## 4 Results
### Comparison of New and Previous Approaches  
The new approach of simultaneously and consistently perturbing ND input for depletion and criticality calculations made it possible to calculate \(\sigma_{ND}^{TOTAL}\) directly. Formerly, the total ND-related uncertainty in keff had to be determined indirectly using the independently computed quantities for \(\sigma_{ND}^{CASMO}\) and \(\sigma_{ND}^{MCNP}\), applying Equation (2) for uncertainty propagation. \[\left(\sigma_{ND}^{TOTAL}\right)^{2}=\left(\sigma_{ND}^{MCNP}\right)^{2}+ \left(\sigma_{ND}^{CASMO}\right)^{2}+2r\;\sigma_{ND}^{MCNP}\;\sigma_{ND}^{ CASMO} \tag{2}\]  
Since the correlation between \(\sigma_{ND}^{CASMO}\) and \(\sigma_{ND}^{MCNP}\) was unknown, a conservative correlation coefficient of \(r=1\) had to be assumed, as in a previous study [4]. In this case, the equation above simplifies to:  
\[\sigma_{ND}^{TOTAL}=\sigma_{ND}^{MCNP}+\sigma_{ND}^{CASMO} \tag{3}\]  
Total ND-related uncertainties obtained via Equation (3) are shown in Figure 5a. \(\sigma_{ND}^{TOTAL}\) values are starting with about 800 pcm, steadily increasing with burnup to finally approximately 1030 pcm and 1140 pcm at 0 and 50,000 years of decay, respectively (It shall be noted here that in the course of the present work, a deficiency of the previous ND-UQ study reported in [4] has been discovered. Namely, the neutron multiplicity and spectrum, \(\overline{\
u}\) and \(\chi\) data, have been unintentionally excluded from the random sampling of the ENDF/B-VII.1 ACE files with the NUSS tool in [4]. It is known from other studies, in particular those also performed with NUSS [25, 28, 34, 42], that these parameters significantly contribute to the total keff uncertainties. In fact, the keff uncertainties (at one standard deviation level) for typical LWR UO2 lattices in water have been assessed in works [17, 24, 43] to be reaching values up to ~600-700 pcm, while in [4] the \(\sigma_{ND}^{MCNP}\) value was erroneously estimated as only ~380 pcm. Therefore, the ND uncertainties results reported in [4] shall be considered as noticeably underestimating the \(\sigma_{ND}^{MCNP}\) component). This clear upward trend for  
Figure 5: (**a**) Total ND-UQ based on previous method; (**b**) new consistent ND-UQ. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **CPU-Time** & **Meshes** & **BUs** & **Decay Times** & **Samples** & **Total Time** \\ \hline
**CASMO5** & 30 min & 41 & & & 200 & 170 d \\
**SERPENT2** & 0.2 min & 41 & 5 & & 200 & 6 d \\
**COMPLINK** & 0.15 min & & 5 & 2 & 200 & 5 h \\
**MCNP6** & 17 h & & 5 & 2 & 200 & 1420 d \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Computational expense for each step of the UQ based on BUCSS-R.  
total uncertainties with increasing burnup level is driven by the \(\sigma_{ND}^{CASMO}\) component while \(\sigma_{ND}^{MCNP}\) is slightly decreasing over fuel depletion. In the present study, on the other hand, \(\sigma_{ND}^{TOTAL}\) results obtained with the new consistent ND-UQ reveal a slight downward trend with increasing burn-up, see Figure 5b. Total standard deviation amounts to about 800 pcm for zero burn-up, decreasing to a minimum of about 520 pcm for 0 years of decay and 590 pcm for 50,000 years of decay, at high burn-ups between 62 and 72 GWd/tHM. The new approach, intrinsically respecting correlations of ND-related uncertainties in depletion and criticality calculations, yields hence significantly lower \(\sigma_{ND}^{TOTAL}\) values for high burnups as compared with the previous method. The next subsection provides more details about this correlation aspect of the new ND-UQ. Furthermore, it can be noticed that the results reported in Figure 5b are consistent with the previous results obtained at PSI for depletion of similar UO2 lattices with the CASMO code and applying stochastic sampling-based nuclear data uncertainties propagation with the PSI tool SHARK-X, when using the ENDF/B-VII.1 nuclear data and covariance matrix library [44; 45].