A numerical model of the neutron noise field in boiling water reactors (BWRs), which can be readily implemented in existing deterministic computer codes, was formulated. The basis of the model is the assumption of separability of the noise field into local and global components. The application of this modeling was twofold: to determine the frequency range above which cross-correlation techniques can be used to measure steam velocities under normal operating conditions and to evaluate the validity of the point kinetics description of the global component of the neutron noise in BWRs. The model was implemented in the code LAPUR-3 and applied to the Hatch-1 BWR nuclear plant. Comparison with experimental results shows good agreement for frequencies above 6 Hz. At lower frequencies the global noise is overestimated, making apparent the limitation of the point kinetics formulation of the global noise component for this large reactor.