Dispersion modelling and 1st-guess source term uncertainties
F i n a l V e r s i o n
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Deliverable number: D4.17
Innovative integrated tools and platforms for radiological emergency preparedness and post-accident response in Europe
Euratom for Nuclear Research and Training Activities: Fission 2013: 323287
PREPARE(WP4)-(14)-05
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Dispersion modelling and 1st-guess source term uncertainties PREPARE(WP4)- (14)-05 Ivan Kovalets Ukrainian Centre for Environmental and Water Projects Prospekt Glushkova Bldg 42 HSE Email:
[email protected] Radek Hofman, Petra Seibert Department of Meteorology and Geophysics, University of Vienna Althanstr. 14, 1090 Vienna, Austria Email:
[email protected],
[email protected] Spyros Andronopoulos National Centre for Scientific Research “Demokritos” Aghia Paraskevi, Attiki, Greece 15310 Email:
[email protected] Final, October 2014
Date released
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Management Summary In this report we review the methodologies that can be used to address the following issues in the frame of an inverse-modelling methodology for calculating the unknown accidental emissions of radionuclides: 1. Estimation of uncertainties in the dispersion model’s calculations 2. Estimation of uncertainties in the 1st-guess estimate of the source term (nuclides emissions rates) The content of this report is based on the existing literature, on the previously released report PREPARE(WP4)-(14)-01 and on the teleconference of 27/03/2014 (minutes PREPARE(WP4)-MN(14)-01).
Project co-funded by the European Commission within the seventh Framework Programme (2007-2011) PU PP RE CO
Dissemination Level Public Restricted to other programme participants (including the Commission Services) Restricted to a group specified by the consortium (including the Commission Services) Confidential, only for members of the consortium (including the Commission Services)
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Contents Management Summary
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Contents
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Introduction First guess source term uncertainty 2.1 Analysis of ratios between the released inventories of different nuclides using the emission scenarios estimated for VVER1000 reactors in Ukraine 2.2 Covariances in the source-term uncertainty
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Methods for error covariance determination 3.1 Model error proportional to observed values 3.2 Simple approximations and parameterized covariance models 3.3 Ensemble approach 3.3.1 Simple example of receptor variation technique 3.3.2 Small-ensemble-related issues
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Discussion 4.1 First-guess source term uncertainty 4.2 Observation error covariance matrix 4.2.1 Measurement component 4.2.2 Model component
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References
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Document History
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1 Introduction Successful application of any advanced inverse modelling method requires correct quantification of error statistics involved in the problem studied. Specifically, in the frame of inverse modelling methodologies that are used for the calculation of an unknown emission of nuclides (see the report PREPARE(WP4)-(14)-01, Kovalets et al., 2014a), important role play the uncertainties in the following quantities: 1. observations (this includes also model error, see below), and 2. a priori (first guess) estimate of unknown parameters (nuclide emission rates etc.). These uncertainties have to be quantified, i.e. we have to determine their probability density distributions along with corresponding statistics fully describing these distributions, e.g. mean value and variance of a normal distribution. This report reviews different possibilities how to treat observation error and first-guess error in the problem of source term estimation in the case of a release of radionuclides from a nuclear facility. We treat the problem as a minimization problem, where the optimal source term x€ is found as
x€ = argmin J (x) where T
T
J (x ) = (y − Mx ) R −1(y − Mx ) + (x − x a ) B −1(x − x a ) = J1 + J 2 .
(1)
Here, y are concentration, deposition or gamma-dose-rate measurements, x a is a first guess estimate and M is a source-receptor sensitivity produced by an atmospheric dispersion model. Observation and first guess errors enter the problem via error covariance matrices R and B, respectively. Inverse modeling methods are based on systematic comparison of measured data with those simulated using a model (the first term on r.h.s of Eq. 1). This means that we cannot rely on the measurement error itself but we have to take into account also errors of the simulation model. The observation error R thus can be decomposed as follows: R = Pmeas + Pmod
(2)
where •
the measurement error Pmeas quantifies the observation error caused by systematic and random errors related to the process of taking the measurement (instrumental error, human factors, random nature of radioactivity etc.), while
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the model error Pmod stems from the fact that our model is imperfect and quantifies the deviation between observed and modelled value for the hypothetical case of perfect knowledge of the source. It includes all relevant sources of errors, such as meteorological impact, parameterizations, numerical discretization and approximations, and the limited representativity of a model working on a given scale or resolution.
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There are different approaches how to treat the observational error. We can describe R as a whole or Pmeas and Pmod separately. Usually, matrices R and B are assumed to be diagonal, i.e., errors are assumed to be uncorrelated. Although this assumption may not be valid, it is widely used because, as Stohl et al. (2012) justify, (a) it simplifies the problem’s solution, (b) error statistics are unknown anyway, and (c) reasonable results can be obtained adopting this assumption. In addition, to cope with the problem of inverse estimation of multiple-nuclides source terms when only gamma dose rate measurements are available, a priori inequality constraints on the ratios of nuclides release rates are applied, of the form
1 x1 (t ) ≤ ≤ ai bi xi (t ) (Kovalets et al., 2014b). The lower and upper limits can be estimated using core inventory analyses and the measurements of activity concentrations and deposition.
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2 First guess source termuncertainty As discussed in Kovalets et al. (2014a,b), the most feasible way of dealing with the issue of unknown nuclide composition when only gamma dose rate measurements are available for source inversion is using prescribed ranges of ratios between the released different nuclides (‘nuclide ratios’) as it was proposed and tested by Saunier et al. (2013). In the simplest case, the same nuclide ratios as in first guess estimations could be assumed. Even though the limits for possible values of nuclide ratios could be established by the user, in case of an operational system some default values should also be made available. This is detailed in the following for certain VVER scenarios. 2.1 Analysis of ratios between the released inventories of different nuclides using the emission scenarios estimated for VVER1000 reactors in Ukraine One possibility to evaluate the range of nuclide ratios to be used in source inversion procedure is to analyze available source term assessments produced by experts in nuclear engineering and nuclear safety analysis. In the present analysis we used the recent source term estimates obtained by the nuclear safety experts for the VVER1000 reactors at Rivne and Zaporizhje NPPs in Ukraine (Energoatom, 2012a,b). In that study the following 7 accident scenarios were analyzed: •
(RNPP1) Full loss of electric power supply together with loss of coolant for Block 3 of Rivne NPP;
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(RNPP2) Full loss of electric power supply together with loss of coolant for Block 4 of Rivne NPP;
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(RNPP3) Same as RNPP1(2) but with taking into account actions on reducing hydrogen concentration;
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(RNPP4) Same as RNPP1(2) but with taking into account reducing pressure in containment;
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(ZNPP1) Full loss of electric power supply together with loss of coolant for Block 1 of Zaporizhje NPP;
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(ZNPP2) Same as ZNPP1 but with taking into account actions on reducing hydrogen concentration;
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(ZNPP3) Same as ZNPP1 but with taking into account reducing pressure in containment.
As we see the considered scenarios were quite similar and related to the same type of reactor (VVER1000) and to the same basic accident (full loss of electric power supply together with loss of coolant). The scenarios differed only by the specific nuclear block which was analyzed and by actions of personnel. In a real-world accident one could expect to have some information about the accident which most probably would be also incomplete. Therefore it is likely that the ranges for the nuclide ratios obtained from similar but slightly different scenarios could be used for source inversion in case of accident at VVER1000 reactor. Similar studies could be performed in future also for other types of reactors to provide RODOS user with information regarding possible ranges for nuclide ratios.
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The information provided in Energoatom (2012a,b) for the above mentioned scenarios was given in graphical form as time plots of total released activity. The released activity was given for different groups of nuclides. The correspondence between nuclide groups used in Energoatom (2012a, b) and those used in JRODOS was established, time plots were digitized manually and processed by JRODOS to produce time dependencies of release rates for different JRODOS nuclide groups (Fig. 1-7). The nuclides corresponding to different JRODOS nuclide groups are presented in Table 1. The minimum and maximum values of the time averaged nuclide ratios as well as the hourly nuclide ratios analyzed for the whole release period are presented in Table 2 (first 2 rows). It is natural that the ranges of the time averaged nuclide ratios are much narrower than the ranges for the hourly nuclide ratios. As it can be seen from the Figures 1-7, some characteristic release subintervals could be identified. The most typical subinterval which exist in all the presented scenarios is a first few hours of the release when release rate of noble gases highly dominates over the release rates of the other nuclides. Therefore it is natural to try to subdivide the whole release period onto a few sub-periods (as it is done in Table 3) during which the hourly nuclide ratios are expected to be less variable as compared to their variation during the whole release interval. The minimum and maximum values for the nuclide ratios corresponding to subintervals identified in Table 3 are presented in Table 2 (the last three rows). Indeed as it is seen from the values presented in Table 2 significant reduction in range of hourly nuclide ratio is achieved for the subinterval 1 when release of noble gases dominates. It could be of some interest to compare the ranges of nuclide ratios obtained in present study with the values used by Saunier et al. (2013). Even though the paper of Saunier et al., (2013) was devoted to Fukushima accident in which BWR reactors where involved while the present study deals with VVER1000 reactors, the range of uncertainties in nuclide ratios could be comparable in both studies. Indeed Saunier et al. (2013) reports the following ranges of the nuclide ratios:
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