The problem with the analysis of noise-induced transitions between patterns in distributed stochastic systems is considered. As a key model, we use the spatially extended dynamical "phytoplankton-herbivore" system with diffusion. We perform the parametric bifurcation analysis of this model and determine the Turing instability zone, where non-homogeneous patterns are generated by diffusion. The multistability of this deterministic model with the coexistence of several waveform pattern-attractors is found. We study how noise affects these non-homogeneous patterns and estimate the dispersion of random states using a new technique based on stochastic sensitivity function (SSF) analysis and the confidence domain method. To investigate the preferences in noise-induced transitions between patterns, we analyze and compare the results of this theoretical approach with the statistics extracted from the direct numerical simulation.