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PROBABILITY OF EXTREME RAINFALLS AND
THE EFFECT ON THE HARRIMAN DAM
1
Yankee Atomic Electric Company 1671 Worcester Road Framingham, Massachusetts 01701
April 1984
8405080221 840427 PDR ADOCK 05000029 P PDR
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| L NOTICE
This document was prepared by Yankee Atomic Electric Company. It is cuthorized for use specifically by Yankee Atomic Electric Company, its sponsor companies, and appropriate subdivisions within the Federal Energy Regulatory Commission and the Nuclear Regulatory Commission. t
With regard to any unauthorized use, Yankee Atomic Electric Company and its officers, directors, agents, and employees assume no liability nor make tny warranty or representation with respect to the contents of this document.
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ACKNOWLEDGEMENTS
This report was prepared by the Yankee Atomic Electric Company's Environmental Sciences Group. The work was performed by George A. Harper, j Thomas F. O'Hara, and John H. Snooks. Dr. C. Allin Cornell, consultant to Y:nkee Atomic, provided technical guidance, and John P. Jacobson performed the technical review.
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TABLE OF CONTENTS
Page
N0TICE...... 11
ACKNOWLEDGEMENTS...... iii
LIST OF FIGURES...... V
1.0 REPORT SUMMARY...... 1
2.0 METHODOLOGY AND RESULTS...... 7
2.1 Extreme Rainfall Estimation...... 7 2.2 Reservoir Response to Extreme Rainfalls...... 9 2.3 Peak Reservoir Elevation Probabilities...... 10
3.0 REFERENCES...... 15
APPENDIX A - Unconditional Approach...... A-1 APPENDIX B - Conversion of DAD Average Rainfall to Exceedance Values...... B-1
APPENDIX C - Example of Unconditional Precipitation Probability Calculation...... C-1
APPENDIX D - Description of Basin Response Model and Input Parameters...... D-1
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. . - ______LIST OF FIGURES
Number Title Page
| 1. Mean Unconditional Rainfall Probability Curve for Upper Deerfield River Basin...... 4
; 2. Peak Reservoir Elevation as a Function of Extreme Rainfalls at Harriman Dam...... 5
3. Peak Reservoir Elevation Probability at Harriman Dam...... 6
4. Unconditional Rainfall Zones...... 12
5. Upper Deerfield River Basin Map...... 13
6. Mean Unconditional and Statistical Probability Comparison...... 14
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/ 1.0 REPORT SUMMARY
- Harriman Dam is a large earth dam in the upper Deerfield River basin located in Whitingham, Vermont. The dam is an integral part of the Deerfield River hydroelectric system and has been generating hydroelectric power for the 10st 60 years. Yankee Atomic Electric Company does not own or operate i Harriman Dam. It is owned and operated by Ecw England Power Company (NEP), a ceparate and distinct corporation, both legally and financially. NEP is rcgulated with respect to Harriman Dam by the Federal Energy Regulatory Commission (FERC) under License No. 2323. The legal authority and rcsponsibility for the dam's control rests with FERC under 19CFR12 (Revision 3-1-81).
Nevertheless, because Yankee is located downstream from the Harriman Dam, we are most interested in the performance of the dam under all loading conditions. Yankee, therefore has assessed the reliability of the dam (1). One issue that has received wide interest is the potential for flooding due to dam overtopping from extreme rainfalls. The interest has evolved because of the differences in the estimate of the possible maximum precipitation event, known as the PMP. The PHP is important because its value determines whether Harriman Dam could be overtopped or not.
The first study to estimate the PMP for the upper Deerfield River basin was performed by Yankee in 1980 (2]. It concluded that the 24-hour, 200- equare-mile PMP estimate should be 14.3 inches. Franklin Research Center (FRC), under contract to the Nuclear Regulatory Commission (NRC), conducted a cecond study in 1982 (3]. FRC corroborated the 1980 Yankee study and recommended a PMP value to within three percent of the Yankee study (14.7 versus 14.3 inches). The NRC, for whatever reasons, did not endorse the FRC results and chose to contract with the National Weather Service (NWS) in 1983 to conduct a third PMP study for the basin. The NWS concluded (4) that the PMP estimate for the basin should be 22+ inches.
The principal difference between these past studies and that reported herein is that the prior studies were deterministic in nature, whereas this
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ctudy addresses extreme rainfall in the upper Deerfield River basin in a probabilistic framework.
This report was not prepared to determine which FMP estimate is estrect. Instead, the objective of this report was to deter 1nine the , probability of a range of extreme basin rainfalls and to quantify the water i Icvel in the Harriman Dam / Reservoir Facility due to these extreme rains. To cecomplish this objective three steps were performed.
In the first step, extreme rainfall probabilities were determined using cn unconditional probability approach. The unconditional methodology is d3 scribed in Section 2 and in more detail in Appendix A. The unconditional probability of the extreme rainfalls are given in Figure 1. The results show that the annual probabilities of the Yankee extreme rainfall, 14.3 inches, and the NWS rainfall, 22+ inches, are 3.5x10 and 2.2x10 , respectively. The annual probability of the Franklin Research extreme rainfall is comparable to the probability for the Yankee extreme rainfall. i In the second step, peak reservoir elevations as a function of extreme rainfalls were determined from a hydrologic model of the upper Deerfield River b: sin. The details of the modeling are described in Appendix D. The results of the basin modeling are given in Figure 2, which depicts peak reservoir clevation as a function of extreme rainfall. The results show that it would tcke a 24-hour extreme basin rainfall of 17 inches to produce a zero-freeboard ccndition (recervoir elevation at dam crest).
Lastly, the results of the first two steps were combined to describe the probabilities associated with peak reservoir elevations resulting from cxtreme rainfalls. These results are given in Figure 3. The results show that the mean annual probability of the reservoir attaining an elevation equal
to the dam crest due to extreme rainfall is 5.6x10~ .
To place the effects of this small probability event into perspective, o review of other safety design criteria is helpful. For example, the NRC has r: viewed the designs of numerous nuclear plants to reconfirm and document the plant's safety. Results from probabilistic risk assessments were used in some
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{ ccses to show that the risks associated with postulated design events were ceceptable. Seismic hazard curves with annual probabilities of 10~ to 10 , for instance, have been accepted generally by the NRC for input to ctructural analysis of critical plant features.
Similar risk levels for other extreme external phenomena (e.g.,
' rainfall induced flooding) should be appropriate for dams. Therefore, a t d: sign rainfall value with an annual exceedance probability of approximately 10 is appropriate. From Figure 2, this corresponds to a 24-hour extreme b: sin rainfall of 12.5 inches. The 14.3-inch Yankee rainfall has an annual
probability of occurrence of 3.5x10 . Hence, it provides considerable margin of safety for Harriman Dam beyond a reasonable design basis event. An coditional margin exists because the Harriman Dam would not be overtopped for 24-hour basin average rainfalls of 17 inches or less (see Figures 2 and 3).
Based on the above discussion, it can be concluded that sufficient m2rgins of safety, beyond the appropriate design basis event, are provided by
L the present configuration of the Harriman Dam / Reservoir Facility.
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2.0 METHODOLOGY AND RESULTS
The purpose of this section is to give an overview of the three steps used to determine the probability of extreme rainfalls in the upper Deerfield River basin and the effect on the Harriman Dam. Each step is described briefly, with details contained in the Appendices.
i 2.1 Extreme Rainfall Estimation
Based upon results from a prior analysis [2], the 24-hour rainfall was identified as the critical rainfall duration to assess dam effects. To sstimate the probability of exceedance associated with various 24-hour rainfall depths, an unconditional (non-parametric) approach was used.
In the unconditional probability approach, no assumption is made concerning the mathematical form of the statistical distribution. In its cimplest sense, the probability of exceeding a particular rainfall depth at a point of interest is estimated by multiplying the annual frequency of the events of such depth occurring anywhere within a large zone of interest times the probability that that event will occur directly over a point of interest. The annual frequency can be calculated from the historical records. The probability of the event occurring an'ywhere within a given zone can be sstimated simply as the ratio of the average storm area in which such a depth is equalled or exceeded to the total area of the large zone of interest. The details of the unconditional methodology are described in Appendix A.
To determine the annual frequency of extreme rainfalls within a given region at various rainfall depths, the data base compiled by the National Weather Service (5) was utilized. This data base consists of Depth-Area-Duration (DAD) tables for 853 major rainfall events throughout the contiguous United States and is categorized by sections for the United States (see Appendix Figure A.1). Since the area of interest is the northeastern United States, data from Sections 9, 19, 20, and 30 were used. From these cections, seven alternative study regions, called zones, were defined to ostimate the unconditional rainf all probability.
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______. The seven different zones were used to ensure that zonation would not bias the results unfairly. Each zone included Section 20, or portions thereof, which contains the upper Deerfield River basin. In addition, the Ctorm activity rate in each zone was assumed to be uniform. That is, a storm in a region is equally likely to have its area of maximum rainfall centered i anywhere in the zone. The unconditional zones and associated areas are listed in Table 1 and are depicted in Figure 4.
For each zone, a curve was developed for rainfalls that extended from 6 to 24 inches (see Figure A.4). These curves were assumed to have an equal likelihood of correctness. Accordingly, the curves were then combined to calculate a mean unconditional rainfall distribution curve (Figure 1).
The probability of the Yankee PMP value of 14.3 inches for 200 square
elles shown on Figure 1 is 3.5x10 . The probability of the NWS 22+ inch
~ rainfall for 200 square miles is 2.2x10 , or over two orders of magnitude Icss likely than the Yankee value.
2.1.2 Extreme kainfall Estimation Comparison
To check the reasonableness of the unconditional rainfall estimates, a ctatistical analysis of rainfall data from stations within the upper Deerfield River basin was performed. Five statistical distributions were used: two-parameter lognormal, three-parameter lognormal Pearson Type III. Log-Pearson Type III, and Type I Extreme value, also called the Gumbel distribution. Each distribution was applied to the maximum annual 24-hour rainfall data for the long-term basin data sets at Somerset Station, Harriman Station Searsburg Station, Harriman Dam, and Readsboro (Figure 5). Both the method of moments and maximum likelihood method were used to estimate the rainfall 1cvel. The methodology and computer programs used in this analysis { cre described in detall in Reference 7. 1
The point rainfall statistical estimates from the analysis were cdjusted to 24-hour basin rainfall values (9, 10]. As in the unconditional cpproach, an equal likelihood of correctness for each distribution was assumed tnd the results combined to compute a mean. The resultant curve, which is the
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; me:n of all the basin stations, is shown on Figure 6. Also shown on the figure is the mean unconditional curve.
As illustrated, at equal rainfall levels the statistical approach yiolds lower probability values than the unconditional approach. The r 1stionship of rainfall probabilities between curves, however, is similar. Far example, the ratio of the Yankee and WS PMP values on both curves still chows that the WS 22+ inch value to be about two orders of magnitude less likely than the Yankee 14.3-inch value.
To check the values of the PMP from the conventional deterministic method, the Hershfield PMP method [10, 11] was used. The method uses the mean , cnd standard deviation of the annual maximum precipitation to calculate a point estimate of the PMP. The Hershfield estimate, which has no probability cssociated with it, has been used by the WS to check its generalized PMP values.
The long-term stations in the basin used for the statistical analysis were also used in the Hershfield analysis. The point PMP estimates from these stations were adjusted to 24-hour, 200-square-mile values (9,10] and then c mbined to produce a mean value. The resultant for the upper basin was a value of 14.6 inches. This value supports the Yankee 14.3-inch PMP value. The WS 22+ inch PMP, on the other hand, exceeds the Hershfield PMP value by over 50 percent.
Lastly, it can be concluded that the extreme rainfall probabilities For example, a calculated from the unconditional method are a stable estimate. it is doubtful that any major storms in the northeast United States are unaccounted for during the last 100 years. Consequently, to change the f cxtreme rainfall probabilities during the next ten to forty years by one order of magnitude would require over ten times the number of previously observed cvents to occur.
2.2 Reservoir Response to Extreme Rainfalls
} To determine the reservoir response to extreme rainfalls, a hydrologic model was developed for the upper Deerfield River basin using the HEC-1 (6)
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ficod model computer program. Based upon the historical distribution of both reservoir elevation and temporal distribution of rainfall, combinations of flood model input parameters were defined. The ficod model program HEC-1, was then executed for each of the defined inputs, and the peak reservoir clevation was calculated as a function of the 24-hour basin rainfall. The t results were then synthesized into a mean representation of peak reservoir clevation as a function of extreme basin rainfall (Figure 2).
For a detailed discussion of the basin modeling refer to Appendix D.
2.3 peak Reservoir Elevation probabilities
The information from the above steps was then combined to describe probabilities associated with peak reservoir elevations. These results, given in Figure 3, allow one to determine the probabilities of attaining specific reservoir elevations. For example, the annual probability of the reservoir
cttaining an elevation equal to the dam crest is 5.6x10 . For the dam to foil by rainfall induced overtopping, the reservoir elevation would have to be over the dam crest for some finite period of time. Hence, the annual probability of failure of Harriman Dam due to extreme rainfall induced cvertopping must be less than the probability to reach dam crest, or less than ~
5.6x10 .
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TABLE 1 )
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Unconditional Rainfall Zones .. , . t 1 ' .
+, .N' Reference 4 ~ Zone Numbers Sections in Zone Area of Zone, mi.2
4 1 20 55,521
' ( 2 20 + 9 104,789 ' l 124,307 - | 3 20 + 19
, 4 20 + 9 + 19 173,575
. t } 5 20 + 19 + 30 200,104
6 20 + 9 + 19 + 30 249,372 ,
20 (inland portion) 36,783 ' 7 ,
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L 3.0 REFERENCES
I 1. Jacobson, J., and G. Harper, 1982, "Harriman Dam Performance Evaluation" YAEC-1298, Yankee Atomic Electric Company, Framingham.
- ) Massachusetts.
2. Yankee Atomic Electric Company, 1980, " Design Basis Flood Analysis, Yankee Atomic Blectric Generating Station, Rowe, Massachusetts", YAEC-1207. Westborough, Massachusetts. {
3. Scherrer, J., " Hydrological Considerations", 1982, (SEP. II-3.A B, B.1, C; III-3.B) Technical Evaluation Report, NRC Contract 03-79-118 Franklin Research Center, Philadelphia, Pennsylvania.
4 Miller, J. F., E. M. Hansen, and D. D. Fenn, September 1983, " Probable Maximum Precipitation for the Upper Deerfield River Basin". Office of Hydrology, National Weather Service. Silver Spring, Maryland.
- 5. Hansen, E. Marshall, November 2, 1982 Personal Correspondence: Storm Listings Compiled for NOAA Technical Memorandum NWS HYDRO-33 " Greatest Known Areal Storm Rainfall Depths for the Contiguous United States". f 6. U.S. Army Corps of Engineers, 1979, " Flood Hydrograph Package (HEC-1), Dam Safety Version", Computer Program 723-X6-L2010, The Hydrologic Engineering Center, Davis, California.
7. Kite, G. W., " Frequency and Risk Analysis in Hydrology", 1977, Water Resources Publications, Fort Collins, Colorado.
8. Yankee Atomic Electric Company October 27, 1983, "Possible Maximum Precipitation in the Upper Deerfield River Basin", Framingham, Massachusetts. i -15-
I
_ - _ _ _ _ _ - _ _ _ . J . - . ______- _ _ _
( 9. U.S. Department of Commerce, 1956, Hydrometeorological R pset No. 33. " Seasonal Variation of the Probable Maximum Precipitation List of the 105th Meridian for Areas from 10 to 1000 Square Miles and 4 Durations of 6, 12, 24 and 48 Hours", Weather Bureau, Washington, D.C.
10. Hershfield, D.M., 1961, " Estimating the Probable Maximum Precipitation", American Society of Civil Engineers, Volume 85, No. HYS, pp. 99-116.
11. Hershfield, D.M., 1965, " Method for Estimating Probable Maximum Rainfall", Journal of American Waterworks Association, Volume 57, No. 8, pp. 965-972.
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APPENDIX A
f Unconditional Approach h
In the unconditional probability approach, no a priori assumption was made concerning the mathematical form of the statistical distribution. In its cimplest sense, the probability of exceeding a particular rainfall depth at a paint of interest is estimated by multiplying the annual frequency of the cvents of such depth occurring anywhere within a large zone of interest times ( the probability that that event will occur directly over a specific point of interest. The former annual frequency can be calculated from the historical records. The latter probability of the event occurring over a specific location can be estimated simply as the ratio of the average storm area in which a depth is equaled or exceeded to the total area of the large zone of interest. The details of the methodology are described below, but the above description is the essence of the approach.
To determine the annual frequency of extreme rainfalls within a siven
{ geographical zone at various rainfall depths, the data base compiled by the National Weather Service for NOAA Technical Memorandum NWS HYDRO-33, " Greatest Known Areal Storm Rainfall Depths for the Contiguous United States", was used (A-1].
The data base consists of Depth-Area-Duration (DAD) tables for 853 major rainf all events throughout the contiguous United States. The earliest ctorm in the data' base is 1819. In the northeastern United States, the data base is complete for at least the last 100 years for moderate sized storms and is likely to be complete for an even longer period for the largest historical otorms. The stom data base is categorized by sections for the United States (Figure A.1) with the site of interest, the upper Deerfield River basin, in the center of Section 20. Since the area of interest is the northeastern United States, data from Sections 9, 19, 20, and 30 were used.
The storm data base was searched and storms in the four sections whose f 24-hour rainfalls exceeded 6.0 inches over any area were chosen for further cnalysis. Application of this criteria reculted in a total of 8 storms in
I A-1
1 _ _ - ______
S:cticn 9, 23 storms in Ssetion 19, 26 storms in Section 20, cnd 28 storms in S ction 30, for a total of 85 storms. The level 6.0 inches is arbitrary, but
' the results should not be sensitive to the value. If, for example, a higher d;pth were used, the number of storms (n) would decrease, but the " average
creas", A >_ X would increase proportionately. The value 6.0 is thought to be cmall enough to give a relatively large sample of storms and large enough to cnsure completeness of the record.
With the basic storms selected, tabulations were prepared for each f storm giving DAD average areas associated with depths of rainfall in 24 hours from 6 inches on up (see Step 3. Appendix C). Previous studies [A-2] have chown that the 24-hour rainfall is the critical value for the upper Deerfield River basin. The areas were interpolated from the DAD tables for each storm in each section. These areas are associated with a specific level of spatial Everage rainfall in 24 hours.
In the unconditional probability analysis, it is desirable to determine the probability of exceedance associated with various rainfall depths. { Therefore, the areas from the DAD tables must be adjusted to exceedance creas. The exceedance area, an area over which the rainfall everywhere equals or exceeds the stated rainfall level, is always less than the DAD area. (Refer to Appendix B for a detailed discussion on the technique used to adjust DAD areas to exceedance areas.)
Exceedance area adjustment factors (Eq. B-17) ranged from 0.39 to 0.52, depending on the specific rainfall event. The DAD areas for each storm were then multiplied by the adjustment factors, which resulted in storm tabulations f cf exceedance areas associated with specific levels of rainfall. At this point, all storms in the four sections were in a tabulated form showing Gxceedance areas associated with rainfalls greater than or equal to a specified level. Once the data are in this form, the annual frequency of cccurrence of a given rainfall depth, and the probability of an event of a given exceedance area occurring anywhere within a zone can be calculated.
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A-2
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At this point, a further refintm:nt of tha modal wzs introduced to cecount for the fact that for some storms in the data base, the areas
I cssociated with high levels of average rainfall were smaller than the area of L the basin. In these cases, even if that historical storm, which occurred comewhere in the study area, had occurred at the basin in question, it would
$ not have produced that average level of rainfall over the basin because it cffected an area actually smaller than the basin. Therefore, the storm tabulations need to be adjusted to account for this. This is referred to as the " finite basin adjustment", P , where 0 1 P 11. For very small 3 3 ratios of the average area to the basin area, P = 0. For larger ratios f 3 (small basins or large storms), the value of P = 1. After some study, it was found adequate simply to set P equal to either 0 or 1. The adjustment 3 was performed on a storm-by-storm basis; if the tabulated exceedance area had en associated DAD average area less than approximately the basin size, the sxceedance area was multiplied by a P3* "" **" "" * " " ** * that specific level of rainfall. For this study the drainage area above Harriman Dam, excluding Somerset, was chosen. This drainage area covers 154
, equare miles. To be conservative, only storm areas with DAD areas of less than 130 square miles were multiplied by P val es f zero (see Step 5, ( 3 Appendix C). After this step, the storm tabulation correction process was complete and probability of exceedance curves could be calculated for each hypothesized " homogeneous" zone (see Steps 6 and 7, Appendix C).
The above description of estimating the unconditional probability of exceeding a specific level of rainfall can be explicitly described in the f following manner:
The probability that the basin is hit by at least one storm causing cpatial average rainfall over the basin greater than or equal to X inches in 24 hours in any given year is defined by:
"P (Equation A.1) P, 3 7 = Py 2
(
' A-3
.-
- ______where,
' P is the annual frequency of occurrence of a storm of "significant size" (e.g., by definition, at least 6 inches of rainfall in 24 hours) occurring in any year in the homogeneous region. P is estimated by:
Number of Si g g ag gor g g in a complete 1 " Number of Years of Complete Record, N * "
By " homogeneous" it is meant that a storm in the region is equally likely to leave its zone of maximum rainfall centered anywhere in the region. This assumption is used to estimate P below as a simple ratio of areas. 2
P is the probability that the storm hits a point at the center of 2 the basin with the capability of producing a spatial average rainfall over the basin greater than or equal to X inches given that the s.torin occurs in the region. P is estimated by: ' 2
.
1 p(d ) A ' n 3 -X P (Equation A.3) 2" A region { where,
n is the number of significant storms in the data set.
A(j) is the exceedance area of the jth storm in the set j gK associated with 2 X inches of rainfall.
- | P is the finite basin site adjustment factor which equals either 0 g f or 1. If the DAD average area of orm j is less than e basin area at the given rainfall level X , P = 0; otherwise, P = 1. 3 3
A . equals the area of the homogeneous region. region
'
A-4 The mathematical basis for Equation A.3 is the " total probability < theorem" argument that, given that a particular storm has a specific value of j the area A(g), then the conditional probability of the event of interest is P time the ratio of areas shown; multiplying by the probability that an 3
, arbitrary storm has that specific area value and integrating over all areas L one obtains P , which in turn is estimated from available data by 2
- Equation A.3.
Putting the two results above together:
P *P (Equation A.1) >g=P 2
n 1- : p - A n 3 -X * * P, = (") (Equation A.4) 7 region
which reduces to
n * : P A ~ ( i=1 P (Equation A.5) e D" h)Gregion)
An alternate reduced form is to define A>X as the "(modified) average enceedancearea"fP A (as in Step 6, Appendix C). Then we have
A> "* ~ P > = f * ^region
1 For this analysis, N, the completeness period was chosen as 100 years. In the range of 24-hour rainfalls of interest (E 10 inches) it was concluded ( that there is a very small likelihood that any storms of such magnitude have been " missed" over the last 100 years in the northeast United States.
For each study region, the probabilities of exceedance were estimated at each rainfall level from 6 inches until the summation term of Equation A.5 equalled zero. A "best-fit" curve through this data then allowed entrapolations to lower probabilities, and therefore, higher rainfalls.
A-5
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f L Seven distinct study regions, called zones, were used in the unconditional approach. The various zones are all combinations of the original four sections in the National Weather Service data base. All zones included Section 20. or portions thereof, which contain the upper Deerfield River basin. The zones and associated areas are listed in Table A.1 and are depicted in Figure A.2.
Included in Table A.1 is Zone 7, which covers a portion of Zone 1. This zone was used to study the implicit assumption that each zone is meteorologically homogeneous. In other words, storm centers are assumed to have an equal chance of being located anywhere throughout the zone. There are, however, generally more storms near the coast than further inland, especially for Zone 1.
As seen in Figure A.3, the average storm activity rate in Zone 1 decreases with increased distance from the southern New England coast. Therefore, from the southern New England coast to about 60 miles inland, at the intersection of the two curves, more storms occur then are accounted for by a homogeneous assumption. Conversely, less storms occur beyond 60 miles north of southern New England. The upper Deerfield River basin lies about 100 f miles north of the southern New England coast, and the storm activity rate here is less than the homogeneous rate. With this fact in mind, Zone 7 was established. It is the area in Zone 1 inland of the 60-mile contour from the southern New England coast. But, because the 1955 Westfield storm, the historic storm of record for New England, occurred about 60 miles inland, Zone 7 has two alternatives. L Zone 7a includes the Westfield storm in the estimation of P , Zone 7b does not.
It should be noted that the National Weather Service [A-3] has raised a f concern that Yankee, in a previous study [A-2), did not include some storms that the National Weather Service feels are controlling storms for PHP estimates in New England. Yankee has shown [A-4) that the National Weather Service concerns one unfounded. However, to further address this issue in a probabilistic framework some rones include the regions where these storms occurred.
A-6
.
------__
Specifically, Section 19 contains the four storms in question: Wellsboro, Pennsylvania (1889); Ewan, New Jersey (1940); Smsthport, Pennsylvania (1942); and Zerbe, Pennsylvania (Hurricane Agnes, 1972). Another storm, Tyro, Virginia (1969) is also mentioned by the National Weather Service [3] as a candidate storm type for consideration over the upper Deerfield River basin. This storm occurred in Section 30. Therefore, even though Yankee has previously ruled these storms out as not appropriate to the upper Deerfield River basin, they have been incorporated into this unconditional probabilistic analysis.
An example of how to calculate an unconditional rainfall probability is given in Appendix C.
Appendix A. References
A-1. Hansen, E. Marshall, November 2, 1982, Personal Correspondence: Stonn Listings Compiled for NOAA Technical Memorandum NWS HYDRO-33, " Greatest Known Areal Storm Rainfall Depliis for Line Contiguous United States".
A-2. Yankee Atomic Electric Company, 1980, " Design Basis Flood Analysis, Yankee Atomic Generating Station, Rowe, Massachusetts", YAEC-1207, Westborough, Massachusetts.
A-3. Miller, J. F., E. M. Hansen, and D. D. Fenn, September 1983, " Probable Maximum Precipitation for the Upper Deerfield River Basin", Office of Hydrology, National Weather Service, Silver Spring, Maryland. {
A-4. Yankee Atomic Electric Company, October 27, 1983, "Possible Maximum Precipitation in the Upper Deerfield River Basin", Framingham, Massachusetts.
A-5. Shipe, A. P. and J. T. Riedel, 1976, " Greatest Known Areal Storm Rainfall Depths for the Contiguous United States", NOAA Technical Memorandum NWS HYDRO-33, Office of Hydrology, National Weather Service, Silver Spring, Maryland.
A-7 TABLE A.1
- Unconditional Rainfall Zones I
Zone Numbers NWS Sections in Zone Area of Zone, mi.2
1 20 55,521
2 20 + 9 104,789
3 20 + 19 124,307
4 20 + 9 + 19 173,575
5 20 + 19 + 30 200,104
6 20 + 9 + 19 + 30 249,372
7 20 (inland portion) 36,783
(
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W _M C e < f. -J O a- [i 1 _O O - z N *NMvW 5 WWWWW e ZZZZZ o OOOOO * NNNNN O || 11 11 11 11 04+XO , O _ _, u . , _ , e . . 7,- e ,- ...... ,n .w .~ O N M * LO O N O O O O O O O O e a e t 8 I i O O O O O O * O., ,e e eo =* en A111186908d 33N60333X3 160NNB _. . _ _ _ _ _ - ______ r ( APPENDIX B i ADJUSTMENT OF DAD STORM AREAS TO EXCEEDANCE STORM AREAS L The basic storm data set used in the unconditional analysis is in the [ form of standard Depth-Area-Duration (DAD) tables. These DAD tables give the (largest) spatial average rainfall for given areas (e.g., 10, 100, 200, 1000, etc. square miles) for each storm. From the basic DAD tables, using interpolation, storm areas are first determined at given levels of average rainfall (e.g., 6, 7, 8... inches). Next, these storm (average rainfall) areas must be adjusted to "exceedance areas," that is, areas over which the rainfall equalled or exceeded a specific level of rainfall. The procedure used to adjust the storm areas to exceedance areas is outlined below. _ As a first step, the rainfall contours are assumed to be essentially circular (see Figure B.1(a)). The approach was to assume that the original information, g(A) (exceedance rainfall as a function of area from the storm center), is available and then calculate h(A), the spatial average rainfall inside the area, in terms of g(A). h(A) is the information available indirectly (after interpolation) from the DAD tables. With h(A) given for a particular storm, it is then pessible to determine g(A). For a given rainfall depth, x, the corresponding area from the storm center could be found by locating the area such that the volume under g(A) . above the plane g(A)=x is equal to the volume (cross-hatched) below that plane (inside of A). As shown in Figure B.1(c), this implies h(A) lies outside (or above) g(A). , , i Given g(A), 1 . 1 A ""* "" E("} " ( S* '" h(A) = Area *# E(^} "A 'o . B-1 - - - '| ______ j To proceed, a particular reasonable functional form for g(A) is assumed. - Let g(A) = g -a: A (Eq. B.2) L Referring to Figure B.l(b), g is the peak rainfall at the center of the storm. The second term of the g(A) function accounts for the decrease in the peak rainfall intensity as one moves away from the center of the storm. f This decrease is proportional to the distance from the storm center, r, to an exponent a times a constant a . Since the area of a circle is described by: A=tr (Eq. B.3) then ' r=A 7 (Eq. B.4) e/2 -a/2 r =A (Eq. B.5) Therefore, Equation B.2 is interpreted as the exceedance rainfall, g(A), at - _ _ . points on the circumference of a circle of area A. Substituting g(A), with A=u from Equation B.2 for g(u) in Equation B.1, 1 h(A) rA (g -a- u du (Eq. B.6) i ={-9 9 9 -3/2 o/2) Evaluating Equation B.6 yields ; 1 a/2 3/2 h(A) =g a- A (Eq. B.7) 9 - ( 2)2 ' This equation is interpreted as the average depth of rain, h(A), within a circle of area A. The DAD tables can be used directly with known values of h(A) and A to estimate the para:neters, g , a , and a, where g , a , and a are determined for each individual storm. B-2 ^ 1 ______._ . ______ Rearranging Equation B.7: i L 2 -a/2 a/2 r A (Eq. B.8) r go - h(A) = (a+2) *o L 2 -a/2 r Let the constants (a+2) *o equal a new constant a y, g - h(A) = a (Eq. B.9) j o 3 A' By making an initial estimate of g equal to the maximum value of h(A), (g - h(A)) is plotted versus A on log-log scale for each storm. The slope of the line equals a/2. Further estimates of g were made using a g increment and the procedure repeated. The line that best fits the data was chosen with associated g , a , and values. The g value, by o 1 o definition, approaches g(A) and h(A) in the limit as A goes to zero. Further, the areas associated with given depths of rainfall (exceedance and spatial average) can be determined from Equations B.2 and B.7, respectively. The ratio of these areas equals the ratio of the excecdance - 4 rainfall depth, d , area to the spatial average rainfall depth, d , area. Therefore, the ratio of areas at equal rainfall depths, d = d , is the e a desired adjustment factor to adjust spatial average rainfall storm areas. Therefore, g(A) =d (Eq. B.10) and h(A) = d, (Eq. B.11) ' Substituting Equation B.10 into Equation B.2, and letting A = A s e a/2 3/2 =g -a r A (Eq. B.12) d, d e . B-3 ______. .___ _ Solving for A t e g -d 2/a " * - A ( 9' d a 1 e o s Substituting Equation B.11 into Equation B.7 and letting A = A d a 2 3/2 a/2 r A * d, = g - (a+2) "o d 9' / a Solving for A , a g -d 2/a A * 9' ' d a (a+22 ' "o And the ratios of areas for the same depths, de=da is ggg -d 2/a A d a * = 9' * -d 2/a a ( ) 2 ( ) a ------ Simplifying Equation B.16 ^d A " d 8 This adjustment procedure is applied on a storm-by-storm basis. The parameters g , a , and a are estimated for each storm. Then the interpolated areas from the DAD tables are adjusted at each given depth (i.e., 2 6, 7, etc. inches) by the adjustment factor of Equation B.17, (3 g)2/a to yield Ade for each storm versus rainfall depth. Note that the adjustment factor is dependent on a only, and not on the depth. B-4 -__ _ _ - ______-.. [ ? [ og(A)=exceedance rainfall -a n -a/2A "! - O % , - , 0 Z Z t T v _ f 0 Area ' 'x + 2)" (b) :-: Storm (x + 1)" Cross-Section (a) Contours of Equal Storm Rainfall Intensity -. .. ,s g(A) = exceedance rainfall h(A) = DAD average rainfall I I.IllL u . i , h(A) j go ' ' , (A) ,, i A (c) g(A), h(A) Relationship FIGURE B.1 STOR51 AREA ADJUST 3 TENT / - . ______ I APPENDIX C L r EXAMPLE OF UNCONDITIONAL RAINFALL PROBABILITY CALCULATION l The following example shows the details involved in calculating the , unconditional rainfall probability. / Example: Calculate the unconditional 24-hour rainfall probabilities for Drainage Basin A with a drainage area of 200 square miles. Steps 1. Choose a representative homogeneous region in which Drainage Basin A lies. For this example, the area of the homogeneous region, A J region equals 25,000 square miles. 2. Sort through storm data base and find the historic storms in the homogeneous region that yielded at least 6 inches of rainfall in 24 hours - - _ - over a finite area. For this example, two storms will meet this criteria. The period of completeness of the historic record, N, is found to be 50 years. The Depth-Area-Duration tables for these storms are as follows: Maximum Average Depth of Rainfall in Inches Duration of Rainfall in Hours Area Square Miles 6 12 18 24 Storm #1 10 3.5 5.2 6.6 8.1 100 2.8 4.4 5.8 7.2 200 2.5 4.2 5.5 6.9 1000 2.2 3.9 4.4 5.8 + ~ f C-1 , I f ------______- ______. ( Storm #2 5.3 6.1 7.3 9.7 , 10 i L 100 4.8 5.6 7.1 8.0 200 4.1 4.9 6.3 7.5 500 3.8 4.7 5.9 7.1 / 1000 3.4 4.1 5.2 5.6 3. Interpolate between areas at 24 hours and tabulate at 1-inch rainfall f increments. Spatial Average Areas. mi2 , 24-Hour Rainfall in Inches Storm #1 Storm #2 9 0 47 8 20 100 7 167 533 - -- - 6 855 867 4. ConvertspatialaverageareastoexceedanceareasgeeAppendixBfor , details). Area adjustment factors (i.e., , see Eq. B.17) will ( r2 + 2) be assumed to be 0.4 and 0.45 for the two storms, respectively. f Exceedance Areas, mi2 24-Hour Rainfall in Inches Storm #1 Storm #2 9 0 21 8 8 45 . 7 67 240 6 342 390 = . 5. , sPadal Multiply the exceedance by P3Q), where P3 (j) average area (Step 3) is less than the basin area, and P =1 ) otherwise. See Appendix A. C-2 i L ______. , i PX3 Exceedance Areas, mi2 24-Hour Rainfall in Inches Storm #1 Storm #2 9 0 0 8 0 0 7 0 240 6 342 390 6. Determine average P X ex eedance areas for the two storms at each 3 rainfall level. Average P X Exceedance 24-Hour Rainfall 3 2 in Inches Area mi 9 0 8 0 _ __ . 7 120 6 366 7. Calculate the annual unconditional probabilities using the following equations: " (Eq. A.5, = 1 P 3. A 2g(j ) ,,, $Xinches " " ^_ ,*~ =- Appendix A (^ region ^region for derivation) = 1.9 x 10~ P >7- inches = (50)(25000) . = 5.9 x 10- P >6- inches = (50)(25000) ( C-3 | _ _ ------_ _. _ APPENDIX D Description of Basin Response Model and Input Parameters . | L To ascertain the effect of extreme rainfall in the upper Deerfield , [ River basin, a basin response model was developed. The HEC-1, Flood Hydrograph Package for Dam Safety Investigations (D-1] computer program was chosen as the model best suited for this analysis. HEC-1 has previously been used extensively by Yankee [D-2] on the upper Deerfield River basin and features the capability of evaluating the overtopping potential of a dam. The three uppermost drainages of the basin (see Figure D.1) were modeled by HEC-1. They were Somerset (30 square miles), Searsburg (60 square miles), and Harriman (94 square miles). Input parameters describing the physical response of the basin were the same as those used in Reference D-2. This basin model configuration was calibrated and verified against the peak floods in the basin and is considered ______to give reliable results (refer to Reference D-2 for a complete discussion on model verification). * In addition to the input parameters describing the physical response of the basin, parameters describing specifies of the rainfall event were necessary to run the model. These input parameters included the amount of rainfall, temporal distribution of rainfall, starting reservoir elevation in Harriman Reservoir, spatial distribution of rainfall, and rainfall infiltration. Sensitivity runs of HEC-1 were performed to determine which of the above parameters had a significant impact on the flood level predicted by the model. From the sensitivity runs it was concluded that the amount of rainfall, the temporal distribution of rainfall, and the starting reservoir elevation in Harriman Reservoir were the key flood parameters. g i In the HEC-1 program, a 24-hour rainfall and the percentages of the 24-hour rainfall in the maximum 6 and 12 hours are used to describe the amount i D-1 E - - _ - - - - - and temporal distribution of the rainfall event. The starting reservoir elevation is used by the model as the reservoir elevation at the beginning of the storm. Determination cf Alternative Starting Conditions , As discussed above, it was determined that in addition to the amount of rainfall, the temporal rainfall distribution and the starting reservoir elevation were important parameters in the modeling process. Therefore, various alternative inputs were needed, each with an associated probability. Probabilities of various levels of rainfall were developed by the procedures described in Section 2. The basin response model was run incrementing the basin average rainfall from 10 to 24 inches over the entire basin. The multi-ratio feature of HEC-1 allows up to nine different rainfall events to be modeled during one computer run. This feature greatly reduced f the number of HEC-1 computer runs. The temporal rainfall is defined as the percentage of the 24-hour ' rainfall occurring in the maximum 6-hour and maximum 12-hour segment of the storm. To determine model input for this parameter, the National Weather Service data base (D-3] was used. This is the same data base as used for the unconditional rainf all probability analysis. Since the Deerfield River basin is in Section 20 of the data base, this data was analyzed to develop the needed input parameter. The 200-square mile rainfall DAD value was used because it is the closest in size to the upper Deerfield River basin, and is usually reported for all major storms. The percentages of the 24-hour rainfall occurring in the maximum 6- and 12-hour periods were obtained for storms in Section 20 with 24-hour, 200 square mile rainfalls greater than or equal to 6.0 inches. This cutoff was chosen as a lower bound of the large type rainfall events of interest in this analysis. A total of 22 storms met this above criterion. From the data, a mean 6- and 12-hour percentage of the 24-hour rainfall was calculated. The , D-2 G-bg .. ______ standard deviation was also determined. Subsequently, the lower limit of 6.0 inches was raised by 1.0 inch increments to check how the mean and standard deviation varied as the number of storms was reduced to include only the 1 L largest storms. These results are shown in Table D.1. The results indicate that the mean and standard deviations are relatively stable. Alternative inputs selected for the basin modeling were the mean (51%) and the mean plus or minus one standard deviation (7%). This resulted in three alternative inputs for temporal rainfall distribution for the 6-hour percentage of the 24-hour rainfall. The probabilities for the three inputs were assigned using the standard normal distribution as a guideline. The mean estimate, 51%, was assigned a probability of 0.60 and the mean estimate plus and minus one standard deviation, 44% and 58%, were assigned probabilities of 0.20 each. The three probabilities sum to 1.0. . Sensitivity runs of HEC-1 were made to determine the impact of the 12-hour percentage on peak reservoir levels in Harriman Reservoir. The f results were not nearly as sensitive to the 12-hour percentage as to the 6-hour percentage. A linear regression was applied to the 6-hour percentage _ - - . (independent variable) versus the 12-hour percentage (dependent variable) . From these results a 12-hour percentage was determined from the appropriate 6-hour value for input to the HEC-1 model. As discussed above, a total of three alternative inputs were generated concerning the temporal rainfall distribution, each with an associated probability. The alternative inputs for the maximum 6-hour and 12-hour percentages of the 24-hour rainfall are: , 1. 51% and 78%, probability = 0.60 s 2. 44% and 69%, probability = 0.20 3. 58% and 87%, probability = 0.20 , Alternative starting conditions for the starting reservoir elevation in Harriman Reservoir were also developed for the basin response modeling. ) I D-3 1 -- ______. _ _ _ _ . ______. . _ _ _ _ _ . _ _ . . ______ Extreme rainfall events in the Deerfield River would most likely result from [ storms of tropical nature, i.e., hurricanes. This conclusion was reached by ' Yankee in Reference D-2 and is supported by meteorological evidence in New England and along the northeastern United States coast. Using data from Reference D-4, the hurricane season was selected as June 30 to October 31. . With the hurricane season set, the historical records of Harriman Reservoir elevation levels were utilized to determine the appropriate starting reservoir levels for the basin response modeling. . A daily reservoir level is obtained at Harriman Dam by the dam's owner, New England Power (NEP). For display purposes, NEP has tabulated the data on a yearly basis, 1924 to the present, for the 10th, 20th, and last day of each month. During the hurricane season, June 30 to October 31, a total of 13 > reservoir elevations are available for each year. With 60 years' of record, there are a total of 780 historical reservoir elevations during hurricane season. The data were sorted into three categories: those less than 1475.7 feet, msl (1370.0 feet NEP Datum), those between 1475.7 feet and 1485.7 feet, msl (1370.0 and 1380.0 feet NEP Datum), and those exceeding 1A85.7 feet, msl .. .. (1380.0 feet NEP Datum). The number of data points in each category and the average of the reservoir elevations in each category were also calculated. The first category included 199 datum points, with an average reservoir elevation of 1467.1 feet msl. The second and third category had 308 and 273 datum points with reservoir elevations averaging 1481.1 feet and 1490.0 feet, respectively. Therefore, three alternative starting conditions were developed for the starting reservoir elevation in Harriman Reservoir. Probabilities were assigned to each elevation based on a frequency of occurrence approach, i.e., the percentage of data points in a specific category. The three alternative starting conditions with their associated probabilities are: 199 1. 1467.1 feet msl, probability = .6 780 ' 308 2. 1481.1 feet msl, probability " * 780 273 3. 1490.0 feet msl, probability * * 780 D-4 . - _ _ _ - _ _ _ _ _ By dsfiniticn, tha three starting rasarvoir elsvations probabilitiss cum to 1.0, exactly. L Use of actual recorded reservoir elevations in the development of these citernative starting conditions incorporates day-to-day fluctuations in reservoir elevations due to rainfall events scattered throughout the hurricane censon. A review of data presented in Reference D-4 was carried out to f investigate the hypothesis that large rainfall events are typically preceded by equal or smaller significant events (antecedent storm) three to five days before the large event. The period of record covered in Reference D-4 is from 1871 to 1977. It was concluded that there is no correlation or evidence cupporting a hypothesis that significant antecedent events precede large rainfall events. It was further concluded that the actual data used to develop the three alternative starting reservoir elevation hypotheses ( cdequately account for conditions preceding a significant hurricane event in the upper Deerfield River basin. With three alternative inputs set for each of the two flood input parameters, temporal rainfall distribution and starting reservoir elevation, the basin response modeling was carried out for rainfall levels of 10 to 24 inches. Because each of the two flood parameters had three alternative inputs, there were nine possible combinations to be run through the basin response model. Each of the nine possible models had a probability associated with it equal to the product of the probabilities associated with the two input parameters. Model input combinations and the associated probabilities f are summarized in Table D.2. The sum of the nine individual basin case probabilities is 1.0. ' The results of the basin response modeling are shown in Figure D.2. These basin response curves describe the peak reservoir elevation for the nine models as a function of the 24-hour basin rainfall. Each of the nine basin response curves has a probability associated with it as described in Table D.2. As a final step, the nine basin response curves were synthesized into a single mean estimate of reservoir elevation as a function of 24-hour rainfall using the previously described probabilitier (Table D.2). This single basin D-5 t _-_------______ r;sponse curve is given in Figure D.3 and is also presented in the main text cf this report as Figure 3. Appendix D References D-1. U.S. Army Corps. of Engineers, 1979, " Flood Hydrograph Package (HEC-1), Dam Safety Version", Computer Program 723-X6-L2010, the Hydrologic Engineering Center, Davis, California. D-2. Yankee Atomic Electric Company, 1980, " Design Basis Flood Analysis, Yankee Atomic Electric Generating Station, Rowe, Massachusetts", YAEC-1207, Westborough, Massachusetts. D-3. Hansen, E. Marshall, November 2, 1982 Personal Correspondence: Storm Listings Compiled for NOAA Technical Memorandum NWS HYDRO-33, " Greatest Known Areal Storm Rainfall Depths for the Contiguous United States". D-4. Neumann, C., G. Cry, E. Casco, and B. Jarvine, 1978, " Tropical Cyclones f of the North Atlantic Ocean, 1871-1977", U.S. Department of Commerce, National Climatic Center, Asheville, North Carolina. { = t { D-6 I _ . . __ _ _ _ . ______- _ _ - _ _ ! TABLE D.1 L Temporal Rainfall Distribution Mean Data Base 6-Hour % Lower Cutoff Nu.tbcr of of 24-Hour Standard Deviation Rainfall. Inches Storms Rainfall of 6-Hour % 6.0 22 52.8 11.1 7.0 15 51.6 6.2 8.0 12 51.3 7.0 " 9.0 11 52.1 6.7 10.0 7 51.0 7.0 i !- . D-7 ------.__ ._-_ L TABLE D.2 Basin Response Input Conditions and Probabilities Input Conditions Starting Temporal Reservoir Distribution Elevation 6-Hour, 12-Hour Case No. Feet. MSL % of 24-Hour Case Probabilities 1 1467.1 51,78 0.26 x 0.60 = 0.156 2 1467.1 44,69 0.26 x 0.20 = 0.052 3 1467.1 58,87 0.26 x 0.20 = 0.052 4 1481.1 51,78 0.39 x 0.60 = 0.234 5 1481.1 44,69 0.39 x 0.20 = 0.078 6 1481.1 58,87 0.39 x 0.20 = 0.070 7 1490.0 51,78 0.35 x 0.60 = 0.210 8 1490.0 44,69 0.35 x 0.20 = 0.070 9 1490.0 58,87 0.35 x 0.20 = 0.070 Sum = 1.000 { { D-8 ' -_ .. " ~ r- * ( DEERFIELD RIVF.R DRAIN AGE BASIN - . , . I \ %'\ -SOMERSET RESERVolR f '% . : ' SEARS G RESE OtR f H vy - an- MARRIMAN * # RESERVOIR sf. D i _) gApp[t uw DA '. /Rh! $tR h 1 s ( f ~ /< > ( l Y (9 y \a * - f ' / , g CMA LEMONT y..J~' ( -s ra !!!!! k CCNNECTICUT RIVER MILES ( , l FIGURE D.1 UPPER DEERFIELD RI\'ER BASIN MAP _ - ____-______.-_ ( f k I L 8 -b 8 j ) -5 \ -E= 8 .4 ? ) N I LLJ (D N (D Cn - h h e o s r WWWw o LL) tn (n to tn - I y WE CCCC O o - I ca C 000U z z = ( zO % O 11 11 il il i m "IE o z &XXM o CU (C E O J =a WE "* bI f - - ~ wd L C % ~7 LL. ' UM z . . . LLJ T 6* E II C U 8- * or r LL. 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