as well as at an essentially zero noise level (1 × 10 from a recent study with best-case and worst-case scenarios for high quality gradient retention measurements . Fits of the above-described simulated gradient data were carried out using both the original parameterization of the NK model and the re-parameterization at ref = 0.3. Initial guesses for S1,ref and S2,ref for the gradient fits using the re-parameterized model were obtained from average values of these parameters for a smaller dataset described previously , see Trials 1-3, lines 3 and 4). Initial guesses for the S1 and S2 parameters for fitting the original NK model were obtained using the these values and the conversion formulas given in Eqs. (7-8) (see Trials 4-6, lines 3 and 4). The initial guesses for k0.3 were determined using the correlation given by Eq. ( ). A similar correlation was obtained for the initial guesses for kw as shown in Eq. ( ) (see row 5 in Table ).