Time-domain simulations of wind instruments can, in principle, deal with non-linear oscillations and are also capable of modeling both the steady-state and the transient behavior of a system. The starting transient is usually an important identifying feature of the instrument that is played. Subtle control of articulation is required from skilled musicians to modulate transients during expressive performance. Focusing on single-reed woodwind instruments, the physical phenomena that underlie different articulation techniques are analyzed. A saxophone player is recorded during portato playing, where articulation is achieved either by the use of the tongue, or by modulating the air flow into the mouthpiece. The bending of the reed and the pressure inside the mouthpiece are measured and a physical model is formulated with the aim to capture the transient effects. Instead of adding new terms (and complexity) to a single mass-spring model, in order to simulate the player's tongue, existing physically meaningful parameters are allowed to vary. In particular, the effect of tonguing is modeled by modulating the equilibrium position of the (lumped) reed and its internal damping, whereas in the case of air-separated tones, only a variation of the blowing pressure is required.