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| number = ML092870644
| number = ML092870644
| issue date = 10/13/2009
| issue date = 10/13/2009
| title = 2009/10/13-Exhibit L - NUREG/CR-6853 - Comparison of Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model
| title = Exhibit L - NUREG/CR-6853 - Comparison of Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model
| author name =  
| author name =  
| author affiliation = NRC/RES
| author affiliation = NRC/RES
Line 18: Line 18:


=Text=
=Text=
{{#Wiki_filter:Indian Point Nuclear Generating Units 2 and 3 Docket Nos. 50-247/ 50-286-L R NRC Staff's Response in Opposition to State of New York's Motion for Partial Summary Disposition of NYS Contention 1611 6A Exhibit L Con~parison of Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model Lawrence Livermore National Laboratory U.S. Nuclear Regulatory Commission - Office of Nuclear Regulatory Research Washington, DC 20555-0001 Comparison of Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model Manuscript Completed: October 2004 Date published:
{{#Wiki_filter:Indian Point Nuclear Generating Units 2 and 3 Docket Nos. 50-247/ 50-286-LR NRC Staff's Response in Opposition to State of New York's Motion for Partial Summary Disposition of NYS Contention 16116A Exhibit L
October 2004 Prepared by C.R. Molenkamp (LLNL), N.E. Bixler, C.W. Morrow (SNL), J.V. Ramsdell, Jr.. (PNNL), J.A. Mitchell (NRC) Atmospheric Science Division Sandia National Laboratories Lawrence Livermore National Laboratory Albuquerque, NM 87 185-0748 Livennore, CA 94550 Pacific Northwest National Laboratory Richland, WA 99352 J.A. Mitchell, NRC Project Manager Prepared for Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 NRC Job Code Y6785 
: 3. MODELS The NIELCOR Accident Consequence Code System Version 2 (MACCS2) (Chanin et al. 1998) was developed at Sandia National Laboratories for the NRC. Its primary use is in performing consequence analyses in support of level-3 probabilistic risk assesslnents (PRAs). It is also used by the NRC for planning purposes and cost-benefit analyses.
MACCS2 is the latest in a series of N RC-sponsored codes for estimating off-site consequences following a release of radioactivc
~naterial into the environment. The first code in the series was CRAC (Calculation of Reactor Accident Consequences), which was developed for the Reactor Safety Study (WASH-1400, 1975). The first version of MACCS was released to the public in 1987. A subsequent version was used in the benchmark PRA study reported in NUREG-1 150. MACCS2 is a vcrsatilc codc, with most of its parametcrs being under uscr control to facilitatc thc pcrformancc of scnsitivity and unccrtainty analyscs.
Thc principal phcnomcna considcrcd by MACCS2 arc atmosphcric transport and dispcrsion (ATD), short- and long-tcrm mitigativc actions, cxposu rc pathways and doscs, dctcrministic and stochastic health cffccts, and cconomic costs. Of thcsc capabilities, only thc ATD proccsscs arc considcrcd in the prcscnt study. Thc at~nosphcric modcls in MACCS2 are rclativcly simplc. Rclcascd matcrial is assumcd to travcl downwind in a straight linc. Thc conccntration profilcs in thc cross- wind and vcrtical dimensions arc approximatcd as being Gaussian.
Thc Gaussian plumc model was choscn for MACCS2 bccausc it requires minimal co~nputational cffort and allows largc numbcrs of rcalizations to bc calculatcd, Thcsc rcalizations rcprcscnt unccrtainty in wcathcr data at thc timc ofa hypothctical aeeidcnt and unccrtainty in other input paramctcrs to rcprcscnt dcgrcc of bclicf. Largc numbcrs of rcalizations (hundrcd s) arc gcncrally necdcd to pcrform PRA and scnsitivity stud ics. 3.1.1 Meteorological Representation The normal calculation mode for MACCS2 is to sample from hourly weathcr data for one year and to calei~late ATD using a Gaussian model in each of 16 directions.
Each direction corresponds to a 22.5 degree-wide sector that is centered on a standard compass point.
Each weather sequence is weighted by its probability of occurrence.
The weather scquences are normally chosen, and have been chosen for this study, to emphasize sampling of sequences beIieved to be important to the prediction of early health effects in an exposed population.
This emphasizes seIection of weather sequences in which it rains while the plume remains within about 32.2 km (20 miles) from the point of release. MACCS2 was used to select the weather sequences that were used in this study. A total of 610 sequences was chosen using the standard weather binning approach.
This approach bins each of the 8760 hours of data in an annual weather file into 36 bins, as shown in Table 1. The last two columns of the table represent the values for the ARM SGP site. The columns in Table 1 show for each weather bin the included stability class or classes, the wind speed range, and the range ofdistances traveled by the plume when rain of a prescribed intensity occurs.
It also shows the overall number of weather sequences in the bin and the number of weather sequences selected from the bin in this study. The algorithm used to determine the number of sequences selected from each bin is the larger of two quantities:
12 or 5% of the number ofsequences in the bin. In 13 cases, the number ofweather sequences in the bin is fewer than
: 12. In these cases, all ofthe sequences in the bin are selected.
Selection of sequences from a bin where not all sequences are chosen is performed by a sequential Monte-Carlo process.
The probability associated with a weather trial is calculated within MACCS2 using the following algorithm.
First, the probability that a weather trial falls into a particular bin, P,, is proportional to the number of trials that are assigned to that bin. whcrc N, is thc nurnbcr of wcathcr trials in bin Band N is thc total nurnbcr ofwcathcr trials for the ycar (8760 in a 365-day ycar). Thc probability for a wcathcr trial from bin B is thcn cxprcsscd as whcrc P, is the probability associatcd with wcathcr trial Tand N,s, is thc nurnbcr of wcather trials samplcd from bin B (givcn in thc last column ofTablc 1). Thus, thc sum of thc probabilitics of thc wcathcr trials sclcctcd from bin B is P,. Valucs for thc probabilitics for cach wcathcr trial wcrc dcter~nincd from thc MACCS2 output and wcrc uscd in thc avcraging proccss for all thc rcsults prcscntcd in this rcport. Thc standard practicc ofallowing wind rotation was used for thc MACCS2 rcsi~lts, which csscntially cxpands thc numbcr ofwcathcr trials by a factor of 16. This practicc was not adoptcd by thc othcr codcs. For cach wcather trial, a sct ofcalculations is pcrfor~ncd to account for thc fact that thc wind could havc bccn blowing in any of thc 16 compass d ircctions.
Each of thc 16 rcsillts for wind rotation is wcightcd by thc Table 1. Description of Weather Bins Used in MACCS2 Bin Stability Wind Rai n Number of Number of N o. Class Speed Weather Weather Range (m/s) Distance Intensity Sequences Sequences (km) (mmlhr) in Bin Selected 1 A1 B 0-3 < 32 0 312 16 2 A/ B > 3 < 32 0 194 12 3 C/ D 0- I < 32 0 13 12 4 Cl D 1-2 < 32 0 100 12 5 C/ D 2 - 3 < 32 0 36 1 18 6 C/ D 3-5 < 32 0 1077 5 4 7 CI D 5 - 7 < 32 0 2202 l I0 X C/ D > 7 < 32 0 2370 l I9 9 E 0- 1 < 32 0 6 6 10 E 1-2 < 32 0 69 12 11 E 2-3 < 32 0 177 12 12 E > 3 < 32 0 998 5 0 13 F 0 - 1 < 32 0 2 9 12 14 F 1-2 < 32 0 67 12 15 F 2- 3 < 32 0 52 12 16 F > 3 < 32 0 3 3 17 all all 0-3 0 - 2 33 1 17 18 all all 3-6 0 - 2 8 8 19 all all 6- 11 0 - 2 3 1 12 2 0 all all 11 -21 0 - 2 I OX 12 2 1 all all 21 -32 0 - 2 118 12 2 2 all all 0 - 3 2-4 3 9 12 2 3 all all 3-6 2-4 1 I 24 all all 6- 11 2-4 1 1 2 5 all all 11 -21 2-4 5 5 2 6 all all 21 -32 2-4 9 9 27 all all 0-3 4-6 2 7 12 28 a I1 all 3-6 4-6 0 0 29 all all 6- 11 4-6 3 3 3 0 all all 11 -21 4-6 5 5 3 1 all all 21 -32 4-6 7 7 32 all all 0 - 3 > 6 27 12 33 all all 3-6 > 6 0 0 34 all all 6-11 > 6 1 1 3 5 all all 11 -21 > 6 4 4 3 6 all all 21 - 32 >6 5 5 Total 8760 610 probability ofthe wind blowing in the specified direction.
The probabilities associated with the possible wind directions are constructed for each weather bin and are proportional to the number of trials in the bin in which the wind blows in the specified d irection.
This probability is given by where P,, is the probability of a sample in bin B having wind direction R and N,, is the number ofweather trials in bin B with wind direction R. The final probability for weather trial T with wind rotation R used in the MACCSZ code is simply the product of the two probabilities, as follows: where P,., is the probability of weather trial T with wind direction R. MACCSZ uses single-point weather data. Thus, it approximates weather data as spatially uniform. The weather data file contains the following information:
Ju lian day ofthe year, hour of the day, wind direction, stability class, and precipitation rate. It also contains seasonal mixing heights (discussed in SLI bsection 5.2). While MACCSZ does not modcl spatial variation in wind conditions, it docs model time dcpcndcncc.
Once a plume is formcd, its dircction is not allowed to changc; howcvcr, thc wind spccd, stability class, and precipitation rate can changc hour-by-hour.


====3.1.2 Atmospheric====
Con~parisonof Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model Lawrence Livermore National Laboratory U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory Research Washington, DC 20555-0001


Transport and Dispersion The plume is assumed to move downwind at the prescribed wind speed adjusted for plume centerline elevation. The plume broadens by dispersion due to atmospheric turbulence as it is transported downwind.
Comparison of Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model Manuscript Completed: October 2004 Date published: October 2004 Prepared by C.R. Molenkamp (LLNL), N.E. Bixler, C.W. Morrow (SNL),
MACCS2 allows dispersion to be treated either by means of a lookup table or as a power-law function of distancc.
J.V. Ramsdell, Jr.. (PNNL), J.A. Mitchell (NRC)
For this work, the standard Tadmor and Gur lookup tablcs (Tadmor and Gur 1969, Dobbins 1979) were used to determine cross-wind and vertical dispersion as a function of downwind distance and stability class. Vertical dispersion is assumed to occur only within the mixing layer.
Atmospheric Science Division                    Sandia National Laboratories Lawrence Livermore National Laboratory          Albuquerque, NM 87 185-0748 Livennore, CA 94550 Pacific Northwest National Laboratory Richland, WA 99352 J.A. Mitchell, NRC Project Manager Prepared for Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 NRC Job Code Y6785
MACCSZ uses four mixing heights to represent the four seasons ofthe year. These mixing heights represent seasonal averages of the daily maxim~itn values of the m ixing heights. Calculation of the mixing heights used in this study is discussed in section 5. The MACCSZ Gaussian plume model treats the ground surface and a surface at the mixing height as planes of retlective symmetry.
: 3. MODELS The NIELCOR Accident Consequence C o d e System Version 2 (MACCS2) (Chanin et al.
: 7. SOURCE TERM Each code requires that the user input a source term, that is, parameters giving the time and duration of the release, the height of the release, buoyancy ofthe released material, and release magnitudes of different rad ionuclides.
1998) w a s developed at Sandia National Laboratories for the NRC. Its primary use is in performing consequence analyses in support o f level-3 probabilistic risk assesslnents (PRAs). It is also used by the NRC for planning purposes and cost-benefit analyses.
This last input is described in all the codes as an inventory ofeach radionuclide at the start ofthe problem and a release fraction of several rad ionuclide chemical element groups. This forlnulation, which allows each code to account for radioactive decay of the various radionuclides from the start of the problem to the release of the material, is not needed for this study. Our source term was formulated to be as simple as possible while still allowing the ATD processes to be compared:
MACCS2 is the latest in a series of N RC-sponsored codes for estimating off-site consequences following a release o f radioactivc ~ n a t e r i a linto t h e environment. The first code in the series w a s CRAC (Calculation of Reactor Accident Consequences), which was developed for the Reactor Safety Study (WASH-1400, 1975). The first version of M A C C S w a s released to the public in 1987. A subsequent version was used in the benchmark PRA study reported in NUREG-1 150.
we chose a single, long-lived radionuclide that does not deposit and a single, long-lived radionuclide that does deposit. Further, the inventory of each of these two radionuclides was arbitrarily chosen as 10'Bq. This does not represent a realistic release from any N RC-licensed facility.
MACCS2 is a vcrsatilc codc, with most o f its parametcrs being u n d e r uscr control to facilitatc thc pcrformancc of scnsitivity and unccrtainty analyscs. Thc principal p h c n o m c n a considcrcd by MACCS2 a r c atmosphcric transport and dispcrsion (ATD),
We chose only two radionuclides instead of tens ofdifferent radionuclides (as could be in a release from a severe accident at a nuclear power plant) because we wanted to avoid confounding the depositions and exposures with short-, medium-, and long-lived material, in case the comparison were to show unfavorable results.
short- and long-tcrm mitigativc actions, cxposu rc pathways and doscs, dctcrministic and stochastic health cffccts, and cconomic costs. O f thcsc capabilities, only thc ATD proccsscs a r c considcrcd in the prcscnt study.
We believed that "trouble-shooting" the differences would be easier with only two radionuclides.
Thc a t ~ n o s p h c r i cmodcls in MACCS2 are rclativcly simplc. Rclcascd matcrial is assumcd to travcl d o w n w i n d in a straight linc. Thc conccntration profilcs in thc cross-wind and vcrtical dimensions arc approximatcd as being Gaussian. Thc Gaussian p l u m c model w a s choscn for MACCS2 bccausc it requires minimal c o ~ n p u t a t i o n a cffort l
As will be seen in the results section, this silnplification was unnecessary.
and allows largc n u m b c r s o f rcalizations to bc calculatcd, Thcsc rcalizations rcprcscnt unccrtainty in wcathcr d a t a at thc timc o f a hypothctical aeeidcnt and unccrtainty in other input paramctcrs t o rcprcscnt dcgrcc of bclicf. Largc n u m b c r s of rcalizations (hundrcd s) arc gcncrally necdcd to pcrform PRA and scnsitivity stud ics.
The characteristics of the source term for this study are given in Table 12. The values of a, and a,, the initial size ofthe plume, are not usually considered part of the "source term," but since they influence the initial plume they are included here. Table 12. Sou rce Term Specification Characteristic Value Location ARM Central Facility Time of release 0.0 s Duration of release 1800 s. uniform Amount of rcleasc, each nuclide 10'" Height of release 50 m Buoyant energy lo" W Because each model has a different arc average exposure and deposition, it is difficult to portray how closely the angular distributions actually agree. Figures 38-49 show the angular distributions normalized by each model's arc average concentration.
3.1.1 Meteorological Representation The normal calculation m o d e for MACCS2 is to sample from hourly weathcr data for one year and to calei~lateATD using a Gaussian model in each o f 16 directions. Each direction corresponds to a 22.5 degree-wide sector that is centered on a standard compass point. Each weather sequence is weighted by its probability of occurrence. The weather scquences a r e normally chosen, and have been chosen for this study, to emphasize sampling o f sequences beIieved to be important to the prediction o f early health effects in an exposed population. This emphasizes seIection o f weather sequences
The ordinate in these plots is logarithmic so that multiplicative changes are proportional to distance, i.e., a value twice the average is just as far above the average line as a value half the average is below, and a value four times the average is twice as far above the average line as a value twice the average. These figures also include the north sector on both sides.
 
The angular distributions of exposure and deposition are quite similar for all models and again reflect the distribution of the wind. The highest values are to the north where the exposure or deposition is 2-3 times the average; intermediate values, near the average, occur in southerly directions; lower values, from one-half to three-quarters of the average, occur to the west of the source; and the lowest values, often less the one- half the average, occur to the east, corresponding to infrequent westerly winds. The largest differences in normalized exposure and deposition occur in sectors to the east and west where the values of exposure and deposition are smaller. In general, the angular distribution from MACCS2 seems to correspond more closely with LODI than RASCAL or RATCHET. This is a bit surprising since RASCAL and RATCHET follow individual plumes more closely than MACCS2, and the annual distributions are averages of individual plumes from the 610 releases just like LODI.
in which it rains while the plume remains within about 32.2 km (20 miles) from the point of release.
Where local maxima (minima) of the curves are displaced, it is often by only one sector; that could be a result of individual plumes taking slightly different tracks and showing up in neighboring sectors. LODI also makes use of upper-level wind data; therefore, wind direction shear with height would be represented in LODI but not in the other models. For most plumes from individual releases, exposure and deposition are confined to two or three sectors. The differences in normalized distributions do not increase with distance, in fact they may even decrease. Larger differences in deposition are probably due to relatively infrequent large rain events occurring at different locations.
MACCS2 w a s used t o select the weather sequences that were used in this study. A total of 610 sequences w a s chosen using the standard weather binning approach. This approach bins each of the 8760 h o u r s of d a t a in an annual weather file into 36 bins, as shown in Table 1. The last t w o columns of the table represent t h e values for the ARM SGP site.
Heavy rain over a period of an hour can deposit most of the depositing material in a local area and largely deplete the plume.
The columns in Table 1 show for each weather bin the included stability class o r classes, the wind speed range, and the range ofdistances traveled by the p l u m e when rain of a prescribed intensity occurs. It also s h o w s t h e overall number of weather sequences in the bin and the n u m b e r of weather sequences selected from t h e bin in this study. The algorithm used to determine the number of sequences selected from each bin is the larger of t w o quantities: 12 o r 5% of the number ofsequences in the bin. In 13 cases, the n u m b e r o f w e a t h e r sequences in the bin is fewer than 12. In these cases, all o f t h e sequences in the bin are selected. Selection of sequences from a bin w h e r e not all sequences are chosen is performed by a sequential Monte-Carlo process.
10.3 Tw o-D imensional Exposure and Deposition While not a primary metric of comparison, it is interesting to examine the two- dimensional exposure and deposition plots from each model; these are shown in Figures 50-52. The differences in these plots are only partly due to differences in results; they also depend on the location and spacing of the data used to construct them and to particular features of the models. The MACCS2 plots are based on radial1 sector exposure (deposition) data, specifically, 29 not very evenly spaced radii from 0.16 to 320.8 km (0.1 to 200 miles) and 16 sectors. In these figures the data are plotted for radii N PJNE 1\IE ENE E ESE SE SSE S SSW SWVVSW W \r\lNWNW NNVV 1\12 Sector Figure 42. Normalized Exposure for Depositing Material on the 16.1-km (10-mile)
The probability associated with a weather trial is calculated within MACCS2 using the following algorithm. First, the probability that a weather trial falls into a particular bin, P,, is proportional to the number of trials that are assigned to that bin.
Arc. MACCS .... .... . .... IIIIIIIIIIIIIIIII N NNE NE ENE E ESE SE SSE S SSW SW WSW VV iNNWNW NN'W N2 Sector Figure 43. Normalized Exposure for Depositing Material on the 32.2-km (20-mile)
whcrc N , is thc nurnbcr of wcathcr trials in bin B a n d N is thc total nurnbcr o f w c a t h c r trials for t h e ycar (8760 in a 365-day ycar). Thc probability for a wcathcr trial from bin B is thcn cxprcsscd as whcrc P, is the probability associatcd with wcathcr trial T a n d N,s, is thc nurnbcr of wcather trials samplcd from bin B (givcn in thc last column ofTablc 1). Thus, thc s u m of thc probabilitics of thc wcathcr trials sclcctcd from bin B is P,. Valucs for thc probabilitics for cach wcathcr trial wcrc d c t e r ~ n i n c dfrom thc MACCS2 o u t p u t and wcrc uscd in thc avcraging proccss for all thc rcsults prcscntcd in this rcport.
Thc standard practicc ofallowing wind rotation w a s used for thc MACCS2 rcsi~lts, which csscntially cxpands thc numbcr o f w c a t h c r trials by a factor o f 16. This practicc w a s not adoptcd by thc othcr codcs. For cach wcather trial, a sct ofcalculations is p c r f o r ~ n c dto account for thc fact that t h c wind could havc bccn blowing in any of thc 16 compass d ircctions. Each of thc 16 rcsillts for wind rotation is wcightcd by thc
 
Table 1. Description of Weather Bins Used in MACCS2 Bin  Stability      Wind                Rai n      N u m b e r of N u m b e r of N o. Class          Speed                              Weather      Weather Range (m/s) Distance Intensity        Sequences Sequences (km)      (mmlhr)    in Bin      Selected 1    A1 B          0-3          < 32          0        312                16 2      A/ B          >3            < 32          0        194                12 3      C/ D          0- I          < 32          0          13                12 4      Cl D          1-2          < 32          0        100                12 5      C/ D          2-3          < 32          0        36 1              18 6      C/ D          3-5          < 32          0        1077                54 7    CI D          5-7          < 32          0      2202              l I0 X    C/ D          >7            < 32          0      2370              l I9 9        E            0- 1          < 32          0          6                6 10      E            1-2          < 32          0          69                12 11      E            2-3          < 32          0        177                12 12      E            >3            < 32          0        998                50 13      F            0- 1          < 32          0          29                12 14      F            1-2          < 32          0          67                12 15      F            2- 3          < 32          0          52                12 16      F            >3            < 32          0          3                3 17      all            all        0-3          0 -2        33 1              17 18      all            all        3-6          0 -2          8                8 19      all            all        6- 11        0 -2        31                12 20      all            all        1 1 -21      0 -2        IOX                12 21      all            all      21 - 3 2      0-2        118                12 22      all            all        0-3          2-4          39                12 23      all            all        3-6          2-4            1                I 24      all            all        6- 11        2-4            1                1 25      all            all        1 1 -21      2-4          5                5 26      all            all      21 - 3 2      2-4          9                9 27      all            all        0-3          4-6          27                12 28      a I1          all          3-6        4-6          0                0 29      all            all        6- 11        4-6            3                3 30      all            all        1 1 -21      4-6            5                5 31      all            all      21 - 3 2      4-6            7                7 32      all            all          0-3          >6          27                12 33      all            all          3-6          >6            0                0 34      all            all        6-11          >6            1                1 35      all            all        1 1 -21        >6          4                4 36      all            all      21 - 32        >6            5                5 Total                                                      8760              610
 
probability o f t h e wind blowing in the specified direction. The probabilities associated with the possible wind directions are constructed for each weather bin and a r e proportional to the number of trials in the bin in which the wind blows in the specified d irection. This probability is given by w h e r e P,, is the probability of a sample in bin B having wind direction R and N,, is the n u m b e r o f w e a t h e r trials in bin B with wind direction R . The final probability for weather trial T with wind rotation R used in the MACCSZ code is simply the product of the t w o probabilities, as follows:
w h e r e P,., is the probability of weather trial T with wind direction R .
MACCSZ uses single-point weather d a t a . Thus, it approximates weather data as spatially uniform. The weather d a t a file contains the following information: Ju lian d a y o f t h e year, hour of the d a y , wind direction, stability class, and precipitation rate. It also contains seasonal mixing heights (discussed in SLIbsection 5.2). While MACCSZ d o e s not modcl spatial variation in wind conditions, it d o c s model time dcpcndcncc. Once a p l u m e is formcd, its dircction is not allowed to changc; howcvcr, thc wind spccd, stability class, and precipitation rate can changc hour-by-hour.
3.1.2 Atmospheric Transport and Dispersion The p l u m e is assumed to m o v e d o w n w i n d at the prescribed wind speed adjusted for p l u m e centerline elevation. The p l u m e broadens by dispersion d u e to atmospheric turbulence a s it is transported d o w n w i n d . MACCS2 allows dispersion to be treated either by means of a lookup table or as a power-law function of distancc. For this work, the standard T a d m o r and G u r lookup tablcs (Tadmor and G u r 1969, Dobbins 1979) were used to determine cross-wind and vertical dispersion as a function of d o w n w i n d distance and stability class.
Vertical dispersion is assumed to occur only within the mixing layer. MACCSZ uses four mixing heights to represent the four seasons o f t h e year. These mixing heights represent seasonal averages of the daily m a x i m ~ i t nvalues of the m ixing heights.
Calculation o f the mixing heights used in this study is discussed in section 5. The MACCSZ Gaussian p l u m e model treats the ground surface and a surface at the mixing height as planes of retlective symmetry.
: 7. SOURCE TERM Each code requires that the user input a source term, that is, parameters giving the time and duration of the release, the height of the release, buoyancy o f t h e released material, and release magnitudes of different rad ionuclides. This last input is described in all the codes as an inventory ofeach radionuclide at the start o f t h e problem and a release fraction of several rad ionuclide chemical element groups. This forlnulation, which allows each code to account for radioactive decay o f the various radionuclides from the start of t h e problem to the release of the material, is not needed for this study. O u r source term w a s formulated to b e as simple as possible while still allowing t h e ATD processes to b e compared: w e chose a single, long-lived radionuclide that d o e s not deposit and a single, long-lived radionuclide that d o e s deposit. Further, the inventory of each of these t w o radionuclides w a s arbitrarily chosen as 1 0 ' B q . This does not represent a realistic release from any N RC-licensed facility.
We chose only t w o radionuclides instead of tens ofdifferent radionuclides (as could be in a release from a severe accident at a nuclear p o w e r plant) because w e wanted to avoid confounding the depositions and exposures with short-, medium-, and long-lived material, in case the comparison w e r e to show unfavorable results. We believed that "trouble-shooting" the differences would be easier with only t w o radionuclides. A s will be seen in t h e results section, this silnplification w a s unnecessary.
The characteristics of the source term for this study are given in Table 12. The values of a, and a,, the initial size o f t h e plume, are not usually considered part of the "source term," but since they influence the initial p l u m e they are included here.
Table 12. Sou rce Term Specification Characteristic                      Value Location                              ARM Central Facility Time of release                        0.0 s Duration of release                  1800 s. uniform A m o u n t o f rcleasc, each nuclide  10'"
Height of release                    50 m Buoyant energy                        lo" W
 
Because each model has a different arc average exposure and deposition, it is difficult to portray how closely the angular distributions actually agree. Figures 38-49 show the angular distributions normalized by each model's arc average concentration. The ordinate in these plots is logarithmic so that multiplicative changes are proportional to distance, i.e., a value twice the average is just as far above the average line as a value half the average is below, and a value four times the average is twice as far above the average line as a value twice the average. These figures also include the north sector on both sides.
The angular distributions of exposure and deposition are quite similar for all models and again reflect the distribution of the wind. The highest values are to the north where the exposure or deposition is 2-3 times the average; intermediate values, near the average, occur in southerly directions; lower values, from one-half to three-quarters of the average, occur to the west of the source; and the lowest values, often less the one-half the average, occur to the east, corresponding to infrequent westerly winds. The largest differences in normalized exposure and deposition occur in sectors to the east and west where the values of exposure and deposition are smaller.
In general, the angular distribution from MACCS2 seems to correspond more closely with LODI than RASCAL or RATCHET. This is a bit surprising since RASCAL and RATCHET follow individual plumes more closely than MACCS2, and the annual distributions are averages of individual plumes from the 610 releases just like LODI.
Where local maxima (minima) of the curves are displaced, it is often by only one sector; that could be a result of individual plumes taking slightly different tracks and showing up in neighboring sectors. LODI also makes use of upper-level wind data; therefore, wind direction shear with height would be represented in LODI but not in the other models. For most plumes from individual releases, exposure and deposition are confined to two or three sectors. The differences in normalized distributions d o not increase with distance, in fact they may even decrease. Larger differences in deposition are probably d u e to relatively infrequent large rain events occurring at different locations. Heavy rain over a period of an hour can deposit most of the depositing material in a local area and largely deplete the plume.
10.3 Tw o-D imensional Exposure and Deposition While not a primary metric of comparison, it is interesting to examine the two-dimensional exposure and deposition plots from each model; these are shown in Figures 50-52. The differences in these plots are only partly d u e to differences in results; they also depend on the location and spacing of the data used to construct them and to particular features of the models. The MACCS2 plots are based on radial1 sector exposure (deposition) data, specifically, 29 not very evenly spaced radii from 0.16 to 320.8 km (0.1 to 200 miles) and 16 sectors. In these figures the data are plotted for radii
 
N PJNE 1\IE ENE E ESE SE SSE S SSW SWVVSW W \r\lNWNW NNVV 1\12 Sector Figure 42. Normalized Exposure for Depositing Material on the 16.1-km (10-mile)
Arc.
MACCS I  I    I  I  I  I          I  I  I    I I I I I I I  I N NNE NE ENE E ESE SE SSE S SSW SW WSW VV iNNWNW NN'W N2 Sector Figure 43. Normalized Exposure for Depositing Material on the 32.2-km (20-mile)
Arc.
Arc.
IVIACCS ..,. ..... ..., K'ASC4L .-.-.- - RATCHET I I I I I I I I I 1 I I I I I 1 I I I N PJNE NE ENE E ESE SE SSE S SSW SVVV\IWd W VVNWI\IW NNVV N2 Sectar Figure 44. Normalized Exposurc for Depositing Material on thc 80.5-km (50-mile)
 
Arc. 11111111111111111 N NNE NE ENE E ESE SE SSE S SSW SWVVWV W WNWI'.lVV NNV'J N2 Sector Figure 45. Normalized Exposure for Depositing Material on the 160.9-km (1 00-m ile) Arc.
IVIACCS
N NNlNNWWNW W WSWSW SSW S SSE SE ESE E ENE NE NNE N2 Sector Figure 46. Normalized Deposition on the 16.9-km (10-mile)
                                ..,...... ..., K'ASC4L
Arc. 111111111/1111111 N NNWNWWNW W WSWSW SSW S SSE SE ESE E ENE NE NNE P.12 Sector Figure 47. Normalized Deposition on the 32.2-km (20-mile)
                                .-.-.-     - RATCHET I                                                               I I   I   I I I   I         I     1   I   I I I I 1 I I I N PJNE NE ENE E ESE SE SSE S SSW SVVV\IWd W VVNWI\IW NNVV N2 Sectar Figure 44. Normalized Exposurc for Depositing Material on thc 80.5-km (50-mile)
Arc.
Arc.
IIIIIIIIIIIIIIIII 1\1 NNlNNWWNW W WSVVSW SSW S SSE SE ESE E ENE NE NNE N2 Sector Figure 48. Normalized Deposition on thc 80.5-km (50-milc)
1  1  1  1  1  1          1    1  1    1 1 1 1 1 1 1  1 N NNE NE ENE E ESE SE SSE S SSW SWVVWV W WNWI'.lVV NNV'J N2 Sector Figure 45. Normalized Exposure for Depositing Material o n the 160.9-km (1 00-m ile) Arc.
Arc. I I I I I I I I I I I I I I I I I I N NNWNWWNW W WbVSW SSLIV S SSE SE ESE E ENE NE NNE N2 Sector Figure 49. Normalized Deposition on the 160.9-km (100-mile)
 
Arc.
N NNlNNWWNW W WSWSW SSW S SSE SE ESE E ENE NE NNE N2 Sector Figure 46. Normalized Deposition on the 16.9-km (10-mile) Arc.
(100 miles). The smooth contours in the plots for MACCS2 are a result ofthe solution technique, the assumed straight line transport, and the wide spacing of the data points (400 points). The LODI figures include some high frequency noise that is a feature of mapping parcels to a grid, especially a high-density (closely-spaced) concentration grid (122,500 individual exposures or depositions are used in constructing the contour plots). RASCAL, RATCHET, and LODI all show features in these annual averages that appear to preserve individual plumes, and there seems to be general agreement about the direction of these plumes. The RASCAL and RATCHET data are in quite close agreement except for the magnitude of the exposure or deposition.
1  1  1  1  1  1  1    1    1  / 1  1  1    1 1 1 1 N NNWNWWNW W WSWSW SSW S SSE SE ESE E ENE NE NNE P.12 Sector Figure 47. Normalized Deposition on the 32.2-km (20-mile) Arc.
This is expected since these models are very closely related and the main difference is the turbulent diffusion formulation.
 
RASCAL and RATCHET also have isolated downwind high deposition contours that are not present in MACCS2 or LODI plots. These are presumably due to rapid wet deposition when rain occurs several hours after the release. The closer spacing of the contours for MACCS2 compared with LODI, as one moves away from the release location, is evidence of the more rapid decrease of exposure and deposition with distance for MACCS2. In general, the similarities in the distributions of exposure and deposition shown by these plots are greater than the differences, particularly when consideration is given to the different density (closeness of spacing) of the underlying data.
I  I  I I  I    I  I  I  I    I  I  I  I    I I  I  I 1\1 NNlNNWWNW W WSVVSW SSW S SSE SE ESE E ENE NE NNE N2 Sector Figure 48. Normalized Deposition on thc 80.5-km (50-milc) Arc.
The more complex models certainly show more detail in structure; however, the smoothed distribution still show the common features that we noted in the previous sections on arc and arc-sector averages.
I I I   I I   I   I I   I   I     I I I   I   I I I I N NNWNWWNW W W b V S W SSLIV S SSE SE ESE E ENE NE NNE N2 Sector Figure 49. Normalized Deposition on the 160.9-km (100-mile) Arc.
10.4 Summary of Results All of the arc average and the great majority of the arc-sector average exposures and depositions are within a factor of two when comparing MACCS2 to the state-of-the-art model, LODI. Similar comparisons of RASCAL and RATCHET to LODI also have most exposures and depositions within a factor oftwo ofLODI. In fact the largest differences in results are between the closely related RASCAL and RATCHET models. We can identify at least two caveats to the discussion of model differences.
 
First, this study was performed in an area with smooth or favorable terrain and persistent winds although with structure in the form of low-level nocturnal jets and severe storms.
(100 miles). The smooth contours in the plots for MACCS2 are a result o f t h e solution technique, the assumed straight line transport, and the wide spacing of the data points (400 points). The LODI figures include some high frequency noise that is a feature of mapping parcels to a grid, especially a high-density (closely-spaced) concentration grid (122,500 individual exposures or depositions are used in constructing the contour plots).
In regions with complex terrain, particularly ifthe surface wind direction changes with height, caution should be used. Second, MACCS2 predicts a too rapid decrease of exposure with distance; this should be considered when MACCS2 is used to estimate consequences at distances greater than 321.8 km (200 miles). However, this second caveat is tempered by the fact that the majority of the deposition (and exposure to depositing material) is within this 321.8-km (200-mile) distance.}}
RASCAL, RATCHET, and LODI all show features in these annual averages that appear to preserve individual plumes, and there seems to be general agreement about the direction of these plumes. The RASCAL and RATCHET data are in quite close agreement except for the magnitude of the exposure or deposition. This is expected since these models are very closely related and the main difference is the turbulent diffusion formulation. RASCAL and RATCHET also have isolated downwind high deposition contours that are not present in MACCS2 or LODI plots. These are presumably d u e to rapid wet deposition when rain occurs several hours after the release. The closer spacing of the contours for MACCS2 compared with LODI, as one moves away from the release location, is evidence of the more rapid decrease of exposure and deposition with distance for MACCS2. In general, the similarities in the distributions of exposure and deposition shown by these plots are greater than the differences, particularly when consideration is given to the different density (closeness of spacing) of the underlying data. The more complex models certainly show more detail in structure; however, the smoothed distribution still show the common features that w e noted in the previous sections on arc and arc-sector averages.
10.4 Summary of Results All of the arc average and the great majority of the arc-sector average exposures and depositions are within a factor of two when comparing MACCS2 to the state-of-the-art model, LODI. Similar comparisons of RASCAL and RATCHET to LODI also have most exposures and depositions within a factor o f t w o ofLODI. In fact the largest differences in results are between the closely related RASCAL and RATCHET models.
We can identify at least two caveats to the discussion of model differences. First, this study was performed in an area with smooth or favorable terrain and persistent winds although with structure in the form of low-level nocturnal jets and severe storms. In regions with complex terrain, particularly ifthe surface wind direction changes with height, caution should be used. Second, MACCS2 predicts a too rapid decrease of exposure with distance; this should be considered when MACCS2 is used to estimate consequences at distances greater than 321.8 km (200 miles). However, this second caveat is tempered by the fact that the majority of the deposition (and exposure to depositing material) is within this 321.8-km (200-mile) distance.}}

Latest revision as of 08:54, 12 March 2020

Exhibit L - NUREG/CR-6853 - Comparison of Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model
ML092870644
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Indian Point Nuclear Generating Units 2 and 3 Docket Nos. 50-247/ 50-286-LR NRC Staff's Response in Opposition to State of New York's Motion for Partial Summary Disposition of NYS Contention 16116A Exhibit L

Con~parisonof Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model Lawrence Livermore National Laboratory U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory Research Washington, DC 20555-0001

Comparison of Average Transport and Dispersion Among a Gaussian, a Two-Dimensional, and a Three-Dimensional Model Manuscript Completed: October 2004 Date published: October 2004 Prepared by C.R. Molenkamp (LLNL), N.E. Bixler, C.W. Morrow (SNL),

J.V. Ramsdell, Jr.. (PNNL), J.A. Mitchell (NRC)

Atmospheric Science Division Sandia National Laboratories Lawrence Livermore National Laboratory Albuquerque, NM 87 185-0748 Livennore, CA 94550 Pacific Northwest National Laboratory Richland, WA 99352 J.A. Mitchell, NRC Project Manager Prepared for Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 NRC Job Code Y6785

3. MODELS The NIELCOR Accident Consequence C o d e System Version 2 (MACCS2) (Chanin et al.

1998) w a s developed at Sandia National Laboratories for the NRC. Its primary use is in performing consequence analyses in support o f level-3 probabilistic risk assesslnents (PRAs). It is also used by the NRC for planning purposes and cost-benefit analyses.

MACCS2 is the latest in a series of N RC-sponsored codes for estimating off-site consequences following a release o f radioactivc ~ n a t e r i a linto t h e environment. The first code in the series w a s CRAC (Calculation of Reactor Accident Consequences), which was developed for the Reactor Safety Study (WASH-1400, 1975). The first version of M A C C S w a s released to the public in 1987. A subsequent version was used in the benchmark PRA study reported in NUREG-1 150.

MACCS2 is a vcrsatilc codc, with most o f its parametcrs being u n d e r uscr control to facilitatc thc pcrformancc of scnsitivity and unccrtainty analyscs. Thc principal p h c n o m c n a considcrcd by MACCS2 a r c atmosphcric transport and dispcrsion (ATD),

short- and long-tcrm mitigativc actions, cxposu rc pathways and doscs, dctcrministic and stochastic health cffccts, and cconomic costs. O f thcsc capabilities, only thc ATD proccsscs a r c considcrcd in the prcscnt study.

Thc a t ~ n o s p h c r i cmodcls in MACCS2 are rclativcly simplc. Rclcascd matcrial is assumcd to travcl d o w n w i n d in a straight linc. Thc conccntration profilcs in thc cross-wind and vcrtical dimensions arc approximatcd as being Gaussian. Thc Gaussian p l u m c model w a s choscn for MACCS2 bccausc it requires minimal c o ~ n p u t a t i o n a cffort l

and allows largc n u m b c r s o f rcalizations to bc calculatcd, Thcsc rcalizations rcprcscnt unccrtainty in wcathcr d a t a at thc timc o f a hypothctical aeeidcnt and unccrtainty in other input paramctcrs t o rcprcscnt dcgrcc of bclicf. Largc n u m b c r s of rcalizations (hundrcd s) arc gcncrally necdcd to pcrform PRA and scnsitivity stud ics.

3.1.1 Meteorological Representation The normal calculation m o d e for MACCS2 is to sample from hourly weathcr data for one year and to calei~lateATD using a Gaussian model in each o f 16 directions. Each direction corresponds to a 22.5 degree-wide sector that is centered on a standard compass point. Each weather sequence is weighted by its probability of occurrence. The weather scquences a r e normally chosen, and have been chosen for this study, to emphasize sampling o f sequences beIieved to be important to the prediction o f early health effects in an exposed population. This emphasizes seIection o f weather sequences

in which it rains while the plume remains within about 32.2 km (20 miles) from the point of release.

MACCS2 w a s used t o select the weather sequences that were used in this study. A total of 610 sequences w a s chosen using the standard weather binning approach. This approach bins each of the 8760 h o u r s of d a t a in an annual weather file into 36 bins, as shown in Table 1. The last t w o columns of the table represent t h e values for the ARM SGP site.

The columns in Table 1 show for each weather bin the included stability class o r classes, the wind speed range, and the range ofdistances traveled by the p l u m e when rain of a prescribed intensity occurs. It also s h o w s t h e overall number of weather sequences in the bin and the n u m b e r of weather sequences selected from t h e bin in this study. The algorithm used to determine the number of sequences selected from each bin is the larger of t w o quantities: 12 o r 5% of the number ofsequences in the bin. In 13 cases, the n u m b e r o f w e a t h e r sequences in the bin is fewer than 12. In these cases, all o f t h e sequences in the bin are selected. Selection of sequences from a bin w h e r e not all sequences are chosen is performed by a sequential Monte-Carlo process.

The probability associated with a weather trial is calculated within MACCS2 using the following algorithm. First, the probability that a weather trial falls into a particular bin, P,, is proportional to the number of trials that are assigned to that bin.

whcrc N , is thc nurnbcr of wcathcr trials in bin B a n d N is thc total nurnbcr o f w c a t h c r trials for t h e ycar (8760 in a 365-day ycar). Thc probability for a wcathcr trial from bin B is thcn cxprcsscd as whcrc P, is the probability associatcd with wcathcr trial T a n d N,s, is thc nurnbcr of wcather trials samplcd from bin B (givcn in thc last column ofTablc 1). Thus, thc s u m of thc probabilitics of thc wcathcr trials sclcctcd from bin B is P,. Valucs for thc probabilitics for cach wcathcr trial wcrc d c t e r ~ n i n c dfrom thc MACCS2 o u t p u t and wcrc uscd in thc avcraging proccss for all thc rcsults prcscntcd in this rcport.

Thc standard practicc ofallowing wind rotation w a s used for thc MACCS2 rcsi~lts, which csscntially cxpands thc numbcr o f w c a t h c r trials by a factor o f 16. This practicc w a s not adoptcd by thc othcr codcs. For cach wcather trial, a sct ofcalculations is p c r f o r ~ n c dto account for thc fact that t h c wind could havc bccn blowing in any of thc 16 compass d ircctions. Each of thc 16 rcsillts for wind rotation is wcightcd by thc

Table 1. Description of Weather Bins Used in MACCS2 Bin Stability Wind Rai n N u m b e r of N u m b e r of N o. Class Speed Weather Weather Range (m/s) Distance Intensity Sequences Sequences (km) (mmlhr) in Bin Selected 1 A1 B 0-3 < 32 0 312 16 2 A/ B >3 < 32 0 194 12 3 C/ D 0- I < 32 0 13 12 4 Cl D 1-2 < 32 0 100 12 5 C/ D 2-3 < 32 0 36 1 18 6 C/ D 3-5 < 32 0 1077 54 7 CI D 5-7 < 32 0 2202 l I0 X C/ D >7 < 32 0 2370 l I9 9 E 0- 1 < 32 0 6 6 10 E 1-2 < 32 0 69 12 11 E 2-3 < 32 0 177 12 12 E >3 < 32 0 998 50 13 F 0- 1 < 32 0 29 12 14 F 1-2 < 32 0 67 12 15 F 2- 3 < 32 0 52 12 16 F >3 < 32 0 3 3 17 all all 0-3 0 -2 33 1 17 18 all all 3-6 0 -2 8 8 19 all all 6- 11 0 -2 31 12 20 all all 1 1 -21 0 -2 IOX 12 21 all all 21 - 3 2 0-2 118 12 22 all all 0-3 2-4 39 12 23 all all 3-6 2-4 1 I 24 all all 6- 11 2-4 1 1 25 all all 1 1 -21 2-4 5 5 26 all all 21 - 3 2 2-4 9 9 27 all all 0-3 4-6 27 12 28 a I1 all 3-6 4-6 0 0 29 all all 6- 11 4-6 3 3 30 all all 1 1 -21 4-6 5 5 31 all all 21 - 3 2 4-6 7 7 32 all all 0-3 >6 27 12 33 all all 3-6 >6 0 0 34 all all 6-11 >6 1 1 35 all all 1 1 -21 >6 4 4 36 all all 21 - 32 >6 5 5 Total 8760 610

probability o f t h e wind blowing in the specified direction. The probabilities associated with the possible wind directions are constructed for each weather bin and a r e proportional to the number of trials in the bin in which the wind blows in the specified d irection. This probability is given by w h e r e P,, is the probability of a sample in bin B having wind direction R and N,, is the n u m b e r o f w e a t h e r trials in bin B with wind direction R . The final probability for weather trial T with wind rotation R used in the MACCSZ code is simply the product of the t w o probabilities, as follows:

w h e r e P,., is the probability of weather trial T with wind direction R .

MACCSZ uses single-point weather d a t a . Thus, it approximates weather data as spatially uniform. The weather d a t a file contains the following information: Ju lian d a y o f t h e year, hour of the d a y , wind direction, stability class, and precipitation rate. It also contains seasonal mixing heights (discussed in SLIbsection 5.2). While MACCSZ d o e s not modcl spatial variation in wind conditions, it d o c s model time dcpcndcncc. Once a p l u m e is formcd, its dircction is not allowed to changc; howcvcr, thc wind spccd, stability class, and precipitation rate can changc hour-by-hour.

3.1.2 Atmospheric Transport and Dispersion The p l u m e is assumed to m o v e d o w n w i n d at the prescribed wind speed adjusted for p l u m e centerline elevation. The p l u m e broadens by dispersion d u e to atmospheric turbulence a s it is transported d o w n w i n d . MACCS2 allows dispersion to be treated either by means of a lookup table or as a power-law function of distancc. For this work, the standard T a d m o r and G u r lookup tablcs (Tadmor and G u r 1969, Dobbins 1979) were used to determine cross-wind and vertical dispersion as a function of d o w n w i n d distance and stability class.

Vertical dispersion is assumed to occur only within the mixing layer. MACCSZ uses four mixing heights to represent the four seasons o f t h e year. These mixing heights represent seasonal averages of the daily m a x i m ~ i t nvalues of the m ixing heights.

Calculation o f the mixing heights used in this study is discussed in section 5. The MACCSZ Gaussian p l u m e model treats the ground surface and a surface at the mixing height as planes of retlective symmetry.

7. SOURCE TERM Each code requires that the user input a source term, that is, parameters giving the time and duration of the release, the height of the release, buoyancy o f t h e released material, and release magnitudes of different rad ionuclides. This last input is described in all the codes as an inventory ofeach radionuclide at the start o f t h e problem and a release fraction of several rad ionuclide chemical element groups. This forlnulation, which allows each code to account for radioactive decay o f the various radionuclides from the start of t h e problem to the release of the material, is not needed for this study. O u r source term w a s formulated to b e as simple as possible while still allowing t h e ATD processes to b e compared: w e chose a single, long-lived radionuclide that d o e s not deposit and a single, long-lived radionuclide that d o e s deposit. Further, the inventory of each of these t w o radionuclides w a s arbitrarily chosen as 1 0 ' B q . This does not represent a realistic release from any N RC-licensed facility.

We chose only t w o radionuclides instead of tens ofdifferent radionuclides (as could be in a release from a severe accident at a nuclear p o w e r plant) because w e wanted to avoid confounding the depositions and exposures with short-, medium-, and long-lived material, in case the comparison w e r e to show unfavorable results. We believed that "trouble-shooting" the differences would be easier with only t w o radionuclides. A s will be seen in t h e results section, this silnplification w a s unnecessary.

The characteristics of the source term for this study are given in Table 12. The values of a, and a,, the initial size o f t h e plume, are not usually considered part of the "source term," but since they influence the initial p l u m e they are included here.

Table 12. Sou rce Term Specification Characteristic Value Location ARM Central Facility Time of release 0.0 s Duration of release 1800 s. uniform A m o u n t o f rcleasc, each nuclide 10'"

Height of release 50 m Buoyant energy lo" W

Because each model has a different arc average exposure and deposition, it is difficult to portray how closely the angular distributions actually agree. Figures 38-49 show the angular distributions normalized by each model's arc average concentration. The ordinate in these plots is logarithmic so that multiplicative changes are proportional to distance, i.e., a value twice the average is just as far above the average line as a value half the average is below, and a value four times the average is twice as far above the average line as a value twice the average. These figures also include the north sector on both sides.

The angular distributions of exposure and deposition are quite similar for all models and again reflect the distribution of the wind. The highest values are to the north where the exposure or deposition is 2-3 times the average; intermediate values, near the average, occur in southerly directions; lower values, from one-half to three-quarters of the average, occur to the west of the source; and the lowest values, often less the one-half the average, occur to the east, corresponding to infrequent westerly winds. The largest differences in normalized exposure and deposition occur in sectors to the east and west where the values of exposure and deposition are smaller.

In general, the angular distribution from MACCS2 seems to correspond more closely with LODI than RASCAL or RATCHET. This is a bit surprising since RASCAL and RATCHET follow individual plumes more closely than MACCS2, and the annual distributions are averages of individual plumes from the 610 releases just like LODI.

Where local maxima (minima) of the curves are displaced, it is often by only one sector; that could be a result of individual plumes taking slightly different tracks and showing up in neighboring sectors. LODI also makes use of upper-level wind data; therefore, wind direction shear with height would be represented in LODI but not in the other models. For most plumes from individual releases, exposure and deposition are confined to two or three sectors. The differences in normalized distributions d o not increase with distance, in fact they may even decrease. Larger differences in deposition are probably d u e to relatively infrequent large rain events occurring at different locations. Heavy rain over a period of an hour can deposit most of the depositing material in a local area and largely deplete the plume.

10.3 Tw o-D imensional Exposure and Deposition While not a primary metric of comparison, it is interesting to examine the two-dimensional exposure and deposition plots from each model; these are shown in Figures 50-52. The differences in these plots are only partly d u e to differences in results; they also depend on the location and spacing of the data used to construct them and to particular features of the models. The MACCS2 plots are based on radial1 sector exposure (deposition) data, specifically, 29 not very evenly spaced radii from 0.16 to 320.8 km (0.1 to 200 miles) and 16 sectors. In these figures the data are plotted for radii

N PJNE 1\IE ENE E ESE SE SSE S SSW SWVVSW W \r\lNWNW NNVV 1\12 Sector Figure 42. Normalized Exposure for Depositing Material on the 16.1-km (10-mile)

Arc.

MACCS I I I I I I I I I I I I I I I I I N NNE NE ENE E ESE SE SSE S SSW SW WSW VV iNNWNW NN'W N2 Sector Figure 43. Normalized Exposure for Depositing Material on the 32.2-km (20-mile)

Arc.

IVIACCS

..,...... ..., K'ASC4L

.-.-.- - RATCHET I I I I I I I I I 1 I I I I I 1 I I I N PJNE NE ENE E ESE SE SSE S SSW SVVV\IWd W VVNWI\IW NNVV N2 Sectar Figure 44. Normalized Exposurc for Depositing Material on thc 80.5-km (50-mile)

Arc.

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 N NNE NE ENE E ESE SE SSE S SSW SWVVWV W WNWI'.lVV NNV'J N2 Sector Figure 45. Normalized Exposure for Depositing Material o n the 160.9-km (1 00-m ile) Arc.

N NNlNNWWNW W WSWSW SSW S SSE SE ESE E ENE NE NNE N2 Sector Figure 46. Normalized Deposition on the 16.9-km (10-mile) Arc.

1 1 1 1 1 1 1 1 1 / 1 1 1 1 1 1 1 N NNWNWWNW W WSWSW SSW S SSE SE ESE E ENE NE NNE P.12 Sector Figure 47. Normalized Deposition on the 32.2-km (20-mile) Arc.

I I I I I I I I I I I I I I I I I 1\1 NNlNNWWNW W WSVVSW SSW S SSE SE ESE E ENE NE NNE N2 Sector Figure 48. Normalized Deposition on thc 80.5-km (50-milc) Arc.

I I I I I I I I I I I I I I I I I I N NNWNWWNW W W b V S W SSLIV S SSE SE ESE E ENE NE NNE N2 Sector Figure 49. Normalized Deposition on the 160.9-km (100-mile) Arc.

(100 miles). The smooth contours in the plots for MACCS2 are a result o f t h e solution technique, the assumed straight line transport, and the wide spacing of the data points (400 points). The LODI figures include some high frequency noise that is a feature of mapping parcels to a grid, especially a high-density (closely-spaced) concentration grid (122,500 individual exposures or depositions are used in constructing the contour plots).

RASCAL, RATCHET, and LODI all show features in these annual averages that appear to preserve individual plumes, and there seems to be general agreement about the direction of these plumes. The RASCAL and RATCHET data are in quite close agreement except for the magnitude of the exposure or deposition. This is expected since these models are very closely related and the main difference is the turbulent diffusion formulation. RASCAL and RATCHET also have isolated downwind high deposition contours that are not present in MACCS2 or LODI plots. These are presumably d u e to rapid wet deposition when rain occurs several hours after the release. The closer spacing of the contours for MACCS2 compared with LODI, as one moves away from the release location, is evidence of the more rapid decrease of exposure and deposition with distance for MACCS2. In general, the similarities in the distributions of exposure and deposition shown by these plots are greater than the differences, particularly when consideration is given to the different density (closeness of spacing) of the underlying data. The more complex models certainly show more detail in structure; however, the smoothed distribution still show the common features that w e noted in the previous sections on arc and arc-sector averages.

10.4 Summary of Results All of the arc average and the great majority of the arc-sector average exposures and depositions are within a factor of two when comparing MACCS2 to the state-of-the-art model, LODI. Similar comparisons of RASCAL and RATCHET to LODI also have most exposures and depositions within a factor o f t w o ofLODI. In fact the largest differences in results are between the closely related RASCAL and RATCHET models.

We can identify at least two caveats to the discussion of model differences. First, this study was performed in an area with smooth or favorable terrain and persistent winds although with structure in the form of low-level nocturnal jets and severe storms. In regions with complex terrain, particularly ifthe surface wind direction changes with height, caution should be used. Second, MACCS2 predicts a too rapid decrease of exposure with distance; this should be considered when MACCS2 is used to estimate consequences at distances greater than 321.8 km (200 miles). However, this second caveat is tempered by the fact that the majority of the deposition (and exposure to depositing material) is within this 321.8-km (200-mile) distance.

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