Symmetric quadratic tetration interpolation using forward and backward operation combination

The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.

Cubic Spline Interpolation for Data Infections of COVID-19 Pandemic in Iraq

In this paper, we use an empirical equation and cubic spline interpolation to fit Covid-19 data available for accumulated infections and deaths in Iraq. For Scientific visualization of data interpretation, it is useful to use interpolation methods for purposes fitting by data interpolation. The data used is from 3 January 2020 to 21 January 2021 in order to obtain graphs to analysing the rate of increasing the pandemic and then obtain predicted values for the data infections and deaths in that period of time. Stochastic fit to the data of daily infections and deaths of Covid-19 is also discussed and showed in figures. The results of the cubic splines and the empirical equation used will be numerically compared. The principle of least square errors will be used for both these interpolations. The numerical results will be indicated that the cubic spline gives an accurate fitting to data.

A Scheme for Estimating Time-Varying Wind Stress Drag Coefficient in the Ekman Model with Adjoint Assimilation

In this study, the time-varying wind stress drag coefficient in the Ekman model was inverted by the cubic spline interpolation scheme based on the adjoint method. Twin experiments were carried out to investigate the influences of several factors on inversion results, and the conclusions were (1) the inverted distributions with the cubic spline interpolation scheme were in good agreement with the prescribed distributions of the wind stress drag coefficients, and the cubic spline interpolation scheme was superior to direct inversion by the model scheme and Cressman interpolation scheme; (2) the cubic spline interpolation scheme was more advantageous than the Cressman interpolation scheme even if there is moderate noise in the observations. The cubic spline interpolation scheme was further validated in practical experiments where Ekman currents and wind speed derived from mooring data of ocean station Papa were assimilated. The results demonstrated that the variation of the time-varying wind stress drag coefficient with time was similar to that of wind speed with time, and a more accurate inversion result could be obtained by the cubic spline interpolation scheme employing appropriate independent points. Overall, this study provides a potential way for efficient estimation of time-varying wind stress drag coefficient.