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
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 fourth-order
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
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