First passage time statistics of Brownian motion with purely time dependent drift and diffusion

► Brownian motion with an absorbing barrier mimics resources at a critical threshold. ► Its time-dependent coefficients μt and σt2/2 resemble external drivers like climate. ► Associated Fokker-Planck equation is solved via the method of images (MoI). ► MoI is applicable to time-dependent problems only if μt and σt2/2 are proportional. ► The results are used to model water availability in snowmelt dominated regions.