ML19340A346

Review & Evaluation of Dames & Moore Verification Study of Hurricane Storm Surge Model.

ML19340A346
Person / Time
Site:	Crystal River
Issue date:	10/04/1973
From:	ARMY, DEPT. OF, CORPS OF ENGINEERS
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ML19340A345	List: ML19340A344 ML19340A346
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NUDOCS 8003160177
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, REVIEW AND EVALUATION OF DAMES AND MOORE'S s VERIFICATION STUDY OF THEIR HURRICANE STORM SURGE MODEL I. BACKGROUND..

A conference was held-on 15 February 1973 between the Atomic Energy ,

Commission (AEC), the National Weather Service (NWS), the Coastal Engineering .Research Center (CERC), and Dames and Moore (DSM). The matter

.under discussion.was' maximum potential storm surge at Crystal River, Florida, a potential site for. nuclear. power facilities. It was. concluded that further i

verification.should.be carried out with historical hurricanes to check the

. validity of the .open coast storm surge models developed respectively by CERC'and Dames and Moore.

II. STATEMENT OF PROBLEM, The Director of the U. S. Army Coastal Engineering Research Center was requested informally by AEC, as part of the existing contract, to provide AEC and DSM with basic oceanographic and wind data of historic hurricanes, to undertake an independent verification of.its model, and to review and

. evaluate'the results of the DSM verification.

III. ANALYSIS OF PROBLEM.

In response to this request,-copies of all available basic data of

i. historic hurricanes' were provided by CERC to ' AEC and DSM, in March 1973.

-In addition, using these data, a verification of its numerical model of hurricane surge prediction was undertaken by CERC and the results have been summari:ed in a report to AEC. Finally,;CERC was requested to review and evaluate ~the DSM Verification Study of their Surge Model.

The following comments resulted from the review and evaluation of the 1

DSM final report.. l A. Comments on Data'and Data Reduction.

1. In the conclusions section the Dames and Moore (DSM) report states that the historical hurricane data received from AEC and used in the

, calibration was deficient. in quantity and quality. DSM received all availa-ble . wind field charts on t',a hurricanes under study. It is recognized that hurricane 1 wind field. charts are 'not as comprehensive as would 'bc desirable

.for'a study.'of'this. type.- Nevertheless sufficient. data was provided, from

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which the analysis could be .made. ' This raw data ints provided by CERC as-a rconvenience an'd a basis from which DSM could~ extract the necessary data.

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2. DGM uses a program called BATCH to linearly interpolate wind speed and wind vector _ directions from digiti:ed wind field data at each wind field chart time interval. The linear interpolation approach Icads to inaccurate wind field data, particularly in the cases where there are abrupt changes in wind direction. Linear interpolations of wind speed values may be acceptabic for some conditions, but abrupt wind direction changes occurring in hurricane wind ficids more appropriately require a subjective evaluation and interpretation, something which cannot be incorporated in a computer program. Although the rapidity by which the computer interpolates the wind field is desirable, a more appropriate approach would have been to plot and interpolate nonlinearly for hourly wind field data from the basic NOAA six or three hour wind field information.

3. In evaluating the results of each traverse DSM concludes and we concur, that the Galveston traverse for Hurricane Carla provided the best quality of data for calibration as it represents an open coast situation.

B. Comments on Basic Differences Between DSM and CERC Models.

1. Both CERC and Dames and Moore (DSM) models make use of the fundamental hydrodynamic equations in one hori:ontal dimension and utili:e identical geometry and basic assumptions in calculating the storm surge.

2. The basic difference between the two models involves the use of a wind stress coefficient. In the DSM model the wind stress coefficient is calculated from the following relationship:

W k = (CSK1 + CSK2 (1 p ) ) 1.17 29 92 where CSJ1 and CSK2 are constants, W in the critical velocity, taken as l 15milesperhourNisthewindvelo8ityandPisthe7tgggphericpressure l at the point where the calculation is made. The term 2h9,isandensity l pressure factor involving a ratio of the local atmospheric ~ pressure and l the normal atmospheric pressure (29.92 inch. of Hg.). The CERC nodel utilizes the following relationship for the wind stress coefficient: l

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K = (1.1 + 2.5 (1 g')') 10 16 C which is Van Dorn's wind str'ess equatio , with C being a multiplier, the other coefficients being equivalent, but not the same in value to those of DSM. The basic disagreement between the two models is the value of these

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coefficients. The main argument of Dames and Moore is that CERC's wind L

stress coefficient equation ignores a prersure dependent density ratio effect. CERC's argument is that in the wind stress equations which arc

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derived empirically, the coefficients CSK1 and CSK2 of DSM are low in value,

'and that the density ratio used by DSM is not realistic since der sity condi-tions depend on moisture content of the air, degree of precipitation, temperature, and other such factors which cannot be easily measured, and which are continuously and unpredictably changing within the area affected by the hurricane. Furthermore, available literature does not support this quantitxcive density ratio eff ect on the wind stress. The use of a peri-pheral piessu.c of 29.92 inches of Hg. is not always appropriate to use, particularly for synthetic hurricanes.

C. Evaluation of the DSM Calibration Method.

1. In its calibration procedure, DSM focuses s',tention upon the components of the wind stress equation using different values of the following:

a. The constant part of wind-stress coefficient (CSK1).

b. The constant multiplier of velocity-dependent part of wind stress coefficient (CSK2) .

c. Bottom friction coefficient (BOTC), and

d. The exponent of depth for bottom friction effect (CO.NSD) .

2. DSM concentrated in calibrating primarily for the coefficients CSK1 and CSK2 and obtaining a "best fit" of calculated ' surge when comparing it to the observed surge hydrographs by varying the values of these coefficients in the wind stress equation, as well as the bottom friction coefficient. The four criteria used by DSM for the condition for "best fit" are in reality one criterion which means, the calculated surge hydrograph should match as well as possible the observed or recorded surge hydrograph.

The fact that in the case of the Galveston traverse, the criteria 1 and 2 were achieved ' c the entire range of CSK1 and CSK2 values investigated, points out tht. there was no need to change or to calibrate the model, in this fashion.

3. According to the DSM evaluation only the results of the Galveston traverse truly satisfied "best fit" conditions, while the Sabine Pass and Eugene Island traverses were less satisfactory, and the Narragansett Bay traverse were shown to be statistically meaningless. "Best fit" was obtained by DSM for values of CSK1 = 0.8 X 10-6 and CSK2 = 1.0 X 10-6 for BFF of 0.003. However, for the sake of " conservatism and accuracy of correlation," the values of CSK1 and CSK2 are designated by DSM to be 1.0 X 10-6 and 1.4 X 10-6, respectisely. DSM concludes that this range of values for CSK1 and CSK2 is not appreciably different than that of previous investigations.

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, s D. Comments on the Statistical Treatment and Accuracy of the D6M Results.

1. The accuracy of calculated hydrograph relative to the observed hydrograph was checked by DSM by the following methods: a) A point-by-point comparison of percent difference between the two hydrographs at each time step, b) computing the sum of the squares of the difference between the two hydrographs for the duration of the hydrograph, and c) comparing the average percent differences of sections of the hydrographs.

2. All three niethods are very similar. Method (a) presents the problem in that if the recorded and calculated hydrographs are out of phase.with the same general _ shape, something which is not uncommon, point-by-point comparison of percent differences is very misleading. Furthermore there may be positive as well as negative differences when the hydrographs cross. All sof the hydrographs analy:ed by DSM are out of phase, and cross.

Method (b) that of using the sum of the squares of differences between the two hydrographs presents the problem in that.the hydrographs agdin are out of phase and, in addition, by squaring the sums even the negative differences become positive and the "best fit" is not a true "best fit."

Method (c), that of looking at the average percent differences of sections

.of the hydrographs and comparing each one-third po? tion with emphasis on the middle-third portion of the hydrograph, is equally ineffective as a statistical method of comparison for the same reasons as cited for method (a) and (b) .

3. To check on the validity of the DSM wind stress equation using their coefficients and their pressure-dependent factor and in order to -

compare it to CERC's wind stress equation, using the same bottom friction factor, the following test was applied. Using the parameters of the probable maximum hurricane, PMH, (Po = 26.7 in. of Hg., Pn = 31.25 in. Hg.,

R = 24 n. mi., Vt = 20 knots, and l' max " 149 9 DP )h wind speeds and pressures were calculated along the hurricane's prime vector for increasing integer distance intervals of the ratio, r/ .R Utilizing these data, both the DSM and CERC wind stress equations were solved and respective values of wind stress coefficients were tabulated in Table 1. To illustrate graphically

-the differences of both the CERC with DSM wind stress coefficients with increasing wind speeds, a plot was prepared (Figure 1). The percent difference between the CERC and the DSM wind stress coefficients were similarly calculated for each wind speed interval and plotted on the same graph. Examination of these graphs indicates that both the CERC and D5M wind _ stress coefficients have approximately the same initial values up to wind. speeds of 20 mph. Beyond wind speeds of 20 mph, the CERC calculated wind stress coefficient increases at a greater rate than the DSM coeffi-

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cient; between 20 and 30 mph, the difference increases to 1S%, at 50 mph to 23%, and at:100 mph to 27%. Also apparent from this graph is that the pressure factor introduced in the DSM wind stress calculation, cannot 4

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~,c possibly conpansate for increased stress due to :tronger winds as the region of maximum winds is approached. As shown, the speeds between I 70-30 mph the DGM wind stress coefficient approaches a plateau value and retains the same or an even lower value in the vicinity of maximum winds (149.9 mph). This does not appear to be consistent with previous investi-gations since wind speed is a more important factor than atmospheric pressure in determining the wind stress.

5 TABLE 1 Comparison of CERC and Dames and Moore Wind Stress Coefficients

/R W P CERC - k DSM -k Difference '.

1 149.9 28.4 3.67 X 10 -6 2.51 X 10 ~0 31.6 2 137.9 29.5 3.65 "

2.59 "

28.8 3 100.0 30.0 3.52 "

2.57 "

26.95 4 86.6 30.2 3.45 "

2.55 "

26.1 5 76.4 30.4 3.3S "

2.53 "

25.1 6 68.2 30.6 3.31 "

2.50 "

24.5 7 60.6 30.6 3.23 "

2.46 "

23.8 8 53.7 30.7 3.14 " "

2.41 23.2 9 48.0 30.8 3.04 "

2.36 "

22.4 10 43.0 30.8 2.94 "

2.30 "

21.8 12 34.8 30.9 2.70 "

2,17 "

19.6 14 28.9 30.9 2.44 "

2.02 "

17.2 16 24.3 31.0 2.15 "

,1.86 "

13.5 18 20.5 31.0 1,61 "

1.67 "

7.7 20 16.9 31.0 1.36 "

1.40 "

- 2.0 22 13.8 31.0 "

1 321 ,/ 1.21 "

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{ Wind Stress Equations.

CERC k = 1.1 [1.1 X 10-6 + 2.5 X 10 -6 Cy ,1 )2) or k = 1.21 X 10-6 + 2.75 X 10-6 (y , 1 ).'

DSM k = [1.0 X 10 -6 J1.4X10-6(y,jp\) y 5

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4. Another inadequacy of the DSM wind stress equation involves

~~~,,. the use in the calibration of a peripheral atmospheric pressure of 29.92 inches of Hg. The use of the atmospheric pressure factor which includes such peripheral pressure wculd not be realistic for a probable maximum hurricane PMH which by definition has a variable peripheral pressure depending on latitude (HUR 7-97). Even for the historic data with which DSM model was calibrated, the 29.92 inenes of Hg. is erroneous as peripheral pressure is asyrptotic in nature.

5. The DSM contention that calibration was achieved using such low values of factors CSK1 = 1.0 X 10-6 and CSK2 = 1.4 X 10-6 and an overall low value of the wind stress coefficient leads to the conclusion that Dames and Moore misinterpreted er interpolated incorrectly the basic wind data. This data cannot be evaluated as it was not included in their report.

IV. CONCLUSIONS AND RECOMMENDATIONS. '

A. The DSM attempt to calibrate the wind stress equation using, not only coefficients related to wind stress, but other variables not directly related to wind stress, is not an appropriate means of calibrating the surge model or the wind stress equation.

B. The recent research study by Whitaker, Reid and Vastano, (Whitaker, R. E. , Reid, R. O. and Vastano, A. C. ,1973, " Drag Coefficient at Hurricane Wind Sneeds as Deduced from the Numerical Simulation of Dynamical Water Level Changes in Lake Okeechobee," Dept. of Oceanography, Texas ASM University, ASM Project 791, Reference 73-13-T, August), using additional data and direction observations of over the water winds, yielded the best results with a value of 2.6 X 10-6 for the tangential stress form, and 3.0 X 10-6 for the form drag term. These are even larger than the 1.1 X 10-6 and 2.5 X 10-6 values used by the CERC's hurricane surge model and consi-derably greater than the CSK1 and CSK2 values of 1.0 X 10-6 and 1.4 X 10-6 suggested by DSM in their calibration. It should be pointed out, however, that the wind drag coefficient used by Whitaker et al. (1973) was verified only for wind speeds ranging from 20 m/sce to 40 m/sce (44.7 miles /hr to 89.5 Liles/hr), and not for the entire wind speed spectrum.

C. The DSM contention that verification of their numerical model was achieved with such a low wind stress coefficient, indicates a strong possibility of ecror in the interpretation and reduction of the basic wind field data used as input for their calibration.

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D. Because of the complexity of the problem and the variability of

. 'different factors entering the calibration process of the hurricane surge model, that is the variability of hurricane parameters, traverses, and conditions, statistical correlation for a number of hurricanes at a number of traverses will be difficult to obtain. The most appropriate approach will be to continue to look at future surge records of one hurricane at two or more traverses, or at several h'urricanes on the same traverse.

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