K. F. Chen, C. H. Hunter, and J. H. Weber (retired)
Westinghouse Savannah River Company
Aiken, South Carolina 29808

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Department of Energy (DOE) regulations outline the requirements for Natural Phenomena Hazard (NPH) mitigation for new and existing DOE facilities. The NPH considered in this report is flooding. The facility-specific probabilistic flood hazard curve defines, as a function of water elevation, the annual probability of occurrence or the return period in years. The facility-specific probabilistic flood hazard curves provide basis to avoid unnecessary facility upgrades, to establish appropriate design criteria for new facilities, and to develop emergency preparedness plans to mitigate the consequences of floods. A method based on precipitation, basin runoff and open channel hydraulics was developed to determine probabilistic flood hazard curves for the Savannah River Site. The calculated flood hazard curves show that the probabilities of flooding existing SRS major facilities are significantly less than 1.E-05 per year.

The Savannah River Site (SRS), a facility in the U.S. Department of Energy (DOE) nuclear complex, encompasses approximately 803 km² in South Carolina and is adjacent to the Savannah River, as shown in Figure 1. Five major SRS streams (Upper Three Runs Creek, Fourmile Branch, Pen Branch, Steel Creek, and Lower Three Runs Creek) feed into the Savannah River, as shown in Figure 2. The SRS was established by the U.S. Atomic Energy Commission in 1950 to produce plutonium and tritium for national defense and additional special nuclear materials for other government uses and for civilian purposes. When the cold war ended in 1991, DOE responded to changing world conditions and national policies by refocusing its missions. The priorities shifted toward waste management, environmental restoration, technology transfer, and economic development.

Flooding can cause structural and non-structural damage, and interrupt critical functions, resulting in huge economic losses. More importantly, if the affected facility contains hazardous or radioactive materials, flooding may result in a significant environmental and health hazard. DOE regulations outline the requirements for Natural Phenomena Hazard (NPH) mitigation for new and existing DOE facilities. Specifically, NPH includes flood events. The facility-specific probabilistic flood hazard curve defines, as a function of water elevation, the annual probability of occurrence or the return period in years. DOE requires determination of the flood elevations as a function of return period up to 100,000 years for Savannah River Site (SRS) facilities. The facility-specific probabilistic flood hazard curves provide basis to avoid unnecessary facility upgrades, to establish appropriate design criteria for new facilities, and to develop emergency preparedness plans to mitigate the consequences of floods. The method used to calculate the flood hazard curves for SRS facilities is presented in this paper.

A straightforward way to determine probabilistic flood hazard curves is to conduct statistical analyses based on measured stream flow records. Savy and Murray (1988) and McCann and Boissonnade (1998) conducted preliminary flood hazard estimates for screening DOE sites in the western United States. The procedures used by Savy et al. follows:

• Select a database on peak flood discharge.
• Estimate the probability of exceedance of individual discharge flow.
• Determine the relationship between flow and flood stage (e.g., stage-discharge relationship).
• Transform the probability-discharge information to determine the probability of exceedance for individual flood elevations using the stage-discharge relationship.

However, the SRS stream flow records could not be used for flood hazard analyses, for the following reasons. One is that the historical flow records include the effects of significant quantities of cooling water discharged from five SRS production reactors that operated for many years. The other is that the record periods (several decades) are too short to calculate a 100,000-year return flood. To address this, a method based on precipitation, basin runoff, and open channel hydraulics was developed to determine the probabilistic flood hazard curves for the Savannah River Site. The procedures presented here were applied to all SRS basins. Development of a flood hazard curve for the H-Area due to Fourmile Branch basin runoff is illustrated.

Design hyetographs were determined from estimates of extreme rainfall by return period for 6-hour and 24-hour storm events.

Extreme rainfall estimates were based on hourly rainfall data from four National Weather Service (NWS) first order observing systems and four National Climatic Data Center (NCDC) cooperative stations. In addition, daily rainfall data from four rain gauges located on the SRS were used. The period of record for each station is summarized in Tables 1 and 2. Station locations are shown in Figure 3.

Stations were selected based on their proximity (all within about 100 km of the SRS) and geographic similarity (located either in the upper coastal plain or lower piedmont regions of South Carolina and Georgia.) The hourly data were extracted from compact disks containing the NCDC TD-3240 data set (EarthInfo, 1995). These hourly data were used to determine 6, and 24-hour rainfall for sequential overlapping intervals beginning with each hour in the station's record. The results were used to create files of annual maximum 6 and 24-hour rainfall values for each of the eight stations.

The hourly rainfall data were recorded over a fixed interval that began on the hour. Since the true maximum rainfall in a given year may occur over an interval which overlaps the fixed interval, empirical factors were used to convert the fixed interval maxima to an estimated 'true' value (Miller, 1982). Adjustment factors for the 6-hour and 24-hour events are 1.02 and 1.01, respectively.

Rainfall data from the four SRS gauges consisted of a once daily reading, usually around 6:00 LST. The annual maxima of daily rainfall for these stations were multiplied by an adjustment factor of 1.13 to approximate a true 24-hour maximum.

An extreme-value distribution of observed yearly maximum rainfall, by rain duration interval, was assumed for each storm event. The average, standard deviation, and coefficient of variation of the yearly maximum rainfall were calculated. The individual maximum rainfall amounts for each station were standardized and used to fit a generalized extreme-value distribution.

Let X_ij be the i^th yearly maximum rainfall for the appropriate rainfall interval for station-j, then the mean , standard deviation , coefficient of variation CV_j, and standardized values t_ij are given by:

(1)

(2)

(3)

(4)

Table 3 gives the average, the standard deviation, and the coefficient of variation for each rainfall interval and station.

The standardized values, t _ij, were used to fit a generalized extreme-value distribution to determine which extreme type distribution was appropriate. A single form of the three possible types of limiting distributions for extreme values has been derived by Fisher and Tippett (1928) and can be modeled by

, k¹ 0 (5)

, k=0 (6)

Here x and a are location and scale parameters, respectively. The shape parameter, k, determines which extreme-value distribution is best represented by the data. Fisher-Tippett Types I, II, and III correspond to k=0, k< 0, and k> 0, respectively. In practice the shape parameter usually lies in the range –(1/2) < k < (1/2). When this is the case, the following can be used to estimate the parameters x , a , and k (Hosking, et al., 1985):

, where

(7)

The error in estimating k using Eq. (7) is less than 0.0009 through the range -(1/2) < k < (1/2).

Given , the scale and location parameters can be estimated successively by

(8)

(9)

The Type I extreme-value distribution, or Gumbel distribution, is a particularly simple special case of the generalized extreme-value (GEV) distribution and is often useful to test whether a given set of data is generated by a Gumbel rather than a GEV distribution. This process is equivalent to testing whether the shape parameter, k, is zero in the GEV distribution. Assuming the null hypothesis H₀: k=0, the estimator is asymptotically distributed as N(0, 0.5633/n). The test may be performed by comparing the statistic

Z= (n/0.5633)^1/2 with the critical values of a standard normal distribution. Significant positive values of Z imply rejection of H₀ in favor of the alternative k>0, and significant negative values of Z imply rejection in favor of k<0. Values of Z (k-ratio) between –1.96 and +1.96 indicate that k is not significantly different from zero with 95% confidence.

The estimates of and the Z-statistic ratio (k-ratio) are given in Table 3. For the 6- and 24-hour rainfall periods, the shape parameter is negative indicating a Type II extreme value distribution.

The estimates of scale and location parameters for the Type II extreme value distribution are given in Eqs. (8) and (9), where the values b₀, b₁, and b₂ are estimated from the data using Eqs. (10) through (12). t _ij are the standardized variables ordered from smallest to largest and ij is the rank.

(10)

(11)

(12)

To get the rainfall amounts for each return period of interest, Eq. (5) must be solved for the station's standardized value, t _P. This results in the expression

, (13)

which gives the rainfall in centimeters for each station for a return period of P years. Estimates of the scale and location parameters ( and ) are given in Table 3. The resulting extreme rainfall estimates for return periods from 10 to 100,000 years are summarized in Table 4.

Both 6-hour and 24-hour storm events have been used to investigate the flood elevations. The extreme rainfall for the 24-hour storm event was selected to calculate flood elevations because it gave conservative results (higher flood elevations).

The HEC-HMS hydrologic model used to predict stream discharge following extreme rain events requires input of time-dependent rainfall intensity (i.e., cm/hr). These data were developed from an examination of the annual maximum rainfall events that occurred at Augusta, GA (period of record 1949-95).

First, the eight highest annual maximum 24-hour events were identified and hourly data for each storm event were extracted from the historical record. The hourly values for each storm were ranked by rainfall amount, then divided by storm total precipitation to give normalized hourly fractions. The normalized fractions were then averaged over the eight storm events to give the ranked fractional amounts for a 'composite' or average storm. Finally, the averaged ranked fractions were re-distributed by hour based on an assumed progression of an idealized, symmetrical storm. The heaviest fractional rainfall was assumed to occur during the mid-point of the event and lighter amounts at the beginning and end of the event. For the 24-hour storm, the mid-point of the event was assumed to occur during hour 8, since the average storm duration for the eight events was 16 hours. The re-distributed sequential rainfall fractions for the 24-hour storm are summarized in Table 5. For a given return period, the composite normalized fractions from Table 5 were multiplied by the corresponding storm total rainfall in Table 4 to determine hypothetical hourly rainfall intensities.

HEC-HMS is a hydrologic modeling system developed by the US Army Corps of Engineers, Hydrologic Engineering Center, to model flood hydrology. HEC-HMS performs precipitation-runoff simulations. HEC-HMS uses the design hyetographs to calculate the flood flows. Additional model parameters required by HEC-HMS are losses, runoff transformation and base flow that characterize the basin properties. The output of HEC-HMS is a basin discharge hydrograph. The input parameters for a specific basin were determined by matching the HEC-HMS output flow with the measured flow for selected historical storm events. The procedures to derive input parameters for a specific basin are presented next.

Rainfall data at SRS are collected from a network of 13 rain gauge stations, as shown in Figure 2. Measurements are taken once a day (usually at 6:00 LST), except for the rain gauge at the Central

The basin-average hourly precipitation is required to calculate basin runoff. The following procedure was used to convert the daily measured precipitation to basin-average hourly rainfall:

The measured hourly flows used to determine the HEC-HMS input parameters were provided by the USGS, Columbia, SC District. The USGS maintains a network of monitoring stations at strategic locations on the Savannah River and SRS streams, and at SRS outfalls, to measure the flows, fluid temperatures, and stage heights.

The additional HEC-HMS input parameters are basin drainage area, loss rate, runoff transformation, and base flow. The basin drainage area was obtained from the USGS Water Resources Data book (Cooney et al. 1995). The area within a basin that is impervious to rain infiltration was estimated from the site map using the ArcView GIS system (1998). The base flow model parameters were adjusted to match the measured base flow. The parameters for the runoff transformation model were adjusted to match the shape of the measured hydrograph, and the parameters for loss were adjusted to match the measured peak flow. The resulting parameters were then used by HEC-HMS to calculate basin peak flow using the design precipitation hyetographs.

The Fourmile Branch basin has about 60 square kilometers of drainage area including much of the SRS F-, H-, and C-Areas (Figure 2). The stream flows to the southwest into the Savannah River Swamp and then into the Savannah River. The banks vary from fairly steep to gently sloping. The floodplain is up to 304.8 meters wide. Fourmile Branch receives effluents from F-, H-, and C-Areas, from a groundwater plume from the Burial Ground and F and H seepage basins, and until June 1985, received large volumes of cooling water from the production reactor in C-Area. Figure 2 shows the gauge stations 02197334, 02197340, 02197342, and 02197344 on Fourmile Branch. There are four highway bridges, one railway bridge, five culvert crossings, and ten breached dams or roadbeds that cross Fourmile Branch.

A storm event on January 6, 1995 was used to develop the Fourmile Branch basin runoff characteristics. The 1/6/95 storm was chosen because it had the highest rainfall intensity and the largest accumulated rainfall.

The average measured rainfall from the six rain gauges (200-H, 200-F, 100-C, CLM, 100-K and 400-D) that cover the Fourmile Branch basin was taken as the average rainfall for the Fourmile Branch basin. The Fourmile Branch basin hourly rainfall for the 1/6/95 storm event is shown in Figure 4.

The Fourmile Branch basin was divided into four sub-basins at gauge stations 02197334, 02197340, 02197342 and 02197344. The drainage area associated with a gauge station includes drainage area of upstream stations. Therefore, each station has a different drainage area, as shown in Figure 2. The sub-basin properties (HEC-HMS input parameters) were determined by matching the model hydrographs with the measured hydrographs at the four gauge stations. Table 6 presents the parameters obtained for the sub-basins. Figures 5 through 8 present the calculated and the measured hydrographs for Fourmile Branch basin during the 1/6/95 storm event at gauge stations 02197334, 02197340, 02197342, and 02197344, respectively. Note that the measured hourly flows for Fourmile Branch at the stations 02197334, 02197340, 02197342 and 02197344, as shown in Figures 5 through 8, were provided by the USGS, Columbia, SC District.

HEC-HMS used the data from the above section (Table 6) and the 24-hour storm design hyetographs to calculate the peak flows at gauge stations 02197334, 02197340, 02197342, and 02197344 as a function of return period. The 24-hour storm design hyetographs were select to provide conservative peak flows. Figure 9 shows the calculated peak flows as a function of return period or annual probability of exceedance. The peak flows were used by WSPRO to calculate the flood elevations, as described next.

The data required for WSPRO are flow, boundary condition, channel geometry and losses, and hydraulic characteristics of the bridges and road crossings. Lanier (1997) used WSPRO to conduct a 100-year recurrence-interval flood plain study for Fourmile Branch Basin in 1996. To conduct the study, 49 cross-sections along the Fourmile Branch were surveyed and 132 synthesized cross-sections were developed using surveyed cross-section data and the 7.5-minute series topographic maps. In addition, elevation data and structural geometry for 4 highway bridges, 1 railway bridge, 5 culvert crossings, and 10 breached dams or old roadbeds were determined. The cross-sections developed by Lanier were extended in both banks to accommodate the higher flood flows for return periods beyond 100 years. The ArcView Geographic Information System was used to obtain the expanded cross-section data.

WSPRO models the basin by subdividing the basin in segments and calculates the water elevation from downstream segment to upstream segment. WSPRO allows different flow at different segments. For Fourmile Branch, the peak flow decreases as drainage area decreases. Therefore, the WSPRO input flow varies along the segment according to the drainage area. The peak discharge was linearly interpolated between drainage areas except for one situation. To avoid extrapolation, the peak discharge at station 02197334 (drainage area of 15.41 km²) was used for the upstream locations where the drainage area is less than 15.41 km². This gives conservative (higher) flood elevations.

One complicating factor in modeling flooding in Fourmile Branch is the presence of five culvert crossings. The WSPRO model cannot calculate the backwater caused by culverts. Therefore, a separate culvert-flow computation must be made to determine the backwater caused by the culvert. The Culvert Analysis Program (CAP) (Fulford 1995) was used to calculate the backwater surface elevations caused by culverts. The CAP code was developed by the USGS and is in the public domain. The calculation procedures used by CAP are based on those presented in Bodhaine (1968).

The analysis of culverts is complicated because they provide a parallel path for flood flows. Under normal conditions, water flows only through the opening in the culvert. Under flooding conditions, the water elevation may exceed the height of the road crossing, resulting in flow over the road crossing as well as through the culvert. This parallel flow path affects the calculation of the flood elevation upstream of the culvert.

For a given return period flow, WSPRO calculated subcritical flow water elevations from downstream to the exit location of a culvert. The water elevation upstream of a culvert was determined from a culvert rating curve. The culvert rating curve is, for a given downstream water elevation, the culvert upstream water elevation as a function of total flow (sum of flow through culvert and overtopping road crossing). This water elevation was used as a boundary condition for the WSPRO analysis of the next upstream reach. The procedure to obtain the culvert rating curves is presented next.

Using this procedure, the rating curves for the five culverts were obtained sequentially, beginning with the most downstream culvert. The downstream elevation for the first culvert is available directly from a WSPRO analysis. Once the rating curve is obtained, the water elevation upstream of the culvert is determined by the known total flow (flood flow). This water elevation is used as a boundary condition for the WSPRO analysis of the next upstream reach.

Figure 10 shows the rating curve for the culverts at Road E-1. Road E-1, not shown in Figure 2, is an improved light duty road about 1 km upstream from the Gauge Station 02197334. The triangles (two kinds of culverts at Road E-1) in Figure 10 show the calculated culvert upstream water elevation as a function of flow through the culverts. The squares in Figure 10 represent the calculated culvert upstream water elevation as a function of flow over the road crossing. The summation of the flows through culverts and over road crossing is the culvert rating-curve, as indicated by circles in Figure 10. For a specified flow (500-year return flow in this case), the culvert upstream water elevation is determined from the rating curve. At each culvert location, eight rating curves were established, one for each return-period flow.

Figure 11 presents the calculated Fourmile Branch basin flood hazard curve near H-Area. The calculated annual probability of 1.E-05 (100,000-year return) flood elevation at H-Area is 72.91 meters above mean sea level. The elevation of H-Area is above 82.30 meters above msl. Therefore, the probability of flooding the facilities at H-Area would be significantly less than 1.E-05 per year.

A method based on precipitation, basin runoff and open channel hydraulics was developed to determine the probabilistic flood hazard curve for the Savannah River Site. The calculated flood hazard curves show that the probabilities of flooding existing SRS major facilities are significantly less than 1.E-05 per year. These results provide basis to avoid unnecessary facility upgrades, and to establish appropriate design criteria for new facilities.

The work performed for this project was funded by the U. S. Department of Energy under contract DE-AC09-96SR18500. The authors wish to express special thanks to personnel at USGS, Columbia, SC, district: T.H. Lanier for providing the WSPRO and CAP input files and having valuable discussions during the model development; T.W. Cooney, F. Melendez, S.W. Ellisor and B.W. Church for providing the hourly flow records.

1. ArcView Version 3.0a, Copyright ^ã. (1998). Environmental Systems Research Institute, Inc.
2. Bodhaine, G. L. (1968). Measurement of Peak Discharge at Culverts by Indirect Methods, USGS, Techniques of Water Resources Investigation, Book 3, Chapter A3, 60p.
3. Cooney, T. W., Jones, K. H., Drewes, P. A., Gissendanner, J. W., and Church, B. W. (1995). Water Resources Data South Carolina Water Year 1995, USGS, Columbia, South Carolina.
4. Earthlnfo, Inc. (1995). NCDC Hourly and 15 Minute Precipitation, Boulder.
5. Fisher, R. A., and Tippett, L. H. C. (1928). "Limiting Forms of the Frequency Distribution of the Largest or Smallest Number of a Sample." Proc. Cambridge Phil. Soc., 24, 180-190.
6. Fulford, J. M. (1995). User’s Guide to the Culvert Analysis Program, USGS Open-File 95-137.
7. HEC-HMS: Hydrologic Modeling System User’s Manual, Version 1.0. (1998). US Army Corps of Engineer, Hydrologic Engineering Center, Davis, CA.
8. Hosking, J. R. M., Wallis, J. R. and Wood, E. R. (1985). "Estimation of the Generalized Extreme-Value Distribution by the Method of Probability-Weighted Moments". Technometrics, August 1985, Vol. 27, 251-261.
9. Lanier, T. H. (1997). Determination of the 100-Year Flood Plain on Fourmile Branch at the Savannah River Site, South Carolina, 1996, p. 8, USGS Water-Resources Investigations Report 96-4271.
10. McCann, M. W. and Boissonnade, A. C. (1988). "Natural Phenomena Hazards Modeling Project, Preliminary Flood Hazard Estimates for Screening, Department of Energy Sites: Albuquerque Operations Office". UCRL-21045, Lawrence Livermore National Laboratory, Livermore, CA.
11. Miller, J. F. (1982). Engineering Meteorolog, Elsevier Scientific Publishing Co., New York.
12. Savy, J. B. and Murray, R. C. (1988). "Natural Phenomena Hazards Modeling Project: Flood Hazard Models for Department of Energy Sites", UCRL-53851, Lawrence Livermore National Laboratory, Livermore, CA.
13. WSPRO, A Computer Model for Water Surface Profile Computations, User’s Manual. (1998). FHWA-SA-98-080, Office of Technology Applications, Federal Highway Administration, Washington, DC.

Appendix II. Notation

The following symbols are used in this paper:

CV_j = coefficient of variation (the standard deviation divided by the mean) for maximum yearly rainfall for station j (divided by 100%) for each rainfall interval;

k = shape parameter for Fisher-Tippet generalized extreme value probability distributions;

= an estimate of k;

N = total number of years, all stations;

n_j = number of years for station j;

P = return period in years for a given amount of yearly rainfall as determined by a fitted Fisher-Tippet generalized exteme value probability distribution;

S_j = standard deviation of the maximum yearly rainfall over n years for station j for each rainfall interval;

X_ij = i^th yearly maximum rainfall for the appropriate rainfall interval (15-min, 1-hr, 3-hr, 6-hr, 12-hr, or 24-hr) for station j;

= average maximum yearly rainfall over n years of record for station j for each rainfall interval;

X_P = Expected rainfall for a return period of P years determined from the fitted Fisher-Tippet’s generalized extreme value distribution;

a = scale parameter for Fisher-Tippet generalized extreme value probability distributions;

= an estimate of a;

G = Gamma function;

t = standardized maximum rainfall;

t_ij = standardized maximum rainfall for i^th year, j^th station for each rainfall interval;

t_P = standardized maximum rainfall for return period P;

x = location parameter for Fisher-Tippet generalized extreme value probability distributions;

= an estimate of x;

b₀ , b₁ , b₂ , and c are intermediate terms used in calculating the Fisher-Tippet GEV parameter estimates.