Several rainfall atlases containing isopluvial maps, applicable for storm durations up to 10 d, frequencies up to 100 y, and drainage areas up to 400 mi², have been published by the National Weather Service (see Table 13-1). These maps were developed by analyzing extensive point-rainfall measurements and, therefore, rainfall depths shown represent point-rainfall values.

Each atlas contains a chart of depth-area ratios designed to account for spatial averaging of rainfall depth with increasing basin area. These depth-area ratios allow the calculation of an areally averaged rainfall depth, given the basin area, storm dura-tion, and point depth obtained from the appropriate isopluvial map. These ratios are referred to as geographically fixed depth-area ratios in order to distinguish them from storm-centered depth-area ratios, which are based on the morphological characteris-tics of individual storms [39].

Traditionally, the development of geographically fixed depth-area ratios has been based on empirical comparisons of point and areal rainfall at the same geographic location. Areal rainfall is approximated by averaging simultaneous gage mea-surements. This requirement of simultaneity limits the amount of usable data to that of recording gages. Therefore, depth-area ratios are developed based on data from a few existing networks of densely placed recording gages. Due to the sparseness of data, durational, frequency, and geographic variations of depth-area ratios cannot be readily ascertained. Therefore, the available data have been condensed into a single graph (based on a 2-y return period) applicable for depth-area reductions across the United States and for return periods up to 100 y. This graph, reproduced from NOAA Atlas 2 (31], is shown in Fig. 2-9(a).

A general methodology to compute regional depth-area ratios has been devel-oped by the National Weather Service. In this method, the depth-area ratios are com-puted using the mean and standard deviations of the annual series of rainfall averages over circular areas. The method is summarized by the following formula:

in which DA = depth-area ratio; x' = relative mean; K = Gumbel frequency factor normalized for a 20-y record length; s' = relative standard deviation; C_v = variance coefficient; and A, D, n and T are area, duration, record length, and return period, respectively. The statistics used in Eq. 14-3 are obtained using procedures described in [32].

A depth-area reduction chart for Chicago based on Eq. 14-3 is shown in Fig. 14-9. The close resemblance between Figs. 2-9(a) and 14-9 is attributed to the fact that the Chicago data had a prominent role in the development of Fig. 2-9(a). Other geographic regions are likely to have different depth-area ratio patterns.

Figure 14-9(a) and (b) shows depth-area ratios decreasing with increasing area and return period, and decreasing with duration. The effect of return period on depth-area ratio is not accounted for by Fig. 2-9(a). In addition, Eq. 14-3 can be used to develop depth-area ratios for areas larger than those depicted in Fig. 2-9 (a). For example, a depth-area reduction chart for Chicago, applicable to areas up to 5000 mi2, is shown in Fig. 14-10.

Standard Project Flood Determinations

Hydrologic design criteria used by the U.S. Army Corps of Engineers are outlined in Civil Engineer Bulletin No. 52-8: "Standard Project Flood Determinations," revised March 1965 [451.

A standard project storm (SPS) for a particular drainage area and season of the year is the most severe flood-producing rainfall depth-area-duration relationship and related isohyetal pattern that is reasonably characteristic for the region. The standard project flood (SPF) is the flood hydrograph derived from the SPS. For areas where snowmelt may contribute a substantial volume to runoff, appropriate allowances are made to increase the value of the SPS. When floods are primarily caused by snowmelt, the calculation of SPF is based on estimates of the most critical combination of snow, temperature, and hydrologic abstractions.

Flood magnitudes are governed by a combina-tion of several factors, among them, the quantity, intensity, temporal, and spatial distribution of precipitation, the infiltration capacity of the soil mantle, and the natu-ral and artificial storage effects. When relatively long periods of streamflow records are available, statistical analyses can be used to develop flood estimates associated with frequencies bearing a reasonable relationship to the record length. However, for large projects, it is necessary to supplement statistical methods with hypothetical de-sign flood estimates based on rainfall-runoff analysis.

Three types of flood estimates are used in flood-control planning and design investigations:

1. Statistical analysis of streamflow records, including individual-station flood-frequency estimates and regional flood-frequency analysis.

2. SPF estimates, which represent flood discharges that are expected to be caused by the most severe combination of meteorologic and hydrologic conditions that are considered to be reasonably characteristic of the region, excluding extremely rare combinations.

3. PMF estimates, which represent flood discharges that are expected to be caused by the most severe combination of critical meteorologic and hydrologic condi-tions that are reasonably possible in the region.

Statistical flood determinations are useful in project investigations, primarily as a basis for estimating the mean annual benefits that may be expected to accrue from the control or reduction of floods of relatively common occurrence.

An SPF serves the following purposes: (1) it represents a standard against which the selected degree of protection may be judged and compared with the protection provided at similar projects in different localities and (2) it represents the flood dis-charge that should be selected as the design flood for the project, where some small risk can be tolerated, but where an unusually high degree of protection is justified because of the risk to life and property.

A PMF is applicable to projects calling for a virtual elimination of the risk of failure. PMF applications are typically in the sizing of spillways for large dams or dams located immediately upstream of heavily populated areas.

Design Flood.

The term design flood refers to the flood hydrograph or peak discharge value that is finally adopted as the basis for engineering design, after giving due consideration to flood characteristics, flood frequency, and flood damage poten-tial, including economic and other related factors.

The selected design flood may be either greater or smaller than the SPF. However, in Corps of Engineers' practice, the SPF is intended to be a practical expression of the degree of protection sought in the design of flood control works. Since SPF estimates are based on generalized studies of meteorologic and hydrologic conditions, they provide a basis for comparing the degree of protection afforded by projects in different localities.

The procedures for ob-taining generalized SPS estimates described in this section are applicable to areas east of the 105th meridian, and primarily to small basins (i.e., those less than 1000 mi², considered as small basins in Corps of Engineers' practice). They are based on data from storms that have occurred primarily in the spring, summer, and fall seasons, during which convective activity is prominent, and are not generally applicable to snow seasons without special adjustments.

Figure 14-11 shows generalized SPS estimates corresponding to a 24-h duration and a 200-mi² area, obtained by reducing PMF isohyets by 50 percent and reshaping them in certain regions to conform with supplementary studies of rainfall characteristics

These SPS estimates are approximately 40 to 60 percent of the associated PMP estimates.

The isohyetal map shown in Fig. 14-11 is termed SPS index rainfall in order to allow conversion to storms covering areas from 10 to 20,000 mi² and durations other than 24 h. The applicable SPS depth-area-duration chart is shown in Fig. 14-12. Criteria for the subdivision of 24-h SPS rainfall into 6-h increments is shown in Fig. 14-13. A standard 96-h SPS isohyetal pattern is shown in Fig. 14-14.

The procedure to develop an SPS estimate for small basins (less than 1000 mi² in Corps of Engineers' practice) is the following:

1. Locate the drainage basin in the map of Fig. 14-11 and determine the SPS index rainfall (inches).

2. Enter Fig. 14-12 with the basin area to obtain the SPS index-rainfall ratios (in percent) for 24-, 48-, 72- and 96-h periods. Multiply these ratios by the SPS index rainfall obtained in step 1 and divide by 100 to calculate the 24-, 48-, 72-and 96-h SPS rainfall depths.

3. The 24-h SPS rainfall depth is the first of four 24-h increments in a 96-h period. Calculate the three remaining 24-h increments by subtracting the 24-, 48-, 72- Figure 14.12 SPS depth-area-duration relation [45]. Figure 14.13 Time distribution of 24-h SPS rainfall [45]. Figure 14.14 Standard 96-h SPS isohyetal pattern [45]. and 96-h SPS values. For instance, the second 24-h increment is equal to the 48-h depth minus the 24-h depth, and so on. 4.

4. Based on an appraisal of hydrologic conditions within the basin, arrange the four 24-h SPS increments in a sequence that is favorable to the production of critical runoff at project locations.

5. Subdivide each 24-h SPS increment into four 6-h increments in accordance with the criteria of Fig. 14-13. The same sequence of 6-h increments is assumed for each day of the SPS.

6. Subtract estimates of hydrologic abstractions from the 6-h incremental SPS val-ues obtained in step 5 to calculate the effective storm hyetograph to be used in the computation of the SPF.

The basic principles involved in the preparation of SPS and SPF estimates for large drainage basins (i.e., those in excess of 1000 mi², considered as large basins in Corps of Engineers' practice) are the same as those applicable to small basins. However, generalization of criteria becomes more difficult as the basin size increases. SPF estimates for small basins are usually governed by the maximum 6-h or 12-h rainfall associated with severe thunderstorms. For large basins, SPF estimates are generally the result of a succession of distinct rainfall events. Although the intensity and quantity of rainfall are important factors in the production of floods in a large basin, the location of 'successive increments of rainfall and the synchronization of intense bursts of rainfall with the progression of runoff are of equal or greater importance. Accordingly, an SPS estimate for a large basin must be based on a review of relevant meteorological data and an assessment of the hydro-logic response characteristics of the basin, including the study of major floods and related historical accounts.

A spillway is an open channel, conduit, or drop structure used to convey water from a reservoir. It may have gates, either manually or automatically controlled, to regulate the flow of water through the spillway. SCS classifies spillways as: (1) princi-pal spillways and (2) emergency spillways. The principal spillway is the lowest ungated spillway designed to convey water from the reservoir at predetermined release rates. The emergency spillway is the spillway designed to convey excess water through, over, or around a dam.

An earth spillway is an unlined spillway. A vegetated spillway is an open channel flow spillway lined with vegetative materials. A ramp spillway is a vegetated spillway constructed over an earth dam in such a way that the spillway is part of the embankment.

The following three elevations are used in spillway design: (1) the emergency-spillway crest elevation, (2) the maximum design pool elevation, and (3) the minimum dam-crest elevation (after proper allowance for settling of the embankment). The emergency-spillway crest elevation is below the maximum design-pool elevation. In turn, the maximum design-pool elevation is below the minimum dam-crest elevation (Fig. 14-15).

Storage volume is the volume of the reservoir measured up to the emergency-spillway crest elevation. Retarding pool storage is the fraction of storage volume which is allocated to the temporary impoundment of flood waters. The emergency-spillway crest elevation is the upper limit of retarding pool storage. Surcharge storage is the portion of the reservoir located between emergency-spillway crest elevation and maxi-mum design-pool elevation. Freeboard is the difference between minimum dam-crest elevation and maximum design-pool elevation (Fig. 14-15).