[Other]

[ホカ]

[他]

Fumio Masuda

Keitarou Hara

Shin\u27ichi Okamoto

オカモト シンイチ

ハラ ケイタロウ

マスダ フミオ

原 慶太郎

増田 文夫

岡本 眞一

TUIS Academic Repository

TOKYOUNIVERSITYOFINFORMATIONSCIENCES東京情報大学研究論集Vol.5  No.1 抜刷特　集東京情報大学ハイテクリサーチセンター国際シンポジウム石井 健一郎 人に近づくコンピュ ター ―人間を知り、人間に迫る―　　 1木ノ内康夫、小沼利光、石橋英水、田村祐一、松本直樹、佐生智一、稲林昌二イメー ジ間の反応に基づく情報処理系の構成　―イメー ジで考えるコンピュ ターの実現に向けて―　　 9山崎和子 動的環境へのエージェントの適応　　　23水谷正大、大森貴博、来住伸子、小川貴英検索エンジンを利用した日本語Webページ数の統計的推定の研究　　　33井関文一、小畑秀文、大松広伸、柿沼龍太郎胸部CT画像からの肺野内３次元構造の抽出　　　47田子島一郎、増田文夫、武井敦夫、原慶太郎、岡本眞一、田中ちえ、白川泰樹全球域３次元拡散モデルを用いた大気中の微量粒子の発生地域特定のための研究　　　57Shin'ichi Okamoto, Keitarou Hara, Atsuo Takei, and Fumio MasudaA Study on Numerical Methods for Air Quality Simulation 65Shin'ichi Okamoto, Keitarou Hara, Fumio Masuda, and Atsuo TakeiA Study on the Atmospheric Dispersion over Complex Terrain 73N.W.Harvey and V.ChantawongAdsorption of Heavy Metals by Ballclay：their Compatition and Selectivity 79A.Wangkiat, H.Garivait, N.W.Harvey, and S.OkamotoApplication of CMB8 Model for Source Apportionment in Bangkok Metropolitan Area 87東京情報大学2001.8ISSN 1343-2001AbstractAlthough the Gaussian plume model is very useful and effective, higher predictive abilityon the complex terrain is also required. Many numerical model were developed, but thenumerical schemes were sometimes still discussed. With this study it is aimed to develop the 3-Dnumerical model based on the most suitable numerical method.Our limited comparative study on numerical methods suggested that the most suitableone may be the Taylor-Galerkin scheme for the discretazation for the advection equation. And,also a filter is attractive for such a Galerkin-type numerical method that has inherent numericalnegative diffusion. Therefore, we developed a 3-D numerical model by using the operator splittingmethod based on the locally one-dimensional Taylor-Galerkin with Forester filter method. Thewind field on the complex terrain is estimated by the high-resolution meteorological model byusing the Four Dimensional Data Assimilation (FDDA) technique. This model was applied to the air quality simulation for Tochigi area. This area is northedge of Kanto plain, and foothill of Ashio mountainous area. The size of objective area is about 10km square. In this area, the intensive meteorological observations and air tracer experiment wereconducted, in which ten pibal stations were deployed. The calculated surface tracerconcentrations were compared with the observed data, and good consistency were obtained. 1.    INTRODUCTIONAir quality simulation models (AQSM’s) belong to the most important tools when making adecision on air pollution prevention program. As for the complex terrain, the US.EPA’s CTDMPLUS andmany other models were developed: for example, VALLEY, COMPLEX I and RTDM, and soon(US.EPA,1993). Although these Gaussian plume models are very useful and effective, higherpredictive ability on the steeper complex terrain is also required. Many numerical models weredeveloped for simulating the global, regional and urban scale air pollution. However, the numericalmethods for these models were sometimes still discussed(Chock,1991; Syrakov and Galperin, 1998).With this study it is aimed to develop the 3-D numerical model based on the most suitable numericalmethod for a three-dimensional air quality simulation model applicable to a site over complex terrain.A Study on the Atmospheric Dispersion over Complex TerrainShin'ichi Okamoto*,  Keitarou Hara*,  Fumio Masuda**,  and  Atsuo Takei**東京情報大学研究論集　Vol. 5 No.1  73*東京情報大学教授**東京情報大学助教授2001年5月16日受理2. MODEL DESCRIPTION2.1 Numerical ModelRecent progress in numerical method has been very rapid, and the number of methodsdeveloped are not countable. The Galerkin finite element method using a chapeau function is anattractive scheme for the discretization of a space derivative. However, the combination with a first-order time differencing makes the scheme unstable, because of computational pseudo-negative diffusion.The Petrov-Galerkin and the Taylor-Galerkin methods can mitigate these situations. An extensiveevaluation study for the numerical methods was carried out by Chock (1991), and it was concluded thatthe Taylor-Galerkin method is one of the most appropriate choices for solving the advection equation.The one-dimensional advection equation descretized by the Taylor-Galerkin method is shown in eq.(1),in case that the wind speed is uniform for the whole computational domain. (1)where, µ is the Courant number ; µ = u ∆ t / ∆ x.The Galerkin-type numerical methods are useful for solving the advection equation. However,these methods produce a great deal of computational noise in highly steep gradient area of the values(concentrations). In order to smooth the computational values, Forester (1977) proposed an iterationsmoothing process, and Chock (1991) called it the Forester filter. This filter is identical to the diffusioncalculation to compensate computational-generated ripples. In this study this filtering method wascombined with the Taylor-Galerkin method. The filtering procedure in each calculation step is expressedby eq.(2)(2)where ø is a function , and its value is one or zero depending on the existence of the numericalripples.  The coefficient v plays a similar role to the diffusion coefficient. The superscript k means thenumber of iterations.Comparative study on numerical methods including the Taylor-Galerkin-Forester method waspresented by Okamoto et al.(1998). The three dimensional diffusion and advection equation on theterrain adjusted coordinate system is solved by the operator splitting method based on the locally one-dimensional Taylor-Galerkin descretization. The concentration at time level n+1 can be calculated by(3)where, Ax and Ay  are horizontal advection and diffusion operators, and Az is the verticaladvection and diffusion, source and sink operator.The vertical diffusion coefficient for tracers was estimated by using the method proposed byShir and Shieh(1974), and the horizontal coefficient was estimated by the incremental difference of σ–yof Pasquill-Gifford diagram. The lid height was estimated by an empirical function based on theaccumulated solar insulation.A Study on the Atmospheric Dispersion over Complex Terrain742.2 Meteorological PreprocessorThe three-dimensional numerical diffusion model requires the mean wind vectors andturbulence or diffusion coefficients for all grid points within the computational domain. In order to fulfillthese requirements, the computational fluid dynamic models were usually applied. Our limitedcomparative study showed that the predictive performances for several CFD models and variationalMASCON models were not so much different (Okamoto, et al., 1996), and the MASCON model was mostconvenient to use. However, the MASCON model can not express the circulating flow within deepvalleys. Although four-dimensional data assimilation may be one of the most useful tools for preparingmeteorological variables for all grid points, there were not so much applications for small areas in whichthe grid space was less than one kilometer. Only a few reference concerning FDDA applied to theseareas could be found (Fast and O’Steen, 1994). By using the simple governing equations and precisemeteorological data, the appropriate results were obtained for the short-range dispersion calculation(Okamoto, et al., 1998a). In this FDDA model, the nonhydrostatic momentum equation and the continuity equation onthe terrain-adjusted grid system were employed. The diffusion coefficients for the momentum wereexpressed by the simplest form; horizontal term was modeled by the grid space and wind velocitygradients; vertical term was expressed by the function of estimated friction velocity. The governingequation was solved by the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE). The tendencyterm were added to the governing equation in order to mitigate the difference between the observed andcalculated values as shown;(4)where, F is a governing equation for variable ø ,  Gø is a nudging coefficient, and w ‘s areweighting coefficients; wT is a temporal weighting function, and w xyz is a spatial weighting function.  Ifthe observation point were located within that grid mesh, wxyz =1; otherwise, wxyz=0. The value of thenudging coefficient was tentatively assumed to be 0.005.3. RESULTSIn order to evaluate the proposed numerical model, an air quality simulation was carried out forTochigi area. This area is north edge of Kanto plain, and foothill of Ashio mountainous area. The size ofobjective area is about 10 km square. In this area, intensive meteorological observations and air tracerexperiment were conducted, in which ten pibal stations were deployed. The surface tracerconcentrations were measured by about forty sampling points. The tracer was released from about fivemeter in height, and sampling duration was 60 minutes. These experiments were conducted inDecember 1980 and April 1981. The air sampling network and pilot balloon sounding points for springexperiment is shown in Fig.1The FDDA result for the neutral case (run 4) is shown in Fig.2. In this case, relatively largedifference in wind direction were observed; south wind was observed in the plane, but wind direction in東京情報大学研究論集　Vol. 5 No.1  75mountainous area was mainly northeast. This tendency was expressed by our simulation. The circulatingflow in the valley was also reproduced by this FDDA model as shown in Fig.3.The calculated surface tracer concentrations were shown in Fig.4. The statistical evaluationscores are shown in Table 1. This result is more satisfactory compared with that by using the wind fieldderived by MASCON model.4. CONCLUSIONA practical air quality simulation model has been developed based on the Taylor-Galerkindiscretization with Forester filter for the advection equation. This model was applied to air qualitysimulation using the Tochigi area dispersion experimental data. When the computing time is taken intoconsideration, the predictive performance of this model is considered to be fairly good. However, a moreextensive validation study and a model refinement will be necessary for dispersion conditions in a verystable drainage flow.  AcknowledgementsWe would like to acknowledge that this study was carried out by the Grant-in-aid for the high-tech Research Center project of the Japanese Ministry of Education, Science, Sports and Culture.ReferenceChock D.P. (1991)  A comparison of numerical methods for solving the advection equation III,Atmospheric   Environment 25A, 853-871.Fast J.D. and O’Steen B.L. (1994)  Atmospheric and dispersion modeling in areas of highly complexterrain employing a four-dimensional data assimilation technique, 8th Joint Conf. On Applications ofAir Poll. Meteor. With A&WMA, Nashville,U.S.a., pp.309-315.Forester C.K. (1977)  Higher order monotonic convective difference schemes, J.Comput. Phys. 23, 1-22.Okamoto S., Sakai K., Matsumoto K., Horiuchi K. and Kobayashi K. (1996)  Development and applicationof a three-dimensional Taylor-Galerkin numerical model for air quality simulation near roadway tunnelportals, presented  in 5th ASAAQ, Seatle,U.S.A.Okamoto S., Takei A., Uosaki,K. and Suzuki M. (1998a)  Airflow analysis on the complex terrain byFDDA, presented in 1998 spring meeting Japan Meteor. Soc., Tokyo,Japan.Okamoto S., Hara K., Masuda F., Takei A., Takahashi H., Horiuchi K. and Suzuki M. (1998b)Comparative study on numerical methods for air quality simulation model, presented in 11th WorldClean Air congress, Durban, South Africa.Shir C.C. and Shieh L.J. (1974) A generalized urban air pollution model and its application to the studyof SO2 distribution in the St.Loise metropolitan area, J.Applied Meteor. 13,185-204.Syrakov D. and Galperin M. (1998)  On some explicit advection schemes for dispersion modellingapplication, preprints 5th Int. Conf. On harmonisation within Atmospheric Dispersion Modelling forRegulatory Purposes 236-243.U.S.EPA (1993)  Guideline on air quality models (revised),  EPA-450/2-78-027R.A Study on the Atmospheric Dispersion over Complex Terrain76東京情報大学研究論集　Vol. 5 No.1  77Constant a* Slope b* Corr.coef. Ave. errorMASCON 98.2 0.516 0.58 398.FDDA 85.9 1.439 0.57 404Wind modelTable 1   Statistical scores for Tochigi experimental dataRegression line y = a + bxA Study on the Atmospheric Dispersion over Complex Terrain78Fig.4  Comparison of the surface tracer concen-tration; (a)MASCON-generated wind was used.(b)FDDA-generated wind was used. (c)obervedconcentration pattern (unit: ppt). 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A Study on the Atmospheric Dispersion over Complex Terrain

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A Study on the Atmospheric Dispersion over Complex Terrain

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