: ( ) ( )( ) ( )
( )( )
G = N X N X X X
N N -1 N 2 S
S
2 3 2
L
ồ − ồ ồ 3 + ồ
−
3 2 3
where:
N = number of observations
X = logarithm of the annual peak discharge
SL = standard deviation of the logarithms of the annual peak discharge GS = coefficient of skew of log values (station skew).
Equation 5-36:
log Q = QL + KSL
where:
QL= mean of the logarithms of the annual peak discharges Q = flood magnitude (cfs or m3/s)
K = a frequency factor for a particular return period and coefficient of skew (values of K for different coefficients of skew, G, and return periods are given in Hydrology).
Skew
The three methods for determining the value of the skew coefficient for the Log Pearson Type III curve fit are as follows:
♦ Gauge data -- Calculate the station skew directly from the gauge data using Equation 5-35. This value may not well represent the skew of the data if the period of record is short or if there are extreme events in the period of record.
♦ Frequency factor -- Figure 5-16 shows the value of generalized skew coefficients across Texas that you may use to determine the frequency factor (K) in place of the station skew.
♦ Weighted skew -- You may compute a weighted skew. Refer to Bulletin 17B for the method to compute a weighted skew.
Note: The mean square error for the generalized skew is 0.35, which replaces the value of 0.55 presented in Bulletin 17B.
Figure 5-16. Generalized Skew Values for Texas
Accommodating Outliers in the Data
Frequency Curve Shape. The distribution of all the annual and historical peak discharges determines the shape of the frequency curve and thus the design-peak discharges. The shape of the frequency curve generated by a Log-Pearson Type III analysis is symmetrical about the center of the curve. Therefore, the distribution of the higher peak discharges affects the shape of the curve, as does the distribution of the lower peak discharges.
Shape Based on Larger Peaks. Most peak stream flow frequency analyses require the larger recurrence-interval peaks more often than those do for the lower recurrence intervals. Most design peaks, for example, are based on 50-year or 100-year recurrence intervals rather than two-year or five-year intervals. Therefore, it is more desirable to base the shape of the frequency curve on the distribution of the larger peaks. You accomplish this by eliminating from the analyses peak discharges that are lower than a low-outlier threshold. The value for the low-outlier threshold, therefore, should exclude those peaks not indicative of the
distribution for the higher peaks. You can subjectively choose this value by reviewing the sequentially ranked values for all of the peak discharges used in the analysis.
Example of Low Outliers. For example, the lowest sequentially ranked peak discharges for a station, in cubic feet per second (cfs) or cubic meters per second (m3/s), are as follows: 0, 10, 25, 90, 450, 495, 630, 800, 1050. The largest difference between sequential values for these discharges is 360 cfs or m3/s, which is the difference between 90 and 450 cfs or m3/s.
Therefore, the distribution of the peak discharges substantially changes below the value of 450 cfs or m3/s, which could be used as the low value threshold.
Low-Outlier Threshold Identification. Equation 5-37 provides a means of identifying the low outlier threshold for a set of data as follows:
Equation 5-37: LOT = 10(aQL+bSL+cG d+ ) where:
LOT = estimated low-outlier threshold (cfs)
QL = mean of the logarithms of the annual peak discharge (see Equation 5-33) SL = standard deviation of the logarithms of the annual peak discharge (see Equation
5-34)
G = coefficient of skew of log values (station skew, see Equation 5-35).
a = 1.09 b = -0.584 c = 0.140 d = -0.799
Note: This equation was developed for English units only and does not currently have a metric equivalent.
High-Outlier Threshold Description. High outlier thresholds represent extremely high peak discharges—those with a recurrence interval larger than indicated by the period of record for
a station. For example, a 100-year peak discharge could be gauged during a 10-year period of record. The frequency curve thus would be unduly shaped by the 100-year peak.
High-Outlier Identification. The USGS has made efforts to identify high outliers, referred to as historical peaks, by identifying and interviewing long-term residents living proximate to the gauging stations.
♦ In many cases, residents have identified a particular flood peak as being the highest since a previous higher peak. These peaks are identified as the highest since a specific date.
♦ In other cases, residents have identified a specific peak as the highest since they have lived proximate to the gauging station. Those peaks are identified as the highest since at least a specific date. The historical peaks may precede or be within the period of gauged record for the station.
Use of Peak Discharge Table. All known historical peak discharges and their associated gauge heights and dates appear in Hydrology and on the USGS web site.
♦ You should use the lowest peak discharge identified on this table for each station as the value for the high-outlier threshold.
♦ You should use the number of years from the highest since (or highest since at least) date to the last year of gauged record as the length of the historical record.
♦ For some stations, however, a historical-peak discharge may have been gauged without knowledge of its historical significance. When this is suspected for a station, you should review and compare the dates for historical peaks from nearby stations to dates of floods for the suspect station. These dates and historical periods may apply to stations where this information is absent.
Recomputation of Statistics. Having identified appropriate outliers, you should re-compute the statistics (Equation 5-33 through Equation 5-37) using a data set that excludes values beyond the established outlier thresholds.
Transposition of Data
You may estimate peak discharge for sites near gauged sites by transposition of stream gauge data by scaling the discharge by a ratio of the drainage areas raised to an exponent of 0.7. You can best use this method as a check of other methods rather than the primary means of estimating design discharge. Additionally, you can repeat this procedure for each
available nearby watershed and average the results. The following presents an example using the results from three sites, as shown in the following table:
Example of Transposition
Watershed Q25 (cfs) Area (sq. mi.)
Gauged watershed A 62000 737
Gauged watershed B 38000 734
Gauged watershed C 45000 971
Ungauged watershed D ? 450
Notes: Because Texas gauges use English measurement units, the following examples are offered in English only:
Gauged watershed A: 62,000(450/737)0.7 =43,895cfs Gauged watershed B: 38,000(450/734)0.7 =26,980cfs Gauged watershed C:45,000(450/971)0.7 =26,266cfs
Gauged watershed D: (43,895 + 26,980 + 26,266) / 3 = 32,380 cfs.
Chapter 5 — Hydrology Equations
Section 11