Commentary Article
Lagrangian Dispersion Model
Commentary Article
Lagrangian Dispersion Model and its Application to Monitor Nuclear Power Plants Michael Schorling Schorling & Partner, Innsbrucker Ring 152, D-81669 Munich, Germany
T1 is the Lagrangian time scale.
Abstract The Lagrangian dispersion model and its advantages while applying it in monitoring nudear power plants in complex terrain at varying meteorological conditions is explained. The software developed has been installed at the Bavarian State Authority to monitor its six nuclear power plants. Input data are routinely measured meteorological data as well as emission data for iodine, aerosols and noble gas.
1
T h e Lagrangian M o d e l
LANGEV1N developed the main idea for the Lagrangian Dispersion Model already in 1908 while working on the Brownian Diffusion (LANGEVrN, 1908), much earlier than the time of application for the Gaussian model in atmospheric research. The Lagrangian model starts at the Langevin Equation i.e. for the horizontal component du/dt = - m a + fir(t)
The mean wind speed u i is to be evaluated in an Eulerian coordinate system as determined by windfield models of different complexity, on the basis of ground or profile measurements or assumptions. The wind speed components have to be transformed into the Lagrangian system in order to continue the computations. With respect to the windspeed fluctuations and the Lagrangian time scale, HANNA has provided parametrisations applicable in flat and moderately complex terrain (HANNA, 1982). With this information, the trajectories can be prognosed step by step. The computation of the concentration pattern is then only a book-keeping problem: In a computational grid, one has to count the numbers n of trajectories passing through as well as the time interval At, while the particles stay in each individual cell. The integral concentration in a cell is: c(i,j) = Y~ ( M A t ) / vol; i and j describe the grid cell in a grid matrix, vol is the effective volume of the cell and M the mass of the particle. The individual particle might have a non-constant mass.
which states that a friction term decelerates the flow and random acceleration enhances it.
In order to determine the mean concentration, one must divide the integral concentration by the duration of the "sampling time".
With respect to the theory and the determination of the above mentioned coefficients, the reader is referred to the literature (LEGG & RAUI'ACH, 1982; THOMSON, 1985). This article only comments the simplicity of this method.
In the model one assumes that the part-ides are independently released at the source and that they are non reactive.
As the movement of particles can be described by a Markov process, the trajectories of these particles can simply be determined by the coordinates. Xinew ~ Xiold + (Ui + Ui')A t;
u~ is the mean wind speed, u i' its fluctuation, A t is the computational time step. This is valid in an Eulerian frame of reference. The trajectories of Lagrangian particles are determined in a Lagrangian coordinate system which provides a high autocorrelation R between the status at two neighbouring time steps R = exp(-
At / T1) -- 1;
ESPR-Environ. Sci. & Pollut. Res. 2 (2) 105-106 (1995) 9 ecomed publishers, D-86899 Landsberg, Germany
The number of particles to be considered determines the accuracy as well as the computing time of the problem. However, by taking into account a kernel density function which determines the spacial weight of a particle, the number of particles can be drastically reduced to about 1 000/h (ScHoea.ING, 1991). The advantages of the Lagrangian approach are: 9 There are no numerical problems such as pseudodiffusion when solving the advection diffusion equation. The Lagrangian formulation gives linear, algebraic equations. 9 The locally and timely varying 3-D windfield can be included by running appropriate windfield models ahead of the dispersion computations. Even simple mass consistant diagnostic models which consider ground a n d / o r profile measurements at different locations of the area of 105
Lagrangian Dispersion Model
News & Views
interest provide a signifcant advantage in accuracy in comparison to Gaussian models (SCHORLING, 1991). 9 C o m p l e x t e r r a i n o r u r b a n , b u i l t - u p areas represent the b o u n d a r y t h r o u g h w h i c h or in w h i c h "particles" are n o t allowed to m o v e . W h e n the b u i l t - u p area can be m o d elled w i t h i n the c o m p u t a t i o n a l grid, it c a n be i n c l u d e d into the c o m p u t a t i o n . T h e p e r f o r m a n c e of a L a g r a n g i a n m o d e l is t h e n significantly better t h a n H i g h w a y 2 or C a l i n e 4 , for e x a m p l e (DABBERDT et al., 1994). 9 T h e timely v a r y i n g source strength can be taken into consideration. 9 T h e timely v a r y i n g c o n c e n t r a t i o n p a t t e r n will n o t be forgotten. T h e history of the p l u m e is t a k e n into a c c o u n t to d e t e r m i n e the spacially a n d t i m e l y v a r y i n g c o n c e n t r a tion p a t t e r n .
2
Input D a t a and Application
To run the model, the meteorological and release data have to be provided. The meteorological data comprises the same data set as required for the Gaussian model; however, more information could and should be incorporated when available to enlarge the advantages of this type of model. There is an alternative for the release data, as release categories according to the German Risk study for nuclear power plants have been predefined in the shell. This allows the user to concentrate on the impact assessment of releases instead of on data acquisition. The Lagrangian model has been applied to build up a m o n i t o r i n g system for B a v a r i a n n u c l e a r p o w e r p l a n t s . T h i s system will also be used for the a n n u a l exercises at the state a u t h o r i t y to assess possible impacts after releases of rad i o n u c l i d e s i n t o the a t m o s p h e r e .
Here, the air concentration and ground contamination due to I 131 and Cs 137, the cloud shine due to Xe 133, and the thyroid and effective dose for children and adults will be computed. A distinction for the near field (0 - 5 km off the source) and far field ( 0 - 5 0 km) takes place. The physical map will be superimposed to the concentration or dose pattern. The computation on a 586 PC takes between 2 and 8 minutes according to the duration of the release and the prevailing atmospheric stability.
3 Literature LANGEVIN:Sur la Theorie du Movement Brownien. Comptes Rendus, Acad. Sciences 145 (1908) LEGG, B. J.; M. R. RauPaCH: Markov Chain Simulation of Particle Dispersion in Inhomogenous Flows. Bound. Layer Met. Vol. 24 (1982) THOMSON, D. J.: A Random Walk Model of Dispersion in Turbulent Flows and its Application to Dispersion in a Valley. Quart. J. R. Met. Soc. 112 (1985) HaNNa, S.: Application in Air Pollution Modelling, in: Atmospheric Turbulence and Air Pollution Modeling by F. T. M. NIEUWSTADT, H. VaN DOG Reidel Publ. Comp. (1982) SCHORL1NG,M." Application of the Lagrangian Dispersion Model to the Regional Scale Using Kernel Density Functions. OECD/NEA Data Bank, Saclay, France (1991) DABBERDT,W.; W. HOYDYSCH,M. SCHORLING,F. YANG, O. HOLYNSKY"Dispersion Modelling at Urban Intersections. submitted to Atmospheric Environment (1994) SCHORLING, M.: Die Berechnung der atmosph/irischen Ausbreitung, Entwicklung und Validierung eines Lagrange Rechenmodells, ecomed-Verlag, Handbuch des Umweltschutzes
News & Views The ACS Division of Analytical Chemistry Establishes Home Page on World Wide Web
Division is extending to each of you a dual invitation: try out our pages and make use of them to the fullest, and make suggestions for things that should be added. The home page is accessed using the following Universal Resource Locator (URL):
by Roland HmSCH ([email protected])
http: / / nexus.chemistry,duq.edu/ analytical/analyticaI.html
he Division of Analytical Chemistry now has its own home page on the widely-usedWorld Wide Web (WWW). This is intended to serve as an information resource for the membership of the Division. It will also be a means for newcomers to the field to find out more about our discipline. The home page is hosted by the Department of Chemistry and Biochmistry at Duquesne University, thanks to the efforts of faculty members Tom ISENHOURand Skip KINGSTON and the departmental staff.
You should add this address to your "hotlist" in your WWW browser. For those who are unfamiliar with the WWW, it is easiest to access the information through a browser such as Mosiac or NetScape. You just enter the above address, exactly as written, when prompted for the URL. No special equipment beyond a reasonably current personal computer is necessary to do this. The plan is to include information in the following categories: 9 Division Business, including announcements of activities, minutes of the Executive Committee, listings of officers, and committee reports. 9 Meetings and Symposia, including notices, calls for papers, and detailed programs for
T
This notice describes some of the key features. As is true with most home pages on the WWW, ours is "under construction", with n e w features and more sources of further information being added constantly. So, the
106
all meetings sponsored or co-sponsored by the Division. 9 Grant and fellowhip information, from government and private agencies. 9 Education in analytical chemistry, including links to home pages for graduate programs in analytical chemistry, institutes and centers, and curriculum innovations. 9 Information on jobs and postdoctoral fellowships. 9 Publications, including ACS books and journals, and other publications. 9 Legislation and public policy. 9 Databases of potential interest to analytical chemists. 9 Other analytical organizations and other sources of information. Suggestions in any of these categories should be made to the editor, Roland F. t-~RSeH, at [email protected] or by calling him at 301-903-3682. He ~ explain the process of setting up a link to your information. Source: DAC Newstetter, Summer 1995
ESPR-Environ. Sci. & Pollut. Res. 2 (2) 1995
Lagrangian Dispersion Model
Commentary Article
Lagrangian Dispersion Model and its Application to Monitor Nuclear Power Plants Michael Schorling Schorling & Partner, Innsbrucker Ring 152, D-81669 Munich, Germany
T1 is the Lagrangian time scale.
Abstract The Lagrangian dispersion model and its advantages while applying it in monitoring nudear power plants in complex terrain at varying meteorological conditions is explained. The software developed has been installed at the Bavarian State Authority to monitor its six nuclear power plants. Input data are routinely measured meteorological data as well as emission data for iodine, aerosols and noble gas.
1
T h e Lagrangian M o d e l
LANGEV1N developed the main idea for the Lagrangian Dispersion Model already in 1908 while working on the Brownian Diffusion (LANGEVrN, 1908), much earlier than the time of application for the Gaussian model in atmospheric research. The Lagrangian model starts at the Langevin Equation i.e. for the horizontal component du/dt = - m a + fir(t)
The mean wind speed u i is to be evaluated in an Eulerian coordinate system as determined by windfield models of different complexity, on the basis of ground or profile measurements or assumptions. The wind speed components have to be transformed into the Lagrangian system in order to continue the computations. With respect to the windspeed fluctuations and the Lagrangian time scale, HANNA has provided parametrisations applicable in flat and moderately complex terrain (HANNA, 1982). With this information, the trajectories can be prognosed step by step. The computation of the concentration pattern is then only a book-keeping problem: In a computational grid, one has to count the numbers n of trajectories passing through as well as the time interval At, while the particles stay in each individual cell. The integral concentration in a cell is: c(i,j) = Y~ ( M A t ) / vol; i and j describe the grid cell in a grid matrix, vol is the effective volume of the cell and M the mass of the particle. The individual particle might have a non-constant mass.
which states that a friction term decelerates the flow and random acceleration enhances it.
In order to determine the mean concentration, one must divide the integral concentration by the duration of the "sampling time".
With respect to the theory and the determination of the above mentioned coefficients, the reader is referred to the literature (LEGG & RAUI'ACH, 1982; THOMSON, 1985). This article only comments the simplicity of this method.
In the model one assumes that the part-ides are independently released at the source and that they are non reactive.
As the movement of particles can be described by a Markov process, the trajectories of these particles can simply be determined by the coordinates. Xinew ~ Xiold + (Ui + Ui')A t;
u~ is the mean wind speed, u i' its fluctuation, A t is the computational time step. This is valid in an Eulerian frame of reference. The trajectories of Lagrangian particles are determined in a Lagrangian coordinate system which provides a high autocorrelation R between the status at two neighbouring time steps R = exp(-
At / T1) -- 1;
ESPR-Environ. Sci. & Pollut. Res. 2 (2) 105-106 (1995) 9 ecomed publishers, D-86899 Landsberg, Germany
The number of particles to be considered determines the accuracy as well as the computing time of the problem. However, by taking into account a kernel density function which determines the spacial weight of a particle, the number of particles can be drastically reduced to about 1 000/h (ScHoea.ING, 1991). The advantages of the Lagrangian approach are: 9 There are no numerical problems such as pseudodiffusion when solving the advection diffusion equation. The Lagrangian formulation gives linear, algebraic equations. 9 The locally and timely varying 3-D windfield can be included by running appropriate windfield models ahead of the dispersion computations. Even simple mass consistant diagnostic models which consider ground a n d / o r profile measurements at different locations of the area of 105
Lagrangian Dispersion Model
News & Views
interest provide a signifcant advantage in accuracy in comparison to Gaussian models (SCHORLING, 1991). 9 C o m p l e x t e r r a i n o r u r b a n , b u i l t - u p areas represent the b o u n d a r y t h r o u g h w h i c h or in w h i c h "particles" are n o t allowed to m o v e . W h e n the b u i l t - u p area can be m o d elled w i t h i n the c o m p u t a t i o n a l grid, it c a n be i n c l u d e d into the c o m p u t a t i o n . T h e p e r f o r m a n c e of a L a g r a n g i a n m o d e l is t h e n significantly better t h a n H i g h w a y 2 or C a l i n e 4 , for e x a m p l e (DABBERDT et al., 1994). 9 T h e timely v a r y i n g source strength can be taken into consideration. 9 T h e timely v a r y i n g c o n c e n t r a t i o n p a t t e r n will n o t be forgotten. T h e history of the p l u m e is t a k e n into a c c o u n t to d e t e r m i n e the spacially a n d t i m e l y v a r y i n g c o n c e n t r a tion p a t t e r n .
2
Input D a t a and Application
To run the model, the meteorological and release data have to be provided. The meteorological data comprises the same data set as required for the Gaussian model; however, more information could and should be incorporated when available to enlarge the advantages of this type of model. There is an alternative for the release data, as release categories according to the German Risk study for nuclear power plants have been predefined in the shell. This allows the user to concentrate on the impact assessment of releases instead of on data acquisition. The Lagrangian model has been applied to build up a m o n i t o r i n g system for B a v a r i a n n u c l e a r p o w e r p l a n t s . T h i s system will also be used for the a n n u a l exercises at the state a u t h o r i t y to assess possible impacts after releases of rad i o n u c l i d e s i n t o the a t m o s p h e r e .
Here, the air concentration and ground contamination due to I 131 and Cs 137, the cloud shine due to Xe 133, and the thyroid and effective dose for children and adults will be computed. A distinction for the near field (0 - 5 km off the source) and far field ( 0 - 5 0 km) takes place. The physical map will be superimposed to the concentration or dose pattern. The computation on a 586 PC takes between 2 and 8 minutes according to the duration of the release and the prevailing atmospheric stability.
3 Literature LANGEVIN:Sur la Theorie du Movement Brownien. Comptes Rendus, Acad. Sciences 145 (1908) LEGG, B. J.; M. R. RauPaCH: Markov Chain Simulation of Particle Dispersion in Inhomogenous Flows. Bound. Layer Met. Vol. 24 (1982) THOMSON, D. J.: A Random Walk Model of Dispersion in Turbulent Flows and its Application to Dispersion in a Valley. Quart. J. R. Met. Soc. 112 (1985) HaNNa, S.: Application in Air Pollution Modelling, in: Atmospheric Turbulence and Air Pollution Modeling by F. T. M. NIEUWSTADT, H. VaN DOG Reidel Publ. Comp. (1982) SCHORL1NG,M." Application of the Lagrangian Dispersion Model to the Regional Scale Using Kernel Density Functions. OECD/NEA Data Bank, Saclay, France (1991) DABBERDT,W.; W. HOYDYSCH,M. SCHORLING,F. YANG, O. HOLYNSKY"Dispersion Modelling at Urban Intersections. submitted to Atmospheric Environment (1994) SCHORLING, M.: Die Berechnung der atmosph/irischen Ausbreitung, Entwicklung und Validierung eines Lagrange Rechenmodells, ecomed-Verlag, Handbuch des Umweltschutzes
News & Views The ACS Division of Analytical Chemistry Establishes Home Page on World Wide Web
Division is extending to each of you a dual invitation: try out our pages and make use of them to the fullest, and make suggestions for things that should be added. The home page is accessed using the following Universal Resource Locator (URL):
by Roland HmSCH ([email protected])
http: / / nexus.chemistry,duq.edu/ analytical/analyticaI.html
he Division of Analytical Chemistry now has its own home page on the widely-usedWorld Wide Web (WWW). This is intended to serve as an information resource for the membership of the Division. It will also be a means for newcomers to the field to find out more about our discipline. The home page is hosted by the Department of Chemistry and Biochmistry at Duquesne University, thanks to the efforts of faculty members Tom ISENHOURand Skip KINGSTON and the departmental staff.
You should add this address to your "hotlist" in your WWW browser. For those who are unfamiliar with the WWW, it is easiest to access the information through a browser such as Mosiac or NetScape. You just enter the above address, exactly as written, when prompted for the URL. No special equipment beyond a reasonably current personal computer is necessary to do this. The plan is to include information in the following categories: 9 Division Business, including announcements of activities, minutes of the Executive Committee, listings of officers, and committee reports. 9 Meetings and Symposia, including notices, calls for papers, and detailed programs for
T
This notice describes some of the key features. As is true with most home pages on the WWW, ours is "under construction", with n e w features and more sources of further information being added constantly. So, the
106
all meetings sponsored or co-sponsored by the Division. 9 Grant and fellowhip information, from government and private agencies. 9 Education in analytical chemistry, including links to home pages for graduate programs in analytical chemistry, institutes and centers, and curriculum innovations. 9 Information on jobs and postdoctoral fellowships. 9 Publications, including ACS books and journals, and other publications. 9 Legislation and public policy. 9 Databases of potential interest to analytical chemists. 9 Other analytical organizations and other sources of information. Suggestions in any of these categories should be made to the editor, Roland F. t-~RSeH, at [email protected] or by calling him at 301-903-3682. He ~ explain the process of setting up a link to your information. Source: DAC Newstetter, Summer 1995
ESPR-Environ. Sci. & Pollut. Res. 2 (2) 1995
