A new methodology is outlined and demonstrated on the improvement of uncertainty and sensitivity analysis based on the random sampling method

Abstract

In several hours of a calm meteorological situation, a relatively significant level of radioactivity may accumulate around the source. When the calm situation expires, a wind-induced convective movement of the air immediately begins. Random realisations of the input atmospheric dispersion model parameters for this CALM scenario are generated using Latin Hypercube Sampling scheme. The resultant complex random radiological trajectories, passing through both calm and convective stages of the release scenario, represent the necessary prerequisite for the prospective uncertainty analysis (UA) and the sensitivity analysis (SA). The novel approximation-based (AB) solution replaces the non-Gaussian sum of individual puffs at the end of the calm period with one Gaussian “super-puff” distribution. This substantially accelerates generation of a sufficiently large number of random realisations for the radiological trajectories, thus facilitating the subsequent UA and SA. Both of these procedures exploit a common mapping between the pairs of calculated output fields on the one hand and the realisation vectors of the associated random input parameters on the other hand. This paper presents the necessary technical background, as well as the idea of the AB solution and its use. Examples of 2-D random trajectories of deposited ¹³⁷Cs are presented in a graphical form. Global sensitivity analysis based on random sampling methods is outlined and improved feasibility o f the originally long-running computation is demonstrated.

Appendix

Demonstration of the “super-puff” concept (AB solution), see Pecha and Kárný (2021).

The CALM scenario ranks among the worst-case episodes of Weather Variability Assessment. Let total inventory $Q_{TOT}^{n}$  = 6.0 E + 07 [Bq] of radionuclide ¹³⁷Cs be discharged into the motionless ambient air during the calm conditions lasting T^CALM = 5 [h], $T^{CALM} = \left( {T_{END}^{CALM} - T_{START}^{CALM} } \right)$ . The release is modelled as a sequence of M instantaneous discrete discharges, the first (oldest puff) for m = 1 at time$T_{START}^{LEAK}$ , the last for m = M at time $T_{END}^{LEAK}$ . The release propagates from the elevated point source of pollution at a height of H (x = 0; y = 0; z = H) over the terrain. The radioactivity progresses during the calm episode time interval $\left\langle {T_{START}^{LEAK} ;\;T_{END}^{CALM} } \right\rangle$. The chain of consecutive discrete puffs $Q_{m}^{n}$ of ¹³⁷Cs, m ∈ {1,…,M}, are ejected stepwise with the time periods Δt_m. The release-source strength $Q_{TOT}^{n}$ /M is initially assumed to be constant within the entire calm episode. After five hours of the calm episode, the wind begins to blow. The convective transport of the radioactivity clew immediately arises. We trace the drifting over the terrain in the next four hours. Meteorological records are extracted from stepwise forecast series for the given point of radioactive release. Hourly meteorological data of the convective transport immediately following the five hour calm episode are shown in Table

Table 1 Convective transport in the subsequent four hours (immediate continuation of the calm episode). Archived meteorological data at point (49° 05′ 00.73″ N, 16° 07′ 26.95″ E) of the Dukovany nuclear power plant: start at Dec 4, 2019, 01.00 CET (time_stamp 2,019,120,401). Rain in the 4th convective hour was chosen deliberately for demonstration purposes

1.

Each puff reflects a partial discharge of the radioactivity $Q_{m}^{n}$, m ∈ {1,…,M}, which dissipates into the motionless ambient atmosphere just until to the calm-period termination. The results of current realistic calm scenario in STAGE I (related to $T_{END}^{CALM}$) are displayed in Fig. 

Fig. 9

Distribution of ¹³⁷Cs concentration in air for separate puffs m having its own age. Red line: procedures of handling the further convective superposition of all puffs m; m ∈ {1,…,M}

9. Radioactivity concentrations of ¹³⁷Cs in air (in the height H) for each individual puff m are shown here. The sharpest shape for the “youngest” puff m = 99, the flattened shape for the “oldest” m = 30, has been expected. The red curve shows, clearly non-Gaussian, shape of the puffs’ superposition.

The radiological results transformed into radioactivity concentration values of ¹³⁷Cs deposited on the ground at the end of the STAGE II (just after 9 h from the same beginning of the CALM start) are shown in Fig. 

Fig. 10

Comparison of two alternative procedures of handling the further convective transport

10. It represents the peripheral distribution (around the angular beam of the computational grid containing maximum values of deposited radioactivity) on the concentric circle c^* (~ 25 [km] around the release point (of the computational grid). The results confirm a good agreement of both compared solutions in the domains of interest (with potential high values of harmful effect on the population). Several variants have been successfully tested including nonlinear releasing, serrated form, the dependency of AB approximation on the number of puffs M, etc.