Located in the central North Island, New Zealand (39.2∘ S 175.6∘ E; Fig. ), the Tongariro Volcanic Centre (TgVC) represents the southernmost expression of the Taupo Volcanic Zone, which is a ca. 300 km long, northeast-trending belt of subduction zone volcanism at the Australian–Pacific plate margin . TgVC is dominated by the andesite–dacite stratovolcanic centres of Tongariro massif (including Mt Tongariro – 1967 m above sea level (a.s.l.) and the Holocene cone of Mt Ngauruhoe – 2287 m a.s.l.) and Mt Ruapehu (2797 m a.s.l.). Radiometric dating of lava flows indicates that cone-building volcanism in the region began before ca. 275 ka , and both centres have exhibited effusive volcanic activity in historical times .

Local climate, as recorded at Whakapapa Village (1100 m a.s.l.; Fig. a) on the northwest flank of Mt Ruapehu, is characterised by high annual precipitation (ca. 2700 mm a-1; Fig. b), with low seasonal variability. For example, winter (JJA) precipitation averages ca. 760 mm, compared to ca. 620 mm in summer. Monthly mean temperatures at this altitude range from ca. 13 ∘C in February to ca. 3 ∘C in July, with an annual average of 7.5 ∘C (AD 2000–2010; ; Fig. c). At 2797 m a.s.l., Mt Ruapehu is the highest peak in the North Island and the only to intercept the present-day end-of-summer snowline. Several small (< 1 km2) cirque glaciers currently exist on the upper mountain slopes (Fig. ). The average annual end-of-summer snowline for the cirque glaciers on Mt Ruapehu is ca. 2500 m . No glacial ice is present on Tongariro massif today.

Abundant geomorphic evidence for glacial erosion and deposition, situated several kilometres down-valley of the present-day ice limits, has long been recognised in the central North Island . Two independent mountain-scale assessments of moraine distribution on Mt Ruapehu have produced mapped reconstructions of a former late Pleistocene ice mass , which are in good agreement with one another (Fig. ). One mountain-scale palaeoglacial reconstruction of a late Pleistocene ice mass has been undertaken for Tongariro massif (, Fig. ). These reconstructions suggest small ice caps/ice fields were present on each volcano, and were drained by several valley glaciers that terminated at elevations between 1100 and 1400 m.

Until recently, age control for glacial landforms on the volcanoes has been based on moraine tephrostratigraphy and morphostratigraphic correlation of moraines to dated glacial formations in the Southern Alps . Recent applications of surface exposure dating to moraine boulders, using locally calibrated cosmogenic 3He , have provided direct, quantitative age constraints for late Pleistocene glacier fluctuations in the central North Island . On the western side of Tongariro massif, show that the innermost moraines in Mangatepopo valley (MPO; Fig. ) were deposited ca. 30–18 ka during the LGM; meanwhile, a moraine positioned outboard of the LGM limits records an earlier glacial advance that occurred prior to 57 ka. These moraines are separated in age by ca. 30–40 kyr, and exhibit markedly different morphology. For example, the older moraine is characterised by lower slope angles (ca. 10–15∘), a more rounded ridge crest, and lower frequency of large (> 1 m3) boulders on the surface. These characteristics likely represent the effects of sub-aerial erosion of the moraine in a periglacial setting during the latter half of the last glacial cycle. In comparison, the LGM moraine exhibits steeper surface slopes (ca. 20–25∘), higher relief, and a more narrow ridge crest.

The new cosmogenic surface exposure dates of confirm previous assignments of the inner Mangatepopo moraines to the LGM (e.g. ) and provide more robust chronological data to support morphostratigraphic correlations of proximal, undated moraines. Using these new insights, we have undertaken independent mapping of moraines on both volcanoes using a combination of field investigations and inspection of aerial imagery. We have identified nine catchments where the LGM ice limits can be defined with reasonable confidence (Fig. ; Table ). Five catchments on Tongariro massif contain well-preserved lateral moraines that delineate valley glaciers terminating between 1100 and 1400 m. On the eastern side of the massif, valley glaciers were present in the Mangahouhounui (MHO), Mangatawai (MTA), and Waihohonu (WAI) valleys, as well as an unnamed tributary stream (labelled here as “UNK”; Fig. ). We also include the dated LGM moraines of Mangatepopo valley (MPO), situated on the western side of the massif. On Mt Ruapehu, we target four former valley glaciers that terminated between 1100 and 1200 m a.s.l. in the Mangatoetoenui (MTO), Wahianoa (WAH), Mangaturuturu (MTU), and Whakapapanui (WHA) valleys (Fig. ; Table ). The former ice limits in each of these nine catchments are well-defined by lateral moraines and correspond closely with the independent LGM ice reconstruction of (Fig. ). Our assignment of an LGM age to undated moraines is primarily based on morphostratigraphic correlation informed by the recent moraine dating and moraine morphology observations from western Tongariro massif and southern Mt Ruapehu (Fig. ; ). Further constraints on the timing of moraine formation and ice extent at the LGM are provided by the age and distribution of pre-, syn-, and post-LGM lava flow emplacement (; ) and the stratigraphic relationship of these flows to both moraines and glaciated valleys.

The aim of this study is to constrain the mean annual temperature and precipitation changes, from present, that may have caused glaciers in central the North Island to advance to their LGM extents, using a glacier modelling approach. Several previous studies have adopted this geologically constrained glacier modelling approach to reconstruct past climate in New Zealand (e.g. ). In this study we use the coupled energy balance–ice flow model of . A key advantage of this model for our purpose is that mass balance and vertically integrated ice flow are calculated in two dimensions, which (1) captures any potential changes in ice divides that may have occurred under greater ice thicknesses in the past (e.g. ) and (2) produces outputs that are readily comparable to the 2-D moraine-based ice mass reconstructions (Fig. ). Furthermore, our physically based model is very similar (e.g. types of input data, required parameterisation) to that of , which has been applied to sites in the Southern Alps to derive quantitative estimates of LGM climate (e.g. ).

As a test of model performance, we compare the modelled, steady-state ice extent and mass balance on Mt Ruapehu summit for present day (i.e. ΔT= 0 and ΔP= 0), against mapped ice extent from Land Information New Zealand topographic maps (Fig. ). Steady-state ice extent modelled using the optimal parameter set listed in Table  shows reasonable agreement with empirical ice extents in the majority of the catchments of interest for this study (e.g. Mangatoetoenui, Wahianoa, Mangaturuturu; Fig. ). However, this simulation also produces ice extents in two catchments, Whangaehu and Whakapapa, which are far greater than observed (Fig. ). Ice accumulation in the Crater Lake basin represents an important source of this excess model ice. Today, Crater Lake is a large body of water (ca. 106–107 m3) that occupies the active volcanic vent and fluctuates in temperature between ca. 10 and 60 ∘C with periodicities of 4–16 months . Thus, the lake represents an important energy source that prevents snow accumulation at the lake site and raises air temperatures and humidity in the vicinity, thus melting ice flowing towards the lake . Neglecting these processes in our model causes ice accumulation at the lake site, which feeds into the Whangaehu and Whakapapa glaciers, thus causing greater ice extents than observed today (Fig. ). Based on the increased frequency of hydrovolcanic products in tephra sequences on the surrounding ring plain, Crater Lake is believed to have formed in the mid- to late Holocene (ca. 3 ka; ). This post-dates the time period of interest for our glacier modelling application. Thus, although the lake currently represents an important energy source controlling snow accumulation patterns, we do not include this energy source in our palaeo-simulations. It is also notable that modelled ice extent in catchments that do not receive ice from Crater Lake (i.e. Mangaehuehu, Wahianoa, Mangatoetoenui) are better aligned with modern observations (Fig. ).

A further source of uncertainty in simulating the small present-day glaciers (e.g. Fig. ) is the role of wind in redistributing snow on the summit region. Previous mass balance observations on Whakapapa and Whangaheu glaciers have noted “inverted snowlines” , whereby winter accumulation has been redistributed by wind, from the glacial accumulation areas to the lower portions of the glaciers. Including a numerical scheme for this process is computationally expensive , and has high uncertainties in topographically complex regions such as Mt Ruapehu, where both the present and past wind fields are largely unknown. Furthermore, wind redistribution of snow is of greater importance for the mass balance of small glaciers , such as the present-day glaciers on Mt Ruapehu, but less important for larger glaciers, such as those that existed during the LGM, where climatic gradients dominate the mass balance profile. We note that the moraine distribution does not indicate any notable asymmetry in the past ice geometry as might be expected if snow redistribution by prevailing winds was an important control on mass balance in the geological past (e.g. ). Thus, we do not attempt to model this process but acknowledge it as a potential source of uncertainty in our mass balance simulations.

We designed a series of three different experiments to constrain the magnitude of LGM cooling in the central North Island and the sensitivity of our results to post-glacial changes in bed topography. In each model simulation, ice thickness is updated by the ice flow model every 5 model years, and mass balance is recalculated every 20 model years. Each simulation is run to an equilibrium state, which is achieved when the rate of ice volume change becomes close to zero and takes 200–350 model years depending on the magnitude of ΔT. We follow the experimental design of previous similar studies (e.g. ) in holding model parameters constant for all simulations (Table ), while iteratively varying temperature and/or precipitation to achieve a fit with the geological evidence. We investigate the sensitivity of our results to this parameterisation by re-running the experiments with systematic variations of key parameters (Table ).

Figure  shows steady-state ice thickness results of Experiment 1, conducted over a domain covering both Mt Ruapehu and Tongariro massif. Also shown are the inferred LGM ice limits of greater and lesser confidence (from Fig. ). Modest coolings of 2–3 ∘C from present are sufficient to produce a small ice mass on Mt Ruapehu, but this temperature change is insufficient to promote ice accumulation on Tongariro massif. A cooling of 4 ∘C is sufficient to meet the well-defined LGM limits in the WAH catchment on southeast Mt Ruapehu; however, the termini of other simulated valley glaciers on this volcano remain well upstream of their mapped limits. In this scenario, ice accumulation on Tongariro is restricted to elevations > ca. 1900 m a.s.l. and therefore remains well short of the mapped LGM limits (Fig. ). Modelled ice extent approaches the LGM limits in the remaining three catchments (MTO, WHA, MTU) on Mt Ruapehu when ΔT = -5 ∘C, and these limits are exceeded in all catchments at ΔT = -6 ∘C. On Tongariro massif, modelled ice extent approaches the moraine limits in several catchments (MPO, MHO, UNK) in response to a cooling of 6 ∘C. At ΔT = -7 ∘C, the individual ice masses of the two volcanoes have merged and ice exceeds the LGM limits in all catchments.

The temperature change required to simulate the LGM ice geometries in each catchment, as delineated by geological evidence, ranges from -4.0 to -6.8 ∘C when precipitation remains unchanged from present (Fig. a). Steady-state equilibrium line altitudes for these simulations range from ca. 1380 to 1660 m a.s.l., which represent depressions of ca. 820–1100 m from present (Table ). Imposing a 25 % increase in modern precipitation reduces ΔT by ca. 0.6 ∘C for all catchments (Fig. ); meanwhile, decreasing modern precipitation by 25 % requires increases in ΔT of ca. 0.8 ∘C (Fig. a).

Sensitivity tests of key energy balance parameters impact the palaeotemperature reconstructions by up to ±0.5 ∘C for the chosen ranges (Fig. b). Altering the albedo of snow (αsnow= 0.67–0.77) and snow temperature threshold (Tsnow= 0–1.5 ∘C) has the greatest effects (ca. ±0.1–0.5 ∘C). Using a temperature lapse rate (dT/dz) of -0.006 ∘C m-1, uniformly applied across all months, decreases ΔT by 0.1–0.2 ∘C. Changing the characteristic ice roughness length (Zice= 0.0008–0.01 m) also causes deviations in ΔT of ±0.1–0.2 ∘C, relative to the optimal setting. Flow parameters Uc and A have a negligible (< 0.1 ∘C) impact on ΔT.

Findings from Experiment 1 highlighted the variability in the LGM palaeoclimate reconstructions that exists, both between volcanoes and between individual catchments. Figure a shows that the Wahianoa (WAH) catchment on Mt Ruapehu requires a conspicuously smaller temperature change from present to match the identified LGM ice limits (ΔT = -4.0 ∘C, when ΔP= 0), compared to all other catchments studied (ca. -5.2 to -6.8 ∘C, when ΔP= 0). Also, there is an offset in the temperature forcings necessary to simulate the mapped LGM ice limits between the two volcanoes. Catchments on Tongariro massif range require coolings of ca. 6.0 to 6.8 ∘C (mean = 6.3 ∘C), when precipitation is unchanged, whilst catchments on Mt Ruapehu require 4.0 to 5.8 ∘C (mean = 5.0 ∘C, or 5.4 ∘C when WAH is removed). Finally, the results presented in Fig.  represent the climatic forcing, from present, required to meet the inferred downstream limits of LGM glaciation. In several catchments, ice spills over ice-marginal indicators, such as lateral moraines, before the geologically constrained termini are reached (Fig. a, b). The possible reasons for the discrepancies, and the potential implications for palaeoclimate estimates, are discussed below (Sect. ).

Figure a shows the change in temperature from present required to simulate the mapped LGM geometries in the nine catchments, using topographic boundary conditions that more closely approximate that of the LGM (Fig. ). When precipitation remains unchanged from present, ΔT ranges from ca. -4.1 to -7.1 ∘C, which represents differences of +0.1 to -0.5 ∘C from Experiment 2 (Fig. b). In all catchments except one (MTO), more cooling was required, relative to Experiment 2 (Fig. b). The greatest changes in ΔT between Experiment 2 and Experiment 3 occurs in the UNK catchment, where ca. 0.5 ∘C of additional cooling is required to simulate the inferred glacial geometries (Fig. b). This change is the result of reduced ice flux from the vicinity of Mt Ngauruhoe, caused by the elevation reduction in the accumulation area, following removal of this Holocene-aged volcanic cone (Fig. ). However, this topographic alteration has less of an impact in the WAI catchment, where ΔT is reduced by 0.2 ∘C, relative to Experiment 2. Whilst removal of Mt Ngauruhoe may act to channel ice flow into the WAI catchment, the overall reduction in elevation reduces snow accumulation, therefore reducing the impact on ΔT. The imposed topographic changes did not improve the poor fit between modelled ice geometry and the geological constraints, as ice still spills over lateral moraines in the WAI and MTA catchments before reaching the inferred LGM termini.

On Mt Ruapehu, the major changes to the topography were made in the MTO catchment, which is the only catchment where ΔT decreased by ca. 0.1–0.2 ∘C, relative to Experiment 2 (Fig. b). In this instance, the removal of syn- and post-LGM lava flows in the upper and middle parts of this catchments has resulted in increased ice flux to the lower valley, despite the overall reduction in elevation. This is caused by a reduction in the ice flux leaving the catchment through overspill, which helps offset the effect of increased temperature caused by the reduction in bed elevation. In the other catchments on Mt Ruapehu (MTU, WAH, WHA), ΔT was reduced by 0.1–0.2 ∘C relative to Experiment 2. Thus, accounting for post-glacial changes in bed topography cannot resolve the anomalous ΔT result in the WAH catchment. Finally, there remains a poor fit between the geologically inferred lateral ice margins in the MTU catchment and those simulated in Experiment 3.

Improved constraint of the timing and extent of late Quaternary volcanism in the central North Island (e.g. ; ) has allowed a test of the impact that changing topographic boundary conditions have on palaeoclimate estimates for glacier modelling. Using topographic reconstructions, informed by these recent field mapping and radiometric dating campaigns, the temperature forcing required to simulate the inferred LGM glaciers is altered by +0.2 to -0.5 ∘C. The majority of the imposed topographic changes serve to remove post-glacial lava flows that have built volcanic cones (e.g. Mt Ngauruhoe) or infilled glacial troughs (e.g. MTO, MPO; Fig. ). Subtraction of these features from the present-day land surface has lowered the glacier bed elevation, which raises the local surface air temperature and explains why most catchments require increased cooling to achieve the LGM limits in Experiment 3, relative to Experiment 2. Thus, our results from experiment 2 may underestimate LGM temperature anomalies by up to 0.5 ∘C. These experiments demonstrate the importance of considering potential post- or syn-glacial (e.g. ) changes in subglacial bed topography, when extracting palaeoclimate information from the glacial record using glacier modelling.

Removal of the post-glacial lava flows in the vicinity of the MTO catchment reduced the temperature forcing required to simulate the LGM ice geometry in that catchment by ca. 0.2 ∘C, relative to Experiment 2. Reduced overspill, as shown by the improved fit between the model output and the lateral moraines, indicates that the retention of ice within the MTO catchment was improved by the imposed topographic changes and this effect was sufficient to offset the decreased accumulation/increased ablation induced by land surface lowering. However, the imposed topographic changes did not improve the fit in all catchments where overspill occurs (e.g. MTA, WAI, MTU); thus, it is probable that the LGM palaeotemperature estimates presented in Fig.  and Fig.  for these catchments overestimate the true magnitude of LGM temperature change. This interpretation is supported by the fact that these catchments require the greatest magnitude of cooling, relative to present, of all catchments on the respective volcanoes. Discounting the reconstructions from these catchments leaves LGM palaeotemperature estimate ranges of -4.1 to -5.4 ∘C for Mt Ruapehu and -6.1 to -6.3 ∘C for Tongariro massif (ΔP= 0; Experiment 3). Thus, accounting for ice overspill and known topographic changes is insufficient to resolve the apparent offset between LGM palaeotemperature estimates between these two volcanoes.

Geometric constraint of well-preserved post-glacial lava flows can be achieved with relative ease via detailed field investigations. However, the recognition of post-glacial erosional events (e.g. sector collapse, fluvial incision) and subsequent topographic reconstruction is less straightforward. Some erosional events are identifiable in the modern landscape on Mt Ruapehu (e.g. Murimotu Formation sector collapse at 10.4–10.6 cal ka BP; ); however, the precise source locations and pre-erosional topographies remain highly uncertain (e.g. ). Such erosional events alter drainage pathways and bed hypsometries, with potential implications for modelled ice distributions and palaeoclimatic reconstruction. For example, it can be hypothesised that the offset in LGM temperature reconstructions between the glacial catchments of Mt Ruapehu and Tongariro massif is caused by post-glacial change in the relative altitudes of the two volcanoes. A post-glacial decrease in the summit altitude of Tongariro massif, relative to Mt Ruapehu, could explain the need for greater cooling on Tongariro massif in the simulations presented here. However, there is little geological evidence to support the notion that Tongariro massif has experienced major post-glacial degradation, nor that Mt Ruapehu has significantly increased in elevation since the LGM. This absence of evidence, combined with the fact that known changes in topographic boundary conditions had relatively little impact on palaeotemperature reconstructions (Experiment 3), makes it unlikely that post-glacial topographic change is the primary source of this systematic offset.

The glacier modelling experiments presented here suggest that stadial conditions in the central North Island were characterised by temperatures 4 to 7 ∘C lower than present (Fig. ). Here we first discuss the possible reasons for the inter-catchment and inter-volcano variability in palaeotemperature reconstructions, before placing our results in the context of other, quantitative palaeoclimate reconstructions from the New Zealand region.

Our results show a ca. 3 ∘C spread in palaeotemperature estimates between individual catchments and a ca. 1 ∘C disparity between the two volcanoes. Given the relatively small influence of known topographic changes as a driver, we consider these differences can be explained predominantly by the combination of three principal factors, which we discuss below.

First, differences in climate forcing may arise from chronological uncertainty. Only two of the catchments studied here (MPO, WAH) have moraines been directly dated to the LGM (), while others are inferred from moraine morphostratigrahy and indirect age constraints (e.g. ; ). Moraines representing glacial advances prior to the LGM have been recognised and dated on Tongariro massif ; therefore, it is possible that some of the limits we targeted predate the LGM. However, noted a distinct morphological difference in the preservation of moraines formed early in the last glacial cycle (> 59 ka) and those constructed during the LGM. The undated moraines targeted in our study had been correlated to the LGM based primarily on their similar morphology and degree of preservation to dated landforms; therefore, we consider it unlikely that our simulations have targeted pre-LGM glacial limits. A separate possibility is that our targets represent different advances within the LGM. This cold climatic interval spans ca. 10 kyr, during which time there were significant fluctuations in climate over millennial timescales . Indeed, exposure ages of LGM moraines do show evidence for multiple moraine building episodes 30–18 ka (e.g. ). Thus, the inter-catchment variability seen in our palaeotemperature estimates may in part reflect the range of temperature cooling events during this prolonged but variable cold period.

Second, inaccuracies in the present-day climate data, particularly precipitation distribution, may impart some error to the palaeotemperature reconstructions. The paucity of high-altitude precipitation data for the present-day represents an important source of uncertainty in both modern and palaeo-applications of glacier mass balance models. For example, find that uncertainty in present-day precipitation distribution imparts uncertainty of up to 25 % in modelled LGM glacier length in the central Southern Alps, which equates to about 0.5 ∘C in the palaeotemperature estimate. The good agreement between observed ice distribution on Mt Ruapehu and ice geometries simulated using the 30-year (AD 1981–2010) average climate data sets (Fig. ) provides confidence that these data sets provide a useful starting point from which to assess the local LGM climate anomaly in catchments on Mt Ruapehu. However, no glaciers exist on Tongariro massif today and there are no climate stations on the volcano; therefore, it is more difficult to assess how representative the modern climate grids are for this region.

Underestimation of the present-day precipitation rate on Tongariro massif provides one possible explanation for our finding that slightly greater temperature forcings are needed to match the LGM limits on Tongariro massif, relative to Mt Ruapehu. The precipitation–temperature relationships presented in Fig. a indicate that precipitation changes of ±25 % are balanced by temperature changes of ± ca. 0.6–0.8 ∘C, which is consistent with similar estimates for the South Island glaciers . Thus, precipitation on Tongariro would need to be increased by 30–50 %, relative to Mt Ruapehu, in order to account for the ca. 1.0–1.3 ∘C temperature difference associated with the inferred LGM glacial limits between the two volcanoes. This magnitude is quite large and we consider it unlikely that the present-day spatial precipitation gradient is inaccurate to such a degree; however, this may still represent an important contributing factor. Potential past changes in local precipitation gradients, for example arising from atmospheric circulation changes (e.g. ), may also contribute. Improved constraint of present and past precipitation rates will reduce these uncertainties.

Third, spatial heterogeneities in key glaciological parameters may account for some of the spatial differences in palaeotemperatures seen in this study. The sensitivity tests presented in Fig. b provide a first-order assessment of the uncertainty imparted by parameters in the energy balance model. Varying key parameters within acceptable bounds causes deviations in reconstructed temperatures of up to ±0.5 ∘C, which indicates that some of the inter-catchment variability in palaeotemperatures (e.g. WAH catchment) could be explained by spatial heterogeneities in model parameters, which are currently assumed uniform across the model domain.

Our sensitivity analyses show that palaeotemperature estimates are most sensitive to albedo (Fig. ), which is unknown for the pre-historic period. Surficial debris lowers the albedo of ice, but can act to enhance or reduce surface melt on glaciers depending on the thickness of the debris layer , which in turn is dictated by sediment availability. measured ice ablation rates of clean and tephra-covered snow on Summit Plateau at Mt Ruapehu and found that tephra thicknesses of up to 7 cm enhanced ablation rates, relative to that of clean snow. In temperate regions, empirical observations have shown that tephra deposited on glacier surfaces is quickly redistributed by surface runoff and thus has a net long-term effect of enhanced surface ablation following deposition . Thus, the presence of thin (centimetre-scale) debris cover on some LGM glaciers in the central North Island may have enhanced ablation and would cause underestimation of palaeotemperatures for these catchments in our model that assumes clean glacier surfaces. This process may contribute to the inter-catchment and/or inter-volcano variability in our LGM palaeotemperature estimates.

Despite these possible sources of uncertainty, the weight of evidence afforded by our multi-catchment approach allows us to say with reasonable confidence that LGM temperatures in the central North Island reached at least 5 ∘C colder than present. Meanwhile it is unlikely that temperatures were depressed by more than 7 ∘C relative to today. This is in good agreement with other quantitative LGM temperature reconstructions from New Zealand (e.g. ; Fig. ), which supports our conclusion that climate represents the dominant signal recorded by the Quaternary moraine record on the central North Island volcanoes. In the next section we discuss our finding in the context of other palaeoclimate records.

The glacier modelling experiments presented here suggest that stadial conditions in the central North Island during the LGM were characterised by temperatures 4 to 7 ∘C lower than present (Fig. ), although most of the catchments studied require cooling of ca. 5.1–6.3 ∘C to achieve the mapped ice limits, when precipitation is unchanged from present. Quantitative estimates of regional changes in precipitation rate during the LGM remain poorly constrained, although evidence from climate modelling , previous glacier modelling , carbon isotopes in speleothems , and diatoms in maar deposits indicates that drier than present conditions prevailed across New Zealand at this time. Precipitation reductions of up to 25 % from present require additional decreases in temperature by up to 0.8 ∘C to achieve the LGM glacial geometries in the central North Island (Fig. ). Such a change in precipitation is likely a maximum estimate given that climate model simulations predict changes in total annual precipitation of < 10 % (e.g. ).

Steady-state equilibrium line altitudes of the simulated LGM glaciers fall between ca. 1400 and 1650 m a.s.l. (Table ), which represent depressions of ca. 800–1100 m, relative to present. Despite methodological differences, our estimate using physically based modelling is in agreement with that of , who manually reconstructed the LGM ELAs on Mt Ruapehu to be 1500–1600 m a.s.l. estimated the ELA of the LGM glacier in the MPO catchment as ca. 1400–1550 m a.s.l., using the accumulation area ratio (AAR) and maximum elevation of lateral moraine (MELM) methods, which agrees well with the model simulation presented here (ca. 1510 m a.s.l., Table ). This good agreement between model and manual reconstruction of glacier ELAs echoes previous similar findings (e.g. ), demonstrating the utility of simple ELA reconstructions for efficient extraction of palaeoclimate data from moraine records.

Lowering of the regional ELA to 1500 m a.s.l. at the LGM is insufficient to promote widespread glaciation in the mountain ranges elsewhere in the North Island, as few other peaks exceed this elevation. The only other existing evidence for LGM glaciation in the North Island comes from the Tararua Range in the southern North Island, where the local pELA was estimated to be ca. 1100 m a.s.l. . This pELA reconstruction is considerably lower than our reconstruction and those from elsewhere in New Zealand , which may represent topo-climatic controls on mass balance of this former cirque glacier, such as wind-driven snow accumulation. The absence of extant glaciers in the Tararua Range precludes robust spatial comparison of ELA depressions to the results presented here. Quantitative palaeotemperature estimates from the North Island have been made using fossil pollen assemblages and groundwater noble gas palaeothermometry, which also indicate LGM temperature depressions of 4–7 ∘C below present , which is consistent with our glacier model results.

Several glacier-based assessments of LGM temperature have previously been made for the South Island, New Zealand, using a variety of different glacier models. Simulations of the entire Southern Alps ice field, using a degree-day model coupled to the Parallel Ice Sheet Model, indicate that the LGM was characterised by temperatures 6–6.5 ∘C colder than present, coupled with a reduction in precipitation of up to ca. 25 % . It is notable that the best-estimate palaeotemperature scenarios did not achieve a good fit between modelled ice extent and the geological evidence in all catchments (, their Fig. 10b), which may also reflect some of the uncertainties discussed in Sect.  above. Using a different glacier model with higher grid resolution and a different representation of modern climate, and achieve a good model fit in one region where did not (e.g. Rakaia), despite using a similar temperature forcing (ΔT = -6.25 to -6.5 ∘C). Using the University of Maine Ice Sheet Model, find that a cooling of 6.25 ± 0.5 ∘C (with no precipitation change) is required to generate an ice extent that matches well-dated moraines in the Lake Ohau catchment. When precipitation is reduced by 30 %, the required cooling increases to 6.9 ∘C. These studies have shown that, despite differences in boundary conditions and formulations for glacier flow, glacier model experiments consistently suggest peak stadial air temperatures during the LGM were 6–7 ∘C cooler in the Southern Alps, which is in good agreement with our estimates from the central North Island.