Atmospheric Dispersion Model Applied in the Nuclear Power Plant Accident Consequence Assessment

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Atmospheric Dispersion Model Applied in the
Nuclear Power Plant Accident Consequence
Assessment

• Zheng Dongqin
• Superviser J. K. C. Leung

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Ensemble Kalman Filter Techniques For Data
Assimilation in Nuclear Emergency
Zheng Dongqin
Questions Can we assimilate the measured
radiological data into nuclear
emergency system to improve the prediction?
Our research Use the Ensemble Kalman Filter and
simulated measured data
to correct the forecast for nuclide
concentration distribution in the
atmosphere given by
Monte Carlo dispersion model .
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Outline

• Motivation
• Algorithm of ensemble Kalman Filter
• Application to nuclear emergency

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Necessity of Data assimilation in Nuclear
Emergency System

• The actions taken in an accident emergency will
  in principle be based upon the dose assessments
  from model predictions.
• Models, however, are prone to large
  uncertainties, and hence model predictions may
  differ significantly from the true radiological
  situation.

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Necessity of Data assimilation in Nuclear
Emergency System

• measurements cannot give a complete picture of
  the actual situation
• Data assimilation is to use observations to
  update model predictions, and hence to reduce the
  uncertainty associated with model-based dose

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Kalman filter KF
?
KF
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KF algorithm
x - Model State Vector M - State Transition
Matrix ? - Transition Model Error P - Model
Error Covariance Q - Transition Model Error
Covariance y - Data Vector H - Measurement
Matrix ? - Observation Error R - Observation
Error Covariance K - Kalman Gain
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Assimilation with an Ensemble Kalman Filter (ENKF)
Take Measurement
Calculate the Kalman Gain
Randomize the State
Propagate the State
Calculate the Covariance
Updated States


Model
1
1
X
1
X
k
k1
__

P
K

2
Model
2
2
X
k1
X
k
k1


3
Model
3
3
X
X
k
k1

Model

Mean
K
X
X
k
k1
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Assimilation with an Ensemble Kalman Filter (ENKF)
Two steps to each assimilation cycle
1. Ensemble forecast
2. Assimilation of new observations
forecast, cycle n1
forecast, cycle n
assimilation
assimilation
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Range of study
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Wind field
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Plume of nuclide
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Distribution of observation points
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Calculation of -ray dose rate from the activity
concentration

• flux of -ray at a point (xo,yo, zo) from
  source of energy E dispersed in air
• Total dose rate

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The EnKF analysis scheme

• Define the matrix holding the ensemble members
• the ensemble perturbation matrix
• ensemble covariance matrix

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The EnKF analysis scheme

• The ensemble of observation vectors are produced
  by adding perturbations to the true observation
  vector as
• Store them in the columns of a matrix
• The ensemble of perturbations can be stored in
  the matrix

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The EnKF analysis scheme

• The observation error covariance matrix
• analysis equation
• Because when forecast errors and
  observation errors are uncorrelated

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The EnKF analysis scheme

• The inverse can be obtained by compute the
  singular value decomposition of the matrix
• So
• Here is a diagonal matrix which can be
  written as

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Primary result
20 members
60 members
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Primary result
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Thank you !