<p>The widespread negative correlation between the atmospheric vapor pressure deficit and soil moisture lends strong support to the complementary relationship (CR) of evapotranspiration. While it has showed outstanding performance in predicting actual evapotranspiration (ET_a) over land surfaces, the calibration-free CR formulation has not been tested in the Australian continent dominantly under (semi-)arid climates. In this work, we comparatively evaluated its predictive performance with seven physical, machine-learning, and land surface models for the continent at a 0.5°&thinsp;&times;&thinsp;0.5° grid resolution. Results showed that the calibration-free CR that forces a single parameter to everywhere produced considerable biases when comparing to water-balance ET_a (ET_wb). The CR method was unlikely to outperform the other physical, machine-learning, and land surface models, overrating ET_a in (semi-)humid coastal areas for 2002&ndash;2012 while underestimating in arid inland locations. By calibrating the parameter against water-balance ET_a independent of the simulation period, the CR method became able to outperform the other models in reproducing the spatial variation of the mean annual ET_wb and the interannual variation of the continental means of ET_wb. However, interannual the grid-scale variability and trends were captured unacceptably even after the calibration. The calibrated parameters for the CR method were significantly correlated with the mean net radiation, temperature, and wind speed, implying that (multi-)decadal climatic variability could diversify the optimal parameters for the CR method. The other physical, machine-learning, and land surface models provided a consistent indication with the prior global-scale assessments. We also argued that at least some surface information is necessary for the CR method to describe long-term hydrologic cycles at the grid scale.</p>