Abstract: The atmosphere can have very sensitive behaviors when two vortices interact in a deformation background flow. This phenomenon is called wave-merger or trough-merger in mid-latitudes; in the tropics, a manifestation of this process is binary tropical cyclones and can also include the extratropical transitions. A linear method is applied to study the wave-merger problem in a confluent background flow when the distance between the vortices is large enough. The behavior of the system is sensitive to the initial position error of the vortices along the direction of the confluent flow. A nonlinear deterministic dynamical system is built for this phenomenon when the interaction between the two vortices can not be neglected. The background flow is confluent (or diffluent), and/or the shear is positive (or negative). The most sensitive region of this phenomenon in parameter space is found analytically. When the initial condition of the system is close to the most sensitive region, a very small difference in initial state can make the system evolve along completely different paths. This sensitivity is identified with the initial distance of the two centers, the initial azimuth, the strength of the background flow, and the sum of the strength of the two vorticity centers. Numerical simulations support the theoretical findings very well. This theory can explain several well-known observational facts. An observational verification, taking the advantage of 21 published wave-merger cases, shows that when the initial conditions are close to the most sensitive region the operational numerical model has a greater chance of a poor prediction as expected from the theory. Based on the characteristics of this problem, a modified ensemble forecast is proposed. In this ensemble, two criteria were used to divide all ensemble members into a relatively 'good' group and a relatively 'bad' group. By using the members in the 'good' group, the ensemble forecast is improved. Finally, the sensitivity structure of the atmosphere on the earth with implications for forecasting is discussed.