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  • While measured flows provide the best data for design purposes, it is not practical to gage all rivers and streams in the state. A set of equations have been developed by the USGS to calculate flows for drainage basins that do not have a streamflow gage. The equations were developed by performing a regression analysis on streamflow gage records to determine which drainage basin parameters are most influential in determining peak runoff rates.

    The equations break the state up into nine unique hydrologic regions. A map of the regions can be found in Appendix 2-2. The various hydrologic regions require different input variables so the designer should determine which set of equations will be used before gathering data for the analysis. Appendix 2-2 also contains precipitation information that is required input for many of the equations. Other input parameters such as total area of the drainage basin, percent of the drainage basin that is in forest cover, and percent of the drainage basin that is in lakes, swamps, or ponds will need to be determined by the designer through use of site maps, aerial photographs, and site inspections.

    The equations are listed in Figures 2-7.1 through 2-7.9. Each figure contains one set of equations for a hydrologic region of the state. Each figure also lists the statistical accuracy of the individual equations and describes the required input parameters for the equations and their limits of usage. The designer should be careful not to use data that is outside of the limits specified for the equations since the accuracy of the equations is unknown beyond these points.

    The designer must be aware of the limitations of these equations. They were developed for natural basins so any drainage basin that has been urbanized should not be analyzed with this method. Also any river that has a dam and reservoir in it should not be analyzed with these equations. Finally, the designer must keep in mind that due to the simple nature of these equations and the broad range of each hydrologic region, the results of the equations contain a fairly wide confidence interval, represented as the standard error.

    The standard error is a statistical representation of the accuracy of the equations. Each equation is based on many rivers and the final result represents the mean of all the flow values for the given set of basin characteristics. The standard error shows how far out one standard deviation is for the flow that was just calculated. For a bellshaped curve in statistical analysis, 68 percent of all the samples are contained within the limits set by one standard deviation above the mean value and one standard deviation below the mean value. It can also be viewed as indicating that 50 percent of all the samples are equal to or less than the flow calculated with the equation and 84 percent of all samples are equal to or less than one standard deviation above the flow just calculated.

    The equations were developed with data ranging through the 1992 water year. They represent updates to the USGS regression equations developed for Washington State in 1973 and the designer should disregard the previous version of the equations.

    The equations are only presented in English units. While WSDOT is in the process of converting to metric units, the equations were developed by the USGS which is not actively converting to metric units. In the interest of keeping the equations in their original form, no metric conversion was performed for this manual. To obtain metric flow data, the designer should input the necessary English units data into the appropriate regression equation and then multiply the results by 0.02832 to convert the final answer to cubic meters per second.

    The OSC Hydraulics Branch has a computer program available for distribution that does the calculations for these equations.

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  • The size of the drainage basin is one of the most important parameters regardless of which method of hydrologic analysis is used. To determine the basin area, select the best available topographic map or maps which cover the entire area contributing surface runoff to the point of interest. Outline the area on the map or maps and determine the size in square meters, acres, or square miles (as appropriate for the specific equations), either by scaling or by using a planimeter. Sometimes drainage basins are small enough that they fit entirely on the CADD drawings for the project. In these cases the basin can be digitized on the CADD drawing and calculated by the computer. Any areas within the basin that are known to be non-contributing to surface runoff should be subtracted from the total drainage area.

    The USGS has published two open-file reports titled, Drainage Area Data for Western Washington and Drainage Area Data for Eastern Washington. Copies of these reports can be obtained from the OSC Hydraulics Branch and the Regional Hydraulics Contacts. These reports list drainage areas for all streams in Washington where discharge measurements have been made. Drainage areas are also given for many other sites such as highway crossings, major stream confluences, and at the mouths of significant streams. These publications list a total of over 5,000 drainage areas and are a valuable time saver to the designer. The sites listed in these publications are usually medium sized and larger drainage basin areas. Small local drainage areas need to be determined from topographic maps as outlined above.

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  • The Washington State Department of Transportation (WSDOT) Olympia Service Center (OSC) Hydraulics Branch uses several methods of determining runoff rates and/or volumes. Experience has shown them to be accurate, convenient, and economical. The following methods will be discussed in detail in subsequent sections of this chapter

    1. The Rational Method
    2. The Santa Barbara Urban Hydrograph (SBUH) Method
    3. Published Flow Records
    4. United States Geological Survey (USGS) Regression Equations
    5. Flood Reports
    Two other methods, documented testimony and high water mark observations, may be used as back-up material to confirm the results of the above statistical and empirical methods. Where calculated results vary from on-site observations, further investigation may be required. The additional two methods are:
    6. Documented Testimony
    Documented testimony of long-time residents should also be given serious consideration by the designer. The engineer must be aware of any bias that testifying residents may have. Independent calculations should be made to verify this type of testimony. The information that may be furnished by local residents of the area should include, but not be limited to the following:
    a. Dates of past floods.
    b. High water marks.
    c. Amount of drift.
    d. Any changes in the river channel which may be occurring (i.e., stability of streambed, is channel widening or meandering?).
    e. Estimated velocity.
    f. Description of flooding characteristics between normal flow to flood stage.
    7. High Water Mark Observations

    Sometimes the past flood stage from a drainage area may be determined by observing high water marks on existing structures or on the bank of a stream or ditch. These marks along with other data may be used to determine the discharge by methods discussed in the Open Channel Flow chapter or the Culverts chapter of this manual.
    Additional hydrologic procedures are available including complex computer models which can give the designer accurate flood predictions. However, these methods, which require costly field data and large amounts of data preparation and calculation time, can rarely be justified for a single hydraulic structure. The OSC Hydraulics Branch should be contacted before a procedure not listed above is used in a hydrologic analysis. For the sake of simplicity and uniformity, the OSC Hydraulics Branch will normally require the use of one of the first five of the seven methods listed above. Exceptions will be permitted if adequate justification is provided.

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