With the aid of a global barotropic model, the role of the interaction of the synoptic-scale disturbance and the planetary flow in block onset is examined by a 4-dimensional variational approach. A cost function is defined to measure the squared errors of the forecasted stream functions during block onset period (day 4 and day 5 in this study) over a selected blocking domain. The sensitivity of block onset with respect to the initial synoptic-scale disturbance is studied by examining the gradient of the defined cost function with respect to the initial (during the first 24 hours) vorticity forcing, which is evaluated by the adjoint integration. Furthermore, the calculated cost function and gradient are connected with the limited-memory quasi-Newton optimization algorithm for solving the optimal initial vorticity forcing for block onset. For two studied cases of block onset (northern Atlantic and northern Pacific) introducing the optimal initial vorticity forcing, the nonlinear barotropic advection process mostly reconstructs these blocking onset processes. The results show that the formation of blocking can be correctly described by a barotropic nonlinear advection process, in which the wave- (synoptic-scale) flow (planetary-scale)interaction plays a very important role. On an appropriate planetary-scale flow, a certain synoptic-scale disturbance can cause the blocking onset by the interaction between the synoptic scale perturbations and the planetary scale basic flows. The extended forecasts show that the introduction of the optimal initial vorticity forcing can predict the blocking process up to the 7th or 8th day in this simple model case. The experimental results in this study show that the 4-dimensional variational approach has a good potential to be applied to study the dynamics of the medium-range weather processes. This simple model case study is only an initial trial. Applying the framework in this study to a complex model will further our understanding of the mechanism of the atmospheric/oceanic processes and improve their prediction.