The Polar UV Imager (UVI) is useful both for determining substorm onset times with precision on the order of 1 min and for making quantitative estimates of global power associated with auroral precipitation. Combining these capabilities, we studied 390 substorms, not necessarily isolated, using the superposed epoch analysis technique. The results quantify the phenomenology of auroral power during substorms. Precipitating auroral power rises with three distinct timescales based on distance from the average onset position. The most dramatic results are seen in the location of the auroral bulge, 2100-0000 magnetic local time (MLT). Integrated over this premidnight sector, auroral power decreases by ~10% in the few minutes before onset. After onset, premidnight auroral power increases by a factor of 3.4 during the first 9 min. The largest increase occurs within 3 min after onset. After peaking at an average of ~9 GW, premidnight auroral power declines at a steady 0.045 GW min-1 over ~100 min. Less dramatic increases with longer risetimes are seen elsewhere on the nightside. Outside the LT of the bulge origin, but close enough that the bulge is likely to eventually reach it, the delay from onset to peak auroral power is ~15--18 min. and the increase is typically in the range of a factor of 2 or 3. Finally, several hours away from the bulge, auroral power increases by less than a factor of 2, with a time delay of ~36--45 min. Predawn, this represents the travel time of hot eastward drifting electrons in the diffuse aurora. Postdusk (1800--2100 MLT), a fairly weak (between 1.5 and 2.0 fold) increase is seen for unclear reasons. Altogether, a substorm averages 59% greater auroral power dissipation over the entire nightside in the 120 min following onset than in the preceding 120 min (152 and 96 TJ, respectively). By contrast, dayside auroral power is virtually invariant during substorms. Uncertainty in defining onset time using Polar UVI images was less than the 3-min bin period adopted. Auroral onset is thus demonstrated to be well specified. ¿ 2001 American Geophysical Union