Long-Term Trends and Its Best Functional Form Estimation of Yearly Maximum and Minimum Temperatures at Cotonou City by Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Method

Abstract

The understanding of the long-term trend in climatic variables is necessary for the climate change impacts studies and for modeling several processes in environmental engineering. However, for climatic variables, long-term trend is usually unknown whether there is a trend component and, if so, the functional form of this trend is also unknown. In this context, a conventional strategy consists to assume randomly the shape of the local trends in the time series. For example, the polynomial forms with random order are arbitrarily chosen as the shape of the trend without any previous justification. This study aims to 1) estimate the real long-term nonlinear trend and the changing rate of the yearly high temperature among the daily minimum (YHTaDMinT) and maximum temperatures (YHTaDMaxT) observed at Cotonou city, 2) find out for these real trend and trend increment, the best polynomial trend model among four trend models (linear, quadratic, third-order and fourthorder polynomial function). For both time series, the results show that YHTaDMinT and YHTaDMaxT time series are characterized by nonlinear and monotonically increasing trend. The trend increments present different phases in their nonmonotone variations. Among the four trend estimations models, the trend obtained by third-order and fourth-order polynomial functions exhibits a close pattern with the real long-term nonlinear trend given by the Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN). But, the fourth-order polynomial function is optimal, therefore, it can be used as the functional form of trend. In the trend increment case, for the YHTaDMaxT time series, the fourth-order fit is systematically the best among the four proposed trend models. Whereas for the YHTaDMinT time series, the third-order and fourth-order polynomial functions present the same performance. They can both be used as the functional form of trend increments. Overall, the fourth-order polynomial function presents a good performance in terms of trend and trend increments estimation.