Accumulation and δ¹⁸O data from Alpine ice cores provide information on past temperature and precipitation. However, their correlation with seasonal or annual mean temperature and precipitation at nearby sites is often low. Based on an example we argue that, to some extent, this is due to the irregular sampling of the atmosphere by the ice core (i.e. ice cores only record precipitation events and not dry periods) and the possible incongruity between annual layers and calendar year due to dating uncertainty. Using daily meteorological data from nearby stations and reanalyses we replicate the ice core from the Grenzgletscher (Switzerland, 4200 m a.s.l.) on a sample-by-sample basis. Over the last 15 yr of the ice core record, accumulation and δ¹⁸O variations can be well reproduced on a sub-seasonal scale. This allows a wiggle-matching approach for defining quasi-annual layers. For this period, correlations between measured and replicated quasi-annual δ¹⁸O values approach 0.8. Further back in time, the quality of the agreement deteriorates rapidly. Nevertheless, we find significant correlations for accumulation and precipitation over the entire length of the record (1938–1993), which is not the case when comparing ice core δ¹⁸O with annual mean temperature. A Monte Carlo resampling approach of long meteorological time series is used to further explore the relation, in a replicated ice core, between δ¹⁸O and annual mean temperature. Results show that meteorologically very different years can lead to quasi-identical values for δ¹⁸O. This poses limitations to the use of δ¹⁸O from Alpine ice cores for temperature reconstructions in regions with a variable seasonality in precipitation.