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We present an analysis of the variability of broad absorption lines (BALs) ina quasar SDSS J141955.26+522741.1 at $z=2.145$ with 72 observations from theSloan Digital Sky Survey Data Release 16 (SDSS DR16). The strong correlationbetween the equivalent widths of BAL and the continuum luminosity, reveals thatthe variation of BAL trough is dominated by the photoionization. Thephotoionization model predicts that when the time interval $\Delta T$ betweentwo observations is longer than the recombination timescale $t_{\rm rec}$, theBAL variations can be detected. This can be characterized as a "sharp rise" inthe detection rate of BAL variation at $\Delta T=t_{\rm rec}$. For the firsttime, we detect such a "sharp rise" signature in the detection rate of BALvariations. As a result, we propose that the $t_{\rm rec}$ can be obtained fromthe "sharp rise" of the detection rate of BAL variation. It is worth mentioningthat the BAL variations are detected at the time-intervals less than the$t_{\rm rec}$ for half an order of magnitude in two individual troughs. Thisresult indicates that there may be multiple components with different $t_{\rmrec}$ but the same velocity in an individual trough.

A sharp rise in the detection rate of broad absorption line variations in a quasar SDSS J141955.26+522741.1