Global climate model (GCM) outputs feature systematic biases that render them unsuitable for direct use by impact models, especially for hydrological studies. To deal with this issue, many bias correction techniques have been developed to adjust the modelled variables against observations, focusing mainly on precipitation and temperature. However, most state-of-the-art hydrological models require more forcing variables, in addition to precipitation and temperature, such as radiation, humidity, air pressure, and wind speed. The biases in these additional variables can hinder hydrological simulations, but the effect of the bias of each variable is unexplored. Here we examine the effect of GCM biases on historical runoff simulations for each forcing variable individually, using the JULES land surface model set up at the global scale. Based on the quantified effect, we assess which variables should be included in bias correction procedures. To this end, a partial correction bias assessment experiment is conducted, to test the effect of the biases of six climate variables from a set of three GCMs. The effect of the bias of each climate variable individually is quantified by comparing the changes in simulated runoff that correspond to the bias of each tested variable. A methodology for the classification of the effect of biases in four effect categories (ECs), based on the magnitude and sensitivity of runoff changes, is developed and applied. Our results show that, while globally the largest changes in modelled runoff are caused by precipitation and temperature biases, there are regions where runoff is substantially affected by and/or more sensitive to radiation and humidity. Global maps of bias ECs reveal the regions mostly affected by the bias of each variable. Based on our findings, for global-scale applications, bias correction of radiation and humidity, in addition to that of precipitation and temperature, is advised. Finer spatial-scale information is also provided, to suggest bias correction of variables beyond precipitation and temperature for regional studies.