  In this work, we develop a Legendre spectral element method (LSEM) for
solving the stochastic nonlinear system of advection-reaction-diffusion models.
The used basis functions are based on a class of Legendre functions such that
their mass and diffuse matrices are tridiagonal and diagonal, respectively. The
temporal variable is discretized by a Crank--Nicolson finite difference
formulation. In the stochastic direction, we also employ a random variable $W$
based on the $Q-$Wiener process. We inspect the rate of convergence and the
unconditional stability for the achieved semi-discrete formulation. Then, the
Legendre spectral element technique is used to obtain a full-discrete scheme.
The error estimation of the proposed numerical scheme is substantiated based
upon the energy method. The numerical results confirm the theoretical analysis.
