Currently, about 12ĝ€¯%-13ĝ€¯% of High Mountain Asia's glacier area is debris-covered, which alters its surface mass balance. However, in regional-scale modelling approaches, debris-covered glaciers are typically treated as clean-ice glaciers, leading to a bias when modelling their future evolution. Here, we present a new approach for modelling debris area and thickness evolution, applicable from single glaciers to the global scale. We derive a parameterization and implement it as a module into the Global Glacier Evolution Model (GloGEMflow), a combined mass-balance ice-flow model. The module is initialized with both glacier-specific observations of the debris' spatial distribution and estimates of debris thickness. These data sets account for the fact that debris can either enhance or reduce surface melt depending on thickness. Our model approach also enables representing the spatiotemporal evolution of debris extent and thickness. We calibrate and evaluate the module on a selected subset of glaciers and apply GloGEMflow using different climate scenarios to project the future evolution of all glaciers in High Mountain Asia until 2100. Explicitly accounting for debris cover has only a minor effect on the projected mass loss, which is in line with previous projections. Despite this small effect, we argue that the improved process representation is of added value when aiming at capturing intra-glacier scales, i.e. spatial mass-balance distribution. Depending on the climate scenario, the mean debris-cover fraction is expected to increase, while mean debris thickness is projected to show only minor changes, although large local thickening is expected. To isolate the influence of explicitly accounting for supraglacial debris cover, we re-compute glacier evolution without the debris-cover module. We show that glacier geometry, area, volume, and flow velocity evolve differently, especially at the level of individual glaciers. This highlights the importance of accounting for debris cover and its spatiotemporal evolution when projecting future glacier changes.