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A New Meteorological Data AssimilationModel for Real-Time Emergency Response

This paper was prepared for submittal to the

10th Joint Conference on theApplications ofAir Pollution Meteorology with the Air and Waste Management Associdion

Phoenix, AZJanuury 11-16,1998

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1. INTRODUCTION

A NEW METEOROLOGICAL DNA ASSIMILATION MODEL FORREAL-TIME EMERGENCY RESPONSE

G. Sugiyama * and S. T. Chan

Lawrence Livermore National Laboratory, Livermore CA

We are developing a new meteorological data assimi-lation model for the Atmospheric Release Advisory Ca-pability (ARAC) project at Lawrence Livermore Na-tional Laboratory, which provides real-time dose as-sessments of airborne pollutant releases. ‘l’he model,ADAPT (Atmospheric Data Assimilation and Parame-trization Twhniques), builds threedimensional meteo-rological fields, which can be used to drive d@ersionmodels or to initialize or evaluate mesoscale models.ADAPT incorporates many new features and substantialimprovements over the current ARAC operational mod-els MEDIC/MATHEW (ARAC, 1997), inchdhg the useof continuous-temain variable-resolution grids, the abil-ity’to treat assorted meteorological data such as temper-atures, pressure, and relative humidity, and a new algo-rithm to produce mass-consistent wind fields. In this pa-per, we will describe the main features of the model, cur-rent work on a new atmospheric stability pararneteriza-tion, and show example results.

2. METEOROLOGICAL DATA

ADAPT uses input derived from ARAC’S land-~urfaceand real-time meteorological databases, archived exper-imental data sets, and analytically generated data. Lo-cal meteorological observations are currently providedto ARAC by the Air Force Global Weather Center, Do-mestic Data Plus, International Data Service, and sup-ported site towers. Gridded analyses and forecast fieldsare obtained from the Fleet Numerical Meteorologicaland Oceanographic Center (NOGAPS model), the Na-tional Weather Service (AW and ETA models), andAIUC adaptations of the mesoscale models NORAPSand COAMPS developed by the Naval Research Labratory (Hodur, 1987 and 1997). Meteorological data isselected for a spatial region that is usually larger than thedomain of the model simulations in order to use the mostcomplete set of information relevant to the problem.

3. COMPUTA~ONAL GRID

The model represents the ground surface by a piece-wise bilinear interpolation of grid-point topographicaldata. Run-time selection of both the number of gridpoints and the grid resolution is provided, along withvariable resolution in both the vertical and horizontal co-ordinates. The former permits a good representation ofthe meteorological fields in the critical near-surface re-gion, while the latter is utilized when warranted by eithertopographical variation or &ta density. For the exam-ples shown in this paper, the vertical coordinate is takento be u= = =;;:zg , where Zg is the ground elevationand ~w is the height of the grid top, the coordinate usedby COAMPS and ARAC’S new dispersion model LODI(Leone et rd., 1997).

4. DATAASSIMILATION

Diverse data assimilation techniques are being devel-oped to meet the needs of a new generation of ARACmodels and to take advantage of the rapidly expand-ing availability of meteorological and land-surface data.ADAPT provides a number of split methods, which per-form separate vertical and horizontal analyses. Fullythree-dimensional analysis are under development. Ad-ditional features include the incorporation of map projec-tions and the treatment of atmospheric and land-surfaceparameters as spatially varying fields.

The vertical analysis is based on an idealized pictureof the atmosphere as divided into a set of layers-the sur-face layer, the boundary layer, and the free atmosphere.Different interpolation methods and empirical parame-terizadons are then used in each layer, depending on at-mospheric conditions. Several techniques are providedto coherently blend surface and tower data with upper airdata and control the use of upper air &ta depending ontheir re~ntativeness in time and space.

A variety of interpolation and extrapolation techniquesare available in ADAFT The simplest class of techniquesis based on direct interpolation

*Correspondingauthor aaifnm: G. S@yanW L-103, F!O. Box 808, Lawrence LivermoreNational Laboratory,Liv-ermore,CA 94550,email sugiyama@llnl.gov

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g *:>- ~.~ 1111%

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:, ,---, . . . . . . . . . . . . .,,

5.20x 105 5.25x105 5.30X 105 5,35x105 5.40X105 5.45x105

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Figure 1: Cape Canaveral winds at 9 m AGL generated Figure 2: Enlargement of the wind field from the pre-from observational data. Every third wind vector is plot- vious figure. Every wind vector is plotted. The vectorsted. The greatest wind speed shown is 3.7 rids. enclosed in circles are the observational data.

where ~~ are observations located at [?%,tk) and W& are

normalized weights. ‘l’heweights are typically monoton-ically decreasing functions of spatial distance or relativetime. A large variety of algorithms are possible, W ondifferent choices of the weighting functions. Examplesinclude bilinear interpolation and methods based on in-verse horizontal distance squared, inverse relative heigh~exponential time difference, and influence radius weight-ing. Spixification of a maximum cutoff distance providesan additional means of controlling the weighting of theinterpolation.

A second group of algorithms uses the method 9f suc-cessive comctions (DaIey, 1991), which may be writtenschematically as

k

where ii is the analyzed field at (?, t) for the jth itera-tion, ~JF~ ) is the J#h observation, and w; are normali-zed weights. l%e weights can be altered with each itera-tion to act as filters for the removal of small scale noise orerrors. One such method implemented in ADAPT is theBarnes algorithm for which w(F’) = exp(-~), with Abeing a varying horizontal influence radius parameter.

5. EXAMPLE: CAPE CANA~

As an example, ADAPT was used to generate windfields for a site surrounding Cape Canaveral in Florida.The graded grid covers a region 180 lon square with agrid top at 4.5 km using 61 grid points in the horizontal

and 41 in the vertical. Figure 1 shows the 9 m aboveground level (AGL) wind field for September 23,1997 at9Z. The field was developed from 49 surface and towerstations and 5 upper air profiles using an inverse-distancesquared sparse data algorithm. Some of the observationaldata may be seen in the enlargement plotted in Figure 2,the plotted observational level being the one nearest inheight to 9 m AGL. Complex wind structure is develojxdnear the site where the meteorological data is dense.

Figure 3 plots the winds at the 9 m AGL level, de-rived from a NORAPS forecast for the same time, usinga bilinear-linear analysis. ‘fhis wind field shows a patternreasonably similar to that in Figure 1, with a generallyonshore flow, veering to the north near the site and ac-celerating to the west near the left hand side of the grid.However the speeds are significantly higher than indi-cated by the observations.

6. MASS-CONSISTENT WIND ADJUSTMENT

The generation of wind fields involves a few specialconsiderations. Interpolation and parameterization maybe performed in either speed and direction or u and u

components. ‘l%einclusion of map projections requiresappropriate adjustments of length scales and dmtions.The vertical wind component can be &termined in thesame fashion as the horizontal components if w data isavailable. However, this is generally not the case. Fur-ther, our applications typically require the wind field tobe non-divergent, a property which is not a priori guar-

anteedby the interpolation methods. An adjustment pro-

@ixto the Poisson equation matrix.

.

3“0’’06=4.5X105 5, OX1O5 5.5x 105 6.OX 105

x (m)

Figure 3: Cape Canaveral winds at 9 m AGL generatedfrom a NORAPS forecast for the same time as in Figure1. Every third vector is plotted. The largest vector shownis 6.8 mk.

cedure based on the variational principle is therefore per-formed to provide the vertical wind component and pro-duce mass-consistent winds.

ADAITs mass-consistent wind algorithm (Chan andSugiyam~ 1997a and 1997b) is based on the followingmixed variational principle

1(U,v, w, A) =

1/[5* ai (u – U“)z+ a; (v – V“)z+ cr? (w – W“)z]d.fl

H au au 8W)+~—+—+=cm$-t & %$/

where (u”, u“, W“) and (u, u, w) are the componentsof the initial and adjusted wind velocity fields, respec-tively, J(z, y, z) is the Lagrange multiplier for the mass-consistency constraint, ct~ and czv are the Gauss pre-cision moduli controlling the vertical and horizontal ve-locity adjustments, and $2is the domain.

l%e finite element method (FEM) is chosen for spa-tial discretization because of its effectiveness in treatingcomplex terrain and its flexibility in dealing with vari-able resolution grids. In addition, the grid-point repre-sentation of the wind fields by FEM offers a more rigor-ous treatment of boundary conditions than the flux-basedstaggered grid representation often used in finite differ-ence approaches. ‘IWOpreconditioned conjugate gradientsolvers are provided to efficiently solve the Poisson equa-tion derived fkom the numerical formulation. The perfor-mance of these iterative solvers is further enhanced bythe addition of a small, block diagonal stabilization ma-

7. ATMOSPHERIC STABILITYTION

PARAMETERIzA-

The primary method for incorporating atmosphericstability effects in ADAPT is by selection of the ratio ofthe Gauss precision moduli, a = cY~/ av , which cOn-

trols the degree of adjustment in the vertical versus thehorizontal wind components. Small values of a inhibitvertical velocity changes and are appropriate for stableflows, forcing steerage around hills, while larger valuesof the parameter produce unstable flows and increase thelikelihood of winds rising over topographic barriers.

For situations involving complex topography and spa-tially varying atmospheric stability, it is appropriate to leta vary over the entire domain. Our approach (Chan andSugiyam% 1997b) is a modification of the Strouhrd num-ber parametrization proposed by Ross et al. (1988) anddeveloped further by Moussiopoulos et rd. (1988). Animproved curve-fitting formula for CY2as a function of lo-cal Strouhal number has been devised along with a gen-eralized formula for determining a characteristic heightdifference to incorporate topographic effects.

The local Strouhal number is defined as

Sti Hzv rgde- dtJ

‘-W’ N=WZ’ —>0dz –

i-St+ , t= –g, g<o (4)

where H is the ckteristic height difference, N isthe Brunt-Vii.istilafrequency, U is the characteristic windspeed, tis the buoyancy time scale, and@ is the potentialtemperature of the atmosphere. The characteristic windspeed is taken to be

U = max(J_(u0)2 + (u0)2 , 0.2m/s) . (5)

For H, we use an inverse-distance weighting of the vary-ing topographic height differences combined with a con-stant term involving the difference between the maxi-nium and minimum terrain heights

H= C(&= – &,n) +(1 – C) “jIJ (6)

~ l/T’ij~,3’

where A~j ~d rij ~ the orographic Might differenceand the horizontal distance between the considered loca-tion for Hand location (i,j) on the terrain grid and ~=and ~i. are the maximum and minimum terrain heights,respectively. The input parameter c varies between zero

4.Tw06

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,.4.,05 56:,05 ,.,.,’3, ,,;,,5. (“,,

F@re 4 San Franciaco Bay area winds and tempemturc(shaded contours) at 10 m AGL.

and one and is used to select an appropriate fincar combi-nation of the two terms. The constem term aflowa treat-ment of flows characterized by a constent Strouhal num-ber.

An exponential relationship between a2 and the 10A.%ouhal number was adopted

{

exp(-1.5S@1.s) str~o=2 = (7)

exp(l.5(-str)’5) Sx<o

bawd on a curve fit to the experimental &ta of Hunt andSny&r (1980). The magnitude of the Strouhal number iscapped hctween [—3,3] to prevent extreme valuea,of a.

8. EXAMPLE: SAN FHANCISCO BAY

The Strouhal number pammeterization of a wss testedon the analytic hill problem studied by Hunt md Snyder(1980) with satisfactory results. A preliminary test us-ing real data waa performed for the San Francisco Bayarea. Tempemhrrc and pressure fields interpolated fromAVN global medel data were combined to prcduce pe-tentkd temperatures. The latter were wed to develop thettiedimensional a field Interpolated wind fields de-rived from a combination of forty Iccal observations andAVN data were then adjusted for maw-consistency.

The grid covers a region 75 km square with 51 hmi-zontsl grid points. The grid top is at 3 km, with 3I ver-tical grid points and a finest resolution of 10 m near theground. lle OZMarch 29, 1997 temperatures and maas-consistent wind field for the 10 m AGL level are shownin F@res 4 and 5 along with the observational data Flg-urc 6 shows temperatures and winda at the u, = 0.157

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Figure 5: .% Francirco Bay area winda and at 10 mAGL. The vectors enclosed by circle wc the observa-tional data.

or z * 475 m levels. The temperatm incmes in-land, with generslly onshore winds, veering to the southnear the surface. Figure 7 plots a vertical cross-sectionthrough the ccntcr of the grid to show the w componentgencmtcd by the mass-adjustment procedure.

9. CONCLUSION

ADAPT simulations have bee” pcrfonn~ to test ~numerics, robustness, and compubtionsl efficiency ofthe model. Evaluation of ADAFT in conjunction withthe new AHAC dispersion mcdel (Leone et al., 1997)arc underway using a variety of archived tracer experi-ment date. Initial compariaens with the current ARACoperational models (ARAC, 1997) indicate that ADAPTprovides significantly imprevcd winds as rcflectcd in thearrival time, sped, and direction of the plume @eater,1997). An impertant factor in the improvement is the use

of a continuous tcrmin rcprcacntation and variable grid.ding, which allows meteorelogicsl festures snd topog-raphy to be more accurately resolved. An initial eprxa-tional veraion is cumcntly undergoing testing by ARAC.

Work has begun to refine the treatment of meteo.relogical &ta, improve atmospheric parametwizations,incorporate momentum as well as mass conservation,

and develop eddy difisivities for dispersion cefcula-tions. Additional assimilation methods arc afso kingimplemented includhg three-dimensional analyaes and

apwoaches tOcOmbining mmlysis and format data withobservations.

ACKNOWLEDGEb4ENTS

The authors would like to acknowledge H. Walker for

I

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,.4”,05 56. ?05 5.8=,05 . ...,,, (.”,

Figure 6 San Francisco Bay mea winda and tempera-tures (shsdcd contours) at u= = 0.157 where Ztv =3000 m.

providing the grid generation mndel and T. Kucznmrskifor tbe graphics package. TMs work was performed un-der the auspices of the U.S. Department of Energy byLavaence Llvennore National Laboratory under Cnn-tract No. W-7405 -ENG-48

REFERENCES

Atmospheric Release Advisory Capability, 1997 User’s

Guide to the CG-MATHEW/ADPIC Models, Version5.O, UCWMA-103581 Rev. 5, Lawrence LivermoreNational Laboratory, L:vermnre, CA.

Cban, S. T.rmd G. Sugiymna,1997a ANew McdeI forGenerating Mass-Consistent Wind Fields over Contin.uous Tezrain, Pmt. ofthe ANS Sixth Topical Meetingon Emergency Preparedness and Emergency Response,Sian Francisco, CA, 375-378.

Chsn, S. T.and G. Sugiyama, 19971x User’s Manuaf forMC.WINIY A New Maaa-Consistent Wmd Model forARAC-3. (in prcpamtion)

1,.,,.,,6 4.,,.,06 ... wd ,.ZCWN

Figure 7 San Francisco Bay area winds at a verticalcross-section at r, = 569 km. The vertical wind com-pnnent is exaggerated by a factor often.

Daley, R., 1991: Atmospheric Data Analysis, CambridgeUniversity Press, Csmbridge, UK, and references citedthcmin.

Hunt, J. C. R and W. H. Snyder, 1980 Experimentson Stably and Neutmlly Stratified Flow over a McdelThree-Dlmensinnal Hill, J. Fluid Mech., 96, part 4,671-704.

Foster, K., 199? private communication.

Leone Jr., J. M., J. Naastrom, and D. Maddix, 1997 AFirst Lcok at the New ARAC Dkpersion Model, Pmt.of ths ANS Sixth Topical Meeting on Emergency Pre-paredness and Enwgenq Response, San Francisco,CA, 383-386.

Moussiopnulos, N. and Th. Flassak, and G. Knktel, 198$+A Refined Diagnostic Whd Mndel Envic Sofiwm, 3,No.2, 85-94.

Ross, D. G., snd I. N. Smith, P. C. Manins, and D. G.Fox, 1988: D@nostic Wind Field Mcdeling for Com-plex Terrain: Mcdel Development and Testing, J. Appl.Meteor, 27,785-796.

Hodur, R. M., 1987: Evacuation of a Regional Mndel withan Update Cycle, Mon. Wea. Rav, 117,2707.

Hodur, R. M. 1997: ‘The Navsl Research Labora-tory’s Cnuplcd Ocean/Atmosphere Mesoscafe Prcdc-tion System (COAMPS), Mon. Wea Rev., 12S, 1414-1430.