Effect of Trends on Detrended Fluctuation Analysis of Precipitation Series

Figure 4

DFA of the series with correlated trend $A{[X(i)]}^p,$ that is, $Y(i)=X(i)+\mathrm{\hspace{0.17em}\hspace{0.17em}}A{[X(i)]}^p,$ where $A=1$, (a) $p=1.8$. (b) $p=1.9$. (c) $p=2.8$. (d) $p=2.9$. (e) $p=3.8$. (f) $p=3.9$. (a)$\to$(b) is the process that crossover $s_{1x}^{(1)}$ changes from $84(<100)$ to $106(>100)$. (c)$\to$(d) is the “vanishing’’ process of $s_{1x}^{(1)}$ and $s_{1x}^{(2)}$ while (e)$\to$(f) is the “vanishing’’ process of $s_{1x}^{(n)},$$n=\mathrm{3,4},5$. Some typical crossovers are tagged by arrows.

(a)

(b)

(c)

(d)

(e)

(f)