Convectively coupled tropical waves (CCTWs) have been shown to significantly modulate rainfall in northern Australia during the Austral summer (December-February; DJF). However, the impact of these waves under varying summer conditions remains unclear. To investigate the influences of these waves in varying background conditions, we divide the period from 1981 to 2020 into years of dry and wet DJF based on the frequency of heavy rain in each season (mean ± 0.5SD). Stronger monsoons, more evaporation, and less frequent El Niño are observed in wetter DJF than in drier DJF. The results show that Madden-Julian Oscillation (MJO) and Equatorial Rossby waves (ER) make a higher contribution to the heavy rain days in drier DJF (i.e., 70% and 58% of the days), compared to the wetter DJF. A higher probability increase in heavy rain is observed during the drier DJF, with amplified (suppressed) impact when wet-wet (wet-dry) wave pair occurs concurrently.