Chalk aquifers are an important source of drinking water in the UK. Due to their properties, they are particularly vulnerable to groundwater-related hazards like floods and droughts. Understanding and predicting groundwater levels is therefore important for effective and safe water management. Chalk is known for its high porosity and, due to its dissolvability, exposed to karstification and strong subsurface heterogeneity. To cope with the karstic heterogeneity and limited data availability, specialised modelling approaches are required that balance model complexity and data availability. In this study, we present a novel approach to evaluate simulated groundwater level frequencies derived from a semi-distributed karst model that represents subsurface heterogeneity by distribution functions. Simulated groundwater storages are transferred into groundwater levels using evidence from different observations wells. Using a percentile approach we can assess the number of days exceeding or falling below selected groundwater level percentiles. Firstly, we evaluate the performance of the model when simulating groundwater level time series using a spilt sample test and parameter identifiability analysis. Secondly, we apply a split sample test to the simulated groundwater level percentiles to explore the performance in predicting groundwater level exceedances. We show that the model provides robust simulations of discharge and groundwater levels at three observation wells at a test site in a chalk-dominated catchment in south-western England. The second split sample test also indicates that the percentile approach is able to reliably predict groundwater level exceedances across all considered timescales up to their 75th percentile. However, when looking at the 90th percentile, it only provides acceptable predictions for long time periods and it fails when the 95th percentile of groundwater exceedance levels is considered. By modifying the historic forcings of our model according to expected future climate changes, we create simple climate scenarios and we show that the projected climate changes may lead to generally lower groundwater levels and a reduction of exceedances of high groundwater level percentiles.