The Zongo-Charquini area is a high-altitude mountain zone in the Cordillera Real (Bolivia; 16° S, 68° W), located 25 km northeast of La Paz. It lies between the dry Altiplano plateau to the west and the wet Amazonian basin to the east, the latter being the main source of moisture for precipitation.

The study site lies within the outer tropics, a transitional zone where tropical climate dominates during the humid austral summer, while subtropical conditions prevail during the dry austral winter. Hence, mass accumulation occurs primarily during the wet summer season, whereas ablation occurs year-round and even during the austral winter when the dry air and predominant clear-sky conditions favor mass loss through sublimation . Given the highly seasonal precipitation regime, glaciers act as buffers for hydrological regime at times when rainfall is low or absent. This is of high importance for urban centers such as La Paz and El Alto, where 30 %–40 % of the potable water is supplied by the glaciers of the Cordillera Real .

The Zongo-Charquini area has been a focus of long-term monitoring. Since 1991, the Institut de Recherche pour le Développement (IRD, France) together with the Universidad Mayor de San Andrés (UMSA, Bolivia) have conducted glaciological monitoring on the Zongo Glacier as part of the GLACIOCLIM program (https://glacioclim.osug.fr/Donnees-des-Andes, last access: 3 November 2026), producing the longest continuous mass-balance record for a glacier in the intertropical Andes . A second monitoring program on Charquini South Glacier has been active since 2002 , providing a second mass-balance dataset used in this study.

Most of the glaciers present today in the Cordillera Real are small ( < 0.5 km²). We interpret the observed ice-marginal moraines as recording periods when glaciers were larger than today and near mass balance equilibrium. The limited erosive effects of flowing meltwater, snowmelt, and frost penetration have preserved a well-defined set of moraines, primarily composed of granodiorite and quartzite. These lithologies favor the growth of Rhizocarpon lichens , which can be used for moraine dating via lichenometry, and also provide suitable material for cosmogenic nuclide dating due to the high quartz content of the quartzites.

have dated moraines in the valley from the Early Holocene and Little Ice Age (LIA). The Early Holocene (∼ 10 ka BP) was characterized by increased summer insolation and warmer global conditions compared to the Late Glacial period, reflecting the transition to interglacial conditions. Glaciers generally experienced sustained retreat during this time, although report a readvance during or just prior to the Late Holocene ( < 4.2 ka). The absence of mid-Holocene moraines suggests that glaciers were smaller than during the late Holocene. Later in the Holocene, the Little Ice Age (∼ 1600–1850 CE) represents a major climatic fluctuation, marked by regional cooling that was strongest in the North Atlantic but also affected tropical mountain regions and other parts of the world.

In this study, we analyzed Early Holocene and LIA ice-marginal moraines from the Zongo, Telata, Charquini South, and Charquini North glaciers (Fig. ). The LIA moraines in the area are characterized by several stages (referred to as M1 to M10), which are representative of the different glacier advances that occurred between 1600 and 1850 . Here, we focus on the maximum LIA extent (M1) dated to around 1680 CE, except for the Zongo glacier, where a large 350 m cliff drop likely complicates the climatic interpretation of the maximum extent. For this reason, our study also considers a slightly younger moraine for Zongo, referred to as M4, which is dated to around 1760 CE . This allows us to contrast glacier conditions above and below this topographic break, and to assess the potential influence of topographic controls on the LIA glacier extent. Table summarizes the main glacier characteristics.

Previous studies have used the accumulation-area ratio (AAR) method or surface energy balance (SEB) modeling to estimate equilibrium-line altitudes (ELAs) for the Early Holocene and the LIA in the Zongo-Charquini area. Assuming specific precipitation conditions, these ELAs were then converted into temperature (cT) and precipitation (cP) anomalies that match the glacier extents recorded by the moraines. Table  summarizes the main climate reconstructions for the studied glaciers, including applied AAR values, estimated ELAs, and their respective climate anomalies.

The main challenge in linking glacier extents to paleoclimate is that a single glacier extent can result from multiple combinations of temperature (T) and precipitation (P) conditions. In this study, we explore three complementary approaches to progressively reduce this range of temperature-precipitation (T-P) conditions.

We achieve this by identifying the range of (T-P) anomalies capable of reproducing a given observed paleoglacier extent. Assuming that ice-marginal moraines represent periods of climatic stability, we interpret these extents as reflecting glaciers in equilibrium with climate. By varying temperature (T) and precipitation (P) anomalies, we determine all combinations that reproduce the observed extent, defining a continuous set of T-P conditions, hereafter referred to as the T-P anomaly curve.

Building on these curves, we then explored three approaches as follows:

a.

Single-glacier analysis: As a first step, we examine the characteristics of the T-P anomaly curve for an individual glacier. By analyzing how key glacier properties (e.g., ELA, volume) vary along the curve under different temperature and precipitation conditions, we assess their potential to provide additional constraints on climate. This step establishes a baseline understanding of how information from a single glacier can help restrict the range of plausible T-P combinations (Fig. a).

Furthermore, we initially work with synthetic glacier extents moraines (see Sect. ) to establish a baseline analysis, and then extend the framework to real paleoglacier moraine records. In both cases, we consider two melt models ( and ; see Sect. ) to account for uncertainty related to the choice of mass balance formulation.

To build the T-P anomaly curve for a given paleoglacier, temperature and precipitation from the present reference climate are perturbed by applying constant anomalies: 5(T,P)=(TERA5+cT,PERA5⋅cP), where cT and cP denote constant temperature and precipitation anomalies applied to the daily time series.

For a given anomaly pair (cT,cP), the glacier SMB is computed annually over the full length of the perturbed climate time series. To represent a glacier in equilibrium with an imposed steady climate, the annual SMB values are averaged and applied as a constant forcing in the ice-flow model. This allows the glacier geometry to progressively adjust to the imposed climatic conditions until equilibrium is reached.

The glacier is considered to have reached equilibrium when its total volume changes by less than a prescribed tolerance λ> 0 over a time window Δt> 0, that is, 6Volume(T,P)(t+Δt)-Volume(T,P)(t)Volume(T,P)(t)≤λ, where Volume(T,P)(t) is the total glacier volume at time t under the climate conditions (T,P).

Once an equilibrium is reached, the modeled glacier front position Xmod(T,P) is compared with the observed front position defined by the marginal moraine Xobs=(xobs,yobs). Their mismatch is quantified using the Euclidean distance: 7d(T,P)=|Xmod(T,P)-Xobs|. If this distance is less than a prescribed tolerance ϵ, the corresponding climate conditions are considered valid, representing plausible climate conditions at the time of moraine formation. Repeating this procedure over multiple temperature-precipitation anomaly pairs identifies a set of valid conditions that trace a curve in temperature–precipitation anomaly space. In this study, the distance tolerance is set to ϵ= 20 m, the equilibrium criterion to λ= 0.001 of glacier volume change, and the time window to Δt= 10 years.

To explore the behavior of the T-P anomaly curves under controlled conditions, we constructed a set of synthetic moraines from the glacier model. All modeled glaciers evolved to equilibrium under a prescribed climate forcing (cT_syn, cPsyn)= (-1, 1), and the resulting glacier front positions were recorded as the coordinates of the corresponding synthetic moraines. These positions were then used to compute and analyze the T-P anomaly curves in this idealized scenario.

These synthetic moraines rely on a few simplifying assumptions that facilitate interpretation and provide a known set of glacier front positions, free from some of the uncertainties inherent to real moraine data. First, all synthetic moraines are coeval by construction, eliminating uncertainties related to moraine dating. Second, the resulting moraine positions are directly controlled by the imposed climate forcing, thereby removing uncertainty associated with the accuracy of the melt model.

The resulting glacier extents obtained under the prescribed climate forcing are shown in Fig. . Due to their differing sensitivities to temperature and incoming radiation, the Oerlemans and Hock melt formulations produce different glacier extents under identical climate conditions, with the Hock model generally yielding slightly lower glacier termini.

Our synthetic experiments show that ice thickness varies along the T-P anomaly curve, while glacier extent and ELA remain invariant (Fig. ). These systematic variations could provide a potential additional constraint on the climate inversion problem by comparing modeled thickness along the T-P anomaly curve with independent estimates of past ice thickness. However, several caveats must be considered. First, the magnitude of these variations depends strongly on the choice of melt model, as illustrated by the longitudinal and cross-sectional profiles (Fig. ), where the Hock model yields an increase of nearly 100 % in ice volume when transitioning from cold and dry to warm and wet conditions, whereas the Oerlemans formulation produces a more moderate increase of  32 %. Such a limited variation would imply that highly detailed geomorphic constraints, such as sharp-crested lateral moraines or trimlines, would be required to meaningfully reduce uncertainties in reconstructions that combine glacier extent and ice thickness, which are often not available in practice.

On the other hand, the choice of melt model also shows a clear impact on the T-P anomaly curves from the synthetic glacier extents, with the Hock model reflecting a stronger sensitivity to temperature relative to precipitation than Oerlemans. While the curves intersect at the imposed climatic reference state, they progressively diverge away from this point, highlighting how inferred climate conditions are highly sensitive to the choice of melt model and to departures from the calibration conditions, which by construction correspond to the imposed climate in the synthetic experiment. This also reinforces the limitation discussed above: an accurate estimate of past ice thickness would still not resolve the ambiguity, as Hock and Oerlemans would map that same thickness onto different T-P solutions.

However, curves from multiple synthetic glacier extents largely overlap within each melt model, without clear intersection points as expected in our conceptual scheme (Fig. b). This indicates that, within the range of geometries, differences in hypsometry and aspect alone are insufficient to generate distinct sensitivity to temperature change, meaning that temperature and precipitation solutions cannot be separated within the synthetic system. In addition, variability in accumulation related to a rain-snow threshold is not represented in our setup, as most precipitation falls as snow across the glacier elevation range, which may further reduce inter-glacier contrasts. Under these simplified, steady-state conditions, glacier extent is primarily governed by surface mass balance (SMB), largely independent of the ice flow model, which mainly acts through feedbacks between surface elevation and SMB. As a result, glaciers do not incorporate additional local or transient effects that may influence how they record climatic conditions, leading all glaciers to converge toward a common T-P solution. In real systems, however, this overlap does not necessarily hold, as transient glacier dynamics – not captured by our steady-state comparison – can decouple a glacier's response from the shared climate signal. , for instance, show that two neighbouring glaciers responded in opposite ways to the same imposed climate change, as a rise in ELA expanded the accumulation area of the higher-altitude glacier while leaving the lower one mostly below the new ELA. A synchronous response should therefore not be expected a priori when climatic conditions inferred from one glacier are applied to another, as moraines from different glaciers do not necessarily record identical climatic signals.

In the case of real moraines, the glacier T-P anomaly curves do not overlap as for the synthetic case, but remain roughly parallel across glaciers (Fig. ). This reflects glacier-specific sensitivities that are not fully captured by the melt model, as well as additional sources of variability such as moraine formation processes and dating uncertainties. For the Early Holocene, the Charquini South moraine indicates relatively warm conditions, comparable to mid-Holocene warmth, whereas Telata and Charquini North suggest cooler conditions, potentially closer to the Younger Dryas (∼ 12 900–11 700 BP). During the LIA, Telata records cooler conditions, while Charquini North and Charquini South cluster under similar, slightly warmer conditions, consistent with their nearly contemporaneous ages.

In the case of Zongo, and despite the age difference, the T-P curve from moraine M4 reflects conditions that align well with those of the other glaciers during the LIA. Moreover, the marked difference between moraine M4 and the mapped Zongo LIA maximum extent would imply a rapid ∼ 1.5 °C temperature shift between the Early and Late LIA, calling into question its climatic interpretation. Results from the surface energy balance analysis of show that uniform cooling alone cannot reproduce the Zongo maximum LIA extent without enhancing albedo effects through changes in the seasonal distribution of precipitation. In terms of equilibrium line altitude, they obtained values of 5000 and 4908 m a.s.l. for the simple cooling and precipitation-distributed scenarios, respectively. The former is consistent with our reconstructed ELA for M4 (5060 m a.s.l.), whereas the latter matches our estimate for the mapped LIA extent (4840 m a.s.l.), suggesting that simple climatic cooling is sufficient to explain M4, but not the mapped Zongo maximum LIA extent. Regional geomorphological patterns show that glaciers in the Cordillera Real preserve a consistent sequence of ∼ 10 closely spaced moraines , whereas Zongo exhibits a pronounced elevation gap between the mapped LIA maximum and the subsequent moraine sequence. This gap coincides with a steep ∼ 400 m drop at the glacier front, with moraine M4 representing the last geomorphologically stable position prior to this topographic break. We hypothesize that this drop defines a threshold beyond which topography strongly modulates ice dynamics, allowing the glacier to extend to lower elevations. During the LIA maximum, a serac fall likely split the Zongo Glacier in two at this location. Assuming continuous ice flow thus introduces a bias in climate reconstruction that likely explains the anomalous climatic signal associated with the mapped extent of the Zongo LIA maximum.

So far, our results highlight the strong influence of melt model choice on the reconstructed climatic signal, and show that glacier responses are not solely governed by hypsometry and aspect – which, as discussed in Sect. 5.1, are insufficient alone to constrain the T-P solution – but also modulated by further glacier-specific factors that introduce additional uncertainty into single-glacier climate reconstructions. Consequently, climate reconstruction based on a unique glacier should be approached with caution. For this reason, we rely on a multi-glacier averaging approach as the basis for our climate reconstruction, as combining multiple glaciers and melt models reduces the influence of site-specific effects and provides a more robust estimate of regional climatic conditions. Still, this approach remains sensitive to extreme values and can be biased by glaciers that deviate strongly from the regional signal, underscoring the importance of a careful climatic and geomorphological interpretation of the moraine record used. In our case, this interpretation led us to identify Zongo's mapped LIA extent as incompatible with our modelling approach, given the strong topographic modulation of ice dynamics at the glacier front and the possibility that the downstream moraines were partly fed by avalanching ice, a process not represented in our model. We therefore excluded it from the multi-glacier average. Had this incompatibility gone unnoticed, our LIA reconstruction would have been biased toward a colder estimate by 0.42 °C (Fig. in the Appendix).

Our climate reconstruction indicates an Early Holocene cooling of -1.3 ± 0.4 °C, in good agreement with the revised estimates from (cT=-1.5 to -1.3 °C), yet warmer than the reconstruction based on the Telata glacier from , likely due to methodological factors in that approach, including assumptions of reduced precipitation, potential overestimation of melt reflected in higher ELA, and the reliance on a single glacier. For the LIA, our reconstruction yields a cooling of -0.8 ± 0.3 °C relative to the present reference climate, in close agreement with the -0.95 °C estimate of . The  0.5 °C Early Holocene-LIA difference in our reconstruction is also consistent with the pattern shown by tropical-scale model-data comparisons . At a broader temporal and spatial scale, this result can be compared to the global synthesis of , which documents coherent multidecadal temperature variability across reconstructions and model simulations. That study reports a LIA cooling of about 0.4 °C relative to 1961–1990, closely matching our estimate of approximately -0.5 °C over the same reference period. Overall, this consistency across spatial scales further supports the robustness of the regional climatic signal derived from our multi-glacier averaging approach.

The reconstructed ELAs and AARs from our model show variable agreement with previous glacier reconstructions (Table ; Fig. ). In particular, Early Holocene ELA estimates tend to be more consistent across studies, whereas LIA estimates exhibit a larger spread across glaciers and reconstructions. For AAR, previous studies often adopt relatively uniform values across glaciers, whereas AAR derived from our simulations shows a wider range of glacier-specific values that more directly reflect differences in glacier hypsometry. This is particularly evident for Chaquini South, where our lower reconstructed AAR likely results from a more accurate representation of the glacier geometry, characterized by a broader and less steep accumulation area. At the same time, the reconstructed climate anomalies remain broadly consistent with independent regional estimates, supporting the robustness of our reconstruction.

Nevertheless, and despite using the most comprehensive ice-flow approximation available, we did not obtain better climate constraints than previous studies based on simpler glacier models – a comparison that, to our knowledge, had not previously been made directly for this type of reconstruction – suggesting that ice-flow complexity is not the limiting factor in this type of T-P reconstruction. Although it remains unclear how a simpler ice-flow model coupled to the same SMB formulation would perform, we would not expect an improvement in the climate constraint. This limited sensitivity of the results to the ice-flow formulation is likely because topography strongly guides and confines ice flow in mountain glacier settings, so, under steady-state conditions, glacier geometry is primarily controlled by the mass-balance distribution rather than by the specific ice-flow approximation . Differences between ice-flow models become more relevant in transient simulations, where ice thickness and internal deformation actively shape the evolution of glacier geometry, and where a full-Stokes approach would therefore be expected to offer a more accurate representation of the glacier response.

From a theoretical point of view, the multi-glacier full-Stokes framework presented here is transferable to other glaciated regions, subject to a few practical and conceptual considerations. First, its application requires a set of coeval, neighboring glaciers with well-preserved moraine records. The appropriate spatial and temporal configuration likely depends on the characteristics of the study area and the climatic signal being reconstructed. Therefore, testing different glacier separations and degrees of temporal overlap would help assess how these factors affect the reliability of the approach. Nevertheless, the approach may remain useful even when the available glaciers are fewer or more widely spaced, particularly in regions where other paleoclimate constraints are limited. Second, the approach relies on the availability of present-day observational data for at least one glacier in the study area, without which melt model parameters cannot be independently constrained.

Besides, the T-P constraint provided by our approach likely depends on the climatic and glaciological setting of the study area. The glaciers studied here differ in hypsometry and aspect, yet present a similarly snow-dominated precipitation regime and are similarly confined by steep valley topography. The extent to which these other features influence T-P sensitivity, and whether stronger contrasts between glaciers could provide more complementary constraints on the reconstruction, remains unclear. It would therefore be valuable to test our approach in settings where glaciers differ more strongly from each other in these respects.

A further limitation inherent to our approach, and to most glacier-based paleoclimate reconstructions, is the assumption that a mapped moraine reflects a glacier in equilibrium with a sustained climate state. However, glacier length can fluctuate substantially in response to interannual climate variability alone, even under an otherwise stationary long-term climate . Such fluctuations could, in principle, produce a moraine at a given position without reflecting a genuine, sustained shift in temperature or precipitation. In this context, the multi-glacier approach limits the effect of glacier-specific stochastic excursions on the reconstructed climate, while the agreement between the resulting T-P curves can help identify potential deviations from the common climatic signal: closely grouped curves support a common climatic interpretation, whereas a strongly deviating curve may point to glacier-specific processes or a stochastic excursion. However, this approach does not fully resolve this source of uncertainty, which remains an open challenge for the field.