  We study several $3\times 3$ systems of conservation laws, arising in
modeling of two phase flow with rough porous media and traffic flow with rough
road condition. These systems share several features. The systems are of mixed
type, with various degeneracies. Some families are linearly degenerate, while
others are not genuinely nonlinear. Furthermore, along certain curves in the
domain the eigenvalues and eigenvectors of different families coincide. Most
interestingly, in some suitable Lagrangian coordinate the systems are partially
decoupled, where some unknowns can be solved independently of the others.
Finally, in special cases the systems reduce to some $2\times2$ models, which
have been studied in the literature. Utilizing the insights gained from these
features, we construct global Riemann solvers for all these models. Possible
treatments on the Cauchy problems are also discussed.
