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Mountain regions are highly sensitive to global climate change. However, large scale assessments of mountain environments remain problematic due to the high resolution required of model grids to capture strong lateral variability. To alleviate this, tools are required to bridge the scale gap between gridded climate datasets (climate models and re-analyses) and mountain topography. We address this problem with a sub-grid method. It relies on sampling the most important aspects of land surface heterogeneity through a lumped scheme, allowing for the application of numerical land surface models (LSMs) over large areas in mountain regions or other heterogeneous environments. This is achieved by including the effect of mountain topography on these processes at the sub-grid scale using a multidimensional informed sampling procedure together with a 1-D lumped model that can be driven by gridded climate datasets. This paper provides a description of this sub-grid scheme, TopoSUB, and assesses its performance against a distributed model. We demonstrate the ability of TopoSUB to approximate results simulated by a distributed numerical LSM at around 10<sup>4</sup> less computations. These significant gains in computing resources allow for: (1) numerical modelling of processes at fine grid resolutions over large areas; (2) efficient statistical descriptions of sub-grid behaviour; (3) a "sub-grid aware" aggregation of simulated variables to coarse grids; and (4) freeing of resources for computationally intensive tasks, e.g., the treatment of uncertainty in the modelling process

TopoSUB: a tool for efficient large area numerical modelling in complex topography at sub-grid scales