Refraction of a Gaussian random sea waves by random ocean currents creates persistent local variations (in the form of lumps or streaks) in average energy and wave action distributions. Multiple high-intensity wave energy hot-spots emerge, and the propagation of waves is reminiscent of lightning branches. Following geometric optics, we use the linearized equations for deep ocean waves and the method of characteristics, to obtain quantitative predictions for the increased probability of very high wave formation when both the refractive effects and wave spectral width are taken into account. Both the wave height and wavenumber distributions are then demonstrated to primarily depend on the strength of refraction relative to the angular spread of the incoming homogeneous random sea. Dramatic effects are obtained in the tail of these distributions even for the modest values that are expected to occur commonly in nature. The stochastic calculation facilitates taking into account the multi-scale character of the currents and eventually, the prior generation of data assimilation algorithms. On a large spatiotemporal scale, the oceanic currents are known because measured by satellite. At intermediate scales, we developed a new stochastic closure: a non-Markovian, multi-scale and low-CPU version relevant for wave refraction simulations. From a given oceanic currents spatial spectrum (typically the Fourier transform of a Matérn covariance), we can define, for each wave vector k, a characteristic time τ(k). Then, we build an Ornstein-Uhlenbeck Gaussian process (v^' ) ̂ with that correlation time, from the spatial Fourier transform of a cylindrical Wiener process B_t. d(v^' ) ̂(k,t)=-1/τ(k) (v^' ) ̂(k,t)dt+ik×f(k) ‖k‖^(-α) d(B_t ) ̂(k) Finally, from an inverse transform, we obtain a random velocity field, (v^' ) ̂, multi-scale in space and time, for our wave-turbulence interaction simulations. From self-similarity assumptions, we estimate amplitude and regularity parameter α by extension of the known spectrum at intermediate scales. For smaller scales, Markovian approaches -- e.g., LU & SALT [2,1,3,4] -- applied in the wave frame. Under certain assumptions, we found an analytical formula for the probability distribution of wave properties (wave vector, frequency and amplitude) at long time. References: Holm, D. D. (2015). Variational principles for stochastic fluid dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2176), 20140963. Mémin, E. (2014). Fluid flow dynamics under location uncertainty. Geophysical & Astrophysical Fluid Dynamics, 108(2), 119-146. Resseguier, V., Li, L., Jouan, G., Dérian, P., Mémin, E., & Chapron, B. (2021). New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics. Archives of Computational Methods in Engineering, 28(1), 215-261. Resseguier, V., Hascoët, E., & Chapron, B. (2023). Random ocean swell-rays: a stochastic framework. In Stochastic Transport in Upper Ocean Dynamics Annual Workshop (pp. 259-271). Springer, Cham.