The Creation of an Historical Meteorological Database for Environmental Dose Assessment

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    1 Savannah River Technology Center, Westinghouse Savannah River Company, Aiken, SouthCarolina, U.S.A.; 2 Oregon State University, Nuclear Engineering and Radiation Health Physics,

    Corvallis, Oregon, U.S.A.( author for correspondence, e-mail:

    (Received 7 November 2001; accepted 7 June 2002)

    Abstract. The focus of this study is to develop wind data for the Savannah River Site (SRS) between1955 and 1961 to be used in an assessment of estimates of atmospheric dispersion and downwind riskat the Savannah River Site. In particular, a study of the uncertainties of radioiodine dosimetry fromthe late 1950s provides the underlying motivation for developing historical windroses at the SavannahRiver Site (SRS). Wind measurement towers did not exist at the SRS until the early 1970s. Threerelatively simple methods were used to create a 19551961 meteorological database for the SRS fora dose reconstruction project. The winds were estimated from onsite measurements in the 1990s andNational Weather Service (NWS) observations in the 1990s and 1950s using (1) a linear regressionmethod, (2) a similarity theory approach, and (3) a simple statistical differences method. The criteriafor determining success were based on (1) how well the mean values and standard deviations of thepredicted wind speed agree with the known SRS values from the 1990s, (2) the shape of the pre-dicted frequency distribution functions for wind speed, and (3) how closely the predicted windrosesresembled the SRS windrose for the 1990s. The linear regression models wind speed distributionfunction was broad, flat, and skewed too much toward higher wind speeds. The similarity theoryapproach produced a wind speed distribution function that contained excess predicted speeds in therange 01.54 m s1 (03 kts) and had excluded bins caused by predictions being made from integervalues of knots in the NWS data. The distribution function from the mean difference method wassmooth with a shape like a Weibull distribution with a shape parameter of 2 and appeared to resembleclosely the SRS 19921996 distribution. The wind directions for all three methods of approach weresuccessfully based on the mean difference method. It was difficult to discern differences amongthe wind roses produced by the three methods so the wind speed distribution functions need to beexamined in order to make an informed choice for dose reconstruction.

    Keywords: dose assessment, meteorology, wind roses

    1. Introduction

    A study of the uncertainties of radioiodine dosimetry from the late 1950s providesthe underlying motivation for developing historical windroses at the SavannahRiver Site (SRS). The larger study examines parameter variability and model sens-itivity in all aspects of internal dosimetry of iodine-131, including atmosphericdispersion and transport, ingestion and inhalation, thyroid uptake, and iodine meta-

    Environmental Monitoring and Assessment 83: 255281, 2003. 2003 Kluwer Academic Publishers. Printed in the Netherlands.

  • 256 A. H. WEBER ET AL.

    bolism in humans. Historical meteorological variables are used in estimating down-wind concentrations of radioiodine in the air, on the ground, and in consumables.A general uncertainty analysis of the Gaussian dispersion model and its sensitivityto joint-frequency inputs has been conducted separately (Hamby, 2002).

    For modeling purposes, it is desirable to utilize meteorological data from thechosen time period. However, prior to this work meteorological data for the Sa-vannah River Site (SRS) did not exist for the 1950s. The Savannah River Sitesmeteorological monitoring program (Parker and Addis, 1993) was not establisheduntil the early 1970s. The focus of the present study is to develop wind data forthe SRS between 1955 and 1961 to be used in an assessment of estimates of atmo-spheric dispersion and downwind risk at the Savannah River Site. With unlimitedresources and under ideal circumstances, very explicit modeling techniques couldbe used to reconstruct historical meteorological data. However, when resources arelimited, other approaches to a reconstruction of winds must be evaluated.

    Efforts to create historical meteorological data can be rather complex and timeconsuming. Kraig (1997) describes dose reconstruction work performed at LosAlamos for weapons experiments from the mid-1940s to early 1960s. Lack ofmeteorological data during many of the tests required Kraig to use averaged con-ditions for the late-afternoon and early-evening time frame (when the tests wereconducted) from a 3 yr database of observations using a single tower located nearthe detonations.

    The meteorology used for the Hanford dose reconstruction effort (mid to late-1940s) is described in Stage et al. (1993). Details are given regarding station in-fluences by local topography, limitations of the data-collection methods, as wellas difficulties in transferring data from original handwritten records or microficheinto a usable database of dose modeling activities.

    When meteorological data are sparse either spatially or temporally, an approachis to use sophisticated atmospheric models initialized with observations from sur-face stations and weather balloons. These models can then create hourly observa-tions over large spatial grids. This implies re-running complex three-dimensionalmesoscale or large-scale models to generate winds over entire years or decadesand results in time-consuming computations (that do not necessarily provide moreaccurate results).

    In the case of the SRS, however, the reasonably close proximity of two NationalWeather Service (NWS) stations enabled the creation of an historical databaseusing three different approaches that are described here. Wind speed and winddirection estimates were obtained by finding mean differences between SRS andNWS stations during the 1990s and creating a set of corrections that were assumedto hold for the 1950s. In a regression approach, statistical regression relationshipsbetween recent SRS and NWS databases for wind speed were determined andapplied to archived NWS data to produce an SRS database for the desired timeperiod. A third approach based on similarity theory was also used to generate windspeeds for the 1950s. In the similarity theory approach, wind speeds from the 10 m


    NWS observations were extended to SRSs 61 m level (under an assumption ofhorizontal spatial homogeneity).

    2. Methods


    The locations of the wind measurement sites, terrain elevations for the region, andsome land-use features are shown in Figure 1. The land use in the South CarolinaPiedmont is primarily agricultural broken by streams, forests and several smallcommunities. The larger cities of Columbia, South Carolina, and Augusta, Georgiaare separated by a distance of about 90 km.

    Wind measurements are taken at the SRS and the NWS sites near the ColumbiaMetropolitan Airport (CAE) and the Augusta Regional Airport at Bush Field (AGS).Although Columbia is roughly twice as far from the SRS as Augusta, the terrainsurrounding the CAE measurement site is more similar to the SRS than the terrainaround AGS. The main difference is that Bush Field lies in the Savannah Riverdrainage basin near swampy terrain. Calms and fog occurrences are much morefrequent at AGS than at CAE or at the SRS.

    Wind measurements at the SRS and the NWS stations have important differ-ences that are summarized in Table I. Perhaps most important is that the meas-urement height at the SRS is 61 m above ground level (AGL), while the NWSstations now typically measure winds at 10 m AGL. In the 1950s through the mid-1960s the wind speed measurement heights were not necessarily at 10 m AGL.According to the National Oceanic and Atmospheric Administrations (NOAA)records of the history of the two sites (NOAA, 1996), the anemometer and windvane were lowered 4.9 m (16 ft) from their height of 11.0 m (36 ft) in 1951 to 6.1 m(20 ft) in the period 19921996 at Columbia (CAE). The same source shows thatAugustas wind instruments were lowered 1.5 m (5 ft) from their height of 7.6 m(25 ft) in 1951 to 6.1 m (20 ft) in the period 19921996. Since wind speed changesapproximately logarithmically with height these rather modest changes in elevationshould have affected the speeds by no more than about 515%. In addition, theNWS instruments are much less sensitive than the SRS instrumentation, and theBush Field data are subject to down-river flow due to the airports geographicallocation (Figure 1). Finally, the NWS values are 1 or 2 min averages at the top ofthe hour (i.e. almost a snapshot), whereas the SRS data are averaged continuouslyover one-hour intervals.

    The SRS wind speed and direction measurements for this project were takenfrom a 61 m tower in H-Area near the center of the SRS. A five-year databasefor the period 19921996 was assembled for dosimetry calculations and this samedatabase was used here. The SRS 19921996 database underwent several qualityassurance procedures prior to being finalized. One of the requirements for the do-simetry calculations was that the meteorological data had to be complete for each

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    Figure 1. Map of the Savannah River Site (SRS) area with Augusta Bush Field (AGS) to the northwestand Columbia airport (CAE) in the northeast corner. Topographic contours are at 25 m (above sealevel) intervals with 50 and 100 m levels highlighted. Lighter shaded filled areas are cities or towns.

    hour of the five-year period. This requirement was possible to meet since SRS hasseven 61 m towers, and whenever the data from the H-Area tower was missing, thewind speed and/or direction could be substituted from one of the remaining towers.

    The first step in developing the desired statistical relationships was to obtainNWSs meteorological data from the National Climatic Data Center (NCDC) (Earth-Info, 1996; Brown, 2001) for all nearby NWS stations in the region and to examineeach station for appropriateness. In addition to AGS and CAE these stations in-cluded Athens and Macon, Georgia; Charlotte, North Carolina; and Charleston,South Carolina. Hourly observations of wind speed, direction, cloud cover, andcloud-height from Bush Field in Augusta, Georgia (AGS) and Columbia, SouthCarolina (CAE) from 19551961 and 19921996 were selected after an initialscreening to reconstruct the winds at the SRS. The other stations in the region were


    Known difference between the winds measured at the National Weather Service, Augusta, Georgia(AGS) Columbia, South Carolina (CAE) and the Savannah River Site (SRS)

    Difference SRS CAE AGS

    Height of sensors 61 m 11.0 to 6.1 m 7.6 to 6.1 m(1951 to 19921996) (1951 to 19921996)

    Instrument High sensitivity Robust instrumentation, Robust instrumentation,sensitivity but low sensitivity. but low sensitivity.

    Averaging time 1 hr (continuous) 2 min (snap-shot) 2 min (snap-shot)Topographical Pine tree forest. Airport location. Airport location.influences Mostly flat within Lies near partially Lies at the edge of

    2.0 km of the tower. developed suburban the Savannah RiverModest terrain landscape. drainage basin.changes beyond.

    rejected for various reasons, such as displaying orographic effects or for exhibitingclimatologically different conditions than the SRS.

    The wind speed frequency distributions for 19921996 for SRS and the twoselected NWS sites are shown in Figures 2ac. As mentioned above, the SRSwind speed data in Figure 2 were taken at the 61 m height with highly sensitiveanemometers. The distribution resembles the theoretical Weibull distribution witha shape parameter of 2 that is expected for accurate, continuous, long-term windmeasurements (Krohn 1997). (Wind speed units of knots (kt) were used in thefigures since the NCDC values are reported in whole knots).

    The AGS and CAE frequency distributions, however, show spikes near zeroreflecting the large number of wind speeds below the threshold of the NWS an-emometer (recorded as a missing direction and a zero for wind speed). Indeed,an examination of the data showed that for the entire period 19921996, virtuallyall the wind speeds below 1.54 m s1 (3 kt) were entered as zeros for the NWSstations.

    To make the NWS distributions appear more realistic, a method was developedto create more representative looking wind speed distributions. Zero wind speedvalues were reassigned a random speed between zero and 1.54 m s1 (3 kt) asfollows: values between 1.03 and 1.54 m s1 (2 and 3 knots) were assigned threetimes as frequently as values between zero and 0.257 m s1 (0.5 knots), and valuesbetween 0.257 and 1.03 m s1 (0.5 and 2 knots) were assigned twice as frequentlyas values between zero and 0.257 m s1 (zero and 0.5 knots).

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    Figure 2a-c. Wind speed frequency distributions for 19921996 for (a) SRS and (b) CAE. Windspeed units of knots are used for clarity since the NWS reports wind speed to the nearest knot.


    Figure 2c. Wind speed frequency distributions for 19921996 for AGS. Wind speed units of knotsare used for clarity since the NWS reports wind speed to the nearest knot.

    The modified NWS wind speed distributions for the two sites are shown inFigures 3ab. The resulting CAE distribution appears reasonable, resembling atruncated Weibull distribution; the AGS distribution looks questionable with twomaxima below 2.57 m s1 (5 kt), as though too many winds had been recordedas calm. Since the shape of CAEs modified wind speed distribution function inFigure 3 appeared to more closely resemble the SRS distribution in Figure 2 thandid the AGS distribution, the CAE wind speed data were given preference in thedata reconstruction for SRS.

    It was also determined that a significant percentage of the Bush Field winddirection data were missing for the periods of interest (including the 1990s). Thiswas mainly due to calm winds being reported, since Bush Field lies in the SavannahRiver drainage basin. The wind measurements at CAE had the advantage of beingmore complete as well as being collected over terrain more similar to the SRS thanthe AGS site, so CAE was given preference to represent wind directions for theSRS for the 1950s. To improve the percentage of direction data recovered for CAEif data were missing for 1, 2 hr, etc., or longer segments up to 8 hr, then persistencefrom the last known non-missing value was utilized. Performing these substitutionsresulted in a gain of 17% so that missing direction data were reduced to onlyabout 0.5% in the final data set.

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    Figure 3a-b. Modified wind speed frequency distributions for 19921996 for (a) CAE, (b) AGS.Modifications were performed on the calms of Figure 2 to distribute them in the range 03 knots.Wind speed units of knots are used for clarity since the NWS reports the wind speed to the nearestknot.


    Mean wind speeds and directions with standard deviations forthe 19921996 time period. CAE and AGS measurements are at6 to 10 m heights; the SRS measurement is at 61 m height fromthe H-Area tower. The mean wind speed values are after the sub-stitutions for calm conditions discussed in the text. Also shownare the number of wind direction values before persistence wasused to increase the amount of data. (Missing wind directions aremainly the result of calm conditions near the surface)

    Number of values Mean Std. Dev.

    SRS speed m s1 43848 3.94 1.50CAE speed m s1 43848 2.99 1.90AGS speed m s1 43846 2.73 1.94SRS direction 43848 (100%)CAE direction 36164 (82.5%)AGS direction 31293 (71.4%)

    Table II shows the number of values and mean wind speed at the three sites(after the data substitution methods for calm winds discussed above were imple-mented for the NWS sites). Table II also shows the number of values of non-calmwind direction measurements before persistence was used to increase the amountof data.

    The wind directions were then categorized into 16 compass sectors (22.5 bins,as required for the dose modeling) clockwise around the compass originating atnorth. The SRS data set and the improved CAE data set were merged into a singlefile with each record in the dataset denoting a different hour within the five-yearperiod.

    A comparison of wind direction data for both Columbia and the SRS during theperiod 19921996 was made to examine the similarities and disparities in the data.The SRSs meteorological data for that period has undergone extensive checks forerrors so it is viewed as the most reliable. The SRSs 61 m windrose from H-Areafor the five-year period 19921996 is shown in Figures 4a and b and shows the CAE10 m windrose for the same period. The CAE windrose has more frequent windsfrom the north than does the SRS windrose, and CAE lacks the frequent windsfrom the northeast that the SRS shows. Figure 4c shows the AGS 10 m windrosefor 19921996. This windrose is nearly symmetrical when reflected about an EWaxis.

    By examining the windroses for other time periods it can be determined whetherthe 19921996 time interval for CAE resembles the long-term average. The win-drose for CAE for the years 19481995 is shown in Figure 5a and the AGS win-drose for the years 19491995 is shown in Figure 5b. The windrose for CAE for

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    Figure 4a-c. Windrose plots for the years 1992 to 1996 for (a) SRS and (b) Columbia. The windroseplots depict the frequency of the direction from which the wind is blowing and the wind speeds.


    Figure 4c. Windrose plots for the years 1992 to 1996 for Augusta, GA. The windrose plots depict thefrequency of the direction from which the wind is blowing and the wind speeds.

    the years 19551961 is shown in Figure 6a and the AGS windrose for the sameperiod is shown in Figure 6b. It can be seen that the windrose for the total periodof recorded data for CAE has many similarities to the windrose from SRS for19921996 shown in Figure 4a. The predominant lobes are from the southwestand northeast directions with relatively few winds from the northwest and south-east. The forty-six year AGS windrose, however, shows a more nearly circularlysymmetrical pattern.

    In addition, the long-term windrose (19481995) for CAE shows a much greatersimilarity to the 19551961 CAE windrose in Figure 6a (and the 19921996 SRSwindrose) than does the CAE windrose for the 19921996 time period. In spiteof the fact that the 19921996 time period (as evidenced by the CAE windrose)is not representative of the longer-term means, it was nevertheless used to providethe basis for representing the wind direction for the SRS. This was done becauseof the availability of high quality measurements at SRS. It was felt that the highquality measurements at SRS would enable accurate difference relationships to beestablished.

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    Figure 5a-b. Windrose plots for the late 1940s to 1995 for (a) Columbia, SC and (b) Augusta, GA.The windrose plots depict the frequency of the direction from which the wind is blowing and thewind speeds.


    Figure 6a-b. Windrose plots for the years 1955 to 1961 for (a) Columbia, SC and (b) Augusta, GA.The windrose plots depict the frequency of the direction from which the wind is blowing and thewind speeds.

  • 268 A. H. WEBER ET AL.


    Scalar averaged wind speeds (VDIFF ) and vector averaged wind direction differ-ences (DIFF ) were determined for each season (4), 22.5 sector (16), and hour ofthe day (24) between SRS and CAE for the 19921996 time period. This made twosets of 1536 different corrections for each of wind speed and direction. The windspeed and direction prediction equations take the following form for each of the1536 different subsets:

    VSRS = VCAE + VDIFF , (1)SRS = CAE + DIFF , (2)

    where VSRS and SRS are the predicted wind speed and direction for SRS, and VCAEand CAE are the wind speed and direction for CAE. The wind direction correctionsin Equation (2) were obtained from the vector components of the wind followingthe methods in Mardia (1972).


    Regression equations for predicting the SRS wind speed for the 19551961 timeperiod from the CAE data during this same period were obtained using SAS (1989)software procedures and the merged SRS and NWS 19921996 data sets. Slopesand intercepts from the linear least-squares regression equations for wind speedwere determined from the 5 yr database for all seasons (4), sectors (16), and hoursof the day (24) for a total of 1536 different sets.

    The linear regressions were performed assuming the SRS speed as the inde-pendent variable with the CAE speed as the dependent variable. This choice wasmade due to the greater reliability, sensitivity, and accuracy of the SRS anemo-meters. This method is akin to the calibration problem in statistics, where onehas a precise, accurate measurement (X) that is not available in all cases sinceit could be expensive, time-consuming, destructive, or non-obtainable. The othermeasurement (Y) is generally cheaper, faster, and readily available (Shukla, 1972).

    To do the regression with Y (the CAE speeds) as the independent variable vi-olates the regression assumption that the independent variable is known withoutappreciable error (Shukla, 1972). The regression assumption is more readily sat-isfied when the SRS speeds are considered the independent variable and the CAEspeeds the dependent variable. Thus, the usual regression equation must be invertedto obtain the calibration or prediction equation for the unavailable SRS speeds,given the available but less precise and accurate CAE speeds for the missing years.

    Data from the 19551961 time period for CAE (and AGS when needed) wereextracted and merged with the regression parameters determined from the 19921996 time-period. These data were corrected for calms and missing directions as


    discussed earlier for the 19921996 data. The sector definitions for the 19551961data were based on CAEs directions as before. The slope (Mreg) and intercept(Breg) for each of the 1536 combinations were then used to predict the SRS windspeed for the 1950s data set:

    VSRS = (VCAE Breg)Mreg

    , (3)

    where VSRS is the wind speed for the SRS and VCAE is the wind speed for Columbia.The overall Pearson correlation coefficient (SAS , 1989) between the meas-

    ured SRS speed and the measured CAE speed at this point was determined to be0.391. This correlation coefficient does not indicate a particularly strong relation-ship between the dependent and independent variables.

    At this point in the procedure, the data were checked for glaring errors. In somecases, unrealistically large estimates (outliers) of VSRS were produced due to verysmall values of Mreg with large VCAE (values far from the mean of the data cangive unrealistically large or small predictions). Either large or small predictionscan have a large error. If the regression is done directly, the large errors are notas readily apparent because of the bias in the estimates and the mean square error.In order to partially counter the effect of these outliers, the predicted speed wasset identically equal to the CAE speed if the predicted SRS speed exceeded 15 ms1 for a given hour since it is rare that SRS wind speeds exceed 15 m s1. Inaddition, if SRSs predicted speed was negative (due to the large random error inthe prediction), it was again set equal to the wind speed for CAE. Fortunately, thenumber of missing, negative wind speed predictions, and wind speed substitutionsgreater than 15 m s1 from the improved CAE data set amounted to only 65 of61 368 cases (the number of hourly observations in the seven-year period). Theseunrealistic predicted wind speeds accounted for barely 0.1% of the data.

    Initially, the regression approach was felt to hold the most promise for produ-cing predicted SRS wind speeds, however because of the low correlation coefficientand other results that are discussed in Section 3, other ways of estimating the SRSwind speeds were sought.


    A third approach was used to provide estimates of wind speed at 61 m for theSavannah River Site using CAE observations based on dimensional analysis orsimilarity theory. This approach was used to determine if it could offer improvedwind speed estimates over the regression approach. Similarity theory applied overlarge horizontal distances has an underlying assumption of horizontally homogen-eous turbulence. The horizontal homogeneity assumption over the 90 km distancebetween SRS and CAE is questionable, but no other 61 m wind speed measure-ment data are easily obtainable in this region. (A few nuclear powered electrical

  • 270 A. H. WEBER ET AL.

    generating stations have measurements near the 61 m height but their wind datadid not exist in the 1950s either).

    The similarity equations for wind speed in the constant flux layer are summar-ized by Panofsky and Dutton (1984) and repeated below for convenience. Similar-ity theory is based on dimensional analysis and begins with a length scale L, theMonin-Obukov length. The theory hypothesizes that the physical properties of theatmospheric surface layer can be specified in terms of the ratio of height above thesurface z, and L where

    L = u3cpT

    kagH(1 + 0.07/B) . (4)

    Here u (m s1) is the friction velocity (square root of the vertical turbulent mo-mentum flux per unit mass), cp (m2 s2 K1) is the specific heat at constant pres-sure, (kg m3) is the air density, T (K) is the air temperature, ka is the vonKarman constant (0.4), g is the acceleration of gravity, H (J m2 s1) is thevertical turbulent heat flux, and B is the Bowen ratio (dimensionless). The Bowenratio is the ratio of sensible to latent heat flux at the surface with values from about0.1 to 5 depending on the composition of the surface.

    In similarity theory the non-dimensional wind shear S becomes a function ofz/L as follows,

    S = kazuuz

    = m( zL

    ), (5)

    where u is the mean wind speed in the boundary layer at some height z above thesurface. The non-dimensional wind shear can be integrated to form the m functionwhere


    ( zL

    )= z/Lz0/L

    [1 m ()]

    , (6)

    and is z/L, the variable of integration.The ratio of wind speeds u1 and u2 at different levels z1 and z2 in the boundary

    layer is given by


    u1= ln(z2/z0) m(z2/L)

    ln(z1/z0) m(z1/L) , (7)

    where z0 is the roughness length of the surface.The function m can be determined from (Wilson, 2001)

    m = 3 ln(

    1 +1 + m|z/L|2/31 +1 + m|z0/L|2/3

    ), (8a)


    TABLE IIIValues of 1/L for various Turner stability classesthat were used to extrapolate 10 m wind speeds to61 m heights for z0 = 10 cm

    Turner stability class Value of 1/L for CAE(Pasquill Class)

    1 (A) 0.1082 (B) 0.0603 (C) 0.0254 (D) 0.05 (E) 0.056 (F) 0.0227 (G) 0.06

    where m = 3.6 (Hgstrm, 1996) for unstable conditions. For stable conditions(Hgstrm, 1996)

    m = 5.3z/L , (8b)and for neutral conditions

    m = 0 . (8c)Golder (1972) determined estimates of L (or 1/L) from the Turner stability classesto use in cases where flux measurements are absent, such as an NWS monitoringstation. In turn, the Turner stability classes can be estimated from time of day,cloudiness, and wind speeds measured near the surface. This stability class determ-ination is discussed in detail in EPA-454/R-99-005 (2000). In our application theCAE and AGS meteorological observations were used to determine the Turner sta-bility classes. The estimates of 1/L given in Table III were obtained from Goldersmethod assuming a roughness length z0 of 10 cm (since the instruments are locatednear airports with a few large roughness elements and terrain changes but wherethe grass and vegetation are kept reasonably short).

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    TABLE IVMean speeds and standard deviations for the 19551961 time period.CAE measurements are at 10 m heights; the SRS predicted windspeed is for the 61 m height

    Speed type and location No. of values Mean St. dev.(m s1) (m s1)

    CAE observed 61368 3.34 2.12

    SRS predicted 61368 4.58 3.18(Linear regression)SRS predicted 61368 4.80 2.84(Similarity theory)SRS predicted 61271 4.26 1.93(Mean difference method)

    3. Results


    The mean values for wind speed for the three methods of determining wind speeddescribed above are presented in Table IV. The predicted mean wind speeds forSRS are greater than the values for the 1990s data (compare with Table II), how-ever, the mean wind speed from CAE is also greater by about 11% than CAEsmean wind speed for the 1990s. The linear regression method produced a largerwind speed value, and the values have a higher standard deviation. The meandifference method produced the closest value to the actual mean speed for SRS1990s data.


    The distribution functions for the predicted wind speeds at the SRS for the years19551961 were determined for all three approaches. The actual CAE wind speeddistribution for the years 19551961 is shown in Figure 7a. The regression resultsare shown in Figure 7b, the similarity theory results are shown in Figure 7c, and thedifference results are shown in Figure 7d. Figure 7b for the regression result showsa very smooth distribution over the wind speed range with a relatively long tailat the higher speeds compared to the CAE distribution. Figure 7b also shows toomany wind speed values in the range 03 kt over the desired Weibull distribution.


    Similarity theory (Figure 7c) shows higher peaks in the mid-range of wind speed,but still has the long tail at the higher wind speed range and (as with Figure 7b) con-tains excess values in the range 03 kt. There are several excluded wind speeds,e.g., those at 9, 12, and 16 kt. These are caused by the fact that the NWS windsare reported to whole knots that when entered into the similarity equations produceidentical values of speed, giving rise to the appearance of excluded wind speeds.The distribution function from the difference method shows the most reasonabledistribution for the SRS predicted wind speeds.


    The mean square error (MSE) was determined for the three methods of predictingwind speed for the 19921996 data. The MSE is determined by

    MSE =C



    (Xij Xij

    )2 / Ci=1

    (ni p) , (9)

    where (Xij Xij ) is the difference between the predicted and actual SRS windspeed, C is the number of categories (1536 in our case), ni is the number of meas-urements of wind speeds in each category; and p = 2 for regression, p = 1 for thedifference method, and p = 0 for the similarity theory method.

    The MSE for the similarity theory method is 5.55 and the MSE for the differ-ence method is 2.53. The MSE for the regression approach is 334.5. The regressionMSE cannot be directly compared with those from the other methods (Shukla,1972). This is the case whether the regression is done with the SRS wind speeds asthe independent variable or the inverse with the SRS wind speeds as the dependentvariable.

    As a result, it is preferable to compare the MSE between the difference methodand the similarity approach. The MSE is lower for the difference method. How-ever, selecting the preferred method of predicting wind speeds should be based onexamining the predicted windroses, wind speed distributions, and residual patternsas well as the method with the smallest MSE.


    Windrose plots for the predicted 19551961 SRS database were generated. Fig-ure 8 shows the predicted winds at SRS for 19551961 using the three methodsdiscussed. The predicted windrose for SRS in all three cases shows a good dealof similarity to the SRS windrose for 19921996 and the windrose for CAE for19551961. Each windrose has strong lobes from the northeast and southwest, asexpected.

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    Figure 7a-d. Wind speed distribution functions for (a) the improved CAE 19551961 data, and (b)the linear regression predictions.


    Figure 7c-d. Wind speed distribution functions for (c) the similarity theory predictions, and (d) themean difference method predictions.

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    Figure 8a-c. Windrose plots as derived for the SRS for the years 1955 to 1961 using (a) Linearregression, and (b) similarity theory. The windrose plots depict the frequency of the direction fromwhich the wind is blowing and the wind speeds.


    Figure 8c. Windrose plots as derived for the SRS for the years 1955 to 1961 using mean differences.The windrose plots depict the frequency of the direction from which the wind is blowing and thewind speeds.


    In each of the three cases, plots of residuals versus actual wind speeds can beused to determine if the models are biased. The residuals are computed by takingthe differences between the actual measured 19921996 SRS wind speeds and thepredicted wind speeds for each of the three models. Plots of residual wind speedas the ordinate and measured wind speed as the abscissa can show biases overthe range of measured wind speeds if they exist. An unbiased model should showrandom scatter about a zero mean difference, a reasonably small range in the overalldifferences, no discernable slope to the pattern of points from left to right, and few,if any, outliers.

    The residual plots are shown in Figure 9 with identical axes for easy compar-ison. The regression models residual plot (Figure 9a) has random scatter aboutzero, no discernable slope, a single outlier at +36 (not shown) and a fairly largerange of 8 to +10 (m s1). The similarity theory models residual plot (Figure 9b)shows an appreciable slope, no real outliers, and a range of 13 to +9 (m s1). The

  • 278 A. H. WEBER ET AL.

    similarity theory residual plot shows bands of positively sloping lines caused bythe fact that the wind speed observations are recorded in whole knots. Each windspeed in whole knots gives rise to a separate line in the plot. The difference modelsresidual plot (Figure 9c) has random scatter about zero, no slope, no outliers, anda range of 2 to +4 (m s1). These residual plot results show that among the three,the mean difference model is preferable.

    4. Conclusions

    Three relatively simple methods were used to create an historical meteorologicaldatabase from onsite and nearby National Weather Service stations. The criteriafor success are based (1) on the mean value and standard deviation of the predictedwind speed and how well these statistics agree with the known SRS values fromthe 1990s, (2) on the shape of the frequency distribution function for wind speed,and (3) on how closely the windrose resembles the SRS windrose for the 1990s.

    The linear regression model produced a set of predictions that were plausible forthe mean value and standard deviation, however the wind speed distribution func-tion was skewed too much toward higher wind speeds. The distribution functionalso contained excess predicted speeds in the range 01.54 m s1 (03 kt) whereaswinds at the SRSs 61 m measurement height do not favor these values. Overallthe distribution function could be said to be too broad and flat to resemble the SRSdistribution.

    The similarity theory approach produced a set of predictions that again wereplausible for the mean value and standard deviation, however the wind speed dis-tribution function contained excess predicted speeds in the range 01.54 m s1(03 kt). The distribution function also contained excluded bins caused by pre-dictions being made from integer values of knots in the NWS data.

    The distribution function from the mean difference method was smoothly shaped,contained no excess values in the 01.54 m s1 (03 kt) range and was not toobroad nor flat to be realistic. The shape of the distribution also appears to re-semble the Weibull distribution with a shape parameter of 2 that careful windmeasurements near the surface normally possess.

    The mean square error was lowest for the difference approach. Also, the re-siduals versus measured wind speeds plots for the three models showed that thedifference method was preferable to the regression and similarity theory models.This was evidenced by the pattern of residuals having a random scatter about zero,no discernable slope over the range of measured wind speed, no outliers, and afairly small range of 2 to +4 (m s1) over the entire ensemble of points.

    The historical dose assessment project does not depend heavily on the accuracyof individual hourly values of wind, but rather on the frequency distributions of thewind speeds and directions. Although any of the three methods may be adequatefor the purpose of retrospective dose estimates, the best statistical wind speeds


    Figure 9a-c. Scatter plots of observed wind speed at SRS for 19921996 versus the residual for the(a) regression method, (b) similarity theory method, and (c) mean difference method.

  • 280 A. H. WEBER ET AL.

    for this purpose seems to come from the mean difference method because of itssuperior wind speed distribution function and lower mean square error. Since thedifference method produced the lowest mean wind speed it should also producethe most conservative dose predictions. The mean difference method is also thesimplest of the three methods to implement.

    The wind direction distribution function for all three methods of approach wasbased on the mean difference method. The mean difference method produced win-droses for all three cases that were very close to the expected windrose shape(SRSs 1990s windrose, Figure 4a). It was felt that this was an important resultthat greatly simplifies the task of providing wind direction data for a site such asSRS where no measurements were being taken in the time period of concern. Closeexamination of each of the windroses produced by the three methods shows thatthe differences among them are difficult to discern so attention must be given to thewind speed distribution functions to be able to make an informed choice among themethods for historical dose assessments.


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