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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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  • When available, published flow records provide the most accurate data for designing culverts and bridge openings. This is because the values are based on actual measured flows and not calculated flows. The streamflows are measured at a gaging site for several years. A statistical analysis (typically Log Pearson Type III) is then performed on the measured flows to predict the recurrence intervals.

    The USGS maintains a large majority of the gaging sites throughout Washington State. A list of all of the USGS gages that have adequate data to develop the recurrence intervals and their corresponding flows is provided in Appendix 2-1. In addition to these values, the OSC Hydraulics Branch maintains records of daily flows and peak flows for all of the current USGS gages. Also, average daily flow values for all current and discontinued USGS gages are available through the Internet on the USGS homepage (note that these are average daily values and not peak values).

    Some local agencies also maintain streamflow gages. Typically, these are on smaller streams than the USGS gages. While the data obtained from these gages is usually of high enough quality to use for design purposes, the data is not always readily available. If the designer thinks that there is a possibility that a local agency has flow records for a particular stream then the engineering department of the local agency should be contacted. The OSC Hydraulics Branch does not maintain a list of active local agency streamflow gages.

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  • General

    The rational method is used to predict peak flows for small drainage areas which can be either natural or developed. The rational method can be used for culvert design, pavement drainage design, storm drain design, and some stormwater facility design. The greatest accuracy is obtained for areas smaller than 40 hectares (100 acres) and for developed conditions with large areas of impervious surface (e.g., pavement, roof tops, etc.). Basins up to 400 hectares (1,000 acres) may be evaluated using the rational formula; however, results for large basins often do not properly account for effects of infiltration and thus are less accurate. Designers should never perform a rational method analysis on a basin that is larger than the lower limit specified for the USGS regression equations since the USGS regression equations will yield a more accurate flow prediction for that size of basin.
    The formula for the rational method is:


    Hydrologic information calculated by the rational method should be submitted on DOT Form 235-009 (see Figure 2-4.1). This format contains all the required input information as well as the resulting discharge. The description of each area should be identified by name or stationing so that the reviewer may easily locate each area.

    [nextpage title=‚ÄĚRunoff Coefficients‚ÄĚ]

    The runoff coefficient ‚ÄúC‚ÄĚ represents the percentage of rainfall that becomes runoff. The rational method implies that this ratio is fixed for a given drainage basin. In reality, the coefficient may vary with respect to prior wetting and seasonal conditions. The use of an average coefficient for various surface types is quite common and it is assumed to stay constant through the duration of the rain storm.

    Frozen ground can cause a dramatic increase in the runoff coefficient. When this condition is coupled with heavy rainfall and, perhaps, melting snow, the runoff can be much greater than calculated values that did not account for these conditions. This condition is common for larger basins that are above 300 m (1000 ft.) in elevation and is automatically accounted for in the USGS regression equations. For small basins where the rational method is being used, the designer should increase the runoff coefficient to reflect the reduction in infiltration and resulting increased surface runoff.

    In a high growth rate area, runoff factors should be projected that will be characteristic of developed conditions 20 years after construction of the project. Even though local storm water practices (where they exist) may reduce potential increases in runoff, prudent engineering should still make allowances for predictable growth patterns.

    The coefficients in Figure 2-4.2 are applicable for peak storms of 10-year frequency. Less frequent, higher intensity storms will require the use of higher coefficients because infiltration and other losses have a proportionally smaller effect on runoff. Generally, when designing for a 25-year frequency, the coefficient should be increased by 10 percent; when designing for a 50-year frequency, the coefficient should be increased by 20 percent; and when designing for a 100-year frequency, the coefficient should be increased by 25 percent. The runoff coefficient should never be increased above 0.90.

    Hydrologic information calculated by the rational method should be submitted on DOT Form 235-009 (see Figure 2-4.1). This format contains all the required input information as well as the resulting discharge. The description of each area should be identified by name or stationing so that the reviewer may easily locate each area.

    [nextpage title=‚ÄĚTime of Concentration‚ÄĚ]

    If rainfall is applied at a constant rate over a drainage basin, it would eventually produce a constant peak rate of runoff. The amount of time that passes from the moment that the constant rainfall begins to the moment that the constant rate of runoff begins is called the time of concentration. This is the time required for the surface runoff to flow from the most hydraulically remote part of the drainage basin to the location of concern.

    Actual precipitation does not fall at a constant rate. A precipitation event will begin with a small rainfall intensity then, sometimes very quickly, build to a peak intensity and eventually taper down to no rainfall. Because rainfall intensity is variable, the time of concentration is included in the rational method so that the designer can determine the proper rainfall intensity to apply across the basin. The intensity that should be used for design purposes is the highest intensity that will occur with the entire basin contributing flow to the location where the designer is interested in knowing the flow rate. It is important to note that this may be a much lower intensity than the absolute maximum intensity. The reason is that it often takes several minutes before the entire basin is contributing flow but the absolute maximum intensity lasts for a much shorter time so the rainfall intensity that creates the greatest runoff is less than the maximum by the time the entire basin is contributing flow.

    Most drainage basins will consist of different types of ground covers and conveyance systems that flow must pass over or through. These are referred to as flow segments. It is common for a basin to have flow segments that are overland flow and flow segments that are open channel flow. Urban drainage basins often have flow segments that are flow through a storm drain pipe in addition to the other two types. A travel time (the amount of time required for flow to move through a flow segment) must be computed for each flow segment. The time of concentration is equal to the sum of all the flow segment travel times.

    For a few drainage areas, a unique situation occurs where the time of concentration that produces the largest amount of runoff is less than the time of concentration for the entire basin. This can occur when two or more subbasins have dramatically different types of cover (i.e., different runoff coefficients). The most common case would be a large paved area together with a long narrow strip of natural area. In this case, the designer should check the runoff produced by the paved area alone to determine if this scenario would cause a greater peak runoff rate than the peak runoff rate produced when both land segments are contributing flow. The scenario that produces the greatest runoff should be used, even if the entire basin is not contributing flow to this runoff.

    The procedure described below for determining the time of concentration for overland flow was developed by the United States Natural Resources Conservation Service (formerly known as the Soil Conservation Service). It is sensitive to slope, type of ground cover, and the size of channel. The designer should never use a time of concentration less than 5 minutes. The time of concentration can be calculated as follows:

    Time of Concentration eq

    [nextpage title=‚ÄĚRainfall Intensity‚ÄĚ]

    After the appropriate storm frequency for the design has been determined (see Chapter 1) and the time of concentration has been calculated, the rainfall intensity can be calculated. Designers should never use a time of concentration that is less than 5 minutes for intensity calculations, even when the calculated time of concentration is less than 5 minutes. It should be noted that the rainfall intensity at any given time is the average of the most intense period enveloped by the time of concentration and is not the instantaneous rainfall. The equation for calculating rainfall intensity is:

    Rainfall Intensity eq

    The coefficients (m and n) have been determined for all major cities for the 2-, 5-, 10-, 25-, 50-, and 100-year mean recurrence intervals (MRI). The coefficients listed are accurate from 5-minute duration to 1,440-minute duration (24 hours). These equations were developed from the 1973 National Oceanic and Atmospheric Administration Atlas 2, Precipitation-Frequency Atlas of the Western United States, Volume IX-Washington. The designer should interpolate between the two or three nearest cities listed in the tables when working on a project that is in a location not listed on the table. If the designer must do an analysis with a storm duration greater than 1,440 minutes, the rational method should not be used.

    [nextpage title=‚ÄĚRational Formula Example‚ÄĚ]

    Compute the 25-year runoff for the Olympia watershed shown above. Three types of flow conditions exist from the highest point in the watershed to the outlet. The upper portion is 10.0 hectares of forest cover with an average slope of 0.15 m/m. The middle portion is 2.5 hectares of single family residential with a slope of 0.06 m/m and primarily lawns. The lower portion is a 2.0 hectares park with 450 mm storm sewers with a general slope of 0.01 m/m.

    Rational Formula Example

    [nextpage title=‚ÄĚFigures‚ÄĚ]

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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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  • There are many differences between the hazard maps of USGS and CyberShake,¬†including, procedures of making hazard maps, required computational resources and¬†results [3, 5]. The USGS National Seismic Hazard maps in California region are derived¬†form source models based on seismological data, geological surveys and earthquake¬†rupture models, and the Next Generation Attenuation (NGA) database [8, 9]. The¬†CyberShake hazard map is constructed by physics-based simulations in the 3D velocity¬†model for all potential earthquake ruptures with Mw ‚Č• 6.0 near Los Angeles region [5].
    The computational resources requirements for generating USGS hazard maps do not mention in the 2008 report of seismic hazard maps update, but the hazard maps should be able to done without a super computer. To generate the CyberShake hazard map, lots of wave propagation simulations are required to build a database for generating synthetic seismograms of potential earthquake ruptures [5]. The computational resource of physics-based seismic hazard maps is much higher than the computational requirement of USGS hazard maps. However, the advances in computer sciences make the computational requirements affordable for CyberShake, also accurate estimations of ground motions are important for a city with a large population. The seismic hazard levels are quit different in the Los Angeles region between two hazard maps. In the USGS hazard map [Figure 1], the high hazard level regions are almost along the fault zones and hazard values decrease as the distance between a site and fault zones increases. In the Los Angeles basin region, the hazard level is about the same in the USGS hazard map [Figure 1]. In the CyberShake hazard map, the hazard values along the San Andreas fault are high, but the width of high hazard zones is narrower. In addition, the CyberShake hazard map in the Los Angeles basin has more details [5]. This probably reflects the source and structure effects in ground motion predictions.

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