<p>Solution of the extended Sawyer–Eliassen (SE) equation is attempted with improvement to investigate the intensification of Supertyphoon Noru (2022), which incorporates time-dependent forcing sources associated with the gradient-wind imbalance, nonlinear residual in tangential wind tendency equation, and hydrostatic imbalance, all requiring nonlinear output at fast time intervals. The SE solutions show that the transverse circulation and vortex intensification induced by each imbalance are sensitive to the choice of time interval, whereas much less sensitive induced by the nonlinear residual. For both imbalances, short intervals retain fast transient fluctuations and then produce disorganized low-level flow, while longer intervals suppress these fluctuations. During the RI period, each imbalance has much weaker impacts on vertical motions and the induced typhoon intensification as compared to the nonlinear residual. Including the nonlinear residual in the forcing source enlarges the solution departure from the nonlinear simulation for this case, whereas including both imbalances yields the better agreement. The impacts of the nonlinear residual appear to be case dependent from our testing on other cases. Thus, careful consideration is needed when including the nonlinear residual in the forcing source of the extended SE equation.</p>