<p>Glacier length fluctuations reflect changes in climate, most notably temperature and precipitation. By this reasoning, moraines, which represent former glacier extent, can be used to estimate past climate. However, estimating palaeoclimate from moraines is not a straight-forward process and involves several assumptions. For example, recent studies have suggested that interannual stochastic variability in temperature in a steady-state climate can cause a glacier to experience kilometre-scale fluctuations. Such studies cast doubt on the usefulness of moraines as climate proxy indicators. Detailed glacial geomorphological maps and moraine chronologies have improved our understanding of the spatial and temporal extent of past glacial events in New Zealand. Palaeoclimate estimates associated with these moraines have thus-far come from simple methods, such as the accumulation area ratio, with unquantifiable uncertainties. I used a numerical modelling approach to approximate the present-day glacier mass balance pattern, which includes the effects of snow avalanching on glacier mass balance. I then used the models to reconstruct palaeoclimate for Lateglacial and Holocene glacial events in New Zealand, and to better understand moraine-glacier-climate relationships. The climate reconstructions come from simulating past glacier expansions to specific terminal moraines, but I also simulated glacier fluctuations in response to a previously derived temperature reconstruction, and to interannual stochastic variability in temperature. The purpose behind each simulation was to identify the drivers of significant glacier fluctuations. The modelling results support the hypothesis that New Zealand moraine records reflect past climate, especially changes in temperature. Lateglacial climate was reconstructed to be 2-3 C lower than the present day. This temperature range agrees well with previous estimates from moraines and other climate proxy records in New Zealand. Modelled temperature estimates for the Holocene moraines are slightly colder than those derived from simpler methods, due to a non-linear relationship found between snowline lowering and glacier length. This relationship results from the specific valley shape and glacier geometry, and is likely to occur in other, similarly-shaped glacier valleys. The simulations forced by interannual stochastic variability in temperature do not show significant (>300 m) fluctuations in the glacier terminus. Such fluctuations can not explain the Holocene moraine sequence that I examined, which extends >2 km beyond the present-day glacier terminus. Stochastic temperature change could, however, in part, cause fluctuations in glacier extent during an overall glacier recession. Modelling shows that it is also unlikely that glaciers advanced to Holocene and Lateglacial moraine positions as a result of precipitation changes alone. For these reasons, temperature changes are a necessary part of explaining past glacier extents, especially during the Lateglacial, and the moraines examined here likely reflect changes in mean climate in New Zealand. The glacier modelling studies indicate that simpler methods, such as the accumulation area ratio, can be used to appropriately reconstruct past climate from glacial evidence, as long as the glacier catchment has a straight forward geometry, shallow bed slope and no tributary glaciers. Non-linear relationships between climate change and glacier length develop when valley shape is more complex, and glaciers within these systems are probably better simulated using a modelling approach. Using a numerical modelling approach, it is also possible to gain a greater understanding of glacier response time, length sensitivities, and estimates of ice extent in valleys within the model domain where geomorphic evidence is not available. In this manner, numerical models can be used as a tool for understanding past climate and glacier sensitivity, thus improving the confidence in the palaeoclimate interpretations.</p>