common derivations
- time dependent from time independent variable: \[\forall t: x(t,:) = x(:)\]
- total uncertainty from random and systematic uncertainty: - symbol - description - unit - variable name - \(\mu_{x}\) - total uncertainty for a variable x - same as that of \(x\) - <variable>_uncertainty {:} - \(\mu^{r}_{x}\) - uncertainty due to random effects for a variable x - same as that of \(x\) - <variable>_uncertainty_random {:} - \(\mu^{s}_{x}\) - uncertainty due to systematic effects for a variable x - same as that of \(x\) - <variable>_uncertainty_systematic {:} - The pattern : for the first dimensions can represent any combination of dimensions for which x {:} exists. \[\mu_{x} = \sqrt{{\mu^{r}_{x}}^2 + {\mu^{s}_{x}}^2}\]
- total uncertainty from vertical covariance: - symbol - description - unit - variable name - \(S_{x}(i,j)\) - covariance for a variable x - square of that of \(x\) - <variable>_covariance {:,vertical,vertical} - \(\mu_{x}(i)\) - total uncertainty for a variable x - same as that of \(x\) - <variable>_uncertainty {:,vertical} - The pattern : for the dimensions can represent any combination of dimensions for which x {:,vertical} exists. \[\forall i: \mu_{x}(i) = \sqrt{S(i,i)}\]