Comparison between test field data and Gaussian plume model

Transcription

1 Environmental Modelling for RAdiation Safety II Working group 9 Comparison between test field data and Gaussian plume model Laura Urso Helmholtz Zentrum München Institut für Strahlenschutz AG Radioecological Modelling and Retrospective Dosimetry(REM) Wien, January

2 Simulation program for determination of population exposure to high doses after the explosion of an RDD device ) Gaussian model with known metereological parameters ) With at least 3 TLD measurements the free parameters can be inversely determined 3) Mathematical approach for inverse modelling: Levenberg-Marquardt Algorithm Two calculated examples: A) Synthetic data produced with HOTSPOT.7 National project: Retrospective dosimetry for the population in emergency situations Contract No 367S456 Bundesamt für Strahlenschutz (BfS) Federal Ministry for the environment, Nature Conservation and Nuclear Safety (BMBF)

3 Equations from SSK report No. 37 pp Gaussian dispersion model χ(x, y, z; H) = Dispersion coefficients a,b,c depend on stability class (from HOTSPOT guide.7) Depletion factor (from HOTSPOT guide.7)) Wet deposition σ y,z (x) = DF(x) = W (x) = πσ y (x)σ z (x)u(x) }{{} ax ( + bx) c [ exp( x exp( Λ πσy (x)u(x) e exp y σy (x) } {{ } ( e (z H) σz (x) H σ σz(x ) z(x )) dx y σy (x) ) + e (z+h) σz (x) } {{ } 3 ] v du π Ground deposition B r (x, y) =Q r (v d DF(x) χ(x, y, ) + W (x))e λ r t Dose conversion factors: submersion gw,r, inhalation gh,r, deposition gb,r submersion dose inhalation dose deposition dose External dose H wr (x, y, z) =Q r χ(x, y, z)g wr H hr (x, y, ) = Q r χ(x, y, z)g hr H br (x, y, ) = Q r (χ(x, y, )v d DF(x)+W (x))b g br K br H tot (x, y, z) =H wr (x, y, z)+h br (x, y, )

4 Dose conversion factors (Zähringer-Sempau BfS-IAR-/97) submersion gw,r (Gy s / Bq m 3 ) TABLE A.3, deposition gb,r (Gy s / Bq m ) TABLE A. Tc-99m Xe-33 Te-3 I-3 Cs-37 SZ Cloud Emitted photon energy (kev) DCF deposition log((gy m )/(Bq s)) Te-3 Tc-99m I-3 Cs-37 6 ZS DRY ZS WET Emitted photon energy (kev) Source homogeneously distributed in the air Source exponentially distributed in the soil with relaxation mass per unit area β DRY =. g/cm WET = g/cm

5 CODE: OPTLMDOSE.f9 MAIN PROGRAM SUBROUTINE FCN.f9 calculates objective function as log(dosedata) - log(dose) SUBROUTINE LMDIF from MINPACK runs optimisation SUBROUTINE COVAR calculates covariance matrix for error estimation cartesian axis: wind direction is x-axis INPUT data namelist: &global_para rnuclide='tc-99m' wind_ref=3.3d theta=.d stability_class = 'A' H=.5d vd=.d h_ref=.d dep_model= DRY I_rain =.d eq_model= EXPONENTIALX xdata=.d Dt_plot=6.d Qr = 5.8D8/ filename_read: x (km), y(km), Dose(Sv), Surface activity (kbq/m ), Dt(s) Radionuclide implemented are: Cs-37, I-3, Xe-33, Te-3, Tc-99m OUTPUT data filename_save: info M 3 N opt_value NORM.6464 unbiased sigmax other output files to produce plots

6 CODE: LEVENBERG-MARQUARDT ALGORITHM in MINPACK F = log(dosedata)-log(dose) If xsol is a solution of a non-linear least square problem then x solves: and orthogonality condition is valid F (x sol ) T F (x sol ) = The algorithm looks for a correction p such that F(x+p) F(x) To find appropriate p, the algorithm solves the problem: min{ f=j p : D p Δ} where D is diagonal scaling matrix and Δ is a step bound m i= f i (x) f i (x) = LMDIF runs various convergency tests between approximation x and the solution xsol INFO : if the final norm of the residual has K significant decimal digits compared to initial one (the assumed tolerance -K is set to square root of machine precision) INFO : the larger components of (D x) have K significant digits compared to initial ones INFO 3: if both and are fulfilled INFO 4: if the norm of the residuals is orthogonal to the Jacobian matrix.this should be examined further: could be F(x)=, some local minimum and accuracy is not implicit

7 Test data from HOTSPOT Surface Activity 5 8 y (m) Total Dose 5 e y (m) e 9 5 e

8 Test data from HOTSPOT - In principle with identical input values and initial guess, initial value for surface activity and dose should be the same as test data. BUT there is a difference of about 4-5% between the two DEPLETION FACTOR x [m] - HOTSPOT CODE and OP_LM_BfS almost identical: the only difference is integration for Depletion factor! - In OPT_LM_BfS GAUSS integration is used to increase the number of steps during integration. HOSPOT uses trapezoidal rule but no possibility to check it

9 Test data from HOTSPOT: result info M 3 N opt_value NORM.6464 unbiased sigmax (sigmax divided by M-N) convergence achieved after 9 iterations 7.5 Exp Dose INI Dose OPT Dose 8 Dose log(sv) x log(m)

10 Test data from HOTSPOT: cloudshine and groundshine Dose cloudshine Dose groundshine 5 e 5 y (m) e 9 y (m) e e Groundshine/Cloudshine

11 Test data from HOTSPOT: results.5. RESIDUAL PLOT OPT RESIDUAL INI RESIDUAL During optimisation, the residuals decrease and mean value goes to zero (.7 - ) The norm of the residual decreases from.6 to.6 (y exp y model ) There is a clear trend in the residual plot - residual is not random! Uncertainty on source term decreases with increasing the number of points Small uncertainty in the result of the fit has to be expected as by fixing the meteorological data the shape of the curve is fixed Optimised source term x points 5 points points 7 points 3 points points point Number of experimental points

12 Experimental data from Prouza et al. TEST : measurements of surface activity &global_para rnuclide='tc-99m' wind_ref=.d theta=.d stability_class ='B' H= 5.d vd=. h_ref=.d I_rain =.d Dt=45.d Qr = 9.D4/ - large uncertainty on deposition velocity vd - Initial source term (measured) is 9 MBq - Along x-direction, experimental profile of the plume is NOT an exponential - --> slow wind and clear Gaussian profile suggest diffusive process also in X direction: possibility for users to choose! - No source partitioning is included - objective function which is minimised is log(bdata+) - log(br+) 8 6 Experiment Gauss fit Surface activity (Bq/m ) diffusivex ( ) ( ) ( ) x x / ó x x = e Fitted Gaussian profile x=5 m, σx=

13 Experimental data from Prouza et al. TEST : results info M N opt_value unbiased sigmax Result strongly depends on deposition velocity for v_d =.8 m/s result is not physical anymore? CONTOUR PLOT log (B r +) INI CONTOUR PLOT log (B +) INI r CONTOUR PLOT log (B +) OPT r Optimised source term log(bq) 9 v d =.5 m/s.5 m/s. m/s.7 m/s 8.8 m/s. m/s.5 m/s. m/s.8 m/s Deposition velocity log(m/s)

14 Experimental data from Prouza et al. TEST EXPERIMENTAL INITIAL OPTIMAL INITIAL FINAL Surface activity log (B r + ) Surface activity log (B r + ) RESIDUAL y (m) The norm of the residual decreases from 4 to The residual clearly follows a trend and is not random but around zero The standard deviation is very small...again by fixing meteorological data the form of the curve underlying the fit is fixed!