In this paper, we investigate a nonlinear system, which describes the marginally unstable baroclinic wave packets in the geophysical fluid. Based on the symbolic computation and Hirota method, bright one- and two-soliton solutions for such a system are derived. Propagation and collisions of the solitons are graphically shown and discussed with beta, which reflects the collision between the wave packet and mean flow, a, which measures the state of the basic flow, and group velocity gamma. gamma is observed to affect the amplitudes of the solitons, and alpha can influence the solitons traveling directions. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions are derived. Properties of the first- and second-order rogue waves are graphically presented and analyzed: The first-order rogue waves are shown in the figures. alpha has no effects on A, which is the amplitude of the wave packet, but with the increase of alpha, amplitude of B, which is a quantity measuring the correction of the basic flow, decreases. When beta is chosen differently, A and B do not keep their shapes invariant. With the value of alpha increasing, amplitudes of A and B become larger. The second-order rogue wave is presented, from which we observe that with alpha increasing, amplitude of B decreases, but a has no effects on A. Collision features of A and B alter with the value of beta changing. When we make the value of gamma larger, amplitudes of A and B increase.